In ASTU, SU is extended through point U to point V, m/STU = (3x + 14)°,
m/UST = (2x + 12)°, and m/TUV = (7x+6)°. What is the value of x?

Answers

Answer 1

By applying the exterior angle property, the value of x is equal to 5.

What is the exterior angle property?

The exterior angle property can be defined as a theorem which states that the measure of an exterior angle in a triangle is equal in magnitude to the sum of the measures of the two remote or opposite interior angles of that triangle.

How to determine the value of x?

In order to determine the value of x in triangle STU (ΔSTU), we would have to apply exterior angle property.

Mathematically, the exterior angle property can be used to model triangle STU (ΔSTU) and this is given by:

m<TUV = m<STU + m<UST

Substituting the given parameters into the formula, we have;

(7x+6)° = (3x + 14)° + (2x + 12)°

7x + 6 = 5x + 16

7x - 5x = 16 - 6

2x = 10

x = 10/2

x = 5.

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Related Questions

picture to the problem sented

Answers

Answer:

Explanation:

For the matrix equation

[tex]2X+A=B[/tex]

We first subtract A from both sides to get

[tex]2X=B-A_{}[/tex]

Now,

[tex]B-A=\begin{bmatrix}{-7} & {-8} & {} \\ {-2} & {6} & {} \\ {4} & {4} & {}\end{bmatrix}-\begin{bmatrix}{-3} & {0} & {} \\ {0} & {3} & {} \\ {-6} & {6} & {}\end{bmatrix}[/tex][tex]B-A=\begin{bmatrix}{-7--3} & {-8-0} & {\square} \\ {-2-0} & {6-3} & {\square} \\ {4--6} & {4-6} & {\square}\end{bmatrix}[/tex][tex]B-A=\begin{bmatrix}{-10} & {-8} & {} \\ {-2} & {-3} & {} \\ {10} & {-2} & {}\end{bmatrix}[/tex]

Hence, we have

[tex]2X=\begin{bmatrix}{-10} & {-8} & {} \\ {-2} & {-3} & {} \\ {10} & {-2} & {}\end{bmatrix}[/tex]

Dividing both sides by 2 gives

[tex]\begin{gathered} X=\frac{1}{2}\cdot\begin{bmatrix}{-10} & {-8} & {} \\ {-2} & {-3} & {} \\ {10} & {-2} & {}\end{bmatrix} \\ \end{gathered}[/tex][tex]X=\begin{bmatrix}{-5} & {-4} & {} \\ {-1} & {-\frac{3}{2}} & {} \\ {5} & {-1} & {}\end{bmatrix}[/tex]

which is our answer!

The resting heart rates for a sample of 15 students are recorded in the following stemplot.

A stemplot titled heart rates has values 55, 63, 65, 69, 69, 69, 69, 70, 71, 73, 73, 74, 75, 76, 77.

What is the mean resting heart rate for this sample?

66.0 beats per minute
69.0 beats per minute
69.9 beats per minute
70.0 beats per minute

Answers

Answer:

C) 69.9 beats per minute

Step-by-step explanation:

Mean is the average.

It is calculated as:

mean = sum of samples/ number of samples

Find it using the equation above:

(55 + 63 + 65 + 69*4 + 70 + 71 + 73*2 + 74 + 75 + 76 + 77)/15 = 1048/15 = 69.866 ≈ 69.9

Correct choice is C

Answer:

c

Step-by-step explanation:

3. Lake City Jr. High Students:*** 12 out of every 18 ride a bus to school*** 9 out of every 15 live in Lake City*** 160 ride a bus to schoolHow many of the Jr. High students do not live in Lake City?

Answers

Let

x ----> total number of students Lake City Jr. High Students

we have that

12 out of every 18 rides a bus to school

160 ride a bus to school

Applying proportion

18/12=x/160

solve for x

x=(18/12)*160

x=240 total students

so

9 out of every 15 live in Lake City

that means

6 out of every 15 does not live in Lake City

Applying proportion

y -----> students that not live in Lake City

6/15=y/240

solve for y

y=(6/15)*240

y=96

therefore

96 students do not live in Lake City

96 children do not live in Lake City

Kyra multiplied 0.27 by a power of ten and got 2.7. What power of ten did she multiply by? Responses

Answers

The power of ten that she multiplied by is 1.

What is an exponent?

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

Since Kyra multiplied 0.27 by a power of ten and got 2.7. This will be illustrated as:

= 0.27 × 10¹

= 2.7

Therefore, the power is 1.

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Use the appropriate form of the percentage formula.What percent of 14.4 is 11.7? Round to the nearest hundredth of a percent.

Answers

Hello there. To solve this question, we'll have to compare the values with two fractions:

To see how much of 14.4 is 11.7, in percentage, we start by considering 14.4 represents 100%, or 100, since we want to find the answer in percent as well.

Then we make:

[tex]\frac{11.7}{x}=\frac{14.4}{100}[/tex]

Cross multiply the numbers:

[tex]11.7\cdot100=14.4\cdot x[/tex]

Divide both sides of the equation by a factor 14.4

[tex]x=\frac{11.7\cdot100}{14.4}[/tex]

Using a calculator, we get that x is equal to:

[tex]81.25[/tex]

Therefore, 11.7 is 81.25% of 14.4!

Find the direction angle of the vector u = -3i+8j. That is, find the angle between 0 and 360° that u makes with the positive x-axis (measured counterclockwise)Do not round any intermediate computations, and round your answer to the nearest whole number.

Answers

we have the vector

u=-3i+8j

see the attached figure, to better understand the problem

we have that

tan(x)=8/3

x=tan^-1(8/3)

x=69.44 degrees

Find out the angle theta

theta=180-x

theta=180-69.44

theta=111 degrees

Drag the red and blue dots along the x-axis and y-axis to graph 3x-5y=20

Answers

Answer:

what red and blue dots?

Step-by-step explanation:

the volume of the prism below is 264 in3. what is the height of the prism

Answers

The volume of any prism = base area x height

Given Volume = 264 in^3

The prism is triangular based

Therefore, its base area = 1/2 x base x height

The base of the triangle= 8in

Height of the triangle = 6in

[tex]\begin{gathered} \text{ Base area = }\frac{1}{2}\text{ x 8 x 6} \\ \text{Base area= 24in}^2 \end{gathered}[/tex][tex]\begin{gathered} \text{ Recall, Volume = Base area x height} \\ H\text{eight = }\frac{\text{Volume}}{\text{Base area}} \\ \text{ Height=}\frac{264in^3}{24in^2} \\ \\ \text{Height}=11\text{ in} \end{gathered}[/tex]

The height of the prism is 11 in.

which fact below has the same difference as 18-6= ?8-1614-814-716-8

Answers

18-6=12

8-16=-8 not equal 18-6

14-8=6 not equal 18-6

14-7=7 not equal 18-6

16-8=8 not equal 18-6

Hence none of the options has the same difference as 18-6

distribute and simply (x- 2)2+9

Answers

Weare asked to used distributive property and reduce the expression:

(x - 2 ) 2 + 9

so we apply distributive property to eliminate the parenthesis, multiplying the factor of "2" by "x" and by "-2":

2 x - 4 + 9

now combine like terms:

2 x + 5

If the question involved instead the following expression:

(x - 2)^2 + 9 (where the "2" was in fact a power affecting the binomial (x-2), then

b=3 y-intercept br Find the slope and y-intercept of the line represented by each table. 3. 0 3 6 9 0 2 х 12 10 19 28 2 37 у у A 4 6 8 x 3 4 5 slope m = slope m= y-intercept br y-intercept

Answers

The slope can be obtained using the formula

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

and the y intercept is the value of y when x is equal to zero.

3. We can choose the points (3,10) and (6,19), then

[tex]m=\frac{19-10}{6-3}=\frac{9}{3}=3[/tex]

From this, we can use the slope-point form of the line equation to obtain the y intercept

[tex]\begin{gathered} y-10=3(x-3) \\ y=3x-9+10 \\ y=3x+1 \end{gathered}[/tex]

Then,

slope =3, y-intercept=1.

4. We choose the points (2,2), (4,3)

[tex]m=\frac{3-2}{4-2}=\frac{1}{2}[/tex][tex]\begin{gathered} y-2=\frac{1}{2}(x-2) \\ y=\frac{1}{2}x-1+2 \\ y=\frac{1}{2}x+1 \end{gathered}[/tex]

Then,

slope = 1/2, y-intercept =1

I need help on 8 please it says find the value of x round each answer to the nearest tenth

Answers

Step 1

Redraw the diagram and use the Pythagoras theorem to find the value of c\x.

Step 2:

Find the value of y from the right-angle triangle of sides: 10, 25 and y using the Pythagoras theorem

Opposite = y

Adjacent = 10

Hypotenuse = 25

[tex]\begin{gathered} \text{Pythagoras theorem} \\ \text{Opposite}^2+adjacent^2=hypotenuse^2 \\ y^2+10^2=25^2 \\ y^2\text{ + 100 = 625} \\ y^2\text{ = 625 - 100} \\ y^2\text{ = 525} \\ y\text{ = }\sqrt[]{525} \\ y\text{ = 5}\sqrt[]{21} \end{gathered}[/tex]

Step 3

Next, use the Pythagoras theorem to find x from the triangle with sides

28, x and y

Hypotenuse = 28

Opposite = x

Adjacent = y

[tex]\begin{gathered} x^2+y^2=28^2 \\ x^2\text{ + (5}\sqrt[]{21})^2=28^2 \\ x^2\text{ + 525 = 784} \\ x^2\text{ = 784 - 525} \\ x^2\text{ = 259} \\ \text{ x = }\sqrt[]{259} \\ x\text{ = 16.1} \end{gathered}[/tex]

Final answer

x = 16.1

x +3 +7 = 2x -10 -x how many solutions does it have

Answers

Answer:

no solution

Step-by-step explanation:

x + 3 + 7 = 2x + 10 - x ( simplify both sides )

x + 10 = x - 10 ( subtract 10 from both sides )

x = x - 20 ( subtract x from both sides )

0 = - 20 ← not possible

this indicates the equation has no solution

What is the domain
of the function?

Answers

The domain of the function is found as [-7, 6].

What is termed as the domain?A function is an mathematical object that accepts input, appears to apply a rule to it, and returns the result. A function can be thought of as a machine that requires in a number, performs some operation(s), and then outputs the result. The domain of a function is the collection of all its inputs. Its codomain is the set of possible outputs. The range refers to the outputs which are actually used.

For the given question,

The graph of the function is given.

By the definition of the domain, the maximum and minimum values of the graph on x axis are 6 and -7 respectively.

Thus, the domain of the function is found as [-7, 6].

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Question 6 of 10Which choice is equivalent to the fraction below when x is an appropriatevalue? Hint: Rationalize the denominator and simplify.Please help

Answers

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Which type of wave does the illustration depict?

Answers

Where is the picture?

If the size of an object is 5.0 cm, and the size of the image formed by a lens is 15.0 cm, what is the magnification of the system?

Answers

The magnification of the system with an object distance of 5 cm and an image distance of 15 cm is 0.33.

A lens is a transmissive optical tool that employs refraction to focus or disperse a light beam.

In optics, magnification refers to the image's size in relation to the item that produced it. The ratio of the image length to the object length, as measured in planes perpendicular to the optical axis, is referred to as linear magnification, also known as lateral or transverse magnification.

The size of an object is u = 5 cm

The size of the image formed by the lens is v = 15 cm

Then the magnification M will be:

Magnification = Image distance/ Object distance

M = v/u

M = 5/15

M = 1/3

M = 0.33

Hence, the magnification of the system is 0.33.

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A man sold 4 times as many tie dyed T shirts as silk screened shirts. He sold 190 shirts altogether. how many tie dyed shirts did he sell?

Answers

Answer: 152 tie dyed T shirts

Let the number of dyed T shirts be = x

Let the number of silk screened shirts be = y

He sold sold 4 times as many tie dyed T shirt as screened shirts

Since x = Tie dyed T shirt

Therefore, x = 4y

x = 4y ------------------- equation 1

He sold 190 shirts all together

x + y = 190 ------------ equation 2

Substitute the value of x = 4y into equation 2

4y + y = 190

5y = 190

Divide both sides by 5

5y/5 = 190/5

y = 38

Since x = 4y

x = 4(38)

x = 152 tie dyed T shirts

Therefore, 152 tie dyed T shirts was sold

According to the question, the man sold 4 times as many tie dyed T shirt as silk screened shirt

This implies that for 1 silk screen shirt sold, he would also sell 4 tie dyed T shirt

Since, x = tie dyed T shirt and y = silk screened shirts

Then, x= 4 x y

x = 4y

The man sold 190 shirts altogether

This implies that, he sold a total of 190 of both tie dyed T -shirt and silk screened shirts

Mathematically,

x + y = 190

Since x = 4y

Then, 4y + y = 190

This Implies that for 1

Nazir was given 5over7 of the fruit basket what fraction of the fruit basket was left over?

Answers

The fraction of the fruit basket is 2/7.

What is fraction?

Fraction represent the parts of a whole or collection of objects. A fraction has two parts. The number on the top of the line is called the numerator. It tells how many equal parts of the whole or collection are taken.  The number below the line is called the denominator.

Total fraction = 1 or can be written as 7/7

Nazir given 5/7 of the fruit basket

1-5/7 = 7-5/7

= 2/7

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in a class of students the following data table summarizes how many students pass a test and completed the homework due the day of the test what is the possibility that a student chosen randomly from the class failed the test

Answers

From the table,

Total number of students that failed the test = 2 + 7 = 9

The total number of students that participated = 10 + 3 + 2 + 7 = 22

The possibility that a student chosen randomly from the class failed the test = ​Total number of students that failed the test divided by the total number of students that participated

= 9/22

Hence, the possibility that a student chosen randomly from the class failed the test is 9/22

numbe

Instructions: Select all of the methods that will find both real andimaginary solutions.Select one or more:Quadratic FormulaCompleting the SquareFactoringSquare RootsCheck

Answers

Let's begin by identifying key information given to us:

Imaginary solutions

Which expression does not belong? 2^3 8 3^2 2^2*2^1

Answers

[tex]\begin{gathered} 2^3=8 \\ 2^2\cdot2^1=4\cdot2=8 \\ All\text{ the expressions are equal to 8, but} \\ 3^2=9\ne8 \\ thus \\ 3^2\text{ does not belong } \end{gathered}[/tex]

What is the range of the function f(x)=√x-8 + 6?Of(x) ≥-8O f(x) ≥-6Of(x) ≥ 6O f(x) ≥ 8

Answers

Hello!

We have the function below:

[tex]f(x)=\sqrt{x-8}+6[/tex]

Let's analyze the graph of it:

Note that for the domain, it starts when x = 8.

For the range, it starts when y = 6.

So, the range of this function is:

[tex]\begin{gathered} [6,+\infty) \\ \text{ or} \\ \boxed{f(x)\geqslant6} \end{gathered}[/tex]

Third alternative.

What is the function g(x) that What is the results when translating the function f(x)=x to the left 12 units and reflecting it over the x-axis?

g(x) =

Answers

The function g(x) that results when translating the function f(x)=x to the left 12 units and reflecting it over the x-axis is g(x) = -|x + 12|

Translating to left ≡ f(x + 12)

Translation up 12 units means g(x)=f(x)+5g(x)=f(x)+5. Reflecting this across the x-axis means g(x)=-(f(x)+12)g(x)=−(f(x)+12)

-(x+12)=-x-12

f(x + 12) = |x + 12|

Reflection of a function f(x) about the x - axis is keeping the x value same but negating the y values

Reflected f'(x) = -y = -f(x)

Taken together

g(x) = -(|x + 12|)

The function g(x) that results when translating the function f(x)=x to the left 12 units and reflecting it over the x-axis is g(x) = -|x + 12|

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what is the answer use the slope intercept form to graph the equation y=7/4x-1

Answers

The equation y = 7/4x - 1​ is in slope-intercept form, with a slope of 7/4 and a y-intercept of -1.

To graph it, you need to locate the point (0, -1) - the y-intercept -, and then use the slope to find another point. From (0, -1) you have to move 4 units to the right, and 7 units up, reaching the point (4, 6). Then, you have to draw the line that passes through theses points, as follows:

A lock on a fence door has a 3 digit combination. Each digit can be any number between 1 – 8. The combinations 123, 456, and 789 are invalid. How many combinations are possible?

Answers

There are a total of 8 possible numbers for each digit and there are 3 digits for the password. Since the problem didn't state that the numbers can't be repeated, then we can apply the following formula:

[tex]C_{n,m}\text{ = }\frac{n!}{m!(n\text{ - m)!}}[/tex]

Where "n" is the range of possibilities for each number and "m" is the number of digits we want to arrange them. So applying the data from the problem gives us:

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It is an equation containg atleast one fraction whose numerator and deniminator are polynomials.A.rational functionB.rational equationC.ratuonal inequalityD.irrational equation

Answers

In a equation, if we have polynomials in the numerator and denominator, this equation is considered a rational equation, similar to the case where fractions are considered rational numbers.

So the correct option is B.

Please help find the x​

Answers

Value of x is 28.

Define parallelogram.

A parallelogram is a geometric object with sides that are parallel to one another in two dimensions. It is a form of polygon with four sides (sometimes known as a quadrilateral) in which each parallel pair of sides have the same length. A parallelogram has adjacent angles that add up to 180 degrees. A unique variety of quadrilateral called a parallelogram has both pairs of its opposite sides parallel and equal. First, it is important to understand that a parallelogram's inner angles add up to 360 degrees (sum of internal angles = 180(n-2) where n is the number of sides in the image).

Given Data

89°, (5x -8)° , (3x+4)° , 51°

As we know, the sum of angles of parallelogram is 360°.

So,

89 + 5x-8 +3x + 4 + 51 = 360

5x + 3x = 360 - 136

8x = 224

x = 28

Value of x is 28.

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true or false?17. The focci of an ellipse are located at 1/3 the length of the major axis from both sides of the center.

Answers

To solve this problem and find if the statement is true, we can start by remembering the general equation for an ellipse:

[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]

where a and b are the major axis and the minor axis for the ellipse, as shown in the following diagram:

The foci of an ellipse, are the focal points of the ellipse, for reference, we show them in the diagram:

The foci can be found using the following equation:

[tex]f=\sqrt[]{a^2-b^2}[/tex]

To prove if the foci f is really 1/3 of the length of the major axis (in this case the major axis is a) we can give random values to a and b.

Values for a and b:

a=6

b=4

If the foci of the ellipse were located at 1/3 of the length of the major axis, we should find that the foci "f" is 1/3 of 6, thus, we should find that f=2, let's see if that is true by substituting a and b into the formula for f:

[tex]f=\sqrt[]{a^2-b^2}[/tex][tex]f=\sqrt[]{6^2-4^2^{}}[/tex][tex]\begin{gathered} f=\sqrt[]{36-16} \\ f=\sqrt[]{20} \end{gathered}[/tex]

solving the square root we find the value of f:

[tex]f=4.47[/tex]

Instead of 2 (which would have been 1/3 of the major axis), we find that f is 4.47, thus the statement "The foci of an ellipse are located at 1/3 the length of the major axis from both sides of the center." Is NOT TRUE.

Answer: False

Given the equation 2(n + 7) - 5 = 29. What two steps are needed to simplify the left side of the equals? Choose the two that apply. *Add 5 to both sidesDistribute the 2Divide both sides by 2Combine like termsSubtract 7 from both sides

Answers

In order to simplify the left side of the equation, the first two steps are:

1) Distribute the 2:

[tex]\begin{gathered} 2\mleft(n+7\mright)-5=29 \\ 2n+14-5=29 \end{gathered}[/tex]

2) Combine like terms:

[tex]\begin{gathered} 2n+14-5=29 \\ 2n+9=29 \end{gathered}[/tex]

So the correct options are Distribute the 2 and Combine like terms.

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