If h(x) represents a parabola whose turning point is at (0, -3) and the function f is defined by
f(x) = h(x + 2) - 5, then what are the coordinates of the turning point off? Explain your reasoning. I’m
let's put h(x) in vertex form, and then let's see if we can get f(x) from there.
\(~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{vertex}{\stackrel{h}{0}~~,~~\stackrel{k}{-3}}\qquad h(x)=a(x-0)^2-3 \\\\[-0.35em] ~\dotfill\)
\(h(x+2)=a[(x+2)-0]^2-3\implies h(x+2)=\underline{a(x+2)^2-3} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{llll} \underline{h(x+2)}-5\implies [a(x+2)^2-3]~~ - ~~5\implies &\boxed{a(x+2)^2-8=f(x)} \\\\ &a[x-\stackrel{h}{(-2)}]^2\stackrel{k}{-8}=f(x)\\\\ &\stackrel{vertex}{-2~~,~~-8} \end{array}\)
190 muitiplied by 186
Answer:
35340
Step-by-step explanation:
please like my answer
Answer: 35340
Step-by-step explanation: just multiply
Convert: 8 quarts = _____ pints
2 pints
4 pints
16 pints
32 pints
Answer:
C. 16 pints
Step-by-step explanation:
1 quart equals to 2 pints
Answer:
answer is 2 pints
Step-by-step explanation:
2 x 4 is 8
what is the nth term in a cube number sequence
Answer:
cube numbers: 1, 8, 27, 64, 125, ... - the nth term is. triangular numbers: 1, 3, 6, 10, 15, ... (these numbers can be represented as a triangle of dots).Step-by-step explanation:
IF IT HELPED UH PLEASE MARK ME A BRAINLIEST :-)Draw a box- and- whisker plot that corresponds to the given data set 31, 12, 8, 25, 23, 17, 20, 13
The box-and-whisker plot that displays the five-number summary of the given data is: option B.
How to Draw a Box-and-whisker Plot?A box-and-whisker plot displays the five-number summary of a data, which includes, the min and max values, medain, upper and lwoer quartiles.
To draw a box-and-whisker plot, find the five-number summary of the data, 31, 12, 8, 25, 23, 17, 20, 13:
Minimum: 8First Quartile: 12.5Median: 18.5Third Quartile: 24Maximum: 31Therefore, the box-and-whisker plot that displays the five-number summary of the given data is: option B.
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I need help!!!!!!!!!
Answer:
its b4 + 7b3 + 4b2 + b5 + 7b4+ 4b3= b5+8b4+11b3+4b2
Answer:
When multiplying, add the exponents, (example) remember if there is "7b" the exponent is one.
Multiply b^2 * b^3 = b^5 (add the exponent 2 + 3 = 5)
Multiply 7b * b^3 = 7b^4 (the exponent of 7b is one, add 1 + 3 for the exponent to become 4)
Multiply 4 * b^3 = 4b^3 (4 doesn't have a variable, the exponent will be 3)
b^2 * b*2 = b^4 (add exponents)
7b * b^2 = 7b^3 (add the exponents 1 + 2)
4 * b^2 = 4b^2
b^2 + 7b + 4
b^3 b^5 + 7b^4 + 4b^3
+
b^2 b^4 + 7b^3 + 4b^2
b^5 + 7b^4 + 4b^3 + b^4 + 7b^3 + 4b^2
\(b^5 + 7b^4 + 4b^3 + b^4 + 7b^3 + 4b^2\)
b^5 + 8b^4 + 11b^3 + 4b^25/6 having denominator 35
Answer:( 175/6)
Step-by-step explanation: 5*35/6=175/6 sour our numerator is 175/6. So sour answer is (175/6)/35
one card is drawn from a pack of 52cards each of the 52 cards being equally likely to be drawn. what is the probability that the card drawn is a king?
The probability of drawing a king from a standard deck of 52 cards is 1/13.
In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.
To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).
The total number of possible outcomes is 52 because there are 52 cards in the deck.
The favorable outcomes, in this case, are the four kings.
Therefore, the probability of drawing a king is given by:
Probability = (Number of favorable outcomes) / (Number of possible outcomes)
= 4 / 52
= 1 / 13
Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.
This means that out of every 13 cards drawn, on average, one of them will be a king.
It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.
Each draw is independent, and the probability of drawing a king is constant.
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Find the value of x, 6,4, 3x, 4x+1
Answer:
If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.
6(3x) = 4(4x + 1)
18x = 16x + 4
2x = 4
x = 2
I need help
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I need help
I need help
The sequence is decreasing as n increases and sequence converges to the value 0.
The given sequence is defined as aₙ = 1 / (7n + 3).
To determine if the sequence converges or diverges, we need to analyze its behavior as n approaches infinity.
As n increases, the denominator 7n + 3 also increases which means that the values of aₙ will get smaller and smaller, approaching zero as n becomes larger.
The sequence converges to the value 0.
The sequence is decreasing as n increases.
The sequence converges to the value 0.
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What is the distance between the points 9 and -8
Answer:
17
Step-by-step explanation:
Distance is the same as difference.
9 - (-8) = 17
Answer:
17
Step-by-step explanation:
9 - (-8) = 17
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A ball is thrown from an initial height of 4 ft with an initial upward velocity of 40 ft/s. The ball's height h (in feet) after t seconds is given by the following. H=4+40t-16t squared. Find all values of t for which the ball's height is 26 feet
Answer:
Step-by-step explanation:
you need o solve 26=4+40t-16t^2
the equation becomes:
the equation becomes:-16t^2+40t+4-26=0
the equation becomes:-16t^2+40t+-22=0 or8t^2-20t+11=0
8t^2-20t+11=0, a=8 , b=-20 c=11 the discriminant =b^2-4ac=(-20)^2-4x8x11=48
t1=(20-squarootof48)/16 =13/16 =0.81 seconds t2=27/16=1.68 second I rounded my answers
I needddd helppp pleaseeeeee
Answer:
D : Obtuse
Step-by-step explanation:
A right angle is 90 degrees.
An acute and obtuse angle are found by looking at the angle between the sides being looked at.
If the angle is GREATER i.e. Angle > 90 , then it is obtuse.
If the angle is LESS THAN i.e. Angle < 90 , then it is acute.
This angle is apparently greater than 90 degrees and therefore is obtuse.
Find m<6. SHOW WORK!!!
Step-by-step explanation:
1 = 138 since they are opposite each other.
2 = 138 as well because of the 'Z'
5 is equal to 138 as it is opposite 2
5+6 = 180
6 = 180 -5
6= 180 -138
6= 42
Look for factors that will help you determine what type of economy exists in Country A.
Based on the clues in this passage, what type of economy does Country A have?
developed
developing
transitioning
command
Based on the limited information provided, it is not possible to definitively determine the type of economy in Country A. More specific details and factors would be necessary to make a conclusive determination.
solve for y. 2x-y=12
Answer:
2x - 12 = y
Step-by-step explanation:
→ Add y to both sides
2x = 12 + y
→ Minus 12 from both sides
2x - 12 = y
find the area of a rectangle with a length of 10 inches and a width of 4 inches
Answer:
40 in²---------------------
Formula for area of a rectangle with dimensions l and w is:
A = lwSubstitute 10 for l and 4 for w:
A = 10*4A = 40 in²l need help with dividing by finding groups
hello
to divide by finding groups, we can use a simple method as counting and circling to indicate each number
i'll give example here
divide 10 by 2
i grouped 10 by 2 into 5 places
These 3 points are on a parabola defining the edge of a ski:
(-4,1)
(-2,0.94)
(0,1)
The general form for the equation of a parabola is .
1.
Use the x- and y-values of 1 to build a linear equation with 3 variables: A, B, and C.
Repeat this process with the other 2 points to build a 2nd linear equation.
Record all three equations in the box below.
2.
Build a matrix equation that represents this system of equations. Record your matrix equation here.
3.
Use a graphing calculator or other graphing utility to find the inverse of the coefficient matrix. Record your result here.
4.
Use the inverse matrix to solve the system of equations. Record the equation of the parabola here.
The equation of the parabola is y = 0.015x^2 + 0.06x + 1
The linear equationsA parabola is represented as:
y = ax^2 + bx + c
The points are given as:
(-4,1), (-2,0.94) and (0,1)
When these points are substituted in y = ax^2 + bx + c, we have the following linear equations
16a - 4b + c = 1
4a - 2b + c = 0.94
c = 1
The matrix that represent the system of equationsIn (a), we have:
16a - 4b + c = 1
4a - 2b + c = 0.94
c = 1
Remove the variables (leaving the coefficients)
a b c
16 -4 1 1
4 -2 1 0.94
0 0 1 1
So, the matrix representation of the system of equations is:
\(\left[\begin{array}{ccc}16&-4&1\\4&-2&1\\0&0&1\end{array}\right] \left[\begin{array}{c}1&0.94&1\end{array}\right]\)
The inverse of the coefficient matrixUsing a graphing calculator, we have the inverse of the coefficient matrix to be
\(\left[\begin{array}{ccc}0.125&-0.25&0.125\\0.25&-1&0.75\\0&0&1\end{array}\right]\)
The solution to the system of equationsUsing a graphing calculator, we have the solution to the system of equations to be
a = 0.015
b = 0.06
c = 1
Recall that:
y = ax^2 + bx + c
So, we have:
y = 0.015x^2 + 0.06x + 1
Hence, the equation of the parabola is y = 0.015x^2 + 0.06x + 1
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An office has 7 male employees and 8 female employees. The manager randomly chooses 2 employees to attend a football game. What is the probability that the manager chooses 2 female employees?
Answer:
Step-by-step explanation:
d is the answeru got it right
Write the number five million four thousand three hundred in standard form.
Answer:
5,040,300 is the standard form
Step-by-step explanation:
which numbers are between 3 1/3 and 8 7/10
there are numbers 2 and 9
4. If y varies jointly as x and z, and y = 24, z = 2 and x = 4,
then find y when x = 12 and z = 2.
The answer is 72.
Step-by-step explanation:
y=kxz
24=k(4)(2)
k=24/(4×2)=3
y=kxz=3(12)(2)=72
If 18 pound of fertilizer covers 25 square feet of ground, how much fertilizer, in pounds, is needed to cover 1 square foot of ground?
Answer:
you need exactly 0.72 fertilizer but since its pounds, you round up so the answer is 1 pound.
Step-by-step explanation:
The amount of fertilizer required to cover 1 square foot of ground is 0.72
What is Proportion?
The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
Given data ,
Amount of fertilizer required to cover 25 square foot ground = 18 pound
Amount of fertilizer required to cover 1 square foot ground = Amount of fertilizer required / total square foot ground
Amount of fertilizer required to cover 1 square foot ground = 18 / 25
Therefore , Amount of fertilizer = 0.72 pound
Hence , the amount of fertilizer required to cover 1 square foot of ground is 0.72
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Compare the two expressions using an inequality symbol. Prove it by showing all working. 1. 23 +5×3_____2+8(35÷7)2. 9×(−2)−(−4)2_____34÷9+2×53. 5×22 −23(−6+3)_____6(2+9)−33 ÷9−4
Trina has a credit card that uses the adjusted balance method. For the first 10
days of one of her 30-day billing cycles, her balance was $780. She then
made a purchase for $170, so her balance jumped to $950, and it remained
that amount for the next 10 days. Trina then made a payment of $210, so her
balance for the last 10 days of the billing cycle was $740. If her credit card's
APR is 17%, which of these expressions could be used to calculate the
amount Trina was charged in interest for the billing cycle?
OA. (30)($780)
365
B.
O C.
D.
0.17
365
0.17
365
0.17
365
30
30
(10 $780+10 $950 +10 $210)
30
10
$780+10$950+10 $740
30
•30) ($570)
The expression that could be used to calculate the amount Trina was charged in interest for the billing cycle is (APR / 365) x 30 days x adjusted balance.
What is the adjusted balance method?The adjusted balance method is one of the methods for computing the finance charge (interest and other fees) for credit cards.
The adjusted balance is the ending balance determined after adjusting the opening balance with purchases and payments.
Credit card interest method = adjusted balance method
Beginning balance = $780
Purchase = $170
Payment = $210
Adjusted balance, AB = $740 ($780 + $170 - $210)
APR = 17% = 0.17 (17/100)
The interest charged = (APR / 365) x 30 days x adjusted balance
= $10.34 [(0.17/365) x 30 x $740]
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cone a is 10 centimeters high and its base has a diameter of 4 centimeters. Cone B is twice as tall with a hight of 20 centimeters and a diameter of 4 centimeters. Cone C is the same height as cone A, 10 centimeters, but the diameter of its base is 8 centimeters. Which cone has the greatest volume?
The cone that has the greatest volume is cone C
How to determine the cone that has the greatest volume?The given parameters in the question are
Cone A
Height = 10 cm
Diameter = 4 cm
Cone B
Height = 20 cm
Diameter = 4 cm
Cone C
Height = 10 cm
Diameter = 8 cm
The volume of a cone can be calculated using the following volume equation
Volume of a cone = 1/3π(d/2)²h
Where
h = height of the cone
r = radius of the cone
d = diameter of the cone
Using the above equations, we have the following computations
Volume of a cone A = 1/3π * (4/2)² * 10
Volume of a cone A = 40/3π
Volume of a cone B = 1/3π * (4/2)² * 20
Volume of a cone B = 80/3π
Volume of a cone C = 1/3π * (8/2)² * 10
Volume of a cone C = 160/3π
We can see that 160/3π is greater than 40/3π and 80/3π
Hence, cone C has the highest volume
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What is the volume of the
rectangular prism?
Answer:
We are already given the length of the prism, so now we need to find the height and width.
4 units across is the width, and 2 units up is the height
In order to find the volume of a rectangular prism we must multiply the length, width, and height.
In this case, 4 is our width, 2 is our height, and 7 is obviously our length.
Now let's multiply;
4 x 2 x 7 = 56 cubic centimeters
to make this easier to multiply we could also do
(4 x 2) x 7 or 4 x (2 x 7)
(2+3)^2+8/2 simplified
The given expression can be simplified to obtain (2 + 3)² + 8/2 = 29.
How to do simplification using arithmetic operation?The arithmetic operations are the fundamentals of all mathematical operations. In order to simplify a given expression various operation has to be done such as division, multiplication, addition and subtraction respectively.These operations follow a rule known as PEDMAS.
The given expression is (2 + 3)² + 8/2.
It can be solved as follows,
(2 + 3)² + 8/2
⇒ 5² + 8/2
⇒ 25 + 4
⇒ 29
Hence, the simplification of the given expression is obtained as 29.
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A company that manufactures machine parts determines that q units of a part will be sold when the price is p = 110 – q dollars per unit. The total cost to produce those q units is C(g) dollars, where C(q) = q³ - 25q² + 2q +3,000
a. For what value of q is the profit maximized?
b. Find the consumer surplus at the level of production that corresponds to maximum profit.