April was asked to determine whether f(x)=x^3 -1 is even, odd, or neither. Here is her work:

Answer:

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

Step-by-step explanation:

To find the x-intercept, substitute 0 for y and solve for x. To find the y-intercept, substitute 0 for x and solve for y.

x-intercept(s): (2,0),(4,0)

y-intercept(s): (0,−16)

Answer:

D     f(x) = -2(x - 3)² + 2

Step-by-step explanation:

The y-intercept occurs at x = 0.

A

f(x) = 2x(x + 14) - 64

f(0) = -64     Not -16

B

f(x) = (x + 4)² + 2x

f(0) = 16     Not -16

C

f(x) = (x - 16)² + 4

f(0) = 260      Not -16

D

f(x) = -2(x - 3)² + 2

f(0) = -18 + 2 = -16   <-------------------- this is it

Finding the equivalent angle of [tex]\theta[/tex], the correct statements are given as follows:

Each angle on the second, third and fourth quadrants will have an equivalent on the first quadrant.

In this problem, the given angle is as follows:

[tex]\theta = \frac{5\pi}{4}[/tex]

It is on the third quadrant, as it is between pi and 1.5 pi, hence the equivalent on the first quadrant, also known as the reference angle, is given by:

[tex]\frac{5\pi}{4} - \pi = \frac{5\pi}{4} - \frac{4\pi}{4} = \frac{\pi}{4}[/tex]

The angle of 45º has equal sine and cosine, and tangent of 1, hence the correct statements are:

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Answer:

The measure of the reference angle is 45 degrees

tan(theta) = 1

Step-by-step explanation:

(i) The measures of the angles are m ∠ TCM = m ∠ TCQ = m ∠ CMQ = 90°.

(ii) The lengths of sides CM and CQ are 2 cm and 2√2 cm, respectively.

(iii) The angle between the side face and the base is equal to θ = cos⁻¹ (2 / MT) and the angle between the slant edge and the base is θ = cos⁻¹ [2√2 / √(4 + MT²)].

In this problem we have a right pyramid as line segment TC is perpendicular to the base PQRS, which means that any line coplanar with PQRS is perpendicular to line segment TC. i) the measures of the angles are m ∠ TCM = m ∠ TCQ = 90°.

Besides, the base PQRS is a square, which is equivalent to four right triangles with angles 45° - 45° - 90° and each triangle can be divided into two right triangles. Hence, the measure of the angle CMQ is 90°.

ii) The length of the sides can be found by the 45-45-90 theorem, which states that the length of the hypotenuse is √2 times the length of any of the legs:

CQ = (√2 / 2) · PQ

CQ = (√2 / 2) · (4 cm)

CQ = 2√2 cm

CM = (√2 / 2) · (2 √2 cm)

CM = 2 cm

iii)  The angle between the side face, one of them contains the line segment MT and the base can be found by the following inverse trigonometric relation: (value of the pyramid height is missing)

θ = cos⁻¹ (CM / MT)

θ = cos⁻¹ (2 / MT)            (1)

Similarly, the angle between the slant edge and the base is found by Pythagorean theorem and inverse trigonometric relation: (value of the pyramid height is missing)

θ = cos⁻¹ (CQ / TQ)

θ = cos⁻¹ [2√2 / √(QM² + MT²)]

θ = cos⁻¹ [2√2 / √(4 + MT²)]          (2)

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Answer:

Step-by-step explanation:

base=b=7.2yd

height =h=7yd

area of parallelogram = b x h

.                                    =7.2yd x 7yd

                                     =50.49[tex]yd^{2}[/tex]

Step-by-step explanation:

every single person will do 1/4 of each job.

divide into 2 group and each person will do half of one job and half of another.

Comparing it to a system of equations, the expression is represented as follows:

18g + 5.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

For this problem, we consider g as the variable. Then:

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Answer:

(f^−1)′(6)=1/(f'(f^-1(6)))

(f^−1)′(6)=1/(f'(f^-6)))

I hope this helps.

Answer:

25 / 4

Step-by-step explanation:

To find the left sum, you need to....
1.) Find Δx

2.) Find [tex]x_{k-1}[/tex]

3.) Find ∑[tex]^n_{k=1}f(x_{k-1})[/tex]Δx

4.) Solve for the left sum

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

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

Find inverse of given function :

[tex]\qquad❖ \: \sf \:y = \sqrt{x} + 7[/tex]

[tex]\qquad❖ \: \sf \: \sqrt{x} = y - 7[/tex]

[tex]\qquad❖ \: \sf \:x = (y - 7) {}^{2} [/tex]

Next, replace x with f-¹(x) and y with x ~

[tex]\qquad❖ \: \sf \:f {}^{ - 1} (x) = (x - 7) {}^{2} [/tex]

we got our inverse function.

Condition : x should be greater or equal to 7

because we will get same value of y for different x if we also include values less than 7.

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

[tex] \huge\mathbb{ \underline{SOLUTION :}}[/tex]

[tex]\longrightarrow\bold{f(x)= \sqrt{7}}[/tex]

To solve for the inverse of a function we begin by re-writing the function as an equation in terms of y.

[tex]\bold{Becomes,}[/tex]

Next step we switch sides for x and y variables and then solve for the y variable as shown below,

[tex]\longrightarrow\sf{y= \sqrt{x}+7}[/tex]

[tex]\bold{Then,}[/tex]

[tex]\longrightarrow\sf{x= \sqrt{y}+7}[/tex]

[tex]\small\bold{Solve \: for \: y \: and \: subtract \: 7 \: from \: the \: both \: }[/tex] [tex]\bold{sides,}[/tex]

[tex]\longrightarrow\sf{x-7= \sqrt{y}}[/tex]

[tex]\small\bold{Square \: both \: sides }[/tex]

[tex]\sf{(x-7)^2=(\sqrt{y})^2}[/tex]

[tex]\sf{(x-7)^2=y}[/tex]

We now re-write in function notation. Take note however that this is the inverse:

[tex]\bold{Where \: y}[/tex] [tex]\sf{=(x-7)^2 }[/tex]

[tex]\longrightarrow\sf{y= (x-7)^2 }[/tex]

[tex]\huge\mathbb{ \underline{ANSWER:}}[/tex]

[tex]\large\boxed{\sf A. \: \: f^{-1}(x)= (x − 7)^2 , \: for \: \underline > 7 }[/tex]

Answer:

The answer is cot(x)

Step-by-step explanation:

[tex] \tan(x) \csc {}^{2} (x) - \tan(x) [/tex]

Rewrite using trig identity

[tex] - \tan(x) + \csc {}^{2} (x) \tan(x) [/tex]

use the Pythagorean idea

[tex] \csc {}^{2} (x) = 1 + \cot {}^{2} (x) [/tex]

[tex] - \tan(x) + (1 + \cot {}^{2} (x)) \tan(x) [/tex]

simplify

[tex] \cot {}^{2} (x) \tan(x) [/tex]

use basic trigonometric identity

[tex] \tan(x ) = \frac{1}{ \cot(x) } [/tex]

simplify

[tex] \cot {}^{2} (x) \frac{1}{ \cot(x) } [/tex]

gives you

[tex] \cot(x) [/tex]

Hope it helps!

Answer:

[tex] \frac{3}{2} [/tex]

Step-by-step explanation:

From the attached photo, we can deduce:

(2,2) as (x1,y1)

(-2,-4) as (x2,y2)

Slope Formula =

[tex] \frac{y1 - y2}{x1 - x2} [/tex]

Now we can substitute these values into the formula to find the slope.

Slope of line =

[tex] \frac{2 - ( - 4)}{2 - ( - 2)} \\ = \frac{2 + 4}{2 + 2} \\ = \frac{6}{4} \\ = \frac{3}{2} (reduced \: to \: simplest \: form)[/tex]

Answer:

  m∠B ≈ 70.8°

Step-by-step explanation:

The Law of Cosines relates three sides of a triangle and the angle opposite one of them.

The law of cosines tells you ...

  b² = a² +c² -2ac·cos(B)

Solving for angle B, we get ...

  B = arccos((a² +c² -b²)/(2ac))

where 'a' and 'c' are the sides adjacent to the angle of interest. We want angle B, so we can fill this formula as follows:

  B = arccos((13² +11² -14²)/(2·13·11))

  B = arccos(94/286)

  B ≈ 70.812°

__

Additional comment

Another angle can be found using the Law of Sines.

  A = arcsin(sin(70.812°)×13/14) ≈ 61.281°

Then angle C is ...

  C = 180° -70.812° -61.281° = 47.907°

Answer:

D.= √29

Step-by-step explanation:

The distance between the two complex numbers,

Z₁=a+bi and Z₂=c+di in the complex plane is

[tex]d = \sqrt{(c - a) {}^{2} + (d - b) {}^{2} } [/tex]

In the Cartesian plane, the distance between, one point and other is (x₁,y₁) and (x₂,y₂) is the distance formula is

[tex]d = \sqrt{(X₂-X₁)² + (Y₂-Y₁)²} [/tex]

To find the distance between the two complex numbers using the formula

[tex]d = \sqrt{(c - a) {}^{2} + (d - b) {}^{2} } [/tex]

where,

[tex]d = \sqrt{(a - b) {}^{2} + (d - b) {}^{2} } \\ d = \sqrt{(6 - 4) {}^{2} + ( - 2 - 3) {}^{2} } \\ d = \sqrt{(2) {}^{2} + ( - 5) {}^{2} } \\ d = \sqrt{4 + 25} = \sqrt{29 \\ } [/tex]

¹³C₈ + ¹³C₉ as a single term from Pascal's Triangle is ¹⁴C₉

Pascal's triangle is a triangle written in such a way that it forms the coefficients of a binomial expansion. The coefficients of the terms are gotten through combination.

Combination is the number of ways r in which n objects can be selected. It is given by ⁿCₓ = n!/x!(n - x)!

Since we have ¹³C₈ + ¹³C₉ and we want to write it as a single term, we have that

So,  ¹³C₈ + ¹³C₉ =  13!/8!5! +  13!/9!4!

= 13!/(8! × 5 × 4!) +  13!/(9 × 8! × 4!)

= 13!/8!4![1/5 + 1/9]

= 13!/8!4! × [(9 + 5)/45]

= 13!/8!4! × 14/45]

= 13!/8!4! × 14/(9 × 5)]

= 14 × 13!/8! × 9 × 4! × 5)]

= 14!/9!5!

= 14!/9!(14 - 9)!

= ¹⁴C₉

So,  ¹³C₈ + ¹³C₉ as a single term from Pascal's Triangle is ¹⁴C₉

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Answer:

90ft

Step-by-step explanation:

43,560ft² = L × l

43,560ft² = 484ft × l

43,560ft² ÷ 484ft = l

l = 90ft

The linear functions with their slopes ranked from least to greatest are given as follows:

E. I, K, J.

A linear function is modeled by:

y = mx + b

In which:

In this problem, we have that:

Hence the linear functions with their slopes ranked from least to greatest are given as follows:

E. I, K, J.

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y=5(14-x)(x) quadratic equation best models the volume of the box .

What is volume of cuboid?

Perimeter = 2(width + length) =28

Let x=width of base, then length of base = (28/2)-x = 14-x

Volume of box = length*width*height

=x(14-x)*5  ⇒ 5x(14-x)(x)

Therefore, y=5(14-x)(x) quadratic equation best models the volume of the box .

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Answer:

Points ABC and points OBC form two separate triangles. Triangle ABC is made up of angles BAC, ABC, ACB, while triangle OBC is made up of angles BOC, OBC, OCB. Since interior angles of triangles add up to 180 degrees, m<BAC + m<ABC + m<ACB = 180 and m<BOC + m<OBC + m<OCB = 180. 180 is equal to 180, so m<BAC + m<ABC + m<ACB = m<BOC + m<OBC + m<OCB.

Since OB bisects <ABC and OC bisects <ACB, m<ABO = m<OBC and m<ACO = m<OCB. We can also say that m<ABC = 2m<ABO and m<ACB = 2m<ACO. Substitute and simplify the equation.

m<BAC + m<ABC + m<ACB = m<BOC + m<OBC + m<OCB

m<BAC + 2m<ABO + 2m<ACO = m<BOC + m<ABO + m<ACO

m<ABO + m<ACO = m<BOC - m<BAC

The slope of the red line that is perpendicular to the green line is: -5/2.

When one line lies perpendicular to another line, the slope of one must be the negative reciprocal of the other line.

If given a number, i.e. a/b, the negative reciprocal of a/b would the opposite value of the reciprocal of a/b.

Reciprocal of a/b is b/a. Negative reciprocal of a/b would therefore be: -b/a.

Given that the slope of the green line is: 2/5. And it is perpendicular to the red line. The slope of the red line would be the negative reciprocal of 2/5.

Negative reciprocal of 2/5 is -5/2.

Therefore, the slope of the red line is: -5/2.

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Correct answer is C. the number of times blue ball appears is 56

Given,

probability of picking a green ball is 0.5,

the probability of picking a blue ball is 0.4,

the probability of picking a red ball is 0.1.

a ball is picked and replaced = 140

Probability = (the number of ways of achieving success) / (the total number of possible outcomes)

Probability provides information about the likelihood that something will happen. Meteorologists, for instance, use weather patterns to predict the probability of rain. In epidemiology, probability theory is used to understand the relationship between exposures and the risk of health effects.

For this item, the number of times that we should expect that a blue ball is picked should be the product of the number of times  and the probability of picking a blue ball (which is equal to 0.4)

                            = (140)(0.4) = 56

Therefore, we should expect that the blue ball will be picked 56 times.

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The exponential function illustrated as f(x)=50(1.02)^x has a growth rate of 2%.

The exponential function is a mathematical function that is represented by e^x. Unless otherwise specified, the term refers to a positive-valued function of a real variable, though it can be extended to complex numbers or generalized to other mathematical objects such as matrices or Lie algebras.

In this case, the function is given as:

f(x)=50(1.02)^x

It should be noted 1 + 2% = 1.02 which us the value in the parentheses.

In conclusion, the growth rate is 2%.

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

[tex]\qquad❖ \: \sf \:g(f( - 5)) = 5[/tex]

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

[tex]\qquad❖ \: \sf \:f(x) = |2x + 9| [/tex]

[tex]\qquad❖ \: \sf \:f( - 5) = |2( - 5) + 9| [/tex]

[tex]\qquad❖ \: \sf \:f( - 5) = | - 10+ 9| [/tex]

[tex]\qquad❖ \: \sf \:f( - 5) = | - 1| [/tex]

[tex]\qquad❖ \: \sf \:f( - 5) = 1[/tex]

next,

g(f(-5)) represents value of y at x = f(-5) = 1

hence,

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

The point which is indicated in the task content; (1, 2) represents; parking costs $2 per hour for the entire day.

What is the interpretation of the point given in the task content; (1,2)?

It follows from convention that the coordinate systems are structured such that the independent variable, x be placed 1st and the dependent variable, y be placed second.

Consequently, since the cost of parking is dependent on the time for which the car is parked, then, it represents parking costs 2 per hour for the entire day.

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Answer:

(x-y)(x-y)(x-y)= x²-yx+x²-yx-yx+y²-yx+y²

2x²-4yx+2y²

(y-x)(y-x)= y²-yx-yx+x²

y²-2yx+x²

-(y²-2yx+x²) = -y²+2yx-x²

2x²-4yx+2y²-y²+2yx-x²= x²-2yx+y²

or

(x−y−1)(x−y)² ≡ x³−x²+3xy²+2xy−y³−y²−3yx³

Answer: 98

Step-by-step explanation:

Area of four walls = Curved surface area

                             = perimeter × height

                              =    28          ×   3.5

                              = 98 m square  

Answer:

It gets more complicated with a six-sided die. In this case if you roll the die, there are 6 possible outcomes (1, 2, 3, 4, 5 or 6). Can you figure out what the theoretical probability for each number is? It is 1/6 or 0.17 (or 17 percent).

[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]

▪ [tex]\longrightarrow \sf{f(x) = |x + 4| + 2}[/tex]

You need to remember that the form of an Absolute Value Function is:

• For the vertex:

[tex]\small\longrightarrow \sf{H= \: \: x -coordinate}[/tex]

[tex]\small\longrightarrow \sf{K= y-coordinate}[/tex]

• For the definition:

If "a" is positive (+) , then the range of the function is:

[tex]\small\longrightarrow \sf{R:y \: \underline > \: k}[/tex]

If "a" is negative (-), the range of the function is:

[tex]\small\longrightarrow \sf{R: y \: \underline < \: k}[/tex]

In this case we can identify that:

[tex]\small\longrightarrow \sf{a = 1}[/tex]

[tex] \small\longrightarrow\sf{a = 2}[/tex]

[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]

[tex] \large \bm{R: {f(x) \in ℝ | f(x) \underline > 2}}[/tex]

The quadratic equation exists [tex]$x^{2}+3 x+2=0$[/tex].

If a quadratic equation exists [tex]$a x^{2}+b x+c=0$[/tex], the utilizing the quadratic equation the solutions for x will be given by

[tex]$x_{1,2}=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$$[/tex]

The solution for x exists

[tex]$x=\frac{-3 \pm \sqrt{3^{2}-4(1)(2)}}{2(1)}[/tex]

Comparing equations (1) and (2) we get, a = 1, b = 3 and c = 2.

Therefore, the quadratic equation exists [tex]$x^{2}+3 x+2=0$[/tex].

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Answer:

One guy said it was B. but I'm going with A.

Step-by-step explanation:

Ramiya is using the quadratic formula to solve a quadratic equation. her equation is x = startfraction negative 3 plus or minus startroot 3 squared minus 4(1)(2) endroot over 2(1) endfraction after substituting the values of a, b, and c into the formula. which is ramiya’s quadratic equation?

The area of the shape is 35 square units

The given shape is a trapezoid, and it has the following side lengths

Parallel bases = 6 and 8

Height = 5

The area of the shape is then calculated as:
A = 0.5 * (sum of parallel bases) * height

Substitute the known values in the above equation

A = 0.5 * (6 + 8) * 5

Evaluate the product

A = 35

Hence, the area of the shape is 35 square units

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The area of the given trapezoid is given as 35 square units

The given shape is quadrilateral known s a trapezoid. The formula for calculating the are of the trapezoid is expressed as;

A = 1/2(a+b)*h

where

a and b are parallel sides

h is the height of the trapezoid.

Given the following parameters

a =6units

b = 8 units

h - 5 units

Substitute to have:

A = 1/2(6 + 8) * 5

A = 1/2(14) *5

A = 7 * 5

A = 35 square units

Hence the area of the given trapezoid is given as 35 square units

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Answer:

(4) (x + 6)(x - 1)

Step-by-step explanation:

Given expression

[tex]x { }^{2} + 5x - 6[/tex]

Find numbers when they are multiplied gives 6 and when they are added which gives 5.

Thus, these numbers are -1 & 6.

[tex]x {}^{2} + 6x - x - 6 \\ x(x + 6) - 1(x + 6) \\ (x + 6) \: \: (x -1 )[/tex]

Can also check the multiplied values of these two values.

Hope it helps!

Answer:

(4)

Step-by-step explanation:

Determine two multiples which when multiplied gives - 6(the last term in the equation), when added, gives +5 (the middle term in the equation).

Multiples are: +6 and -1

input the two multiples in place of the middle term (+5x)

=x^2+6x-1x-6

Collect like terms

=x(x+6)-1((x+6)

Answer= (x+6)(x-1)

Confirm answer above:

Open bracket

x(x-1)+6(x-1)

x^2-x+6x-6

x^2+5x-6 (initial equation).