Answer:
a=0.7
A Area
0.49
Using the formula
A=a2
Solving fora
a=A=0.49=0.7
Which is an equation of the parabola that intersects the x-axis at points (-1, 0) and (3, 0)? Show your work or explain how you determined your answer. A. y = x2 + 2x - 3 B. y = x2 + 3x + 2 C. y = x2 - 2x - 3 D. y = x2 - 3x + 2
Answer:
[tex]\displaystyle \large{y=x^2-2x-3}[/tex]
Step-by-step explanation:
The given points are (-1,0) and (3,0) to find an equation of parabola. Notice that they say or the given points are x-intercepts, which means they make it easier for us to find an equation of parabola using these x-intercepts.
Quick Note:
x-intercepts are simply the roots or solutions of quadratic equation, so if our root is x = -2 then we can write as (-2,0) and write back to x+2=0.So what we are going to do is to write the roots’ equation back as [tex]\displaystyle \large{x+\alpha =0}[/tex]
Our points or roots are given, therefore:
If x = -1 then x+1=0
If x = 3 then x-3=0
Then multiply x+1 with x-3 because if (x-1)(x+3)=0 then x-1=0 or x+3=0:
[tex]\displaystyle \large{(x+1)(x-3)=0}[/tex]
Convert 0 to y since we want to find a function:
[tex]\displaystyle \large{(x+1)(x-3)=y}\\\displaystyle \large{y=(x+1)(x-3)}[/tex]
Expand the expressions in and simplify to standard form:
[tex]\displaystyle \large{y=x^2-3x+x-3}\\\displaystyle \large{y=x^2-2x-3}[/tex]
Therefore, the equation is [tex]\displaystyle \large{y=x^2-2x-3}[/tex]
__________________________________________________________
Summary
If we are given the points [tex]\displaystyle \large{(\alpha ,0)}[/tex] and [tex]\displaystyle \large{(\beta ,0)}[/tex] with wideness of the graph or a-value = 1 then the parabola equation is:
[tex]\displaystyle \large{y=(x-\alpha )(x-\beta )}\\\displaystyle \large{y=x^2-\beta x-\alpha x+\alpha \beta }\\\displaystyle \large{y=x^2-(\beta +\alpha )x+\alpha \beta }[/tex]
__________________________________________________________
Others
If you have any doubts about my answer, explanation or this question, do not hesitate to let me know in the comment!
Jayce and Lara each made q bowl of punch. Lara used 6 times as much as much lemonade as Jayce did. if Jayce used 3/4 if a cup of lemonade, how many cups did Lara use?
Answer: 4.5
Step-by-step explanation:
6 x 3/4 = 18/4 divided that and it equals 4.5
The total cost of a pizza and 3 drinks is $19. The price of the pizza is $10 and each drink is the same price, d. What is the prive of the one drink?
Answer:
each of the drinks are $3
Step-by-step explanation:
10 d d d /19 d=3
hope it help
Answer:
$3
Step-by-step explanation:
pizza-p
drink-d
p+3d=19
p=$10
10+3 (d)=19
3 (d)=19-10
3 (d)=9
d=9÷3
d=$3
Without solving, identify whether this equation has a solution that is positive, negative, or zero: It is positive Solve the equation.
Answer:
Step-by-step explanation:
Find the 78th term of the arithmetic sequence -4, -2, 0, ...−4,−2,0,...
Answer:
0
Step-by-step explanation:
-4, -2, 0
the 3rd number is always a 0 so if you do the sequence 78 times the 78th term will be a 0
A two-sample t test of the hypothesis H0: mu1 - mu2 = 0 versus HA: mu1 - mu2 > 0 produces a p-value of 0.03. Which of the following must be true? I. A 90 percent confidence interval for the difference in means will contain the value 0. II. A 95 percent confidence interval for the difference in means will contain the value 0. III. A 99 percent confidence interval for the difference in means will contain the value 0.
Considering the p-value of of the test, it is found that the correct option is:
III. A 99 percent confidence interval for the difference in means will contain the value 0.
What is the p-value and the confidence interval?If the p-value is less than the [tex]\alpha[/tex] level, given by 1 subtracted by the confidence level, it does not contain the value tested at the null hypothesis.If it is more, it contains the value tested at the null hypothesis.In this problem, we have that the p-value is of 0.03, hence the confidence interval will contain the value of 0, tested at the null hypothesis, for confidence levels above 97%, hence option III is correct.
More can be learned about p-values at https://brainly.com/question/13873630
Does anyone know this? I'm stuck on it.
Answer:
For the first triangle:
Sides xz and xy are of equal length
Angles z and y are of equal measure
For the second triangle:
Sides pr and qr are of equal length
Angles p and q are of equal measure
Step-by-step explanation:
Those tiny line segments intersecting the sides indicate that those sides are equal.
Hope that helps!
what the geometric mean of 18 and 30 as a square root?
The geometric mean of 18 and 30 is the product of 18 and 30 square rooted, so:
[tex]\sqrt{18*30} =\sqrt{540} =\sqrt{9*4*15} =\sqrt{36*15} =6\sqrt{15}[/tex]
Hope that helps!
Janelle says that lines l and m are skew lines.
Planes B and A intersect. Plane B is vertical and contains vertical line n. Plane A is horizontal and contains horizontal line m. Line m and n are perpendicular. Line l is on plane A and it is slightly diagonal.
Is Janelle correct?
Yes, because the lines are not parallel.
Yes, because the lines will intersect.
No, because the lines are in the same plane.
No, because the lines are perpendicular.
Answer:
C: No, beacause the lines are in the same plane.
Step-by-step explanation:
because skewed lines must lie in different planes.
just trust moi <3
The lines are in the same plane option third "No, because the lines are in the same plane" is correct.
What is a perpendicular line?Lines that intersect at a right angle are named perpendicular lines. Lines that are always the same distance apart from each other are known as parallel lines.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have two lines shown in the picture, line l, and line m.
As we know the skew lines are in different planes and do not intersect.
Thus, the lines are in the same plane option third "No, because the lines are in the same plane" is correct.
Learn more about the perpendicular line here:
brainly.com/question/18271653
#SPJ5
Which expression is not equivalent to 2² + 10+12?
Option 3 is not equivalent!
(Hope I could help!)
Find the area of the figure.
Answer: 300 ft^2
Step-by-step explanation:
First, find the area of the rectangle on the bottom:
Area of a rectangle = length * width = 18 * 12 = 216
Now, find the area of the trapezoid:
Area of a trapezoid = (base 1 + base 2) / 2 * height → (10 + 18) / 2 * 6 = 84
Add these together: 216 + 84 = 300 ft^2 :)
can somone help me i need this quick ill give brainlist
Answer:
A
Step-by-step explanation:
40/100+ 3/10 AKA 30/100=70/100
subtract 70 from 100 and you get 30
so 30/100 donuts are cinnamon
hope that helps
What is the answer to this?
Answer:
2
Step-by-step explanation:
i was told it was correct and 3x1=3 6 divided by 3=2
is how i figured it out.
enter the value of 4 1/4 - 5/7 + (-2/7) - (-3)
Answer:
[tex]=6\frac{1}{4}[/tex]
Step-by-step explanation:
[tex]4\frac{1}{4}-\frac{5}{7}+\left(-\frac{2}{7}\right)-\left(-3\right)[/tex]
[tex]4\frac{1}{4}=\frac{4\cdot 4+1}{4}[/tex]
[tex]=\frac{17}{4}[/tex]
[tex]=\frac{17}{4}-\frac{5}{7}+\left(-\frac{2}{7}\right)-\left(-3\right)[/tex]
[tex]=\frac{99}{28}+\left(-\frac{2}{7}\right)-\left(-3\right)[/tex]
[tex]=\frac{99}{28}-\frac{2}{7}-\left(-3\right)[/tex]
[tex]=\frac{13}{4}-\left(-3\right)[/tex]
[tex]=\frac{13}{4}+3[/tex]
[tex]=\frac{25}{4}[/tex]
[tex]\frac{25}{4}=6\frac{1}{4}[/tex]
[tex]=6\frac{1}{4}[/tex]
-{ModPatrol}
can someone help please????
2. Tania went to Italy. She changed £325 into euros (€). The exchange rate was £1 = €1.68 (a) Change £325 into euros (E).
Answer:
£325 is €546
Step-by-step explanation:
325 times 1.68 is 546
There are 224 boys and 168 girls in the seventh grade. In which class is the ratio of boys and girls equivalent to the ratio in the seventh grade? Class Boys Girls A 12 8 B 18 10 C 15 9 D 16 12
Answer:
C
Step-by-step explanation:
Because 3 goes into both 15 and 9 and make 3:3
No other numbers make an equivalent ratio
(4, 6) (-3, -2) Find the slope
Answer:
The value of the slope would be:
8/7
Step-by-step explanation:
Have a great rest of your day
#TheWizzer
Answer:
[tex] slope = \dfrac{8}{7} [/tex]
Step-by-step explanation:
(4, 6) and (-3, -2)
[tex] slope = \dfrac{y_2 - y_1}{x_2 - x_1} [/tex]
[tex] slope = \dfrac{-2 - 6}{-3 - 4} [/tex]
[tex] slope = \dfrac{-8}{-7} [/tex]
[tex] slope = \dfrac{8}{7} [/tex]
pls help with this Its on ixl
Answer:
142 cm squared
Step-by-step explanation:
the formula used was 2(lw + wh +lh)
where l is length
w is width
and h is height
Answer:
142
Step-by-step explanation:
5 x 3 = 15 Times by 2 = 30
7 x 5 = 35 Times by 2 = 70
7 x 3 = 21 Times by 2 = 42
Ron started the day with a score of +12.
He lost 4 points, gained 3 points, and then
lost 15 points. What was his score then?
+ 12 - 4 + 3 - 15
= 12 + 3 - 4 - 15
= 15 - 19
= - 4
Answer:
He has -4 points. if I'm not mistaken
Step-by-step explanation:
12 - 4 + 3 - 15 = -4
I apologize if I am incorrect
The price of the stereo system
decreased from $210 to $126.
What was the percent of decrease?
Answer:
40%
Step-by-step explanation:
The amount of decrease is $84, so now all you need to do is convert 84/210 into a percentage. Divide both sides by 2.1 so the denominator is 100 (percent is a ratio with a denominator of 100) and the answer will be 40/100, which is 40%.
calculate the value of the marked angle
Angle 1 and Angle _____________ are supplementary angles.
Answer: number 2
Step-by-step explanation: so a supplementary Angle adds up to a 180 angle so it would be number 2 I think.
Determine whether the following sequence is geometric. If so, find the common ratio,
1.-3.9. - 27,...
Answer:
Yes, the sequence is geometric
common ratio (r) = -3
Step-by-step explanation:
Given:
[tex]a_1=1[/tex][tex]a_2=-3[/tex][tex]a_3=9[/tex][tex]a_4=-27[/tex]If a sequence is geometric, common ratio [tex]r[/tex]:
[tex]r=\dfrac{a_4}{a_3}=\dfrac{a_3}{a_2}=\dfrac{a_2}{a_1}[/tex]
Substituting the given values:
[tex]\implies \dfrac{a_4}{a_3}=\dfrac{-27}{9}=-3[/tex]
[tex]\implies \dfrac{a_3}{a_2}=\dfrac{9}{-3}=-3[/tex]
[tex]\implies \dfrac{a_2}{a_1}=\dfrac{-3}{1}=-3[/tex]
Therefore, as
[tex]\dfrac{a_4}{a_3}=\dfrac{a_3}{a_2}=\dfrac{a_2}{a_1}=-3[/tex]
the sequence is geometric with common ratio of -3
f(x)=−1/2(x−2)^2 −4 Graph it
Answer:
Step-by-step explanation:
Found this when searching on the internet. Hope it helps... Maybe???
n the past you paid $800 per month to rent your apartment. You now pay $900 per month for your rent. What is the percent increase in your rent?
Answer:
12.5%
Step-by-step explanation:
900 - 800 = 100
Gotta pay $100 more
100 / 800 = 0.125
Select the correct answer.
Tracy wants to make a cylindrical model. The height of the cylindrical model, H(V), in inches, is modeled by this
equation, where Vis the volume of the cylindrical model, in cubic inches.
H(V) = 2. 6937
What is the average rate of change of the model's height when its volume changes from 512 cubic inches to
1,000 cubic inches?
The model's height increases by approximately 21. 52 inches for every 1-cubic-inch increase in its volume.
The model's height increases by approximately 0. 022 inch for every 1-cubic-inch increase in its volume.
The model's height increases by approximately 0. 011 inch for every 1-cubic-inch increase in its volume.
The model's height increases by approximately 26. 9 inches for every 1-cubic-inch increase in its volume.
The average rate of change of the height function is slope of the height function
The model's height increases by approximately 0.011 inch for every 1-cubic-inch increase in its volume.
How to determine the average rate of change?The height function is given as:
[tex]H(V) = 2.69\sqrt[3]{V}[/tex]
When V = 512, the function becomes
[tex]H(512) = 2.69\sqrt[3]{512}[/tex]
[tex]H(512) = 21.52[/tex]
Similarly;
When V = 1000, the function becomes
[tex]H(1000) = 2.69\sqrt[3]{1000}[/tex]
[tex]H(1000) = 26.9[/tex]
The average rate of change is then calculated as:
[tex]H' = \frac{H(1000) - H(512)}{1000 - 512}[/tex]
This gives
[tex]H' = \frac{26.9 - 21.52}{1000 - 512}[/tex]
[tex]H' = \frac{5.38}{488}[/tex]
Evaluate the quotient
[tex]H' = 0.01102459016[/tex]
Approximate
[tex]H' = 0.011[/tex]
Hence, the model's height increases by approximately 0.011 inch for every 1-cubic-inch increase in its volume.
Read more about average rate of change at:
https://brainly.com/question/8728504
Answer:
The model’s height increases by approximately 0.011 inch for every 1-cubic-inch increase in its volume.
Step-by-step explanation:
Plato/Edmentum
What is -4x^2-6x-4 in vertex form?
[tex]y = - 4 ({x + \frac{3}{4} })^{2} - \frac{7}{4} \\ [/tex]
what are the solutions to the equation?
Answer:
x = -2 and 1
Step-by-step explanation:
Given :
f(x) = x+2
g(x) = -x²+4
The solution to the equation f(x) = g(x)
=> x+2 = -x²+4
=> x²+x = 4-2
=> x²+x -2 = 0
By factorisation
=> x²+2x-x -2 = 0
=> x(x+2) -1(x+2)
=> (x+2) (x-1)
x = -2 and 1
We want to find the zeros of this polynomial:
p(x) = (x+2) (2x^2 + 3x-9)
Answer:
x = - 2, x = - 3, x = [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
to find the zeros equate p(x) to zero , then
(x + 2)(2x² + 3x - 9) = 0 ← factor the quadratic
(x + 2)(x + 3)(2x - 3) = 0
equate each factor to zero and solve for x
x + 2 = 0 ⇒ x = - 2
x + 3 = 0 ⇒ x = - 3
2x - 3 = 0 ⇒ 2x = 3 ⇒ x = [tex]\frac{3}{2}[/tex]