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The equation for parabolic graphed function is y = [tex]-3x^{2} -24x-45[/tex].
What is parabola graph?
Parabola graph depicts a U-shaped curve drawn for a quadratic function. In Mathematics, a parabola is one of the conic sections, which is formed by the intersection of a right circular cone by a plane surface. It is a symmetrical plane U-shaped curve. A parabola graph whose equation is in the form of f(x) = ax2+bx+c is the standard form of a parabola.
The given graph has 2 intercept at x axis x = -3, x = -5
y = a (x+3) (x+5)
using the intercept (-4, 3)
3 = a (-4 +3)(-4+5)
3 = a (-1)(1)
a =-3
y = -3(x+3)(x+5)
y = -3 [x(x+5) +3(x+5)]
y = [tex]-3x^{2}-24x-45[/tex]
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Related Questions
Aaquib can buy 25 liters of regular gasoline for $58.98 or 25 liters of permimum gasoline for 69.73. How much greater is the cost for 1 liter of premimum gasolinz? Round your quotient to nearest hundredth. show your work :)
YOU WILL GET 70 POINTS!
Answers
The cost for 1 liter of premium gasoline is $0.43 greater than the regular gasoline.
What is Cost?This is referred to as the total amount of money and resources which are used by companies in other to produce a good or service.
In this scenario, we were given 25 liters of regular gasoline for $58.98 or 25 liters of premium gasoline for $69.73.
Cost per litre of premium gasoline is = $69.73 / 25 = $2.79.
Cost per litre of regular gasoline is = $58.98/ 25 = $2.36.
The difference is however $2.79 - $2.36 = $0.43.
Therefore the cost for 1 liter of premimum gasoline is $0.43 greater than the regular gasoline.
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A house has increased in value by 35% since it was purchased. If the current value is S432,000, what was the value when it was purchased?
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The value of the house when it was purchased = $32000
Explanation:The original percentage value = 100%
The current percentage value = 100% + 35% = 135%
Current value = $432000
Original value = x
[tex]\begin{gathered} The\text{ current value =}\frac{135}{100}\times The\text{ original value} \\ \\ 432000=1.35\times x \\ \\ x=\frac{432000}{1.35} \\ \\ x=$ 320000 $ \end{gathered}[/tex]The value of the house when it was purchased = $32000
The cost to mail a package is 5.00. Noah has postcard stamps that are worth 0.34 and first-class stamps that are worth 0.49 each. An equation that represents this is 0.49f + 0.34p = 5.00Solve for f and p.If Noah puts 7 first-class stamps, how many postcard stamps will he need?
Answers
ANSWER
[tex]\begin{gathered} f=\frac{5.00-0.34p}{0.49} \\ p=\frac{5.00-0.49f}{0.34} \\ p=4.618\approx5\text{ postcard stamps} \end{gathered}[/tex]EXPLANATION
The equation that represents the situation is:
[tex]0.49f+0.34p=5.00[/tex]To solve for f, make f the subject of the formula from the equation:
[tex]\begin{gathered} 0.49f=5.00-0.34p \\ \Rightarrow f=\frac{5.00-0.34p}{0.49} \end{gathered}[/tex]To solve for p, make p the subject of the formula from the equation:
[tex]\begin{gathered} 0.34p=5.00-0.49f \\ \Rightarrow p=\frac{5.00-0.49f}{0.34} \end{gathered}[/tex]To find how many postcard stamps Noah will need if he puts 7 first-class stamps, solve for p when f is equal to 7.
That is:
[tex]\begin{gathered} p=\frac{5.00-(0.49\cdot7)}{0.34} \\ p=\frac{5.00-3.43}{0.34}=\frac{1.57}{0.34} \\ p=4.618\approx5\text{ postcard stamps} \end{gathered}[/tex]18. Yvonne paid $18.72 for 8 gallons of gas. How much would she have spent on gas if she had only needed 5 gallons of gas?
Answers
As given by the question
There are given that $18.72 for 8 gallons of gas.
Now,
Since, $18.72 for 8 gallons of gas;
Then,
First calculate the price of one-gallon gas
So,
[tex]\frac{18.72}{8}=2.34[/tex]The price og one g
Use the slope and y-intercept to graph the line whose equation is given. 2 y = -x + 5x+1
Answers
ok
y = -2/5 + 1
This is the graph
The length of a rectangular pool is 6 meters less than twice the width. If the pools perimeter is 84 meters, what is the width? A) Write Equation to model the problem (Use X to represent the width of the pool) B) Solve the equation to find the width of the pool (include the units)
Answers
I have a problem with the perimeter of a pool expressed in an unknown which corresponds to "x"
The first thing to do is to pose the corresponding equation, this corresponds to section A of the question
For the length, we have a representation of twice the width minus 6, i.e. 2x-6
For the width we simply have x
Remember that the sum of all the sides is equal to the perimeter which is 84, However, we must remember that in a rectangle we have 4 sides where there are two pairs of parallel sides, so we must multiply the length and width by 2
Now we can represent this as an equation
[tex]2(2x-6)+2x=84[/tex]This is the answer A
Now let's solve the equation for part B.
[tex]\begin{gathered} 2(2x-6)+2x=84 \\ 4x-12+2x=84 \\ 6x=84+12 \\ x=\frac{96}{6} \end{gathered}[/tex][tex]x=16[/tex]In conclusion, the width of the pool is 16
do you think you'd be able to help me with this
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x = wz/y
Explanation:[tex]\frac{w}{x}=\frac{y}{z}[/tex]To solve for x, first we need to cross multiply:
[tex]w\times z\text{ = x }\times y[/tex]Now we make x the subject of the formula:
[tex]\begin{gathered} To\text{ make x stand alone, we n}ed\text{ to remove any other variable around x} \\ \text{divide both sides by y}\colon \\ \frac{w\times z}{y}\text{ =}\frac{\text{ x }\times y}{y} \end{gathered}[/tex][tex]x\text{ = }\frac{wz}{y}[/tex]Use Vocabulary in Writing 9. Explain how you can find the product 4 X 2 and the product 8 X 2 Use at least 3 terms from the Word List in your explanation.
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Okay, here we have this:
what's the answer for proportions 4/n+2=7/n
Answers
Explanation
[tex]\frac{4}{n+2}=\frac{7}{n}[/tex]we need to solve for n
Step 1
cross multiply
[tex]\begin{gathered} \frac{4}{n+2}=\frac{7}{n} \\ 4\cdot n=7(n+2) \\ 4n=7n+14 \\ \end{gathered}[/tex]Step 2
subtract 4n in both sides
[tex]\begin{gathered} 4n=7n+14 \\ 4n-4n=7n+14-4n \\ 0=3n+14 \end{gathered}[/tex]Step 3
subtract 14 in both sides,
[tex]\begin{gathered} 0=3n+14 \\ 0-14=3n+14-14 \\ -14=3n \end{gathered}[/tex]Step 4
Finally, divide both sides by 3
[tex]\begin{gathered} \frac{-14}{3}=\frac{3n}{3} \\ n=-\frac{14}{3} \end{gathered}[/tex]I hope this helps you
A rectangular room is 1.5 times as long as it is wide, and its perimeter is 26 meters. Find the dimension of the room.The length is :The width is :
Answers
The rectangular room is 1.5times as long as it is wide and its perimeter is 26m. Let "x" represent the room's width, then the length of the room can be expressed as "1.5x"
The perimeter of a rectangle is equal to the sum of twice the width and twice the length following the formula:
[tex]P=2w+2l[/tex]We know that:
P=26m
w=x
l=1.5x
Then, replace the measurements on the formula:
[tex]\begin{gathered} 26=2x+2\cdot1.5x \\ 26=2x+3x \end{gathered}[/tex]From this expression, you can calculate x, first, add the like terms:
[tex]26=5x[/tex]Second, divide both sides by 5 to determine the value of x:
[tex]\begin{gathered} \frac{26}{5}=\frac{5x}{5} \\ 5.2=x \end{gathered}[/tex]The width is x= 5.2m
The length is 1.5x= 1.5*5.2= 7.8m
Find the coordinates of the other endpoint of a segment with the given endpoint and Midpoint M.T(-8,-1)M(0,3)
Answers
If we have 2 endpoints (x1, y1) and (x2, y2), the coordinates of the midpoint will be:
[tex]\begin{gathered} x=\frac{x_1+x_2}{2} \\ y=\frac{y_1+y_2}{2} \end{gathered}[/tex]Now, we know the coordinates of one endpoint (x1, y1) equal to (-8, -1) and the midpoint (x, y) equal to (0,3), so we can replace those values and solve for x2 and y2.
Then, for the x-coordinate, we get:
[tex]\begin{gathered} 0=\frac{-8+x_2}{2} \\ 0\cdot2=-8+x_2 \\ 0=-8+x_2 \\ 0+8=-8+x_2+8 \\ 8=x_2 \end{gathered}[/tex]At the same way, for the y-coordinate, we get:
[tex]\begin{gathered} 3=\frac{-1+y_2}{2} \\ 3\cdot2=-1+y_2 \\ 6=-1+y_2 \\ 6+1=-1+y_2+1 \\ 7=y_2 \end{gathered}[/tex]Therefore, the coordinates of the other endpoint are (8, 7)
Answer: (8, 7)
In a class of 30 students, 14 take tea and 20 take coffee. How many take both tea
and coffee?
Answers
Answer:
4
Step-by-step explanation:
[tex]20 + 14 = 34[/tex]
[tex]34 - 30 = 4[/tex]
Given 5x + 2y=22 and that y=1, find x
Answers
In a linear equation both variables are dependent on each other
Then to find x
first reorder and put x as one term only
x = (22- 2y)/5
now replace y by its given value y= 1
then x= (22- 2•1)/5 = 20/5= 4
Date: t rates to determine the better buy? b. Stop and Shop: 6 packages of Oreos cost $15.00 Key Food: 5 packages of Oreos cost $13.25
Answers
To determine the better buy you have to calculate how much one package costs in each shop.
1) 6 packages cost $15.00
If you use cross multiplication you can determine how much 1 package costs:
6 packs ______$15.00
1 pack _______$x
[tex]\begin{gathered} \frac{15.00}{6}=\frac{x}{1} \\ x=\frac{15}{6}=\frac{5}{2}=2.5 \end{gathered}[/tex]Each package costs $2.5
2) 5 packages cost $13.25
5packs_____$13.25
1 pack______$x
[tex]\begin{gathered} \frac{13.25}{5}=\frac{x}{1} \\ x=\frac{13.25}{5}=2.65 \end{gathered}[/tex]Each package costs $2.65
For the second purchase each package cost $0.15 more than in the first purchase.
Is best to buy the 6 packages at $15.00
find the simple interest earned, to the nearest cent, for each principal interest rate, and time.
Answers
Answer:
$8.40
Explanation:
From the given statement:
Principal = $840
Time = 6 Months
Rate = 2%
Note that Time must be in Years, therefore:
Time = 6 Months = 6/12 = 0.5 Years
[tex]\begin{gathered} \text{Simple Interest }=P\times R\times T \\ =840\times2\%\times0.5 \\ =840\times0.02\times0.5 \\ =\$8.40 \end{gathered}[/tex]The simple interest earned is $8.40
A taxi service charges $3 for the first mile and then $2.25 for every mile after that. The farthest the taxi will travel is 35 miles. If X represents the number of miles traveled, and Y represents the total cost of the taxi ride, what is the most appropriate domain for the solutions?
Answers
Solution:
Given:
[tex]\begin{gathered} A\text{ taxi service charges \$3 for the first mile} \\ \text{ \$2.25 for every mile after that.} \\ \text{The farthest the taxi will travel is 35 miles.} \end{gathered}[/tex]Since x represents the number of miles traveled
y represents the total cost of the taxi ride
From the description, the number of miles the taxi will travel is between 0 and 35miles since 35 miles is the farthest it could go.
This means the domain which refers to the set of possible input values will be;
[tex]\begin{gathered} x>0\text{ because the service is charged once a certain distance is covered.} \\ \text{when no distance is covered, no charge is made.} \\ \text{Also,} \\ x\le35\text{ because the farthest is 35miles. This means the ta}\xi\text{ can not travel beyond 35miles.} \\ \\ \text{From the descriptions made, the domain will be:} \\ 0Therefore, the most appropriate domain for the solutions is;
[tex]0 The correct answer is OPTION B.Find all solutions in[0, 2pi): 2sin(x) – sin (2x) = 0
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Based on the answer choices, replace the pair of given values and verify the equation, as follow:
For x = π/4, π/6
[tex]2\sin (\frac{\pi}{4})-\sin (\frac{2\pi}{4})=2\frac{\sqrt[]{2}}{2}-1\ne0[/tex]the previous result means that the given values of x are not solution. The answer must be equal to zero.
Next, for x = 0, π
[tex]\begin{gathered} 2\sin (\pi)-\sin (2\pi)=0-0=0 \\ 2\sin (0)-\sin (0)=0-0=0 \end{gathered}[/tex]For both values of x the question is verified.
The rest of the options include π/4 and π/3 as argument, you have already shown that these values of x are not solution.
Hence, the solutions for the given equation are x = 0 and π
Find an expression equivalent to the one shown below.913 x 9-6OA. 79OB.919OC. 97OD. 9-78
Answers
Answer:
C. 9⁷
Explanation:
We will use the following property of the exponents:
[tex]x^a\times x^b=x^{a+b}[/tex]It means that when we have the same base, we can simplify the expression by adding the exponents. So, in this case, the equivalent expression is:
[tex]9^{13}\times9^{-6}=9^{13-6}=9^7[/tex]Therefore, the answer is C. 9⁷
Josslyn placed $4,400 in a savings account which earns 3.2% interest, compounded annually. How much will she have in the account after 12 years?Round your answer to the nearest dollar.
Answers
The equation for the total amount after compounded interest is as follows:
[tex]A=P(1+\frac{r}{n})^{nt}^{}[/tex]Where A is the final amount, P is the initial amount, r is the annual interest, n is how many times per year the interest is compounded and t is the time in years.
Since the interest is compounded annually, it is compounded only once per year, so
[tex]n=1[/tex]The other values are:
[tex]\begin{gathered} P=4400 \\ r=3.2\%=0.032 \\ t=12 \end{gathered}[/tex]So, substituteing these into the equation, we have:
[tex]\begin{gathered} A=4400(1+\frac{0.032}{1})^{1\cdot12} \\ A=4400(1+0.032)^{12} \\ A=4400(1.032)^{12} \\ A=4400\cdot1.4593\ldots \\ A=6421.0942\ldots\approx6421 \end{gathered}[/tex]So, she will have approximately $6421.
need help. first correct answer gets brainliest plus 15 pts
Answers
We are given that lines V and 0 and lines C and E are parallel.
We are asked to prove that ∠15 and ∠3 are congruent (equal)
In the given figure, angles ∠3 and ∠7 are "corresponding angles" and they are equal.
[tex]\angle3=\angle7[/tex]In the given figure, angles ∠7 and ∠6 are "Vertically opposite angles" and they are equal.
[tex]\angle7=\angle6[/tex]Angles ∠6 and ∠14 are "corresponding angles" and they are equal.
[tex]\angle6=\angle14[/tex]Angles ∠14 and ∠15 are "Vertically opposite angles" and they are equal.
[tex]\angle14=\angle15[/tex]Therefore, the angles ∠15 and ∠3 are equal.
[tex]\angle3=\angle7=\angle6=\angle14=\angle15[/tex]solve the following system of equations-5x-3y=-16-3x+2y=-21x=y=
Answers
-5x - 3y = -16
-3x + 2y = -21
Solving for y the first equation:
-5x + 16 = 3y
y = (-5/3)x + (16/3)
Using this value of y into the second equation:
-3x + 2(-5/3)x + 2(16/3) = -21
-3x - (10/3)x + 32/3 = -21
Multiplying all by 3:
-9x - 10x + 32 = -63
-19x = -63 - 32 = -95
x = 95/19
Using this value of x into the y we found with the first equation:
y = (-5/3)x + 16/3
y = (-5/3)(95/19) + 16/3 = -475/57+ 304/57 = -171/57
y = -171/57
x = -31/19 = -1.6315
y = -171/57 = -3
Answer:
x = -1.6315
y = -3
An advertising company plans to market a product to low-income families. A study states that for a particular area the mean income per family is $25,174 and the standard deviation is $8,700. If the company plans to target the bottom 18% of the families based on income, find the cutoff income. Assume the variable is normally distributed.
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help me please.......
Answers
Let
x -----> the larger room
y -----> the smaller room
we have that
x=2y
we have
y=25 3/4 ft
Convert to an improper fraction
25 3/4=25+3/4=103/4 ft
Find the value of x
x=2y
x=2(103/4)
x=103/2 ft
Convert to mixed number
103/2=51.5=51+0.5=51 1/2 ft
the answer is51 1/2 fthe larger roomhe larger room
A baby cows growth. About how many pounds does the baby cow gain each week?
Answers
Growth per week = 124 - 122 = 126 - 124 = 2
. = 2 pounds + 1 pound additional
. = 3
Then answer is
OPTION B) 3 pounds
Write an equation of the line that passes through (4, 3) and is parallel to the line defined by 5x-2y-3. Write the answer in slope-intercept form (if possible)
and in standard form (Ax+By-C) with smallest integer coefficients. Use the "Cannot be written" button, if applicable.
Answers
The final answer to the question is highlighted in the box
A game fair requires that you draw a queen from a deck of 52 ards to win. The cards are put back into the deck after each draw, and the deck is shuffled. That is the probability that it takes you less than four turns to win?
Answers
The probability (P) is winning in less than four turns can be decomposed as the following sum:
The probability of winning in one turn is
[tex]P(\text{Winning in turn 1})=\frac{\#Queens}{\#Cards}=\frac{4}{52}.[/tex]The probability of winning in the second turn is
[tex]\begin{gathered} P(\text{ Winning in the second turn})=P(\text{ Lossing (in turn 1)})\cdot P(\text{ Winning (in turn 2)}), \\ \\ P(\text{ Winning in the second turn})=\frac{\#NoQueens}{\#Cards}\cdot\frac{\#Queens}{\#Cards}, \\ \\ P(\text{ Winning in the second turn})=\frac{48}{52}\cdot\frac{4}{52}\text{.} \end{gathered}[/tex]The probability of winning in the third turn is
[tex]\begin{gathered} P(\text{ Winning in the third turn})=P(\text{ Lossing (in turn 1)})\cdot P(\text{ Lossing (in turn 2)})\cdot P(\text{ winning (in turn 3)}), \\ \\ P(\text{ Winning in the third turn})=\frac{\#NoQueens}{\#Cards}\cdot\frac{\#NoQueens}{\#Cards}\cdot\frac{\#Queens}{\#Cards}, \\ \\ P(\text{ Winning in the third turn})=\frac{48}{52}\cdot\frac{48}{52}\cdot\frac{4}{52}\text{.} \end{gathered}[/tex]Adding all together, we get
[tex]\begin{gathered} P(\text{ Winning in less than four turns})=\frac{4}{52}+\frac{48}{52}\cdot\frac{4}{52}+\frac{48}{52}\cdot\frac{48}{52}\cdot\frac{4}{52}, \\ \\ P(\text{ Winning in less than four turns})=\frac{469}{2197}, \\ \\ P(\text{ Winning in less than four turns})\approx0.2135, \\ \\ P(\text{ Winning in less than four turns})\approx21.35\% \end{gathered}[/tex]AnswerThe probability of winning in less than four turns is (approximately) 21.35%.
School: Practice & Problem Solving 7.1.PS-18 Question Help A rectangle and a parallelogram have the same base and the same height. How are their areas related? Provide an example to justify your answer The areas equal. A rectangle has dimensions 5 m by 7 m, so its area is m² A parallelogram with a base of 5 m and a height of 7 m has an area of (Type whole numbers.)
Answers
The image shown below shows the relationship between areas of rectangle and parallelogram
It can be seen that the areas are equal when they have the same sides or dimension
A rectangle has dimensions 5 m by 7 m, so its area is 5m x 7m = 35m²
A parallelogram with a base of 5 m and a height of 7 m has an area of 5m x 7m = 35m²
Suppose that the distribution for total amounts spent by students vacationing for a week in Florida is normally distributed with a mean of 650 and a standard deviation of 120. Suppose you take a simple random sample (SRS) of 35 students from this distribution.
What is the probability that an SRS of 35 students will spend an average o between 600 and 700 dollars? Round to five decimal places
Answers
The probability that an SRS of 35 students will spend an average o between 600 and 700 dollars is 98.61%
Given,
The mean of the normal distribution, μ = 650
Standard deviation of the distribution, σ = 120
n = 35
By using central limit theorem, standard deviation for SRS of n, δ = σ/√n = 120/√35
The z score = (x - μ) / σ
By using central limit theorem,
z score = (x - μ) / δ
Here,
We have to find the probability that an SRS of 35 students will spend an average o between 600 and 700 dollars:
(p value of z score of x = 700) - (p value of z score of x = 600)
z score of x = 700
z = (x - μ) / δ = (700 - 650) /( 120/√35) = (50 × √35) / 120 = 2.46
p value of z score 2.46 is 0.99305
z score of x = 600
z = (x - μ) / δ = (600 - 650) /( 120/√35) = (-50 × √35) / 120 = -2.46
p value of z score -2.46 is 0.0069469
Now,
0.99305 - 0.0069469 = 0.9861031 = 98.61%
That is, the probability that an SRS of 35 students will spend an average o between 600 and 700 dollars is 98.61%
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which property justifies the following statement if 3x=9,then x=3.
Answers
Answer:
Multiplication Property
Division Property
This can be justified using multiplication property and division property:
Multiplication property:
If both sides of equation:
3x = 9
are multiplied by 1/3, we have:
x = 3
Division property
Divide both sides of the equation:
3x = 9 by 3, we have:
x = 3
A polynomial function is given.
Q(x) = −x2(x2 − 9)
(a) Describe the end behavior of the polynomial function.
End behavior: y → as x → ∞
y → as x → −∞
Answers
The end behavior of the polynomial is:
y → −∞ as x → ∞
y → −∞ as x → −∞
How is the end behavior?Here we have the polynomial:
Q(x) = -x²*(x² - 9)
Remember that polynomials with even degrees have the same behavior for the negative values of x than for the positive, in this case if we expand the polynomial we get:
Q(x) = -x⁴ + 9x²
The leading coefficient is negative, then the end behavior will tend to negative infinity in both ends, then we get:
y → −∞ as x → ∞
y → −∞ as x → −∞
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