Mathematics High School

Please help I have a test on this and I’m not sure how to do this

Answers

Answer 1

ANSWER

[tex]y=-\frac{1}{4}x^2+\frac{3}{4}x+1[/tex]

EXPLANATION

We want to find the equation for the function graphed.

We see that the function passes through -1 and 4 on the x-axis and 1 is the y-intercept.

These are called the roots of the function. The roots are the x values where the function equals 0.

We can find the function by applying the roots:

[tex]y=a\mleft(x-x_1\mright)\mleft(x-x_2\mright)[/tex]

where x1 and x2 are the roots.

a = leading coefficient

Therefore, we have that:

[tex]\begin{gathered} y=a(x-(-1))(x-4) \\ y=a(x+1)(x-4)_{} \end{gathered}[/tex]

Expand the brackets:

[tex]\begin{gathered} y=a(x^2-4x+x-4) \\ y=ax^2-4ax+ax-4a \\ y=ax^2-3ax-4a \end{gathered}[/tex]

Now, we have to find a.

To do that, we use the y-intercept of the function (0, 1). The y-intercept is the value of the function when x is 0.

Therefore, when x = 0, y = 1:

[tex]\begin{gathered} 1=0-0-4a \\ \Rightarrow-4a=1 \\ a=-\frac{1}{4} \end{gathered}[/tex]

Now, substitute the value of a into the function obtained earlier.

[tex]\begin{gathered} y=-\frac{1}{4}x^2-3(-\frac{1}{4})x-4(-\frac{1}{4}) \\ \Rightarrow y=-\frac{1}{4}x^2+\frac{3}{4}x+1 \end{gathered}[/tex]

That is the equation of the function graphed.

Related Questions

help meeeeeeeeeeeeeee pleaseeeeeee

Answers

Answer: 9.7 seconds

Step-by-step explanation:

[tex]16t^2 =1503\\\\t^2 =1503/16\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7[/tex]

1. These are added to a picture to make it look more realistic.
Ospaces
Ohorizon lines
Oshadows
O sketches

Answers

How does adding shadows affect a picture?For images to be properly balanced, light and shadow contrast is crucial. Shadow can provide drama to a certain area of the composition of an image while light makes an image appear brighter. For black-and-white images, using shadows to add contrast is extremely important because you won't be using color to add interest or contrast. With the addition of depth and realism, shadows can significantly enhance the overall aesthetics and usability of any design. Shadows in design should effectively integrate into the overall design and mimic the real-world, organic behavior of light and shadow-casting.

Therefore, (C) shadows are added to a picture to make it look more realistic by enhancing the aesthetics of the picture.

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Christina needs a new pair of basketball shoes for the upcoming season. The original price of the shoes she wants is $79.99. The tax on the shoes is
3.4%. What is the amount of tax Christina will pay?

Answers

Answer:

Christina will pay $82.71 after tax

please help asap !!!!!!! <33 I'll mark you as the brainliest

Answers

Answer:

n = 3

Step-by-step explanation:

Hope this helps you! :))

Answer:

n= 3

Step-by-step explanation:

when there is a multiplication with the same base, you can rewrite the base and make the sum of the exponents

3^(5+n) = 3^8

5 +3 = 8

so n=3

Convert 6 feet per hr to miles per year

Answers

We can convert this using the following conversion process:

[tex]\frac{6ft}{h}\cdot\frac{1mile}{5280.0196ft}\cdot\frac{1h}{0.0001141\text{year}}=9.9593\text{mile}/\text{year}[/tex]

Therefore, the equivalent is 9.9593miles/year.

Can someone help? :)

Answers

Average rate of change of [tex]y = x^2 + 4x - 1\\[/tex] over the interval [tex]-4 \leq x \leq 1[/tex] is 1

What is average rate of change of a curve?

Average rate of change of a curve is equal to the slope of the curve and is obtained by dividing the change in functional value by the change in the value of the domain.

Here,

[tex]y = x^2 + 4x - 1\\[/tex]

At x = -4,

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

At x = 1

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

Average rate of change of [tex]y = x^2 + 4x - 1\\[/tex] over the interval [tex]-4 \leq x \leq 1[/tex]

= [tex]\frac{4 - (-1)}{1- (-4)}\\\\\\\frac{5}{5}\\\\1[/tex]

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Solve you may use fraction circle pieces to help you you don’t really have to use

Answers

[tex]\begin{gathered} a)\frac{3}{4} \\ b)\frac{5}{4} \\ c)\frac{7}{8} \\ d)\frac{5}{8} \end{gathered}[/tex]

1) Let's use the fraction circles then to solve this sum of fractions:

1) Note that since these fractions do not have the same denominator we can write out the following. Placing the LCM as the denominator\div

[tex]\begin{gathered} a)\frac{1}{2}+\frac{1}{4}=\frac{4\div2\times1+4\div4\times1}{4}=\frac{3}{4} \\ b)LCM(2,4)=4 \\ \frac{1}{2}+\frac{3}{4}=\frac{4\div2\times1}{4}+\frac{4\div4\times3}{4}=\frac{5}{4} \\ c)\text{LCM(4,}8)=8 \\ \frac{3}{4}+\frac{1}{8}=\frac{6+1}{8}=\frac{7}{8} \\ d)\text{LCM(}4,8)=8 \\ \frac{1}{4}+\frac{3}{8}=\frac{2+3}{8}=\frac{5}{8} \end{gathered}[/tex]

Note that for 'c' and "d" we have made it faster. Since this is the same principle.

Write your answer as an integer or decimal to the nearest 0.5. 5 4 3 NO -3 3 4 -1 А -3 -4 B -5 )

Answers

Answer:

(-2.5, 4.5)

Explanation:

To know the coordinates of point D, we need to identify the projection of this point on the x-axis and the y-axis. So:

Since the projection in the x-axis is a number between -2 and -3 and the projection in the y-axis is a point between 4 and 5, the coordinates of D are:

(-2.5, 4.5)

What is the value of x when the Richter

scale rating is 7.5? Round your answer

to the nearest hundredth.

Answers

The value of x = 31622776.6.

To find what is the value of x when the Richter scale rating is 7.5.

To round your answer to the nearest hundredth.

if no base is stated, then assume base 10

[tex]log(x) = log_{10} (x)[/tex]

Lets remember that [tex]a = log_{b}(c)[/tex] translates to [tex]b^{a} = c[/tex]

[tex]r = log(x)[/tex]

[tex]r = log_{10}(x)[/tex] translates to [tex]10^{r} = x[/tex]

so when r=7.5, what is x

[tex]10^{r} = x\\\\10^{7.5} = x[/tex]

31622776.60168379 = x

round to nearest ???

thousandth? 31622776.601 = x

hundredth? 31622776.60 = x

tenth? 31622776.6 = x

Hence the answer is the value of x = 31622776.6.

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Marty can make four modifications to his car. He chooses to upgrade the tires, fuel, engine, and driver using the expression 4t + 2f + 3e + 1d to calculate the total cost. Which of these values represents the total cost of these upgrades?

Answers

The total cost of the upgrades is $3280.

What is the total cost?

It is an economic measure that sums all expenses paid to the product, purchase, and investment. It refers to the overall cost of a product which includes both fixed and variable components of the cost. It works by allocating all the costs of doing business to the goods or services for sale. These are composed of both total fixed costs and total variable costs.

The given expression is 4t+2f+3e+1d

From the table, The values of t, f, e, and d in the cost column are 50, 40, 600, and 1200.

Substituting the values in the above equation.

4(50) + 2(40) + 3(600) + 1(1200) = 3280

Therefore, the total cost is $3280.

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The complete question is:

what are expressions that are equivalent to 2²×7²

Answers

The value equivalent to the expression 2² × 7² is 196.

What is an equation? What is a coefficient?

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. In a equation say : ax + b, [a] is called coefficient of [x] and [b] is independent of [x] and hence is called constant.

We have the following expression -

2² × 7²

The given expression is -

2² × 7²

Solving, we get -

(2 x 2) x (7 x 7)

4 x 49

196

Therefore, the value equivalent to the expression 2² × 7² is 196.

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Return Submit et Income 10 1 point If Betty has a gross income of $3000 a month, what would her total deductions be for the table? Deduction Percentage of gross income 6.2% Type your answer... Social Security Medicare 1.45% Income tax 12.5% Medical $300 Submit Previous

Answers

The answer is very simple

The total deductions would be

total deductions = 3000*0.062 + 3000*0.0145 + 3000*0.125 + 300

total deductions = 904.5

Use the isosceles trapezoid ABCD to answer the following questions.DA. If mZA = 45°, find the measure of the angles:mLB=mLC=mLD-B. If AC = 3x - 16 and BD = 10x - 86, find x.X=

Answers

In an isosceles trapezoid, we can find symmetries in angles and side lengths.

For example, Angles A and B are congruent, i.e., they have the same measure

Angles D and C are also congruent.

Write these two terms as a sum, then write in standard form: 4b and the opposite of 4b+ 20

Answers

We have

And the opposite of "4b + 20" is:

[tex]\begin{gathered} -(4b+20) \\ -4b-20 \end{gathered}[/tex]

We can write the sum of these 2 expressions as:

[tex]\begin{gathered} (4b)+(-4b-20) \\ =4b-4b-20 \\ =-20 \end{gathered}[/tex]

1.) At a conference, there are 176 math teachers and 16 science teachers.

In the last three years, Franks basketball team won 20 more games than they lost. if they won 130 games, what was the ratio of wins to looses? Write in fraction form.

Red
2.) Green Beans are canned by 2 companies. The Del Monte Company sells
14.5 oz for $1.75 and the Green Giant company sells 15.5 oz for $1.95.
Who has the best deal?

3.) A set of tires for your car cost $435.00. What is the cost for one tire?

4.) In the last three years, Frank's basket ball team won 20 more games than
they lost. If they won 130 games, what was the ratio of wins to losses?
Write in fraction form.

the difference between 75% of a number and 20% of the same number is 378.9 what is 40% of that number?

Answers

[tex]\begin{gathered} \text{ If we note by "x" our number, then} \\ 0.75\cdot x-0.2x=378.9 \\ (0.75-0.2)x=378.9 \\ 0.55x=378.9 \\ x=\frac{378.9}{0.55} \\ x=688 \end{gathered}[/tex]

Thus, the 40% of the number is

[tex]688.909\cdot0.4=275.563[/tex]

a cell phone tower cast a shadow 10 feet long at the same time that a 75-foot building casts a shadow 15 feet long. how tall is the cell phone tower?

Answers

Answer:

50 feet

Step-by-step explanation:

Please help me, I'd be more than happy to contribute.

Answers

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: write the given function

[tex]y=f^{^{\prime}}(x)[/tex]

STEP 2: Define the points at which a graph is increasing.

We say that a function is increasing on an interval if the function values increase as the input values increase within that interval. The derivative of a function may be used to determine whether the function is increasing or decreasing on any intervals in its domain. If f′(x) > 0 at each point in an interval I, then the function is said to be increasing on I. f′(x) < 0 at each point in an interval I, then the function is said to be decreasing on I.

STEP 3: Show the points where the graph was increasing

We write the x coordinates of the intervals, therefore the intervals will be:

[tex](-2,2)[/tex]

What is the range of the function f(x) = x^2 - 2x -15?*

Answers

For this problem, we are given a certain function and we need to determine its range.

The function is:

[tex]f(x)=x^2-2x-15[/tex]

This quadratic function has a minimum value in its range, which is represented by its vertex. The best way to determine the range is to find the coordinates of the vertex of this function, therefore we have:

[tex]\begin{gathered} x_{vertex}=\frac{-b}{2a}=\frac{2}{2}=1\\ \\ y_{vertex}=f(1)=(1)^2-2(1)-15=1-2-15=-16 \end{gathered}[/tex]

The minimum value in the range is -16, which means that the range is:

[tex]\lbrace f(x)|f(x)\geqslant-16\rbrace[/tex]

The correct option is the second one.

10.Which of these operations should be completed firstwhen solving an equation?a. xb. +c. ()d. +

Answers

Given the list of symbols:

x, +, ( ), ÷

Let's determine the operations that should be completed first when solving an equation.

To solve an equation, we are always required to apply the PEMDAS theorem.

PEMDAS is an acronym for:

0. P,arentheses

1. E,xponents

2. M,ultiplication

3. D,ivision

4. A,ddition

5. S,ubtraction.

This shows the order in which the operations in an equation should be solved.

We can see that the first operation which is to be completed is the parenthesis.

Therefore, using the PEMDAS theorem, the operation that should be first completed when solving an equation is the parenthesis ().

ANSWER:

C. ( )

How far from the farmhouse will the airplane be after it has traveled 4 miles at the same altitude?

Answers

Given:

Altitude = 3 miles

Let's determine how far from the farmhouse the airplane will be if it has travelled 4 miles at the same altitude.

The figure below represents this situation:

To find the distance, apply pythagorean theorem:

[tex]c^2=a^2+b^2[/tex]

Where:

a = 3 miles

b = 4 miles

Thus, we have:

[tex]\begin{gathered} c^2=3^2+4^2 \\ \\ c^2=9+16 \\ \\ c^2=25 \end{gathered}[/tex]

Take the square root of both sides:

[tex]\begin{gathered} \sqrt[]{c^2}=\sqrt[]{25} \\ \\ c=5 \end{gathered}[/tex]

Therefore, the distance between the airplane and the farmhouse is 5 miles.

ANSWER:

5 miles

PLEASE HELP ME OUT WITH THIS X^2+10x+25

Answers

Answer:

(x+2)(x+5)

Step-by-step explanation:

60 POINTS!!! HELPFind any asymptotes or holes in the function below. Explain how you arrived at your answer. SHOW YOUR WORK AND THE STEPS YOU TOOK.

Answers

The function given is,

[tex]y=\frac{x-6}{(x-1)(x-6)}[/tex]

Since , the leading coefficient of numerator is less than the leading coefficient of denominator .

Therefore, there is no horizontal asymptotes.

For finding the vertical asymptotes, substitute the denominator is equal to 0.

[tex](x-1)=0\text{ , }(x-6)=0[/tex][tex]x=\text{ 1,6.}[/tex]

The vertical asymptotes are 1 and 6.

To find the hole in the function,

[tex](x-6)[/tex]

is crossed out in numerator and denominator.

So, if we set up x-6 equals to 0.

The hole in the function is, when

[tex]x=6.[/tex]

Match each system of linear equations with the correct number of solutions.

Answers

1) Linear equation has no solutions.

2) It has one solution.

3) It has many solutions.

Define linear equation.

The points where the lines representing the intersection of two linear equations intersect are referred to as the solution of a linear equation. In other words, the set of all feasible values for the variables that satisfy the specified linear equation constitutes the solution set of the system of linear equations.

Given,

Linear equations:

1) 3x - y = 4

6x - 2y = 8

Multiplying 3x - y = 4 by 2

6x - 2y = 8

0 = 0

It has no solutions.

2) -3x + y = 7

2x - 4y = -8

2(x - 2y ) = -8

x - 2y = -4

Multiplying x - 2y = -4 by 3

-3x + y = 7

3x - 12y = -12

-11y = -5

y = 5/11

It has one solution.

y = -4x -5

y = -4x + 1

It has many solutions.

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suppose each license plate in a certain state has three letters followed by three digits. The letters H and L and the digits 1, 2, and 9 are not used. So, there are 24 letters and 7 digits that are used. Assume that the letters and digits can be repeated. How many license plates can be generated using this format.

Answers

Number of license plates = 24 x 24 x 7 x 7 x 7

= 197568

when solving the following system of equations using the elimination method, what would be the appropriate first step?A) multiply the bottom equation by 2B) multiply the top equation by 4 C) subtract the system D) add the system

Answers

Answer:

A) multiply the bottom equation by 2

Explanation:

Our goal in using the elimination method is to eliminate one variable so that we can solve for another independently.

Therefore, the first step would be to multiply the bottom equation by 2 so that the term with x becomes -4x so that it can cancel when the bottom equation Is added to the equation at the top.

Multiplying the bottom equation by -2 gives

[tex]\begin{gathered} 2(-2x+5y=25) \\ -4x+10y=50 \end{gathered}[/tex]

Now, our system becomes

[tex]\begin{gathered} 4x+7y=28 \\ -4x+10y=50 \end{gathered}[/tex]

adding the two equations gives

[tex]\begin{gathered} 4x+7y=28 \\ -4x+10y=50 \\ -------------- \\ 17y=78 \end{gathered}[/tex]

we can now solve for y and then use its value to find the value of x.

Therefore, the correct first step in solving the equations is to multiply the bottom equation by 2.

Given the graph f(x)=4^x write a function that results from each given transformation. A. f(x)=4^x is shifted 4 units up. What is the equation of the new function?B. f(x)=4^x is shifted 3 units down. What is the equation of the new function?C. f(x)=4^x is shifted 2 units left. What is the equation of the new function?D. f(x)=4^x is shifted 5 units right. What is the equation of the new function?E. f(x)=4^x is reflected about the x-axis. What is the equation of the new function?F. f(x)=4^x is reflected about the y-axis. What is the equation of the new function?

Answers

Given:

There are given that the function:

[tex]f(x)=4^x[/tex]

Explanation:

To find any transformation, we need to use the parent function which is given.

Then,

(A): Shifted 4 units up:

[tex]\begin{gathered} f(x)=4^x \\ f(x)=4^x+4 \end{gathered}[/tex]