URGENT!! I have been trying to ask this question for a while but I keep getting fake answers: Find an equation in standard form for a parabolic function that goes through the points (1,-12) (3,16) and has a stretch factor of 2
Answer:
Step-by-step explanation:
y=a(x-h)^2+k
-12=a(1-h)^2+k
16=a(3-h)^2+k
subtract
a(3-h)^2-a(1-h)^2=28
a[(3-h)^2-(1-h)^2]=28
a=2
2[(3-h)^2-(1-h)^2]=28
(3-h)^2-(1-h)^2=14
9+h^2-6h-(1+h^2-2h)=14
9+h^2-6h-1-h^2+2h=14
-4h+8=14
-4h=6
h=-3/2
16=2(3+3/2)^2+k
16=2×81/4+k
k=16-81/2=-49/2
so y=2(x+3/2)²-49/2
Answer: y=a(x-h)^2+k
-12=a(1-h)^2+k
16=a(3-h)^2+k
subtract
a(3-h)^2-a(1-h)^2=28
a[(3-h)^2-(1-h)^2]=28
a=2
2[(3-h)^2-(1-h)^2]=28
(3-h)^2-(1-h)^2=14
9+h^2-6h-(1+h^2-2h)=14
9+h^2-6h-1-h^2+2h=14
-4h+8=14
-4h=6
h=-3/2
16=2(3+3/2)^2+k
16=2×81/4+k
k=16-81/2=-49/2
so y=2(x+3/2)²-49/2
Step-by-step explanation:
PLEASE HELP!! what is the equation for the parabolic function that goes through the points (-3, 67) (-1, 1) and has a stretch factor of 9
Answer:
[tex]f(x)=9(x+\frac{1}{6})^2-\frac{21}{4}[/tex]
Step-by-step explanation:
So, we need to find the equation of a parabolic function that goes through the points (-3,67) and (-1,1) and has a stretch factor of 9.
In other words, we want to find a quadratic with a vertical stretch of 9 that goes through the points (-3,67) and (-1,1).
To do so, we first need to write some equations. Let's use the vertex form of the quadratic equation. The vertex form is:
[tex]f(x)=a(x-h)^2+k[/tex]
Where a is the leading coefficient and (h,k) is the vertex.
Since a is the leading coefficient, it's also our stretch factor. Thus, let a equal 9.
Also, we have two points. We can interpret them as functions. In other words, (-3,67) means that f(-3) equals 67 and (-1,1) means that f(-1) equals 1. Write the two equations:
[tex]f(x)=a(x-h)^2+k\\f(-3)=67=9((-3)-h)^2+k[/tex]
And:
[tex]f(x)=a(x-h)^2+k\\f(-1)=1=9((-1)-h)^2+k[/tex]
Now, we essentially have a system of equations. Thus, to find the original equation, we just need to solve for the vertex. To do so, first isolate the k term in the second equation:
[tex]1=9(-1-h)^2+k\\k=1-9(-1-h)^2[/tex]
Now, substitute this value to the first equation:
[tex]67=9(-3-h)^2+k\\67=9(-3-h)^2+(1-9(-1-h)^2)[/tex]
And now, we just have to simplify.
First, from each of the square, factor out a negative 1:
[tex]67=9((-1)(h+3))^2+(1-9(((-1)(h+1))^2)[/tex]
Power of a product property:
[tex]67=9((-1)^2(h+3)^2)+(1-9((-1)^2(h+1)^2))[/tex]
The square of -1 is positive 1. Thus, we can ignore them:
[tex]67=9(h+3)^2+(1-9(h+1)^2)[/tex]
Square them. Use the trinomial pattern:
[tex]67=9(h^2+6h+9)+(1-9(h^2+2h+1))[/tex]
Distribute:
[tex]67=(9h^2+54h+81)+(1-9h^2-18h-9)[/tex]
Combine like terms:
[tex]67=(9h^2-9h^2)+(54h-18h)+(81+1-9)[/tex]
The first set cancels. Simplify the second and third:
[tex]67=36h+73[/tex]
Subtract 73 from both sides. The right cancels:
[tex]67-73=36h+73-73\\36h=-6[/tex]
Divide both sides by 36:
[tex](36h)/36=(-6)/36\\h=-1/6[/tex]
Therefore, h is -1/6.
Now, plug this back into the equation we isolated to solve for k:
[tex]k=1-9(-1-h)^2[/tex]
First, remove the negative by simplifying:
[tex]k=1-9((-1)(h+1))^2\\k=1-9((-1)^2(h+1)^2)\\k=1-9(h+1)^2[/tex]
Plug in -1/6 for h:
[tex]k=1-9(-\frac{1}{6}+1)^2[/tex]
Add. Make 1 into 6/6:
[tex]k=1-9(-\frac{1}{6}+\frac{6}{6})^2\\ k=1-9(\frac{5}{6})^2[/tex]
Square:
[tex]k=1-9(\frac{25}{36})[/tex]
Multiply. Note that 36 is 9 times 4:
[tex]k=1-9(\frac{25}{9\cdot4})\\ k=1-\frac{25}{4}[/tex]
Convert 1 into 4/4 and subtract:
[tex]k=\frac{4}{4}-\frac{25}{4}\\ k=-\frac{21}{4}[/tex]
So, the vertex is (-1/6, -21/4).
Now, plug everything back into the very original equation with 9 as a:
[tex]f(x)=a(x-h)^2+k\\f(x)=9(x+\frac{1}{6})^2-\frac{21}{4}[/tex]
And this is our answer :)
plzzz help! will give branliest if you can do this one!!! i also need help with other math problems
Answer:
The answer is d
Step-by-step explanation:
What is the product of -8 and 5? A. 40 B. -40 C. 13 D. -3
Answer:b-40
Step-by-step explanation:
Louise measured the perimeter of her rectangular scrapbook to be 148 cm. If the scrapbook is 38 cm wide, how long is the scrapbook?
Answer:
36cm
Step-by-step explanation:
38 × 2 = 76
148 - 86 = 72
72/2 = 36
Write the following statements in equation form: If the sum of a number and its two fifth is 70
Answer:
[tex]x + \frac{2}{5} \times x = 70 \\ x + \frac{2}{5} x = 70[/tex]
Answer:
Let it be x the number.
We have to sum to x two fifths of him and we know the result is 70, so:
[tex]x + \frac{2}{5}x = 70[/tex]
We could also solve it:
[tex]\frac{5x}{5}+\frac{2x}{5}=\frac{350}{5}[/tex]
[tex]5x + 2x = 350[/tex]
[tex]7x = 350[/tex]
[tex]x=\frac{350}{7}=50[/tex]
What is the first step for solving this problem: 12÷ 6(3)+8
Answer: The first step would be to divide 12 by 6.
Step-by-step explanation:
Answer:
Division.
Step-by-step explanation:
There are two rules that you follow. One is PEMDAS, and the other is the left -> right rule.
Note that PEMDAS =
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
The order of operation is: P , (E & R) , (M & D) , (A & S), parenthesis meaning they can be interchangeable, due to the left -> right rule.
Solve:
First, divide:
12/6 = 2
Next, multiply:
2 x 3 = 6
Finally, add:
6 + 8 = 14
14 is the answer.
what is 9000/16000 as a decimal
Answer:
It is 0.56 Hope this helps!
Step-by-step explanation:
Answer:
0.5625
Step-by-step explanation:
divide and you get 0.5625. Simplified to the nearest tenth is .6
to the nearest hundreth if .56
you have set a goal to drink more water every day. your water bottle holds 0.5 liters of water in the equation below, b is the number of times you drink all the water in your bottle and L is the number of liters of water you drink. The relationship between these two variables can be expressed by the following equation: L=0.5b Identify the dependent and independent variable.
Answer:
Step-by-step explanation:
B is the independent variable since the amount of times you drink the water is controlled by you.
I is the dependent variable since it's depending on how much water you're drinking
Plz help me Now! Thx
Answer:
A or/and B
Step-by-step explanation:
in A the hundreds value is 8 and [tex]\frac{8}{10} = 0.8[/tex]
in B he hundreds value is 7 and [tex]\frac{7}{10} =0.7[/tex]
hope this helps you!
Answer:
C. 1.404
Step-by-step explanation:
The 1000ths place is the 1 in 0.01
The 100ths place is the 1 in 0.001
A = 0.881
The number in the 1000ths place is 1
The number in the 100ths place is 8
1/8 is not 1/10
B = 0.722
The number in the 1000ths place is 2
The number in the 100ths place is 2
2/2 is not 1/10
C = 1.404
The number in the 1000ths place is 4
The number in the 100ths place is 0
BUT the numbe rin the 100ths place could also be written as 40, where the 4 from the 40 has moved up a place to 10th
in which case, 4/40 = 1/10
What is the simplified form of 3√7 - 5√7? A. -2√7 B. 2√7 C. -√14 D. 15√7
Your fitness tracker overestimates the number of steps you take by 5%. The trackers indicates that you took 7350 steps today. Write and solve an equation to find the actual number of steps you took today.
the answer is 140000 steps
Answer:
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbdrtgaethrtththt
Step-by-step explanation:
What is the relationship between the value of the 4 in 3,642 and the value of the 4 in 5,401?
Answer: The 4 in the number 5,401 is 10 times greater than the 4 in the number 3,642.
In the number 3,642 the number 4 is in the Tens Place.
In the number 5,401 the number 4 is in the Hundreds Place.
Tens < Hundreds
40 < 400
Q: How do we know it's 10 times greater?
A: Multiply!
You multiply 40×10 and get 400! To see if the answer is right divide 400÷40 and get 10. Or divide 400÷10 and get 40.
Basically, when you're multiplying something by 10 you just add a 0. When you divide by 10 you remove a 0.
That's how the number 4 in 5,401 is 10 times greater than the number 4 in 3,642.
Consider the line 9x+5y=6 What is the slope of a line parallel to this line? What is the slope of a line perpendicular to this line?
Answer:The equation of the line is 9x-5y=9
5y=9x-9
y=9/5x-9/5
Comparing with y=mx+c we get slope m=9/5
Slope of a line parallel to this line=9/5
Slope of a line perpendicular to this line=-5/9
Step-by-step explanation:
A jeweler uses 3.685 grams of gold to make a ring. Enter the word form for 3.685.
Answer:
three and six hundrend eighty five thousands grams of gold
Step-by-step explanation:
Show that AC and BD bisect each other if A(–3, –5), B(2, –3), C(3, 5), and D(–2, 3). Find AC and BD
Answer:
Step-by-step explanation:
midpoint of AC=((-3+3)/2,(-5+5)/2)=(0,0)
midpoint of BD=((2-2)/0,(-3+3)/2)=(0,0)
coordinates of midpoint of AC and BD are same.
∴ AC and BD bisect each other.
[tex]AC=\sqrt{(3-(-3))^2+(5-(-5))^2 } =\sqrt{6^2+10^2} =\sqrt{136} =2\sqrt{39} \\BD=\sqrt{((-2-2)^2+(3-(-3))^2} =\sqrt{16+36} =\sqrt{52} =2\sqrt{13}[/tex]
Midpoint of AC and BD is ( 0, 0 ), so both bisects each other.
The value of AC = 2 √39 and BD = 2 √13
Here, points given as,
A(–3, –5), B(2, –3), C(3, 5), and D(–2, 3).
We have to find, AC and BD.
What is distance between two points?
Distance between two points [tex]P(x_{1} ,y_{1} )[/tex] and [tex]Q(x_{2} ,y_{2} )[/tex] is given by:
[tex]d(P, Q) = \sqrt{(x_{2}- x_{1} )^2 +(y_{2}- y_{1} )^2 }[/tex]
Now,
Midpoint of AC = [tex](\frac{-3+3}{2} ), (\frac{-5+5}{2} ) = ( 0, 0 )[/tex]
Midpoint of BD = [tex](\frac{-2+2}{2} ), (\frac{-3+3}{2} ) = ( 0, 0 )[/tex]
Hence, Both AC and BD bisects each other.
And, Distance between A and C is,
AC = [tex]\sqrt{(3 - (-3))^2 +(5 - (-5))^2 } = \sqrt{36 + 100} = \sqrt{136} = 2\sqrt{39}[/tex]
Distance between B and D is,
BD = [tex]\sqrt{( -2 -2))^2 +(3 - (-3))^2 } = \sqrt{16 + 36} = \sqrt{52} = 2\sqrt{13[/tex]
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A small, test batch of lemonade used 1/4 cups of sugar added to 1 cup of water and 1/4 cup of lemon juice. After confirming it tasted good, a larger batch is going to be made with the same ratios using 10 cups of water. How much sugar should be added so that the large batch tastes the same as the test batch?
Answer:2 and a half cups of sugar
Step-by-step explanation:
1/4*10
Which statement best illustrates using the vertical line test to determine if the graph below is a function of x?
A. The graph is not a function of x because the line x = 0 intersects the graph at two points.
B. The graph is a function of x because the line x = 5 does not intersect the graph.
C. The graph is not a function of x because the line y = 0 intersects the graph at two points.
D.The graph is a function of x because the line y = 5 does not intersect the graph.
PLS HELP!!!!
Answer:
A. The graph is not a function of x because the line x = 0 intersects the graph at two points.
Step-by-step explanation:
Which of the following is another way to express the difference between -5 and 8?
-5 - (-8)
-5 + 8
8 - 5
-5 + (-8)
What is-3.28-(4.4)+(-p) p=9.7?
Answer:
-17.38
Step-by-step explanation:
-3.28-(4.4) = -7.6
-7.6+(-9.7) = -17.38
the volleyball team needs new uniforms. the students plan to sell plush toy Eagles ( the school mascot) for $5 each. The students find three companions on-line that sell stuff mascots. Company A cell's 12 eagles for $34.08. Company B cells 15 equals for $42.90. Company C charges $50.58 for 18 eagles. which company has the Best Buy?
Answer:
Company C
Step-by-step explanation:
You divide the amount of money it all costs to the number of plushies they are selling it for.
A: 34.08/12 = $2.84 each
B: 42.90/15 = $2.86 each
C: 50.58/18 = $2.81 each
So C has the least amount of money spent for a greater amount of plushies so C would be the Best Buy.
Your fitness tracker overestimates the number of steps you take by 5%. The trackers indicates that you took 7350 steps today. Write and solve an equation to find the actual number of steps you took today.
The equation (1 + 0.05)x = 7350 to find the actual number of steps you took today will be 7,000.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.
Your fitness tracker overestimates the number of steps you take by 5%. The trackers indicate that you took 7350 steps today.
Let x be the actual number of steps. Then the equation will be given as,
(1 + 0.05)x = 7350
x = 7350 / 1.05
x = 7,000
The actual number of steps you took today will be
(1 + 0.05)x = 7350
x = 7350 / 1.05
x = 7,000
The equation (1 + 0.05)x = 7350 to find the actual number of steps you took today will be 7,000.
More about the percentage link is given below.
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The coordinates of three of the vertices of parallelogram ABCD are A(2, 0), B(4, 3), C(3, 1). How many possibilities are there for the position of the fourth vertex? What are coordinates of the fourth vertex?
Answer:
If you are given 3 vertices of a parallelogram, as a Geometry student, you will be asked to find the exact coordinates of the 4th vertex. Just so that you can put your mind at ease, there can be different answers depending on how you decide to "draw" or "shape" your parallelogram. So if your answer is different than another student, it does not mean that you have done it incorrectly.
Suppose I am given 3 points as such, and I am looking for the coordinates of D:
A (2, 3)
B (8, 1)
C (11, 5)
D (x, y)
The line segments that make up our parallelogram is AD is parallel to BC, and CD is parallel to AB. Since the definition of a parallelogram is a quadrilateral with 2 pairs of parallel sides, we can use this fact to find the coordinate to the 4 vertex. A pair of parallel side also means that these 2 lines have the same slope. So if we do this on both pairs of parallel lines, we should have 2 equations with 2 variables, which should be simple to solve.
Slope of CD = Slope Slope of AB
(y - 5)/(x - 11) = (1 - 3)/(8 - 2)
(y - 5)/(x - 11) = -2/6
6(y - 5) = -2(x - 11)
6y - 30 = -2x + 22
equation #1: 6y + 2x = 52
Slope of AD = Slope of BC
(y - 3)/(x - 2) = (5 - 1)/(11 - 8)
(y - 3)/(x - 2) = 4/3
3(y - 3) = 4(x - 2)
3y -9 = 4x - 8
equation #2: 3y - 4x = 1
We now we have 2 equations with 2 variables, and we can use any method (substitution, linear combination, matrix) to solve for the x and y coordinates.
equation #1: 6y + 2x = 52
equation #2: 3y - 4x = 1
Multiply equation by -2
Equation 2: -2(3y - 4x = 1)
Equation 2: -6y + 8x = -2
Add equation 1 to equation 2
equation 1: 6y + 2x = 52
equation 2: -6y + 8x = -2
eq 1 + eq 2: 10x = 50
x = 5
Use any of the original equation to solve for y:
6y + 2x = 52
6y + 2(5) = 52
6y = 42
y = 7
So the 4th vertex for my first answer will be (5, 7)
If we draw the parallelogram in a different way using the given vertices, we will be looking for a different 4th vertex. So in our original question:
A (2, 3)
B (8, 1)
C (11, 5)
D (x, y)
Our line segments in this case will be draw as such:
AC is parallel to BD and CD is parallel to AB.
Slope of AC = slope of BD
(5 - 3)/(11 - 2) = (y - 1)/(x - 8)
2/9 = (y - 1)/(x - 8)
2(x - 8) = 9(y - 1)
2x - 16 = 9y - 9
equation 1: 2x - 9y = 7
Slope of CD = slope of AB
(5 - y)/(11 - x) = (3 - 1)/(2 - 8)
(5 - y)/(11 - x) = 2/-6
-6(5 - y) = 2(11 - x)
-30 + 6y = 22 - 2x
equation 2: 2x + 6y = 52
Solve the following linear system:
equation 1: 2x - 9y = 7
equation 2: 2x + 6y = 52
eq 1 - eq2: -15y = -45
-15y = -45
y = 3
Substitute y = 3 into any one of the original equation:
equation 1: 2x - 9y = 7
2x - 9(3) = 7
2x - 27 = 7
2x = 34
x = 17
So by drawing the parallelogram in a different way, the 4th vertex of this parallelogram is (17, 3).
Step-by-step explanation:
See Answer
The fourth coordinate for the given parallelogram will be (5, 7).
What is a parallelogram?A basic quadrilateral with two sets of parallel sides is known as a parallelogram.
A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.
There are 4 types of parallelograms, including 3 special types. The four types are parallelograms, squares, rectangles, and rhombuses.
Given the parallelogram ABCD are A(2, 0), B(4, 3), C(3, 1).
Now,
The slope of AB = Slope of CD
(y - 5)/(x - 11) = (1 - 3)/(8 - 2)
6(y - 5) = -2(x - 11)
⇒ 6y + 2x = 52 will be the first equation.
Now,
The slope of BC = Slope of AD
[(y - 3)/(x - 2)] = [(5 - 1)/(11 - 8)]
[(y - 3)/(x - 2)] = 4/3
3(y - 3) = 4(x - 2)
⇒ 3y - 4x = 1 will be the second equation.
Now, By substitution
x = 5 and y = 7
Hence "The fourth coordinate for the given parallelogram will be (5, 7)".
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Squidward loves playing his clarinet and believes it attracts more jellyfish than any other instrument he has played. In order to test his hypothesis, Squidward played a song on his clarinet for a total of 5 minutes and counted the number of jellyfish he saw in his front yard. He played the song a total of 3 times on his clarinet, and then repeated the experiment using a flute and a guitar. He also recorded the number of jellyfish he observed when he was not playing an instrument. The results are shown in the chart. number of jellyfish attracted to each instrument trial / without music / clarinet / flute / guitar 1 / 5 / 15 / 5 / 12 2 / 3 / 10 / 8 / 18 3 / 2 / 12 / 9 / 17 1) what is the dependent value? 2) what is the independent variable? 3) what should be Squidward’s conclusion? 4) are the results reliable? why or why not?
Answer:
1. The amount of jellyfish attracted ,
2. The type of instrument played ,
3. The guitar attracts the most jellyfish,
4. the results are reliable. there are no big outliers .
Is the value of the 8 in 12.984 the same as the value of the 8 in 7.38? Justify your response.
Answer:
Yes because they are both in the hundredths place
Step-by-step explanation:
Pls help me!! ASAP I WILL GIVE BRAINLIEST Brandon's bread recipe calls for milk powder, sugar, and flour in a ratio of 2:3:15, respectively. How many pounds of each does Brandon need if the three ingredients together weigh 2 lb?
Answer:
0.2 pounds of milk
0.3 pounds of sugar
1.5 pounds of flour
Step-by-step explanation:
If we have the ratio [tex]2:3:15[/tex], then we know that all of these ingredients together will be [tex]15+3+2=20[/tex]. If we want the whole thing to weight 2 pounds, then the total weight of everything else will be [tex]20\div2=10[/tex] percent of the original.
So,
[tex]2\cdot0.1=0.2\\\\3\cdot0.1=0.3\\\\15\cdot0.1=1.5[/tex]
We can confirm this is correct because [tex]1.5+0.3+0.2=2[/tex].
Hope this helped!
Step-by-step explanation:
Simple formula [tex]\frac{item ratio}{total ratio}[/tex]×total amount
milk powder; ×2= 0.2 lb
sugar; [tex]\frac{3}{20}[/tex]×2= 0.3 lb
flour; [tex]\frac{15}{20}[/tex]×2= 1.5 lb
To check you can add them up :)
Hope this helps :)
The answers are bold*
If 38 = 11 + 3x, what is the value of x ?
Answer:
38-11=3x
27=3x
27/3=x
x=9
[tex]38=11+3x[/tex] collect like-terms
[tex]38-11=3x[/tex] subtract
[tex]27=3x[/tex] divide
[tex]x=\frac{27}{9}[/tex]
[tex]x=9[/tex]
plug [tex]x[/tex] in the equation to make sure of the answer
[tex]38=11+3x\\38=11+3(9)\\38=11+27\\38=38[/tex]
Find the number if 18 is taken away from 8 times of a number gives 30.
Answer:
Let the number be x.
8 times that number would be 8x, and taking away 18 from it 8x - 18. Knowing the result of doing this is 30, we can write the following equation:
8x - 18 = 30
And solve it. First we pass the -18 to the sight umming:
8x = 30 + 18
8x = 48
Then the 8 which is multiplying to the right dividig:
x = 48/8 = 6
Now we verify we have done it preporly:
8x - 18 = 30
8 * 6 - 18 = 30
48 - 18 = 30 TRUE
Answer:
x =6
Step-by-step explanation:
Translate into algebraic equation =
[tex]8(x)-18= 30\\= 8x-13=30[/tex]
Let's solve for x
[tex]\mathrm{Add\:}18\mathrm{\:to\:both\:sides}\\8x-18+18=30+18[/tex]
Simplify
[tex]8x=48[/tex]
Divide both sides by 8
[tex]\frac{8x}{8}=\frac{48}{8}[/tex]
Simplify
[tex]x =6[/tex]
the ratio of males to females at a camp is 5 to 4. If there are 40 males at the camp, how many females are there?
Answer:
5 males : 4 females
40 males : X females
5/40 =4/X
(cross multiplication)
5x = 4*40
5x = 160
(divide both sides by 5)
X = 32
therefore, there are 32 females at the camp
Julie printed out a picture of each of the four members of her favorite band to decorate her bedroom door. Each picture measures 8 inches by 10 inches. Once decorated, how many square inches of Julie's door will be covered by these pictures?
Answer:
360 square inches
Step-by-step explanation:
(8*10)*4
80*4
360