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Explanation:
Compare the given equation to the vertex form y = a(x-h)^2 + k
You'll see that a = 3, h = 4 and k = 7
The vertex is (h,k) = (4,7)
The value of 'a' determines if the parabola opens upward or downward. Since a > 0, it opens upward. This furthermore leads to the vertex being the lowest point on the parabola.
The value of 'a' also determines how vertically stretched or compressed the parabola is.
Answer:
1. The vertex of the graph of the function is (-4, 7)
2. The vertex represents a minimum value
3. The equation represented by the new graph is g(x) = (x + 4)² + 1
Step-by-step explanation:
The given quadratic function is given in vertex form, y = a·(x - h)² + k, as follows;
g(x) = (x + 4)² + 7
1. By comparing the given quadratic function and the vertex form of a quadratic equation, we have;
a = 1, h = -4, and k = 7
The vertex of the graph of the function, (h, k) = (-4, 7)
2. Given that a = 1 > 0, the graph of the quadratic function opens upwards and the vertex represents a minimum value
3. Shifting the graph 6 units down from where it is now will give;
The vertex = (h, k - 6) = (-4, 7 - 6) = (-4, 1)
h = -b/(2·a), k = (-b²/(4·a) + c = -a·h² + c
c = k + a·h²
Therefore, initial value of the constant term, c = -1×(-4)² + 7 = 23
After the shifting the graph 6 units down, c = 23 - 6 = 17
∴ k = 1 = -a·(-4)² + 17
∴ -16/16 = -1 = -a
a = 1
Therefore, the equation represented by the new graph is g(x) = (x + 4)² + 1.
For the data in the table, does y vary directly with x? If it does, write an equation for the direct variation.
TABLE
x y
-------
2 10
4 24
6 36
Answer:
y does not vary directly with x
Step-by-step explanation:
The equation for direct variation is
y = kx ← k is the constant of variation
If k is constant for all ordered pairs in the table then direct variation.
k = [tex]\frac{y}{x}[/tex]
(2, 10 ) → k = [tex]\frac{10}{2}[/tex] = 5
(4, 24 ) → k = [tex]\frac{24}{4}[/tex] = 6
(6, 36 ) → k = [tex]\frac{36}{6}[/tex] = 6
Since k is not constant for all pairs then y does not vary directly with x
Jake studied
z
hours for a big test. Julie studied half as long.
Write an algebraic expression for long Julie studied.
Answer:
(1/2)z
Step-by-step explanation:
the given tables shows the number of shirts and pants different people own. what number correctly completes the table so that each person has the same ratio of pants to shirts
Answer:
He needs 15 shirts
Step-by-step explanation:
We can use a ratio to solve
4 pants 6 pants
--------------- = -------------
10 shirts x shirts
Using cross products
4x = 10 *6
4x = 60
Divide each side by 4
4x/4 = 60/4
x = 15
He needs 15 shirts
if you found any words about mathematics, tell me please
Answer:
geometry
Step-by-step explanation:
left side of paper
Dan spent 0.125 of his money in snacks, 1/4 on travelling and saved the
rest. If he saved $65, how much money did he have at first?
Answer:
89.38
Step-by-step explanation:
65 times 0.125 = 8.125
65 times 0.25 = 16.25
16.25 plus 8.125 plus 65 = 89.38 dollars
2
0
-1
-2
2
-2
(-3.4)
What is the equation of the given line?
y = -4x
x = -4
y = -4
Answer:y=-4
Step-by-step explanation:
A silo contains 60,000 pounds of grain.
How many tons are in 60,000 pounds?
Answer:
30
Step-by-step explanation:
Answer:
30
Step-by-step explanation:
I took the quiz, I hope this helps!
please help! can you explain it to me?
Answer:
It is increasing before x = -2 and from x = 0 to x = 2
Step-by-step explanation:
Option 1 - you can see the line going down starting at -2 and that means the line is decreasing but the choice says "It is increasing before x = 0". This contradicts the actual graph.
Option 2 - The line isn't increasing before x= -1, it's actually decreasing as seen in the graph.
Option 3 - The line doesn't even touch the point before x = -3 so this choice makes no sense.
Option 4 - Since all the other choices were eliminated this is the only choice standing. Looking at the line it is increasing before x = -2.
equations equivalent to x/4+1/3=5/6
PLEASE HELP IM BEING TIMED
Answer:
1
Step-by-step explanation:
Any number to the 0 power is equal to 1.
Hope that this helps!
Answer:
1 is correct
Any number that is raised to the power of 0 is 1, and any number that’s raised to the power of 1 is itself
girlcome 5324611502
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Answer:
Hi there! Subscribe to my animations Y0UTUBE channel! Channel name: Let Me Explain Studios. Have a nice day!
Step-by-step explanation:
What is the area of the following picture ( HELP PLEASE )
Answer:
area=l*b
10*8
80#
Step-by-step explanation:
hope you like it
THE Roger manages an ice cream stand. He keeps track of how many minutes each customer stands in line. Wait Times (in minutes 1.5 13 5 ET Roger wants to organize the data to make a line plot. Drag the numbers to show the frequency for each wait time Numbers may be used more than once. 4 || 5 Frequency 21 Hi Next >
Answer:
0.5 = 2
0.75 = 2
1.0 = 3
1.25 = 4
1.5 = 5
2.0 = 2
2.25 = 1
2.5 = 1
I only need help on number six
Answer:
288 inches = 8 yards
Step-by-step explanation:
Answer:
[tex]6 . \: 8 \: yards \: = \: 288 \: inches[/tex]
[tex]8. \: 18 \: feets \: = \: 216 \: inches[/tex]
[tex]10. \: \frac{1}{3} \: yards \: = 12 \: inches[/tex]
Step-by-step explanation:
6. 1 yard = 36 inches
8 yards = 36 × 8
= 288
8. 1 feet = 12 inches
18 feets = 12 × 18
= 216 inches
10. 1/3 into decimal = 0.33333333333
1/3 yards = 0.33333333333 × 36
= 12 inches
Hope it is helpful....Solve for x. Round to the nearest tenth, if necessary.
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9
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Q
75°
R
Indra was is wrapping the blocks below how much wrapping paper does she need
Answer:
D) 180
Step-by-step explanation:
Formula for Surface area of Rectangular prism is
A = 2(lw+wh+lh)
A = 2(6*8 + 8*3 + 6*3)
A = 2(48 + 24 + 18)
A = 2 * 90
A = 180
Write the inverse function for the function, ƒ(x) =1/2 x + 4. Then, find the value of ƒ -1(4). Type your answers in the box.
ƒ -1(x) =
ƒ -1(4) =
Answer:
0
Step-by-step explanation:
Given that f(x) = 1/2x + 4
Let y = f(x)
y = 1/2 x + 4
Replace y with x
x = 1/2 y + 4
Make y the subject of the formula
1/2y = x - 4
y = 2(x-4)
If x = 3
y = 2(4-4)
y = 2(0)
y = 0
Hence ƒ -1(4) is 0
Students were asked whether they walk, drive, or ride the bus to school. The results. by gender, are shown in the table.
Walk Drive Ride Bus
Male 30 60 10
Female 20 50 30
Select all the statements that illustrate conditional probability?
A. of all students, the probability of choosing a male.
B. Of the students who walk, the probability of choosing a female.
OC. of all students, the probability of choosing a male who walks.
D. Of the females. the probability of choosing one who rides the bus.
E. Of all students, the probability of choosing a student who drives.
Answer:
B. Of the students who walk, the probability of choosing a female.
D. Of the females, the probability of choosing one who rides the bus.
Step-by-step explanation:
Conditional probability is the chance of something happening provided that something else has previously occured (think dependent events).
For example, the probability of getting into college P(college) is Event A.
The probability of receiving dormitory housing P(housing) is Event B.
First, the person must get into college before they are even able to receive dormitory housing. Therefore, this is a situation of conditional probability. The "condition" of being accepted into the college (Event A) is necessary before the individual can attempt Event B, housing.
The key word in the question is "Of all the students." This means that from the first instance, you are only calculating one probability.
However, in B, it first singles out "all the students who walk."
Therefore p(walk) must be met before p(gender) can happen.
Same with D, it singles out "of the females."
Therefore p(gender) must be met before p(transportation) can happen.
C does have two categories, but since it is still out of the general draw pool "of all students," it is not conditional. No condition needs to be met first to choose a male who walks out of ALL students.
PLS ANSWER RN
What is the area of AJKL?
Answer:
8.5
Step-by-step explanation:
slope of the line that contains KL
(y2 - y1)/(x2-x1)
(0-1)/(7-3)
m = -1/4
slope of the line that contains JK
(5-1)/(4-3)
m = 4
the linea are perpendicular so triangle is right
area = (leg1 x leg2)/2
KL = [tex]\sqrt{(7-3)^2 + (0-1)^2} = \sqrt{16 + 1} = \sqrt{17}[/tex]
KJ = [tex]\sqrt{(4-3)^2 + (5-1)^2}= \sqrt{1 + 16} = \sqrt{17}[/tex]
area = (√17)^2/2 = 17/2 = 8.5
The diagram shows a cubeAh=11.3cn correct to the nearest millimetre calculate the lower bound for the length of an edge of the cub you must show all your working
Answer:
Lower bound for the length of the edge = 42.5 cm
Step-by-step explanation:
From the picture attached,
FH is the diagonal of square EFGH.
Therefore, length of diagonal FH = [tex]\sqrt{FG^2+HG^2}[/tex]
(By applying Pythagoras theorem)
In triangle AFH,
AH² = AF² + FH²
= AF² + [tex](\sqrt{FG^2+HG^2})^2[/tex]
= AF² + FG² + HG²
AH² = 3HG²
(11.3)² = 3(HG²)
HG = [tex]\sqrt{\frac{127.69}{3}}[/tex]
HG = 42.563 cm
For distance correct to the nearest mm, lower bound for the length of the edge = 42.5 cm
And upper bound for the length of the edge = 43.6 cm
The side lengths of a cu be are congruent, so the edge length of the cu be is 65 mm
The length of diagonal A H is given as:
[tex]\mathbf{AH = 11.3cm}[/tex]
Considering triangle A FH, we have:
[tex]\mathbf{AH^2 = A\ F^2 + FH^2}[/tex]
So, we have:
[tex]\mathbf{11.3^2 = A\ F^2 + FH^2}[/tex]
Considering triangle HE F, we have:
[tex]\mathbf{FH^2 = EF^2 + EH^2}[/tex]
Substitute [tex]\mathbf{FH^2 = EF^2 + EH^2}[/tex] in [tex]\mathbf{11.3^2 = A\ F^2 + FH^2}[/tex]
[tex]\mathbf{11.3^2 = A\ F^2 + EF^2 + EH^2}[/tex]
The side lengths of a cu be are congruent.
This means that: A F = EF = EH
So, we have:
[tex]\mathbf{11.3^2 = A\ F^2 + A\ F^2 + A\ F^2}[/tex]
Evaluate like terms
[tex]\mathbf{11.3^2 = 3A\ F^2}[/tex]
Evaluate squares
[tex]\mathbf{127.69 = 3A\ F^2}[/tex]
Divide both sides by 3
[tex]\mathbf{42.563= A\ F^2}[/tex]
Take square roots
[tex]\mathbf{6.52= A\ F}[/tex]
Rewrite as:
[tex]\mathbf{A\ F = 6.52cm}[/tex]
Convert to m m
[tex]\mathbf{A\ F = 6.52 \times 10mm}[/tex]
[tex]\mathbf{A\ F = 65.2\ mm}[/tex]
Approximate
[tex]\mathbf{A\ F = 65\ mm}[/tex]
Hence, the edge length is 65 mm
Read more about cu bes at:
https://brainly.com/question/23261883
Encuentre el volumen de 35 kg de oro
The perimeter of the figure below, in inches.
Answer:
just use a calculator and add all the numbers-
Step-by-step explanation:
add
67-2x+89/2+7-8x=0
help me please
Answer:
x = 11.85
Step-by-step explanation:
[tex]67 - 2x + \frac{89}{2} + 7 -8x = 0\\\\67 + \frac{89}{2}+7 = 8x + 2x\\\\\frac{134 + 89 +14}{2} = 10x\\\\10x = 118.5\\\\x = 11.85[/tex]
Answer:
[tex]x = 11 \frac{17}{20}[/tex] or [tex]\frac{237}{20}[/tex]
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
what is 10000000000+10000000000
Answer:
20000000000000000000000000000
pls help alot of points
Answer:
the perimeter is given in__in__, the height in_in___, and area of the base in_in²__.
so
none of the above.
Answer:
d
Step-by-step explanation:
none of the above
What is the area of the figure? NO LINKS!!
Answer:
Area of the figure is 88 square inches
Explain how to solve the following equation in your own words:
9x-13=23
Answer:
[tex]x = 4[/tex]
Step-by-step explanation:
[tex]9x-13=23[/tex]
[tex]9x=23+13[/tex]
[tex]9x = 36[/tex]
[tex]x = \frac{36}{9} [/tex]
[tex]x = 4[/tex]
Hope it is helpful....Answer:
X=4
Step-by-step explanation:
9x-13=23
9x=23+13
x=(23+13)/9
x=4
Kirenna's boss, Tanae, believes that women are not capable of making top-level decisions. Kireena's decisions are often sidelined by those of Tanae. When Kirenna confronts Tanae, he terminates her employment. Which of the following is the most appropriate suit that will help Kirenna?
a. a retaliation lawsuit
b. a forgery lawsuit
c. a reverse discrimination suit
d. a public policy violation lawsuit
e. a civil right infringement lawsuit
Answer:
e. a civil right infringement lawsuit
Step-by-step explanation:
A civil right infringement lawsuit is a lawsuit filed by an offender whose civil rights have been violated by others. Civil rights are those rights of the citizens that is guaranteed by the Constitution of the United States to its people. They are right to equality, right to freedom, right to employment and all those rights that is included in the Bill of Rights of the US constitution.
So, when Kirenna was terminated by her boss, Tanae on the grounds on the discrimination of gender, Kirenna can file a civil right infringement lawsuit against her boss, Tanae.
match the prefixes with the metric unit
Answer:
kilo =1*10^3 grams
nano=one millionth
micro=0.01 litres
centi=0.0000000001 meters
Step-by-step explanation:
how to find the surface area of composite figures