Write a quadratic function in standard form whose graph passes through (-5,0),(0,-8),(4,0)
Answers
[tex]y = -1.25 x^{2}+ 5[/tex] is the needed quadratic function in standard form.
What is a quadratic equation?A quadratic equation is one with a single degree 2-variable and has the general form [tex]a x^{2} + bx + c = 0.[/tex] a, b, and c is the constant value, and x consists of a variable.
The quadratic equation's x-intercepts are (-5, 0). That indicated that the quadratic equation's two elements are (x + 5) and (x -0).
f(x) = a (x + 5) (x - 0) (x - 0)
= ax+5a
f(x) = [tex]ax^{2} +5x[/tex]
The quadratic equation's graph goes through (4, 0). Therefore, we must change equation 1 to read x = 4 and f(x) = 0.
0 = a × 4² + (5 × 4)
0 = a × 16 +20
a = [tex]\frac{-20}{16}[/tex]
=-1.25
The quadratic equation is known to have the form ax² + bx + c = 0.
f(x) = -1.25[tex]x^{2}[/tex] + 5x
Consider y= F(x)
∴ The required quadratic equation of function in the standard form is Y = -1.25 x² + 5x.
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Related Questions
You invest $940 into an account that
earns 8% simple interest. What is the final
In the account after 6 years
Answers
The final amount in the account after 6 years is $6,354.4
This is a problem with simple interest. We can solve this problem by following a few steps.
I have invested $940 into an account that earns 8% simple interest.
We have to use a formula to solve this problem.
I = P× r× t
Where I = amount of interest.P is denoted as the principal amount of money which is $940 as per the question.r is denoted as simple interest which is 8%, according to the question.t represents the period which is 6 years or 72 months as 1 year is equal to 12 months.So, the interest after 6 years is, (940 × 8 × 72) / 100 = $5,414.4
The total amount after 6 years is ( 940+ 5414.4 ) = $6,354.4 [ Total amount = principal amount + interest ]
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4) At a farm the ratio of cows to horses was 7: 1. If there were 49 cows at the farm, how
many horses were there?
Answers
Antoine purchased 1.8 kilograms of apples and 315 dekagrams of oranges. This was 1,350 grams more than the weight of bananas he purchased. What was the weight of the bananas Antoine purchased in grams?
Answers
First, let's get all the values to grams.
1.8 kilograms is equal to 1800 grams.
315 deka grams is equal to 3150 grams.
1350 is already in grams.
So Antoine purchased 1800 grams of apples and 3150 grams of oranges. Adding them up, we have a total of:
[tex]1800+3150=4950[/tex]Since this: 4950 grams, is 1350 grams more than the wieght of bananas, than, the weight of banas, "b", is:
[tex]\begin{gathered} b+1350=4950 \\ b=4950-1350 \\ b=3600 \end{gathered}[/tex]This is already in grams, so the wieght of the banaas in grams is 3600.
ersion with whole number valuesA flower bed has the shape of a rectangle 8 yards long and 3 yards wide. What is its area in square feet?Be sure to include the correct unit in your answer.ft
Answers
Given that length =8 yards and width = 3 yards of the rectangle bed.
Recall the formula for the area of the rectangle is
[tex]A=\text{length }\times width[/tex][tex]\text{Substitute length =8 yards and width=3 yards, we get}[/tex][tex]A=8\text{ yards }\times3\text{ yards}[/tex][tex]A=8\times3yards^2[/tex][tex]A=24yards^2[/tex]We know that one yard=3 feet.
[tex]\text{yards}^2=(3\text{ f}eet)^2[/tex][tex]\text{yards}^2=\text{ 9 f}eet^2[/tex][tex]\text{Substitute }yards^2=9\text{ f}eet^2\text{ in the area of the rectangle as follows.}[/tex][tex]A=24\times9\text{ fe}et^2[/tex][tex]A=216\text{ fe}et^2[/tex]Hence the area of the rectangle flower bed is 216 square feet.
Match the coordinate rule with the reflection that produces it.Column AColumn B1.Reflect across the x-axisa. (b, a)2.Reflect across the y-axisb. (a, b)3.Reflect across the originC. (-b, -a)4.Reflect across the line y = xd. (-a, -b)5.Reflect across any horizontal line. Ex: y = -2e. (a, -b)f. (2x-a, b)6.Reflect across any vertical line. Ex: x = 5g. (a, 2y-b)
Answers
4. Reflect across the line y = x ------- (b,a)
for reflection across the line y=x, the value of x and y coordinates are interchanged;
[tex](x,y)\rightarrow(y,x)[/tex]5. Reflect across any horizontal line. Ex: y = -2 ......... (a,2y-b)
for reflection across any horizontal line, the x coordinate remain the same but the y coordinate is subtracted from twice the value of the y coordinate of the line of reflection.
[tex](x,y)\rightarrow(x,2y_1-y)[/tex]6. Reflect across any vertical line. Ex: x = 5 ---------- (2x-a, b)
for reflection across any vertical line, the y coordinate remain the same but the x coordinate is subtracted from twice the value of the x coordinate of the line of reflection.
[tex](x,y)\rightarrow(2x_1-x,y)[/tex]if y =3x^3 + 2x^2 - 5x + 2, find d^3y/dx^3
Answers
Answer:
18
Step-by-step explanation:
[tex]\frac{dy}{dx}=9x^2 + 4x-5 \\ \\ \frac{d^2 y}{dx^2}=18x+4 \\ \\ \frac{d^3 y}{dx^3}=18[/tex]
Translate and solve, what percentage of 375 is 225
Answers
The mathematical expression for the word statement is,
[tex]x\text{ \% of 375=225}[/tex]Solve for x
[tex]\frac{x}{100}\times375=225[/tex][tex]\frac{375x}{100}=225[/tex]Multiply both sides by 100
[tex]\begin{gathered} 100\times\frac{375x}{100}=100\times225 \\ 375x=22500 \end{gathered}[/tex]Divide both sides by 375
[tex]\begin{gathered} \frac{375x}{375}=\frac{22500}{375} \\ x=60\text{ \%} \end{gathered}[/tex]Hence, the answer is
[tex]60\text{ \%}[/tex]A company prices its tornado insurance using the following assumptions:
• In any calendar year, there can be at most one tornado.
• In any calendar year, the probability of a tornado is 0.09.
• The number of tornadoes in any calendar year is independent of the number of tornados in any other calendar year.
Using the company's assumptions, calculate the probability that there are fewer than 2 tornadoes in a 14-year period.Round your answer to 4 decimals.
Answers
0.4834
There can only be one tornado every year on the calendar. This indicates that there are only two conceivable outcomes of the event: either there will be one tornado or none at all.
The likelihood of a tornado in any given year is 0.14. This indicates that an event's chance of occurring is fixed. p = 0.14
The frequency of tornadoes in one year is unrelated to the quantity in other years. This indicates that the incidents are unrelated to one another.
The likelihood that there won't be more than two tornadoes in a 12-year period has to be calculated. This indicates that the number of trials, n, is set at 12.
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Find the equation of a line parallel to the line y = −5/4x + 7. Write the equation in Standard Form (Ax + By = C).
Answers
The equation to be found is parallel to
[tex]y=2x+5[/tex]2 lines that are parallel have the same slope. Therefore,
[tex]\begin{gathered} m_1=m_2 \\ m_2=2 \end{gathered}[/tex]The equation to be found is containing the point (3, 3)
[tex]\begin{gathered} y=mx+b \\ \text{where} \\ m=\text{slope} \\ b=y-\text{intercept} \\ 3=2(3)+b \\ 3-6=b \\ b=-3 \end{gathered}[/tex][tex]y=2x-3[/tex]Solve for the given variables
Answers
Answer:
7.5?
Step-by-step explanation:
I'm not sure but i think 60=8x so you would do 60÷8 and it's 7.5
PLEASE HELP ITS DUE SOON! I DONT GET ANY OF THIS! HELP WOULD BE MUCH APPRECIATED! NEED THIS DONE BEEN STUCK ON THIS FOR WAY TO LONG!
YOU WILL GET 100 POINTS IF YOU HELP! QUESTION DOWN BELOW!!!!!
Answers
ΔMNQ ≅ ΔONP are Congruent triangle.
What do you mean by congruent?
Two figures are considered to be "congruent" if they can be placed perfectly over one another. Both of the bread slices are the same size and shape when positioned one on top of the other. Congruent refers to things that are exactly the same size and shape.1) MN = ON ⇒ Given
2) ∠1 = 2 ⇒ Angles are equal because sides are equal.
3) MN = ON,MP = OQ ⇒ Given
4) ΔNMP and ΔNQO are isosceles trisngle.
5) PN = QN ⇒ Given
6) PQ = QP ⇒ Line segment
7) MP + PO = OQ + QM ⇒ Adding = amount to = line segment
8) ΔMNQ ≅ ΔONP = Congruent
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x y w z is a quadrilateral with verticals W 1 - -4 - x - -4
Answers
Midpoint formula
We are given the points
X=(-4,2)
Y=(1,-1)
Z=(-2,-3)
W=(1,-4)
They define the quadrilateral XYWZ
To find the intersection of the diagonals, we can use the Midpoint Formula
This formula gives us the midpoint of a segment defined by points (x1,y1) (x2,y2) as follows:
[tex]xm=\frac{x1+x2}{2},\text{ ym=}\frac{y1+y2}{2}[/tex]We must identify the opposite points of the quadrilateral and calculate the midpoint between them
Segment XY:
Midpoint of XY:
[tex]x_m=\frac{-4+1}{2}=-\frac{3}{2}[/tex][tex]y_m=\frac{2-1}{2}=\frac{1}{2}[/tex]Midpoint of ZW:
[tex]x_m=\frac{1-2}{2}=-\frac{1}{2}[/tex][tex]y_m=\frac{-3-4}{2}=-\frac{7}{2}[/tex]Finally, find the midpoint of the opposite sides' midpoints:
[tex]x_c=\frac{-\frac{3}{2}-\frac{1}{2}}{2}=-1[/tex][tex]y_c=\frac{\frac{1}{2}-\frac{7}{2}}{2}=-\frac{3}{2}[/tex]The intersection of the diagonals is the point (-1,-3/2)
which is greater a unit rate of -4 or 2
Answers
Answer: Hi that would be 2, hope that helps!
Step-by-step explanation:
Sarah used the Quadratic Formula to solve the equation x² - 4x - 16 = 0. What should her solutions be?
Answers
Answer
x = (2 + 2√5)
OR
x = (2 - 2√5)
Explanation
In order to use the quadratic formula for the general quadratic equation,
ax² + bx + c = 0 is given as
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]For x² - 4x - 16 = 0,
a = 1
b = -4
c = -16
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-(-4)\pm\sqrt[]{(-4)^2-4(1\times-16)}}{2(1)} \\ x=\frac{4\pm\sqrt[]{16+64}}{2} \\ x=\frac{4\pm\sqrt[]{80}}{2} \\ \sqrt[]{80}=\sqrt[]{16\times5}=\sqrt[]{16}\times\sqrt[]{5}=4\sqrt[]{5} \\ x=\frac{4\pm\sqrt[]{80}}{2} \\ x=\frac{4\pm4\sqrt[]{5}}{2} \\ x=2\pm2\sqrt[]{5} \\ x=2+2\sqrt[]{5} \\ OR \\ x=2-2\sqrt[]{5} \end{gathered}[/tex]Hope this Helps!!!
evaluate 7x^2+2(3x-8)-5x for x=3. show your work
Answers
The value of the expression 7x² + 2(3x - 8) - 5x for x = 3 will be 50.
What is substitution method?
Find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.
Given that;
The expression is,
7x² + 2(3x - 8) - 5x
Now, The value of the expression 7x² + 2(3x - 8) - 5x for x = 3 calculated as;
The expression is,
7x² + 2(3x - 8) - 5x
Now, For the value of expression 7x² + 2(3x - 8) - 5x for x = 3 , we can substitute x = 3;
7x² + 2(3x - 8) - 5x
7 (3)² + 2 (3 × 3 - 8) - 5 × 3
7 × 9 + 2 (9 - 8) - 15
7 × 9 + 2 × 1 - 15
63 + 2 - 15
65 - 15
50
So, For x = 3,
⇒ 7x² + 2(3x - 8) - 5x = 50
Thus, The value of the expression 7x² + 2(3x - 8) - 5x for x = 3 will be 50.
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help please thank you
Answers
Problem
Express the number 0.00005348 in terms of a power of 10
Solution
For this case we just need to count the number of zeros before the first number different from 0 and if we do this we have 5 numbers before 5 so we can write the number like this:
5.348 x10^-5
[tex]5.348x10^{-5}[/tex]Consider the quadratic equation below. 412 - 5= 3 + 4 Determine the correct set-up for solving the equation using the quadratic formula.
Answers
Given:
[tex]4x^2-5=3x+4[/tex]To find:
The correct setup for solving the equation using the quadratic formula.
Explanation:
It can be simplified as,
[tex]\begin{gathered} 4x^2-5-3x-4=0 \\ 4x^2-3x-9=0 \end{gathered}[/tex]Here,
[tex]\begin{gathered} a=4 \\ b=-3 \\ c=-9 \end{gathered}[/tex]Using the quadratic formula,
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]Plugging in the values, we get
[tex]x=\frac{-(-3)\pm\sqrt{(-3)^2-4(4)(-9)}}{2(4)}[/tex]Final answer:
The correct choice is D.
If the paint costs $1.50 per square meter, how much will she spend to cover the entire wall with paint?
Answers
To find the price to paint the entire wall, we just need to find the area of the wall and multiply by the price per square meter.
The area of a square is given by the product of the side length by itself. Since the measure of the side is 3 meters, the area is
[tex]A=3^2=9[/tex]9 m².
The unitary price per square meter is $1.50. Multiplying this value by the area, we have
[tex]9\times1.5=13.5[/tex]It will cost $13.50 to paint the wall.
I need help solving this question
Answers
The three numbers are 61, 427 and 161.
What is the sum of numbers?
A summation, also known as a sum, is the outcome of adding two or more numbers or quantities. There are always an even number of terms in a summation. There could be only two terms, or there could be one hundred, thousand, or a million. There are summations with an infinite number of terms.
As given, one number is 7 times the first number, third number is 100 more than the first number and the sum of three numbers is 649.
Suppose the first number is x, then the second number is 7x and the third number is x + 100.
Sum of these three numbers is, 649.
x + 7x + x + 100 = 649
9x = 549
x = 61
Therefore, the first number is 61, the second number is 7x = 427, and the third number is x + 100 = 161.
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A line that passes through (3, 1) and (0, -3) A line that passes through (-1,-5) and (2, 4)
Answers
The equation of a line is given by
[tex]y-y_1=m(x-x_1)[/tex]where m is the slope and (x1,y1) is a point on the line.
The slope is given by
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Fisrt line:
In this case the slope is
[tex]\begin{gathered} m=\frac{-3-1}{0-3} \\ =\frac{-4}{-3} \\ =\frac{4}{3} \end{gathered}[/tex]The the equation is
[tex]y-1=\frac{4}{3}(x-3)[/tex]Second line:
In this case the slope is
[tex]\begin{gathered} m=\frac{4-(-5)}{2-(-1)} \\ =\frac{4+5}{2+1} \\ =\frac{9}{3} \\ =3 \end{gathered}[/tex]Then the equation is
[tex]\begin{gathered} y-(-5)=9(x-(-1)) \\ y+5=9(x+1) \end{gathered}[/tex]Consider the market for jet ski rentals in the small town of Isleton. Suppose that in Isleton, there are many sellers of jet ski rentals, each one selling an identical jet ski. Therefore, each seller is a perfectly competitive firm and possesses no market power. The following graph shows the demand (D) and supply curves (S = MC) in the jet ski rental industry in Isleton.
Answers
Which expression is equivalent to the following complex fraction?SIMI3+3y+5x2(y-2x)2(y-2x)3y-5xo122(y-2x)(3y-5x)x²,2x²y²2(y-2x) (3y-5x
Answers
Solution
For this case we can do the following:
[tex]\frac{\frac{2}{x}-\frac{4}{y}}{-\frac{5}{y}+\frac{3}{x}}[/tex]We can start with the numerator and we have:
[tex]\frac{2}{x}-\frac{4}{y}=\frac{2y-4x}{xy}=\frac{2(y-2x)}{xy}[/tex]For the denominator we have:
[tex]-\frac{5}{y}+\frac{3}{x}=\frac{3y-5x}{xy}[/tex]And replacing we got:
[tex]\frac{\frac{2(y-2x)}{xy}}{\frac{3y-5x}{xy}}=\frac{2(y-2x)}{3y-5x}[/tex]Then the correct answer would be:
[tex]\frac{2(y-2x)}{3y-5x}[/tex]What is 7/9 ÷ 2/3 please help
Answers
Solution:
Given;
[tex]\frac{7}{9}\div\frac{2}{3}[/tex]Change the division sign to multiplication and reciprocate the other side;
[tex]\frac{7}{9}\times\frac{3}{2}=\frac{7}{6}[/tex]ANSWER:
[tex]\frac{7}{6}=1\frac{1}{6}[/tex]Use the net to find the surface area of the prism. 5 ITL 13 m 5 IT 13 m 12 m 29 m 12 m 13 YTL 5 ICE 29 YTL 5 YC Not drawn to scale 930 m2 o 11,310 m2 0 45,240 m2 118 m2
Answers
To find the surface area of the prism, we will consider the areas of each part of the net
For part A
Area of A = L x B = 29 x 5 = 145
Area of B = L X B = 29 x 13 = 377
Area of C = L x B = 29 x 12 =348
Area of D = 1/2 x H X B = 1/2 x 12 x 5 = 30
Area of E = 1/2 x H x B = 1/2 x 12 x 5 = 30
Total Area = 145 + 377 + 348 + 30 + 30
PLease tell me if its linear exponential quadratic please
Answers
Answer:
Linear
Step-by-step explanation:
X values are increasing equally by 1. Y values are decreasing equally by 2. So, the graph is a linear graph.
Geri encarga arreglos florales para un almuerzo de agradecimiento para un maestro.Planea comprar hasta ocho arreglos de mesa que cuestan $5 cada una,con una tarifa de $10 por todo el pedido.Representa gráficamente la función para el precio.
Answers
From the graph drawn above, we can see the relationship between the flower arrangements and the cost of ordering each of them.
On the x axis you have the number of orders,and on the y axis you have the cost of each order. Each flower arrangement costs $5, and the cost of fare is $10. That means the cost for each order would shown as follows;
1 order = 5 + 10 (15)
2 orders = 10 + 10 (20)
3 orders = 15 + 10 (25)
4 orders = 20 + 10 (30)
5 orders = 25 + 10 (35)
6 orders = 30 + 10 (40)
7 orders = 35 + 10 (45)
8 orders = 40 + 10 (50)
Therefore, the ordered pair for this graph is as follows;
(1, 15), (2, 20), (3, 25), (4, 30), (5, 35), (6, 40), (7, 45), (8, 50)
That is, when x = 1, y = 15, when x = 2, y = 20..., and so on.
21 out of 24 did their edpuzzle what percent did their edpuzzle?
Answers
1) To calculate it, we can set a proportion
24--------100%
21---------x
Cross multiply it
x =2100/24
x=87.5
87.5%
Answer: 87.5% did
Step-by-step explanation:
the base of the triangle prism shown below is a right triangle. What is the lateral surface area of the prism
Answers
Given data:
The given triangular prism.
The expression for lateral surface area is,
[tex]\begin{gathered} LS=(8\operatorname{mm}+\text{ 6mm +}10\text{ mm)}\times12\text{ mm} \\ =288\text{ sq-mm} \end{gathered}[/tex]Thus, the lateral surface area is 288 sq-mm.
Estimate the point(s) at which the graph of f has a local maximum or a local minimum.
Answers
The graph of f has a local maximum of coordinates at (-2.5, 30) and a local minimum of coordinates at (2.5, -30)
What are Maxima and Minima of a Function?The curve of a function has peaks and troughs called maxima and minima. A function may have any number of maxima and minima. Calculus allows us to determine any function's maximum and lowest values without ever consulting the function's graph.
As per the given graph,
From the given graph it is noticed that the highest point of the function is (-2.5, 30), therefore the local maxima is (-2.5, 30).
From the given graph it is noticed that the lowest point of the function is (2.5, -30), therefore the local maxima is (2.5, -30).
The graph of f has a local maximum of coordinates at (-2.5, 30)
The graph of f has a local minimum of coordinates at (2.5, -30)
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jeriel leans a 26 foot ladder against a wall so that it forms an angle of 61 with the ground .
Answers
To solve this problem we will use the following diagram:
where d is the distance between the base of the ladder and the wall.
Using the cosine we get:
[tex]\cos 61^{\circ}=\frac{d}{26ft}.[/tex]Multiplying the above equation by 26ft we get:
[tex]\begin{gathered} \cos 61^{\circ}\times26ft=\frac{d}{26ft}\times26ft\text{.} \\ d=26ft\cdot\cos 61^{\circ}\text{.} \end{gathered}[/tex]Then:
[tex]d\approx12.60505013ft\approx12.61ft.[/tex]Answer: 12.61.