Answer:
y = -x + 7
Step-by-step explanation:
As we move from (8, 0) to (0, 8), we see x decreasing by 8 ('rise') and y increasing by 8 ('run'). Thus, the slope of this line is m = rise/run = 8/(-8) = -1.
Starting from y = mx + b and substituting 8 for x, 0 for y and -1 for m, we get:
0 = -1(8) + b, or b = 8
Then the equation of the line through the two given points is y = -x + 8. Any line parallel to this one has the same slope: m = -1.
Repeat the above work to find the y-intercept of the line parallel to y = -x + 8 that goes through (2, 5):
5 = -2 + b, or b = 7
Then the desired line (final answer) is y = -x + 7
Write an equivalent expression.
1. 8(y - 7)
2. -2x + 7
3. 3/5x + 2/5 + 3/5x
Answer:
8(y - 7) =8y-7-2x+7=7/2=3.5The equivalent expressions are;
1. 8 (y - 7) = 8y - 56
2. - 2 (x + 7) = - 2x - 14
3. 3/5x + 2/5 + 3/5x = (6x + 2) / 5
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expressions are;
1. 8 (y - 7)
2. - 2 (x + 7)
3. 3/5x + 2/5 + 3/5x
Now,
Solve all the expression as;
1. 8 (y - 7) = 8 × y - 8 × 7
= 8y - 56
Thus, 8 (y - 7) = 8y - 56
2. - 2 (x + 7) = - 2 × x - 2 × 7
= - 2x - 14
Thus, - 2 (x + 7) = - 2x - 14
3. 3/5x + 2/5 + 3/5x = 3/5x + 3/5x + 2/5
= (3x + 3x)/ 5 + 2/5
= 6x / 5 + 2/ 5
= (6x + 2) / 5
Thus, 3/5x + 2/5 + 3/5x = (6x + 2) / 5
Therefore, The equivalent expressions are;
1. 8 (y - 7) = 8y - 56
2. - 2 (x + 7) = - 2x - 14
3. 3/5x + 2/5 + 3/5x = (6x + 2) / 5
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what is the least common denominator of 10 and 14
Answer:
70
Step-by-step explanation:
Given -
the least common denominator of 10 and 14 is - *70*
Prime factor of 14 are 2 and 7
14 = 2 * 7
Prime factor of 10 are 2 * 5
10 = 2 * 5
Now Multiplying the highest exponent prime factor to calculate the LCM of 14 and 10
LCM (10,14) = 2 * 5 * 7
LCM (10,14) = 70
An ice cream shop sells ice cream cones, c, and
milkshakes, m. Each ice cream cone costs $1.50
and each milkshake costs $2.00. Donna has $19.00
to spend on ice cream cones and milkshakes. If she
must buy 5 ice cream cones, which inequality could
be used to determine the maximum number of
milkshakes she can buy?
Answer:
$7.50+m > $19
The inequality to be used for determining the maximum number of milkshakes she can buy will be in the form of:
[tex]\$7.50+\$2.00\rm{m}\leq \$19.00[/tex]
The inequality in the position or the relationship between two variables in order to make the total either greater than, less than, or greater than equal to, or less than equal to the total amount.
The inequality can be between numbers or algebraic expressions.
In the given case,
Per unit cost of ice cream cone $1.50 Per unit cost of milkshakes $2.00 The total amount for spending is $19.00 Number of ice cream cones bought 5To determine the inequality for the number of milkshakes the inequality will be formed as follows:
The total cost of ice cream cones will be added with the total cost of milkshakes (where m is the number of milkshakes) and the sign used will be greater than or equal to the given amount to be spent.
Therefore, the inequality will be [tex]\$7.50+\$2.00\rm{m}\leq \$19.00[/tex]
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Sally is paid to walk her neighbor’s dog every day.Every month she is paid she puts away $20 and saves the rest.Write an expression that represents the amount she will save in 6 months if she earns m dollars each month.If she’s paid $65 each month how much will she save in 6 months?
Answer: she would have saved 120$$
Step-by-step explanation:
Solve for x. Round your answer to the nearest tenth if necessary.
70°
6
X
Answer:
Tan 70 = opp/adj
Tan 70 = x/6
multiply by 6 on both sides
16.5 = x
what is cosec32°/sec58°=
Answer:
1
Step-by-step explanation:
Using the cofunction identity
sec(90 - x) = cosecx , then
sec(90 - 58)° = cosec32° , so
[tex]\frac{cosec32}{sec58}[/tex]
= [tex]\frac{cosec32}{cosec32}[/tex]
= 1
What is the slope of the line that passes through the points (5, 6)(5,6) and (5, 9) ?(5,9)? Write your answer in simplest form.
Answer:
The slope is undefined.
Step-by-step explanation:
You can use slope formula (y - y)/(x - x) and you will get a zero on the bottom (never allowed) OR notice that the x's are the same so sketch a graph, the line is vertical...that means that slope is undefined.
is zero a rational number?
Answer:
yes
Step-by-step explanation:
we know that every integer is a rational number and Zero can be represented as the ratio of two integers.
What’s 10^102????????€
Answer:
(2^102•5^102)
Step-by-step explanation:
(10)^102 = (2•5)^102 = 2^102 • 5^102
Researchers claim that 90% of people are left handed. Suppose the researchers' claim is true. Mrs. Reyes has a Statistics class with 30 students. What is the probability that exactly 25 of them are left handed?
Answer:
10.23% to the nearest hundredth.
Step-by-step explanation:
This is a Binomial Probability Distribution.
If exactly 25 are left handed then exactly 5 are right handed.
So (probability that exactly 25 are left handed)
= 30C5*(0.1)^5(0.9)^25
= 0.1023047706
= 10.23%.
The probability that exactly 25 students out of 30 are left-handed, assuming the researchers' claim is true, is approximately 0.2031, or about 20.31%.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
Example:
The probability of getting a head in tossing a coin.
P(H) = 1/2
We have,
This problem involves the binomial probability distribution, where we have a fixed number of trials (30 students in this case), and each trial has two possible outcomes (left-handed or not left-handed).
The probability of success (a student being left-handed) is 0.9, based on the researchers' claim.
The probability of a failure (a student not being left-handed) is 1 - 0.9 = 0.1.
We want to find the probability that exactly 25 students out of 30 are left-handed.
This can be calculated using the binomial probability formula:
[tex]P(X = k) = ^nC_ kp^k (1 - p)^{n-k}[/tex]
where:
n = 30 (the number of trials)
k = 25 (the number of successes we want)
p = 0.9 (the probability of success in each trial)
Plugging in the values, we get:
[tex]P(X = 25) = ^{30}C_ {25}~ 0.9^{25} ~0.1^5[/tex]
Using a calculator or statistical software, we can find that:
P(X = 25) ≈ 0.2031
Therefore,
The probability that exactly 25 students out of 30 are left-handed, assuming the researchers' claim is true, is approximately 0.2031, or about 20.31%.
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Show Work to factor the binomials.
[tex](14)\\\\x^2 + 14x +45\\\\=x^2 +5x +9x +45\\\\=x(x+5) +9(x+5)\\\\=(x+9)(x+5)\\\\(15)\\\\x^2 +18x +45\\\\=x^2 +15x +3x +45\\\\= x(x+15) +3(x+15)\\\\=(x+3)(x+15)\\\\\\(16)\\\\x^2+46x+45\\\\=x^2 +45x +x +45\\\\=x(x+45) +(x+45)\\\\=(x+45)(x+1)[/tex]
Tell whether each equation has one, zero, or infinitely many solutions.
Solve the equation if it has one solution.
4x + 2 = x + 8 PLZZZZZ
Answer:
Exactly One Solution
Step-by-step explanation:
4x + 2 = x + 8
3x = 6 Simplify.
x = 2 Divide by 2.
Answer:
One solution, x = 2
Step-by-step explanation:
4x + 2 = x + 8 (Given)
4x = x + 6
(The 2 is subtracted from the right side, therefore the left side is also subtracted. 8 becomes 6.)
3x = 6
(The x is subtracted from the right side to the left side. Thus turning the 4x into 3x)
x = 2
(The 3 is divided out to get x alone. So, the 6 has to be divided by 3 as well, turning it into 2)
The roots of the equation 0 = x^3+ 2x^2– 3x are: _________.
These are the x-intercept values at these points: _________.
if x and y are positive numbers xy = 96 what is the value of x
The value of x is 96/y where y is not equal to zero.
Given the expression that relates x and y as xy = 96
We are told that x and y are positive numbers. To get the value of x, we will divide both sides by y as shown:
[tex]xy = 96\\\frac{xy}{y} =\frac{96}{y} \\x = \frac{96}{y} \\[/tex]
From the result, we can conclude that the value of x is 96/y where y is not equal to zero.
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I need answers to these questions
Answer is in the attached file...
Find the missing factor
Answer:
[tex](x^4y^5)(x^2y^4)[/tex]
Step-by-step explanation:
Keep these things in mind:
[tex]x^3\times x^3=x^{3+3}=x^6\\\\(x^3)^3=x^{3\times3}=x^9[/tex]
Using those, simplify the left side of this equation:
[tex](x^2y^3)^3\\x^6y^9[/tex]
Now we know what the exponents need to become, so we can find the difference between those and what we have on the right:
[tex]6-4=2\\9-5=4[/tex]
We need to add a 2 to the x, and add a 4 to the y.
[tex](x^4y^5)(x^2y^4)[/tex]
questions
124 - 444 = ...
345 - (-7) × (-6) = ...
Answer:
-320; 303
Step-by-step explanation:
Well... you could really just use a calculator to do this, I mean?
124 - 444 = -320
345 - (-7)*(-6) = 345 - 42 = 303
Answer:
1) 320
2) 303
Step-by-step explanation:
1) simple Subtraction
2) first multiply -7 & -6 = 42
then 345-42 = 303
Pls due tmr pls pls fast I need it like rn
Answer:
Step-by-step explanation:
50 of 100
= 50%
120 of 1
= 1.2%
there is a proportional relationship between x and y. complete the table with the missing values
Answer:
I think you forgot to attach the table
An amusement park has two themed resorts, Stargazer Suites and Retro Retreat. The graph and table below display the cost of the stay, y, for different numbers of nights, x, for the two different resorts.
Which statement correctly compares the nightly rates at Stargazer Suites and Retro Retreat?
The nightly rate at Stargazer Suites is $15 more than the nightly rate at Retro Retreat.
The nightly rate at Stargazer Suites is $25 more than the nightly rate at Retro Retreat.
The nightly rate at Retro Retreat is $30 more than the nightly rate at Stargazer Suites.
The nightly rate at Retro Retreat is $80 more than the nightly rate at Stargazer Suites.
The nightly rate at each resort is the same.
Answer:
to confusing
Step-by-step explanation:
Answer:
The nightly rate at Stargazer Suites is $25 more than the nightly rate at Retro Retreat.
Step-by-step explanation:
if r and s represent the solutions of the equation below and r>s, what is the value of the difference r-s?
(3x+14)x=5
Answer:
16/3
Step-by-step explanation:
(3x + 14)x = 5
3x² + 14x = 5
3x² + 14x - 5 = 0
3x² + 15x - x - 5 = 0
3x(x + 5) - 1(x + 5) = 0
(3x - 1)(x + 5) = 0
x = 1/3 & -5
Here,
r = 1/3
s = -5
r - s
1/3 - (-5)
1/3 + 5
1 + 15/3
16/3
the value of the difference r-s is [tex]\bold{\frac{16}{3}}[/tex]
Answer:
Solution given:
(3x+14)x=5
opening bracket
3x²+14x=5
3x²+14x-5=0
Doing middle term factorisation
3x²+(15-1)x-5=0
3x²+15x-x-5=0
3x(x+5)-1(x+5)=0
(3x-1)(x+5)=0
either
x=-5
or
3x-1=0
3x=1
x=⅓
According to question value of x is r>s
so
⅓>-5
so
r=⅓
and
s=-5
Now
r-s=⅓-(-5)=[tex]\frac{1+5*3}{3}=\frac{16}{3}[/tex]
80 as the product of it prime factors in ascending order
Answer:
Factors of 80: 1, 2, 4, 8, 10, 20, 40, and 80.
Prime Factorization of 80: 80 = 24 × 5.
Step-by-step explanation:
Answer:
This is true
Step-by-step explanation:
This is true because of the communitive property that makes the numbers you multiply the same product in different orders
How many weeks will Sanjay need to ride his bike to work in order to ride 150 kilometers?
Answer:
This is because he rides 37.5 k/m every week. Multiply that by four and you get 150
Answer:
Sanjay will need to ride his bike to work for 4 weeks in order to ride 150 kilometers.
what is the slope of the line that goes through 11,2 and 14,16
Step-by-step explanation:
m = y2-y1/x2-x1
m = 16 - 2/ 14 - 11
m = 14/3
m = 14 / 3
Hope it helps.
Evaluate -(2-6)(23).
O A. -8
B.
1/8
C. 8
O D.
- 1 / 8
Answer:
92
Step-by-step explanation:
- ( 2 - 6 )
= - ( - 4 )
= 4
- ( 2 - 6 ) ( 23 )
= 4 x 23
= 92
The evaluation of - (2- 6) ( 23) is 92
In mathematics, evaluation is a systematic method used in solving expressions. From the given information, we need to first solve the expressions in the brackets before multiplying them together.
From the given information:
= - ( 2 - 6) (23)
= - ( -4) (23)
= 4 × 23
= 92
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Hey guys, i need help on this one, thanks in advance.
Find the slope of the equation:
x - 5 = 3 ( y + 4 ) -2y + 1
if you could add step's please do.
Answer:
slope = 1
Step-by-step explanation:
1) expand those brackets on the left side my multiplying
x - 5 = 3y + 12 - 2y + 1
2) simplify by collecting like terms
x - 5 = y + 13
3) bring -5 to the right side by adding 5
x = y + 18
4) let's rearrange this equation in the form y = mx + c where m is the gradient (slope) and c is the y intercept. by subtracting 18 on both sides
y = (1)x - 18 (there is a 1 in front of the x, but we don't write it like that. m is 1)
y = x - 18
the slope is the gradient, which is 1
!!!!!!!!!!!!!!determine which of these are perpendicular parallel or none
Answer:
Parallel: a and c
Perpendicular: a and b, c and b
Step-by-step explanation:
Basically you would want to isolate for y.
Line a:
4y - 12x = 20
4y = 12x + 20
y = 12x/4 + 20/4
y = 3x + 5
Line b:
3y = -x+2
y = -x/3 + 2/3
Line c:
y=3x - 1
Now look at each line and compare their slopes.
-Lines a and c have same slope., thus they are parallel.
-lines a and b are perpendicular because the slopes are negative reciprocals each other
-lines b and c are also perpendicular
i need help... I cant figure This one out!! Lol someone help!
Answer:
x= 48
Step-by-step explanation:
x+90+42=180
x= 48
please mark brainliest
If you subtract 17 from my number and multiply the difference by -2, the result is -10." What is the number?
Answer:
22
Step-by-step explanation:
-10/-2 is 5
5+17 is 22
Can you Explain your thinking.
Answer:
Record yourself explaining your thoughts and listen to the recording. Continue re-recording what you say and listening to your recording until it sounds they way you want it to.