The step that would not be necessary in solving 5x + 15 + 2x = 24 + 4x is D. Use the distributive property.
What is an equation?An equation is a pair of algebraic equations with the equal sign (=) in the middle and the same value.
To solve the equation 5x + 15 + 2x = 24 + 4x, we need to simplify and manipulate the equation to isolate the variable on one side.
First, we can combine like terms:
5x + 2x - 4x = 24 - 15
3x = 9
Then, we can isolate x by dividing both sides by 3:
x = 3
Therefore, the correct steps to solve this equation are:
B. Collect variable terms on one side.
C. Collect like terms.
A. Isolate the variable.
We do not need to use the distributive property in this problem.
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Find the average rate of change of the function defined by the following table.
x y
-2 -5
2 35
6 75
10 115
A careful examination of the data in the table shows that for each 4 unit increase in x, y increases by 40.
It's valid to surmise that the average rate of change is 40/4, or 10. This is the slope of the line thru the given points.
Answer:
1/10
Step-by-step explanation:
The x goes up by 4 and the y goes up by 40
= 4/40 = 1/10
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Sort the sequences to whether they are arithmetic, geometric, or neither
1) 98.3 , 94.1 , 89.9 , 85.7
2) 1 ,0 , -1 ,0
3) 1.75 , 3.5 , 7 ,14
4) -1 ,1 , -1 ,1
5) -12, -10.8, -9.6, -8.4
her answer is right but you just have to switch 4 and 5 around 4 is geometric while 5 is arithmetic
Final Answer:
Each sequence is tested for a common difference or ratio to determine if it is arithmetic or geometric. The sequences 98.3, 94.1, 89.9, 85.7 and -12, -10.8, -9.6, -8.4 are arithmetic, 1.75, 3.5, 7, 14 is geometric, and 1, 0, -1, 0 as well as -1, 1, -1, 1 are neither.
Explanation:
To determine if a sequence is arithmetic, geometric, or neither, we look for a common difference or ratio between consecutive terms.
For the sequence 98.3, 94.1, 89.9, 85.7, we subtract consecutive terms: 94.1 - 98.3 = -4.2, 89.9 - 94.1 = -4.2, 85.7 - 89.9 = -4.2. The common difference is -4.2, so this sequence is arithmetic.The sequence 1, 0, -1, 0 does not have a common difference or ratio, so it is neither arithmetic nor geometric.For 1.75, 3.5, 7, 14, the ratios are 3.5/1.75 = 2, 7/3.5 = 2, and 14/7 = 2. The common ratio is 2, so this sequence is geometric.The sequence -1, 1, -1, 1 alternates signs without a common difference or ratio, so it is neither.For the sequence -12, -10.8, -9.6, -8.4, the difference is -10.8 - (-12) = 1.2, -9.6 - (-10.8) = 1.2, -8.4 - (-9.6) = 1.2. The common difference is 1.2, making it an arithmetic sequence.Anna is selling tickets to her tennis tournament. An adult ticket costs $20 and a student ticket costs $16. Anna collects $1020 for a total of 55 tickets. How many adult and how many student tickets has Anna sold?
Anna sold 35 adult tickets and 20 student tickets.
Explanation:Let's assume that Anna sold x adult tickets and y student tickets. From the given information, we can form the following equations:
Equation 1: x + y = 55 (total number of tickets)
Equation 2: 20x + 16y = 1020 (total amount collected)
We can solve this system of equations using the substitution method or the elimination method. Let's use the elimination method. First, multiply Equation 1 by 16 so that the coefficients of y cancel out when added to Equation 2:
16x + 16y = 880 (equation obtained by multiplying Equation 1 by 16)
20x + 16y = 1020 (Equation 2)
Now subtract Equation 1 from Equation 2:
20x + 16y - (16x + 16y) = 1020 - 880
4x = 140
Divide both sides of the equation by 4:
x = 35
Substitute the value of x into Equation 1:
35 + y = 55
y = 55 - 35
y = 20
whats the bisector of an obtuse angle forms
acute angles
right angles
obtuse angles
straight angles
Answer:
A.Acute angle
Step-by-step explanation:
We are given that an obtuse angle
We have to find that which type of angle of bisector of an obtuse angle.
Bisector of an obtuse angle means it is divided into two equal parts.
Obtuse angle is that angle whose measurement is greater than 90 degrees and less than 180 degrees.
Suppose, we have an obtuse angle =100 degrees
After bisection , it divides into two equal parts
Let x and x are two equal parts of given obtuse angle
[tex]x+x=100[/tex]
[tex]2x=100[/tex]
[tex]x=\frac{100}{2}=50[/tex]
Each angle measurement=50 degrees < 90 degrees
The angle which is less than 90 degrees and greater than zero degrees is called acute angle.
Hence, the bisector of an obtuse angle forms acute angles.
Answer:A.Acute angle
What is a correct congruence statement for the triangles shown?
Suppose △AYH≅△ZRL.
What is the corresponding congruent part for each segment or angle?
ZR¯¯¯¯¯
RL¯¯¯¯¯
∠L
∠Z
ah_____ yh___ ay__
What is the area of the rectangle?
60 units²
66 units²
70 units²
74 units²
Consider the following three statements:
As children grow older, their weight increases.
As children grow older, they expand their vocabulary.
As children's weight increases, their vocabulary expands.
Does statement #3 describe a correlational relationship? A causal relationship? Explain your answer.
Actually the third
statement would only be classified as correlational relationship.
Correlational relationship means that the one occurrence can
occur at the same time with another; they could be associated but does not
really imply that one causes the other.
Answer:Actually the third statement would only be classified as correlational relationship.
Correlational relationship means that the one occurrence can occur at the same time with another; they could be associated but does not really imply that one causes the other.
Step-by-step explanation:
Sand dollars are animals that live buried in the sand of shallow coastal waters. The thin circular body of a sand dollar is usually 2 to 4 inches wide. Find the area of a sand dollar that is 3 inches wide.
Answer:
The area of a sand dollar that is 3 inches wide is [tex]7.0686 inch^2[/tex]
Step-by-step explanation:
Width of sand dollar's circular body = d = 3 inches
Radius of the sand dollar's circular body = r
[tex]r=\frac{d}{2} = \frac{3 inch}{2}=1.5 inches[/tex]
Area of circle = [tex]\pi r^2[/tex]
So, the area of a sand dollar that is 3 inches wide:
[tex]A=3.14\times (1.5 inch)^2=7.0686 inch^2[/tex]
The area of a sand dollar that is 3 inches wide is [tex]7.0686 inch^2[/tex]
Which equation describes a line with a slope of -8 and includes the point (-4, 7)?
Can you guys please help me with math? (Pt 2.)
(I've attached the picture)
Elian is placing a rectangle in the coordinate plane. He knows that the shorter side of the rectangle is half the length of the longer side. He places the longer side on the x-axis.
What coordinates should he assign to the top-left vertex of the rectangle?
Enter your answer in the boxes.
Let
x--------> the length side of the rectangle
y-------> the width side of a rectangle
we know that
[tex]y=\frac{1}{2}x[/tex] ------> equation A
[tex]x=2a\ units[/tex] ---------> given problem (see the graph)
substitute the value of x in the equation A
[tex]y=\frac{1}{2}2a=a\ units[/tex]
therefore
the answer is
the top-left vertex of the rectangle is the point [tex](0,a)[/tex]
Which should be the first step in solving the equation 1.2 w -3.8= 12.4
1. Add 3.8 to both sides of the equation.
2. Subtract 1.2 from both sides of the equation.
3. Multiply both sides of the equation by 1.2.
4. Divide both sides of the equation by 3.8.
Answer:
Option 1 - Add 3.8 to both sides of the equation.
Step-by-step explanation:
Given : Equation [tex]1.2w-3.8=12.4[/tex]
To find : Which should be the first step in solving the equation?
Solution :
Equation [tex]1.2w-3.8=12.4[/tex]
Step 1 - Adding 3.8 both side,
[tex]1.2w-3.8+3.8=12.4+3.8[/tex]
[tex]1.2w= 16.2[/tex]
Step 2 - Divide 1.2 both side,
[tex]\frac{1.2w}{1.2}=\frac{16.2}{1.2}[/tex]
[tex]w=13.5[/tex]
Therefore, The first step in solving the equation is 'Add 3.8 to both sides of the equation.'
So, Option 1 is correct.
Mateo is draining a pool at a rate of 1/8 of a gallon every 1/2 hour. If he continues to drain the pool , how much waters will be drained in 1 hour?
Manuel rode his bicycle at an average speed of 13 miles per hour for 1 hours. of d = the total distance he rode, which choice is the most reasonable value for d?
The sum of the angle measures of a polygon with n sides is 1440. find n
The number of sides of the polygon that has a sum of the angles 1440° will be 10.
What is a polygon?The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
Let 'n' be the number of sides of the polygon. Then the sum of the interior angles of the polygon is given as,
Sum of angles = (n - 2) × 180°
The sum of the angle measures of a polygon with n sides is 1440. Then the number of sides of the polygon is given as,
(n - 2) × 180° = 1440°
(n - 2) = 1440° / 180°
(n - 2) = 8
n = 8 + 2
n = 10
The number of sides of the polygon that has a sum of the angles 1440° will be 10.
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ROUND 4,719,429 TO THE NEAREST 10,000
Ms. Frazier chooses two students to come to the board from a class of 12 boys and 8 girls. What is the probability that she will select a girl student first and a boy student second?
The probability that Ms. Frazier selects a girl first and a boy second from her class is 24/95, calculated by multiplying the probability of selecting a girl (8/20) by the probability of selecting a boy thereafter (12/19).
Explanation:To calculate the probability that Ms. Frazier will select a girl student first and a boy student second from her class of 12 boys and 8 girls, we need to use the concept of conditional probability because the selection of the second student depends on the first.
The total number of students is 12 boys + 8 girls = 20 students. The probability of selecting a girl first is the number of girls divided by the total number of students, which is 8/20. Once a girl is selected, there are now 19 students left. The probability of selecting a boy next is the number of boys left (which is still 12) divided by the new total, which is 12/19. The joint probability of both events happening in succession (selecting a girl then a boy) is found by multiplying the probabilities of the two individual events.
So, the probability of selecting a girl first and a boy second is (8/20) × (12/19) = 96/380. This simplifies to 24/95 when we divide both numerator and denominator by 4.
Therefore, Ms. Frazier has a probability of 24/95 to choose a girl first and a boy student second.
The probability of selecting a girl student first and a boy student second is approximately 0.2526.
Explanation:To find the probability of selecting a girl student first and a boy student second, we need to calculate the probability of each event separately and then multiply them together.
Step 1: Probability of selecting a girl student first
Number of girls: 8Total number of students: 12 boys + 8 girls = 20Probability of selecting a girl student first = Number of girl students / Total number of students = 8/20 = 0.4Step 2: Probability of selecting a boy student second
Number of boy students: 12Total number of students after selecting a girl student: 20 - 1 = 19Probability of selecting a boy student second = Number of boy students / Total number of students after selecting a girl student = 12/19 ≈ 0.6316Step 3: Multiply the probabilities from Step 1 and Step 2:
Probability of selecting a girl student first and a boy student second = Probability of selecting a girl student first × Probability of selecting a boy student second = 0.4 × 0.6316 ≈ 0.2526joanna bought 1 1/2 pounds of apples, 3/4 pounds of strawberries, 1/2 pound of grapes, 1 3/4 pounds of oranges, and 1 1/4 pounds of pears. How many pounds of fruit Joanna bought in all?
Greg, marcia, peter, jan, bobby and cindy go to a movie and sit next to each other in 6 adjacent seats in the front row of the theater. if marcia and jan will not sit next to each other, in how many ways different arrangements can the 6 people sit?
Solve for x. x−14=38 Enter your simplified answer in the box.
Answer:
52
Step-by-step explanation:
Ann and betty shared the sum of money in the ratio 2:3, if ann received $60 less than betty, what was the total sum of money shared
Please Hurry!! Use any model you choose to solve the story problem. Macy is making a border out of strips of wall boarder placed end to end along the 12-foot wall in her room. Each strip 1/3 is foot long. How many strips of wall border will Macy need?
Macy needs 36 strips of wall border to cover a 12-foot wall, calculating by multiplying the wall's length by the reciprocal of 1 strip's length.
To solve how many strips of wall border Macy will need, we divide the total length of the wall by the length of each strip. Macy's wall is 12 feet long, and each strip is 1/3 foot long. So, we divide 12 by 1/3 or multiply 12 by the reciprocal of 1/3.
Here is the calculation step by step:
Convert 1/3 to its reciprocal by flipping the numerator and denominator, which gives us 3/1 or just 3.Multiply the length of the wall, 12 feet, by 3.The volume of a rectangular prism is calculated using the formula V = lwh, where V is the volume of the prism, l and w are the length and width of the base of the prism, respectively, and h is the height of the prism.
Rewrite the formula to find the width of the base of the prism if the volume, length of the base, and height of the prism are already known.
Answer:
[tex]w=\frac{V}{lh}[/tex]
Step-by-step explanation:
As per the statement:
The volume of a rectangular prism is calculated using the formula:
[tex]V = lwh[/tex] ....[1]
where, V is the Volume of the prism
l is the lenght
w is the width
h is the height of the prism respectively.
We have to Rewrite the formula to find the width of the base of the prism.
Divide equation [1] by [tex]lh[/tex] to both sides we have;
[tex]\frac{V}{lh} = \frac{lwh}{lh}[/tex]
Simplify:
[tex]\frac{V}{lh} = w[/tex]
or
[tex]w=\frac{V}{lh}[/tex]
Therefore, the the formula to find the width of the base of the prism,if the volume, length of the base, and height of the prism are already known is:
[tex]w=\frac{V}{lh}[/tex]
To find the width of a rectangular prism when the volume, length, and height are known, you can rearrange the formula V = lwh to solve for width, resulting in the formula w = V / (lh).
Explanation:The volume of a rectangular prism is calculated using the formula V = lwh, where V is the volume, l is the length, w is the width, and h is the height. If we know the volume (V), the length of the base (l), and the height of the prism (h), and we want to find the width (w), we can rearrange the formula to solve for width.
To do this, you divide both sides of the equation by the length and the height. As a result, the formula to find the width when the volume, length, and height are known is w = V / (lh). By dividing the volume by the product of the length and the height, you can find the width of the base of the prism.
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A figure drawn in the coordinate plane has the coordinates J(‒1,5), K(6,5), L(9,1) and M(2,1).
1) Use what you have learned in this unit to prove that the figure is either a parallelogram, rectangle, square or a rhombus.
2) Use what you have learned in this lesson to find the area and perimeter of the figure.
The graph of f(x) = 2^x + 1 is shown below. Explain how to find the average rate of change between x = 0 and x = 3.
simplify ( 1/2A + 1/2B )^2
Ingrid is making a quilt using squares that measure 5in on each side. What is the length of a diagonal of one of the quilt squares?
Answer:
8.7 Maybe.
Step-by-step explanation:
A translation of directed line segment from the origin to (0,-3) followed by a reflection around the line y=x
To translate a directed line segment from the origin to (0,-3), simply subtract 3 from the y-coordinate. To reflect a point across the line y=x, swap the x and y coordinates. The reflected point of (0,-3) would be (-3,0).
Explanation:To translate a directed line segment from the origin to (0,-3), we can simply subtract 3 from the y-coordinate. The new coordinate would be (0,-3).
To reflect a point across the line y=x, we swap the x and y coordinates. So the reflected point of (0,-3) would be (-3,0).
A1 Plumbing Service charges $35 per hour plus a $25 travel charge for a service call. Good Guys Plumbing Repair charges $40 per hour for a service call with no travel charge. How many hours must a service call be for it to be better for you to call A1 Plumbing Service?
A1 = 35x+25
Good guys = 40x
35x+25 = 40x
subtract 3x x from each side
25 = 5x
divide each side by 5
x = 25/5 = 5
so 5 hours they would be the same cost, anything over 5 hours and A1 would be better
so X>5 for A1 to be the better price
2x-1
Evaluate the algebraic expressions for the given values of the variable
Divide. (359)÷(−223) Enter your answer as a mixed number, in simplified form,
Answers
the answers is-3.245 hope this helps subscribe to my channel Elite_Raider Perez
Answer:
-3.245 I hope this helped hun! :3