30 points high school geometry question

Hey there! :)

Answer:

m∠QPR = 25°.

Step-by-step explanation:

Given:

m∠QPS = 40°

m∠RPS = 8x + 7°

m∠QPR = 9x + 16°

m∠QPS = m∠RPS + m∠QPR, therefore:

40° = 8x + 7° + 9x + 16°

Combine like terms:

40° = 17x + 23°

Subtract 23° from both sides:

17° = 17x°

Divide both sides by 17:

x = 1°

If m∠QPR = 9x + 16°, substitute in 1 for 'x':

9(1) + 16 = 9 + 16 = 25°.

We need to find the value of x.

If R is on the interior of of <QPS, then m<QPR + m<RPS = m<QPS.

Now substitute the measures into the equation.

9x + 16 + 8x + 7 = 40.

Now combine like terms to get 17x + 23 = 40.

Now subtract 23 form both sides to get 17x = 17.

Now divide both sides by 17 to find that x = 1.

Now to find m<QPR which measures 9x + 16°, we can substitute in a 1.

So we have 9(1) + 16 which is 25.

So m<QPR is 25°.

Answer:

Step-by-step explanation:

Given: <AOB and an interior point D.

Prove: a point, D, in the interior of an angle is equidistant from the sides of the angle, then it belongs to the angle bisector of the angle.

Join D to A and B, then;

OA ⊥ AD (right angle property)

OB ⊥ BD (right angle property)

AD = BD (angle bisector theorem)

<AOD = <BOD (congruent angle property)

ΔAOD = ΔBOD (congruence property of triangles)

Therefore, point D lies on the bisector of <AOB.

Answer:

B & C

Step-by-step explanation:

Answer:

x = 5/3                    x = -1

Step-by-step explanation:

|3x–1|=4

The solution to an absolute value equation has a positive and a negative solution

3x-1 =4    3x-1 = -4

Add 1 to each side

3x-1+1 = 4+1      3x-1+1 = -4+1

3x =5                 3x = -3

Divide by 3

3x/3 = 5/3           3x/3 = -3/3

x = 5/3                    x = -1

Answer:

x=1 2/3,x=-1

Step-by-step explanation:

There are two solutions. In the first solution, 3x=4-1=4 so x=1 2/3

The second solution is when 3x-1 equals negative 4 but because of the absolute value, is positive 4. In this case, it would be x=-1

Answer:

3/10

Step-by-step explanation:

1/5 of total income - spent on car

remainder income = 4/5

3/8 of remainder = 3/8 ×4/5 = 3/10(of total income spent on rent)

the word "of" means you can find it by multiplication

e.g. 2 of 1/2 means 2 × 1/2 which is 1

Answer:

the answrr is option a 9

Answer:

p > q

Step-by-step explanation:

We khow that the sum of a triangle's angles is 180°

■■■■■■■■■■■■■■■■■■■■■■■■■■

Let's start with the triangle containing p

● p+60+50 = 180

● p+110 = 180

● p = 180-110

● p= 90°

So p is a right angle

□□□□□□□□□□□□□□□□□□

The second triangle

● q+ 80+30 = 180

● q+ 110 = 180

● q = 180-110

● q = 70°

Then q is also a right triangle

■■■■■■■■■■■■■■■■■■■■■■■■■

We can deduce that p > q

Answer:

The first relation is not a function.

Step-by-step explanation:

If you see two points in which one is vertically above the other, then it is not a function. In other words, if in a relation, two points have the same x-coordinate and different y-coordinates, that relation is not a function. The only example in which this happens is the first graph.

The first relation is not a function.

Answer:

26% or 10/39

Step-by-step explanation:

Since box A has 5 dark chocolates and 10 milk chocolates, there are 15 chocolates in all. Box B has 24 chocolates in total (12 milk, 12 dark). So there is a total of 39 chocolates in all.

There are 10 milk chocolates in Box A, so the probability of choosing any one milk chocolate out of the total 39 is 10/39 or in percentage, 26%.

Answer:

[x]   f(x)

[-6]  13

[-3]   4

[0]   1

[3]   4

[9]   28

Step-by-step explanation:

f(0) = (1/3)(0^2)+1 = 1

f(3) = (1/3)(3^2)+1 = 4

f(9) = (1/3)(9^2)+1 = 28

Answer:

f(4) = 4

Step-by-step explanation:

We have x = 4 so we use the middle line of the piecewise function since 0≤x≤4

f(x) = x

f(4) = 4

Answer:

-729

Step-by-step explanation:

[tex]-9^3 = -9 x (-9) x (-9) =[/tex]

          [tex]-9x(-9) = 81[/tex]

                   [tex]81x(-9)=-729[/tex]

Answer:

15 units

Step-by-step explanation:

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

d = √[(9 - (-6))² + (8 - 8)²]

d = √[(15²) + (0²)]

d = √15²

d = 15

Answer:

15 units

Step-by-step explanation:

9-(-6) = 15

Answer:

8 and 8/35

Step-by-step explanation: simplify the equation hope this helps:)

Answer:

9 27/35

Step-by-step explanation:

3 3/5 * 2 5/7

Change each to an improper fraction

( 5*3 +3)/5  * ( 7*2+5)/7

18/5 * 19/7

342/35

Change back to a mixed number

35 goes into 342 9 times

342-315 = 27   with 27 left over

9 27/35

Answer:

A) C

B) 47 inches

Step-by-step explanation:

A)  The range on the horizontal axis is 0 to 5, we cannot tell how many students collected the exact number of bottles.

The correct option would be the number of students who collected exactly 4 bottles.

B) The mean of a data set is written as:

[tex]mean = \frac{sum \: of \: terms}{number \: of \: terms}[/tex]

[tex]mean=\frac{45+48+49+40+53}{5}[/tex]

[tex]mean=\frac{235}{5}[/tex]

[tex]mean=47[/tex]

The average height of the students is 47 inches.

Answer:

A & B

Step-by-step explanation:

Answer:

21 and 67

21<x<67

Step-by-step explanation:

The smallest side with two sides of 23 and 44 must be more than 44-23=21

The largest side with two sides of 23 and 44 must be less than 44+23=67

So the range is between 21 and 67.

As an equation, it would be 21<x<67

Answer:

21 and 67

21<x<67

Step-by-step explanation:

Answer:

y-3=-2(x+0)

Step-by-step explanation:

Answer:  see below

Step-by-step explanation:

Use the slope (m) formula: [tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Let (x₂, y₂) = (2, -1) and (x₁, y₁) = (0, 3)

[tex]m=\dfrac{-1-3}{2-0}=\dfrac{-4}{2}=-2[/tex]

Use the Point-Slope form y - y₁ = m(x - x₁) where m = -2 & (x₁, y₁) = (0, 3):

y - 3 = -2(x - 0)      -->    y - 3 = -2x

Use the Point-Slope form y - y₁ = m(x - x₁) where m = -2 & (x₁, y₁) = (2, -1):

y - (-1) = -2(x - 2)      -->    y + 1 = -2(x - 2)

Answer: 63 degrees.

Step-by-step explanation:

Angles in a triangle add up to 180 degrees.

Therefore: 54 + y + y = 180

So 54 + 2y = 180

So 2y = 126

Therefore y = 63 degrees.

Answer:

5|x+2|-1

Step-by-step explanation:

Evidence is included

Answer:

y-intercept of the line MN = 2

Standard form of the equation ⇒ x + y = 2

Step-by-step explanation:

Coordinates of the ends of a line MN → M(-3, 5) and N(2, 0)

Slope of a line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

                        = [tex]\frac{5-0}{-3-2}[/tex]

                        = -1

Equation of the line MN passing through (-3, 5) and slope = -1,

y - 5 = (-1)(x + 3)

y - 5 = -x - 3

y = -x + 2

This equation is in the y-intercept form,

y = mx + b

where m = slope of the line

b = y-intercept

Therefore, y-intercept of the line MN = 2

Equation in the standard form,

x + y = 2

the first one is : -1

the second one is: y-5 = -1 ( x + 3)

the third one is: -x + 2

the first one to the right side is: 0,2

and the second one on the right side is: x+y=2

your welcome

Answer:

D

Step-by-step explanation:

From the graph, the solutions are x = -2 and x = 3, therefore, the equation must be (x - (-2)) * (x - 3) = (x + 2)(x - 3).

Answer:

8

Step-by-step explanation:

If you want the dot product, here it is:  (0)(0) + (-2i)(4i) = 8

Answer:

Below

Step-by-step explanation:

● 2-a > -12+4

●2-a > -8

Substract 2 from both sides

● 2-a-2 > -8-2

● -a > -10

Multiply both sides by -1 and switch the sign

● a < 10

So if a is less than 10 we aren't sure if it is less than 6 but it could be greather than it .

Yes, you are correct! The six is bigger because it comes down to a negative number when subtracting from 2

hope this helps!

Answer

the answer is (-3,-5)

Step-by-step explanation:

Answer:

(-1,1), (1,3), (2,2)

Step-by-step explanation:

To dilate an object, we need to multiply the x and y values by the given scale factor.

In this case the scale factor is 1/3 --> 1/3(x, y)

Before-> After dilation

1/3(-3,3) = (-1,1)

1/3(3,9) = (1,3)

1/3(6,6) = (2,2)

Please leave a 'thanks' if this helps!

Step-by-step explanation:

1.) first simplify or combine like terms.[tex]\frac{3a}{5} -p-\frac{p}{9}+\frac{7p}{3} -\frac{q}{10}+\frac{1}{9}[/tex]

2.) then condense. [tex]\frac{3a}{5} +\frac{11p}{9}-\frac{q}{10}+\frac{1}{9}[/tex].

Answer:

Step-by-step explanation:

It is comes under geometric sequence;

40 , 80 , 160 ,320 , ........

First term = a = 40

Common ratio = r = 2

nth term = [tex]ar^{n-1}\\[/tex]

Number of sheep on the farm by the end of each year = [tex]40*(2)^{n-1}\\[/tex]

Answer: 2:3

Step-by-step explanation:

2:5,

3+2=5, which is the total amount,

2 is the number of white chocolate candies

Let's set this up in equation form!

We know that 15 equals b and 8 together.

15 = b + 8

b = 7

The value of b that makes the equation true is 7.

Hope this helps!! :)