3 questions 40 points

The correct answer is that the focus is, (0,−2)

Answer:

The correct option is C.

Step-by-step explanation:

The given equation is

[tex]-\frac{1}{4}(y+2)^2=(x-1)[/tex]

Multiply both the sides by -4.

[tex](y+2)^2=-4(x-1)[/tex]            .... (1)

Where, (h,k) is vertex and (h+p,k) is focus.

The standard form of a parabola is

[tex](y-k)^2=4p(x-h)[/tex]              ..... (2)

From (1) and (2), we get

[tex]k=-2,h=1,4p=-4\Rightarrow p=-1[/tex]

The focus of the parabola is

[tex](h+p,k)=(1-1,-2)=(0,-2)[/tex]

The focus of the given parabola is (0,-2). Therefore the correct option is C.

You have to observe that [tex] x^4 [/tex] and 625 are both squares (of [tex] x^2 [/tex] and 25, respectively). So, you can use the "difference of square" pattern for factorization:

[tex] a^2-b^2 = (a+b)(a-b) [/tex]

to write

[tex] x^4 - 625 = (x^2+25)(x^2-25) [/tex]

Note that, again, [tex]x^2-25[/tex] is a difference of square:

[tex] x^2-25 = (x+5)(x-5) [/tex]

On the other hands, [tex] x^2+25 [/tex] admits no factorization, because it's a second-degree polynomial (thus a parabola) with no solutions.

So, the whole expression becomes

[tex] x^4 - 625 = (x^2+25)(x+5)(x-5) [/tex]

Angle (3x+31)° and angle (2x-6)° are supplementary angles. Then the value of the variable x is 31°.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

Angle (3x+31)° and angle (2x-6)° are supplementary angles. Then we have

(3x + 31)° + (2x - 6)° = 180°

5x + 25° = 180°

5x = 155°

x = 31°

Then the value of the variable x is 31°.

Your question was incomplete, probably the question was...

Find the value of x. Angles (3x+31)° and (2x-6)° are supplementary angles.

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The value of  x equals 31°.

The value of (x) can be found by solving the equation formed by the two angles in the given question:

Given angles:

Linear pair property:  The sum of the measures of two angles forming a linear pair is (180°).

Now,

Set up the equation: (3x + 31) + (2x - 6) = 180

=>  (3x + 2x) + (31 - 6) = 180

=> 5x + 25 = 180

Solve for (x):  5x = 155 =>  x = 31

Therefore, the value of (x) is 31°.

Disclaimer : I attached the image of complete question

The formula for 'w' in terms of the perimeter 'P' and length 'l' of the rectangle is w = (P - 2l)/2.

To solve for 'w' in the formula for the perimeter of a rectangle, P = 2(l + w), we need to isolate 'w' on one side of the equation.

P = 2(l + w)

First, distribute the 2 to both terms inside the parentheses:

P = 2l + 2w

Now, subtract 2l from both sides to move it to the other side of the equation:

P - 2l = 2w

Finally, divide both sides by 2 to solve for 'w':

w = (P - 2l)/2

Therefore, the formula for 'w' in terms of the perimeter 'P' and length 'l' of the rectangle is:

w = (P - 2l)/2

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A- Strong Positive

Hope this helps!

Answer:

A- Strong Positive

Hope this helps!

Step-by-step explanation:

we know that

f(3) is the value of the function when x is equal to 3

so

For x=3

see in the graph

f(3)=6

see the attached figure

therefore

the answer is

f(3)=6

According to the graph in the problem, f(3) = 6

In the graph we have curve and line. we look out for domain of 3

The domain of 3 is the point on the graph where x axis is 3. At this point we trace to the graph and find the corresponding value on the y axis

This gives the solution of the graph

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33%

Percentage = 49/149 * 100

                   = 32.88%

Round the answer:

                            = 33%

The correct answer would be diameter. A chord is a line segment connecting two points on a circle's circumference. When the chord passes through the center of a circle it is called a diameter.

Final answer:

The line segment that passes through the center of a circle and has both endpoints on the circle is called a diameter.

Explanation:

The line segment which passes through the center of a circle and has both endpoints on the circle is called a diameter.

A diameter is the longest chord in a circle and it divides the circle into two equal halves. It passes through the center, and any point on the circumference of the circle is equidistant from the center.

For example, in the circle below, AB is a diameter:

If we want to verify that g ( x ) is the inverse of f ( x ) we have to show that:

( f ° g ) = ( g ° f )

f ( g ( x ) )=  3 · ( 1/3 x ) = x

g ( f ( x ) ) = 1/3 · ( 3 x ) = x

Answer:

C ) 1/3 ( 3 x )

Answer:

Step-by-step explanation:

To verify if two functions are inverse, we have to find the composition of such functions, that is:

[tex]f(g(x))[/tex]; which results must be the variable [tex]x[/tex] to be inverse functions.

We know that: [tex]f(x)=3x;g(x)=\frac{1}{3}x[/tex].

Replacing on the composition:

[tex]f(g(x))=3(\frac{1}{3}x)=x[/tex]

Therefore, the expression that has to be used to verify that these functions are inverse is C.

Answer:

9.8

Step-by-step explanation:

Answer:

Its A. 9.8 on APEX hope this helps!!

Answer:

z-score will be:  7.741....  and it will be unusual.

Step-by-step explanation:

Human body temperatures have a mean of 98.20 degrees Fahrenheit and a standard deviation of 0.62 degrees Fahrenheit.

So here,  [tex]\mu= 98.20[/tex] and [tex]\sigma= 0.62[/tex]

Formula for z-score is:   [tex]z= \frac{X-\mu}{\sigma}[/tex]

Thus, the z-score for 103.00 degrees Fahrenheit will be.......

[tex]z(X=103.00)= \frac{103.00-98.20}{0.62}=7.741...[/tex]

As, here the z-score is more than 2 standard deviations above the mean, so 103.00 degrees Fahrenheit is unusual for human body temperature.

Answer:

Answer:

78 dollars /6.5 hours = 12 dollars .

Your rate is 12 dollars per hour.

Step-by-step explanation:

(A) Bella's TV ratio of sides: 36"/27" = 1.333...

Lenny's: 52"/29.25" = 1.777...

Bella's and Lenny's TVs are NOT similar - their side ratios are different. Bella's is 4:3 while Lenny's is close to 16:9.

(B) Bella's TV has an exact ratio of 4:3 (36/27=4/3) and so is the older type.

Lenny's TV has a ratio of 52"/29.25". Divide both 52 and 29.25 by 3.25 to get 16/9, or 16:9. So Lenny's is the newer type.

[tex]f(x)=x^4-2x^3+2x-1=x^4-x^3-x^3+x+x-1\\\\=x^3(x-1)-x(x^2-1)+1(x-1)\\\\=x^3(x-1)-x(x^2-1^2)+1(x-1)\\\\=x^3(x-1)-x(x+1)(x-1)+1(x-1)\\\\=x^3(x-1)+(x-1)(-x(x+1)+1)\\\\=(x-1)(x^3-x(x+1)+1)\\\\=(x-1)(x^3-x^2-x+1)\\\\=(x-1)[x^2(x-1)-1(x-1)]\\\\=(x-1)(x-1)(x^2-1)\\\\=(x-1)(x-1)(x^2-1^2)\\\\=(x-1)(x-1)(x-1)(x+1)[/tex]

[tex]Used:\\\\a^2-b^2=(a-b)(a+b)[/tex]

Answer:

I think the answer is false I am not A 100%sure but most likely false

Step-by-step explanation:

m = [tex]\frac{1}{2}[/tex],   (x₁ , y₁) = (-2, -4)

y - y₁ = m(x - x₁)

y -(-4) = [tex]\frac{1}{2}[/tex](x - (-2))

y + 4 = [tex]\frac{1}{2}[/tex](x +2)

y + 4 = [tex]\frac{1}{2}x[/tex] + 1

     y = [tex]\frac{1}{2}x[/tex] - 3

Answer: A

Answer:

Option D

Step-by-step explanation:

See the letters in the word deadline.

We have d and e repeated twice , and a,l,i,n once.

There are in total 8 letters

These 8 letters can be arranged in 8x7x6...1 = 8! ways

But since there are repititions of letters, we have 2! x 2! times repeated letters.

Hence we have to divide by 2!x2!

No of ways = [tex]\frac{8!}{2!*2!}[/tex]

Option D is right

For this case we have:

We define the following variable

x : Speed of the car in South direction

By definition, we know that:

[tex]Distance = Speed * Time[/tex]

For the car in north direction:

[tex]D1 = V1 * T1\\D1 = 50mph * 3h\\D1 = 150 miles[/tex]

For the car in south direction:

[tex]D2 = V2 * T2\\D2 = x * 3\\D2 = 3x[/tex]

The distance between both cars, after 3 hours, is:

[tex]D = D1 + D2[/tex]

So, we have:

[tex]345 = 150 + 3x[/tex]

Clearing x;

[tex]3x = 345-150\\3x = 195\\x = 65[/tex]

Thus, the speed of the car in the south direction is [tex]x = 65mph[/tex]

Answer:

Option B

Answer: B. 65 MPH

Step-by-step explanation:

[tex]a_1=4\\\\a_2=4+6=10\\\\a_3=10+6=16\\\\a_n=a_{n-1}+6,\ a_1=4[/tex]

Answer:

9.68E5

Step-by-step explanation:

Hey there! The correct answer is D.1 the reason is because the number of the data is plotted incorrectly.

≈ 3927 litres

the volume (V) of a cylinder is calculated using the formula

V = πr²h ( r is the radius of base and h is the height )

V= π × 100² × 250 = 7853981.634 cm³

[tex]\frac{1}{2}[/tex] V = 3926990.817 = [tex]\frac{3926990.817}{1000}[/tex] ≈ 3927 litres

[tex]\frac{w}{xy} = \frac{-6}{-3(4)} = \frac{-6}{-12} = \frac{1}{2}[/tex]

Answer: [tex]\frac{1}{2}[/tex]

Answer:

-1/2

Step-by-step explanation:

-4 x 10= -40

-5 x 16= -80

-40 is half of -80, so the fraction would be -1/2

Hope this helps! <3

The product of the given expression of a fraction is -1/2.

It is required to find the product.

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

Given:

The product of the given expression of fractions in simplified form.

According to given question we have,

[tex]\frac{-4}{5} *\frac{10}{16} \\\\=\frac{-40}{80} \\\\=\frac{-1}{2}[/tex]

so, the fraction would be -1/2.

Therefore, the product of the given expression of a fraction is -1/2.

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