What is the solution to the following system of equations?

Applying the definition of similar triangles, the value of x is determined as: 12.5.

In a triangle like the one shown above, the line that intersects the two sides of the triangle divides the two sides of the triangle to form similar triangles. Thus, their corresponding sides are proportional to each other.

Therefore, we would have:

(x + 5) / 5 = (10 + 4) / 4

(x + 5) / 5 = 14/4

4(x + 5) = 5(14)

4x + 20 = 70

4x = 70 - 20

4x = 50

x = 50/4

x = 12.5

Learn more about similar triangles on:

https://brainly.com/question/11920446

#SPJ1

Answer:

40   40   100°

Step-by-step explanation:

Is that TRIANGLE FGH?

    the angles add to 180

        180 / ( 4 + 4 + 10 ) = 10

then each angle is       4 x10       4 x 10     and  10 x10

Number of shirts = dependent variable

Cost of the purchases = independent variable

Answer:

The equation representing the proportional relationship between j and m is m = 3j/4 .

Step-by-step explanation:

Writing an Equation to Represent a Proportional Relationship

What is proportional relationship?

A proportional relationship between two quantities is when the two quantities vary directly with one and other. Meaning if one item is doubled, the other item is also doubled.

Going back to the given problem above, we have the table showing the proportional relationship between j and m.

j | 4 | 12 | 20 |

m | 3 | 9 | 15 |

Solution:

Step #1

The proportional relationship can be written as:

m/j = ¾ = ‌9⁄12‌ = ‌15⁄20‌ = ¾

Step #2

So, the equation representing this proportional relationship is:

m = ¾ × j/1 = 3j/4

Final Answer:

The equation representing the proportional relationship between j and m is m = 3j/4 .

Step-by-step explanation:

Answer:

Step-by-step explanation:

y = 3 (x-1)(x+ 7 )    this graph will intercept the x axis  when y = 0

 0 = 3 ( x-1)(x+7)     so you can see this = 0   when x =1   or when x = -7

                                  these are the x-axis intercepts

         the vertex will be right in the middle between the intercepts found above    ....... at  x = -3    

          plug this value in to find the y coordinate   3 ( -3-1)(-3+7) = -48

                   vertex is   -3, -48

               the axis of symmetry is the value of the x coordinate of the vertex

                          x = - 3

        direction of opening will be upward.....

   see attached graph

Answer:

0.04

Step-by-step explanation:

30+5+0.1+0.009 is 35.109

35.149 - 35.109= 0.04

35.149 = 30+5+0.1+ ____ +0.009

= 30 + 5 + 0.1 + x + 0.009

= 35.109 + x

x is the unknown value, so what number add to the 35.109 gives 35.149? That's what we're after.

35.149 = 35.109 + x

- 35.109 both side

0.04 = 0 + x

Thus, x = 0.04

(35.109 - 35.109 cancles each other & we get x on its own because 0.04 - 0 gives you 0.04)

Hope this helps!

The value of the angle ∠BCA when approximated to 3 significant figures is;  20.4°

From the attached image of the triangle ABC showing the side lengths x and y, we can see clearly that it is a right angle triangle.

Now, since we want to find the value of the angle ∠BCA, then it means we have to use trigonometric ratio to get;

x/y = sin BCA

Plugging in the relevant values gives us;

8/23 = sin BCA

∠BCA = sin⁻¹(8/23)

∠BCA = 20.355

Approximating to 3 significant figures gives us;

∠BCA = 20.4°

Read more about Trigonometric Ratios at; https://brainly.com/question/13276558

#SPJ1

Answer:

(- 9, 2 )

Step-by-step explanation:

under a reflection in the y- axis

a point (x, y ) → (- x, y ) , then

(9, 2 ) → (- 9, 2 )

Answer:

32...................

Using a linear function, it is found that you would need roughly 24 hours of training to have a monthly pay of $1500.

A linear function is modeled by:

y = mx + b

In which:

Looking at the table, the pay increases $200 each 10 hours of work, hence the slope is:

m = 200/10 = 20

Then:

y = 20x + b

When x = 10, y = 1220, hence:

y = 20x + b

1220 = 20(10) + b

b = 1020.

Then the pay for x hours of training is:

y = 20x + 1020.

For a pay of $1500, we have that:

y = 20x + 1020.

1500 = 20x + 1020.

20x = 480

x = 24

You would need roughly 24 hours of training to have a monthly pay of $1500.

More can be learned about linear equations at https://brainly.com/question/24808124

#SPJ1

Answer:

CD = 13

Step-by-step explanation:

since Δ ABD and Δ CBD are congruent , then corresponding sides are congruent, so

CD = DA = 13

Answer:

13

Step-by-step explanation:

We know that if two triangles are congruent, the corresponding element of those are also equal.

Given that,

ABD Δ ≡ CBD Δ

Therefore, the corresponding elements are also equal.

AD = CD

AD = 13 units

∴ CD = 13 units

The amount of aspirin that would be in the patient's body is; 281.25.

A) The amount of aspirin in the patient's body after 2 hours can be evaluated as follows;

a = 500×(3/4)² = 4500/16 = 281.25.

B) The number 500 as used in the equation represents the amount of aspirin in the patient's body prior to taking the medicine, at time, t= 0.

C) The fraction 3/4 as used in the task content is the factor of change in aspirin content in the patient's body.

Read more on exponential functions;

https://brainly.com/question/14197900

#SPJ1

Boy is 22.5 feet high from the ground

The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trig ratios are evaluated with respect to sides and angles.

The given question can be solved by sin, as value of perpendicular is to be evaluated and height and angle is provided. Let height from the ground be x

sin(22.5°) = x / 58

x = 58sin22.5 = 58(.38258)  =  22.5 feet high.

Thus the Boy is 22.5 feet high from the ground.

Learn more about trigonometry here :

https://brainly.com/question/26719838

#SPJ4

A motorcycle traveling at 70 miles per hour overtakes a car traveling at 40 miles per hour that had a three-hour head start. How far from the starting point are the two vehicles.

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

The car is 120 miles away when the motorcycle starts.

The bike gains on the car at 30 mph (70-40).

It takes 4 hours for the bike to close the gap (120/30).

In 4 hours, the bike and the car are 280 miles from the starting point.

---------

4*70 = 280

7*40 = 280

Since Distance = Speed x Time, and in this case, the distances are equal, we, therefore, have: 70T = 40(T + 3)

70T = 40T + 120

30T = 120

T=4, which makes the distance that both vehicles traveled, highlight_green280miles, calculated as (70 * 4), or (40 * 7).

It also means that the motorcycle took 4 hours to travel 280 miles, and the car took 3 hours more, or 7 hours to travel the same distance.

Learn more about Distance:

https://brainly.com/question/12356025

#SPJ4

It's B

Slope is negative, the other must be positive due to m1 x m2 = - 1

m1 = -2/5

The diagram shows a gradient of -2/5. So, the

reciprocal of this valve to make - 1 is 5/2 (which is the - 2/5 flipped upside down, but positive)

-2/5 x 5/2 = - 10/10 (or - 1)

Thus, the perpendicular line to this has a gradient of 5/2.

Hope this helps!

Answer:

y=3x-4

Step-by-step explanation:

Answer:

[tex] \frac{8}{24} [/tex]

Step-by-step explanation:

If Adam's family uses 8lb of apples to make pie. We know that 3 x 8 = 24, so it's probably approximately 3 out of 18.

The formulas and the equivalent formulas are

W = X - Y                                    X = W +Y

W = X/Z - Y                                 X = Z(W + Y)

W = (X - Y)/Z                               X = WZ+Y

W = XY                                       X =W/Y

To do this, we simply make X the subject of the formula in expressions on the left.

So, we have:

W = X - Y

This gives

X = W + Y

W = X/Z - Y

This gives

X/Z = W + Y

X = Z(W + Y)

W = (X - Y)/Z

This gives

X - Y = WZ

X = WZ + Y

W = XY

This gives

X =W/Y

Read more about equivalent expressions at:

https://brainly.com/question/27733205

#SPJ1

Complete question

Match each formula on the left with an equivalent formula on the right.

W = X - Y                                     X =W/Y

W = X/Z - Y                                 X = Z(W + Y)

W = (X - Y)/Z                               X = WZ+Y

W = XY                                       X = W +Y

Answer:

  d.  102°

Step-by-step explanation:

We can use the relations ...

to write equations that let us find x and all of the angles in ∆PQR.

The congruence relation ∆ABC ≅ ∆PQR tells us that ∠P = ∠A. Using the given expressions for these angles, we have ...

  ∠P = ∠A

  8x +4 = 5x +16

  3x = 12 . . . . . . . . . subtract (5x+4)

  x = 4 . . . . . . . . . divide by 3

Then the measure of angle P is ...

  ∠P = 8x +4 = 8(4) +4 = 36 . . . . . degrees

Angle Q in ∆PQR is given as ...

  ∠Q = 10x +2 = 10(4) +2 = 42 . . . . . degrees

Then the measure of angle R needed to make the total of angles in ∆PQR be 180° is ...

  ∠R = 180° -36° -42° = 102°

Angle R is 102°.

__

In summary:

Answer: the amount of liters that would fill the glass tank's volume can not be found

Step-by-step explanation:

there is not enough information to find out how many liters could fill the glass tanks volume

The required volume of glass tank = Vb +Vw liters

Volume, is defined as the ratio of the mass of object to its density.

Andrei wants to fill a glass tank with marbles, and then fill the remaining space with water.

Volume of pebbles = Vb
Volume of water = Vw
Volume of glass tank = Vg
Vg = Vb + Vw

Thus, the required volume of glass tank is = Vb + Vw liters

Learn more about Volume here:
https://brainly.com/question/1578538

#SPJ1

Using relations in a right triangle, it is found that:

The ratio of 8 to 15 is equals to tan B.

The relations in a right triangle are given as follows:

Researching the problem on the internet, we have that:

Hence the tangent of B is:

tan(B) = 8/15.

Which means that:

The ratio of 8 to 15 is equals to tan B.

More can be learned about relations in a right triangle at https://brainly.com/question/26396675

#SPJ1

Answer:

28 ft^2

Step-by-step explanation:

The room is in the shape of a square.  That means the base of the room (width and length) will have the same dimensions.

Length x Width = 49 ft^2

Length = Width

Length^2 = 49 ft^2

Length  = 7 feet

Width is also 7 feet

The height of the room is 4 feet, plenty for non-humans.  One wall area would be (7 ft)*(4 ft) = 28 ft^2

Answer:

6 cookies per day.

Step-by-step explanation:

if she is going to sell 18 cookies within 3 days, would divide that problem, (18 divided by 3) which will get you selling 6 cookies per day during that 3-day challenge.

Answer:

(x - 5)(x + 5)

Step-by-step explanation:

x² - 25 ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b)

x² - 25

= x² - 5²

= (x - 5)(x + 5)

Answer:

Step-by-step explanation:

(x-5) +(x+5)

Answer:

Que is talking about a syrup which contains 50% of sugar .

Que asked : amount of sugar syrup from X grams of sugar.

Explanation :

if a sugar syrup contains 50% of sugar , that means that the half of the solution contains sugar and half is solvent .

means , 2 × amount of sugar = solution (syrup)

now , we are given x grams of sugar

then , solution can be made with x grams of sugar = 2 × (X grams) = 2X gram of solution or sugar syrup.

.

.

Mark BRAINLIEST!

A bisector is a line that divides a given line or angle into two equal parts or measures. So that the required statements and reasons are given below:

              STATEMENT                                                 REASONS

1. BC bisects <ABD                                 Given

2. m<ABC = [tex]26^{o}[/tex]                                       Bisection property of an angle

3. 2(m<ABC) = [tex]52^{o}[/tex]                                   Sum of angles of a bisected angle

4. m<ABC = m<CBD                                Congruent parts of a bisected angle

5. <mABC + m<ABC =  [tex]52^{o}[/tex]     Sum of an individual angle of a bisected angle

6.  m<ABC + m<CBD = [tex]52^{o}[/tex]                      Sum of angles of a bisected angle

7. m<ABC + m<CBD = m<ABD          Sum of the angles of a bisected angle

The above statements and reasons are majorly centered on a bisector, the angles formed due to the bisection of a given angle, and the bisected angle.

For more clarifications on the bisection of an angle, visit: https://brainly.com/question/5799105

#SPJ1

Answer:

1. BC bisects <ABD | Given

2.m<ABD=52 | Given

3.m<ABC = m<CBD | Definition of Bisector

4.m<ABC + m<CBD = m<ABD | Angle Addition Postulate

5.m<ABC + m<CBD =52 | Substitution Property

6.m<ABC + m<ABC =52 | Substitution Propery

7.2(m<ABC)=52 | Addition

8.m<ABC=26 | Division Property

Step-by-step explanation:

Edge 2022

Answer:

1/49.

Step-by-step explanation:

(−7)^-2

=  1 /(- 7)^2

= 1/49.

Answer:

b - 140

Step-by-step explanation:

an angle bisector divides an angle in half

so

half of the angle is 70

the other half is 70

so

70 + 70 = 140

b is your answer

Answer: B. 140°

Step-by-step explanation:

Hi!

An angle bisector just cuts the angle in half.

Therefore, if one half is 70°, the other half is also 70°!

To find the measure of the angle just add them!

70° + 70° = ?

= 140°

So, your answer is B. 140°

Hope this helps and have a great day!

Answer:

Step-by-step explanation:

Maybe..

8/10

12/15

16/20

20/25

24/30

28/35

32/40

36/45

40/50

Any one of these is equal to the ratio of 4 over 5.

Answer:

No, the person who answered first is wrong

I'll give you the correct answer

Step-by-step explanation:

He the two equivalent ratios of 4 : 5 are 8 : 10 and 12 : 15.

thank you, this is the correct answer

hope that hepls