B = 54°, c = 15, a =_?___ (Round answers to
the nearest hundredth.)

Answer:

your question is wrong, it's not an expression but a quadratic equation. if so your answer will be x=8±2√7

Step-by-step explanation:

by using, completing the square method

x²-16x-4=0

x²-16x=4

x²-16x+(-16×0.5)²=4+(16×0.5)²

x²-16x-8²=4+8²

(x-8)²=68

x-8=√68

x-8=±2√7

so x=8±2√7

please next time write the correct question

The value of c/b when the quadratic equation x² + 1300x + 1300 is written in the form (x + b)² + c, b and c being constants is -648.

The given quadratic expression needs to be expressed using the perfect square method to be of the form (x + b)² + c.

We express the quadratic expression x² + 1300x + 1300 using the perfect square method following these steps:

x² + 1300x + 1300

= x² + 2x(1300/2) + (1300/2)² + 1300 - (1300/2)²

= x² + 2x(650) + (650)² + 1300 - (650)²

= (x + 650)² + 1300 - 422500

= (x + 650)² - 421200.

Comparing this to (x + b)² + c, we get:

b = 650, and c = -421200.

Therefore, the value of c/b = (-421200)/650 = -648.

Therefore, the value of c/b when the quadratic equation x² + 1300x + 1300 is written in the form (x + b)² + c, b and c being constants is -648.

The question seems improper. The proper question is:

" The quadratic x^2+1300x+1300 can be written in the form (x + b)^2+c, where b and c are constants. What is c/b?"

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The range of the function is f(x) <= 4

The attached graph is the missing piece in the question

The function f(x) is given as:

The above means that, the value of the function do not exceed y = 4

Hence, the range of the function is f(x) <= 4

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The smallest of the even integers is 8.

It is a well-known fact that the sum of the first n odd numbers is n^2. This makes the sum of the first 8 odd numbers equal to 64.

Let n be equal to the smallest of the 5 even integers. Then (n+2) is the next highest, (n+4) even higher, and so on.

This sets up the equation n+(n+2)+(n+4)+(n+6)+(n+8)+4=64

Now we solve:

5n+24 = 64

5n = 40

n = 8

The smallest of the even integers is 8.

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The two real values that are not in the domain of the composition are x = 2 and x = -2.

Here we have:

f(x) = 1/x

g(x) = x^2 - 4

The composition is:

f°g = f(g(x)) = 1/(x^2 - 4)

The two values that are not in the domain are the values of x such that g(x) = 0, because we can't divide by zero.

g(x) = 0 = x^2 - 4

4 = x^2

±√4 = x

±2 = x

So g(x) = 0 when x = 2 or x = -2, so these are the two real values that are not in the domain of f°g.

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Answer:

A

Step-by-step explanation:

cone volume equals

V=π/3r²h

(1782=π/3r²h) multiplied by 3 to get rid of the denominator

5346=πr²h

cylinder v=πr²h by substitution the volume would be the same as cone 5346

Answer:

awnser D is the only function

The value of the washing machine after 6 years with 20% depreciation every year is $78.64.

Depreciation is the practice of subtracting a business asset's cost over a number of years as opposed to just one.

Depreciation is used to adjust the cost of a productive asset with a longer-than-year-long useful life to the income generated by operating the asset. The expense of the asset is typically dispersed across the years that it is utilized.

Calculation for the asset value after depreciation of 20% every year.

The purchasing cost of washing machine is $300.

The rate after 6 years is-

Rate = purchased price×[tex](1-r)^{t}[/tex]

       = 300×[tex](1-0.2)^{6}[/tex]

       = 300×[tex]0.8^{6}[/tex]

       = 78.64

The cost of washing machine after 6 years will be $78.64.

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Answer:

Step-by-step explanation:

Answer:

inverse variation: xy=20

Step-by-step explanation:

Direct Variation is when y increases as x increases and is linear

Inverse Variation is when y decreases as x increases although it's not linear and the x and y has a constant product.

By observing the table, you'll see as x increases, y decreases. You'll also notice a constant product of 20 between x and y. (2 * 10) =  20. (4 * 5) = 20. ( (8 / 1) * (5 / 2) = 40/2 = 20))... and so on. So the function can be represented as xy = 20

Answer:

x = 1

y = -2

Step-by-step explanation:

x = 19 + 9y

3x- 3y = 9

________

3(19+9y)-3y=9

y=-2

x=19+9(-2)

x=1

(1,-2)

Answer:

[tex] - x = - 1 - 9y \\ \frac{ - x}{ - 1} = \frac{ - 1}{ - 1} - \frac{9}{ - 1} \\ x = 1 + 9y...(3) \\ 3(1 + 9y) - 3y = 9 \\ 3 + 27y - 3y = 9 \\ 3 + 24y = 9 \\ 24y = 9 - 3 \\ 24y = 6 \\ \frac{24y}{24} = \frac{6}{24} \\ y = \frac{1}{4} \\ \\ \\ \\ x = 9( \frac{1}{4} ) + 1 \\ x = \frac{9}{4} + 1 \\ x = \frac{13}{4} [/tex]

Step-by-step explanation:

ATTACHED IS THE SOLUTION!

The value of DF = 20.

Two objects are similar if they have the same shape, or one has the same shape as the mirror image of the other.

Given:

Using theorem

If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.

ΔSDF/Δ RTY = (SD/RT)= (DF/TY)=  (FS/ YR)

ar ΔSDF² / ar  ΔRTY² = 16/81

SD/ RT = 4/9

SD = 4x,  RT= 9x

SD= 8

4x = 8

x = 2

So,

RT=  9*2 = 18

SF = RT -2

SF = 16

(SD/RT)= (FS/ YR)

8 / 18 = 16/ YR

YR= 36

TY= 9 +RY = 45

(DF/TY)=  (FS/ YR)

DF / 45= 16/ 36

DF=20

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The set of real numbers for the equation x – 2 = √(2x – 1) will be 5.

The solution of the equation means the value of the unknown or variable.

The equation is given below.

x – 2 = √(2x – 1)

Square on both side, then we have

               (x – 2)² = 2x – 1

         x² – 4x + 4 = 2x – 1

         x² – 6x + 5 = 0

   x² – 5x – x + 5 = 0

x(x – 5) – 1(x – 5) = 0

       (x – 5)(x – 1) = 0

                         x = 1, 5

The set of real numbers for the equation x – 2 = √(2x – 1) will be 5.

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Answer: Option 2

Step-by-step explanation:

The vertex must have a y-coordinate of 5, so eliminate options 3 and 4.

Also, since there must be a maximum, the coefficient of [tex]x^2[/tex] must be negative. So, eliminate option 1.

This leaves us with option 2.

There are 120 five digit numbers that can be created

The digits are given as:

2, 3, 5, 7 and 8

Since there are no conditions, and the digits cannot be repeated.

Then the number of digits is:

Digits = 5!

Expand

Digits = 5 * 4 * 3 * 2 * 1

Evaluate

Digits = 120

Hence, there are 120 five digit numbers that can be created

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The volume of the sphere is 2308.4 mm³

From the question, we are to determine the volume of the sphere

The volume of a sphere is given by the formula

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

Where V is the volume

and r is the radius

From the given information,

Diameter, d, of the sphere = 16.4 mm

r = 16.4/2

r = 8.2 mm

∴ [tex]V=\frac{4}{3}\times 3.14 \times 8.2^{3}[/tex]

V = 2308.394

V ≅ 2308.4 mm³

Hence, the volume of the sphere is 2308.4 mm³

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The graph of the inequality will be B. on a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the right of the line is shaded.

It can be deduced that the coordinates satisfy the equation of the line.

3y = 2x - 12

Divide through by 3.

y = 2/3x - 4.

The slope is 2/3.

In conclusion, the correct option is B.

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Answer:

b

Step-by-step explanation:

Using proportions, the percentage change in the cost of manufacturing the kitchen cabinet was a increase of 5.5%.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The standard cost is given as follows:

S = 250 + 120 + 60 = $430.

After the increases, the price will be given as follows:

S = 250 x 1.1 + 120 x 1.08 + 60 x 0.82 = $453.8.

The price increased. The percent change, given by the change divided by the initial value, is:

P = 23.8/430 x 100% = 5.5%.

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Answer:

C. 0≤x≤7

Step-by-step explanation:

It is not choice D. because it has y instead of x. It is supposed to be x because it is asking for domain.

Hope this helps!

The value of P(A and C) is 0.18

From the tree diagram, we have the following probability values:

P(A) = 0.6

P(C) = 0.3

The probability P(A and C) is then calculated as:

P(A and C) = 0.6 * 0.3

Evaluate

P(A and C) = 0.18

Hence, the value of P(A and C) is 0.18

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The angle based on the information given about the rail is 163°.

From the information given, the value of angle 2 will be:

17° + x = 180° (angle on a straight line)

Collect like terms

x = 180° - 17°

x = 163°

In this case, it should be noted that angle 1 and 2 are alternate angles. Therefore, angle 1 will be 163°.

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Answer:

211.68 miles

Step-by-step explanation:

21.6 x 9.8

The value of the side b and c will be 58.57 units and 36.86 units, and angle ∠B will be 107°.

Let the triangle ABC, with side measures |BC| = a. |AC| = b. |AB| = c.

Then by the sine law, we have

[tex]\rm \dfrac{\sin\angle A}{a} = \dfrac{\sin\angle B}{b} = \dfrac{\sin\angle C}{c}[/tex]

The sum of angles of triangle is 180°.

∠A + ∠B + ∠C = 180°

36° + ∠B + 37° = 180°

                  ∠B = 107°

Then the side b will be

sin 36° / 36 = sin 107° / b

                b = 58.57 units

Then the side c will be

sin 36° / 36 = sin 37° / c

                c = 36.86 units

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Answer:

Please review the equation format.  I made an assumption (below) for this answer.

-0.57

Step-by-step explanation:

5x2 45x 24 = 0 is not a quadratic formula,

5x^2 + 45x + 24 = 0 is, however.  Also, it gives -.8.43 as one solution.  The other is −0.569351, or -0.57 to the nearest hundredth.

The other solution of the given quadratic equation would be -0.57

Quadratic Equation

An algebraic equation of the second degree in x is known as a quadratic equation. The quadratic equation is written as ax² + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.

The given quadratic equation is,

5x² + 45x + 24 = 0

Here,

a = 5

b = 45

c = 24

Applying the Quadratic Formula

The quadratic formula for the two roots of a quadratic equation is given as,

[tex]x=\frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex]       ........... (1)

and [tex]x=\frac{-b+\sqrt{b^{2}+4ac } }{2a}[/tex]   ............ (2)

Substituting the values of a, b, and c in equation (1), we get,

x = -8.43

Calculating the Second Root

Now, the other solution can be found by substituting the values of a, b, and c in the equation (2),

[tex]x=\frac{-45+\sqrt{45^{2}+4(5)(24) } }{2(5)}[/tex]

[tex]x=\frac{-45+\sqrt{(2505) } }{10}[/tex]

[tex]x=-0.57[/tex]

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Answer:

A. Scalene

E. Obtuse

Step-by-step explanation:

Obtuse are angles that are greater than 90°

Scalene is not congruent sides.

Answer:

h(x) = 2^(x) - 1.

Step-by-step explanation:

Let's look at each equation:

f(x) = -3x +7, Well as x increases, since it's multiplication, there are "going to be more" -3's, so it's going to be decreasing.

g(x) = -4(2^x). While 2^x is increasing, because "there are going to be more 2's multiplied by each other" as x increases, it's being multiplied by a negative number, so it's actually going to be decrasing

h(x) = 2^(x) - 1. Here's it's going to be increases as x goes towards infinity because "there are going to be more 2's multiplied by each other", and there isn't any negative sign, while there is a negative 1, it's constant, so the overall value will be increasing

Answer:

x = 4

Step-by-step explanation:

Since they are parallel, we use the formula  

[tex]\frac{part}{part} = \frac{part}{part}[/tex]

[tex]\frac{14}{x} =\frac{7}{2}[/tex]

7x = 28

x = 4

Answer:

9

Step-by-step explanation:

Because line PQ and line PR are both tangent to circle S, it would result in them being equal. So first to find PQ, you would have to find the value of variable x. To do this you would set both equations equal to each other and solve

6x - 9 = 2x + 3

-2x       -2x

4x - 9 = 3

    +9   +9

4x = 12

x = 3

Now you have to substitute 3 back into the equation for PQ:

6(3) - 9

18 - 9

= 9

Resulting in PQ = 9, to check your answer, take the value of x (3) and substitute it into PR and you should also get 9

2(3) + 3

6 + 3

= 9