1. What is the length of RT?
Q
T
S
60°
60°
32

Algebraic expressions include both alphabet and number so that the value of the alphabet is to be determined. Thus the steps taken by Tyler are correct if x = 22.

ii. Tyler made no mistake.

Algebraic expressions include both alphabet and number so that the value of the alphabet is to be determined. The value of the alphabet in the expression would be determined by applying mathematical operations appropriately.

To solve the question given to Tyler, we have:

[tex]\sqrt{x + 3}[/tex] = -5

square both sides of the equation to have;

(x + 3) = [tex](-5)^{2}[/tex]

x + 3 = 25

collect like terms to get;

x = 25 - 3

  = 22

x = 22

1. Thus the equation is true if x = 22.

2. Tyler did not make any mistake in solving for x.

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Answer:

23 is the answer

Solutions of the equation are 22.5°, 30°.

The given equation is sin(5θ) - sin(3θ) = cos(4θ)

We take left side of the equation

sin(5θ) - sin(3θ) = 2cos ((5θ+3θ)/2) (sin(5θ-3θ)/2)

=2cos4θsinθ  [From sum-product identity]

Now we can write the equation as

2cos(4θ)sin(θ) = cos(4θ)

2cos(4θ)sinθ - cos(4θ) = 0

cos(4θ)[2sinθ - 1] = 0

cos(4θ) = 0

4θ = 90°

θ = 90/4

θ = 22.5°

and (2sinθ - 1) = 0

sinθ = 1/2

θ = 30°

Therefore, solutions of the equation are 22.5°, 30°

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The equation that represents the  Myra's age given Talat age is as follows:

t = m + 5

Myra is 5 years younger than her sister Talat

Myra age is represented by m while Talat age is represented by t.

Hence,

m = age of Myra

t = age of Talat

Myra is 5 years younger than Talat. This means Talat is 5 years older than Myra.

Therefore, the equation that represents the  Myra's age given Talat age is as follows:

t = m + 5

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Answer:

Step-by-step explanation:

The correct powers of x are not displayed in several of the goods.

Algebra tiles are mathematical manipulatives that help pupils better comprehend algebraic thinking and its ideas. These tiles have shown to give beginning algebra pupils in elementary, middle, high, and college concrete models.

Blocks called algebra tiles can be used to symbolize constant, linear, and quadratic terms. Small yellow squares stand in for constant blocks, green rectangles for linear blocks, blue squares for quadratic blocks, and red squares for negative sides for all other types of blocks.

Future:

The image shows,

3x(2x - 1) = 6x² - 3x

This should be the appropriate representation on the tile:

_____+x _____ +x _____ +x

+x _ +x² ______+x² ______+x²

|

+x__ +x² _____ +x² ______+x²

|

- __ -x ______ -x _______-x

+6x² - 3x

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By the comparison test, the series converges.

We have

[tex]\dfrac1{k\sqrt{k+2}} \le \dfrac1{k \sqrt k} = \dfrac1{k^{3/2}}[/tex]

so we can compare to a convergent [tex]p[/tex]-series,

[tex]\displaystyle \sum_{k=1}^\infty \frac1{k\sqrt{k+2}} \le \sum_{k=1}^\infty \frac1{k^{3/2}} < \infty[/tex]

By the comparison test, the series converges.

What are convergence series and diverging series?

If the infinite series converges to a real number it is called converging if not then it is called diverging series.

If the larger series is convergent the smaller series must also be convergent. Likewise, if the smaller series is divergent then the larger series must also be divergent.

For this series to be converging it must follow the following :

⇒ [tex]| \frac{t_{n+1} }{t_{n} } | \leq 1[/tex]

⇒Putting n = 1

[tex]| \frac{t_{2} }{t_{1} } | \leq 1[/tex]

[tex]\t_{2} t_{1}[/tex] [tex]t_{2}[/tex]= 1/4

[tex]t_{1}[/tex]=1/[tex]\sqrt{2}[/tex]

[tex]\frac{t_{2} }{{t_{1} }}[/tex] = 1/2[tex]\sqrt{2[/tex]

⇒ t₂/t₁≤1

⇒ Hence it converges

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[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex] \qquad❖ \: \sf \: {b}^{2} - 9b + 14[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex] \qquad❖ \: \sf \:(b - 2) \sdot(b - 7)[/tex]

[tex] \qquad❖ \: \sf \:(b \sdot b) + (b \sdot - 7) - (2 \sdot b) - (2 \sdot - 7)[/tex]

[tex] \qquad❖ \: \sf \: {b}^{2} - 7b - 2b + 14[/tex]

[tex] \qquad❖ \: \sf \: {b}^{2} - 9b + 14[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

[tex] \sf \:(b - 2) \sdot(b - 7) = {b}^{2} - 9b + 14[/tex]

Answer:

b² - 9b + 14

Step-by-step explanation:

(b - 2) × (b - 7)

= b×b - 7b - 2b + 2×7  (Expand)

= b² - (7b + 2b) + 14  (gather like terms)

= b² - 9b + 14

Answer:2,695

Step-by-step explanation: just add.

The function that represents the number of people at the fair after x hours is f(x) = 68 + 1.5x

What is the function that represent the number of people at the fair?

The function that represents the number of people at the fair is known as a linear function. A linear function is any function that graphs to a straight line. The dependent variable in the linear function increases by a constant number.

Linear functions can be represented by : y = mx + c

Where:

f(x) = 68 + (1.5x)

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Answer:

When x is -6, y will be 18

When x is -5 y will be 15

Step-by-step explanation:

Create a proportion

y/x

-9/3 = x/-6  What do we need to multiply 3 by to get 6?  -2, so we will multiply -9 by -2 to get 18

Some people like to solve by cross multiplying.

That would give us

(-9)(-6) = 3x  

54 = 3x  divide both sides by 3

18 = x

Set up the second problem as a proportion

-9/3 = x/-5  This is a little trickier.  I am trying to think what I have to multiply 3 by to get -5.  3(-5/3)  will give me -5, so I will multiply the top number that I know (-9) by (-5/3) to find my x.

(-9)(-5/3) = 45/3  or 15

The value of x in the equation –x (–1) = 3x (–5) is x = 1

Linear equations are equations that have constant average rates of change, slope or gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the equation is given as

–x (–1) = 3x (–5)

Remove the bracket in the above equation

-x - 1 = 3x - 5

Collect the like terms in the above equation

3x + x = 5 - 1

Evaluate the like terms in the above equation

4x = 4

Divide both sides by 4 in the above equation

x = 1

Hence, the value of x in the equation –x (–1) = 3x (–5) is x = 1

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Answer:

-3, or D

Step-by-step explanation:

The expression x³+3x² is a cubic unit representation of the prism's volume.

Having 6 faces, 12 edges, and 8 vertices, a right rectangular prism is a three-dimensional object. Angles between the base and sides are right angles in a right rectangular prism. Rectangles make up each of the six faces.

We have provided that to:

In a right rectangular prism, the height is three units more than the base's length.

The square base has edges that are x units long.

How much volume does a rectangular prism have?

Volume of the rectangular prism = width × length × height

V =  W × L × H   ....................(1)

We've indicated that the

bigger by three than the base's length, h

and  the length of the base is x:

Hence,

               H = X +3

          Length of the base = X

           Width = X

Adding the values l h and w to the formula (1) yields,

V = W × L × H

= X × X × (X+3)

= (X²) × (X+3)

= X³ + 3X³

Consequently, the phrase

               X³ + 3X³

represents, in cubic units, the prism's volume.

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The algebraic solution to the situation is as follows:

x + y = 750

10x + 6y = 6860

The number of adult and student are 590 and 160 respectively.

One adult ticket for a school play costs 10 dollars and one student ticket costs 6 dollars.

One evening,750 people attended the play and the total receipts were 6860.

Therefore,

let

x = number of adult ticket

y = number of student tickets

Therefore,

x + y = 750

10x + 6y = 6860

10x + 10y = 7500

10x + 6y = 6860

4y = 640

y = 640 / 4

y = 160

Hence,

x  = 750 - y

x = 750 - 160

x = 590

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Answer:

Below in bold.

Step-by-step explanation:

Standard form is Ax + By = C

where A, B and C are integers  and A must be positive.

So the first 2 are already in standard form but the last 2 can be converted to standard form by multiplying each term by -1:

-12x+3y=27

= -1*-12x + -1*3y = -1*27

12x - 3y = -27   is the answer.

The last one is:

24x + 12y = -60.

Based on the given perimeter of the polygon and the length of each side; the length of the longest side of the polygon is 29 cm

Perimeter of the polygon = x + (x + 6) + (x + 5) + (x + 1) + (x + 8) + (x + 4)

150 = x + x + 6 + x + 5 + x + 1 + x + 8 + x + 4

150 = 6x + 24

150 - 24 = 6x

126 = 6x

x = 126/6

x = 21

The longest side of the polygon is (x + 8)

= 21 + 8

= 29 cm

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5x² + 9x - 1 is  the expression that represents a quadratic expression.

What is  quadratic expression?

A quadratic expression is of the form

ax² + bx +c = 0                    where a ≠ 0

The give options are-

9x - 2

5x² + 9x - 1

-2x³ + 8x² - 7x +1

[tex]x^{4} - 12 x^{3} + 8x^{2} - 7x +1[/tex]

From the given options, the only expression which is quadratic is

5x² + 9x - 1

wChoose the expression that represents a quadratic expression. 9x − 2 5x2 9x − 1 −2x3 8x2 − 7x 1 x4 − 12x3 8x2 −here a =5, b=9 and c=-1

Therefore, 5x² + 9x - 1 is  the expression that represents a quadratic expression.

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The mean GPA is greater than 2.75.

To find the GPA:

Therefore, the mean GPA is greater than 2.75.

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The value of a = 11

What is complex numbers ?

Let  a + i b = (a,b)

       c + i d = (c , d)

the distance between two points = [tex]\sqrt{( a - c)^{2} + (b -d )^{2} }[/tex]

put values in the formula -

[tex]\sqrt{(a- (-9))^{2} + (3 - 24 )^{2} }[/tex] = 29

square both sides

[tex]{(a + 9)^{2} + (21)^{2} } = 29^{2}[/tex]

(a + 9)² = 841 - 441 ⇒ 400

(a + 9) = √400 = + 20

a =  +20 -9

So,  a = -29  or 11

Therefore, the value of a = 11

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[tex]a = \frac{\pi.r {}^{2} }{4} = \frac{3.14 \times 10 {}^{2} }{4} = \frac{3.14 \times 100}{4} [/tex]

[tex]a = 78.5[/tex]

Answer:

Below in bold,

Step-by-step explanation:

a. There's is only one card that fits this description so

Probability = 1/52.

b. There are 2 black Kings so

Probability = 2/52 = 1/26.

c. There are 2 of these - 7 of diamonds and 7 of hearts

so

Probability = 2/52 = 1/26.

d.  There 13 diamonds and 13 hearts so

Probability = 26/52 = 1/2.

e.  There  26 black cards

Probability = 26/52 = 1/2.

The percentage of increase in the size is 25%

According to the statement

We have to given that the

Size of the granola packages from 16 ounces to 20 ounces.

And we have to find the percentage of the size of the crunchee's granola packages.

So, For this purpose,

The formula to calculate the percentage of increase in the size is :

Percentage to increase the size = present size - past size / present size.

Now substitute the values in the given formula is

Percentage to increase the size = (20 - 16 / 16)*100

After solving it

Percentage to increase the size = (4/16) *100

Percentage to increase the size = 25%

So, The percentage of increase in the size is 25%

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Answer:

ph : perimeter = 4 sides of the base; p*h = the area of the sides of that prism

B : 2 areas of the base = top and bottom

A right prism consists of a rectangle and two undersides S night prism =

 S rectangle + 2S base

the length of the rectangle is the circumference of the base which is P  so A = ph + 2B

Answer:

see explanation

Step-by-step explanation:

3- digit numbers starting with 5 are

528 and 582

3- digit numbers starting with 2 are

258 and 285

3- digit numbers starting with 8 are

825 and 852

there are 6 possible 3- digit numbers

258 , 285 , 528 , 582 , 825 , 852

Answer:

2.5 feet

Step-by-step explanation:

Since circumference is just pi(we're using 3.14 in this case) * diameter, which is our answer, we need to divide the circumference(which is 7.58) BY 3.14, which is pi. This leaves us with the diameter, which is 2.5. The unit is already feet, so we needn't do anything about that.

When measuring variables, it is often preferable to use a small sample size because the smaller the sample the greater the chance of a spurious result.

Therefore, when measuring variables, it is often preferable to use a small sample size because the smaller the sample the greater the chance of a spurious result.

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Answer:

0.1 cases

Step-by-step explanation:

100(1-0.90)^3

100(0.10)^3

100(0.001)

0.1

The distance between the two schools on the map is (C) 4.2 inches.

To find the distance:

On the map,2 inches represents 5 miles.

Thus, we can write:

Since the actual distance between the two schools is 10.6 miles.

Multiplying both sides by 10.6 in equation (1).

Therefore, the distance between the two schools on the map is (C) 4.2 inches.

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The complete question is given below:
Kim is drawing a map of the different schools in her school district. she knows that her middle school is 10.6 miles away from the middle school that her best friend attends. if every 2 inches on the map represents 5 miles, how far apart will the two schools be on the map, to the nearest tenth of an inch?

(A) 0.2 inch

(B) 0.9 inch

(C) 4.2 inches

(D) 26.5 inches

Answer:

6 1/10

Step-by-step explanation:

In order to add fractions, we have to make the denominators equal.  we can multiply 1/2 by 5/5 and get 5/10, and multiply 3/5 by 2/2 and get 6/10, to make the denominator equal. Now we add the fractions. 4 5/10 + 1 6/10 = 5 11/10 = 6 1/10