Find the measure of Angle B

Answer:

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

Step-by-step explanation:

Parent function: f(x) = x^2

To show this in a way that may look more familiar, f(x) = 1(x - 0)^2 + 0

Vertex form: f(x) = a(x - h)^2 + k

We know a = 1, because the slope is the same as the parent function.

Vertex: (h,k)

We can see that the vertex of the graph is (-4, -5)

So h = -4 and k = -5

Now all we need to do is plug the variables into our equation.

f(x) = a(x - h)^2 + k

f(x) = 1(x + 4)^2 - 5

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

Answer:

[tex]{ \tt{ = \frac{7}{9} \div \frac{1 }{3} }} \\ = { \bf{ \frac{7}{9} \times \frac{3}{1} }} \\ = \frac{7}{3} [/tex]

Answer:

94 cm^2

Hope it helps!

Answer:

[tex]y\ =\ \ \tan\theta\ +2[/tex]

Step-by-step explanation:

Answer:

74.8% approximately

Step-by-step explanation:

Area of circle is pi×r^2=pi×4^2=16pi=50.27 approximately

Area of pentagon (assumption regular pentagon)=5/2×apothem×side length=5/2(3.2)(4.7)=37.6

So the probability that it lands in the red is 37.6/50.27 approximately =74.8% approximately

Answer:

not sure, sorry : p

Step-by-step explanation:

Answer:

f(g(x)) =

[tex] {x}^{6} + 6 {x}^{4} + 8x^{2} + 2[/tex]

Step-by-step explanation:

put g(x) instead of any x in f(x)

[tex] {(x ^{2} + 2) }^{3} - 4( {x}^{2} + 2) + 2[/tex]

Answer:

[tex]P(pink) = P(pink |\ female) = 0.6[/tex]

Step-by-step explanation:

Given

[tex]\begin{array}{ccc}{} & {Male} & {Female} & {Pink} & {156} & {72} \ \\ {Yellow} & {104} & {48} \ \end{array}[/tex]

Required

Why [tex]prefers\ pink\ lemonade[/tex] and [tex]female[/tex] are independent

First, calculate [tex]P(pink |\ female)[/tex]

This is calculated as:

[tex]P(pink |\ female) = \frac{n(pink\ \&\ female)}{n(female)}[/tex]

[tex]P(pink |\ female) = \frac{72}{48+72}[/tex]

[tex]P(pink |\ female) = \frac{72}{120}[/tex]

[tex]P(pink |\ female) = 0.6[/tex]

Next, calculate [tex]P(pink)[/tex]

[tex]P(pink) = \frac{n(pink)}{n(Total)}[/tex]

[tex]P(pink) = \frac{156 + 72}{156 + 72 + 104 + 48}[/tex]

[tex]P(pink) = \frac{228}{380}[/tex]

[tex]P(pink) = 0.6[/tex]

So, we have:

[tex]P(pink) = P(pink |\ female) = 0.6[/tex]

Hence, they are independent

Answer:

P(pink lemonade | female) = P(pink lemonade) = 0.6.

Step-by-step explanation:

A

Answer:

Step-by-step explanation:

If a point (x, y) is reflected across y = -x, coordinates of the image point will be,

(x, y)→ (-y, -x)

Following this rule,

Vertices of the triangle will be,

(3, 1) → (-1, -3)

(3, -2) → (2, -3)

(6, -3) → (3, -6)

Therefore, image of the given triangle A will be,

(-1, -3), (2, -3) and (3, -6)

Answer:

Step-by-step explanation:

x²-4=0

(x+2)(x-2)=0

x=-2,2

solution is x∈{-2,2}

Answer:

OP = discount amount × 100 / discount %

Step-by-step explanation:

if I understand this correctly, the actual sale price was 36% (100-64) of the originally marked price.

original price (OP) = 100%

64% of OP = 30

1% of OP = 30/64

OP (100%) = 100 × 30/64

this could be simplified to 100 × 15/32, but this hinders is finding the global formula :

OP = discount amount × 100 / discount %

Answer:

The values of x for which the function can be replaced by the Taylor polynomial if the error cannot exceed 0.001 is 0 < x < 0.3936.

Step-by-step explanation:

Note: This question is not complete. The complete question is therefore provided before answering the question as follows:

Determine the values of x for which the function can be replaced by the Taylor polynomial if the error cannot exceed 0.001. f(x) = e^x ≈ 1 + x + x²/2! + x³/3!, x < 0

The explanation of the answer is now provided as follows:

Given:

f(x) = e^x ≈ 1 + x + x²/2! + x³/3!, x < 0 …………….. (1)

[tex]R_{3}[/tex] = (x) = (e^z /4!)x^4

Since the aim is [tex]R_{3}[/tex](x) < 0.001, this implies that:

(e^z /4!)x^4 < 0.0001 ………………………………….. (2)

Multiply both sided of equation (2) by (1), we have:

e^4x^4 < 0.024 ……………………….......……………. (4)

Taking 4th root of both sided of equation (4), we have:

|xe^(z/4) < 0.3936 ……………………..........…………(5)

Dividing both sides of equation (5) by e^(z/4) gives us:

|x| < 0.3936 / e^(z/4) ……………….................…… (6)

In equation (6), when z > 0, e^(z/4) > 1. Therefore, we have:

|x| < 0.3936 -----> 0 < x < 0.3936

Therefore, the values of x for which the function can be replaced by the Taylor polynomial if the error cannot exceed 0.001 is 0 < x < 0.3936.

the way to do these recurring decimals is by firstly separating the repeating part or recurring part and then multiply it by some power of 10 so we move it to the left, lemme show

[tex]3.5\overline{41}\implies \cfrac{35.\overline{41}}{10}\qquad \stackrel{\textit{say that the repe}\textit{ating part is }~\hfill }{x = \overline{0.41}\qquad \qquad \textit{so that }35.\overline{41}=35+\overline{0.41}=35+x}[/tex]

now, let's multiply that repeating part by some power of 10 that moves the 41 to the left, well, we have two repeating decimals, 4 and 1, so let's use two zeros, namely 100 or 10², thus

[tex]100\cdot x = 41.\overline{41}\implies 100x - 41+\overline{0.41}\implies 100x = 41+x\implies 99x=41 \\\\\\ \boxed{x =\cfrac{41}{99}}\qquad \qquad \textit{so then we can say that}~~\cfrac{35.\overline{41}}{10}\implies \cfrac{35+\frac{41}{99}}{10} \\\\\\ \cfrac{~~\frac{3506}{99}~~}{10}\implies \cfrac{~~\frac{3506}{99}~~}{\frac{10}{1}}\implies \cfrac{3506}{99}\cdot \cfrac{1}{10}\implies \cfrac{3506}{990}\implies \blacktriangleright \stackrel{\textit{which simplifies to}}{\cfrac{1753}{495}} \blacktriangleleft[/tex]

Answer:

hello!

where are you from ?

Step-by-step explanation:

option 4 is correct ...there is no constant ratio.

Answer:

[tex]Height = 12cm[/tex]

Step-by-step explanation:

Given

[tex]Volume = 1200cm^3[/tex]

The dimension of the base is:

[tex]Base =10cm[/tex]

[tex]Sides = 13cm[/tex]

See comment for complete question

Required

The height of the base

To do this, we make use of Pythagoras theorem where:

[tex]Sides^2 = (Base/2)^2 + Height^2[/tex]

So, we have:

[tex]13^2 = (10/2)^2 + Height^2[/tex]

[tex]13^2 = 5^2 + Height^2[/tex]

[tex]169 = 25 + Height^2[/tex]

Collect like terms

[tex]Height^2 = 169 - 25[/tex]

[tex]Height^2 = 144[/tex]

Take square roots of both sides

[tex]Height = 12cm[/tex]

Answer:

Step-by-step explanation:

x : 100 = 7740 : 98 000 000

x = (7740 * 100)/98 000 000

x = 0.007898 %

A percentage is a hundredth of a number      Then                                                    [tex]\displaystyle\bf \frac{7740}{98\cdot10^6} \cdot100=\frac{387}{49000} \approx 0,00789\%[/tex]                                                      

Answer:

A. 96.0 square units

Step-by-step explanation:

The formula for the area of a triangle when we know the side length of two sides and the measure of an included angle of a triangle is given as:

A = ½*a*b*Sin C

Where,

a = 13

b = 15

C = 80°

Plug in the values into the formula

A = ½*13*15*Sin 80

A = 96.0187559

A = 96.0 square units (nearest tenth)

Answer:A

Step-by-step explanation: I took the test

Answer:

The equation of the line is y=7x

Answer:

yes is correct 6/6 = 1 / 3*2=6 =1

Answer:

nonsense. what's the difference between 6/6 or 1 .

Answer:

a) 83,b) -4,c) 48,d) 16,e) 8

Answer:

Probability[(X - μ) < 1.1] = 0.6046

Step-by-step explanation:

Given:

σ² = 64

Mean μ = 34

Find:

Probability[(X - μ) < 1.1]

Computation:

Standard deviation σ = √σ²

Standard deviation σ = √64

Standard deviation σ = 8

Probability[(X - μ) < 1.1] = Probability[-1.1 < (X - μ) < 1.1]

Probability[(X - μ) < 1.1] = Probability[-1.1/(8/√38) < (X - μ) < 1.1/(8/√38)]

Using z table

Probability[(X - μ) < 1.1] = 0.6046

Answer: D) Increase the sample size and decrease the confidence level.

Step-by-step explanation:

A reduced interval width means that the data is more accurate. This can only be achieved if the sample size is increased because a larger sample size is able to capture more of the characteristics of the variables being tested.

A smaller confidence interval will also lead to a reduced interval width because it means that the chances of the prediction being correct have increased.

Answer:

x = 11

Step-by-step explanation:

I assume you want x, so I simply rearranged the terms, subtracted, and simplified.

Answer:

x=2

Step-by-step explanation:

We have

y = 2x-1

y= 4x-5

Therefore, as 2x-1=y=4x-5, we can say that

2x-1=4x-5

add 1 to both sides to make one side have only x components

2x = 4x-4

subtract 4x from both sides to separate the x components

-2x = -4

divide both sides by -2 to separate the x

x = 2

Answer:

Step-by-step explanation:

Answer:

[tex]x = \dfrac{1 + i\sqrt{47}}{6}[/tex]   or   [tex]x = \dfrac{1 - i\sqrt{47}}{6}[/tex]

Step-by-step explanation:

[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]

We have a = 3; b = -1; c = 4.

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

[tex]x = \dfrac{1 \pm \sqrt{1 - 48}}{6}[/tex]

[tex]x = \dfrac{1 \pm \sqrt{-47}}{6}[/tex]

[tex]x = \dfrac{1 + i\sqrt{47}}{6}[/tex]   or   [tex]x = \dfrac{1 - i\sqrt{47}}{6}[/tex]

Answer:

Step-by-step explanation:

Because of the Isosceles Triangle Theorem, the angles across from the congruent sides will be congruent. That means that the angle x also measures 42 degrees.

Answer:

3264:221

Step-by-step explanation:

If by last year there were 221 students and 12 teachers at Hilliard School, then;

221students = 12teachers

To find the equivalent ratio for 272students, we can say;

272students = x teachers

Divide both expressions

221/272 = 12/x

Cross multiply

221 * x = 272 * 12

221x = 3264

x = 3264/221

x = 3264:221

This gives the required proportion

Answer:

[tex]\{0, 1, 2, 3\}[/tex] is a partition of Z

Step-by-step explanation:

Given

[tex]$$A _ { 0 } = \{n \in \mathbf { Z } | n = 4 k$$,[/tex] for some integer k[tex]\}[/tex]

[tex]$$A _ { 1 } = \{ n \in \mathbf { Z } | n = 4 k + 1$$,[/tex] for some integer k},

[tex]$$A _ { 2 } = { n \in \mathbf { Z } | n = 4 k + 2$$,[/tex] for some integer k},

and

[tex]$$A _ { 3 } = { n \in \mathbf { Z } | n = 4 k + 3$$,[/tex]for some integer k}.

Required

Is [tex]\{0, 1, 2, 3\}[/tex] a partition of Z

Let

[tex]k = 0[/tex]

So:

[tex]$$A _ { 0 } = 4 k[/tex]

[tex]$$A _ { 0 } = 4 k \to $$A _ { 0 } = 4 * 0 = 0[/tex]

[tex]$$A _ { 1 } = 4 k + 1$$,[/tex]

[tex]A _ { 1 } = 4 *0 + 1$$ \to A_1 = 1[/tex]

[tex]A _ { 2 } = 4 k + 2[/tex]

[tex]A _ { 2} = 4 *0 + 2$$ \to A_2 = 2[/tex]

[tex]A _ { 3 } = 4 k + 3[/tex]

[tex]A _ { 3 } = 4 *0 + 3$$ \to A_3 = 3[/tex]

So, we have:

[tex]\{A_0,A_1,A_2,A_3\} = \{0,1,2,3\}[/tex]

Hence:

[tex]\{0, 1, 2, 3\}[/tex] is a partition of Z

Answer:

C.) 8 pounds

Hope that can help