Look at the function below. f(x)=−x2−2x+8

Which function is an equivalent form that can be used to identify the maximum value of the function?

a. f(x)=−(x+1)2+7 b. f(x)=−(x+1)2+9 c. f(x)=−(x+2)(x−4) d. f(x)=−(x−2)(x+4)

Answer:

8

Step-by-step explanation:

bResponses

y = 8

y, = 8

y = 3

y, = 3

y=−3

Then to isolated the variable we add 4x to both sides of the equation.

Now, to isolate the constant terms we add 6 to both sides:

Answer:

-6

Step-by-step explanation:

Answer:

-6

Step-by-step explanation:

did the test

We are asked to determine the second quartile or median of a data set. To do that we will first order the data set from smaller to largest number:

Now we determine the median. Since there is an even number of digits, the median is the number in the middle, which is 39.

Answer; 0 ,2?

Step-by-step explanation:

im not so sure tbh its a lil confusing dont they tell how many years its been?

7 groups of 2/7 is equivalent to the whole, which is represented by the number 2.

When we have 7 groups of 2/7, we are essentially multiplying the fraction 2/7 by the whole number 7. To perform this operation, we can use the following formula:

a/b × c/d = ac/bd

where a, b, c, and d are any numbers, and a/b and c/d are two fractions.

In our case, a is 2, b is 7, c is 7, and d is 1. This is because we want to multiply 2/7 by 7 to get 7 groups of 2/7. Therefore, we can substitute these values into the formula:

2/7 × 7/1 = (2 × 7) / (7 × 1) = 14/7

The result is a fraction 14/7, which can be simplified to 2. This means that 7 groups of 2/7 is equal to 2. To simplify this further, we can say that if we divide a whole into 7 equal parts, each part is 2/7. If we have 7 of these parts, we have the whole.

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By completing the square the function will be, g(x)=4(x-2)²-9

The standard form of the quadratic equation will be ax²+bx+c=0.

Equate the given equation with standard form of equation and determine the values of a, b, and c.

a=4

b=-16

c=7

For completing the square, add and subtract \(\frac{b^2}{4a}=\frac{(-16)^2}{4\times4}=16\) in the given equation.

g(x)=4x²-16x+16-16+7

g(x)=(4x²-16x+16)-9

g(x)=4(x²-4x+4)-9

The term x²-4x+4 is equivalent to (x-2)².

g(x)=4(x-2)²-9

So, the given function is same as g(x)=4(x-2)²-9.

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Answer:

b. 30 > 2d

   15 > d

c. 15/f < 5

   15 < 5f

   5 < f

d. 42 \(\leq\) 50 - m

   42 + m \(\leq\) 50

   m \(\leq\) 8

Answer:

C) 1

Step-by-step explanation:

f(x) = 3x - 4 when x = 3

= 3(3) - 4

= 9 - 4

= 5

g(x) = x^2 when x = 2

= 4

Subtract both values.

5 - 4 = 1

Best of Luck!

True. Summarizing allows you to focus on the important information by finding the introduction, topic sentence and conclusion.

Summarizing is a technique that helps to distill the main points of a text by identifying the introduction, topic sentence, and conclusion. It involves condensing the information to focus on the most important aspects and omitting unnecessary details.

This process enables the reader to grasp the core message of the text quickly and efficiently.

By summarizing, one can communicate the key ideas in a concise and clear manner, making it easier for others to understand and engage with the information presented.

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Answer:

b ≈ 54.94

Step-by-step explanation:

using the Sine rule in Δ ABC

\(\frac{a}{sinA}\) = \(\frac{b}{sinB}\) = \(\frac{c}{sinC}\)

where a is the side opposite ∠ A, b is opposite ∠ B , c is opposite ∠ C

we require to calculate ∠ B

∠ B = 180° - (42 + 41.5)° = 180° - 83.5° = 96.5°

to find b using the pair of ratios

\(\frac{b}{sinB}\) = \(\frac{a}{sinA}\) ( substitute values )

\(\frac{b}{sin96.5}\) = \(\frac{37}{sin42}\) ( cross- multiply )

b × sin42° = 37 × sin96.5° ( divide both sides by sin42° )

b = \(\frac{37sin96.5}{sin42}\) ≈ 54.94 ( to 2 decimal places )

Answer:

X = 4x-18

Step-by-step explanation:

X = “a number”^^

The following sets of side dimensions could be combined to create a right triangle 6, 8, 13 is √3, √13, 4.

In the triangle, there are three angles: two acute angles and one 90-degree angle. The hypotenuse, perpendicular, and base are the terms used to describe the sides of a right-angled triangle.

The next choice shows the triangle's side length:

The point is,

The hypotenuse square of a right-angled triangle is equal to the sum of its squares on its other two sides, according to Pythagoras' Theorem.

Using Pythagoras' Theorem.

Use the formula:

a² + b² = c²

For 4, 8, 11

4, 8, 11

4² + 8² = 16 + 64 = 80

11² = 121

80 is not equal to 121 it cann ot form a right triangle

For 6, 8, 13

6² + 8² = 36 + 64 = 100

13² = 169

100 is equal to 169 - 69 can form a right triangle

For √3, √5, 8

(√3)² + (√5)² = 3 + 5 = 8

8² = 64

8 is equal to 64 cannot form a right triangle

For √3, √13, 4

(√3)² + (√13)² = 3 + 13 = 16

4² = 16

16 is equal to 16 can form a right triangle

In order to create a right triangle, one may utilise the following set of side measurements √3, √13 and 4 form a triangle.

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Answer:

-50 because your taking out 50 dollars

The graph of the equation is shown below

From the question, we are to graph the given equation

The given equation is

-3 = 5x - y

To graph the equation,

First we will determine the x-intercept and y-intercept

x-intercept

Put y = 0 in the equation

-3 = 5x - 0

-3 = 5x

x = -3/5

y-intercept

Put x = 0 in the equation

-3 = 5(0) - y

-3 = 0 - y

-3 = -y

y = 3

Using the x-intercepts and y-intercepts, we can plot the graph of the equation.

The graph of the equation is shown below

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Answer:

4

Step-by-step explanation:

If you add up all of those, you get 24. Then you divide by 6. 24/6 = 4.

Answer:

67°F

Step-by-step explanation:

-4-63 = - 67°F

Therefore temperature difference=67

Answer:

The table represents a linear function.

Step-by-step explanation:

Graphed, the points go in a straight line, and you are able to draw a line through it. The equation for the line is y = 4x + 4.

The equation of the line that passes through the point (7, 6) with slope 0 is y = 6

Given,

The points which the line passes, (x₁, y₁) = (7, 6)

Slope of the line, m = 0

We have to find the equation of the line:

We know that,

y - y₁ = m(x - x₁)

So,

y - 6 = 0(x - 7)

y - 6 = 0

y = 6

That is,

The equation of the line that passes through the point (7, 6) with slope 0 is y = 6

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Answer:

7 cookies are left out, If Amanda packs 11 boxes of cookies.

Step-by-step explanation:

Amanda has to pack cookies in boxes. The function describes how many cookies she puts in a certain number of boxes:

\(c=-6b+ 73\)

here variable c represents number of cookies and variable b represents the number of boxes packed.

We need to find If she packs 11 boxes, how many cookies are left out.

We are given:

b = 11

We need to find c

Putting value of b and finding value of c in the equation.

\(c=-6b+ 73\\c=-6(11)+73\\c=-66+73\\c=7\)

So, we get the value of c: c=7

Therefore,  7 cookies are left out, If Amanda packs 11 boxes of cookies.

Answer:

≈ 11.78 in

Step-by-step explanation:

The arc length is calculated as

arc = circumference of circle × fraction of circle

     = 2πr × \(\frac{\frac{\pi }{4} }{2\pi }\) ( cancel 2π on numerator/ denominator )

     = 15 × \(\frac{\pi }{4}\)

     = \(\frac{15\pi }{4}\)

     ≈ 11.78 in ( to 2 dec. places )

Answer: 7725.5775

Step-by-step explanation:

d=27

r=d/2=27/2=13.5

the volume of the spherical balloon= 3.14*r^3

                                                       = 3.14*(13.5)^3

                                                       = 7725.5775

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Answer:

2029

Step-by-step explanation:

60L = 2028.84oz

round to the nearest whole number =2029

Answer:

(0.7044 ; 3.0956)

Step-by-step explanation:

Given:

GROUP A:

n1 = 25

x1 = 12.7

s1 = 2.2

GROUP B :

n2 = 25

x2 = 10.8

s2= 2.0

The obtain the confidence interval assuming unequal population variance :

(x1 - x2) ± tα/2[√(s1²/n1 + s2²/n2)]

The degree of freedom :

df = (s1²/n1 + s2²/n2)² ÷ (s1²/n1)²/n1-1 + (s2²/n2)²/n2-1

The degree of freedom :

(2.2²/25 + 2²/25)² ÷ (2.2²/25)²/24 + (2²/25)²/24

df = 0.12503296 ÷ (0.0015617 + 0.0010666)

df = 47.57 ;

df = 48

Tcritical value ; α = 95% ; df = 48

Tcritical = 2.0106

C.I = (12.7 - 10.8) ± 2.0106[√(2.2²/25 + 2²/25)]

C.I = 1.9 ± (2.0106 * 0.5946427)

C.I = 1.9 ± 1.1955887

C. I = (0.7044 ; 3.0956)

Answer:

The vertex of the function is at (–3,–16)

The graph is increasing on the interval x > –3

The graph is positive only on the intervals where x < –7 and where

x > 1.

Step-by-step explanation:

The graph of \(f(x)=(x-1)(x+7)\) has clear zeroes at \(x=1\) and \(x=-7\), showing that \(f(x) > 0\) when \(x < -7\) and \(x > 1\). To determine where the vertex is, we can complete the square:

\(f(x)=(x-1)(x+7)\\y=x^2+6x-7\\y+16=x^2+6x-7+16\\y+16=x^2+6x+9\\y+16=(x+3)^2\\y=(x+3)^2-16\)

So, we can see the vertex is (-3,-16), meaning that where \(x > -3\), the function will be increasing on that interval

To determine the amount of gunpowder to stock in inventory, we can use the concept of standard normal distribution and the z-score. The z-score represents the number of standard deviations that a given value falls from the mean.

Given the mean demand of 20 pounds and the standard deviation of 2 pounds, we can find the z-score that corresponds to the 2% chance of running out of gunpowder. Using a standard normal distribution table, we can see that the z-score for the 2% tail of the distribution is 2.33.

Next, we can use the z-score to find the corresponding demand value. This can be done using the formula:

z = (x - mean) / standard deviation

Where x is the demand value and mean and standard deviation are given. Solving for x, we have:

x = mean + z * standard deviation

x = 20 + 2.33 * 2

x = 20 + 4.66

x = 24.66

So, the amount of gunpowder to stock in inventory is 24.66 pounds to have only a 2% chance of running out of gunpowder in any given month.

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The relationship between the total cost and the amount of sugar is an illustration of a linear equation.

The given parameters are:

\(\mathbf{Base = 3500}\) --- the cost of renting the truck

\(\mathbf{Rate = 125}\) -- the cost of each ton transported

So, the equation is:

\(\mathbf{S = Base + Rate \times C}\)

Substitute known values

\(\mathbf{S = 3500 + 125 \times C}\)

\(\mathbf{S = 3500 + 125C}\)

Hence, the equation that relates C to S is: \(\mathbf{S = 3500 + 125C}\)

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Answer:

340=10*340 calculated

Answer:

340

Step-by-step explanation:

i know math alot

Answer:

Answer is A I believe

Step-by-step explanation:

The value of w from the given triangle VWX is 5 units. Therefore, option D is the correct answer.

Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.

The formula for sine rule is sinA/a=sinB/b=sinC/c

From the given triangle VWX, ∠X=51°, ∠W=16° and VW=x=14.

Here, sinX/x=sinW/w

sin51°/14=sin16°/w

0.7771/14=sin16°/w

0.7771/14=0.2756/w

0.0555=0.2756/w

w=0.2756/0.0555

w=4.965

w≈5

Therefore, option D is the correct answer.

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