Answer:
f(x) = (x - 2)² + 2
Step-by-step explanation:
The vertex form of the quadratic function is:
f(x) = a(x - h)² + k
where:
(h, k) = vertex
The axis of symmetry is the imaginary vertical line where x = h
a = determines whether the graph opens up or down, and how wide or narrow the graph will be.
h = determines the horizontal translation of the parabola.
k = determines the vertical translation of the graph.
Given the vertex occurring at point (2, 2), along with one of the points on the graph, (4, 6):
Substitute these values into the vertex form of the quadratic function:
f(x) = a(x - h)² + k
6 = a(4 - 2)² + 2
6 = a(2)² + 2
6 = 4a + 2
Subtract 2 from both sides:
6 - 2 = 4a + 2 - 2
4 = 4a
Divide both sides by 4:
4/4 = 4a/4
1 = a
Therefore, the quadratic function in vertex form is: f(x) = (x - 2)² + 2
A filter in the shape of a cone has a diameter of 3 inches and a height of 4 inches.How much liquid can the filter hold without it overflowing?
A) π in³
B) 3π in³
C)12π in³
D)36 π in³
please answer this Thank you
[tex] \huge ༆ \bf{Answer} ༄[/tex]
The liquid that the cone can store is its volume, So let's calculate the volume of cone
It is given by : -
[tex] \sf \: v = \dfrac{1}{3} \pi {r}^{2} h[/tex]radius = diameter ÷ 2 = 3 ÷ 2 = 1.5 in
height = 4 inches
[tex] \sf \: v = \dfrac{1}{3} \pi \times 1.5 \times 1.5 \times 4[/tex][tex] \sf \: v = \pi \times 1.5 \times 2[/tex][tex] \sf \: v = 3\pi \: \: in {}^{3} [/tex]The liquid that the cone can hold without overflowing is 3π in³
[tex]꧁ \: \frak{Eternal \: Being } \: ꧂[/tex]
Find the surface area of the square pyramid below.
Answer:
Step-by-step explanation:
Answer:
96 cm or B
Step-by-step explanation:
Base-l*w, 6*6, 36
Side 1-(h*w)1/2, (30)1/2, 15
Side 2-Same as 1
Side 3-Same as 1
Side 4-Same as 1
15+15=30, 15+15=30, 30+30=60, 60+36=96
96 cm
Write y=-3x+2 in standard form
Answer:
3x+y=2
Step-by-step explanation:
The equation is in slope intercept form.
y=mx+b
Standard form is given by:
ax+by=c
y=-3x+2
3x+y=2
please quick answer i’ll mark brainliest
Answer:
1.363
Step-by-step explanation:
Area of the sector is x/360 * pi * r^2
A = 40/360 * pi * 7*7
= 1/9 * 22/7 * 49
= 1/9 * 22 * 7
= 17.111111
Area of the triangle OMN = 1/2 ab sin C
so here A = 1/2 * 7 * 7 * sin 40
= 49/2 * sin 40
= 15.748296437320213494904763542728
so, Area of shaded segment is
= Area of sector - area of triangle
= 17.1111111 - 15.748296437320213494904763542728
= 1.363
-2 1/4 - -4/5 Please help me hurry!!!!
Answer:
-1.45
Step-by-step explanation:
-2 14--4/5=-1.45
Algebra A regular pentagon has once I represented by 3X +2 and another side represented by 2X +5. Find the length of the sides of the pentagon
Answer:
3x + 2 = 2x + 5
3x = 2x +3
x = 3
3x + 2 = 18
2x + 5 = 11
Step-by-step explanation:
Answer:
3X +2 = 2X +5
grouping of like one's
3X - 2X = 5 -2
subtract
X = 3
Question 2
Find the area of the shaded region. Express your answer in terms of it.
3 in
6 in
-
9 in
O
12 in
18 in
ina
When Julius crossed the Rubicon, he had with him 3 times as many soldiers as he
needed to conquer Rome. If he had 26,000 soldiers with him, how many were needed
to conquer Rome?
86,000 :)
hope it helped!
Use a calculator . Round to the nearest tenth of a degree given cos 0=0.8458
0.8458 rounded to the nearest tenth is 0.8 given cos is 0.696706709347
What are the roots of the equation 4x^2+24x+45=0 in simplest a+bi form?
Answer:
X=(-1.5, 7.5)
Step-by-step explanation:
Simplifying
4x2 + -24x + -45 = 0
Reorder the terms:
-45 + -24x + 4x2 = 0
Solving
-45 + -24x + 4x2 = 0
Solving for variable 'x'.
Factor a trinomial.
(-3 + -2x)(15 + -2x) = 0
Set the factor '(-3 + -2x)' equal to zero and attempt to solve:
Simplifying
-3 + -2x = 0
Solving
-3 + -2x = 0
Move all terms containing x to the left, all other terms to the right.
Add '3' to each side of the equation.
-3 + 3 + -2x = 0 + 3
Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3
Combine like terms: 0 + 3 = 3
-2x = 3
Divide each side by '-2'.
x = -1.5
Simplifying
x = -1.5
Set the factor '(15 + -2x)' equal to zero and attempt to solve:
Simplifying
15 + -2x = 0
Solving
15 + -2x = 0
Move all terms containing x to the left, all other terms to the right.
Add '-15' to each side of the equation.
15 + -15 + -2x = 0 + -15
Combine like terms: 15 + -15 = 0
0 + -2x = 0 + -15
-2x = 0 + -15
Combine like terms: 0 + -15 = -15
-2x = -15
Divide each side by '-2'.
x = 7.5
Simplifying
x = 7.5
Solution
x = {-1.5, 7.5}
combine like terms and solve x
12x + 3 - 4x - 6 = 5
5x - 4 + 7 + 6x - 4x = 24
Answer:
12x + 3 - 4x - 6 = 5
x=1
5x - 4 + 7 + 6x - 4x = 24
x=3
evaluate x-2y when x =0.75 and y =0.96
Step-by-step explanation:
x = 0,75
y = 0,96
= x - 2y
= 0,75 - 2.0,96
= 0,75 - 1,96
= -1,21
HELP SOMEONE HEEEEEEEEEEEEEEEEEEEEEELP! which graph is the right one?
Which graph represents an exponential function?
Answer:
The answer is...
Step-by-step explanation:
what is -37x85
what is 28x-43
what is -53x-98
Answer:
1. -3145
Step-by-step explanation:
I couldnt solve the other one because they don't have a equal sign. Something like 28x-43= ?
Answer:
-37x85= -3145
28x-43=-1204
-53x-98=5194
those are ur answers
Step-by-step explanation:
GIVING BRAINLIEST! PLS SHOW WORK!!
Answer:
30
Step-by-step explanation:
all traiangles have to same vetec
Answer:
Since the angle on the top is a 90 degree as you might have noticed.
And the other angle is 30 degrees.
Then the last angle should be 60 degrees.
(Because every angle in a triangle should add up to 180 degrees)
I don't know about the measure of the sides tho.
Hope that helps !
nine times a number subtracted from another number
9x mean 9 multipled with an unkown number and 9x is subtracted from another unknown number 'y' . you can substitute with any letters you want ,but you have to use two different letters.
Helppp me Please!!!!! :)
Answer:
[tex]x = 30 \\ y = 10[/tex]
Step-by-step explanation:
[tex]8x + 6y = 300 \\ x + y = 40 \\ 6x + 6y = 240 \\ 2x = 60 \\ = > x = 30 \\ y = 10[/tex]
Help a Brother Out On The evalute expressions
Answer:
4. - 11
5. 3
6. 14
7. - 60
that it is
A Distributive Property and GCF
56+42
Answer:
98
Step-by-step explanation:
you at 56 in to 42
Answer:
98
pa brainless
Step-by-step explanation:
please brainless
Which of the following sets of ordered pairs is not a function?
{(-1, 2), (1, 3), (1, 5), (-3, 4)}
{(0, 2), (1, 4), (2, 5), (3, 6)}
{(-4, 3), (-1, 1), (-2, 5), (3, 7)}
{(0, 2), (1, 2), (2, 2), (3, 2)}
Answer:
1
first choice
Step-by-step explanation:
in a function, the x-value never repeats.
(found in brainly)
6) A truck driver drove 120 miles in 45 mintues. What is the speed of the truck in miles
per hour?
Answer:
22.5 mph
Step-by-step explanation:
45/120 to find how many miles in one minute
0.375 miles / 1 minute x 60
22.5 miles / 60 minutes
super easy question for 50 points and brainliest
7 = s²
s = x + 2
7 = (x + 2)²
7 = (x + 2)(x + 2)
7 = x² + 2x + 2x + 4
7 = x² + 4x + 4
x² + 4x = 3
what is 916 divied by 320
Answer:
2.8625
This is 916 divided by 320
Answer:
Full Answer - 2.8625
Rounded - About 3
Nearest Tenth - 2.9
Nearest Hundredth - 2.86
Step by Step:
Shown Below
Hope this Helps
Adult men have heights with a mean of 69.0 inches and a standard deviation of 2.8 inches. Find the z-score
of a man 72.4 inches tall. (to 2 decimal places)
Work Shown:
z = (x - mu)/sigma
z = (72.4 - 69.0)/(2.8)
z = (3.4)/(2.8)
z = 1.2142857 .... which is approximate
z = 1.21
Z-score of a man who is 72.4 inches tall is 0.45.
Understanding the concept of the z-score helps us gauge how far a value is from the mean in terms of standard deviations.
A z-score, denoted as , measures the deviation of a data point from the mean in terms of standard deviations. It's calculated using the formula:
= ( - ) /
Where:
- is the value we want to find the z-score for (72.4 inches in this case).
- is the mean of the dataset (69.0 inches).
- is the standard deviation of the dataset (2.8 inches).
Plugging in the values:
= (72.4 - 69.0) / 2.8 = 1.25 / 2.8 ≈ 0.446
Rounded to two decimal places, the z-score is approximately 0.45.
This means that a man who is 72.4 inches tall is roughly 0.45 standard deviations above the mean height of adult men.
In other words, his height is a bit taller than the average height by about 0.45 times the standard deviation.
This positive value indicates that the man's height is above the mean. If the z-score were negative, it would mean the height is below the mean. By using z-scores, we can compare data points from different distributions and understand how unusual or typical a particular value is within its dataset.
Z-scores help us quantify the relative position of a data point, providing a standardized way to interpret its significance in the context of the dataset's characteristics.
In summary, the z-score of a man who is 72.4 inches tall is approximately 0.45, indicating that his height is slightly above the average height of adult men.
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Consider an economy made up of 100 people, 50 of whom hold jobs, 10 of whom are
looking for work, and 15 of whom are retired. The unemployment rate is approximately:
17 percent
10 percent
25 percent
20 percent
12 percent
Answer:
20 por cento de cada um , que colocar
The unemployment rate is approximately 17 per cent. The correct option is A.
To calculate the unemployment rate, we need to consider the number of unemployed individuals (those looking for work) divided by the total labour force (those employed plus those looking for work).
Given:
Total population = 100
Employed individuals = 50
Individuals looking for work (unemployed) = 10
Total labour force = Employed + Unemployed
Total labor force = 50 + 10 = 60
Unemployment rate = (Unemployed / Total labour force) x 100
Unemployment rate = (10 / 60) x 100 ≈ 16.67 percent
Rounding to the nearest whole number, the unemployment rate is approximately 17 per cent.
Therefore, the correct answer is option A.
To know more about an expression follow
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can one of yall help me pls :)
Answer:
Omg i love geometry hehe your in luck :D
Step-by-step explanation:
15.65 should be your answer if i have calculated correctly.
What type of function is represented by the table of values below?
A. exponential
B. cubic
C. quadratic
D. linear
COS(α+β); SINα=- 1/3, α IN QUADRANT IV, TANβ=7/3, β IN QUADRANT III
PLEASE, I HAVE BEEN TRYING TO FIND THE ANSWER FOR 3 HOURS, AND I HAVE SPENT LIKE 1000 POINTS
Recall the angle sum identity for cosine,
cos(α + β) = cos(α) cos(β) - sin(α) sin(β)
Then given sin(α) = -1/3, we have
cos(α + β) = cos(α) cos(β) + 1/3 sin(β)
α is in quadrant IV, so 3π/2 < α < 2π, and so sin(α) is negative and cos(α) is positive. Then from the Pythagorean identity, we get
sin²(α) + cos²(α) = 1
⇒ cos(α) = √(1 - sin²(α)) = 2√2/3
β is in quadrant III, so π < β < 3π/2, so both sin(β) and cos(β) are negative. If we multiply both sides of the previous identity by 1/cos²(α) and replace α with β, we get
sin²(β)/cos²(β) + cos²(β)/cos²(β) = 1/cos²(β)
⇒ tan²(β) + 1 = 1/cos²(β)
⇒ 1/cos(β) = -√(tan²(β) + 1) = -√58/3
⇒ cos(β) = -3/√58
Also recall that by definition,
tan(β) = sin(β)/cos(β)
⇒ sin(β) = tan(β) cos(β) = 7/3 • (-3/√58) = -7/√58
Putting everything together, we find that
cos(α + β) = 2√2/3 • (-3/√58) + 1/3 • (-7/√58) = -(6√2 + 7)/(3√58)
or more clearly,
[tex]\cos(\alpha + \beta) = -\dfrac{6\sqrt2 + 7}{3\sqrt{58}}[/tex]
algerbraic expression in shape
ANYONE PLZ HELP GIVING BRAINLIEST ASAP
:)))
Answer:
C
Step-by-step explanation:
The shape is composed of a square and a semi circle
area of square = a × a = a²
The diameter of the semi circle is c , then radius = [tex]\frac{1}{2}[/tex] c = [tex]\frac{c}{2}[/tex]
area of semi circle = [tex]\frac{1}{2}[/tex] πr² = [tex]\frac{1}{2}[/tex] π × ([tex]\frac{c}{2}[/tex] )² = [tex]\frac{1}{2}[/tex] π × [tex]\frac{c^2}{4}[/tex] = [tex]\frac{\pi c^2}{8}[/tex]
area of shape = a² + [tex]\frac{\pi c^2}{8}[/tex] → C
Please help with this question
Answer:
The question or equation is not clear.....