A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. If c represents child bikes and a represents adult bikes, determine which system of inequality best explains whether the company can build 20 child bikes and 6 adult bikes in the week. (2 points)

Answer:

169=169

Step-by-step explanation:

The pythagoras theorem states that if

[tex] {a}^{2} + {b}^{2} = {c }^{2} [/tex]

Then the triangle is a right triangle

So

[tex]{5}^{2} + {12}^{2} = {13}^{2} [/tex]

[tex]25 + 144 = 169[/tex]

[tex]169 = 169[/tex]

Therefore A is a right triangle

Answer:

Step-by-step explanation:

now the longest edge is 13 cm so : 13²must be equal to 5²+12²

so this triangle must be right angled

The answer is the second image from left to right (B). Examples of direct and inverse variations are showed in the image below. :)

Answer:

8 inches.

Step-by-step explanation:

From the statement we have that they first made two identical square pyramids, each with a base area of 100 square inches.

Ab = s ^ 2 = 100

Therefore each side would be:

s = (100) ^ (1/2)

s = 10

So, side of the square base = 10 inches

Then they tell us that they glued the bases of the pyramids together to form the precious stone. The surface area of the gemstone is 520 square inches, so for a single pyramid it would be:

Ap = 520/2 = 260

For an area of the square pyramid we have the following equation:

Ap = 2 * x * s + s ^ 2

Where x is the height of each triangular surface and s is the side of the square base

Replacing we have:

260 = 2 * x * 10 + 10 ^ 2

20 * x + 100 = 260

20 * x = 160

x = 160/20

x = 8

Therefore, the value of x is 8 inches.

Answer: $27.825

Step-by-step explanation:

From the question, we are informed that Robert want to buy a sports cap that is on sale for 25% off and the original price is 35$. This means the price of the sports car will be:

= Original price - Discount

= $35 - (25% × $35)

= $35 - (0.25 × $35)

= $35 - $8.75

= $26.25

We are further told that there is a sales tax of 6%. The amount that Robert will need to pay for the cap will be:

= $26.25 + (6% × $26.25)

= $26.25 + (0.06 × $26.25)

= $26.25 + $1.575

= $27.825

Answer:

27.83

Step-by-step explanation:

Answer:

a) DE is 12 cm

b) CE is 2 cm

Step-by-step explanation:

In the two triangles [tex]\triangle ABC[/tex] and [tex]\triangle ADE[/tex].

[tex]\angle A[/tex] is common.

BC || DE

[tex]\Rightarrow \angle B = \angle D\ and \\ \Rightarrow \angle C = \angle E[/tex]

[tex]\because[/tex] two parallel lines BC and DE are cut by BD and CE respectively and the angles are corresponding angles.

All three angles are equal hence, the triangles:

[tex]\triangle ABC[/tex] [tex]\sim[/tex] [tex]\triangle ADE[/tex].

Ratio of corresponding sides of two similar triangles are always equal.

[tex]\dfrac{AB}{AD} = \dfrac{BC}{DE}\\\Rightarrow \dfrac{9}{9+3} = \dfrac{9}{DE}\\\Rightarrow \dfrac{9}{12} = \dfrac{9}{DE}\\\Rightarrow DE = 12\ cm[/tex]

[tex]\dfrac{AB}{AD} = \dfrac{AC}{AE}\\\Rightarrow \dfrac{9}{9+3} = \dfrac{6}{AC+CE}\\\Rightarrow \dfrac{9}{12} = \dfrac{6}{6+CE}\\\Rightarrow 6+CE = \dfrac{4\times 6}{3}\\\Rightarrow 6+CE = 8\\\Rightarrow CE = 2\ cm[/tex]

So, the answers are:

a) DE is 12 cm

b) CE is 2 cm

Answer:

For the drop down menu:

i) x + y

ii) z²

iii) ½ xy

The complete question related to this found on brainly (ID:16485977) is stated below:

Mario writes the equation (x+y)² = z² +4( 1/2 xy) to begin a proof of the Pythagorean theorem. Use the drop-down menus to explain why this is a true equation.

_____finds the area of the outer square by squaring its side length.

_____finds the area of the outer square by adding the area of the inner square and the four triangles.

These expressions are equal because they both give the areas of outer space.

Find attached the diagram of the question.

Step-by-step explanation:

Pythagoras theorem is a formula that shows the relationship between the sides of a right angled triangle.

Pythagoras theorem

Hypotenuse ² = opposite ² + adjacent ²

From the diagram of the question.

Hypotenuse = z

Opposite = y

Adjacent = x

z² = x² + y²

Area of outer square = area of inner square + 4(area of triangles)

area of inner square = length² = (x+y)²

Expanding area of the outer square:

(x+y)² = (x+y)(x+y) = x²+xy+xy+y²

(x+y)² = x²+y²+2xy

= z² + 2xy

Area of inner square = length² = z²

Area of triangle = ½ base × height

= ½ × x × y = ½ xy

Area of outer square = area of inner square + 4(area of triangles)

(x + y)² = z² + 4(½xy )

Therefore, it is a true equation.

( x + y )² finds the area of the outer square by squaring its side length.

z² + 4( 1/2xy ) finds the area of the outer square by adding the area of the inner square and the four triangles.

These expressions are equal because they both give the areas of outer space.

So for the drop down menu:

i) x + y

ii) z²

iii) ½ xy

Answer:

6,8

Step-by-step explanation:

Answer:

Exponential growth

Step-by-step explanation:

This is not a negative so it is growing.

Hope this helps!

Answer:

y = 5  1/4

Step-by-step explanation:

For direct or inverse variation relation

relation between two variable and y can be expresses in form of

y = kx  where k is constant of proportionality .

Only thing happens in inverse relation is that when x increases then y decreases and vice versa. That is care by constant of proportionality

__________________________________

Thus, let the inverse relation be

y = kx

given

when y = 6 then x = 8

we will plug this value in y = kx

6 = k*8

=>k = 6/8 = 3/4

Thus,

relation is

y = 3/4 x

we have to find y when x = 7 ,

lets put x = 7 in y = 3/4 x

y = 3/4 *7 = 21/4 = 5 1/4

Thus, when x = 7 then y = 5 1/4

Answer:

See Attached Image, Explanation in order to understand how to calculate is below.

Step-by-step explanation:

The Jar Contains 20 Coins.

The probability that it is a 1p coin is 1/5

The probability that it is a 2p coin is 1/2

The total value of the coins in the jar is 59 pence.

The Section in bold is vitally important in this question.

We know we have 4 combinations of 1p, 2p , 5p & 10p in order to make 59p, and only have 20 coins to make it.

--------------------------------------------------------------------------------------------------------------

Calculate 1p:

1/5 of 20 = 4

We know the answer is 4 as we have 20 coins, you find 1/5 of 20.

Calculate 2p:

1/2 of 20 = 10

We know the answer is 10 as we have 20 coins, you find 1/2 of 20.

10 (2p Coins) + 4 (1p coins) = 14

20 coins - 14 (2p & 1p coins) = 6.

Now we only have 6 remaining coins for both 5p and 10p.

Calculate 5p:

We know we currently have a total of 24p if we subtract that from 59 we are left with 35.

So we can work establish here that we are not going to need many 10p's. As we only have 6 coins left!.  

5x5 = 25p.

Therefore you need 5, 5p's

Calculate 10p:

With 1 pence left out of the 20, we need 1 10p.

--------------------------------------------------------------------------------------------------------------

Hope this helps, mark as brainilest if found useful.

There are 1 10p coin of each type in the jar.

Given that ;

The Jar Contains 20 Coins.

Probability that it is a 1p coin is 1/5

Probability that it is a 2p coin is 1/2

The total value of the coins in the jar is 59 pence.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

We know we have 4 combinations of 1p, 2p , 5p & 10p. so to make 59p, and only have 20 coins to make it.

Calculate 1p:

1/5 of 20 = 4

The answer is 4 as we have 20 coins, find 1/5 of 20.

Calculate 2p:

1/2 of 20 = 10

The answer is 10 as we have 20 coins, you find 1/2 of 20.

10 (2p Coins) + 4 (1p coins) = 14

20 coins - 14 (2p & 1p coins) = 6.

Now we only have 6 remaining coins for both 5p and 10p.

Now Calculate 5p:

We know that we have a total of 24p if we subtract that from 59 we are left with 35

5x5 = 25p.

Therefore we need 5, 5p's

Now Calculate 10p:

With 1 pence left out of the 20, we need 1 10p.

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Answer:

[tex] \frac{105}{4} [/tex]

please see the attached picture for full solution..

hope it helps...

Good luck on your assignment..

Answer: 4:3.

Step-by-step explanation:

Given: Point P is [tex]\dfrac{4}{7}[/tex] of the distance from M to N.

To find: The ratio in which the point P partition the directed line segment from M to N.

If Point P is between points M and N, then the ratio can be written as

[tex]\dfrac{MP}{MN}=\dfrac{MP}{MP+PN}[/tex]

As per given,

[tex]\dfrac{MP}{MP+PN}=\dfrac{4}{7}\\\\\Rightarrow\ \dfrac{MP+PN}{MP}=\dfrac{7}{4}\\\\\Rightarrow\ \dfrac{MP}{MP}+\dfrac{PN}{MP}=\dfrac{7}{4}\\\\\Rightarrow\ -1+\dfrac{PN}{MP}=\dfrac{7}{4}\\\\\Rightarrow\ \dfrac{PN}{MP}=\dfrac{7}{4}-1=\dfrac{7-4}{4}=\dfrac{3}{4}\\\\\Rightarrow\ \dfrac{PN}{MP}=\dfrac{3}{4}\ \ \or\ \dfrac{MP}{PN}=\dfrac{4}{3}[/tex]

Hence, P partition the directed line segment from M to N in 4:3.

Answer:

(6,2)

Step-by-step explanation:

y=-1/2x+5

y=2x-10​

-1/2 x+5 =2x-10  to find the solution y=y ( point of intersection of two lines)

-1/2 x-2x = -10-5 solve for x

-5/2 x=-15

x=-30/-5=6

y=2x- 10 substitute  x in the equation to get y

y=2(6)-10

y=2

(2,3)

Dont put the other answer, it’s wrong I

did the math.

Answer:

Question 1:

a. The answer is B because the graph inclined really quickly and then it inclined at a much slower pace, suggesting that the person was running and then walking.

b. The answer is C because you can see on the graph that after a while, the distance from the starting point goes back to 0, indicating that the person forgot something at home.

Question 2:

a. The dashed line reaches the bottom at 15:30 so the answer is C.

b. Siobhan travels 8 km to go from home to school so the answer is 2 * 8 = 16 which is option D.

Question 3:

The answer is C because after the distance from the starting point increased, it then decreased and came back to the original point suggesting that he walked, turned around and walked back to the starting point.

Answer:

first page : a) A because it is the shortest time with no stop

b) C the graph goes up and return to the start point after a while

second page : it is at 3:30 0r 15:30

b): 8 km going to schools and 8 coming back is 16

third page it is C because he walk up a certain distance and come back to the starting point

Answer:

B. 3\sqrt(x)-2

Step-by-step explanation:

A polynomial cannot have a variable in the denominator

A constant is a polynomial

3\sqrt(x)-2 and this cannot be simplified to get rid of the variable in the denominator so it is not a polynomial

Answer:

B

Step-by-step explanation:

dashed line above the shaded area, shaded area below dashed boundary line

Answer:

There is no error, Amad is correct.

Step-by-step explanation:

Khan Academy Checked.

Amad had done no error. His conclusion is true.

Two triangles are said to be congruent if their sides are equal in length, the angles are of equal measure, and they can be superimposed on each other.

For example,

In the figure given above, Δ ABC and Δ PQR are congruent triangles. This means that the corresponding angles and corresponding sides in both the triangles are equal.

Sides: AB = PQ, BC = QR and AC = PR;

Angles: ∠A = ∠P, ∠B = ∠Q, and ∠C = ∠R.

Therefore, Δ ABC ≅ Δ PQR

The following are the congruence theorems or the triangle congruence criteria that help to prove the congruence of triangles.

As, from the given cases the prediction of congruency of two triangles is correct. There is no error he made.

Hence, Amad had not made any error.

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Answer:

c  ≥ -5

Step-by-step explanation:

-5c +2 ≤ 27

Subtract 2 from each side

-5c +2-2 ≤ 27-2

-5c ≤25

Divide by -5, remembering to flip the inequality

-5c/-5 ≥25/-5

c  ≥ -5

Answer: [tex]x\geq 5[/tex]

Step-by-step explanation:

[tex]-5x+2\leq 27\\Subtract\\-5x\leq 25\\Divide\\x\geq 5[/tex]

It's important to remember that when you divide both sides of an inequality by a negative number to flip the sign.

Hope it helps <3

Step-by-step explanation:

Answer:

C. x>4

Step-by-step explanation:

3/(x-4) > 0

3>0, so

x-4 >0

x > 4

Answer:

1/16

Step-by-step explanation:

Total = 32 footballers

25 stretch regularly.

3 injure last year

now, 22 stretch regularly.

out of 32, 8 are injured. Therefore, 32-8=24 should stretch regularly but only

22 stretch regularly. Therefore, 24-22 =2 are not stretching regularly.

fraction of players are not stretching regularly = 2/32 =1/16

Answer:

a. Domain = All real numbers

Range = y ≥ 2

b. Domain = -4 < x ≤ 4

Range = 0 ≤ y < 4

Answer:

Measure of angle T = 25 degrees and TU = 12

Step-by-step explanation:

Tamar is measuring the sides and angles of Triangle T U V to determine whether it is congruent to the triangle below. For triangle K L M, side K M is 27 millimeters, side L M is 20 millimeters, and side K L is 12 millimeters. Angle K is 45 degrees, angle M is 25 degrees, angle L is 110 degrees. Which pair of measurements would eliminate the possibility that the triangles are congruent? Measure of angle T = 25 degrees and Measure of angle U = 45 degrees Measure of angle T = 110 degrees and Measure of angle V = 25 degrees Measure of angle T = 25 degrees and TU = 12 Measure of angle T = 110 degrees and UV = 27

Answer:  Two triangles are congruent to each other if they have the same shape and size (i.e the same sides and angles).

The ways used to find congruence are:

1) Angle-side-angle: If two angles and an included side of a triangle is equal to the two angles and corresponding side of another triangle, then they are equal.

2) Side-side-side: If all three sides of a triangle is equal to the three sides of another triangle, then the two triangles are congruent.

3) Side angle side: If two sides and an included angle of a triangle is equal to the two sides and corresponding angle of another triangle, then they are equal.

4) Hypotenuse - leg: If the hypotenuse and one leg of a triangle is equal to the hypotenuse and leg of another triangle then they are equal.

5) Angle angle side: If two angles and an non included side of a triangle is equal to the two angles and corresponding side of another triangle, then they are equal.

Measure of angle T = 25 degrees and TU = 12 would eliminate the possibility that the triangles are congruent because if T = 25°, then the side opposite angle T (UV) is suppose to be 12

Answer:

the answer is C

Step-by-step explanation:

I got it right on my final exam on edge

Answer:

Infinite solutions

Step-by-step explanation:

Both lines have the same slope and y-intercept, therefore they are the same line and intersect at all points, resulting in infinite solutions.

Answer: The tank which has 3 m side.

Step-by-step explanation: A cube is a form that has equal sides. To calculate the volume of it, multiply all three sides:

V = length*width*height

Since they are all the same, volume will be:

V = s³

One tank has a 3 m side, so its volume is:

V = 3³

V = 27 m³

The other has half of the first one side, then s = [tex]\frac{3}{2}[/tex] and volume will be:

V = [tex](\frac{3}{2})^{3}[/tex]

V = [tex]\frac{27}{8}[/tex] m³

As you can see, the volume of the second tank is [tex]\frac{1}{8}[/tex] smaller than the first one. Therefore, the tank which has 3 m side can store more water than the  tank with side measuring half of the first.

Answer:

[tex] \frac{97pi}{18} m [/tex]

Step-by-step Explanation:

==>Given:

radius (r) = 10 m

m<VCW = 97°

==>Required:

Length of arc VW

==>Solution:

Formula for length VW is given as 2πr(θ/360)

Using the formula, Arc length = 2πr(θ/360), find the arc length VW in the given circle

Where,

θ = 97°

r = radius of the circle = 10 m

Thus,

Arc length VW = 2*π*10(97/360)

Arc length VW = 20π(97/360)

Arc length VW = π(97/18)

Arc length VW = 97π/18 m

Our answer is,

[tex] \frac{97pi}{18} m [/tex]

Answer

y= 12.5x + 210,000

Step-by-step explanation:

This is a linear function because it is increasing constantly by 12.5 percent so it will me written as y=mx+b

The value of function that represents the situation is,

⇒ P = 210,000 (1.125)ⁿ

Where, n is number of years.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The situation is,

⇒ A population of 210,000 increases by 12.5% each year​.

Now, Let number of years = n

Hence, The value of function that represents the situation is,

⇒ P = 210,000 (1 + 12.5%)ⁿ

⇒ P = 210,000 (1 + 0.125)ⁿ

⇒ P = 210,000 (1.125)ⁿ

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Answer: 3 < t < 4

Step-by-step explanation:

Given the following information :

Initial Velocity of projectile = 112 ft/s

Height (h) above the ground after t seconds :

h = –16t2 + 112t

To calculate the time when h exceeds 192 Feets (h >192)

That is ;

-16t^2 + 112t = > 192

-16t^2 + 112t - 192 = 0

Divide through by - 16

t^2 - 7t + 12 = 0

Factorizing

t^2 - 3t - 4t + 12 =0

t(t - 3) - 4(t - 3) = 0

(t-3) = 0 or (t-4) =0

t = 3 or t=4

Therefore, t exist between 3 and 4 for height in excess of 192ft

–16(3)^2 + 112(3) = 192 feets

–16(4)^2 + 112(4) = 192 feets

3 < t < 4

Answer:

Perimeter = 22

Step-by-step explanation:

To find the perimeter, we will follow the steps below:

A = (-1,-1), B = (2,3), C = (5,3), D = (8,-1).

First, we will find the distance AB

A = (-1,-1), B = (2,3)

|AB| = √(x₂-x₁)²+(y₂-y₁)²

x₁ = -1    y₁=-1     x₂=2     y₂=3

we can now proceed to insert the values into the formula

|AB| = √(x₂-x₁)²+(y₂-y₁)²

      = √(2+1)²+(3+1)²

      = √(3)²+(4)²

      = √9 + 16

      =√25

      = 5

|AB| = 5

Next, we will find the distance BC

B = (2,3), C = (5,3),

|BC| = √(x₂-x₁)²+(y₂-y₁)²

x₁ = 2    y₁=3    x₂=5     y₂=3

we can now proceed to insert the values into the formula

|BC| = √(x₂-x₁)²+(y₂-y₁)²

      = √(5-2)²+(3-3)²

      = √(3)²+(0)²

      = √9 + 0

      =√9

      = 3

|BC|=3

Next, we will find the distance CD

C = (5,3), D = (8,-1).

|CD| = √(x₂-x₁)²+(y₂-y₁)²

x₁ = 5    y₁=3    x₂=8    y₂=-1

we can now proceed to insert the values into the formula

|CD| = √(x₂-x₁)²+(y₂-y₁)²

      = √(8-5)²+(-1-3)²

      = √(3)²+(-4)²

      = √9 + 16

      =√25

      = 5

|CD|=5

Next, we will find the distance DA

D = (8,-1)      A = (-1,-1)

|DA| = √(x₂-x₁)²+(y₂-y₁)²

x₁ = 8    y₁=-1   x₂=-1    y₂=-1

we can now proceed to insert the values into the formula

|DA| = √(x₂-x₁)²+(y₂-y₁)²

      = √(-1-8)²+(-1+1)²

      = √(-9)²+(0)²

      = √81 + 0

      =√81    

      = 9

|DA|=9

PERIMETER = |AB|+|BC|+|CD|+|DA|

                     =5 + 3+5 +9

                     =22

Perimeter = 22