A student used factor by grouping to factor the expression below. How can you tell that the student made an error when factoring? explain the error.
students work:
6x^2 - x - 12
6x^2 - 9x + 8x - 12
3x(2x - 3)-4(-2 + 3)
Answers
The student made an error when factoring because they did not factor the expression correctly. The correct factoring of the expression is 6x^2 - x - 12 = 6x(x - 2) - 3(4).
What is common factor?A common factor in math is a number that can be divided into two or more numbers without a remainder. For example, the common factors of 10 and 15 are 1, 5, and 10. The greatest common factor (GCF) is the largest number that divides both numbers evenly. In this example, the GCF of 10 and 15 is 5. Common factors are useful for simplifying fractions, solving equations, and finding the lowest common multiple.
When factoring by grouping, it is important to remember that the factors of the first and last terms of the expression must multiply to equal the middle terms. In this example, the first and last terms are 6x^2 and -12 respectively. These numbers do not multiply to equal -x, which is the middle term.
The student should have factored the expression by dividing the first and last terms by the greatest common factor (GCF). The GCF of 6x^2 and -12 is 6x, so the expression can be factored as 6x(x - 2) - 3(4).
When factoring by grouping, it is also important to remember to factor out the common factor first. In this example, the common factor is 3x, so the expression should be factored as 3x(2x - 3) - 4(2 - 3).
In conclusion, the student made an error when factoring the expression because they did not factor the expression correctly. The proper way to factor the expression is to divide the first and last terms by the greatest common factor and factor out the common factor first.
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Related Questions
An open box (no lid) with a square base has a volume of 4 cubic feet. What dimensions will minimize the surface area?
Answers
If a square base has a volume of 4 cubic feet, the dimensions that minimize the surface area are: x = 2√2 and h = 4/x^2 = 1/2.
Let x be the side length of the square base and h be the height of the box. Since the volume is 4 cubic feet, we have:
V = x^2h = 4
Solving for h, we get:
h = 4/x^2
The surface area of the box, A, is given by:
A = x^2 + 4xh
Substituting h in terms of x, we get:
A = x^2 + 4x(4/x^2) = x^2 + 16/x
To minimize A, we take the derivative with respect to x and set it equal to zero:
dA/dx = 2x - 16/x^2 = 0
Solving for x, we get:
x = 2√2
To ensure that this is a minimum, we take the second derivative:
d^2A/dx^2 = 2 + 32/x^3
At x = 2√2, this is positive, indicating a minimum.
The box has a square base with side length 2√2 feet and height 1/2 feet.
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Find the area of the sector whose radius and central angle are 42cm and 60° respectively.
Answers
Answer:
Step-by-step explanation:
[tex]D=\frac{\theta}{360} \times2\times\pi \times r[/tex]
[tex]D=\frac{60}{360} \times2\times\pi \times 42[/tex]
[tex]=\frac{1}{6} \times84\times\pi[/tex]
[tex]=12\pi cm^2[/tex]
For isosceles trapezoid LNOP, m\angle N=84m∠N=84, m\angle O=\left(4y-4\right)m∠O=(4y−4), now find the value of y, m\angle Lm∠L and m\angle Pm∠P
Answers
When we simplify the equation, we obtain: 2y + 20 = 56 2y = 36 y = 18 Hence, mL = 140 – 2y = 104°, mP = 104°, and mN = mO = (180° – mL – 84° – (4y–4)°)/2 = 76°.
The base angles are equivalent because the LNOP is an isosceles trapezoid. As a result, mP = mL. Since we now know that a quadrilateral's total angles equal 360°, we can say. 360° = mL + mN + mO + mP Inputting the values provided yields: m∠L + 84° + (4y-4)° + m∠L = 360° When we simplify the equation, we obtain: 2m∠L + 4y + 80 = 360 2m∠L = 280 - 4y m∠L = 140 - 2y The non-parallel sides of LNOP are congruent since it is an isosceles trapezoid. As a result, mN = mO. We are aware of: 180° - mL = mN + mO Inputting the values provided yields: 84° + (4y-4)° = 180° - (140-2y)° When we simplify the equation, we obtain: 2y + 20 = 56 2y = 36 y = 18 Hence, mL = 140 – 2y = 104°, mP = 104°, and mN = mO = (180° – mL – 84° – (4y–4)°)/2 = 76°.
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Estimate a 20% tip on a dinner bill of $169. 86 by first rounding the bill amount to the nearest ten dollars
Answers
Answer:
Tip is $34
Round up bill amount $170
Step-by-step explanation:
20/ 100 x 170 = $34
Tip is $34
BILL plus tip is $204
A road race is 6 kilometers long. There is a water station at the halfway mark. How many meters away from from the start line is the water station
Answers
Answer: 3000m
Step-by-step explanation:
Half of 6 km is 3 km
To convert to meters multiply 3 times 1000
That will give you 3000m=3km
Alex is a single taxpayer with $80,000 in taxable income. His investment income consists of $500 of qualified dividends and short-term capital gains of $2,000. Use the tables to complete the statement
Answers
Due to Alex's salary falling inside the 22% tax bracket, his short-term capital gains would be subject to the same rate of taxation as his income.
What is short-term capital?A profit realized from the sale of a capital asset, such as a piece of personal or investment property, that has been possessed for one year or less is referred to as a short-term gain.
These profits are classified as ordinary income subject to tax at your personal income tax rate. Gain earned by selling assets that are held for a year or less are called short-term capital gains.
Alex is a single taxpayer who has taxable income of $80,000.
His investment income is made up of $2,000 in short-term capital gains and $500 in qualifying dividends.
As a result of his tax rate income falling between 38,601 and 425,800, which is below 15%, his qualifying dividends would be subject to a 15% tax.
Hence, we must deduct 15% of 500 and 22% of 2000 before combining them.
15% x 500
= 15 x 5
= 75
22% x 2000
= 22 x 20
= 440.
The total is = 75 + 440 = 515.
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Each day for the next 4 days, there is a 40% chance of a thunderstorm. Use the simulation shown, where the digits 1 through 4 represent days with a thunderstorm, to estimate the probability of a thunderstorm on at least 3 of the next 4 days. Round your anwser to the newrest tenth percent if necessary
Answers
Therefore , the solution of the given problem of probability comes out to be there is a 37.5% chance of thunderstorms occurring on at least three of the next four days.
What is probability, exactly?The primary goal of the form of patterns defined as hyper parameters is to calculate the likelihood that a remark is accurate or a specific event will occur. Any number between 0 but instead 1, where 1 usually denotes assurance and range 0 typically connotes possibility, can be used to represent chance. A probability diagram shows the chance that a specific event will occur.
Here,
We must count the number of outcomes in which there are 3 or 4 thunderstorms in order to calculate the chance that a thunderstorm will occur on at least 3 of the following 4 days using the simulation.
We can see from the programme that there are 6 scenarios where there are at least 3 thunderstorms:
=> 1-2-3-4
=> 1-2-4-3
=> 1-3-2-4
=> 1-3-4-2
=> 1-4-2-3
=> 1-4-3-2
Since there are a total of 16 potential outcomes (since a thunderstorm can occur every day or not), the likelihood of at least 3 thunderstorms is:
=> 6/16 = 0.375
This means that there is a 37.5% chance of thunderstorms occurring on at least three of the next four days.
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0.062 in standard form
Answers
Answer:
6.2 × 10-2
Step-by-step explanation:
given f(x)=x^3-x^2-5x-3 and the factor x-3, find the zeros of the function f(x).
Answers
3 | 1 -1 -5 -3
| 3 6 3
|-------------
| 1 2 1 0
The result of the synthetic division is 1x^2 + 2x + 1, which can be factored as (x+1)(x+1). Therefore, the zeros of f(x) are:
f(x) = 0 if x = 3, -1, -1
So the zeros of the function f(x) are 3, -1, and -1.
Alexander went to the store to buy some walnuts. The price per pound of the walnuts is $8 per pound and he has a coupon for $1 off the final amount. With the coupon, how much would Alexander have to pay to buy 2 pounds of walnuts? Also, write an expression for the cost to buy pp pounds of walnuts, assuming at least one pound is purchased.
Answers
Alexander would have to pay $15 to buy 2 pounds of walnuts with the coupon. The expression is cost = ($8/pound) x pp - $1.
What is a cost function?The functional connection between cost and output is referred to as the cost function. It examines the cost behaviour at various output levels under the assumption of constant technology. An essential factor in determining how well a machine learning model performs for a certain dataset is the cost function. It determines and expresses as a single real number the difference between the projected value and expected value.
Given that, the price per pound of walnuts is $8.
2 pounds x $8/pound = $16
Alexander would get $1 off the final amount.
Thus,
$16 - $1 = $15
So Alexander would have to pay $15 to buy 2 pounds of walnuts with the coupon.
The expression for the cost can be written as:
cost = ($8/pound) x pp - $1
Hence, Alexander would have to pay $15 to buy 2 pounds of walnuts with the coupon. The expression is cost = ($8/pound) x pp - $1.
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Find and simplify the difference quotient \( \frac{f(x+h)-f(x)}{h} \) for the following function. \[ \begin{array}{c} f(x)=6 \\ \frac{6(x+h-1)}{h} \\ x \end{array} \]
Answers
The simplified difference quotient for the function [tex]\(f(x)=6\) is \(\frac{x+h-1}{h/6}\).[/tex]
The difference quotient for the function \(f(x)=6\) is given by the formula \( \[tex]frac{f(x+h)-f(x)}{h}\)[/tex]. To simplify this difference quotient, substitute the given value of \(f(x)\) into the equation:
[tex]\( \frac{f(x+h)-f(x)}{h} = \frac{f(x+h)-6}{h} \).[/tex] Next, substitute the value of \(f(x)\) into the numerator:
[tex]\frac{6(x+h-1)}{h} \\[/tex] .
Finally, divide both sides of the equation by 6 to simplify the equation:
[tex]\( \frac{6(x+h-1)}{h} = \frac{x+h-1}{h/6} \)[/tex]
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Unit 8: Right Triangles & Trigonometry
Homework 4: Trigonometric Ratios &
Finding Missing Sides
Answers
In the right-angled triangle ABC the value of line segment BD is obtained as x = 21.91.
What is a right-angled triangle?
Any two sides of a triangle's three sides must always add up to more than the third side since a triangle is a regular polygon with three sides. This distinguishing characteristic of a triangle. A right-angle triangle is one that has angles between its two sides that equal 90 degrees.
A right-angled triangle ABC with drawn with angle B = 90°.
A line BD is drawn which is perpendicular to AC.
The angle BDC is also 90 degrees.
The measure for line segment AD = 12 and CD = 40.
The measure for line segment BD is x.
The side BD is common for triangle ABC and BDC.
So, by the formula of indirect measurement we have -
DC / BD = BD / AD
Substitute the values in the equation -
40 / x = x / 12
x² = 480
x = 21.908
x = 21.91
Therefore, the value of x is obtained as 21.91.
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Answer:
Sin Q
7/25
Cos Q
24/25
Tan Q
7/24
Sin R
24/25
Cos R
7/25
Tan24/7
Step-by-step explanation:
can I get help with this question?
Answers
Answer:
A'(-2, 0)B'(0, 1)C'(1, -1)Step-by-step explanation:
You want the coordinates of triangle ABC after dilation by a factor of 1/2.
DilationWhen the center of dilation is the origin, each of the coordinates is multiplied by the dilation factor:
(x, y) ⇒ (x/2, y/2)
A(-4, 0) ⇒ A'(-2, 0)
B(0, 2) ⇒ B'(0, 1)
C(2, -2) ⇒ C'(1, -1)
A boy 5m tall observes a bird on top of a pole 20m high at an angle of elevation 30°, calculate the horizontal distance between the boy and the pole
Answers
Answer:
34.28 meters
Step-by-step explanation:
We can use trigonometry to solve this problem. Let's call the horizontal distance between the boy and the pole "d". Then we can draw a right triangle with the boy's height (5m) as one leg, the distance "d" as the other leg, and the hypotenuse being the distance from the boy's eyes to the top of the pole (which we don't know yet).
We can use the angle of elevation to find the length of this hypotenuse. The angle of elevation is the angle between the horizontal and the line of sight from the boy's eyes to the top of the pole. Since the boy is looking up at the bird, this angle is also the same as the angle between the hypotenuse and the vertical (i.e. the angle at the top of the triangle). So we have:
tan(30°) = opposite/adjacent
where "opposite" is the height of the pole (20m) and "adjacent" is the hypotenuse. Solving for "adjacent", we get:
adjacent = opposite/tan(30°) = 20/tan(30°)
We can simplify tan(30°) to 1/√3, so:
adjacent = 20/(1/√3) = 20√3
Now we can use the Pythagorean theorem to find the horizontal distance "d":
d^2 + 5^2 = (20√3)^2
Simplifying and solving for "d", we get:
d = √[(20√3)^2 - 5^2] = √(1200 - 25) = √1175
So the horizontal distance between the boy and the pole is approximately 34.28 meters (rounded to two decimal places
13 Convert 20 to a percentage.
Answers
Answer:
13/20 written as a decimal is 0.65 and as a percent is 65%
1) Make the denominator 100 (20 x 5)
2) Multiply by five from the numerator too (13 x 5 = 65)
What is the value expression
2( X + 4) - (y * 8)
when x= 1/8
and y= 3/16
a 11/4
b 65/2
c 21/4
d 27/4
Answers
Answer:
d. 27/4, or 6.75
Step-by-step explanation:
[tex]2( \frac{1}{8} + 4) - ( \frac{3}{16} \times 8)[/tex]
[tex]2( \frac{33}{8} ) - \frac{3}{2} [/tex]
[tex] \frac{33}{4} - \frac{3}{2} = \frac{33}{4} - \frac{6}{4} = \frac{27}{4} = 6.75[/tex]
Without using a calculator, find the values of the integers a and b for which the solution of the equation (a) x√24 + √96 = √108 + x√12 is √a + b₁ (b), x√40 =x√5 + √10 is a + √№b 7
Answers
(a) The solution of the equation is √6 + 2.
(b) a = 10 and b = 2, and the solution of the equation is √10 + 7.
What is the solution of the equation?
((a) To solve this equation, we need to isolate the term with the variable x on one side and move all other terms to the other side.
Let's start by simplifying each term using the fact that;
√24 = √(4 × 6) = 2√6,
√96 = √(16 × 6) = 4√6,
√108 = √(36 × 3) = 6√3, and
√12 = √(4 × 3) = 2√3.
Then, we have:
x√24 + √96 = √108 + x√12
2x√6 + 4√6 = 6√3 + 2x√3
2(√6 + 2√3) = (x√3 + 2x√6)
2√6 + 4√3 = x(√3 + 2√6)
Now, we can equate the coefficients of √6 and √3 on both sides to get a system of equations:
2 = x
4 = 2x
Solving this system, we find that x = 2 and therefore a = 6 and b₁ = 2.
So, the solution of the equation is √6 + 2.
(b) To solve this equation, we also need to isolate the term with the variable x on one side and move all other terms to the other side.
Let's start by squaring both sides of the equation to eliminate the square roots:
(x√40)² = (x√5 + √10)²
40x² = 5x² + 10 + 2x√50 + 10
35x² - 20 = 2x√50
Now, we can square both sides again to eliminate the remaining square root:
(35x² - 20)² = (2x√50)²
1225x⁴ - 1400x² + 400 = 0
This is a quadratic equation in x². We can solve it using the quadratic formula:
x² = (1400 ± √(1400² - 4 × 1225 × 400)) / (2 × 1225)
x² = (1400 ± 200) / 245
x² = 2 or x² = 8/7
Since x² cannot be negative, we have x² = 2 and therefore x = √2.
Substituting this value of x back into the original equation, we have:
x√40 = x√5 + √10
√80 = √10 + √10
√80 = 2√10
So, a = 10 and b = 2, and the solution of the equation is √10 + 7.
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Isabella's ice cream parlor uses waffle cones that have a diameter of 5 in. and a height of 6 in. what is the volume of ice cream that completely fills one cone to the top? enter your answer as a decimal in the box. use 3.14 for pi.
Answers
The volume of ice cream that fills one waffle cone to the top is 13.09 cubic inches.
The waffle cone has the shape of a circular cone. The volume of a cone is given by the formula [tex]V = (1/3) * \pi * r^2 * h[/tex], where r is the radius of the circular base and h is the height of the cone.
The diameter of the cone is given as 5 inches, so the radius is half of the diameter, or 2.5 inches. The height is given as 6 inches. Substituting these values into the formula, we get:
V = [tex](1/3) * 3.14 * (2.5 inches)^2 * 6 inches[/tex]
V = 13.09 cubic inches
Therefore, the volume of ice cream that completely fills one waffle cone to the top is 13.09 cubic inches (rounded to two decimal places).
To find the volume of ice cream that fills the waffle cone completely to the top, we first note that the waffle cone has the shape of a circular cone. We use the formula for the volume of a cone, which is [tex]V = (1/3) * \pi * r^2 * h[/tex], where r is the radius of the circular base and h is the height of the cone.
We are given the diameter of the cone, which is 5 inches, and we find that the radius is half of the diameter, or 2.5 inches. We are also given the height of the cone, which is 6 inches. Substituting these values into the formula, we can calculate the volume of the cone as 13.09 cubic inches (rounded to two decimal places). Therefore, the volume of ice cream that completely fills one waffle cone to the top is 13.09 cubic inches.
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Nancy has twice as many apples as jay. Jay has 3 more apples than Ava. Nancy has 22 apples. How many apples dose Ava have?
Answers
Answer:
8 apples
Step-by-step explanation:
Step-by-step explanation:
n = Nancy's apples.
j = Jay's apples.
a = Ava's apples.
n = 22
n = j × 2
j = n / 2 = 22/2 = 11
j = a + 3
a = j - 3 = 11 - 3 = 8
Ava has 8 apples.
Frankie is flying to Seattle, Washington from Detroit, Michigan. He
leaves at 12 pm Eastern time. The flight is 5 hours. What time will it be in
Seattle (Pacific time) when he lands
Answers
Justin is joining a gym the gym is offering a discount on the fee to join and on the monthly rate the discounted price in dollars the gym charges can be represented by the equation Y equals 10 X +5
Part A what are the slope and the Y intercept of the equation what do the slope and y-intercept each represent in this situation ?.
Part B the regular price in dollar the gym charges can be represented by the equation Y equals 15 X +20. How much money in dollars does Justin save the first month by joining the gym at the discounted price rather than the regular price
Part C Justin create a system of equation based on the equation from part a and the equation from part B, the solution to the system of equation is (-3, -25) Why is the point (-3, ,-25) not possible solution in this solution ?
Answers
Part A:
The equation Y = 10X + 5 is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. Therefore, in this equation, the slope is 10 and the y-intercept is 5.
The slope represents the rate of change in the monthly rate of the gym membership. For every one unit increase in the number of months, the monthly rate will increase by $10. The y-intercept represents the initial cost of joining the gym, which is $5.
Part B:
To find out how much money Justin saves the first month by joining the gym at the discounted price, we need to calculate the difference between the regular price and the discounted price for the first month.
The regular price for the first month can be found by plugging in X = 1 into the equation Y = 15X + 20, which gives Y = 35.
The discounted price for the first month can be found by plugging in X = 1 into the equation Y = 10X + 5, which gives Y = 15.
Therefore, Justin saves $20 (35 - 15) the first month by joining the gym at the discounted price rather than the regular price.
Part C:
The system of equations is:
Y = 10X + 5 (discounted price)
Y = 15X + 20 (regular price)
The solution to the system of equations is (-3, -25), which means that if X = -3, then Y = -25 is a solution to both equations. However, this solution is not possible in this situation because X represents the number of months, which cannot be negative. Therefore, the point (-3, -25) is not a valid solution.
harrison St thomas St, and Denny Way are parallel. on broad St, the distance between mercer St and Denny way is 0.7 miles. the distance between those same streets on aurora ave is 0.45 miles
Answers
The distance between Thomas St and Denny Way on Broad St is 0.1 miles.
How do we calculate?0.45 miles on Aurora Ave is equivalent to the distance between Mercer St and Denny Way on Broad St.
0.2 miles on Aurora Ave is equivalent to the distance between Thomas St and Denny Way on Aurora Ave.
We say X be the distance between Thomas St and Denny Way on Broad St,
and have the following proportion:
0.45 miles / (Mercer St to Denny Way on Broad St) = 0.2 miles / (Thomas St to Denny Way on Broad St)
Solving for x, we get:
x = 0.45 miles x (Thomas St to Denny Way on Broad St) / (Mercer St to Denny Way on Broad St) = 0.45 * 0.2 / 0.7 = 0.1286 miles
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Complete question:
Use the following information and the map of downtown Seattle to answer questions one and two. Harrison St, Thomas St, and Denny Way are parallel. On Broad St, the distance between Mercer St and Denny Way is 0.7 miles. The distance between those same streets on Aurora Ave is 0.45 miles.
a) On Aurora Ave the distance between Thomas St to Denny Way is 0.2 miles. What is the distance
between these two streets on Broad St? Round your answer to the nearest tenth of a mile.
Molly knows that 30% of the students at her school are boys and that there are 600 boys at her school. She wants to find the total number of students at the school, because she needs to order t-shirts for all the students.
What is the total number of students at Molly's school?
Answers
Answer:
Step-by-step explanation:
You ask yourself, "600 is 30% of how many students?". In equation form this looks like:
600 = .30x
Divide both sides by .30 and you'll get that the number of students is 2000
6) (8 pts) A hospital is interested in evaluating the percent of patients entering the emergency department who are admitted to the hospital. Data for randomly selected day was collected and out of 187 patients who entered the emergency department, 42 were admitted to the hospital. a) (6 pts) Calculate a 90% two-sided confidence interval for p, the percent of people entering the emergency department who are admitted to the hospital. b) (2 pts) In planning staffing to care for admitted patients, the hospital has assumed that 25% of people who enter the emergency department are admitted to the hospital. Based on your answer to part (a), is it reasonable for the hospital to use this assumption? Explain your answer using information from part (a)
Answers
90% people entering the emergency department is within the interval of [0.1559, 0.2933].
The confidence interval of the percent of patients entering the emergency department who are admitted to the hospital is [0.1763, 0.3137]. It is not reasonable for the hospital to assume that 25% of people who enter the emergency department are admitted to the hospital. Here's why.How to calculate a 90% two-sided confidence interval for p, the percent of people entering the emergency department who are admitted to the hospital:$$CI_p =\bigg(\hat{p}-Z_{\alpha/2}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}, \hat{p}+Z_{\alpha/2}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\bigg)$$ where $\hat{p} = \frac{x}{n}$, $\alpha = 0.10$, $Z_{\alpha/2} = 1.645$ (for a 90% confidence interval), and $n = 187$. The margin of error is given by $$ME = Z_{\alpha/2}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$Plugging in the values, we get $$\hat{p} = \frac{42}{187} = 0.2246$$$$ME = 1.645 \cdot \sqrt{\frac{0.2246\cdot 0.7754}{187}} \approx 0.0687$$Therefore, the confidence interval for $p$ is $$CI_p = (0.2246-0.0687, 0.2246+0.0687) = (0.1559, 0.2933)$$The 90% two-sided confidence interval for the percent of people entering the emergency department who are admitted to the hospital is [0.1559, 0.2933].Since the interval doesn't include 0.25, the hospital should not use the assumption that 25% of people who enter the emergency department are admitted to the hospital. This is because the interval does not overlap with the value of 0.25. As a result, we are 90% confident that the true proportion of people who are admitted to the hospital after entering the emergency department is within the interval of [0.1559, 0.2933].
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How are the products of -3(1) and - 3(-1) the same? How are they different?
Answers
Answer:
Step-by-step explanation:
45342
a particle moves along the x-axis so that at any time t>0, its velocity is given by v(t)=4-6t^2. if the particle is at a position x=7 at t=1 time, what is the position of the particle at time t=2?
Answers
Answer:
-11.
Step-by-step explanation:
We know that the velocity function v(t) is the derivative of the position function x(t).
So, we can integrate v(t) to find x(t) up to a constant of integration:
∫v(t) dt = ∫(4 - 6t^2) dt = 4t - 2t^3 + C
where C is the constant of integration.
We can find the value of C by using the initial condition that the particle is at position x=7 at t=1:
x(1) = 4(1) - 2(1)^3 + C = 7
C = 5
So, the position function is:
x(t) = 4t - 2t^3 + 5
To find the position of the particle at time t=2, we can substitute t=2 into the position function:
x(2) = 4(2) - 2(2)^3 + 5 = -11
Therefore, the position of the particle at time t=2 is -11.
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Farmer Naxvip wanted to sell some hopts and totts at the market. She planned to charge $3 per hopt and $7 per tott. She expected to make at least $84. She expected to sell at most 24 units.
Write a system of statements, in standard form, modeling the relationships between amounts of hopts (x) and amount of totts (y).
Answers
Answer:
Let x be the number of hopts and y be the number of totts.
The first statement relates to the total amount of money expected to be made:
3x + 7y ≥ 84
This inequality states that the total revenue from selling hopts and totts should be at least $84.
The second statement relates to the total number of units expected to be sold:
x + y ≤ 24
This inequality states that the total number of hopts and totts sold should be at most 24 units. Therefore, the system of inequalities in standard form is:
3x + 7y ≥ 84
x + y ≤ 24
where x ≥ 0 and y ≥ 0 (since we cannot sell a negative number of hopts or totts).
Answer: Let "x" be the number of hopts that Farmer Naxvip plans to sell, and let "y" be the number of totts that she plans to sell. Then we can write the following system of inequalities to model the relationships between the amounts of hopts and totts:
3x + 7y >= 84
x + y <= 24
The first inequality represents the condition that Farmer Naxvip expects to make at least $84, while the second inequality represents the condition that she expects to sell at most 24 units.
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7. A man wishes to invest $3500. He can buy savings bonds which pay simple
interest at the rate of 12% per annum or he can start a savings account which
pays compound interest at the same rate. Calculate the difference in the
amounts of the two investments at the end of the 3 years.
a)
1200 x 9 x2
=
Answers
Robert is currently 10 years old.Given that five years ago Sharon was twice as old as Robert was then, we can set up the following equation: y + 5 = 2(y)
We are given the information that Sharon is five years older than Robert, and five years ago Sharon was twice as old as Robert was then. This means we can create a system of equations to solve for Robert's age.
Let x = Robert's current age
Let y = Robert's age five years ago
Given that Sharon is five years older than Robert, we can set up the following equation:
x + 5 = Sharon's current age
Given that five years ago Sharon was twice as old as Robert was then, we can set up the following equation:
y + 5 = 2(y)
Solving the first equation for x, we get x = Sharon's current age - 5. Substituting this into the second equation, we get:
y + 5 = 2(Sharon's current age - 5)
Solving this equation for y, we get y = (Sharon's current age - 5)/2.
Since Sharon is five years older than Robert, Sharon's current age is x + 5. Substituting this into our equation for y, we get:
y = (x + 5 - 5)/2
Simplifying this equation, we get y = x/2. This means that Robert's age five years ago was half of his current age.
Since we know that Robert is currently 10 years old, Robert's age five years ago was 5. Therefore, Robert is currently 10 years old.
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PQR is a right angled triangle at P nad ahs PQ
Answers
The length QR of the right angle triangle is 26 cm.
How to find the side of a right triangle?A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
Therefore, the side of a right angle triangle can be found using Pythagoras's theorem as follows:
Hence,
c² = a² + b²
where
c = hypotenusea and b are the other legsTherefore,
24² + 10² = QR²
576 + 100 = QR²
QR² = 676
QR = √676
QR = 26 cm
Therefore,
length of QR = 26 cm
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Todd and Eric went to the book store. Eric spent $15 less than three times the
amount that Todd spent. If the shoppers spent a total of $197 in books, How much
did Eric spend?
$34
$53
$65
$71
$29
$59
$48
Answers
If the shoppers spent a total of $197 in books, the amount that Eric spend is $144.
How much did Eric spend?Let's assume that Todd spent x dollars in the bookstore.
According to the problem, Eric spent $15 less than three times the amount that Todd spent, which can be written as:
3x - 15
The total amount spent by both shoppers is $197, so we can set up the equation:
x + (3x - 15) = 197
Simplifying and solving for x, we get:
4x - 15 = 197
4x = 212
x = 53
Therefore, Todd spent $53 in the bookstore.
To find how much Eric spent, we can substitute Todd's value into the expression we derived for Eric's spending:
3x - 15 = 3(53) - 15 = 144
So Eric spent $144 in the bookstore.
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