Answers
Answer:
[tex]f(x)=2(x+4)^2-27[/tex]
Step-by-step explanation:
Complete the square
[tex]f(x)=2x^2+8x+5\\f(x)=2(x^2+8x+\frac{5}{2})\\f(x)+2(\frac{27}{2})=2(x^2+8x+\frac{5}{2}+\frac{27}{2})\\f(x)+27=2(x^2+8x+16)\\f(x)+27=2(x+4)^2\\f(x)=2(x+4)^2-27[/tex]
This tells us that the vertex of the parabola is [tex](-4,-27)[/tex].
Related Questions
Write the following fraction as a decimal number. 4/3/100 4.003 4.03 4.33 4.34
Answers
Answer:
133.3 <-- goes on forever
I think the rest are in decimal form.
!!100!! POINTS PLEASE HELP
Answers
Answer:
[tex]\sf x = 6\dfrac{2}{3} \ \ or \ \ 6.67 \ (rounded \ to \ nearest \ hundreth)[/tex]
Build a proportional equation:
[tex]\rightarrow \sf \dfrac{AB}{AD} = \dfrac{BC}{DE}[/tex]
[tex]\rightarrow \sf \dfrac{10}{x+10} = \dfrac{6}{10}[/tex]
[tex]\rightarrow \sf 10(10) = 6(x+10)[/tex]
[tex]\rightarrow \sf 100 = 6x+60[/tex]
[tex]\rightarrow \sf 40= 6x[/tex]
[tex]\rightarrow \sf x = 40/6[/tex]
[tex]\rightarrow \sf x = \dfrac{20}{3}[/tex]
[tex]\rightarrow \sf x = 6\dfrac{2}{3}[/tex]
Answer:
Step-by-step explanation:
1. Create a porportianal equation. ab/ad=bc/de
2. plug in the variables for each line segment. 10/x+10=6/10
3. multiply each side by x + 10. (6x+60)/10=10
4. Multiply each side by 10. 6x+60=100
5. simplify. 6x=40 3x=20
6. divide each side by 3. x=20/3
(Sorry about my last answer)
You start at (8, 0). You move right 2 units. Where do you end?
Answers
Answer:
(10,0)
Step-by-step explanation:
Moving right 2 units will increase the x value by 2 since you are going further 'down the corridor'. Hope this helps.
Find the perimeter and area of the following
Answers
16. PM = 26x + 8x^2y
A = 52x^3y
17. Area = 33a^5b
A charitable organization holds a canned food drive to benefit the local food bank. The number of cans collected by the volunteers of the organization as they came in are 2, 6, 12, 16, 2, 6, 13, 17, 3, 8, 13, 19, 4, 10, 14, 19, and 5.
Pls help. I need the first and third quartile and the median
Answers
Answer:
Step-by-step explanation:
Minimum: 2
Quartile Q1: 4.5
Median: 10
Quartile Q3: 15
Maximum: 19
The number of sweets in a bag are normally distributed with mean 48 and standard deviation 4.
What is the probability that a bag selected at random contains more than 50 sweets? Give your answer as a decimal correct to 3 significant figures.
Answers
Answer:
0.33 recurring
Step-by-step explanation:
assuming alol the fractions are equal, find the total number of possibilities and assign one for each number
If I get 10 dollars a week how much money will I have saved up in 9-years I WILL GIVE 55 POINTS
Answers
Answer:
$4,680
Step-by-step explanation:
Rate : 10 dollars a week
Per year : 10 x 52 = $5209 x 520 = $4,680You will have saved up $4,680 in 9 years.
9. A triangle has sides whose lengths are 5, 12, and 13. A similar triangle could have sides with lengths
of ? Give side lengths of two different similar triangle.
Answers
Answer:
One similar triangle: 15, 36 and 39
Another similar triangle: 10, 24, 26
Step-by-step explanation:
When a triangle is similar, it has corresponding sides that are each longer are shorter than the original triangle by a scale factor.
Scale factorA scale factor is a number that you multiply the original triangle's sides by. After multiplying each original side, you get the side lengths of a new and similar triangle.
The original sides from the question are 5, 12 and 13.
First similar triangleLet's pick 3 to be a scale factor.
Multiply every original side by the scale factor to get the side lengths of a similar triangle.
5 × 3 = 15
12 × 3 = 36
13 × 3 = 39
∴ One similar triangle can have the sides 15, 36 and 39.
Second similar triangleLet's pick another scale factor: 2
Now, we do the same. Multiply the original sides by the scale factor.
5 × 2 = 10
12 × 2 = 24
13 × 2 = 26
∴ Another similar triangle can have the sides 10, 24 and 26.
Choosing a scale factorWe can pick almost any number to be a scale factor. If we pick a scale factor that is:
greater than 1, then the similar triangle will be larger.a fraction, then the similar triangle will be smaller.We can make an infinite amount of other similar triangles just by changing the scale factor.
Which is greater: 10 centimeters or 103 millimeters? How much greater?
PLEASE HELP
Answers
Answer:
Step-by-step explanation:
103 millimeters because 10 mm= 1 cm, so 100 mm is the same as 10 cm and 3 more mm makes it more
A cube has a side length of 6 cm. The cube is reduced by a scale factor of 1/3. Find the volume of the reduced cube. 2 cm3 4 cm3 6 cm3 8 cm3
Answers
Answer:
8 cm
Step-by-step explanation:
because when it's reduced we multiply the side length by 1/3 * 6 = 2cm and the volume will equal v = a^3 = 2^3 = 8cm
Answer:
8cm
Step-by-step explanation:
step1: 6/3=2
volume of a cube =x*x*
v
:=8cm
v=2×2×2
vvv v
Which set only contains numbers that make the inequality true? x + 19 < 28 {10, 11, 12, 13} {10, 11, 12, 13} {3, 4, 5, 6} {3, 4, 5, 6} {12, 13, 14, 15} {12, 13, 14, 15} {7, 8, 9, 10}
Answers
{3, 4, 5, 6}
Step-by-step explanation:Inequalities represent the value of a variable by comparing them to other values.
Inequality Signs
Before answering the question, make sure you understand the different inequality signs.
< - This sign represents less than. This means that the value on the left is less than the value on the right.> - This sign represents greater than. This means that the value on the left is greater than the value on the right.< - This sign means less than or equal to. So, the value on the left will be less than or the same as the value on the right.> - This sign means greater than or equal to. So, the value on the left will be greater than or the same as the value on the right.Solving the Inequality
To make this question easier to answer, we can solve the inequality. Solving an inequality involves isolating the variable.
To do this subtract 19 from both sidesx < 9Finding the Set
Now that we solved the inequality we can look for the correct set of numbers. Since we solved the inequality, we know that all of the correct values should be less than 9. However, because there was no equal to sign, 9 is not included in the set. The only set that has only correct solutions is {3, 4, 5, 6}.
Building a Storage Container
You are being asked to design an enclosed water storage container. You are given a budget of
$100 to build the container. It has been determined that the best material to make the container
costs $10 per m². (In other words your surface can not cost more than $100.) What is the
largest amount of water your container can hold? You will need to explain to your boss the
reasoning because they have a business degree and do not really remember any of their
geometry work from school.
Answers
Answer:
2973.5 liters
Step-by-step explanation:
You are being asked to find the volume of the largest possible container that has a given surface area. The volume will depend on the shape. If shape is not specified, we know a sphere has the largest volume for a given area.
__
areaThe available area is ...
($100) / ($10/m²) = 10 m²
diameterThe area of a sphere with diameter d is ...
A = πd²
Then the diameter for the given area is ...
10 m² = πd²
(10/π) m² = d² . . . . . divide by π
√(10 m²/π) = d ≈ 1.78412 m . . . . . . diameter of the largest sphere
volumeThe volume of a sphere is given by ...
V = 4/3πr³ = (π/6)d³
For the diameter found above, the volume of the sphere will be ...
V = (π/6)(1.78412 m)³ ≈ 2.97354 m³
There are 1000 liters in a cubic meter, so the largest amount of water that can be contained is ...
2.97354 m³ × (1000 L/m³) = 2973.54 L
The largest amount of water the container can hold is about 2973.5 liters.
This is easy but I’m very slow please help mi amor
Answers
The government conducted a study and collected the given data. use the
data to answer the following questions.
speed (mph) 45 55 65 75
fuel (mpg) 43 45 38 32
find the quadratic regression model that represents the relationship
between speed and fuel. round your answer to two decimal places
Answers
The quadratic regression equation is y = -0.02x^2 + 2x - 6
How to determine the quadratic regression?The table of values is given as:
speed (mph) 45 55 65 75
fuel (mpg) 43 45 38 32
Next, we determine the regression equation using a graphing calculator (see attachment)
From the graphing calculator, we have:
a = -0.02, b = 2 and c = -6
A quadratic regression is represented as:
y = ax^2 +bx + c
So, we have:
y = -0.02x^2 + 2x - 6
Hence, the quadratic regression equation is y = -0.02x^2 + 2x - 6
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A spinner is divided into 15 identical sectors and labeled 1 through 15.
How many spins are expected for a multiple of 4 to be spun 30 times?
Select from the drop-down menu to correctly complete the sentence
The spinner is expected to have to spin approximately Choose times for a multiple of 4 to be spun 30 times.
A. 113
B. 120
C. 150
D. 225
Answers
if a square is drilled out from a cylinder what will be the lateral surface area,total surface area,base area and the volume of the cylinder
Answers
The cylinder is a three-dimensional shape and it has a radius, diameter and a height
How to determine the lateral surface area?Assume the square has the following dimensions:
Base dimensions = x
Height = h
Assume the cylinder has the following dimensions:
Radius = r
Height = h
When the square is drilled out, the lateral surface area would be:
Lateral Area = Cylinder - Square
This gives
[tex]Lateral = 2\pi rh - 4xh[/tex]
Factor out 2h
[tex]Lateral = 2h( \pi h - 2x)[/tex]
How to determine the total surface area?Using the same dimensions in (a), we have:
Total surface Area = Cylinder - Square
This gives
[tex]Area = 2\pi r(r +h) - 2(2x^2 - xh)[/tex]
Factor out 2
[tex]Area = 2[\pi r(r +h) - (2x^2 - xh)][/tex]
How to determine the base area?Using the same dimensions in (a), we have:
Base area = Cylinder - Square
So, we have:
[tex]Base = \pi r^2 - x^2[/tex]
How to determine the volume?Using the same dimensions in (a), we have:
Volume = Cylinder - Square
So, we have:
[tex]Volume = \pi r^2h - x^2h[/tex]
Factor out h
[tex]Volume = h(\pi r^2 - x^2)[/tex]
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Can you use Pythagorean Theorem to find the missing side?
Answers
Answer:
b=20
Step-by-step explanation:
[tex] {b}^{2} = {c}^{2} - {a}^{2} \\ b = \sqrt{ {25}^{2} - {15}^{2} } \\ b = 20[/tex]
WHAT IS THE LENGTH!!!
the area is 107.95
the base is 12
the height is 12.7
the length is x
Answers
The figure is a trapezoid (or trapezium), and the exact length of the trapezoid is 5 units
How to determine the length?The figure is a trapezoid with the following parameters:
Area = 107.95
Base= 12
Height = 12.7
Length = x
The area of a trapezoid is:
Area = 0.5 * (Base + Length) * Height
So, we have:
0.5 * (12 + Length) * 12.7 = 107.95
Evaluate the product
(12 + Length) * 6.35 = 107.95
Divide both sides by 6.35
12 + Length = 17
Subtract 12 from both sides
Length = 5
Hence, the length of the trapezoid is 5 units
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Complete the square and graph: 9y²−x − 18y +10=0
Answers
Answer:
See below ~
Step-by-step explanation:
Completing the square :
9y² - x - 18y + 10 = 09y² - 18y + 9 - 9 - x + 10 = 0(3y - 3)² - x + 1 = 0Graph :
Answer:
x = 9(y - 1)² + 1
see attached for graph
Step-by-step explanation:
Completing the squareGiven equation:
9y² - x - 18y + 10 = 0
As there is a y² in the equation, this implies it is a sideways parabola.
To complete the square for a sideways parabola, collect the y variable terms on the left and everything else on the right:
⇒ 9y² - 18y = x - 10
Factor out the leading coefficient from the left side:
⇒ 9(y² - 2y) = x - 10
Take the coefficient of y, half it, then square it: (-2 ÷ 2)² = 1
Add this inside the parentheses, and add the distributed value of this to the right side:
⇒ 9(y² - 2y + 1) = x - 10 + 9
Factor the parentheses and simplify the right side:
⇒ 9(y - 1)² = x - 1
Add 1 to both sides to make x the subject:
⇒ x = 9(y - 1)² + 1
Graphing the parabolaConic form of a sideways parabola with a horizontal axis of symmetry:
x = a(y - k)² + h
(where (h, k) is the vertex and y = k is the axis of symmetry)
If a > 0, the parabola opens to the right, and if a < 0, the parabola opens to the left.
Therefore, for x = 9(y - 1)² + 1
vertex = (1, 1)axis of symmetry: y = 1a > 0 ⇒ the parabola opens to the rightTo find the x-intercept, set y = 0 and solve for x:
⇒ x = 9(0 - 1)² + 1
⇒ x = 9(-1)² + 1
⇒ x = 9(1) + 1
⇒ x = 10
Therefore, the y-intercept is (10, 0)
As the axis of symmetry is y = 1, the other value of y when x = 10 is y = 2
Plot the vertex and points. Add an axis of symmetry to help draw the curve. Draw the parabola opening to the right.
**graph attached**
Eric and bianca are drawing a model of a city park in the cordinate
Answers
For Eric and Bianca to be able to draw a model of a city park in the coordinate, they can follow the description in the image attached.
What is a Coordinate system?In the are of math and geometry, a coordinate system is known to be a kind of a system which is known to often uses a lot of numbers or only one to show the position of any given points.
Note that to be able to design the part to their taste and with the right coordinates, For Eric and Bianca to be able to draw a model of a city park in the coordinate, they can follow the description in the image attached.
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Answer:
Vertex Q has an x-coordinate of 7. To form quadrilateral QRST, vertex T must be 3 units down from vertex Q. Vertex T should be at (7,3) .
Bianca is correct.
Step-by-step explanation:
Hope this helps.
tony wants to rent a bike. bike rentals cost $7.50 for a half hour. if tony rents a kayak for two hours and 30 minutes, how much will it cost him?
Answers
37.50
Step-by-step explanation:
Select the correct answer. which sum or difference is modeled by the algebra tiles? a. (-x2 2x 3) − (x2 − 2x − 1) = -2x2 2 b. (-x2 2x 3) − (-x2 2x 1) = -2x2 2 c. (-x2 2x 3) (-x2 2x 1) = -2x2 2 d. (-x2 2x 3) (-x2 − 2x − 1) = -2x2 2
Answers
The sum or difference modeled by the algebraic tiles is (-x²+2x+3) + (-x²-2x-1) = -2x²+2
How to determine the sum or difference?From the complete question, we have the following expressions:
(-x²+2x+3) and (-x²-2x-1)
Add both expressions
(-x²+2x+3) + (-x²-2x-1)
Expand
-x²+2x+3 -x²-2x-1
Collect the like terms
-x² -x² + 2x - 2x + 3 -1
Evaluate the like terms
-2x²+2
Hence, the sum or difference modeled by the algebraic tiles is (-x²+2x+3) + (-x²-2x-1) = -2x²+2
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does someone know this answer
Answers
[tex]\bold{ANSWER:}[/tex]
Sample 3: 6 boys; 7 girls
[tex]\bold{SOLUTION:}[/tex]
A yard dart is thrown from a height of 3 feet with an initial velocity of 25 feet per second at an elevation angle of 70°. how long is the dart in the air? round to the nearest tenth. 0.7 seconds 0.8 seconds 1.5 seconds 1.6 seconds
Answers
Based on the height the yard dart is thrown from, the inital velocity, and the elevation angle, the length of time the dart is in the air is 1.6 seconds.
What amount of time did the dart spend in the air?This can be solved using a projectile motion calculator which can show you the velocity of the dart and the time it spent in the air.
Plugging in the given values above, we find that the yard dart spent a total of:
= 1.6 seconds in the air
In conclusion, option D is correct.
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A car has an average speed of 45 miles per hour. how long will it take to travel 360 miles? which equation and decimal form are represented by the visual model?
Answers
Answer:
It would take 8 hours to drive 360 miles.
Step-by-step explanation:
360/45=8
D=R*T
Simplify the expression: 4(n - 3) - 2(-3 + n)
Answers
Answer:
[tex]2(n-3)=2n-6[/tex]
Step-by-step explanation:
[tex]4(n-3)-2(-3+n)\\\\4(n-3)-2(n-3)\\\\(4-2)(n-3)\\\\2(n-3)[/tex]
Helpppppppppppppppppppp
Answers
Answer:
See below ~
Step-by-step explanation:
Q1
y = (x + 3i)(x - 7)y = x² + 3ix - 7x - 21y = x² + (3i - 7)x - 21Q2
y = (x - √5)(x - i)y = x² - √5x - ix + √5iy = x² - (√5 + i)x + √5iOrange County wanted to determine how its students did on a standardized test, so the county took a random survey of 25 students. Out of the 25 students, 4 scored "1" on the test, 8 scored "2" on the test, 5 scored "3" on the test, 5 scored "4" on the test, and 3 scored "5" on the test.
Answers
The model could be improved by using a step function.
which expression has a value of 2/3?
(8+24) (12 × 4)
824 12 x 4
8+ (2412) × 4
8+24 (12 x 4)
Answers
Answer:
(8 + 24) ÷ (12 x 4) = 2/3
Step-by-step explanation:
To Find: an expression that has a value of 2/3
Solution :
A. [8 + (24 ÷ 12)] x 4
= [8 + (2)] x 4
= 10 x 4
= 40
B. (8 + 24) ÷ (12 x 4)
= 32 ÷ 48
= 2 ÷ 3
= 2/3
C. 8 + (24 ÷ 12) x 4
= 8 + 2 x 4
= 8 + 8
= 16
D. 8 + 24 ÷ 12 x 4
8 + 2 x 4
= 8 + 8
= 16
The correct option is :
(8 + 24) ÷ (12 x 4) = 2/3
A cone with a radius 3 feet is shown. Its approximate volume is 140 cubic feet.
Answers
Answer:
the answer to this question should be 14.85
