The graph shows the function f(x).
f(x)
Which equation represents f(x)?
a.f(x) = -√√x
b. f(x) = -√√x-1
c. f(x)=√√/-x-1
d. f(x)=√x

we have that

The volume of a rectangular prism is given by the formula

where

V=252 cm3

H=3 cm

W=x cm

L=W+5 --------> L=x+5

substitute given values in the formula

Solve the quadratic equation

using the formula

a=3

b=15

c=-252

substitute

The values of x are

x=7 cm and x=-12 cm ( is not a solution because is a negative number)

The width is 7 cm

therefore

m∠4=m∠8 (Corresponding angles are equal)

[tex]4x+2=86\\4x=86-2\\4x=84\\\frac{4x}{4} =\frac{84}{4} \\x=21[/tex]

x=21°

The simplified expressions for each case are given as follows:

1 - a) 11g.

1 - b) 3m.

1 - c) -k².

2 - a) 8x + 11y.

2 - b) 2a + b - 2c.

3 - a) 5q + 7.

3 - b) 6r + 3s + 7t.

An expression is simplified combining the like terms, that is, adding or subtracting, depending on the signal, the terms that have the same variable and the same exponent.

For item 1, the variables are common for all terms, hence we just add the terms keeping the variable, hence:

For item 2, there are multiple variables, hence we combine the terms of each variable(we cannot add terms with x and y, for example), as follows:

Item 3 works similarly to item 2, as there are multiple variables, hence we combine the terms with each variable(or with the constant = no variable), as follows:

The questions are missing and are given by the image at the end of the answer.

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Given:

Required:

We need to find the value of x when P(x)=80.

Explanation:

Solve for x.

Divide both sides by 25.

Final answer:

See a horizontal line from point 80 on the y axis and mark the intersection point on the graph.

The given equation is,

So, from this equation , we have to find the value of x. The left hand side of the equation has x with 1/3 as coefficient, therefore, inorder to make it x, we have to,

as the thress get cancelled. If we do some operation on one side of the equal sign, it is to be applied on the other side also so as to maintain the equivalency.

So here we have to multiply by 3.

But in option, there is no as such given , but it is given that divide by 1/3.

which is equuivalent to multiplying by three.

So the option " Divide by 1/3" is correct.

Answer:

Hey! So basically, 7 1/2 x 2 = 15 and 15 x 3 = 45

Hope this helped! :D

Answer:

Explanation:

Here, we want to get the amount of money Eric earns per week

Let the amount earned be n

Now, to get the value earned, we have to subtract the value he had before from what he has now or simply add what he had before to what he earned now and equate to his total balance now

Mathematically, we have that as:

Based on the distance that has to be jogged to get to work, and the current speed, the constant pace that is needed to get to work is 327 meters per minute

First, find out how much of the journey has already been jogged:

= Meters per minute x Number of minutes

= 600 x 8

= 4,800 meters

Distance left to get to work:

= 9,700 - 4,800

= 4,900 meters

The constant pace can be found by the formula for speed:

= Distance / time

= 4,900 / 15 minutes

= 327 meters per minute

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The numeric value of the subtraction function at x = 8 is given by:

(g - f)(8) = 0.5.

To find the numeric value of a function or of an expression, we replace each instance of the input variable in the function by the desired value.

To find the subtraction function, we find the numeric value of each function, then subtract them, as follows:

(g - f)(8) = g(8) - f(8).

Function f(x) is defined as follows:

f(x) = (x + 3)/(x² - 4x - 21).

At x = 8, the numeric value is given as follows:

f(8) = (8 + 3)/(8² - 4(8) - 21) = 11/11 = 1.

Function g(x) is defined as follows:

g(x) = log4(x).

At x = 8, the numeric value is given as follows:

g(8) = log4(8) = 1.5, as 4^(1.5) = 8.

Hence the numeric value of the subtraction function is given by:

(g - f)(8) = g(8) - f(8) = 1.5 - 1 = 0.5.

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The quotient is equal to  [tex]x^{2} +x+1[/tex]

Given

The provided equation is as follows:

[tex]\frac{x^{2}+1 }{x-1}[/tex]

What exactly is synthetic division

The synthetic division method is a quick way to divide polynomials.

When divided by the linear factor, it is also known as the polynomial division technique of a specific instance.

Therefore,

The quotient is as follows:

[tex]\frac{x^{2}+1 }{x-1}[/tex]

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

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

[tex]x^{2} +x+1[/tex]

As a result, the quotient is

[tex]x^{2} +x+1[/tex]

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Answer: C

Step-by-step explanation:

The area of a triangle is 1/2 x base x height.

The area of a triangle is 24.

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices

The area of a triangle is given by:

Area = 1/2 x base x height

We have,

A triangle ABC.

Angle bisectors are AD, BE, and CF, which intersect at I as shown in the figure below.

DI = 3

DI = AI = 3

Height of the triangle = AD = AI + DI = 3 + 3 = 6

BD = 4 = BC

Base of the triangle = BC = BD + DC = 4 + 4 = 8

The area of a triangle:

= 1/2 x base x height

= 1/2 x 8 x 6

= 1 x 4 x 6

= 24

Thus,

The area of a triangle is 24.

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The line of reflection is the line that bisects the line joining any point on the shape ABC and a corresponding point on the shape A'B'C'.

S

Step 1: Find the gradient of the line AA'.

Step 1: Let's review the information given to us to answer the exercise correctly

Amount of pure drug in the solution = 8 grams

Amount of solution = 75 mL

Step 2: Let's answer the question, as follows:

Percent strength of the solution = Amount of pure drug in the solution/Amount of solution * 100

Replacing with the values we know:

Percent strength of the solution = 8/75 * 100

Percent strength of the solution = 0.10666 * 100

Percent strength of the solution = 10.67% (Rouding to the next hundredth)

Tenth = one decimal place

Hundreth = two decimal places

Thousandth = three decimal places

Answer:

Step-by-step explanation:

12-2=10

9+7-10=6

Only brother: 9-6=3

Only Sister: 7-6=1

Both:6

Answer:

Step-by-step explanation:

Check image below for explanation

If .5 gallon covers 200

and Susan needs 246.75

1 whole gallons covers 400 (too much)

.5 gallon = 200 paint

?? gallon = 46.75 paint

200 / 46.75 = 4.27807487

.5 / 4.27807487 = 2.13903744

2.13903744 gallon = 46.75 paint

So,

.5 gallon+ 2.13903744 gallon = 2.63903744 gallons

(200 paint + 46.75 paint = 246.75 paint)

Answer: Melissa sleeps for 8 hours and wakes up at 7 am.

Step-by-step explanation: For this i was able to do just eliminate some answer. "Melissa sleeps for 7 hours and wakes up at 8 am," in this case Melissa would drink coffee because she slept less than 8 hours. "Melissa sleeps for 9 hours and wakes up at 5:30 am," in this case Melissa would drink coffee since she had woke up at 5:30 am. "Melissa sleeps for 7 hours and wakes up at 6 am," in this case Melissa would drink coffee since she had less than 8 hours of sleep. In conclusion, The only time Melissa wouldn't had drank coffee is when she had slept for 8 hours and woke up at 7 am. That is because had slept more than 8 hours and had woke up after 7 am.

The expression of the fraction 10¹/₅ - 2¹/₆ as a mixed fraction is;  8¹/₃₀

We want to subtract two fractions.

Now, fractions could be either proper fraction, improper fraction or mixed fraction.

Now, a proper fraction simply means the numerator is smaller than the denominator, a mixed fraction simply means a whole number and a proper fraction while an improper fraction simply means the numerator is bigger than the denominator

We are given the operation;

10¹/₅ - 2¹/₆

Converting to improper fraction gives;

51/5 - 13/6

Factorizing gives us;

1/30((51 * 6) - (13 * 5))

= 241/30

Converting to mixed fraction gives 8¹/₃₀

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in this problem

the graph define a function, because the x-value has only one output (one value of y)

Answer:

Step-by-step explanation:

Total marbles:

Green marbles made of glass:

Required probability:

Solution

1. Reflect Across The y - axis

Using (4, 5)

=======================================================

Reason:

The discriminant is

d = b^2-4ac

which is the stuff under the square root in the quadratic formula.

We have these three cases

The graph shows we have 2 solutions. Each solution is an x intercept, aka "root". We go for the case in which d > 0. Therefore, the discriminant is positive.

Is this a simple random sample: Yes, because each student and sample of 100 has the same chance of being selected.

A simple random sample can be defined as a subset of items that are selected from a larger data set or statistical population, with each member of the subset having an equal or the same probability (chance) of being selected.

This ultimately implies that, each member of the subset are selected by chance and randomly, and as such a simple random sample is an unbiased representation of a larger data set or a statistical population.

In this context, we can reasonably infer and logically deduce that the data set or statistical population described in this scenario is a simple random sample.

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The trigonometric ratios of an angle represented with its terminal side are given by the following equations:

The first angle terminal side is located at (10, -11), then we get:

Similarly, for the second angle:

Orthocenter

Let

A(2,0)

B(3,2)

C(6,0)

step 1

Find out the slope AB

m=(2-0)/(3-2)

m=2/1

m=2

Remember that

If two lines are perpendicular, then, their slopes are negative reciprocal

so

the slope of the altitude that passes through C is -1/2

Find out the equation of the altitude that passes through C

y=mx+b

we have

m=-1/2

point C(6,0)

substitute

0=-(1/2)(6)+b

solve for b

0=-3+b

b=3

equation is y=-(1/2)x+3 -------> equation 1

step 2

Find out the slope BC

m=(0-2)/(6-3)

m=-2/3

so

the slope of the altitude that passes through A is 3/2

Find out the equation of the altitude that passes through A

y=mx+b

we have

m=3/2

point A(2,0)

0=(3/2)(2)+b

solve for b

0=3+b

b=-3

y=(3/2)x-3 ------> equation 2

step 3

the intersection point equation 1 and equation 2 is the orthocenter

y=-(1/2)x+3 -----> equation 1

y=(3/2)x-3 ------> equation 2

solve the system

solve by graphing

using a graphing tool

the intersection point is (3,1.5)

that means

the orthocenter is (3,1.5)

see the attached figure to better understand the problem

Answer:

Explanations

Inequalities expressions are expressions not separated with an equal sign. The inequality signs are <, >, ≤ and ≥.

From the given question, we are to write the given inequality in interval notation.

Interval notation are represent using the set notation symtion sym

Answer:

$1.12

Step-by-step explanation:

x = 8

6x = 53.76

6(8) = 53.76

48 burgers = 53.76

Divide 53.76 by 48 for cost per burger (53.76 ÷ 48)

The patient's systolic blood pressure will be lowered by 48.709< m<56.091 at a 98% confidence interval.

What is a confidence interval?

The reduction in systolic blood pressure is, mean, x=52.4

Sample size, n=25

Standard deviation, s=8.5

We must determine the t value for a 90% Confidence interval because the sigma is unknown.

From Inverse t Distribution Calculator, the Confidence interval is 0.98 and the degree of freedom is 25-1=24:

One-sided t-Score: 2.1715

We can now determine the standard error E:

E=2.1715(8.5/√25)=3.691

We can now create the confidence interval by:

x - E < m < x+ E

52.4-3.691< m<52.4+3.691

48.709< m <56.091

The patient's systolic blood pressure will be lowered by 48.709< m <56.091 at a 98% confidence interval.

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Divide fractions

3.1/3.2

PART 1,

Pithagorean theorem

x^2 =™9^2 + 12^2 = 81 + 144 = 225

then

x=√225 = 15

PART 2

x^2 = 10^2 + 24^2 = 100 + 576 = 676

then

x= √676 = 26

PART 3

10 ^ 2 = x^2 + 6^2

So then

10^2 - 6^2 = x^2

100 - 36 = x^2

64 = x^2

√64 = 8 = x

PART 4

24^2 = x^2 + 6^2

So then write

24^2 -6^2 = x^2

576 - 36 = x^2

As a result

540 = x^2

Then

√540 = x

SOLUTION:

Step 1:

In this question, we are given the following:

Step 2:

The details of the solution are as follows:

The correct answers are:

CONCLUSION:

The final answers are:

OPTION B and OPTION D