Complete the proof that ∠PST≅∠QRT.
S
P
Q
R
T

Answer:

x = 20°

Step-by-step explanation:

x° + 2x°+ (x+10)° = 90°

4x° + 10° = 90°

4x° = (90 -10)°

x° = (80/4)°

x = 20°

Hope this helps

Answer:

x = 20

Step-by-step explanation:

Key points:

Diagram notation

In the diagram, there are three angles, each with an expression representing the measure of their angle (in degrees).  Angles are adjacent (next to each other with the same vertex) such that collectively they form one large angle.

The small square in the lower left corner means that the large angle is a right angle.  All right angles are 90°.

Note:  The expressions for each angle all have a degree marking, so each angle is measured in degrees.  The unknown value x, is a number without any units, the expression is simplified, and then the units "degrees" are applied.  So in the end, the answer for "x" will not have units; "x" will just be a number.

Angle Addition Postulate

The Angle Addition Postulate states that the sum of the measures of two adjacent angles is equal to the measure of the large angle formed by those adjacent angles.  

[tex](\text{measure of first angle})+(\text{measure of second angle})=(\text{measure of the combined angle})[/tex]

Solving the given problem

By applying the Angle Addition Postulate a couple times, the sum of the measures of all three angles in the diagram is equal to the measure of the large angle formed by those three angles.

[tex](\text{measure of first angle})+(\text{measure of second angle})+(\text{measure of third angle})=(\text{measure of the large right angle})[/tex]

or

[tex](x)+(2x)+(x+10)=(90)[/tex]

From here, to solve for x, we'll need to combine like terms, isolate x, and simplify.

Start with the Associative Property of Addition to combine like terms:

[tex](x+2x+x)+10=90\\4x+10=90[/tex]

To isolate x, subtract 10 from both sides and simplify...

[tex](4x+10)-10=(90)-10\\4x=80[/tex]

... then divide by 4 on both sides and simplify.

[tex]\dfrac {4x}{4}=\dfrac {80}{4}\\x=20[/tex]

So, x=20

The measure of the angle PUT is 13 degrees and the measure of the angle PQR = 21 degrees

When two lines or rays converge at the same point, the measurement between them is called a "Angle."

We have triangles shown in the picture.

In the first triangle SUT:

PU is bisecting the angle SUT:

The measure of angle PUT:

Angle PUT = Half of Angle SUT

= 26/2

= 13 degrees

In the triangle SQR:

Angle SQP = Angle PQR

Angle SQP  = 21 degrees

Angle PQR = 21 degrees

Thus, the measure of the angle PUT is 13 degrees and the measure of the angle PQR = 21 degrees

Learn more about the angle here:

brainly.com/question/7116550

#SPJ1

If the distance on the map is 5.5​ cm. Then the actual distance between two town will be 11 miles.

The complete question is given below.

The scale on a map is 1 cm to 2 miles. What is the actual distance between two town if the distance on the map is 5.5​ cm.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

The scale on a map is 1 cm to 2 miles.

If the distance on the map is 5.5​ cm.

Then the actual distance between two town will be

⇒ 5.5 cm = 5.5 × 2 miles

⇒ 5.5 cm = 11 miles

More about the dilation link is given below.

https://brainly.com/question/2856466

#SPJ1

Answer:

Multiply the denominator and numerator with root 2 to get a fair denominator and simplify if needed. Hope it helps

Answer:

1 + √3 - √5

Step-by-step explanation:

The given √2/√2 equals 1, and so we now have 1 + √3 - √5, whose denominator is the integer 1.  There's nothing left to rationalize.

The value of x will be 158. The value of x is obtained by simplifying the equation.

A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

Identity used;

(x+a)(x-a) = x² - a²

Given expression;

3(x-7)(x+7) - (x-1)(3x+2) = 13

Solving the equation step by step;

[tex]\rm 3(x^2 - 7^2 ) - [x(3x+2)-1(3x+2) ]= 13\\\\ 3x^ 2 -147 -[3x^2 +2x -3x-2] = 13 \\\\ 3x^2 -147 -[3x^2 -x-2] = 13\\\\ 3x^2-147-3x^2 +x+2 = 13 \\\\ x= 13+145 \\\\ x= 158[/tex]

Hence, the value of x will be 158.

To learn more, about equations, refer;

https://brainly.com/question/10413253

#SPJ1

The expression for the area of the rectangular swimming pool is given as follows:

A = w² + 100w + 2100.

The area of a rectangle of length l and width w is given by the multiplication of these measures, that is:

A = lw.

In this problem, considering the width of 70 meters and a length of 30 meters, plus the floor of w meters, we have that:

Hence the area is given as follows:

A = l x wi = (30 + w)(70 + w) = w² + 100w + 2100.

More can be learned about the area of a rectangle at https://brainly.com/question/10489198

#SPJ1

Answer:

3x-2y=13

Step-by-step explanation:

Answer:

y = -1

Step-by-step explanation:

Because the coordinate of U and U' is (5, 0) and (5, -2), the line that is right in the middle would be y = -1.
Or you can compare two of the coordinates to create the line of reflection.

For example: R (0,0), R'(0, -2)

                      U(5, 0), U'(5, -2)

The middle points are (0, -1) (5, -1).

In this case, y = -1.

Answer:

0

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

listing the factors of both numbers

factors of 10 are 1, 2, ,5, 10

factors of 3 are 1, 3

the only common factor to both is 1

the greatest common factor is 1

Answer:

A. $1500.00

Step-by-step explanation:

Assuming this is a simple interest savings account.

Simple interest formula

I = Prt

where:

Given:

Substitute the given values into the formula and solve for P:

⇒ I = Prt

⇒ 225 = P(0.03 ×5)

⇒ 225 = P(0.15)

⇒ P = 225 ÷ 0.15

⇒ P = 1500

Therefore, Timothy started the account with $1500.00.

Answer:The following what

Step-by-step explanation:

what is the following and there is no questions.

Answer:

- 9,800,000,000

Step-by-step explanation:

9.8 * [tex]10^{-9}[/tex]

Simplify 10 with exponent

[tex]{10}^{-9}[/tex] = -10 with 9 zeroes

Rewrite

[tex]{10}^{-9}[/tex] = -1,000,000,000

Place back into expression

9.8 * -1,000,000,000

Simplify by multiplying

- 9,800,000,000

Let me know if you have any questions!

Answer:

C is the answers for the question

Step-by-step explanation:

please mark me as brainlest

Answer:

or D

Answer:

432 mm²

Step-by-step explanation:

We need to cut out 3x3 squares from corners and make an open box. It's height will be 3mm(see the plan). So volume will be:
V = 12 * 12 * 3 = 432mm²

Answer:

1. [tex]x = 2.45s[/tex]

2. The diving board is 45 ft high.

Step-by-step explanation:

• When Lindsey is 30 feet in the air, y = 30.

[tex]30 = -16x^2 + 33x +45\\\\-16x^2 + 33x +15 = 0\\\\16x^2 - 33x -15 = 0\\[/tex]

Using quadratic formula, solve for x:

[tex]x = \frac{33 + \sqrt[]{(-33)^2 - 4(16)(-15)} }{2(16)}[/tex]

[tex]x = 2.45s[/tex]

• If we calculate the height of Lindsey in the air when she is standing on the diving board, we can find the height of the diving board above the ground.

When she is standing on the board, x = 0 as no time has passed after jumping.

[tex]y = -16(0)^2 + 33(0) +45\\\\y = 45 ft[/tex]

Answer:  2/6+5/6 + 1.167

Answer:

1.16

Step-by-step explanation:

Answer:

y = 3

x = -15        

Step-by-step explanation:

When substituting, we want to get rid of one of the variables. (It's easiest ot find the variable in terms of other variable)

so, we know that...

 x + 5y = 0

    - 5y     - 5y

x = -5y

We can plug this x-value into the second equation to find our y-value:

 3y + 2x = -21

  3y + 2(-5y) = -21

3y - 10y = -21

      -7y = -21

     ÷ -7      ÷ -7

y = 3

So, if x = -5y,

x = -5y

x = -5(3)

x = -15

(we can test these values in one of the original equations):

    x + 5y = 0

(-15) + 5(3)= 0

-15 + 15 = 0

 {true}                        

so, y = 3 ; and x = -15    

hope this helps!! :)

Answer: [tex]\angle STU=34^{\circ}, \angle TVW=116^{\circ}[/tex]

Step-by-step explanation:

By the alternate interior angles theorem,

[tex]3x+4=2x+14\\\\x+4=14\\\\x=10\\\\\implies \angle STU=3(10)+4=\boxed{34^{\circ}}[/tex]

By the alternate interior angles theorem, [tex]\angle UTV=82^{\circ}[/tex], and we also know that [tex]\angle TUV=34^{\circ}[/tex].

Thus, by the exterior angle theorem,

[tex]\angle TVW=82+34=\boxed{116^{\circ}}[/tex]

Answer:

1

Step-by-step explanation:

Solutions to a systems of equations are when the (x, y) of two equations are equal with both equations remaining true or in other words when both equations intersect. So by looking at the graph, both equations seem to be linear so there should only be 0, 1, or infinitely many solutions. Since they do have one intersection there is only 1.

Answer:

The system of equations only has 1 solution.

Explanation:

This can be seen by looking at the graph and seeing where the lines were to intersect. For example, if the lines were parallel and never intersected, then there would be 0 solutions. On the other hand, if the lines were essentially the same and overlapped at every point, then there would be infinitely many solutions.

Answer: C

Step-by-step explanation: The graph is going to go up because the +9.5 isn't in any parentheses. If it was, that would mean it would move horizontally. I hope this helps!

The correct statement:

It is the graph of y = x translated 9.5 units up.

The correct option is c.

The equation y = x represents a straight line passing through the origin with a slope of 1. When we have the equation y = x + 9.5, it means that for every x-value, the corresponding y-value is obtained by adding 9.5 to the original x-value. This translation in the y-direction shifts the entire graph upward by 9.5 units.

To visualize this, imagine the original line y = x. Each point on this line has an x-coordinate and a corresponding y-coordinate, which are the same due to the equation y = x. When we add 9.5 to each y-coordinate, the line shifts vertically by 9.5 units without any change in slope or horizontal position.

The other options can be eliminated because the statement does not mention changing the slope or the horizontal position of the graph. Instead, it specifically describes a vertical translation, indicating a movement in the y-direction. Therefore, the correct answer is c.

To learn more about translation in geometry;

https://brainly.com/question/2373420

#SPJ2

The distance that measures 7 units is the distance between points M and P

The complete question is in the attached image

The points are given as:

L= -7

M = -1

N = 2

P = 6

The distance between any points A and B is calculated using:

AB = |B - A|

Using the above formula, we have:

MP = |6 -(-1)|

Evaluate the difference

MP = |7|

Remove absolute bracket

MP = 7 units

Hence, the distance that measures 7 units is the distance between points M and P

Read more about distance at:

https://brainly.com/question/7243416

#SPJ1

Answer:  [tex]x^2[/tex]  and  [tex]-2[/tex]

Step-by-step explanation:

original :

[tex](10x^3+3x^2)+(-20x-6)[/tex]

factored :

[tex]x^2(10x+3)+-2(10x+3)[/tex]

Answer :

[tex]x^2[/tex]  and  [tex]-2[/tex]

Answer:

40

Step-by-step explanation:

it's 8+8+8+7+9 so it's gonna be 40

Answer:

Coordinates follow (x,y) so to find a solution to the line you want to find a point in (x,y) form which is on the line.

This means (1,3) is a solution because at x=1 and y=3 it is on the line.

C | (1,3)

Answer:

26,28

Step-by-step explanation:

We can make a system of equations based on the information given

first we can make one for the perimeter

and one for the area using herons formula

(x and y are the two unknown sides)

[tex]84=30+x+y[/tex]

[tex]336=\sqrt{42(12)(42-x)(42-y)}[/tex]

Now solve for x and y or you can find it by graphing

x and y = 26 and 28, the order does not matter since they are both unkown

so the two sides are 26 and 28