Mathematics Middle School

This system has one solution.

{y=−2x+4y
{=x2+4x+13

What is the y-coordinate of the solution?

Enter your answer in the box. y =[]

Answers

Answer 1
Hello there!
I have just taken the test on this answer and I got 10...
I hope this helps!!
Answer 2

Answer:

The y-coordinate of the solution is, 10

Step-by-step explanation:

Given the system of equation:

[tex]y = -2x+4[/tex]            ....[1]

[tex]y=x^2+4x+13[/tex]         ....[2]

Equate the equation [1] and [2] we have;

[tex]-2x+4 = x^2+4x+13[/tex]

Add 2x to both sides of an equation:

[tex]4 = x^2+6x+13[/tex]

Subtract 4 from both sides we have;

[tex]0= x^2+6x+9[/tex]

or

[tex]x^2+6x+9=0[/tex]

Using perfect square:

[tex](x+a)^2 = x^2+2ax+a^2[/tex]

⇒We can write the equation as:

[tex]x^2+2 \cdot 3x+3^2=0[/tex]

then;

[tex](x+3)^2 = 0[/tex]

⇒[tex]x+3 = 0[/tex]

Subtract 3 from both sides we have;

x = -3

Substitute value of x in [1] we have;

[tex]y = -2(-3)+4[/tex]

⇒[tex]y =6+4=10[/tex]

Solution for the given system of equation = (-3, 10)

Therefore, the  y-coordinate of the solution is, 10

Related Questions

A car is traveling at a speed of 75 km/h. Identify the correct conversion factor setup required to compute the speed of the car in m/s.
A)
75km
1hr
x
1000m
1km
x
1hr
60min
x
60s
1min
B)
75km
1hr
x
1000m
1km
x
1hr
60min
x
1min
60s
C)
75km
1hr
x
1000m
75km
x
1hr
60min
x
1min
60s
D)
75km
1hr
x
1000m
75km
x
1hr
60min
x
60s
1min

Answers

i think the answer is B

Therefore, the speed of the car in m/s is [tex]\frac{75000}{3600}[/tex] m/s i.e., option (B) is correct.

What is the equation?

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Here given that,

A car is traveling at a speed of [tex]75[/tex] km/h.

As we know,

[tex]1km=1000m[/tex]

[tex]1h=60s[/tex]

So,

[tex]75[/tex] km/h=[tex]\frac{75(1000)}{3600}[/tex] m/s

[tex]=\frac{75000}{3600}\\\\[/tex]

Hence, the speed of the car in m/s is [tex]\frac{75000}{3600}[/tex] m/s i.e., option (B) is correct.

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what number when increased by 75% of itself will equal to 80?

Answers

[tex] p\%=\dfrac{p}{100}\to 75\%=\dfrac{75}{100}=0.75\\\\n-the\ number\\\\the\ equation:\\\\n+0.75n=80\\\\1.75n=80\ \ \ \ |:1.75\\\\n=\dfrac{80\cdot100}{1.75\cdot100}\\\\n=\dfrac{8000}{175}\\\\n=\dfrac{8000:25}{175:25}\\\\n=\dfrac{320}{7}\\\\n=45\dfrac{5}{7} [/tex]

Can someone please explain number 11?

Answers

here is your answer
Have a good day

Find the unknown. 531 = ( × 6) + 21

Answers

The answer would be x = 85
X=85 is your
answer.

What are the dimensions of the rectangle shown below? Remember to use the axes on the coordinate grid to help you.

answer chices are not there i need to type it in

Answers

each grid line is 2 units

A is located on X = -10, B is located on X = 2
 the distance between A and B  = 12 units

A is located on Y = 2, D is located on Y = -6
the distance between A and D = 8 units

 the dimension of the rectangle is 12 by 8




The correct answer to this question is the fact the rectangle is 12 by 8!

The formula for glue says to add 55 mL of hardener to each container of resin. How much hardener should be added to 16 containers of resin? Write your answer in liters.

Answers

Final answer:

To determine how much hardener is required for 16 containers of resin, multiply 55 mL by 16 to get 880 mL, and then convert this to liters by dividing by 1,000, resulting in 0.88 liters of hardener needed.

Explanation:

To determine how much hardener should be added to 16 containers of resin, we must multiply the amount needed for one container by the number of containers. The formula given states that 55 mL of hardener is required for each container of resin. To find the total amount for 16 containers, we perform the following multiplication:

Calculate the total milliliters needed: 55 mL/container × 16 containers = 880 mL.Convert the total milliliters to liters:
Since 1 liter is equivalent to 1,000 milliliters, divide the total milliliters by 1,000 to get the volume in liters. 880 mL ÷ 1,000 = 0.88 L.

Therefore, 0.88 liters of hardener should be added to 16 containers of resin.

Final answer:

To determine the amount of hardener needed for 16 containers of resin, multiply 55 mL by 16 to get 880 mL and then convert that to liters, resulting in 0.88 liters of hardener.

Explanation:

To find out how much hardener should be added to 16 containers of resin, where each container requires 55 mL of hardener, you need to do a simple multiplication operation. Multiply the amount of hardener needed for one container by the number of containers:

Multiply 55 mL by 16:Now, convert milliliters to liters. Since there are 1,000 milliliters in a liter:

Therefore, you should add 0.88 liters of hardener to the 16 containers of resin.

Below is a graph that represents the total profits for a third month. Write the equation of the line that represents this graph. Show your work or explain how you determined the equations.

Answers

The linear function that represents this graph is given by:

y = 300 - 0.6667x.

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

From the graph, when x = 0, y = 300, hence the y-intercept is of b = 300. The amount decays to 0 when the x-intercept is of x = 450, hence the slope is given by:

m = -300/450 = -0.6667.

Which means that the equation is:

y = 300 - 0.6667x.

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Is my answer correct or incorrect? Explain please. Thank you

Answers

yes because 3 * 2 * 4 = 24
3 sandwich choices
2 side item choices
4 beverage choices

Let's say the sandwich choices were PB&J, Ham, and Turkey
Let's say the sides were fries and mandarin oranges
Let's say the beverages were water, orange juice, milk, soda

PB&J
Ham
Turkey

                                        Fries
                                        Mandarin Oranges

Water
OJ
Milk
Soda

The combinations can be as follows:

PB&J, Fries, Water
PB&J, Fries, OJ
PB&J, Fries, Milk
PB&J, Fries, Soda
PB&J, Mandarin Oranges, Water
PB&J, Mandarin Oranges, OJ
PB&J, Mandarin Oranges, Milk
PB&J, Mandarin Oranges, Soda
Ham, Fries, Water
Ham, Fries, OJ
Ham, Fries, Milk
Ham, Fries, Soda
Ham, Mandarin Oranges, Water
Ham, Mandarin Oranges, OJ
Ham, Mandarin Oranges, Milk
Ham, Mandarin Oranges, Soda
Turkey, Fries, Water
Turkey, Fries, OJ
Turkey, Fries, Milk
Turkey, Fries, Soda
Turkey, Mandarin Oranges, Water
Turkey, Mandarin Oranges, OJ
Turkey, Mandarin Oranges, Milk
Turkey, Mandarin Oranges, Soda

So your answer is correct: There's 24 lunch combinations that can be made.

Hope that helps!

Evaluate the expression. If necessary, round to the nearest hundredth.

log 2.8

Answers

the answer is 0.447158 and rounded it is 0.45
I got .45, I'm not sure if this is right but I hope it helps!

x^2-6x=-1 If the quadratic equation has real solutions, what are the solutions? Explain. Estimate irrational solutions to the nearest tenth.

Answers

x^2 -6x +1 = 0
a=1
b = -6
c = 1

Use the quadratic formula
x = [-b  +- sq root (b^2 -4ac)] / 2a
x = [--6 +- sq root (36 - 4)] / 2
x = [ 6 +- sq root (32)] / 2
sq root (32) = 5.657

x1 = [ 6 + 5.657] / 2
x1 = 11.657 / 2
x1 = 5.8285
x1 = 5.82 (to nearest tenth)

x2 = [ 6 - 5.657] / 2
x2 = .343 / 2
x2 = .1715
x2 = .2 (to nearest tenth)


It takes typically $27 to fill up your tank up with gas. You have allotted no more than $108 on gasoline for your trip. A) Write and B) solve an inequality to find out how many times you will get to fill up your tank up witj gas.

Answers

A) 27x ≤ 108
B) x ≤ 4

Explanation
Let x be the number of times you can fill up.  It takes $27 each time, so this gives us 27x.  We are budgeting no more than $108 on gas, so this means our inequality will be "less than or equal to":
27x ≤ 108

To solve this, we divide both sides by 27:
27x/27 ≤ 108/27
x ≤ 4

Final answer:

The student can fill up their gas tank up to 4 times within their $108 budget for gasoline. The inequality used to determine this is 27n ≤ 108, solved by dividing both sides by 27.

Explanation:

To solve the student's question regarding how many times they can fill up their gas tank within a $108 budget, we need to set up an inequality and solve it. Let's define the variable n as the number of times they can fill up their tank.

Step A: Write the Inequality

Since it costs $27 to fill up one tank, and the student has budgeted no more than $108 for gas, the inequality will be:

27n ≤ 108

Step B: Solve the Inequality

To find out how many times the student can fill up the tank, we divide both sides of the inequality by 27:

n ≤ [tex]\frac{108}{ 27}[/tex]

n ≤ 4

Therefore, the student can fill up their gas tank up to 4 times within their budget.

Please someone help!!! The sides of the base of a square right prism are 16 cm each and the height of the prism is 10 cm. what is the surface area of this prism?

Answers

the surface area is 1152 cm^2

Answer:

C

Step-by-step explanation:

Find the mean and median of these data: 2,5,9,11,17,19

Answers

Mean = add up all the numbers and divide the sum by the number of numbers you added up.

Median = arrange the data from least to greatest and find the number in the middle. 

2, 5, 9, 11, 17, 19

Mean:
2 + 5 + 9 + 11 + 17 + 19 = 63
63 ÷ 6 = 10.5
The mean of the data is 10.5.

Median:
2, 5, 9, 11, 17, 19
The middle numbers are 9 and 11.
Find the mean between them, which is 10. 
The median of the data is 10.

A bicycle rider increases his speed from 5 m/s to 15 m/s in 10 seconds

Answers

To find the acceleration of the bicycle rider, we are going to use the acceleration formula: [tex]a= \frac{v_{f}-v_{i}}{t} [/tex]
where
[tex]a[/tex] is the acceleration 
[tex]v_{i}[/tex] is the initial speed 
[tex]v_{f}[/tex] is the final speed 
[tex]t[/tex] is the time 

We know from our problem that increases his speed from 5 m/s to 15 m/s in 10 seconds, so his initial speed is 5 m/s and his final speed is 15 m/s; therefore, [tex]v_{i}=5[/tex], [tex]v_{f}=15[/tex], and[tex]t=10[/tex]. Lets replace those values in our formula:
[tex]a= \frac{v_{f}-v_{i}}{t} [/tex]
[tex]a= \frac{15-5}{10} [/tex]
[tex]a= \frac{10}{10} [/tex]
[tex]a=1[/tex]

We can conclude that the acceleration of the bicycle rider 1 m/s^2

HELP!!!!!!!!!!!!!!!!

Answers

Part A: Draw 5 (1 whole blocks). Then, under that draw 1/4's until you reach the end of the 1 wholes.

PartB: Sally needs 5 cups of sugar. If this is 14 of the number she needs to make cake, how many cups does she need?

PartC: Turn 5 into 5/1 keep 5/1 change the sign to multiplication, then flip 1/4 so it is 4/1. 

Pleaseee help

If you multiplied a number by 1/2, the result would be

1. Less than 1
2. Half of the original number
3. A fourth of the original number
4. Twice as large as the original number

Answers

a fourth of the original number
The answer is 2. You get half the original answer.

The school is 625 meters far from Alex house. It took him 15 minutes to go from home to school, and run back to home in 10 minutes. What was Alex's average speed?

Answers

his average speed was 50 m/min

Simplify the expression. (2x^2y)^3

Answers

Answer:

8x6y3 3 and six put at top between y and and three

Sure, I'd be happy to show you how to simplify this expression. Here are the steps:

1. In this expression, we have three numbers that are being multiplied together, 2, x^2, and y, and the entire product is raised to the power of 3.

2. Let's take each part of the product individually and raise them to the power of 3.

  For the first part, 2 raised to the power of 3: this gives us 8, since 2 * 2 * 2 equals 8.

3. The next part is [tex]x^2[/tex] raised to the power of 3. When raising a power to another power, we multiply the powers together. Therefore, (x^2)^3 becomes x^(2*3), which can be simplified to x^6.

4. Finally, y raised to the power of 3 remains as y^3.

5. So, when we put together all three parts, we obtain the simplified expression, and (2x^2y)^3 simplifies to 8x^6y^3.

So, the simplified expression for (2x^2y) ^3 is 8x^6y^3.

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combine terms 12a+26b-(4b+16a)

Answers

12a-16a=-4a ; 26b-4b= 22b
-4a+22b is your answer

What is the slope that passes through the pair of points? (-1, 4), (3, 12)
A. -2
B. 2
C. 4
D. -4

Answers

Use the formula (since I can’t put special characters) y sub 2 minus y sub 1 divided by x sub 2 minus x sub 1 and plug the coordinates into this equation
Answer:
slope = 2

Explanation:
The slope of the line can be calculated using the following rule:
slope = [tex] \frac{y2 - y1}{x2 - x1} [/tex]

In the given, we have:
point (-1 , 4) representing (x1 , y1)
point (3 , 12) representing (x2 , y2)

Substitute with the givens in the above formula to get the slope as follows:
slope = [tex] \frac{12 - 4}{3 - -1} = 2[/tex]

Hope this helps :)

Help I can’t find the area

Answers

We have
two rectangles 71cm x 23cm
two rectangles 71cm x 28cm
two rectangles 23cm x 28cm

The surface area of this figure:

[tex]A_S=2\cdot71\cdot23+2\cdot71\cdot28+2\cdot23\cdot28\\\\=3,266+3,976+1,288=8,530\ cm^2[/tex]

Answer: A. 8,530 cm².

It took 25.5 bottles to fill a cooler and each bottle contained 1.8 liters. How many liters are in the cooler

Answers

There are 45.9 liters in the cooler. 25.5 * 1.8 is 45.9.
There are 45.9 liters in the cooler 25.5*1.8

ow do I put circumference, diameter, and pi into a formula

Answers

Just use the formula to find circumference!

C = ᴨd 

PLEASE HELPPPPPPPPPPPPPPP

Answers

8-(2/x)
"Minus" means subtraction, and "quotient" means division.
8 - 2/x
"eight minus" 8-
"the quotient" .. ÷ ..
"of two" 2 ÷
"and a number x" 2 ÷ x
8 - 2/x
i think, i'm not 100% sure

#22 #24 and #26 HELP

Answers

#22)
4(t - 8) + 20 = 5
Distribute the 4.

4t - 32 + 20 = 5
Combine like terms.

4t - 12 = 5
Add 12 to both sides.

4t = 17
Divide both sides by 4.

t = 4.25


#24)
17 = -5(3 + w) + 7
Distribute the -5.

17 = -15 - 5w + 7
Combine like terms.

17 = -8 - 5w
Add 8 to both sides.

25 = -5w
Divide both sides by -5.

w = -5


#26)
9 = -(r - 5) + 11
Distribute the -.

9 = -r + 5 + 11
Combine like terms.

9 = -r + 16
Subtract 16 from both sides.

-7 = -r
r = 7

The triangle shown must be a right triangle if x= in

A) 8
B) 12
C) 16
D) 144

Answers

Here is how you do it!

a^2 + b^2 = c^2
5^2 + b^2 = 13^2
25 + b^2 = 169
b^2 = 144
b = 12

The square root of 144 is 12, so your answer is B) 12

Hope this helps!

Answer:

The value of x is 12 in

Step-by-step explanation:

Given the right angled triangle having sides 5 in , 13 in and x in

We have to find the value of x.

By applying Pythagoras theorem, we get

[tex]Hypotenuse^{2} = Base^{2} + Perpendicular^{2}[/tex]

⇒ [tex]13^{2}=x^{2}+5^{2}[/tex]

⇒  [tex]169=25+x^{2}[/tex]

⇒  [tex]x^{2} = 144[/tex] ⇒ x=12 in

Hence, length of base is x in i.e 12 in

What is the solution of the equation

Answers

2(2x - 5) = 3x + x - 2x
Distribute the 2.

4x - 10 = 3x + x - 2x
Combine like terms.

4x - 10 = 2x
Subtract 4x from both sides.

-10 = -2x
Divide by -2.

5 = x
x = 5
I'm pretty sure it's x=5
Hope this helps!

anyone know how to solve by giving me not only an explanation in words but can show me the equation, to solve the problem below? thanks

3(x+7)=6(x+2)

Answers

Distribute : 3x + 21 = 6x + 12

Simplify : 9 = 3x

Divide : x = 3

x = 3
So, to solve this problem you have to distribute on both sides. this would bring the equation to 3x+21=6x+12. You then can subtract 3x from both sides to bring the equation to 21=3x+12. Then, subtract 12 from both sides. The equation is now 9=3x. To isolate x, divide both sides by 3. This leaves you with x=3, so the solution to 3(x+7)=6(x+2) is x=3, or (3,0)
I hope this helps!
-Raiden

which of the following represents the formula that could be used to find the height of the cone

Answers

If you know the volume then:
(3 * Cone Volume) / (PI * radius^2) = height

 

The front flap of a tent is shaped like an isosceles triangle. The base of the triangle is 16 feet and the height of the triangle is 6 feet. What is the length of the congruent sides of the triangle?

Answers

thats easy sense isosceles triangles are small you need to have small angles so you just add 16 and 6 to get both of the angles so that equals 22 and there is your answer 22 feet ur welcome.
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