As the guest was sneaking away, the groundskeeper was 4 feet (or 48 inches) away and pushed an 84-inch ladder onto the suspect. The very top of the ladder hit the guest on the top of the head. Find the height of the guest in inches the convert to feet.

Answer:

78.55cm^2

Step-by-step explanation:

area of a circle = πr^2

where π= 3.142

r= radius= diameter/2

radius= 10/2= 5

area= 3.142×(5)^2

area= 3.142×25=78.55cm^2

The value of b is 7 and a statement which is true about the x-intercepts of this function is that it can have up to 2 x-intersept.

The x-intercept is the point on the coordinate at which a line, curve or plane intersect with the x-axis.

Number 5 is the one x-intercept of the equation,

[tex]y = x^2 + bx + 10[/tex]

Put the value of y as 0 and x as 5 at the to find the value of b.

[tex]0= 5^2 + b\times 5 + 10\\0= 5^2 + b\times 5 + 10\\0=25+5b+10\\5b=35\\b=7[/tex]

Thus, the value of b is 7.

The given equation is a quadratic equation, and a quadratic equation may have 2 x-intercept. Thus, the true statement is that x-intercepts of this function can be up to 2.

Hence, the value of b is 7 and a statement which is true about the x-intercepts of this function is that it can have up to 2 x intercept.

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Answer:

18 centimeters

Step-by-step explanation:

Divide the circumference by π, or 3.14 for an estimation. The result is the circle's diameter.

Divide the diameter by 2.

There you go, you found the circle's radius

[tex]\boxed{ x= 2}[/tex]

[tex]4x+3=3x+5[/tex]

Subtract 3 from both sides :

[tex]4x + 3 = 3x + 5[/tex]

[tex]4x + 3-3 = 3x + 5-3[/tex]

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

Subtract 3x from both sides :

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

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

[tex]x = 2[/tex]

[tex]\sf{\qquad\qquad\huge\underline{{\sf Answer}}}[/tex]

The value that satisfies the first degree equation is: x = 2.

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf Verification:[/tex]

[tex] \qquad \sf \dashrightarrow42 + 3 = 32 + 5[/tex]

[tex] \: \: \qquad \sf \dashrightarrow 8 + 3 = 6 + 5[/tex]

[tex] \: \: \qquad \sf \dashrightarrow11 = 11[/tex]

Solving a first degree equation

The objective of the problem is to know what is the number that allows the stated equality to be fulfilled, for this it is necessary to clear the value of x.

The formulation is first degree:

[tex] \: \: \: \: \: \: \: \: \: \: \: \boxed{ \Rrightarrow\bf 4x + 3 = 3x + 5}[/tex]

The variables must be grouped in the same term, in this case we will do it in the left term, and the constants (numbers) in the right.

1) Subtract -3x from both terms:

[tex] \qquad \sf \dashrightarrow4x + 3 - 3x = 3x - 3x + 5[/tex]

[tex] \qquad \sf \dashrightarrow \: x + 3 = 5[/tex]

2) Subtract three units for each term:

[tex] \qquad \sf \dashrightarrow \: x + 3 - 3 = 5 - 3[/tex]

[tex] \qquad \sf \dashrightarrow \: {x =2 \: ✔}[/tex]

I hope I've helped : )

Answer:

-2

Step-by-step explanation:

3(a+1.5)=-1.5

a+1.5 = - 1.5/3 = - 0.5

a = - 0.5 - 1.5 = - 2

Answer:

Step-by-step explanation:

3a + 4.5 = -1.5

3a = -6

a = -2

Answer:

y=ab^x

y=6.0.8^x

Step-by-step explanation:

find exponential function by substituting given values into y=ab^x and the solve

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[tex]\blue{\textsf{\textbf{\underline{\underline{Question:-}}}}[/tex]

             Solve x²-5x+6

[tex]\blue{\textsf{\textbf{\underline{\underline{Answer:-}}}}[/tex]

(x-2)(x-3)

[tex]\blue{\textsf{\textbf{\underline{\underline{How\:to\:Solve:-}}}}[/tex]

                      First, we think of two numbers such that

     If we multiply them, we'll get 6

      If we add them, we'll get -5

These numbers are -2 and -3.

Write them here:

(x-2)(x-3)

Now, how do we get (x-2)(x-3) from x(x-2)-3(x-2)?

Notice that (x-2) is the common term, so we factor it out:

(x-2)

And now, we write the other two terms that are left in the parentheses:

(And the terms left are x and -3)

(x-2)(x-3)

Notice that we ended up with the same answer.

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Recall the Maclaurin expansion for cos(x), valid for all real x :

[tex]\displaystyle \cos(x) = \sum_{n=0}^\infty (-1)^n \frac{x^{2n}}{(2n)!}[/tex]

Then replacing x with √5 x (I'm assuming you mean √5 times x, and not √(5x)) gives

[tex]\displaystyle \cos\left(\sqrt 5\,x\right) = \sum_{n=0}^\infty (-1)^n \frac{\left(\sqrt5\,x\right)^{2n}}{(2n)!} = \sum_{n=0}^\infty (-5)^n \frac{x^{2n}}{(2n)!}[/tex]

The first 3 terms of the series are

[tex]\cos\left(\sqrt5\,x\right) \approx 1 - \dfrac{5x^2}2 + \dfrac{25x^4}{24}[/tex]

and the general n-th term is as shown in the series.

In case you did mean cos(√(5x)), we would instead end up with

[tex]\displaystyle \cos\left(\sqrt{5x}\right) = \sum_{n=0}^\infty (-1)^n \frac{\left(\sqrt{5x}\right)^{2n}}{(2n)!} = \sum_{n=0}^\infty (-5)^n \frac{x^n}{(2n)!}[/tex]

which amounts to replacing the x with √x in the expansion of cos(√5 x) :

[tex]\cos\left(\sqrt{5x}\right) \approx 1 - \dfrac{5x}2 + \dfrac{25x^2}{24}[/tex]

The distance from point P to the foot of the flagpole is 13.42m. So, The height of the flagpole will be 17.7 m.

Trigonometric ratios for a right-angled triangle are from the perspective of a particular non-right angle.

In a right-angled triangle, two such angles are there which are not right-angled(not of 90 degrees).

The slanted side is called the hypotenuse.

From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called the base.

We know that

[tex]tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}[/tex]

Let x be the distance from point P to the foot of the flagpole.

So, From point P the height h of the flagpole will be

[tex]tan(53) = \dfrac{height}{x}\\\\tan(53) x = h\\\\h = 1.32x[/tex]

From point Q, the height h will be

[tex]tan(28) = \dfrac{height}{20+x}\\\\tan(28) (20+x )= h\\\\h = 0.53 (20+x )[/tex]

From both values of h, we get

x = 13.42

Put the value of x in the first value of h,

h = 1.32 ( 13.42)

h = 17.7

Hence, the height of the flagpole will be 17.7 m.

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Answer:

D. None of these

Step-by-step explanation:

(5×10^8)(4×10^3)

=20 × 10^11

All the terms are being multiplied. There is no distributive property (FOIL) here. Rearrange the numbers in any order that helps you.

5 × 4 × 10^8 × 10^3

Add exponents to multiply the 10's.

and in proper scientific notation, one last change would give you

2.0 × 10^12

The consumption of electricity in May based on the model will be 1225kw.

The model that's given to calculate the consumption is:

C = 1200 + 5t

May = 5th month

The consumption in May will be:

C = 1200 + 5t

C = 1200 + 5(5)

C = 1200 + 25

C = 1225Kw

In conclusion, the consumption of electricity in May based on the model will be 1225kw.

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Answer:

52 units^2

Step-by-step explanation:

Given:-

Length(L): 4

Width(W): 3

Height(H): 2

Surface area = 2(LW+WH+HL)

2(4×3+3×2+2×4)

2(12+6+8)

52 units^2

Hope this answers your question!!

Answer:

6h

Step-by-step explanation:

If Olivia teaches 6 classes that are 1 hour, she teaches 6×1 is 6 hours.

If the classes are two hours, she teaches 6×2 is 12 hours.

Try with numbers to see what math operation you are doing. Its times.

6×h is written 6h

6h is the  expression that shows the total number of hours she teaches

An expression is combination of variables, numbers and operators.

Given,

Each painting class Olivia teaches is h hours long.

The number of classes teached by Olivia in a week is 6.

We need to find an expression that shows the total number of hours she teaches

6h is the required expression.

h is the variable because its value will be changed.

Hence, 6h is the  expression that shows the total number of hours she teaches

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Answer:

1 = 10

Step-by-step explanation:

0.5 x X = 15

15/0.5 = 30

30/3 = 10

Answer:

Step-by-step explanation:

I don't know what is meant by "analyze the function," but I can draw the functions.

Answer:

17/4

or

17 ÷ 4

Step-by-step explanation:

This equals 4.25.

hope this helps

have a good day

The quotient of seventeen and four in the mixed fraction form will be 4 ¹/₄. Then the correct option is A.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Convert the statement 'quotient of seventeen and four' into a mathematical expression. Then we have

⇒ 17 / 4

Convert the fraction number into a mixed fraction number, then we have

⇒ 17 / 4

⇒ 4 ¹/₄

The quotient of seventeen and four in the mixed fraction form will be 4 ¹/₄. Then the correct option is A.

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The missing options are given below.

A. 4 1/4      B. 4 3/4      C. 3 1/4      D. 3 3/4

Answer:

112.5 pi

Step-by-step explanation:

hi, to find this we need to know the formula for the area of a circle. it is:

a=pi*radius^2

so the radius is 30/2=15

now we can just plug 15 in to find the area.

a=pi*15^2

a=225pi

now, that is the area for the full circle, but here it is a semi circle, so we just divide 225 pi by 2 to get

112.5 pi, or 112.5π

Answer:

1/5x^4

Step-by-step explanation:

To change a negative exponent to a positive one, flip it into a reciprocal. This is what I have done here.

Answer:

D. 7

Step-by-step explanation:

42 + 70 = 112 stamps altogether.

112 can be divided by 2, 4, 7, 8, 14, 16, 28, 56

to be more simpler, since there are options, we can cross out the other numbers not shown in the options. then see that 6 and 10 are not divisible by 112, so cross them out. it will left with option A and option D.

option A is 2. if he uses two pages, then each page should have a total of 56 stamps. however, foreign stamps have an amount of 42 only, so it is quite impossible to fit in more than 42.

option D is 7. if he uses 7 pages, then each page could fit in 16 stamps.

so the answer will be option D.

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[tex]\blue\textsf{\textbf{\underline{\underline{Question:-}}}}[/tex]

3x²=75. What is x?

[tex]\blue\textsf{\textbf{\underline{\underline{Answer and How to Solve:-}}}}[/tex]

First, divide by 3 on both sides:-

x²=25       Next, take the square root of both sides:-

x=5, x=-5 (remember, x² =x times x (x times itself); 5 times itself gives 25, and -5 times itself also results in 25)

[tex]\dashrightarrow\bigstar\boxed{\boxed{\underline{\bold{So\:the\:value\:of\:x\:is\:5\:and\:-5}}}}\dashleftarrow[/tex]

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Considering the piece-wise function, the value of the function at x = 2, that is, g(2), is given by:

C. 1.

It is a function that has different definitions based on the input.

In this problem, the function is defined by:

Due to the equal sign, x = 2 is part of the second definition, hence:

g(2) = 2³ - 9(2)² + 27(2) - 25 = 1.

Which means that option C is correct.

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Answer:

no because nkow one can explain

Answer:

Slope = 1

Step-by-step explanation:

Step-by-step explanation:

The domain of the function is all real numbers less than or equal to −2 - FALSE;

The domain of the function is all real numbers less than or equal to 9 - FALSE;

The range of the function is all real numbers less than or equal to −2 - FALSE;

The range of the function is all real numbers less than or equal to 9 - TRUE.

PS. the domain is (-∝;+∝); the range is (-∝;9].

By definition of tangent,

tan(θ - x) = sin(θ - x) / cos(θ - x)

Expand the sine and cosine terms using the angle sum identities,

sin(x ± y) = sin(x) cos(y) ± cos(x) sin(y)

cos(x ± y) = cos(x) cos(y) ∓ sin(x) sin(y)

from which we get

tan(θ - x) = (sin(θ) cos(x) - cos(θ) sin(x)) / (cos(θ) cos(x) + sin(θ) sin(x))

Also recall the Pythagorean identity,

cos²(x) + sin²(x) = 1

from which we have two possible values for each of cos(θ) and sin(x):

cos(θ) = ± √(1 - sin²(θ)) = ± 3/5

sin(x) = ± √(1 - cos²(x)) = ± 12/13

Since there are 2 choices each for cos(θ) and sin(x), we'll have 4 possible values of tan(θ - x) :

• cos(θ) = 3/5, sin(x) = 12/13 :

tan(θ - x) = -56/33

• cos(θ) = -3/5, sin(x) = 12/13 :

tan(θ - x) = 16/63

• cos(θ) = 3/5, sin(x) = -12/13 :

tan(θ - x) = -16/63

• cos(θ) = -3/5, sin(x) = -12/13 :

tan(θ - x) = 56/33

Now

cos(ø-x)

sin(ø-x)

So

tan(ø-x)

Answer:

x=1.13

Step-by-step explanation:

isolate the variable and the numbers and solve.

The effective rate of interest is given by the same formula but with the disbursed amount which is $838.50.

Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.

Philippa took out an $860 discounted loan for a period of m months and the simple interest rate was 6%. The amount that was actually disbursed into her bank account was $838.50.

Then the effective interest rate of this loan, to the nearest 0.01% will be

So, from the question the interest that is deducted = $860-$838.50 = $21.50

Now, I = Prt/100

So, t = 100 (I/Pr) = 0.42 years = 5months

therefore m = 5months

So, the effective rate of interest is given by the same formula but with the disbursed amount which is $838.50.

I = Prt/100

Therefore, r = 100 (I/Pt) = 6.15%

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Answer:

a. 3

b. 12

c. In. and "

d. ft. and '

Step-by-step explanation:

c. 13in. or 13"

d. 13ft. or 13'