[tex]h = - \frac{b}{2a} \\ k = \frac{4ac - {b}^{2} }{4a} [/tex]
Vertex Form[tex]y = a{(x - h)}^{2} + k [/tex]
Where the a-term determines how wide, narrow, upward or downward the graph is.
The h-term determines the horizontal shift of graph. (x-axis)
The k-term determines the vertical shift of graph. (y-axis)
The vertex of graph is at (h,k). We can find the vertex by using the given formulas.
Find the vertexFrom the equation, the coefficients are:
[tex] \begin{cases} a = - 1 \\ b = 12 \\ c = - 31 \end{cases}[/tex]
Substitute these values in the formulas.
Find the value of h
[tex]h = - \frac{12}{2( - 1)} \\ h = - \frac{12}{ - 2} \\ h = - \frac{ - 6}{1} \longrightarrow - ( - 6) = 6 \\ h = 6[/tex]
Hence, the value of h is 6.
Find the value of k
[tex]k = \frac{4( - 1)( - 31) - {(12)}^{2} }{4( - 1)} \\ k = \frac{124 - 144}{ - 4} \\ k = \frac{ - 20}{ - 4} \longrightarrow \frac{5}{1} = 5 \\ k = 5[/tex]
Hence, the value of k is 5. Then we substitute both value of h and k in the vertex form
Rewrite the equation of vertex form by substituting the value of h and k[tex]y = a {(x - h)}^{2} + k \\ y = - 1 {(x - 6)}^{2} + 5 \\ y = - {(x - 6)}^{2} + 5[/tex]
AnswerSince the vertex is at (h,k). Therefore the value of h is 6 and k is 5. Therefore:
[tex] \large{(h, k)=(6, 5)}[/tex]
(6,5) is the vertex.
What % is 2000 from 40,000
Answer:
5%
Step-by-step explanation:
2000/40000 = 0.05
All you do is divide both numbers and you'll get the decimal form which in this case is 0.05 which means 5%.
Answer:
5%
Step-by-step explanation:
2000/40000 x 100 = 5%
select all that apply: the quotient of 0.04 and g
Answer:
A, B, C, and F is your possible answers
The quotient of means to divide so it could be any symbol and they could switch places when dividing.
find values of the shape
Answer: Sorry mate it didn't pop up anyway hi man how's it been
Answer:
P: 23
H: 12
B: 16
Step-by-step explanation:
Your welcome :)
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! WILL MARK THE BRAINLIEST! 20 PTS!
A rectangular prism has a volume of 198 cm³. A rectangular pyramid has the same height as the rectangular prism and a base that is congruent to the base of the rectangular prism. What is the relationship between the volume of the rectangular prism and the rectangular pyramid?
a. The volume of a rectangular pyramid is 3 times the volume of a rectangular prism. The volume of the rectangular pyramid is 594 cm3.
b. The volume of a rectangular pyramid is 13 the volume of a rectangular prism. The volume of the rectangular pyramid is 66 cm3.
c. The volume of a rectangular pyramid is 12 the volume of a rectangular prism. The volume of the rectangular pyramid is 99 cm3.
d. The volume of a rectangular pyramid is 2 times the volume of a rectangular prism. The volume of the rectangular pyramid is 396 cm3.
Answer:
i need an answer to have you figured it out yet
Step-by-step explanation:
Answer:
B - (Probably)
Step by step explanation:
the Volume of the Pyramid = Volume of Prism / 3
198cm^3 / 3 = 66cm^3
A florist sold 12 flower bouqets yesterday, including 2 daisy bouquets. Based on past data, how many of the next 18 boquetes sold should you expect to be daisy bouquets?
Answer: 3
Step-by-step explanation:
A florist sold 12 flower bouqets yesterday, which included 2 daisy bouquets. This shows that the fraction of daisy bouquet is 2/12 = 1/6.
Therefore, if there are 18 boquetes sold, the number that's expected to be daisy bouquets will be:
= 1/6 × 18
= 3
A spider is climbing up a wall. During the daytime it climbs 5 cm, but then slips back 2 cm during the night. If it started climbing from the bottom of the wall on the morning of January 30th, on what day would it first reach a height of 74 cm?
Answer:
28 days
Step-by-step explanation:
Hope this helps. Good Luck!!
The spider would reach the height of 74 cm on 24th February by the end of the day.
What is expression in mathematics?An expression in mathematics is a combination of terms both constants and variables.
Given is that a spider is climbing up a wall. During the daytime it climbs 5 cm, but then slips back 2 cm during the night.
The net distance covered by the spider in one day -
D{n} = 5 cm - 2 cm = 3cm
The spider would reach 74 cm up in -
{x} = 74/3
{x} = 24.7
This means that the spider would reach the height of 74 cm on 24th February by the end of the day.
Therefore, the spider would reach the height of 74 cm on 24th February by the end of the day.
To solve more questions on expressions, visit the link below -
https://brainly.com/question/27911936
#SPJ2
96/38n X 25/45 (multiplying rational expressions .simplify.)
[tex] \frac{96}{38} \frac{25}{45} [/tex]
That's my answer I hope it helps #brainliestbunch - _ - ;)[tex] \frac{96}{38} \frac{25}{45} [/tex]
That's my answer I hope it helps #brainliestbunch - _ - ;)Someone please help me quick! Pleaseee
Answer:
B
Step-by-step explanation:
Reflect x-axis means (x,y) becomes (x, -y)
Shrink by 1/3 means f(x) = x becomes f(x) = 1/3x
Up 4 units means f(x) = x becomes f(x)= x + 4
So lets put that together
[tex]f(x) = \sqrt{x}[/tex]
[tex]f(x) = -\sqrt{x}[/tex]
[tex]f(x) = -\frac{1}{3} \sqrt{x}[/tex]
[tex]f(x) = -\frac{1}{3} \sqrt{x} + 4[/tex]
What are the coordinates of Image A (-2,7) after a dilation with a center at the origin and a scale factor of 3?
A. A prime (-5,4)
B. A prime (2,-7)
C. A prime (-6,21)
D. A prime (1,10)
Answer:
3
Step-by-step explanation:
3.
9 ft
7 ft
26 ft
find the area of the shape
Answer: The answer is 1638 ft
Step-by-step explanation:
The formula to find area is L x W x H
Length x Width x Height
So 9 ft x 7 ft x 26 ft = 1638 ft
9 1⁄8 − 4 3⁄8 =
subtract
Answer:
4.75 or 4 3/4
Step-by-step explanation:
Simple, 9 1/8- 4 3/8 first you want to take away 1 from 9 and add 8/8 to 1/8 because 8/8 is 1 whole once you done this you want to do 8 9/8-4 3/8 and get 4 6/8 now simplify by 2 and get 4 3/4.
solve both problems please
A piece of ribbon is 950 centimeters long. What is the length of the piece of ribbon in meters?
Answer:
9.5 meters
Step-by-step explanation:
There are 100 centimeters in a meter
950/100 = 9.5
Answer:
9.5 meters
Step-by-step explanation:
divided by 100
5x + 2y = -10
3x + y = 66
please show work
Answer:
x=142, y=-360. (142, -360).
Step-by-step explanation:
5x+2y=-10
3x+y=66
----------------
5x+2y=-10
-2(3x+y)=-2*66
-----------------------
5x+2y=-10
-6x-2y=-132
-------------------
-x=-142
x=142
3(142)+y=66
426+y=66
y=66-426
y=-360
Answer:
1- 5x+2y+−2y=−10+−2y
5x=−2y−10
[tex]\frac{5}{5}[/tex]= [tex]\frac{-2y-10}{5}[/tex]
x= [tex]\frac{-2}{5}y-2[/tex]
2- 3x+y+−y=66+−y
3x=−y+66
[tex]\frac{3x}{3} = \frac{-y+66}{3}[/tex]
[tex]x=\frac{-1}{3}y+22[/tex]
Step-by-step explanation:
This is the answers :)
Can one of y’all please help me this is Urgent
Answer:
B
Step-by-step explanation:
It’s the only one with sides that correlate
What does (8/7)^4 equal?
Answer:
17
Step-by-step explanation:
that's what it equals to
Someone please help (10 points each)
Answer:
80
Step-by-step explanation:
Answer:
x is 80 because it is equal to the other side.
Step-by-step explanation:
A submarine is 984.6 feet BELOW Sea Level. It dives down another 122.4 feet. What is the elevation of the submarine after the dive? HINT
Answer:
1107 feets below sea level
Step-by-step explanation:
Given that :
Initial elevation of submarine = 984.6 feets below sea level
Depth of dive from initial elevation = 122.4 feets below sea level
The elevation after the dive :
Initial elevation + depth of dive
984.6 + 122.4
= 1107 feets below sea level
help please thanks :))))
Answer:
19 cmStep-by-step explanation:
The diagonals of the bases form a rectangle with sides containing A and B points.
AB is the diagonal of the formed rectangle and its length is:
AB = [tex]\sqrt{5^2 + 16^2+7^2 } = \sqrt{25 + 256+49 } = \sqrt{369} }[/tex] = 19 cmAnswer:
[tex]\huge{\underline{\mathtt{\red{A}\pink{N}\green{S}\blue{W}\purple{E}\orange{R}}}}[/tex]
19 cm
The diagonals of the bases form a rectangle with sides containing A and B points.
AB is the diagonal of the formed rectangle and its length is:
[tex]\tt AB = \sqrt{5^2 + 16^2+7^2 } = \sqrt{25 + 256+49 } = \sqrt{369} } = 19 cm [/tex]
HELP LOL IT MY LIL SIS HELPP
Answer:
what did ur lil sis do??? hurry call the police and get immediate help right away ok
Step-by-step explanation:
A metalworker has a metal alloy that is 15% copper and another alloy that is 65% copper. How many kilograms of each alloy should the metalworker combine to create 50 kg of a 45% copper alloy? PLZZZ ANSWER QUICK
40 PTS!!!
Answer:
The answer is 60 kg of a 42% alloy, we'd need 24 kg of 15% copper and 36 kg of 60%
Step-by-step explanation:
Which expression is equivalent to -4x - 36?
Answer:
if it's not multiple choice, I'd say 36 + 4x
Step-by-step explanation:
Commutative property
Answer:
D.) -4(x + 9)
Step-by-step explanation:
Plz mark brainliest
simplify the following:
7x + 5 - 3x?
i need help with this
Answer:
4x+5
Step-by-step explanation:
1. You collect all the like-terms together which would be 7x and 3x
so it would be 7x-3x which would be 4x
since 7-3=4
them we collect 4x and 5 and we get 4x+5
make sure you write the variable answer first
Hope this helps and answers your question! Have a great day/night!
The lines s and t intersect at point R.
What is the value of y?
Enter your answer in the box.
Answer:
y = 29
Step-by-step explanation:
Since the angles are vertical they are equal
4y - 8 = 79 + y
3y = 87
y = 29
Answer:
The other person is correct! :)
Step-by-step explanation:
I took the quiz on k12 sooo
Apply the distributive property to create an equivalent expression.
4(3+1/4c-1/2d
Answer: 4(3+1)/4c-q^1/2d i think tht is how you do it...
Step-by-step explanation:
apply the distribuitive property to create an equivalent expression
4
(
3
+
1
)
4
c
−
q
1
2
d
Write the problem as a mathematical expression.
apply the distribuitive property to create an equivalent expression
4
(
3
+
1
)
4
c
−
q
1
2
d
Simplify.
4
(
3
+
1
)
4
c
−
q
2
d
Add
3
and
1
.
4
⋅
4
4
c
−
q
2
d
Simplify the denominator.
Tap for more steps...
4
⋅
4
8
c
d
−
q
2
d
Multiply
4
by
4
.
16
8
c
d
−
q
2
d
Multiply the numerator by the reciprocal of the denominator.
16
2
d
8
c
d
−
q
Multiply
16
2
d
8
c
d
−
q
.
Tap for more steps...
32
d
8
c
d
−
q
negative 16 divided by negative 10
Answer:
the answer is 1.6
Step-by-step explanation:
when calculating a problem like negative 16 divided by negative 10, you can simply ignore the fact that they are negative numbers and divide 16 by 10 to get the answer.
Help please, If your mom is making a garden and she wants it it be 5 yards how much cm is that
Answer:
it would be 457.2 cm or if you want it simplified then it would be 457 cm
hope this helped :)
Name the slope of the line that is perpendicular to 3y-4x=5
A car travels 825 miles in 15 hourso How many
miles does the can
travel in
I hour. Helps
ASAP
Find f(g(3)) given:
*
f (x) = 2x2 – 1
g(x) = 3x
h(x) =
j(x) = x - 5
Answer:
161
Step-by-step explanation:
Given the functions
f (x) = 2x^2 – 1
g(x) = 3x
we are to find f(g(3))
First look for the composite function f(g(x))
f(g(x)) = f(3x)
f(3x) = 2(3x)² - 1
f(3x) = 2*9x² - 1
f(3x) = 18x² - 1
f(g(x)) = 18x² - 1
Substitute x = 3 into the result
f(g(3)) = 18(3)² - 1
f(g(3)) = 18*9- 1
f(g(3)) = 162-1
f(g(3)) = 161
Hence f(g(3)) is 161