The equations which have exactly one solution are:
Choice A: [tex]-78x+52=-52x-78[/tex]
Choice C: [tex]58x+52=78x-78[/tex]
Choice D: [tex]58x+52=-78x-78[/tex]
Explanation:
Choice A: [tex]-78x+52=-52x-78[/tex]
Adding both sides by 52x, we have,
[tex]-26x+52=-78[/tex]
Subtracting both sides by 52,
[tex]-26x=-130[/tex]
Dividing both sides by -26,
[tex]x=5[/tex]
Hence, the equation [tex]-78x+52=-52x-78[/tex] has exactly one solution.
Thus, Choice A is the correct answer.
Choice B: [tex]52 x+52=52 x-78[/tex]
Subtracting both sides by 52x,
[tex]52=-78[/tex]
Since, both sides are not equal.
It has no solution.
Thus, Option B is not the correct answer.
Choice C: [tex]58x+52=78x-78[/tex]
Subtracting both sides by 78x,
[tex]-20x+52=-78[/tex]
Subtracting both sides by 52,
[tex]-20 x=-130[/tex]
Dividing both sides by -20,
[tex]x=6.5[/tex]
Hence, the equation [tex]58x+52=78x-78[/tex] has exactly one solution.
Thus, Choice C is the correct answer.
Option D: [tex]58x+52=-78x-78[/tex]
Adding both sides by 78x,
[tex]136x+52=-78[/tex]
Subtracting both sides by 52,
[tex]136x=-130[/tex]
Dividing both sides by 136,
[tex]x=-\frac{65}{68}\\x=-0.956[/tex]
Hence, the equation [tex]58x+52=-78x-78[/tex] has exactly one solution.
Thus, Choice D is the correct answer.
Answer
a
Step-by-step explanation:
it must =180
3x - 1 + 9x - 7 + 19 = 180 what does x equal
Answer: x≈ 14 . 08
Step-by-step explanation:
Given :
3x - 1 + 9x - 7 + 19 = 180
The first thing is to collect the like term , then we have
3x + 9x - 1 - 7 + 19 = 180
12x + 11 = 180
subtract 11 from both sides
12x = 180 - 11
12x =169
divide through by 12
x = 169/12
x = 14.083333333333
x≈ 14 . 08
what is the square of half of a number is 32?
Answer:
16
Step-by-step explanation:
BC is parallel to DE. What is the length of BC? 7 8 9 6
Step-by-step explanation:
The length of BC 7 8 9 6 would probaly wouldnt be parallel but most likely be perpendicular if not intersecting
Suppose you bought supplies for a party. Three rolls of streamers and fifteen party hats cost $30. Later, you bought two rolls of streamers and four party hats for $11. Write and solve a system of equations to determine the cost of streamers and party hats, find their costs.
Final answer:
To determine the cost of streamers and party hats, a system of linear equations is created and solved. The streamers cost $2.50 each, and the party hats cost $1.50 each after solving the system by the elimination method.
Explanation:
To find the cost of streamers and party hats, we need to set up a system of linear equations based on the information provided. Let's denote the price of one roll of streamers as s and the price of one party hat as h.
From the first purchase:
3s + 15h = $30
From the second purchase:
2s + 4h = $11
Now, we'll solve the system using substitution or elimination method. For simplicity, we'll use the elimination method.
First, let's multiply the second equation by 3.75 to match the number of hats in the first equation:
7.5s + 15h = $41.25
Subtract the first equation from this new equation:
7.5s + 15h - (3s + 15h) = $41.25 - $30
4.5s = $11.25
s = $2.50
With the cost of a streamer found, substitute s = $2.50 into the second original equation:
2($2.50) + 4h = $11
$5 + 4h = $11
4h = $6
h = $1.50
Therefore, the cost of one roll of streamers is $2.50 and the cost of one party hat is $1.50.
Final answer:To determine the cost of streamers and party hats, a system of linear equations is created and solved. The streamers cost $2.50 each, and the party hats cost $1.50 each after solving the system by the elimination method.Explanation:To find the cost of streamers and party hats, we need to set up a system of linear equations based on the information provided. Let's denote the price of one roll of streamers as s and the price of one party hat as h.From the first purchase:3s + 15h = $30From the second purchase: 2s + 4h = $11Now, we'll solve the system using substitution or elimination method. For simplicity, we'll use the elimination method.First, let's multiply the second equation by 3.75 to match the number of hats in the first equation:7.5s + 15h = $41.25Subtract the first equation from this new equation:7.5s + 15h - (3s + 15h) = $41.25 - $304.5s = $11.25s = $2.50With the cost of a streamer found, substitute s = $2.50 into the second original equation:2($2.50) + 4h = $11$5 + 4h = $114h = $6 h = $1.50Therefore, the cost of one roll of streamers is $2.50 and the cost of one party hat is $1.
the three points (3, -5) , (-a+2,3) and (2a+3, 2) lie on the same line. what is a?
Answer:
a = -7/23.
Step-by-step explanation:
For them to lie on the same line the slope of the line joining the first 2 points must equal the slope of the line joining the second and third points.
so (3 - -5) / (-a+2 - 3) = (2 - 3) /[(2a + 3) - (-a + 2)]
8 / (-a - 1) = -1 / (3a + 1) Cross multiply:
-1(-a - 1) = 8(3a + 1)
a + 1 = 24a + 8
-7 = 23a
a = -7/23.
To find the value of a, we can set the slopes between pairs of points equal to each other and solve for a. The value of a is 14/13.
Explanation:To determine the value of a such that the points (3, -5), (-a+2,3), and (2a+3, 2) lie on the same line, we can use the slope formula. The slope between two points (x1, y1) and (x2, y2) is given by the formula: m = (y2 - y1) / (x2 - x1). We'll calculate the slopes for the two pairs of points and set them equal to each other to find a.
Let's start by finding the slope between the first two points: (-a+2, 3) and (3, -5).
The slope is: m1 = (3 - (-5)) / (-a+2 - 3), which simplifies to m1 = 8 / (-a-1).
Next, let's find the slope between the second and third points: (2a+3, 2) and (3, -5).
The slope is: m2 = (2 - (-5)) / (2a+3 - 3), which simplifies to m2 = 7 / (2a).
Setting the two slopes equal to each other, we have: m1 = m2. Plugging in the expressions for m1 and m2, we get: 8 / (-a-1) = 7 / (2a). To solve for a, we'll cross-multiply and simplify the equation.
After simplifying, we find that a = 14/13.
Learn more about linear equations here:https://brainly.com/question/18751934
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Your new place needs a 12 ft by 18 ft rug. You notice that these sides are 50% longer than the rug from your old place. What were the dimensions of the old rug
Answer:
The dimensions of the old rug are 8 ft by 12 ft
Step-by-step explanation:
Let
x ----> the length of the old rug
y ----> the width of the old rug
we know that
[tex]100\%+50\%=150\%=150\100=1.5[/tex]
so
The dimensions of the old rug multiplied by the factor 1.5 must be equal to the dimensions of the new rug
so
[tex]1.5x=12\\x=8\ ft[/tex]
[tex]1.5y=18\\y=12\ ft[/tex]
therefore
The dimensions of the old rug are 8 ft by 12 ft
What is the slope of line a?
3/4
-4/3
-3/4
4/3
Answer:
The correct slope is 3/4
Step-by-step explanation:
If we take (0,1) and (4,4) as our points, we find (4-1)/(4-0)=3/4
Hope this helped!
If a cube has the area of 144 m^2 on each face, then what would the surface area be?
Answer:
[tex]\text{Surface area of cube}=864\text{ m}^2[/tex]
Step-by-step explanation:
We have been given that a cube has the area of 144 m^2 on each face.
We know that a cube has 6 faces, so total surface area of given cube would be 6 times area of its one face.
[tex]\text{Surface area of cube}=6\times 144\text{ m}^2[/tex]
[tex]\text{Surface area of cube}=864\text{ m}^2[/tex]
Therefore, the total surface area of the cube would be 864 square meters.
Answer:
the answer will be 864 m^2
Step-by-step explanation:
6*144 m^2 = 864 m^2
To simplify the express 1/2 (60+8)Martha used which property in step1
Answer:
34
Step-by-step explanation:
BODMAS (Bracket, Division, Multiplication, Addition, Subtraction )rule
First we solve brackets :
60+8=68
1/2(68)= 34
Find the surface area of the following triangular prism.
Answer: 144 ft squared
Step-by-step explanation:
Let's find the two bases first. They are triangles with a base of 6 and a height of 8. The formula for the area of a triangle is b * h * 1/2 = 6 * 8 * 1/2 = 24. There are two so you would do 24 * 2 which is 48.
Then let's find the area of the other three faces, all of which have a length of 4. One has a width of 8 so you would do 4 * 8 which is 32. Another has a width of 6 so you would do 4 * 6 which is 24. The last one has a width of 10 so you would do 4 * 10 which is 40.
Add up the areas of the two bases and three faces together:
48 + 32 + 24 + 40 = 144 ft squared
Hope this helped!
Hello ! Do you know the ways of arranging the letters in the word TOY?
Answer:201525
Step-by-step explanation:
In permutations, the order of items matters. The word 'TOY' can be arranged in 6 different ways, calculated using the formula: n!/(n-r)!.
Explanation:The student is asking a mathematical question related to permutations. Permutations refer to the arrangements of items where the order is important. In this instance, the student is interested in arranging the letters in the word 'TOY'. To calculate the number of ways to arrange these letters, we use the formula: n!/(n-r)!. Here, 'n' is the total number of items and 'r' is the number of items to choose and arrange.
Since 'TOY' has three distinct letters, then 'n' would be 3 and 'r' would also be 3. Applied to the formula, this becomes 3!/(3-3)!. Once you calculate this, you get 6. Therefore, there are 6 possible arrangements of the word 'TOY'.
Learn more about Permutations here:
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Use long division to write the fraction 2/9 as a decimal
Answer:
.2 repeating
The drawing will help
If f(x) = 2x^2 + 5 and g(x) = 6 + f(x) , what is the value of f(4) + g(3) ?
Answer: 66
Step-by-step explanation:see attachment.
If this helps you please rate brainest
Answer:
66
Step-by-step explanation:
at the movies theater, the clayton family bought 4 fountain drinks and 3 bags of popcorn and paid 22.50. The Hanks family bought 5 fountain drinks and 2 bags of popcorn and paid 23.75. How much is an fountain drink
Answer:
Therefore the price of an foundation drink is $ 3.20(approx).
Step-by-step explanation:
Let the price of one fountain drink be x and one beg of popcorn be y.
The Clayton family bought 4 fountain drinks and 3 begs of popcorn and paid $22.50. The Hanks family bought 5 fountain drinks and 2 begs of popcorn and paid $23.75.
According to the problem,
4x+3y=22.50..............(1)
5x+2y=23.75..............(2)
Equation (1)×5 - Equation (2)×4
20x+15y-(20x+8y)=112.5-91
⇔20x + 15y -20 x-8y=21.5
⇔7y=21.5
⇔y = 3.07
putting the value of y in equation (1)
4x+3×3.07 =22.50
⇔4x=22.50 -9.21
⇔x=3.20
Therefore the price of an foundation drink is $ 3.20(approx).
What is the answer to this?
(2i-6)(3i-9)
Remember that i² = -1. Using FOIL...
(2i-6)(3i-9) = 6i²-36i+54
Now simplify by subbing in -1 for i².
6(-1)-36i+54 = 48-36i
answer: 48-36i
I DO NOT KNOW HOW TO DO THIS. PLEASE PROVIDE AN EXPLANATION!
Simplify
Answer:
[tex]x^{4} -3x+2x^{3} y[/tex]
Step-by-step explanation:
use photo math and it will help with any math problem
do exponents first!
2x^5 = 32x
-6x^2 = -36x
4x^4y= 256xy
32x-36x+256xy/2x
Compare like terms, 32x-36x = -4x^2
-4x^2+256xy/2x
do, -4x^2=-16
-16+256xy/2x
Thats all, hope this is helpful!!!!!!!(:
3*4³ Simplify answer 30 points
Answer:
the answer is 192
Step-by-step explanation:
because 4^3 is 64
and if you multiply it by 3 it will give you 192
your welcome have a nice day!
Answer: 192
Step-by-step explanation:
3*4³
Since there is an exponent we have to do that first
4³
4*4*4=64
Plug 64 in 4³'s place
3*64
=192
How do you solve the problem 4 2/3×13 using common core math
A football field is 120 yards long by 53 yards wide. What is the total area
Answer:
6360
Step-by-step explanation:
the steps is just 120 times 53 which equals 6360. area= length multiplied by width
The area of a football field that is 120 yards long and 53 yards wide is 98,304,000 square inches.
To calculate the total area of a football field that is 120 yards long and 53 yards wide, you can use the formula for the area of a rectangle, which is length× width.
Step 1: Identify the dimensions of the field. The football field is 120 yards long and 53 yards wide
Step 2: Convert the dimensions into a consistent unit of measure, such as feet. Since there are 3 feet in a yard, multiply each dimension by 3.
Length in feet: 120 yards× 3 feet/yard = 360 feet
Width in feet: 53 yards × 3 feet/yard = 159 feet
Step 3: Calculate the area in feet. Area = Length × Width.
Area = 360 feet × 159 feet = 57,240 square feet
Step 4: To get the area in square inches, recognize that there are 12 inches in a foot, so the area in square inch\
es is:
Area in square inches = 57,240 ft²× (12 inches/foot)² = 98,304,000 square inches.
This calculation shows that the total area of the football field is approximately 98,304,000 square inches.
Help!! Marking branniest
Basically, we are trying to find the equation that goes through the two points shown in the table. The points are: (5,30) and (10,55). The equation of a line is y=my+b where m is the slope and b is the y intercept. To find slope look for the change in y over the change in x.
Slope = (55-30)/(10-5)=5
We can stop here because the only answer choice with a slope of five is choice A.
Answer: A
Timed need answer ASAP
Answer:
6
4 squared= 16
16÷8=2
2×3=6
Answer: the answer is 6
Step-by-step explanation:
Solve 9/4x-5/6=-13/12x
Answer:
4
Step-by-step explanation:
Cuzzzzz I know this stuff realy well
To solve this, you need to isolate/get x by itself in the equation:
[tex]\frac{9}{4}x-\frac{5}{6}=-\frac{13}{12} x[/tex] Subtract 9/4x on both sides
[tex]-\frac{5}{6} =-\frac{13}{12} x-\frac{9}{4} x[/tex] To combine fractions, the denominator has to be the same. They both have a least common denominator (LCD) of 12, so multiply -9/4x by 3/3 to make the denominator 12
[tex]-\frac{5}{6} =-\frac{13}{12}x -(\frac{3}{3})\frac{9}{4}x[/tex]
[tex]-\frac{5}{6} =-\frac{13}{12}x-\frac{27}{12} x[/tex]
[tex]-\frac{5}{6} =-\frac{40}{12} x[/tex] Multiply the reciprocal of -40/12 to get x by itself, which is -12/40 [basically flipping the fraction or switching the numerator and the denominator]
[tex](-\frac{12}{40})-\frac{5}{6} =(-\frac{12}{40})-\frac{40}{12} x[/tex] [two negative signs cancel each other out and become positive]
[tex]\frac{60}{240} =x[/tex] Simplify the fraction
[tex]\frac{1}{4} =x[/tex]
Help me find out this prom or
Please I will do anything by btntntnthtjtbtjtjtitjtbt yjtntit titbybtititjybt
Answer:
80 percent
Step-by-step explanation:
Answer:
80 percent
Step-by-step explanation:
Jimmy dean made 15 sausages in 3 hours. At this same rate , how many sausages did he make in 8 hours
Answer:
40
Step-by-step explanation:
15/3=5
5*8=40
Jimmy Dean would make 40 sausages in 8 hours, based on a calculation using his rate of sausage making determined from the 15 sausages he made in 3 hours.
Explanation:If Jimmy Dean made 15 sausages in 3 hours, we can calculate the rate at which he makes sausages and then use this rate to find out how many he would make in 8 hours. First, find the sausage-making rate by dividing the total sausages made by the total hours worked:
Rate = Total Sausages / Total Hours = 15 sausages / 3 hours = 5 sausages per hour
Next, we multiply this rate by the number of hours we are interested in, which is 8 hours:
Sausages in 8 hours = Rate * 8 hours = 5 sausages/hour * 8 hours = 40 sausages
Therefore, at the same rate, Jimmy Dean would make 40 sausages in 8 hours.
The radius of a circle is 15. Using π, which equation expresses the ratio of the circumference to the diameter of a circle?
A: C=15πr
B: C15=π
C: C=r30π
D: C30=π
Answer:
The equation which expresses the ratio of the circumference to the diameter of a circle is [tex]\frac{C}{30}=\pi[/tex] ⇒ D
Step-by-step explanation:
π is the ratio between the circumference of the circle and the length of its diameter
[tex]\frac{C}{d}=\pi[/tex] , where
C is the circumference of the circled is the diameter of the circle∵ The circumference of the circle is C
∵ The radius of the circle is 15 units
∴ r = 15 units
- Find the diameter of the circle
∵ The diameter of the circle d = 2 r
∴ d = 2(15) = 30 units
∴ The diameter of the circle is 30 units
∵ [tex]\frac{C}{d}=\pi[/tex]
∵ d = 30 units
∴ [tex]\frac{C}{30}=\pi[/tex]
The equation which expresses the ratio of the circumference to the diameter of a circle is [tex]\frac{C}{30}=\pi[/tex]
The monthly revenue, f(x) for the Sweet Treats Ice Cream truck
can be modeled by the function f(x) = 2x^2+ 16x – 20, where x is the number
of months the truck has been in business.
Which statement is true for the situation? ALGEBRA NATION
Answer:
The vertex is (-4, -52), and it represents the minimum for the function.
Step-by-step explanation:
(05.01 MC)
Which statement best describes the area of Triangle ABC shown below?
A triangle ABC is shown on a grid. The vertex A is on ordered pair 4 and 5, vertex B is on ordered pair 5 and 2, and the vertex C is on ordered pair 3 and 2.
It is one-half the area of a rectangle with sides 2 units × 3 units.
It is twice the area of a rectangle with sides 2 units × 3 units.
It is one-half the area of a square of side length 3 units.
It is twice the area of a square of side length 3 units.
Answer:
It is one-half the area of a rectangle with sides 2 units × 3 units.
Step-by-step explanation:
we have the coordinates of triangle ABC
A(4,5),B(5,2),C(3,2)
Plot the coordinates of triangle to better understand the problem
see the attached figure
step 1
Find the area of triangle ABC
The triangle ABC is an isosceles triangle `(AB=AC)
The area of triangle ABC is
[tex]A=\frac{1}{2}(BC)(AM)[/tex]
we have
[tex]BC=5-3=2\ units[/tex] ---> difference of the x-coordinates
[tex]AM=5-2=3\ units[/tex] ---> difference of the y-coordinates
substitute
[tex]A=\frac{1}{2}(2)(3)=3\ units^2[/tex]
step 2
Find one-half the area of a rectangle with sides 2 units × 3 units
[tex]A=\frac{1}{2} (2)(3)=3\ units^2[/tex]
therefore
The area of triangle ABC is one-half the area of a rectangle with sides 2 units × 3 units
Answer:
It is one-half the area of a rectangle with sides 2 units × 3 units.
Step-by-step explanation:
Is the slope of 5,0 and 8,4 positive,negative, zero or undefined?
Parallelogram ABCD has coordinates A(-1,10) B(2, -1) C(5,4) and D(-4,5). Find the coordinates of where diagonals AC and BD intersect at. Enter your answers as numbers.
The coordinates of where diagonals AC and BD intersect at O(2,7).
Step-by-step explanation:
We are given coordinates as A(-1,10) and C(5,4).And we know that the diagonals of parallelogram always bisect each other.
Let us consider O is the intersection point among the diagonals AC and BD. So, the point O bisects the line AC into two equal parts, and also it is the mid-point of AC.
We can find point O using the midpoint formula as,
O (x,y) = ([tex]\frac{(x1+x2)}{2}[/tex] , [tex]\frac{(y1+y2)}{2}[/tex])
= ([tex]\frac{(-1+5)}{2}[/tex] , [tex]\frac{(10+4)}{2}[/tex])
= ([tex]\frac{4}{2}[/tex], [tex]\frac{14}{2}[/tex])
= (2,7)
So Diagonals AC and BD intersects at the point O (2,7).
Jason and Jeremy work together at a juggling-ball factory. Jason lives 25 miles away from the factory and drives at 60 miles per hour. Jeremy lives 35 miles away from the factory and drives at 70 miles per hour. If they leave their houses at the same time, then
(a) who arrives at the factory first ?
(b) how long is it until the other person arrives?
Jason arrives at the factory first
It takes 5 minutes until the other person arrives
Solution:
The time taken is given by formula:
[tex]Time\ taken = \frac{distance}{speed}[/tex]
Jason lives 25 miles away from the factory and drives at 60 miles per hour
Therefore, time taken by Jason is:
[tex]Time\ taken = \frac{25}{60}\ hour[/tex]
Convert to minutes
1 hour = 60 minutes
Therefore,
[tex]Time\ taken = \frac{25}{60} \times 60\ minutes = 25\ minutes[/tex]
Jeremy lives 35 miles away from the factory and drives at 70 miles per hour
Therefore time taken by Jeremy is:
[tex]Time\ taken = \frac{35}{70}\ hour\\\\Time\ taken = \frac{35}{70} \times 60\ minutes\\\\Time\ taken = 30\ minutes[/tex]
They leave their houses at the same time
25 minutes < 30 minutes
Thus Jason arrives first
Jason arrives to the factory in 25 minutes
Jeremy arrives to the factory in 30 minutes
⇒ 30 - 25 = 5 minutes
Jeremy arrives after Jason by 5 minutes
It takes 5 minutes until the other person arrives