Answer:
h = -3
The value h = -3 translates the graph of the parent function [tex]y=x^2[/tex] 3 units to the left.
Step-by-step explanation:
The graph of [tex]f(x)=(x-h)^2+k[/tex] contains the points (-6, -2) and (0, -2).
This is the equation of parabola in vertex form, where [tex](h,k)[/tex] are the coordinates of the vertex.
If the graph has a vertex at [tex](h,-5),[/tex] then [tex]k=-5.[/tex]
So, the equation of the parabola is
[tex]f(x)=(x-h)^2-5[/tex]
If the graph passes through the points (0,-2) and (-6,-2) (these two points lie on the same horizontal line y = -2), then the parabola vertical line of symmetry divides the segment between these points into two congruent segments. Hence, the equation of the line of symmetry is
[tex]x=\dfrac{0+(-6)}{2}=-3[/tex]
The vertex lies on the line of symmetry, so its x-coordinate is -3. Thus, (-3,-5) is the vertex.
The value h = -3 translates the graph of the parent function [tex]y=x^2[/tex] 3 units to the left.
Answer:
Sample Response: The absolute value function is symmetric. Since the points (–6, –2) and (0, –2) have the same output, the points are the same distance from the line of symmetry. Between –6 and 0 is the value of –3. So, the vertex must have an x-coordinate of –3, which is the value of h. This would translate the graph of the parent function 3 units to the left.
Simplify -8.6 + 2.3 + 1
-5.3
-7.3
-9.9
Answer:
-5.3.
Step-by-step explanation:
-8.6 + 2.3 + 1
= -6.3 + 1
= -5.3.
Consider g(x) = −x^2 + 12x − 32 Part A: Write g(x) in vertex form, identify the vertex, and determine the x-intercepts.
Answer:
(x - 6)² = - (y - 4)
The vertex of the parabola will be (6,4).
The x-intercepts are at (8,0) and (4,0).
Step-by-step explanation:
Given the equation of parabola is g(x) = y = - x² + 12x - 32 .......... (1)
Now, converting the equation to vertex form.
Here, y = - x² + 12x - 32
⇒ y = - (x² - 12x + 36) + 4
⇒ y - 4 = - (x - 6)²
⇒ (x - 6)² = - (y - 4) ........... (2) (Answer)
Now, the vertex of the parabola will be (6,4) and it opens down. (Answer)
Let the x-intercept of the parabola is at (h,0).
Hence, from equation (2) we get,
(h - 6)² = - (0 - 4) = 4
⇒ h - 6 = ± 2
⇒ h = 8 or h = 4
Therefore, the x-intercepts are at (8,0) and (4,0). (Answer)
You work for 6.5 hours at a rate of $11.50 / hour.
You buy dinner that costs $12, and give a 20% tip.
How much money are you left with?
Answer:
[tex]\$60.35[/tex]
Step-by-step explanation:
step 1
Find the total amount of money worked
Multiply 6.5 hours by the rate $11.50 / hour.
[tex]6.5(11.50)=\$74.75[/tex]
step 2
Find the total cost of the dinner
Remember that
[tex]100\%+20\%=120\%=120/100=1.2[/tex]
so
the cost of the dinner plus the tip is equal to
[tex]\$12(1.2)=\$14.4[/tex]
step 3
Find the amount of money left
Subtract the total cost from the total amount of money
so
[tex]\$74.75-\$14.4=\$60.35[/tex]
Find the slope of a line:(3,6) and (7,-2)
Answer:
Step-by-step explanation:
3. From (3x² + x-14) subtract (-x² – 3x – 2).
Answer:
W
Step-by-step explanation:
Tvivyvyvububi
Answer:
4x^2+4x-12
Step-by-step explanation:
(3x^2+x-14)-(-x^2-3x-2)
3x^2+x-14+x^2+3x+2
3x^2+x^2+x+3x-14+2
4x^2+4x-14+2
4x^2+4x-12
A company produces three combinations of mixed vegetables that sell in 1-kg packages. Italian style combines 0.4
kg of zucchini, 0.3
kg of broccoli, and 0.3
kg of carrots. French style combines 0.5
kg of broccoli and 0.5
kg of carrots. Oriental style combines 0.2
kg of zucchini, 0.3
kg of broccoli, and 0.5
kg of carrots. The company has a stock of 17 comma 800
kg of zucchini, 28 comma 300
kg of broccoli, and 38 comma 900
kg of carrots. How many packages of each style should it prepare to use up existing supplies?
Answer:
Italian style = 18,000 packages
French style = 14,000 packages
Oriental style = 53,000 packages
Step-by-step explanation:
See the attached figure to represent the question
let the number of packages of Italian style = x
let the number of packages of French style = y
let the number of packages of Oriental style = z
Italian style ⇒ 0.4 kg of zucchini, 0.3 kg of broccoli, and 0.3 kg of carrots.
French style ⇒ 0.5 kg of broccoli and 0.5 kg of carrots.
Oriental style ⇒ 0.2 kg of zucchini, 0.3 kg of broccoli, and 0.5 kg of carrots.
The amount of zucchini ⇒ 17,800 = 0.4x + 0 * y + 0.2z
The amount of broccoli ⇒ 28,300 = 0.3x + 0.5y + 0.3z
The amount of carrots ⇒ 38,900 = 0.3x + 0.5y + 0.5z
Solving the 3 equations together to find x , y and z
Using the calculator:
x = 18,000 ⇒ Italian style packages
y = 14,000 ⇒ French style packages
z = 53,000 ⇒ Oriental style packages
Find 66 2/3 precent of 87. Find 1 precent of 3,620
62 1/2 precent of x is 5 what is x. 300 precent of k is 42 what is k
Final answer:
To find percentages of numbers, convert the percent to a decimal and then multiply. To find the unknown quantity in an equation involving percentages, divide the given number by the percent expressed as a decimal.
Explanation:
To find 66 2/3 percent of 87, first convert the percent to a decimal by dividing it by 100: 66 2/3 ÷ 100 = 0.6667. Then multiply the decimal by 87: 0.6667 x 87 = 58.33. So, 66 2/3 percent of 87 is approximately 58.33.
To find 1 percent of 3,620, divide 3,620 by 100: 3,620 ÷ 100 = 36.2. So, 1 percent of 3,620 is 36.2.
To find x in the equation 62 1/2 percent of x is 5, first convert the percent to a decimal: 62 1/2 ÷ 100 = 0.625. Then divide 5 by the decimal: 5 ÷ 0.625 = 8. So, x is 8.
To find k in the equation 300 percent of k is 42, first divide 42 by 300: 42 ÷ 300 = 0.14. So, k is 0.14.
Square root of 24 divided by square root of 27
Answer:
= 2/27 square root of 6
Step-by-step explanation:
:)
Answer:
2/27
Step-by-step explanation:
What are the missing measures in the diagram
Answer:
J=67
T=67
G=180-67-67
St=5
HJ=3.7
Step-by-step explanation:
The two triangles are equal.
Since the triangle at isosceles, two sides/angles are equal.
The measure of the angles and the sides are:
m∠J = 67
m∠T = 67
m∠G =46
ST = 5 cm
HJ = 3.7 cm
We have,
ΔGHJ ≡ Δ STU
This means,
The corresponding sides and angles are the same.
Now,
GH = ST = GJ = SU = 5cm
And,
HJ = TU = 3.7 cm
Now,
The sum of the angles in the triangle = 180
In GHJ,
m∠J = 67
This is because angles opposite to the equal sides are the same.
Now,
∠G + ∠H + ∠J = 180
∠G + 67 + 67 = 180
∠G = 180 - 134
m∠G = 46
And,
m∠T = 67
Since ΔGHJ ≡ Δ STU.
Thus,
The measure of the angles and the sides are:
m∠J = 67
m∠T = 67
m∠G =46
ST = 5 cm
HJ = 3.7 cm
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WHATS THE SLOPE? HELPPPP
Answer:
slope = 0
Step-by-step explanation:
The graph of g(x) is a horizontal line parallel to the x- axis.
Since it is parallel to the x- axis it has a slope of zero
What is 9 over 4 equal
Answer:
2.25
Step-by-step explanation:
Answer:
2.25
Step-by-step explanation:
4 goes into 9, two times which is why 2 is your whole number and 4 X 2 =8
The .25 is "4 x .25=1. And 8+1 equals 9.
Plz answer number 3!
If two or more points have the same domain or x value, then it is not a function because points cannot have identical x values, only y values.
With this in mind, C is not a function because there are two 4s in the domain.
So looking at this our answer would be C because when you are trying to find if it is not a function you have to look for repeated X values or domains if there I s a problem with a repeated X value that would not be a function but if the Y values were to repeated that doesn’t really matter so yeah. Hopefully this helps!
Factor the following expression completely.
9y^4 - 4x^6
Answer:
(3y^2+2x^3)(3y^2-2x^3)
Step-by-step explanation:
Need help with question number 9. Can’t figure it out.
Answer:
C
Step-by-step explanation:
the answer to C is 7/12
Simplify 25/100 eiejevskkehs
Solve write the differences 505-167=
Answer:
338 is the difference
Step-by-step explanation:
505-167=338
The difference between 505 and 167 is calculated using standard subtraction techniques, including borrowing, to arrive at a final answer of 338.
Explanation:To solve the subtraction problem 505 - 167, we can use the standard algorithm for subtraction:
Start by writing the numbers vertically with the larger number on top:505- 167Subtract the rightmost digits: 5 - 7. Since 5 is less than 7, we need to borrow from the tens place.After borrowing, we have 15 - 7, which equals 8.Now, move on to the tens place. Remember, we borrowed 1 from here, so it's 0 now, not 1. 0 - 6 can't be done, so we borrow again from the hundreds place. It's now 10 - 6, which equals 4.Finally, in the hundreds place, we have 4 (since we borrowed 1) minus 1, which equals 3.Write down the results to get the final answer: 338.The difference between 505 and 167 is 338.
-3x+2y=-3
4x-y=-1 what is the answer
Answer:
X= -9/10
y= -2 3/5
Step-by-step explanation:
Multiply equation one by 4 and equation two by 3 to eliminate X
it becomes
-12x + 8y =-12
12x - 3y = -1
add equation one and two,
you'll be left with 5y= -13
divide both sides by 5
y = -13/5 improper fraction
= -2 3/5
Now substitut y = -2 3/5 into any of the original equations to get x.
using equation two, we have
4x -(-2 3/5) = -1
4x + 2 3/5 = -1
4x = -1 - 2 3/5
the LCM of 5 is 5 , so
4x = -5-13/5
4x = -18/5
crossmultiply
4x x 5 = -18
20x = -18
divide both sides by 20
we have x = -18/20, when you cancel further , you have x = -9/10
Subtract —b+3 from —11b —4
Answer:
Step-by-step explanation:
STEP 1:
-11b-4-(-b+3)....bracket the equation that you are subtracting and add a mins sign infront of the bracket because you are asked to subtract -b+3 from -11b-4.
STEP 2:
-11b-4+b-3
the minus sign infront of the bracket changes the minus sign to a positive (+)sign because a minus(-) timesed by a minus is a positive(+). and a minus timesed by a positive(+) is a negative(-)
STEP 3:
-10b-7
add the b values together(11b-b) = 10b
add the numericals together -4+(-3)= -7
STEP 4:
final answer is -10b-7
What is 50% of 38?
How do I do this?
Answer:
19
Step-by-step explanation:
50% = 1/2
therefore 1/2 of 38
= 19
Answer: 19
Step-by-step explanation: We need to write 50% as a decimal by moving the decimal point 2 places to the right to get .50. Next, the word "of" means multiply, so we have (.50)(38) which is 19.
find an equation of the line such that the points (2/5,5) and (-2/5,4) are on the line.
The equation of the line is y = [tex]\frac{5}{4}[/tex] x + [tex]\frac{9}{2}[/tex]
Step-by-step explanation:
The form of the linear equation is y = mx + b, where
m is the slope of the line, [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] b is the y-intercept, to find b substitute x and y in the equation by the coordinates of any point on the line∵ A line passes through points ( [tex]\frac{2}{5}[/tex] , 5) and ( [tex]-\frac{2}{5}[/tex] , 4)
∴ [tex]x_{1}[/tex] = [tex]\frac{2}{5}[/tex] and [tex]x_{2}[/tex] = [tex]-\frac{2}{5}[/tex]
∴ [tex]y_{1}[/tex] = 5 and [tex]y_{2}[/tex] = 4
- Substitute them in the rule of the slope to find m
∵ [tex]m=\frac{4-5}{-\frac{2}{5}-\frac{2}{5} }[/tex]
∴ [tex]m=\frac{-1}{-\frac{4}{5}}=\frac{5}{4}[/tex]
- Substitute it in the form of the equation
∴ y = [tex]\frac{5}{4}[/tex] x + b
- To find b substitute x and y in the equation by the coordinates
of any point on the line
∵ Point ( [tex]\frac{2}{5}[/tex] , 5) lies on the line
∴ x = [tex]\frac{2}{5}[/tex] and y = 5
∴ 5 = [tex]\frac{5}{4}[/tex] ( [tex]\frac{2}{5}[/tex] ) + b
∴ 5 = [tex]\frac{1}{2}[/tex] + b
- Subtract [tex]\frac{1}{2}[/tex] from both sides
∴ [tex]\frac{9}{2}[/tex] = b
∴ y = [tex]\frac{5}{4}[/tex] x + [tex]\frac{9}{2}[/tex]
The equation of the line is y = [tex]\frac{5}{4}[/tex] x + [tex]\frac{9}{2}[/tex]
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a set of golf clubs is marked at 25% off. If the regukar price is $630, find the discount and sale price
Answer:
472.5
Step-by-step explanation:
This one is simple.
They way you figure this out is your times the amount of money for the original cost by the discout so the equation is 630 times .25 equals 157.5. You then take that disount price and minus it from the original price, which is 630 so the eqation 630 minus 157.5 equals 472.5.
Hope this helps and have a great day
Determine the approximate value of θ.
a. 38.7∘
b . 51.3∘
c. 36.9∘
d. 53.1∘
53.1LaTeX: ^\circ
Tan(angle) = opposite / adjacent
Tan(angle) = 4/5
Angle = arctan(4/5)
Angle = 38.66
Angle = 38.7
A box was 3/4 full of marbles. The box fell on the floor. Thirty marbles fell out. This was 20% of the marbles in the box. How many marbles would a full box contain?
Answer:
200 marbles please rate brainliest
Step-by-step explanation:
Emma has n containers. She will put
cup of berries into each container.
Which expression represents the total amount of berries, in cups, that Emma will put into the containers?
The total amount of berries, in cups, that will be in Emma's containers is represented by the expression n in mathematics , due to the multiplication principle of counting.
Explanation:The subject of this question is mathematics, specifically, arithmetic and algebra. Emma has n containers and plans to put one cup of berries into each container. To find the total amount of berries, in cups, that Emma will put into the containers, you multiply the number of containers by the number of cups per container. Since Emma is putting 1 cup of berries in each container, the expression that represents the total amount of berries Emma will put into the containers is simply n.
This is due to the Multiplication Principle of Counting, which states that if one event can occur in m ways and a second can occur independently of the first in n ways, then the two events can occur in m x n ways. Here, the two events are 'number of containers' and 'cups of berries per container', with the 'number of containers' being variable, represented as n and the 'cups of berries per container' being a constant '1'.
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What is 8/10 devided by 2/10
Answer:
4
Step-by-step explanation:
8 2 8 10 80 8
- divide - -------> KCF - multiply - = - simplify = - = 4
10 10 10 2 20 2
Simplify a squared x b x b four x b
Answthat 16 is 42,
Step-by-step explanation:
Understand factoring. ...
Divide by the smallest prime number possible. ...
Rewrite the square root as a multiplication problem. ...
Repeat with one of the remaining numbers. ...
Finish simplifying by "pulling out" an integer. ...
Multiply integers together if there are more than one.
A garden table and a bench cost 725 combineThe garden table cost 75 more than the bench what is the cost of the bench
The cost of bench is 325.
Step-by-step explanation:
Given,
Combined cost of table and bench = 725
Let,
x be the cost of garden table
y be the cost of bench
According to given statement;
x+y=725 Eqn 1
x = y+75 Eqn 2
Putting value of x from Eqn 2 in Eqn 1
[tex](y+75)+y=725\\y+75+y=725\\2y=725-75\\2y=650[/tex]
Dividing both sides by 2
[tex]\frac{2y}{2}=\frac{650}{2}\\y=325[/tex]
The cost of bench is 325.
Keywords: linear equation, substitution method
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The diameter of the sun is about 1.39 × 10^6 kilometers. The diameter of the Earth is about 1.27 × 10^4 kilometers. How many times larger in diameter is the sun than the Earth? Write your answer in scientific notation, and round the coefficient to the nearest hundredths place.
Answer:
1.09 x 10^2
Step-by-step explanation:
1.39 x 10^6 / 1.27 x 10^4 = 1.09448818898
1.09448818898 is rounded 1.09
10^6-4 = 10^2
So, 1.09 x 10^2
The sun is approximately 109.29 times larger in diameter than the Earth.
Explanation:To determine how many times larger in diameter the sun is compared to the Earth, we divide the diameter of the sun by the diameter of the Earth.
The diameter of the sun is 1.39 × 106 kilometers, while the diameter of the Earth is 1.27 × 104 kilometers.
Dividing the diameter of the sun by the diameter of the Earth, we get (1.39 × 106) / (1.27 × 104) = 109.29.
Therefore, the sun is approximately 109.29 times larger in diameter than the Earth.
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Tricia completed the square of the quadratic function f(x) = x² + 14x + 2 and determined the coordinates of the minimum value are (-7, - 47). Which equation must be Tricia's result?
f(x = (x +7)² + 47
f(x) = (x + 7)² - 47
f(x) = (x - 7)² + 47
f(x) = (x - 7)² - 47
Answer:
The co-ordinates which give the minimum value for the quadratic function are (-7, -47)
Step-by-step explanation:
i) the quadratic function f(x) = [tex]x^{2}[/tex] + 14x + 2
= [tex]x^{2}[/tex] + 14x + 49 - 49 + 2
= [tex](x + 7)^{2}[/tex] - 49 + 2
= [tex](x+7)^{2}[/tex] - 47
ii) The minimum value of the result of the quadratic equation in i) will be achieved when [tex](x + 7)^{2}[/tex] is zero as any square value is always positive and thus the minimum value of a square is always zero.
iii) [tex](x + 7)^{2}[/tex] is zero when x = -7 and when x = -7 then y = f(x) = -47
iv) The co-ordinates which give the minimum value for the quadratic function are (-7, -47)
There are 4 people jogging. There are 5 more people walking than jogging. How many people are walking.
Answer:
Step-by-step explanation:
4 + 5=9
We are certain that 4 people are jogging and it is given that mote 5 people are walking rather than jogging so from these statement we can see that only 5 people are walking.
What do you mean by jogging?Running at a slow and regular pace, especially as a form of exercise, usually runs half an hour before breakfast. Exercise and training the purpose of jogging is to Health benefits of running and jogging helps build strength because it is heavy exercise strengthens muscles. improves cardiovascular fitness. burn a lot of kilojoules.
Jogging is a form of aerobic exercise in which running speed is less than 6 miles per hour. Jogging regularly can help you lose weight, especially if you also change your diet.
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