Solve the following equations . a² = 64. 2x-2 = 16. 3y² = 27​

The equations equivalent to 1/4 (8x + 56) = 20 are

1. 56 + 8x = 80

2.14 = 20 - 8x

4.2x = 6

5. x = 3

An equation is a mathematical expression that shows the relationship between two variables.

Since we have the equation 1/4(8x + 56) = 20, and we want to find all the equations that are equivalent to it, we solve the equation.

So, we proceed as follows.

1/4(8x + 56) = 20

Expanding the brackets, we have

8x/4 + 56/4 = 20

2x + 14 = 20

Subtracting 14 from both sides, we have that

2x = 20 - 14

2x = 6

x = 6/2

x = 3

Also, in 1/4(8x + 56) = 20

Multiplying through by 4, we have that

8x + 56 = 80

2x + 14 = 20

Subtracting 2x from both sides, we have that

14 = 20 - 2x

So, the equations are

1. 56 + 8x = 80

2.14 = 20 - 8x

4.2x = 6

5. x = 3

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The sοlutiοn οf the given prοblem οf area cοmes οut tο be the cοmpοsite shape in the picture has a surface area οf 96 square centimetres.

Its tοtal size can be determined by figuring οut hοw much rοοm wοuld be required tο cοmpletely cοver the οutside. The surrοundings have alsο been taken intο cοnsideratiοn when calculating the surface οf a trapezοidal shape. The tοtal measurements οf sοmething are determined by its surface area. Hοw many edges there are between a cubοid's fοur trapezοidal ends indicates hοw much water it can cοntain in its interiοr.

Here,

Let's start by listing each separate surface that cοntributes tο the cοmpοsite shape. There are twο triangles and fοur squares.

We can use the fοllοwing methοd tο determine the area οf each rectangle:

=> Length = 5 centimetre, width = 4 cm, sο area = 5 cm x 4 cm = 20 cm² fοr rectangle 1.

=> Rectangle 2 has a surface area οf 20 cm² because its length is 5 cm and width is 4 centimetres.

=> Rectangle 3 has a 6 centimetre length and a 4 cm width,

=> area =  6 cm x 4 cm, οr 24 cm².

=> Rectangle 4 has a 6 centimetre length and a 4 cm width, sο

=> area =  6 cm x 4 cm, οr 24 cm².

The fοllοwing algοrithm can be used tο determine each triangle's area:

=> area =  (Base × Height) / 2

Area οf Triangle 1 :  (2 cm x 4 cm) / 2 = 4 cm²

Area οf Triangle 2: (2 centimetre x 4 cm) / 2 = 4 cm²

Tοtal Surface Space equals 96 cm² (20 cm², 20 cm², 24 cm², 24 cm², 4 cm², 4 cm²)

Cοnsequently, the cοmpοsite shape in the picture has a surface area οf 96 square centimetres.

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The point on the number line that is 1/4 of the way from point 0 to -3 is located at the point 3/4.

What is a number line?

A number line is a straight line that represents the real numbers as points or marks on the line. The numbers increase from left to right, and each point on the line corresponds to a specific number.

To find the point on the number line that is 1/4 of the way from point 0 to -3, we can use the following formula:

point = starting point + fraction of distance * total distance

The starting point is 0, and the total distance is the distance between 0 and -3, which is 3. So the total distance is 3.

Now, we need to find the fraction of the distance that is 1/4 of the total distance. This can be written as:

fraction of distance = 1/4

So the formula becomes:

point = 0 + 1/4 * 3

Simplifying the expression, we get:

point = 3/4

Therefore, the point on the number line that is 1/4 of the way from point 0 to -3 is located at the point 3/4.

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To find the number of points at which the graph of the function intersects the x-axis, we need to find the roots of the equation:

4x^2 - 9x + 9 = 0

We can use the quadratic formula to find the roots:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

In this case, a = 4, b = -9, and c = 9, so:

x = (-(-9) ± sqrt((-9)^2 - 4(4)(9))) / 2(4)

x = (9 ± sqrt(81 - 144)) / 8

x = (9 ± sqrt(-63)) / 8

Since the discriminant is negative, the roots are complex and the graph does not intersect the x-axis. Therefore, the answer is b. 0.

The double number line, along with the formula y = 8x + 58, can be used to determine the number of adults needed to supervise a given number of children on a field trip.

The double number line shows the relationship between the number of adults and the number of children they can supervise on a field trip. The table below represents the same relationship:

Adults  Children

8         66

15         99

The formula used to calculate the number of children supervised by a given number of adults is y = 8x + 58, where y is the number of children and x is the number of adults. This formula can be derived by looking at the two points given in the table above. For 8 adults, the corresponding number of children is 66, so 66 = 8x + 58. Solving this equation yields x = 7, which means that 7 adults are needed to supervise 66 children. At 15 adults, the number of children goes up to 99, so 99 = 8x + 58. Solving this equation yields x = 11.25, which means that 11.25 adults are needed to supervise 99 children.

The equation can also be used to calculate the number of adults needed to supervise a given number of children. For example, if the field trip involves 45 children, the equation y = 8x + 58 can be used to calculate the number of adults needed. Substituting 45 for y yields 45 = 8x + 58, which when solved yields x = 5.625. This means that 5.625 adults are needed to supervise 45 children.

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Answer:

102 cubic inches

Step-by-step explanation:

The formula for a volume of a sphere is as follows:

[tex]V = \frac{4\pi r^2}{3}[/tex]

Hence, substituting r=2.9 into this equation,

[tex]\frac{4\pi (2.9)^3}{3}\\\\=\frac{4\pi (24.4)}{3}\\\\=102.160404[/tex]

Hence, the answer is 102 cubic inches.

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Answer: slope is 1/9

Step-by-step explanation:

Answer:

1/6

Step-by-step explanation:

i  used a website math-way . its a very accurate response. it usually is at least but you should use it.

The factored form of the quadratic expression 2x² - 9x - 11 is: a. (2x - 11)(x + 1).

To factor the quadratic expression 2x² - 9x - 11, we need to find two binomials that when multiplied together give us the original quadratic expression. Here are the steps to follow:

Step 1: Multiply the coefficient of the x² term (2) and the constant term (-11) to get -22.

Step 2: Find two numbers whose product is -22 and whose sum is the coefficient of the x term (-9). These numbers are -11 and 2.

Step 3: Rewrite the quadratic expression by splitting the x term into -11x + 2x, using the two numbers found in step 2:

2x² - 11x + 2x - 11

Step 4: Group the first two terms and the last two terms together and factor out the greatest common factor (GCF) of each group:

(2x² - 11x) + (2x - 11)

x(2x - 11) + (2x - 11)

Step 5: Factor out the common binomial factor of (2x - 11):

(2x - 11)(x + 1)

The answer is: a. (2x - 11)(x + 1)

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After answering the prοvided questiοn, we can cοnclude that Sο the equatiοn estimated amοunt charged per hοur when the client οrders 80 hοurs οf wοrk is $60.85.

In mathematics, an equatiοn is a statement that implies the unity οf twο traits. An equatiοn cοnsists οf twο sides separated because οf an analytical sοlutiοn (=). Fοr instance, the debate "2x + 3 = 9" asserts that the remark "2x + 3" equals the valuatiοn "9". The gοal οf sοlving equatiοns is tο determine the amοunt οr values οf the variable in the mοdel) that wοuld allοw the equatiοn tο really be true.

Fοrmulae can be simple οr cοmplex, regular οr nοnlinear, and cοntain οne οr mοre variables. Fοr example, in the equatiοn "x² + 2x - 3 = 0," the variable x is elevated tο the secοnd pοwer. Lines are used extensively in mathematics, including algebra, equatiοns, and geοmetry.

Let's start by using the given infοrmatiοn tο set up twο equatiοns:

C(70) = $4900

C(80) = C(70) - ($4/10) * 80

C(80) = C(70) - $32

C(80) = $4900 - $32

C(80) = $4868

$4868 / 80 = $60.85 per hοur

Sο the estimated amοunt charged per hοur when the client οrders 80 hοurs οf wοrk is $60.85.

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Answer:

3.876 x 10^7 in standard form is 38,760,000.

Step-by-step explanation:

Answer:

38,760,000

Step-by-step explanation:

To write 3.876 x 10^7 in standard form, you need to move the decimal point to the left or right, depending on whether the exponent is positive or negative. In this case, the exponent is positive, so you need to move the decimal point 7 places to the right.

Starting with 3.876, move the decimal point to the right 7 places to get:

38,760,000

So 3.876 x 10^7 in standard form is 38,760,000.

Answer:

1.92

Step-by-step explanation:

25x  = 36 + 12

25x = 48

x = 1.92

Let's check

25 x 1.92 = 36 + 12

48 = 48

So, 1.92 is the correct answer.

The value of the expression 4x+1/3y² when x = 2 and y = 3 is 1/3

In mathematics, a change of variables is a basic technique used to simplify problems in which the original variables are replaced with functions of other variables. The intent is that when expressed in new variables, the problem may become simpler, or equivalent to a better understood problem.

Finding the value of the expression, we substitute the given values for the variables

(4x+1)/(3y²

when x = 2 and y = 3

4( 2) +1/3(3)²

= 8 + 1/( 3 × 9)

= 9/27

= 1/3

therefore the value of the expression is 1/3

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Answer:

25 Hours

Step-by-step explanation:

Answer:

length of a side is 3

Step-by-step explanation:

if it is a square, the sides are equal. The diagonal will divide the square into 2 isosceles right triangles with diagonal is the hypotenuse

Pythagorean theorem: c^2 = a^2 + b^2

since a = b in isosceles right triangle

c^2 = 2a^2

18 = 2a^2

a^2 = 18/2 = 9

a = √9 = 3

The linear function with the greatest slope is at option A.

The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line. Finding the slope between two separate locations and calculating the slope of a line are related tasks. In general, we require the values of any two separate coordinates of a line in order to determine its slope.

Find the slope for all the function to determine the highest rate:

A. The slope of g(x) is 1, since the change in y is 1 for every 1 unit increase in x.

B. The slope of f is -4/8 or -1/2.

C. The slope of the line passing through (-1, 3) and (2, -3) is (-3 - 3)/(2 - (-1)) = -2/3.

We observe that the slope of linear equation in A is greater.

Hence, the linear function with the greatest slope is at option A.

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If Jasper and Corey have saved up a total of $78.0 and Jasper has saved 6 dollars more than twice as much as Corey, Corey has saved $24, for a total of $78.

Let's use C to represent the amount of money Corey has saved.

We know that Jasper has saved 6 dollars more than twice as much as Corey, so we can write an equation to represent this relationship:

J = 2C + 6

where J is the amount of money Jasper has saved.

We also know that the total amount of money saved by Jasper and Corey is $78, so we can write another equation to represent this:

J + C = 78

Now we can substitute the first equation into the second equation to get an equation with only one variable:

(2C + 6) + C = 78

Simplifying the equation, we get:

3C + 6 = 78

Subtracting 6 from both sides, we get:

3C = 72

Dividing both sides by 3, we get:

C = 24

Therefore, Corey has saved $24. We can use the first equation to find out how much Jasper has saved:

J = 2C + 6 = 2(24) + 6 = 54

So Jasper has saved $54.

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64,000÷10 to the fourth power is equal to 0.64 × 10⁴

In mathematics, an algebraic expression is a combination of variables, constants, and mathematical operations, such as addition, subtraction, multiplication, and division, that represents a quantity or a relationship between quantities.

To solve this, we need to remember the order of operations, which is parentheses, exponents, multiplication and division (performed left to right), and addition and subtraction (also performed left to right).

First, we need to calculate 10 to the fourth power:

10 to the fourth power means 10 multiplied by itself four times:

10⁴ = 10,000

Now we can substitute that value into the original expression:

64,000 ÷ 10,000 =  0.64 × 10⁴

Therefore, 64,000÷10 to the fourth power is equal to  0.64 × 10⁴

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Answer:

+ 7

Step-by-step explanation:

To find the nth term rule simply we just have to find the difference between the numbers

Difference between numbers

The difference between all our numbers is 7!

Hope this helps, have a lovely day! :)

Answer:

Step-by-step explanation:

The maximum volume of paint that can be stored in the cylindrical tank occurs when it is completely filled. The formula for the volume of a cylinder is:

V = πr^2h

where V is the volume, r is the radius, and h is the height.

In this case, the height of the cylindrical tank is 8 feet and the radius is 3 feet. So we can substitute these values into the formula to get:

V = π(3^2)(8)

V = π(9)(8)

V = 72π

Therefore, the maximum volume of paint that can be stored in the tank is 72π cubic feet, which is approximately 226.2 cubic feet if we round to one decimal place.

Answer:

True:)

Step-by-step explanation:

Answer:

Step-by-step explanation:where are you ???

Answer:

To find an appropriate measure of center, we need to determine the typical or central value of the data. There are several measures of center, such as mean, median, and mode.

However, in this case, we need to consider the extreme value of 8, which is significantly lower than the rest of the values. This value may be an outlier, and including it in the calculation of the mean could skew the result.

Therefore, the most appropriate measure of center in this case would be the median, which is the middle value when the data set is ordered.

To find the median, we first need to order the data set:

8, 20, 22, 23, 23, 24

There are six values in the data set, so the median will be the average of the two middle values, which are 22 and 23.

Median = (22 + 23) / 2 = 22.5

Therefore, the most appropriate measure of center for this data set would be the median of 22.5.

Answer:

(w⁴)⁵

=w⁴*⁵

Answer=w²⁰

The mass of a 6.75 kg bowling ball is equivalent to 67.5 hg, 67.5 dag, 6750 g, 67500 cg, or 6750000 mg.

Mass is a measure of the amount of matter an object contains. The equation used to convert between mass units is:

Mass (m) = Mass (M) × Conversion Factor

For example, if we want to convert 6.75 kg to hg (hectograms), the formula and calculation would be:

m (hg) = M (kg) × 100

m (hg) = 6.75 kg × 100

m (hg) = 67.5 hg

Similarly, we can convert 6.75 kg to dag (decagrams) using the formula:

m (dag) = M (kg) × 10

m (dag) = 6.75 kg × 10

m (dag) = 67.5 dag

To convert 6.75 kg to g (grams), the formula and calculation are:

m (g) = M (kg) × 1000

m (g) = 6.75 kg × 1000

m (g) = 6750 g

We can also convert 6.75 kg to cg (centigrams) using the formula:

m (cg) = M (kg) × 10000

m (cg) = 6.75 kg × 10000

m (cg) = 67500 cg

Finally, to convert 6.75 kg to mg (milligrams), the formula and calculation are:

m (mg) = M (kg) × 1000000

m (mg) = 6.75 kg × 1000000

m (mg) = 6750000 mg

In conclusion, the mass of a 6.75 kg bowling ball can be equivalent to 67.5 hg, 67.5 dag, 6750 g, 67500 cg, or 6750000 mg.

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Answer:

• (0,12)

• (1,6)

• (9,8)  

• (-2,19)

• (8,3)    

Step-by-step explanation:

See the attached graph.

The two inequalities are graphed and the points that are solutions to both equations are all those in the purple area of the graph (the result of the red and blue solutions that overlap [= purple]).  The individual points are added to find which points do, or do not, fall within the solution set of both inequalities:

• (0,12)   Yes

• (-2,0)    No

• (-6,13)    No

• (1,6)      Yes

• (9,8)     Yes

• (-2,19)   Yes

• (8,3)      Yes

• (0,10)     No

Daniel and Liz have conflicting claims about how much time students spend on homework.

Daniel claims that more than half of students spend 2 1/2 hours or more on homework, while Liz claims that more than half spend less than 2 1/2 hours. To determine who is correct, we must look at the actual data.

If, when we look at the data, we find that more than half the students spend 2 1/2 hours or more on homework, then Daniel is correct. Conversely, if more than half the students spend less than 2 1/2 hours on homework, then Liz is correct. It is important to note that the answer may depend on the sample size of the data we are looking at.

If the sample size is small, then it may be difficult to definitively answer the question. However, if the sample size is large, then it may be possible to provide a definite answer. In conclusion, to determine who is correct, we must look at the actual data. If the sample size is large enough, then it may be possible to definitively answer the question of who is correct.

Daniel says that more than half of the students spent 2.5 hours or more on homework, while Liz says more than half of the students spent less than 2.5 hours on homework. Liz's assertion is correct. So, Liz is correct since more than half of the students spent less than 2.5 hours on homework.

If Daniel were correct, the total percentage would be more than 100 percent, which is impossible since the total percentage is always 100 percent when the data set is of a limited population. The arithmetic mean of the time the students spend on their homework can be calculated using a statistical concept called a measure of central tendency.

The mean is used in this case. A measure of central tendency is a way of summarizing a data set using a single value that represents the entire collection of data in a condensed form. The mean is calculated by adding up all of the data and then dividing by the number of data points. To discover if the assertion that Liz is correct is accurate, more data is needed.

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answer: 35.50

explanation; 4.60 x 7 = 32.20

( price for the 7 dvds )

+ 3.30

( video game price )

What must be true for the triangles to be similar to each other by SAS is: y = z, and c/f = a/e, where y = z = 50°; c = 4, f = 3; a = 8; e = 6.

SAS stands for "side-angle-side", which means that if two triangles have two pairs of corresponding sides that are proportional in length and the included angles between them are congruent, then the triangles are similar.

Therefore, for the triangles to be similar by SAS, we would have:

y = z, and

c/f = a/e

Assigning values, we would have:

y = z = 50°

c/f = 4/3

a/e = 8/6

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i) The expression relating price and output assuming it is linear is Price per unit = -20 × Number of units sold + c.

ii) The total cost function, assuming it is linear is 2000 + 10 × Number of units sold.

iii)  The business woman need to produce 114 products to achieve breakeven.

(i) The expression relating price and output assuming it is linear can be written as:

Price per unit = m × Number of units sold + c

where m is the slope of the line and c is the y-intercept.

We can find the slope by using the two points (20, 300) and (13, 440):

m = (440 - 300) / (13 - 20) = 140 / (-7) = -20

So, the expression relating price and output is:

Price per unit = -20 × Number of units sold + c

(ii) The total cost function assuming it is linear can be written as:

Total cost = Fixed cost + Variable cost per unit × Number of units sold

Given that the fixed cost of production is GH₵2,000 with a variable cost per unit of GH¢10, the total cost function can be expressed as:

Total cost = 2000 + 10 × Number of units sold

(iii) To find the level of production at which the business woman will breakeven, we need to find the point at which the total cost equals the total revenue. Since the total revenue is simply the product of the price per unit and the number of units sold, we can set these two equations equal to each other:

Price per unit × Number of units sold = Total cost

Substituting the expressions we found in parts (i) and (ii), we get:

(-20 × Number of units sold + c) × Number of units sold = 2000 + 10 × Number of units sold

Simplifying and solving for the number of units sold, we get:

20 × Number of units sold^2 - 20c × Number of units sold - 2000 = 0

Using the quadratic formula, we get:

Number of units sold = (-(-20c) ± sqrt((-20c)^2 - 4 × 20 × (-2000))) / (2 × 20)

Simplifying, we get:

Number of units sold = (c + sqrt(c^2 + 2000)) / 2

Since we know that the business woman can sell 300 units a day at a price of GH¢20 and 440 units a day at a price of GH¢13, we can set up a system of equations to solve for the y-intercept, c:

-20 × 300 + c = 20c + 2000

-20 × 440 + c = 13c + 2000

Solving this system of equations, we get:

c = 2400/3 ≈ GH₵800

Therefore, the level of production at which the business woman will breakeven is:

Number of units sold = (800 + sqrt(800^2 + 2000)) / 2 ≈ 113.7 units

She should produce at least 114 units to breakeven.

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