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X is 3

Refer to picture

Answer:

[tex]\large\boxed{x=53^o}[/tex]

Step-by-step explanation:

We know: the sum of the measures of the angles of the triangle is equal to 180 °.

Therefore e have the equation:

[tex]x+45^o+82^o=180^o[/tex]

[tex]x+127^o=180^o[/tex]        subtract 127° from both sides

[tex]x=53°[/tex]

Answer:

x = 14

Step-by-step explanation:

3x+2x-7=2x+35

then solve for x

Answer:

x = 14

Step-by-step explanation:

We are given that A, B and C are collinear points and B is in between A and C.

The length from A to B is [tex] 3 x [/tex], length from B to C is [tex] 2x - 7 [/tex] and AC is [tex] 2 x + 35 [/tex].

We are to find the value of x.

[tex] A B + B C = A C [/tex]

[tex] 3 x + 2 x - 7 = 2 x + 3 5 [/tex]

[tex] 3 x + 2 x - 2 x = 3 5 + 7 [/tex]

[tex] 3 x = 4 2 [/tex]

[tex] x = \frac { 4 2 } { 3 } [/tex]

x = 14

To simplify the expression, combine the exponents and evaluate the values to get the simplified expression 1/12.

To simplify the expression, we can combine the exponents of the same base. Let's break it down step-by-step:

So, the simplified expression is 4-1 * 3-1 * 40. Any number raised to the power of 0 is equivalent to 1, so the expression can be further simplified to 4-1 * 3-1 * 1. Finally, we can evaluate the values: 4-1 = 1/4, and 3-1 = 1/3.

Therefore, the simplified expression is (1/4) * (1/3) = 1/12.

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The expression [tex]\(\frac{4^{-3} \times 3^4 \times 4^2}{3^5 \times 4^{-2}}\)[/tex] simplifies to [tex]\(\frac{4}{3}\).[/tex]

To simplify the expression [tex]\(\frac{4^{-3} \times 3^4 \times 4^2}{3^5 \times 4^{-2}}\)[/tex], follow these steps:

So the simplified expression is [tex]\(\frac{4}{3}\)[/tex] .

Corrected question:

What is the simplified expression for [tex]\(\frac{4^{-3} \times 3^4 \times 4^2}{3^5 \times 4^{-2}}\)[/tex]

Answer:

Step-by-step explanation:

4b-1=b

3b-1=0

3b=1

b=1/3

24b=

24(1/3)=

8

Equations are expression separated by an equal sign. The value of 24b if 4b-1 = b is 8

Equations are expression separated by an equal sign

Given the expresion

4b - 1 = b

Find the value of "b"

4b - b = 1

3b = 1

b = 1/3

Determine the value of 24b

24b = 24(1/3)

24b = 8

Hence the value of 24b if 4b-1 = b is 8

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Answer:

x=5, y=22.36, z=11.18

Step-by-step explanation:

Use mean extremes

10^2=sqrt(20x)

Solving x = 5

for y:

y=sqrt(20(20+5))=22.36

for z:

z=sqrt(5(20+5))=11.18

Answer:

[tex]\large\boxed{(x+1)^2+(y-7)^2=100}[/tex]

Step-by-step explanation:

The equation of a circle in standard form:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

(h, k) - center

r - radius

We have the center (-1, 7) and the radius r = 10. Substitute:

[tex](x-(-1))^2+(y-7)^2=10^2\\\\(x+1)^2+(y-7)^2=100[/tex]

Answer:

Step-by-step explanation:

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ANSWER

A. (x+4)

EXPLANATION

The given binomial is

[tex] {x}^{2} + 12x + 32[/tex]

Split the middle term:

[tex] {x}^{2} + 8x + 4x + 32[/tex]

Factor;

[tex]x(x + 8) + 4( x + 8)[/tex]

Factor further;

[tex](x + 8)(x + 4)[/tex]

Therefore

[tex](x + 4)[/tex]

is a factor.

5/15 or 1/3 would be the correct answer

Answer:

1725

Step-by-step explanation:

50+65=115 divided by 2 =57.5     57.5*30H= 1725

d=4n

315=5n+10d

315=5n+40n

315=45n

315/45=n

7=n

d=4n

d=4(7)

d=28

28 dimes and 7 nickels

Answer:

145°

Step-by-step explanation:

The angle is 90°+55°=145°

Answer: 145°

Step-by-step explanation:

The angle of straight lines is always 180°, so I took 180 and subtracted 55 from it, and then 90 to get 35. I got 90 because the x and y axis are perpendicular to each other, and the angle between perpendicular lines is always 90. 35° is the angle of the small un marked section to the left of the circles, so to get the angle of the circle-like line, I did 180-35 to get 145°.

Answer:

2

Step-by-step explanation:

3(2)+30=36

Answer:

-36

Step-by-step explanation:

We don't need one, do we? It's just simple math.

An equation is formed of two equal expressions. The number which when divided by -3 gives 12 as the result is -36. The correct option is A.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the number be represented by x.

Given that the number when divided by -3 gives 12 as the result. The given situation can be written in the form of an equation as,

x/-3 = 12

Solving the equation to get the value of x,

x/-3 = 12

x = 12 × -3

x = -36

Hence, the number which when divided by -3 gives 12 as the result is -36.

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Answer: 20

Step-by-step explanation:

6/30 = 0.2

0.2 times 100 = 20

Final answer:

After setting up a proportion and solving the equation 0.30x = 6, we find that there are 20 students in Mrs. Rutherford's class.

Explanation:

To determine how many students are in Mrs. Rutherford's class when 30% like chocolate ice cream and we know that 6 students like chocolate ice cream, we can set up a proportion where 30% (or 0.30) of the total number of students (which we will call x) is equal to 6. Therefore, the equation to find x is 0.30x = 6.

To solve for x, we divide both sides of the equation by 0.30:

0.30x = 6

x = 6 / 0.30

x = 20

So, there are 20 students in Mrs. Rutherford's class.

Answer:

The product of the slopes of line a and line is -1.

Perpendicular lines a and b intersect at a right angle, or 90 degrees. This is independent of whether they are increasing or decreasing, or their steepness on a graph.

The statement about lines a and b that is true when they are perpendicular is that they form a 90-degree angle with each other. The concept of perpendicularity in geometry refers to lines, planes, or surfaces that intersect at a right angle.

Terms like increasing or decreasing line or the steepness of a line do not apply here as they pertain to the slope of the line in the context of a graph, which is distinct from the concept of perpendicularity.

For example, saying line A is a decreasing line while line B is an increasing line, does not describe their perpendicular relationship. Instead, they intersect or meet at a right angle (90 degrees), proving their perpendicular nature.

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The equation doesn't provide enough context to definitively solve for 'r'. Given the original equation r16 ≥ 8, r shouldn't be less than 1 if only integer values are accepted.

In Mathematics, the original equation provided here, 'r16 ≥ 8', seems to indicate that a value 'r' is being multiplied by 16 and the product should be greater than or equal to 8. To solve for 'r', you would normally divide both sides of the equation by 16. However, each sub-question provided 'r ≥ 2', 'r ≤ 2', 'r ≥ 128', and 'r ≤ 128', indicates different potential solutions for 'r'. Without the proper context or further information it is difficult to properly solve for 'r'. Given the original equation, if only integer values are allowed, 'r' should not be less than 1 to maintain the inequality. Further clarification on the nature of 'r' and the context of the question is highly recommended.

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Answer:

91,125

Step-by-step explanation:

V=Bh

V=l*w*h

V=45*45*45

V=2,025 *45

V=91,125

Answer:

50,505 cm

Step-by-step explanation:

In order to calculate this you just have to calculate the length necessary to create a wooden box with the volume of 454545 cubic centimeters, and now you just have to calculate since you have the base of the area, measuring 3 cm by 3 cm, that would be 9 square centimeters, so you just have to divide the desired volume by 9 square centimeters:

454545/9=50,505 cm

So the length of the wooden box should be 50,505 cm in order to have a 454545 cubic centimeters wooden box.

f(x)= 9x^3+ 2x^2 -5x+ 4

g(x)= 5x^3 -7x+ 4

f(x) - g(x)

= (9x^3+ 2x^2 -5x+ 4) - (5x^3 -7x+ 4)

= 9x^3+ 2x^2 -5x+ 4 -5x^3+ 7x -4

= (9x^3 -5x^3)+ 2x^2+ (7x -5x)+ (4-4) (combine like terms)

= 4x^3+ 2x^2+ 2x

= 2x* (2x^2+ x+ 1)

The final answer is 2x* (2x^2+ x+ 1).

The final answer in factored form is 2x(x² + x + 1).

f(x) = 9x³ + 2x² - 5x + 4

g(x) = 5x³ - 7x + 4

To find f(x) - g(x) ,, we subtract g(x) from f(x) term by term.

f(x) - g(x) = (9x³ + 2x² - 5x + 4) - (5x³ - 7x + 4) = 4x³ + 2x² + 2x

The final answer in factored form is 2x(x² + x + 1).

Answer: There are 180 dogs in the shelter.

Step-by-step explanation:

Let be "c" the number of cats in the shelter and "d" the number of dogs in the shelter.

You know that the total number of dogs and cats in the animal shelter is 275. Then you can express this with:

[tex]d+c=275[/tex]

If the number of cats is 5 more than one half of the number of dogs, you can express it with:

[tex]c=\frac{d}{2}+5[/tex]

Then, substitute [tex]c=\frac{d}{2}+5[/tex] into [tex]d+c=275[/tex] and solve for "d" to calculate the number of dogs that are in the shelter. Then:

[tex]d+c=275\\\\d+\frac{d}{2}+5=275\\\\d+\frac{d}{2}=275-5\\\\\frac{2d+d}{2}=270\\\\\frac{3d}{2}=270\\\\3d=270*2\\\\d=\frac{540}{3}\\\\d=180[/tex]

Answer:

x=1

Step-by-step explanation:

8x+4y=12y

-4y         -4y

8x=8y

x=1

Answer:

9/5 = 9 x  1/ 5

Answer:

9/5 = 9 * 1/5

Step-by-step explanation:

p(x) * r(x) = ab^x * cd^x

p(x) * r(x) = (a*c)*(b^x*d^x)

p(x)*r(x) = ac(bd)^x

For the last step, I used the rule that (ab)^x = a^x*b^x

The product of two exponential functions p(x) = ab^x and r(x) = cd^x is calculated by following the rules of exponents in mathematics, resulting in p(x) * r(x) = a * c * (bd)^x

The student is asking for the product of two exponential functions. If p(x) = ab^x and r(x) = cd^x, their product can be calculated as follows:

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Answer:

Step-by-step explanation:

a1 = 3(1) - 7 = - 4

a2 = 3(2) - 7 = -1

d = a2 - a1

d = -1 - (-4)

d = -1 + 4

d = 3

a60 = 3(60) - 7

a60 = 180 - 7

a60 = 173

n = 60

Sum = (a1 + a60) * n / 2

Sum = (-4 + 173) * 60/2

Sum = (169)*30

Sum = 5070

==================

Just to check, we'll use the second summation formula

d = 3

n = 60

a1 = -4

Sum = (2*a1 + (n - 1)*d )*n / 2

Sum = (2*(-4) + (60 -1)*3)* 60/2

Sum = (-8 + 59*3) * 30

Sum = (177 - 8)*30

Sum = 169 * 30

Sum = 5070

Same answer.

Answer:

Step-by-step explanation:

Tracey Earns in week= $102.45

Tracy=2x-12.45

102.45=2x-12.45

2x= 102.45+12.45

2x=114.90

x= 114.90/2

x=$57.45

Kayla earns 57.45 dollars

The equation is n = (102.45 + 12.45) x 2.

And Kayla earns $229.8.

Two algebraic expressions having same value and symbol '=' in between are called as an equation.

Given:

In a week, Tracey earns $12.45 less than twice the amount Kayla earns. Tracy earns $102.45.

Let n be the amount Kayla earns.

Then,

Kayla earns,

n = (102.45 + 12.45) x 2

n = $229.8

Therefore, Kayla earns $229.8.

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Answer: GCF = x

Step-by-step explanation:

x(x^3/x + x^2/x + -6x/x)

x(x^2 + -6)

x(x - 2)(x + 3)

Answer:

x(x + 3)(x - 2)

Step-by-step explanation:

Factor out x from each term

= x(x² + x - 6)

To factor the quadratic

Consider the factors of the constant term (- 6) which sum to give the coefficient of the x - term (+ 1)

The factors are + 3 and - 2, since

+ 3 × - 2 = - 6 and + 3 - 2 = + 1, hence

x² + x - 6 = (x + 3)(x - 2)

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

x³ + x² - 6x = x(x + 3)(x - 2) ← in factored form

Answer:

The answer to 4-3 is 1.

Step-by-step explanation:

The quadratic code '4 - 3' corresponds to the mathematical expression "4 minus 3," which equals 1.

The quadratic equation '4 - 3' is a simple algebraic equation that can be decoded as follows:

Start with the number 4.

Subtract 3 from it.

So, the decoded mathematical expression is:

4 - 3 = 1

The result is 1.

Therefore, the quadratic code '4 - 3' corresponds to the mathematical expression "4 minus 3," which equals 1.

This demonstrates how to decode and interpret a simple algebraic expression, showing that when you subtract 3 from 4, the result is 1.

It's a basic example of performing arithmetic operations on numbers.

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The probable question may be:

Decode the quadratic expression '4 - 3​' to reveal the mathematical expression it represents. Provide the complete mathematical expression that corresponds to the given quadratic code.

Answer:   c) 286.5 in²

Step-by-step explanation:

S.A.= 2π r · h

      = 2π (7.3/2) · 12.5

      = 2π (3.65) (12.5)

      = 286.5