Answer:
r = 7
Step-by-step explanation:
Use the distributive property by multipling the -8 to the 2r and the -8, do the same thing on the other side with the -3.
Afterwards, combine like terms by adding 64 and 6.
Next, add 3r to the left side, I usually choose the number with the variable (the letter) that looks like it will be easier to subtract. This leaves only 21 on the right side.
Next subtract 70 from both sides
Divide -13 by both sides
You should get the answer of r=7
Least common multiple for 8,12,and24
Answer:
Its 24
Step-by-step explanation:
Question 10 of 11 Step 1 of 1
Correct
Thcorrect
One group (A) contains 390 people. Three fifths of the people in group A will be selected to win $100 fuel cards. There is another group (B) in a nearby town that will
receive the same number of fuel cards, but there are 553 people in that group. What will be the ratio of nonwinners in group Ato nonwinners in group B after the
selections are made? Express your ratio as a fraction or with a colon.
Answer
keypad
Restore Your Guth
2019 Hawkes Learning
Final answer:
To find the ratio of nonwinners in group A to nonwinners in group B, subtract the number of winners from the total number of people in each group. The ratio of nonwinners in group A to nonwinners in group B is therefore 156:319.
Explanation:
To find the ratio of nonwinners in group A to nonwinners in group B, we need to determine the number of winners in each group and subtract that from the total number of people in each group to find the nonwinners.
In group A, three-fifths of the 390 people will win fuel cards, which is equal to (3/5) * 390 = 234 people winning cards. So, the number of nonwinners in group A is 390 - 234 = 156.
In group B, the same number of fuel cards will be given out, but there are 553 people in that group. So, the number of nonwinners in group B is 553 - 234 = 319.
The ratio of nonwinners in group A to nonwinners in group B is therefore 156:319.
Write an equation of the line passing through each of the following pairs of points. a (−10, 4), (2, −5)
Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 10, 4) and (x₂, y₂ ) = (2, - 5)
m = [tex]\frac{-5-4}{2+10}[/tex] = [tex]\frac{-9}{12}[/tex] = - [tex]\frac{3}{4}[/tex], thus
y = - [tex]\frac{3}{4}[/tex] x + c ← is the partial equation of the line
To find c substitute either of the 2 given points into the partial equation
Using (2, - 5), then
- 5 = - [tex]\frac{3}{2}[/tex] + c ⇒ c = - 5 + [tex]\frac{3}{2}[/tex] = - [tex]\frac{7}{2}[/tex]
y = - [tex]\frac{3}{4}[/tex] x - [tex]\frac{7}{2}[/tex] ← equation of line
Compare the integers -13 and 15
A set of bivariate data was used to create a least squares regression line. Which of the following is minimized by the line
A) the sum of the residuals
B) the sum of the squared residuals
C) the sum of the absolute value of the residuals
D) the influence of outliers
E) the slope
Answer:
B) The sum of the squared residuals
Step-by-step explanation:
Least Square Regression Line is drawn through a bivariate data(Data in two variables) plotted on a graph to explain the relation between the explanatory variable(x) and the response variable(y).
Not all the points will lie on the Least Square Regression Line in all cases. Some points will be above line and some points will be below the line. The vertical distance between the points and the line is known as residual. Since, some points are above the line and some are below, the sum of residuals is always zero for a Least Square Regression Line.
Since, we want to minimize the overall error(residual) so that our line is as close to the points as possible, considering the sum of residuals wont be helpful as it will always be zero. So we square the residuals first and them sum them. This always gives a positive value. The Least Square Regression Line minimizes this sum of residuals and the result is a line of Best Fit for the bivariate data.
Therefore, option B gives the correct answer.
The only correct option that is minimized by the least squares regression line is;
Option B; the sum of the squared residuals.
We want to find the correct option that minimizes the line. Let's look at the options ;
Option A; This statement is not correct because If you do a summation of the residuals, you would get a value of 0.
Option B; Since error needs to be minimized so that the line is a close to the points as possible and as seen above that the sum of the residuals is zero. Then before we sum them, we need to first of all square the residuals which will always give a positive value. Thus, since the Least Square Regression Line minimizes the sum of residuals, then this option is correct.
Option C; This option is wrong because the sum of the absolute values of the residuals is not a method for in creation of least squares regression line
Option D; This option is wrong because the influence of outliers has nothing to do with the topic in question.
Option E; This option is wrong too because slope has nothing to do with the topic in question.
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6.
Tickets to a basketball game cost $1.50
o a basketball game cost $1.50 for students and $3.25 for adults. The
school made $752.25 and sold 358 tickets. How many student and how many
adult tickets were sold?
Answer: Adult tickets = 123
Student tickets = 235
Step-by-step explanation:
Let x represent the number of adult tickets sold and
let y represent the number of student tickets sold
Then create two equations: Quantity & Cost
Cost: 3.25x + 1.50y = 752.25
Qty: x + y = 358
I am going to solve the system using the substitution method.
You can also solve using the elimination method.
Since x + y = 358
then y = 358 - x
Substitute y in the Cost equation with 358 - x and solve for x
3.25x + 1.50(358 - x) = 752.25
3.25x + 537 - 1.50x = 752.25
1.75x + 537 = 752.25
1.75x = 215.25
x = 123
Now substitute x with 123 into the Quantity equation to solve for y
x + y = 358
123 + y = 358
y = 235
Saleem says 45 × 32 is the same as (45 × 3) + (45 × 2). Explain Saleem’s error using words, numbers, and/or pictures.
Answer:
[tex]45\times 32 \neq (45\times 3) + (45\times 2)[/tex]
Step-by-step explanation:
First we will evaluate the value of the expressions.
[tex]45\times 32 = 1440[/tex]
[tex](45\times 3) + (45\times 2) = 225[/tex]
Hence, Saleem made an error in the evaluation of product of 45 and 32.
Saleem did a mistake in placing the values that is in 32, 3 is at ten's place so he should have multiplied 45 by 30 instead of 3.
The product can be evaluated in a correct manner as:
[tex](45\times 30) + (45\times 2) = 1350 + 90 = 1440[/tex]
i don’t understand how to find this. can anyone break it down for me .
Answer:
See below.
Step-by-step explanation:
There is an infinite number of values of x that make each answer true. The problem is asking "for which value" with value in the singular, so I thought it was asking to choose one answer from several, and only one was correct.
1a.
Any number between 8 and 9 is correct.
Examples: 8.1, 8.01, 8.2, 8.3, 8.4, 8.9, 8.95, etc.
As I wrote above, there is an infinite number of correct answers.
1b.
Examples: 8.91, 8.92, 8.93, 8.99, 8.905, 8.97, etc.
Answer:
Assuming that inequalities are a valid answer for this question:
1a. 8 < x < 9
1b. 8.9 < x < 9.1
Step-by-step explanation:
Really, there's no exact answer. For example, on 1a, it could be 8.1, 8.11, 8.2, 8.99999, etc. Inequalities are used to denote the fact that the x value can be anywhere between two values. In 1a, x is between 8 and 9, and in 2a, x is between 8.9 and 9.1.
what is the point slope form of a line with slope 3 that contains the point (2, 1)
Answer:
y - 1 = 3(x - 2)
y - 1 = 3x - 6
y = 3x - 5
Answer:
The point slope form of the line is y-1=3(x-2).
Step-by-step explanation:
If a line passes through a points [tex](x_1,y_1)[/tex] with slope m, then the point slope form of the line is
[tex]y-y_1=m(x-x_1)[/tex] .... (1)
where, m is slope.
It is given that the slope of a line is 3 and it passes through the point (2,1).
Substitute m=3, [tex]x_1=2\text{ and } y_1=1[/tex] in equation (1), to find the point slope form of the line.
[tex]y-(1)=(3)(x-(2))[/tex]
[tex]y-1=3(x-2)[/tex]
Therefore the point slope form of the line is y-1=3(x-2).
Can someone please help me with these questions thank you
2-51
“Plot triangle ABC with vertices A(0,0), B(3,4), and C(3,0) on graph paper. Using the origin as the point of dilation, enlarge it by 2 factors (Imagine using two rubber bands). Label this new triangle A’B’C’.
A) What are the side lengths of the original triangle, ABC?
B) What are the side lengths of the enlarged, A’B’C?
C) Calculate the area and the perimeter of A’B’C.
Answer:A) What are the side lengths of the original triangle, ABC?
B) What are the side lengths of the enlarged, A’B’C?
C) Calculate the area and the perimeter of A’B’C.
The required measure of the angle x and y is 45° and 109° respectively.
A triangle with two sides and two congruent angles is called an isosceles triangle.
Here,
A)
triangle is isosceles, so the two angles will be equal, and the sum of the angles in the triangle is 90°.
2x + x + x = 180
4x = 180
x = 180 / 4
x = 45
Similarly,
(B)
Some of the remote interior angles is equal to the remote exterior angle,
71 + (180 - 142) = y
y = 71 + 38
y = 109°
Thus, the required measure of the angle x and y is 45° and 109° respectively.
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x y
3 −2
6 3
9 8
12 13
Determine whether the table represents a proportional relationship. If a proportional relationship exists, what is the constant ratio of
y
x
?
A) yes;
5
3
B) yes;
3
5
C) yes;
1
3
D) The table does not represent a proportional relationship.
Answer:
A.Step-by-step explanation:
Yes, they have a proportional relationship.
The table shows sequences, where x-values increase +3, and y-values increase +5, that is, while x increases 3 unites, y increases 5 units, this ratio between variables can be described as the slope:
[tex]m=\frac{13-(-2)}{12-3} =\frac{15}{9}=\frac{5}{3}[/tex]
This fraction or ratio is referring to what we said in words, while y increases 5 units, x increases 3 units. We observe that is a positive ration, this means that magnitudes are both increasing.
Therefore, the right answer is the first one A.
-x^2 +9x-12 in vertex form
please help !!!
Answer:
see explanation
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
To obtain this firm use the method of completing the square
Factor out - 1 from each term
y = - (x² - 9x + 12)[tex]\frac{33}{4}[/tex]
To complete the square
add/subtract (half the coefficient of the x- term )² to x² - 9x
y = - (x² + 2( - [tex]\frac{9}{2}[/tex])x + [tex]\frac{81}{4}[/tex] - [tex]\frac{81}{4}[/tex] + 12 )
= - ( (x - [tex]\frac{9}{2}[/tex])² - [tex]\frac{33}{4}[/tex] )
y = - (x - [tex]\frac{9}{2}[/tex] )² + [tex]\frac{33}{4}[/tex] ← in vertex form
Ten years ago,a father was five times as old as his son.their combined age now is 80.find the age of the son
Answer:
The son is now 20. The father is now 60
Step-by-step explanation:
The son was 10, ten years ago. Five times that was 50 years, the age of the father. Now they have both aged 10 years, and the son is 20 and the father is 60. Add them together, and it makes 80.
CAN EXPLAIN FURTHER
appreciate brainliest but it doesn't matter
Answer:
20 years old
Step-by-step explanation:
10 → Ten years ago
50 → The father was five times as old as his son.
Current Ages
20 → Son
60 → Father
[tex]20 + 60 = 80[/tex]
I am joyous to assist you anytime.
Clinton’s garden is 12.25 m long and 14 m
wide. Find the perimeter of Clinton’s garden.
Answer:
P = 52.5
Step-by-step explanation:
P = ( L + L ) + ( W + W )
P = ( 12.25 + 12.25 ) + ( 14 + 14 )
P = 24.5 + 28
P = 52.5
Hello!
because of the way Clinton's yard is measured, it must be a rectangle.
here is the equation to find the perimeter of a rectangle:
L2 + W2 = P
12.25 * 2 = 24.5
14 * 2 = 28
24.5 + 28 = 52.5
your answer is: The perimeter of Clinton's yard is 52.5 Meters
I hope this helps, and have a nice day!
given: f(x)=3 - x; g(x) = -2x find f[g(2)]
Answer:
7
Step-by-step explanation:
To calculate f(g(2)) evaluate g(2) then evaluate f(x) for this value
g(2) = - 2(2) = - 4, then
f(- 4) = 3 - (- 4) = 3 + 4 = 7
Find the value of x in each case
Answer:
x=17
Step-by-step explanation:
we know that
The sum of the internal angles of a triangle must be equal to 180 degrees
so
In the triangle ABC
m∠A+m∠B+m∠C=180°
substitute the values and solve for m∠C
4x+49°+m∠C=180°
m∠C=180°-49°-4x
m∠C=131°-4x
In the triangle EDC
m∠E+m∠D+m∠C=180°
we have
m∠E=x
m∠D=100°
m∠C=131°-4x -----> by vertical angles
substitute the values
[tex]x+100\°+(131\°-4x)=180\°\\-3x+231\°=180\°\\3x=231\°-180\°\\3x=51\°\\x=17[/tex]
The value of x for the given geometric problem is determined to be 17 by using the concept that the sum of the internal angles of a triangle is equal to 180 degrees.
Explanation:We are looking to find the value of x where two triangles are involved.
First, according to the laws of geometry, the sum of the internal angles of a triangle must be equal to 180 degrees.
So, in triangle ABC, m∠A+m∠B+m∠C=180°.
If we have m∠A = 4x and m∠B = 49°, then by substituting these values, m∠C becomes 180° - (49° + 4x) i.e 131° - 4x.
In the triangle EDC, the summation m∠E + m∠D + m∠C also equals 180°.
If m∠E=x, m∠D=100°, and m∠C=131°-4x, we can form an equation of x + 100 + 131 - 4x = 180 which simplifies to 231 - 3x = 180. Solving this equation gives x = 17.
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Write the equation of the line with the given slope and y-intercept. Undefined slope, (0,-6)
Answer:
y = -6
Step-by-step explanation:
The y intercept is when x equals 0 , and as you can see in the coordinate, the x is zero so the y is -6. Since the slope is undefined, the answer is y=-6. I know that seems confusing, but when the slope is undefined, it just means that it is a straight line.
Find the sum or difference in simplest form 1 3/7 + 10 6/7
Answer:
[tex]12\frac{2}{7}[/tex]
Step-by-step explanation:
we have
[tex]1\frac{3}{7} +10\frac{6}{7}[/tex]
step 1
Convert mixed number to an improper fraction
[tex]1\frac{3}{7}=\frac{1*7+3}{7}=\frac{10}{7}[/tex]
[tex]10\frac{6}{7}=\frac{10*7+6}{7}=\frac{76}{7}[/tex]
step 2
Substitute in the expression above and find the sum
[tex]\frac{10}{7}+\frac{76}{7}=\frac{86}{7}[/tex]
Convert to mixed number
[tex]\frac{86}{7}=\frac{84}{7}+\frac{2}{7}=12\frac{2}{7}[/tex]
Peter has been saving his loose change for several days. When he counted his quarters and dimes, he found they had a total value of $13.10. The number of quarters was 15 more than 3 times the number of dimes. How many quarters and how many dimes did Peter have?
it wont give me the answer.. i have to pay for it, and my homework is due in 3 hours...HELP?
Answer: Dimes: 11
Quarters: 48
Step-by-step explanation:
48/4= 12.00
11•0.10= 1.10
12+1.10= 13.10
what is the gcf of 25 and 14
Four hot air balloons each descend 295 feet per minute for 7 minutes. Find the total change in altitude for all 4 balloons.
The total change in altitude for all 4 balloons is
nothing feet.
Answer:
"total change in altitude for all 4 balloons is 8260 feet"
Step-by-step explanation:
295 feet per minute, so in 7 minutes:
Descend (for 7 minutes) = 295 * 7 = 2065 feet
This is for a single balloon.
So for 4 balloons, this would be:
2065 * 4 = 8260 feet in total
So, total change in altitude for all 4 balloons is 8260 feet
4y + 9 = - 4y - 7. Please explain to me how to do it.
You want to keep the variable on the left and number on right.
So, we need to get rid of 9 and -4y. Let's start with 9.
4y+9=-4y-7
Subtract nine from both sides.
4y=-4y-16
Now add 4y on both sides.
8y=-16
Finally, divide both sides by 8 to get y=-?.
8y/8=-16/8
Therefore, the answer is y=-2.
y = (x + 3)^2 -4 and identify the axis of symmetry
Answer:
Step-by-step explanation:
the line for equation : x = - 3
Oranges are on sale for $0.78 per pound. Bananas are on sale for $0.50 per pound. Debbie buys only oranges at the store this week. Is the total price she pays proportional to the pounds of oranges she purchased?
Answer: May you please have answer choices. Please forgive me if I am being rude but I am not.
Answer:
Yes, the total price is proportional to the pounds of oranges she purchased.
Step-by-step explanation:
The price of oranges is $0.78 per pound.
So, the price $0.78 corresponds to one pound, in a way, that is called direct proportionality.
This means that the price will increase or decrease in a constant ratio, depending on the amount of pounds purchased.
For example:
If she buys 1 pound of oranges she will pay $0.78. Ratio is 0.78 (0.78/1)
If she buys 2 pounds of oranges she will pay $1.56. Ratio is 0.78 (1.56/2)
If she buys 2.5 pounds of oranges she will pay $1.95. Ratio is 0.78 (1.95/2.5)
If she buys 3 pounds of oranges she will pay $2.34. Ratio is 0.78(2.34/3)
We can see that ratio is constant, then we can say that the total price she pays is proportional to the pounds of oranged purchased.
Joe practiced his trumpet 3/4 hour on Monday and 7/12 hour on Tuesday. How long did he practice altogether?
2 hours
1 1/3 hours
2 2/3 hours
5 1/3 hours
Answer: 1 1/3 hours
Step-by-step explanation:
3/4 hour = 45 minutes
7/12 hour =35 minutes
45 +35 = 80 minutes ÷ 60 minutes = 1 1/3 hours
You have $200 on a savings account and$100 in a checking account each week you add $50 to your savings account and $30 to your checking account Write an expression in simplest form that represents the total amount of money in both accounts after w weeks
Answer:
The expression is (80w+300)
Step-by-step explanation:
Let
y ----> the total amount of money in both accounts
s ----> the amount of money in saving account
c ----> the amount of money in checking account
w ----> the number of weeks
we know that
saving account
s=50w+200 -----> equation A
checking account
c=30w+100 ----> equation B
To find out the total amount of money in both accounts, sum equation A and equation B
y=s+c
substitute
y=(50w+200)+(30w+100)
y=(50w+30w)+(200+100)
y=80w+300
therefore
The expression is (80w+300)
175,000
In Scientific notation
Answer:
1.75*10 to the power of 5
Step-by-step explanation:
start by moving the decimal over until only one number is in front of the decimal. this is because in scientific notation a number can't be higher than 9.
check how many places you move the decimal over (5). 1.75000 needs to be simplified (since that's the point of scientific notation) and can be simplified to 1.75.
the answer is 1.75 multiplied by ten to the power of digits the decimal moved (5) so the answer is 1.75*10 to the power of 5
175,000 in scientific notation is 1.75 × [tex]10^5[/tex].
To express the number 175,000 in scientific notation, follow these steps:
Move the decimal point in the number to the position after the first non-zero digit. For 175,000, this is 1.75.
Count the number of places the decimal point has moved to determine the exponent of 10. In this case, the decimal point moves 5 places to the left.
Combine the number obtained in the first step with the power of 10 determined in the second step. Thus, 175,000 in scientific notation is 1.75 × [tex]10^5[/tex].
This provides a concise representation of the number.
When F(x)=-3 What is X
If BD = 7x - 10, BC = 4x – 29, and CD = 5x – 9, find each value.
[tex]\bf \underset{\leftarrow \qquad \textit{\large 7x-10}\qquad \to }{\stackrel{4x-29}{\boxed{B}\rule[0.35em]{10em}{0.25pt}} C\stackrel{5x-9}{\rule[0.35em]{17em}{0.25pt}\boxed{D}}} \\\\\\ BD=BC+CD\implies 7x-10=(4x-29)+(5x-9) \\\\\\ 7x-10=9x-38\implies 7x+28=9x\implies 28=2x \\\\\\ \cfrac{28}{2}=x\implies 14=x \\\\[-0.35em] ~\dotfill\\\\ \stackrel{BC}{4(14)-29\implies 27}~\hfill \stackrel{CD}{5(14)-9\implies 61}~\hfill \stackrel{BD}{7(14)-10\implies 88}[/tex]
13 feet in 5 steps unit rate
2.6 feet per step is the answer