The area of a triangle formed by points of intersection of parabola y=a(x−1)(x−4) with the coordinate axes is 3. Find a if it is known that parabola opens downward.

Answers

Answer 1

Answer:

[tex]a=-\dfrac{1}{2}[/tex]

Step-by-step explanation:

Given the parabola

[tex]y=a(x-1)(x-4)[/tex]

To find y-intercept, substitute [tex]x=0:[/tex]

[tex]y=a(0-1)(0-4)\\ \\y=4a[/tex]

Hence, [tex](0,-4a)[/tex] is the point of intersection with y-axis.

To find x-intercept, substitute [tex]y=0:[/tex]

[tex]0=a(x-1)(x-4)\\ \\x_1=1\ \text{or}\ x_2=4[/tex]

Hence, points [tex](1,0)[/tex] and [tex](4,0)[/tex] are the points of intersection with x-axis.

Find the area of the triangle formed:

[tex]A_{\triangle}=\dfrac{1}{2}\cdot \text{Base}\cdot \text{Height}\\ \\\text{Base}=|4-1|=3\\ \\\text{Height}=|4a|\\ \\A_{\triangle }=\dfrac{1}{2}\cdot 3\cdot |4a|=6|a|[/tex]

Since the area of the triangle is 3, you have

[tex]6|a|=3\\ \\6a=-3\ [\text{Parabola goes downward}]\\ \\a=-\dfrac{1}{2}[/tex]


Related Questions

Pollsters take a survey of people at a ball game to collect and analyze data about favorite leisure activities of Star City’s residents. Would this study be biased? Why or why not?

Answers

Answer:

D: Yes, it is biased. The sample of people at the ball park is not representative of Star City’s residents.

Step-by-step explanation:

Just finished the quiz on edge.

The result is biased because it is not representative of all the residents of Star City.

What is bias?

Bias in research has to do a delibrate attaept to tilt the outcome of a study towards a particular result . The survey described here ought to be representative.

The fact that only the  people at a ball game were polled shows that the survey is not representative of all the residents of Star City.

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Find y by itself 7y=14x-21

Answers

Answer: y=2x-3

Step-by-step explanation:

divide both sides by 7

7y/7=(14x-21)/7

y=2x-3

7y=14x-21

Divide both sides of the equation by 7

Y=2x-3 is the final solution

Find c.
Round to the nearest tenth:
Help
27 CM
C= [? ]cm
Acellus!!

Answers

Answer:

a = 44.1 cm

Step-by-step explanation:

Using the Law of Sines is the way to go, but before you use it we need the measure of angle A.

180 - 102 - 28 = A so

A = 50 degrees.  Now setting up the Law:

 and cross multiply to get

27sin50 = asin28 and

so,

a = 44.1 cm

(this isn't my answer, cr Luv2Teach on brainly. i just saw that the same question was posted and was already answered)

Solve 7 2/3 - 6 1/8 =

Answers

Answer:

1 13/24

Step-by-step explanation:

1. 2x - 12 = 6

2. 2x + 6= 8

3. 12s - 12=12

4. 14s + 6 = 35

5. 3s - 12 = 6

6. 18t + 9 = 34

7. 21x + 7 = 28

8. 50y + 5 = 105

9. 1/4x - 6 = 24

10. 13x + 2 = 18

11. 6 - 3x = 18

12. 14 + s = 21

13. 16x - 4 = 28

14. 19x - 1 + 3 = 40

15. 10t = 194

16. 400x + 100 = 1100

17. 40 - 3x + 3 = 113

(Please help me with these problems all is appreciated)

Answers

Answer:

see the attached pictures please

Find the value of x

Answers

Answer:

85

Step-by-step explanation:

All triangles equal 180

Answer:

85

Step-by-step explanation:

(A triangle is 180 degrees)

52 + 43 = 95

180 - 95 = 85


The three-dimensional figure below is a solid rectangular prism with a hole in the shape of another rectangular prism going through the center of it. Find the volume of the solid in cubic millimeters.
A.60
B.300
C.540
D.780

Answers

the correct answer is A

Find the next three terms of the geometric sequence -8, 12, -18,27

Answers

Answer:

-40.5, 60.75, -91.125

Step-by-step explanation:

first you want to find the common difference. So just divide 12 by -8, which is -1.5 and then multiply 27 by -1.5, which is -40.5 and continue two more times.

Solve for x.
-25x + 175 > 225 and 5x - 83 ≥ - 73

Answers

Answer: No Solutions

Step-by-step explanation:

Which of the following statements best explains how the graphs misrepresent the data?

A.The graphs were created with different colors.

B.The graph for City B makes its population appear much smaller, but its population is only a little smaller than City A.

C.The graphs use different scales, making it appear that City A has a larger population than City B.

D.The graphs do not include information for the years between 1950 and 2000, so there is not enough information to compare their populations.

Answers

Answer:

C

Step-by-step explanation:

The scale for graph A is 500 and the scale of graph B is by 500000 making it very unrepresentative

Hey, can yall help me with this question?

Answers

SIR YOUR ANSWER IS B. I K FO SHO. THANK YOU. HOPE THIS HELPS. MIND MARKING BRAINLIEST AGAIN? XD THANKS

What is the mean of 12,9,17,15,10

Answers

Answer:

12.6

Step-by-step explanation:

Add them together and divide by the amount of numbers

12.6 the mean is adding them together and dividing by how many numbers are in the sum

Candace used a compass to draw the circle shown here. She then used the same compass setting to mark off arcs on
the circumference. She kept making arcs until she met her starting point. What figure will she form if she joins the arc
marks in order?


A)an irregular hexagon
B)a regular hexagon
C)overlapping triangles
D)no figure will be formed

Answers

Answer:

B

Step-by-step explanation:

Candace used a compass to draw the circle shown here. She then used the same compass setting to mark off arcs on the circumference. She kept making arcs until she met her starting point. In this way, she has marked 6 arcs. When connecting all points (intersection points), the formed figure will be a hexagon.

Since all arc have the same measure, this hexagon will be regular hexagon (hexagon with all congruent sides).

Answer:

the answer is "a regular hexagon"(B)

Step-by-step explanation:

There's no better way to answer it then how  frika did.

Circle in the coordinate plane??​

Answers

Answer:

2, -2, 9

Step-by-step explanation:

since your center is (2, -2) and your radius is 3 units.

Blake Ewasko's charge account uses the unpaid balance method to compute the finance


charges at a monthly periodic rate of 2.15%. During the month, he charged $189.34, made a 100.00


payment, and had a $21.54 finance charge. Find Blake's new balance.

Answers

Answer:

$1,114.66

Step-by-step explanation:

Data provided in the question:

Monthly periodic rate = 2.15% = 0.0215

current Charges = $189.34

Payment made = $100.00

Finance charge = $21.54

Now,

Previous balance = Finance charges ÷ Rate

= $21.54 ÷ 0.0215

= $1001.86

Unpaid balance = Previous balance + Current charges - Payment

= $1001.86 + $189.34 - $100.00

= $1091.2

New balance = Unpaid balance × ( 1 + Rate )

= $1091.2 × ( 1 + 0.0215)

= $1,114.66

Given Information in  the question:

Monthly periodic rate = 2.15% = 0.0215 Current Charges = $189.34 Payment made = $100.00 Finance charge = $21.54

Previous balance = Finance charges ÷ Rate  

Previous balance = $21.54 ÷ 0.0215  Previous balance = $1001.86

Unpaid balance = Previous balance + Current charges - Payment  

Unpaid balance = $1001.86 + $189.34 - $100.00  Unpaid balance = $1091.2

New balance = Unpaid balance × ( 1 + Rate )  

New balance= $1091.2 × ( 1 + 0.0215)  New balance= $1,114.66

Blake's new balance is $1114.66.

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Janelle and Lisbeth are picking berries. Janelle picks Three-fourths of a quart more than Lisbeth picks every hour. The equation representing the scenario is 3 (x) + 3 (x + three-fourths) = 8. Which statements about the scenario and the equation are true? Check all that apply.

Answers

Answer:

The scenario is translated to Lisbeth's berries + Janelle's berries = 8 quarts.The expression x represents the quarts of berries that Lisbeth picks each hour.The girls picked berries for 3 hours

Step-by-step explanation:

i) Lisbeth picks x quarts berries every hour is given.

ii) Janelle picks (x + three fourths) quarts berries every hour is also given.

iii) It is also give that if Janelle and Lisbeth pick berries for 3 hours then the

   equation representing that fact is given by 3(x) + 3(x+three-fourths) = 8

iv)From the above three equations we can say that the following are true

The scenario is translated to Lisbeth's berries + Janelle's berries = 8 quarts.The expression x represents the quarts of berries that Lisbeth picks each hour.The girls picked berries for 3 hours.

4 1/2÷ 1 1/4 correctly answer in simplest form​

Answers

Answer:

3 3/5

Step-by-step explanation:

Which pair of rectangles is similar? Plzzzx help me

Answers

Option 1 is correct

Step-by-step explanation:

Similarity means two images having same shape or one image can be obtained by uniformly scaling the other image.

In the given options, one rectangle is larger and the other is smaller so we have to check which pair of rectangles contain rectangle that is obtained by scaling the other rectangle.

So

We can find the scale factor by dividing the sides of larger rectangle by dividing the respective sides in smaller rectangle.

Option 1:

[tex]Scale\ for\ length = \frac{9}{3} = 3\\Scale\ for\ width = \frac{15}{4} = 3.75[/tex]

As the scale is not same for both sides ( not uniform), so the rectangles are not similar

Option 2:

[tex]Scale\ for\ length = \frac{6}{2} = 3\\Scale\ for\ width = \frac{8}{4} = 2[/tex]

As the scale is not same for both sides ( not uniform), so the rectangles are not similar

Option 3:

[tex]Scale\ for\ length = \frac{6}{3} = 2\\Scale\ for\ width = \frac{15}{8} = 1.875[/tex]

As the scale is not same for both sides ( not uniform), so the rectangles are not similar

Option 4:

[tex]Scale\ for\ length = \frac{9}{3} = 3\\Scale\ for\ width = \frac{12}{4} = 3[/tex]

As the scale is same for both sides(Uniform), so the rectangles are similar

Hence,

Option 1 is correct

Keywords: Rectangles, similarity

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Below is a map of Yellowstone Park. The scale for the map is 1cm = 25 miles.

Mrs. Fowler went on a trip from Old Faithful to Canyon.

What is the actual distance from Old Faithful to Canyon in MILES?

A 5 miles

B 62.5 miles

C 15 miles

D 75 miles

Answers

Answer:

Option D. 75 miles

Step-by-step explanation:

Looking at the Yellowstone Park map we can see that Mrs. Folwer went from Old Faitful to the Canyon by covering a straight line of [tex]3cm[/tex].

This tells us that we do not need extra calculations to find the distance covered on the map. We also know that the map scale is given as [tex]1cm=25miles[/tex]. So similarly we do not need to do extra ratio conversions.

Thus we know that if [tex]1cm=25miles[/tex] and she covered [tex]3cm[/tex] on the map, we can just multiply covered distance with the equivalency of [tex]cm[/tex] in [tex]miles[/tex] as follow:

[tex]Distance=(3cm) (25 miles)=75miles[/tex]

Thus Mrs. Folwer's actual distance from Old Faithful to Canyon in Miles is 75 miles. (which is given in Option D.)

Four friends are going to split the cost of a pizza. If p stands for the cost of the pizza, which of the following expressions could represent what each friend will pay?

A.4p
B.p - 4
C.p
D.p/4

Answers

Answer: A

Step-by-step explanation:

Answer: A.) 4p

Step-by-step explanation:

Solve for X.

-10

10

180

125

Answers

Answer:

x+125+x+75=180

2x+200=180

2x=-20

x= -10

-10+75= 65

-10+125=115

-12=
−12=
\,\,-2a+6
−2a+6

Answers

a = 9

Step-by-step explanation:

We are given -12 = -2a +6

so to find the value of a,

move 6 from rhs to lhs by changing its sign

rhs = right hand side

lhs = left hand side

-12 - 6 = - 2a

-18 = -2a

dividing -18 by -2, we get a = 9

Hence, a = 9 is the required answer.

What do u call a destroyed angle

Answers

A rect angle cause the angle is reckt

Final answer:

A destroyed angle is called a zero angle in mathematics.

Explanation:

In mathematics, a destroyed angle is typically referred to as a zero angle. A zero angle is an angle that measures 0 degrees. It is formed when two lines coincide and create a straight line.

For example, if you have two lines that are parallel to each other and you take a protractor to measure the angle between them, you would get a measurement of 0 degrees, indicating a zero angle.

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What is the domain of f(x)=1\2x​

Answers

Answer:

Domain:(-∞,∞),(x∈R)

Which ordered pair is a solution of the equation?
y = 4x +9
Choose 1 answer:
Only (-3,3)

Only (–2, 2)

Both (–3, 3) and (-2, 2)

Neither

Answers

Neither ! X= -9/4 and Y=9

Neither of the ordered pairs is a solution to the equation y = 4x + 9.

The correct option is Neither.

Which of the ordered pairs is a solution?

Given the equation in the question:

y = 4x + 9

To determine which ordered pair is a solution of the equation y = 4x + 9, you can plug each pair into the equation and see if it holds true.

y = 4x + 9

For (-3, 3):

y = 4x + 9

Plug in the x and y values:

3 = 4(-3) + 9

3 = -12 + 9

3 = -3

(-3, 3) is not a solution.

For (-2, 2):

y = 4x + 9

Plug in the x and y values:

2 = 4(-2) + 9

2 = -8 + 9

2 = 1

(-2, 2) is not a solution.

The option Neither is the correct answer.

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What is 1 + 1 times the square root of pie times by 0.005

Answers

Answer:

[tex]1+1\cdot \sqrt{\pi }\cdot 0.005=1[/tex]

Final answer:

The expression 1 + 1 times the square root of pi times by 0.005 requires calculating the square root of pi, multiplying by 0.005, and adding that product to 1, following the order of operations.

Explanation:

To solve the equation 1 + 1 times the square root of pi times by 0.005, follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction). The equation can be unfolded as 1 + 0.005√π.

Now, to solve this equation we follow the below steps:

For π = 3.14, the value of √π is 1.77Multiplying 1.77 with 0.005 we have 0.0088Adding 1 to 0.0088 we have the final result as 1.0088

So, the value of 1 + 0.005√π is 1.0088.

F(x)=3x+5
G(x)=4x^2-2
H(x)=x^2-3x+1
Find f(x) + g(x)-h(x)
A.6x^2+6x-1
B.5x^2+4
C.3x^2+2
D.3x^2+6x+2

Answers

Answer:

Step-by-step explanation:

F(x) = 3x + 5

G(x) = 4x^2 - 2

H(x) = x^2 - 3x + 1

F(x) + G(x) - H(x) =

3x + 5 + 4x^2 - 2 - (x^2 - 3x + 1) =

3x + 5 + 4x^2 - 2 - x^2 + 3x - 1 =

3x^2 + 6x + 2 <===== ur answer

Answer:

it's a D

Step-by-step explanation:

3x^2+6x+2

Will mark brainliest once it becomes available

Answers

Answer:

m=47

Step-by-step explanation:

Answer:

m=47

Step-by-step explanation:

Consider the following piece-wise function. Which of the below correctly describes the graph shown?

Answers

Answer:

C.

[tex]f(x)=\left\{\begin{array}{l}\dfrac{1}{2}x-3,\ \ x<2\\ \\3x-8,\ \ x\ge 2\end{array}\right.[/tex]

Step-by-step explanation:

The graph of the piecewise function consists of two linear functions which graphs meets at point with x-coordinate x = 2.

1. The left linear function is determined for all x < 2 and is passing through the points (0,-3) and (-2,-4). So, its slope is

[tex]\dfrac{-4-(-3)}{-2-0}=\dfrac{-1}{-2}=\dfrac{1}{2}[/tex]

and its equation is

[tex]y-(-3)=\dfrac{1}{2}(x-0)\\ \\y=\dfrac{1}{2}x-3[/tex]

2. The right linear function is determined for all x ≥ 2 and is passing through the points (2,-2) and (3,1). So, its slope is

[tex]\dfrac{1-(-2)}{3-2}=\dfrac{3}{1}=3[/tex]

and its equation is

[tex]y-1=3(x-3)\\ \\y=3x-8[/tex]

3. Hence, the expression for the piece-wise function is

[tex]f(x)=\left\{\begin{array}{l}\dfrac{1}{2}x-3,\ \ x<2\\ \\3x-8,\ \ x\ge 2\end{array}\right.[/tex]

The slope of a line is the rate of change. The correct option is the first option.

What is the slope of a line?

The slope of a line is the rate of change, also it can be described as the gradient of a line is a number that helps to know both the direction and the steepness of the line.

In order to know the correct option of function that describes the graph, we will find the function of the graph, therefore,

Let's find the equation of the first function that is on the left side of the graph.

We know that the slope of the line is given by the formula,

[tex]\text{Slope of the line} = \dfrac{y_2-y_1}{x_2-x_1}[/tex]

Considering the two of the points of the slope,

[tex](x_1, y_1) = (2,-2)\\(x_2, y_2) = (-4,-5)\\[/tex]

Substituting the values to know that slope of the line, therefore,

[tex]\text{Slope of the line}, m= \dfrac{-5-(-2)}{-4-2} = \dfrac{-3}{-6} = \dfrac{1}{2}[/tex]

Now, using one of the points to know the value of the constant,

[tex]y=mx+c\\y_2 = mx_2+c\\-5=(\dfrac{1}{2}\times -4)+c\\-5=-2+c\\-3=c[/tex]

Hence, the equation that will represent the graph for the values of x less than -2 is [tex]y=\dfrac{1}{2}x-3[/tex].

Since, there are only two options that match this condition, the first option and the third option, now other functions will represent the rest of the graph, therefore, for the value of x greater than -2 (x≥-2).

Hence, the correct option is the first option.

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Help plz?!

A and B are complementary angles. If m A is 30°, what is the measure of B?

A:60°

B:150°

C: 40°

D: 90°

Answers

your answer is 60 Degrees because 60 + 30 = 90 degrees

( you need it to sum to 90 Degrees)

A because since a complementary angle is an angle that adds up to 90°, 30+60=90.
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