Answer:
[tex]y=(x+4)^{2}-37[/tex]
Step-by-step explanation:
we know that
The equation of a vertical parabola into vertex form is equal to
[tex]y=a(x-h)^{2}+k[/tex]
where
(h,k) is the vertex of the parabola
if a> 0 then the parabola open upward (vertex is a minimum)
if a< 0 then the parabola open downward (vertex is a maximum)
In this problem we have
[tex]y=x^{2}+8x-21[/tex]
Convert to vertex form
Complete the square
[tex]y+21=x^{2}+8x[/tex]
[tex]y+21+16=(x^{2}+8x+16)[/tex]
[tex]y+37=(x^{2}+8x+16)[/tex]
[tex]y+37=(x+4)^{2}[/tex]
[tex]y=(x+4)^{2}-37[/tex] --------> equation in vertex form
The vertex is the point [tex](-4,-37)[/tex]
the parabola open upward (vertex is a minimum)
Answer:
the answer is y=(x+4)^2-37
Step-by-step explanation:
The legs of a right triangle are 13 and 22 inches long. Needa says that the hypotenuse is 17.7 inches long and Monifa says that it is 25.6 inches long. Is either of them correct? Explain
starting value 16 increases by 50% with each teem
George does not like the fact that his neighborhood makes it mandatory to pay a yearly fee to use the pool. He conducts a survey of all the neighborhood families to help support his case that the yearly fee should be voluntary. The survey asks questions about pool usage and financial statistics of the families. Is this a valid survey? Why or why not?
find the value of the combination
round the following number to the nearest hundredth which one of the numbers is in the hundreds place and does it go up or down I don't know which number is the hundredths place
he circle shown below has AB and BC as its tangents: AB and BC are two tangents to a circle which intersect outside the circle at a point B. If the measure of arc AC is 160°, what is the measure of angle ABC? (1 point) 80° 40° 60° 20°
Answer:
m∠ABC=20°
Step-by-step explanation:
Consider quadrilateral ABCO. The sum of the measures of all interior angles in quadrilateral ABCO is equal to 360°.
Lines BA and BC are tangent to the circle, then the radii OC and OA are perpendicular to the tangent lines BC and BA. Therefore,
m∠BCO=90°;m∠BAO=90°.The measure of the angle AOC is 160° (because the measure of arc AC is 160°). So,
m∠ABC+m∠BCO+m∠BAO+m∠AOC=360°,
m∠ABC=360°-(m∠BCO+m∠BAO+m∠AOC)=360°-(90°+90°+160°)=20°.
From a group of 10 candidates, a committee of 4 people is selected. In how many different ways can the committee be selected?
On a softball field, home plate is 43 feet from the pitcher’s mound. A ball is hit at an angle of 27° east of the pitcher’s mound. The ball travels 162 feet before it is caught by an outfielder. Law of cosines: a2 = b2 + c2 – 2bccos(A) Rounded to the nearest foot, the outfielder must throw the ball feet to return it to the pitcher.
Answer:
The outfielder must throw the ball 125 feet to return it to the pitcher.
Step-by-step explanation:
It is given that On a softball field, home plate is 43 feet from the pitcher’s mound. A ball is hit at an angle of 27° east of the pitcher’s mound. The ball travels 162 feet before it is caught by an outfielder.
Now, applying the law of cosines,
[tex]a^2=b^2+c^2-2bccosA[/tex],
Putting b=43, c=162 and A=27°, we have
[tex]a^2=(43)^2+(162)^2-2(43)(162)cos27^{\circ}[/tex]
[tex]a^2=1849+26244-12413.4[/tex]
[tex]a^2=15679.6[/tex]
[tex]a=125.21[/tex]
[tex]a[/tex]≈[tex]125 feet[/tex]
Thus, the outfielder must throw the ball 125 feet to return it to the pitcher.
find the surface area
Six cakes cost 3.60. How much do seven cakes cost
The area of a triangular block is 25 square inches. If the base of the triangle is twice the height, how long are the base and the height of the triangle?
Genna can build a cabinet in 4 hours. Claude can build a cabinet in only 3 hours. Which of the following can be used to determine the amount of time it would take for Genna and Claude to build a cabinet together? (2 point
I NEED HELP PLEASE??!!!???
if an object is shot with an initial velocity , vo, in feet per second(ft/s) the velocity, v, in ft/s is given by the formula v=v0 -32t, where t is time in seconds. find the initial velocity of an object if the velocity after 3 seconds is 31 ft/s
To find the initial velocity, we rearrange the given velocity equation to solve for the initial velocity, then substitute the given values. The initial velocity is found to be 127 ft/s.
Explanation:The given formula for velocity is v = v0 - 32t, where 'v' is the velocity at a certain time 't', and 'v0' is the initial velocity. In this case, we're given that v is 31 ft/s after 3 seconds. To find the initial velocity 'v0', you need to rearrange the equation to solve for 'v0'. This gives:
v0 = v + 32t
Substituting the given values into the rearranged equation gives:
v0 = 31ft/s + 32(3s)
This simplifies to:
v0 = 31ft/s + 96ft/s = 127ft/s
So the initial velocity of the object is 127 ft/s.
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One half of some number
Suppose P(E) = 0.3. Find P(not E). Suppose P(not E) = 65%. Find P(E).
What is the relationship between E and not E?
Dylan made his credit card payment at noon on the payment due date. According to Consumer Protection Law, how much time does the bank have to credit the payment to his account?
Answer:
Step-by-step explanation:
The transaction time is 24 hours or one business day.
Dylan made his credit card payment at noon on the payment due date. According to Consumer Protection Law, how much time does the bank have to credit the payment to his account? So, it is the same day/date or within 24 hours.
Final answer:
Banks are typically required to credit card payments to the customer's account by the end of the business day on which the payment was made, according to Consumer Protection Law. This ensures consumers are not unfairly charged late fees if payments are made on the due date.
Explanation:
The question concerns the timeframe within which a bank is required to credit a payment to a customer's account, according to Consumer Protection Law. If Dylan made his credit card payment at noon on the payment due date, the bank is typically required to credit the payment to his account by the end of that business day.
This requirement ensures that consumers are not unfairly penalized with late fees if they make their payment on the due date. It's essential for consumers to understand the specific policies of their credit card issuer and the relevant consumer protection laws to avoid any unnecessary charges. Timely payments are crucial for maintaining good credit health and avoiding additional fees.
Identify the percent of change as increase or decrease then find the percent of change round to the nearest tenth of a percent (if necessary)
1. 6 yards to 36 yards
2. 6 hits to 3 hits
3. 120 meals to 52 meals
4. 35 words to 115 words
Which ordered pair is identified by the letter "G" on this coordinate grid?
One number is 4 less than twice a second number. find a pair of such numbers so that their product is as small as possible.
Answer:
Numbers are -2 and 1.
Step-by-step explanation:
Let x be the second number,
⇒ First number = 4 less than twice a second number
= 2 × Second number - 4
= 2x - 4
Thus, the product of first and second number is,
[tex]f(x) = x(2x-4)[/tex]
[tex]\implies f(x) = 2x^2 - 4x[/tex]
Differentiating with respect to x,
[tex]f'(x) = 4x -4[/tex]
Again differentiating with respect to x,
[tex]f''(x) = 4[/tex]
Now, for maximum or minimum,
[tex]f'(x)=0[/tex]
[tex]\implies 4x - 4 = 0\implies 4x = 4\implies x = 1[/tex]
Since, for x = 1, f''(x) = Positive,
Therefore, the function f(x) is minimum for x = 1,
⇒ The product is smallest for x = 1,
Hence, the second number = x = 1,
And, first number = 2x - 4 = 2 - 4 = -2
Dana and her 4 friends are going on a camping trip. Dana wants to see how much fruit she can share so everyone will get the same amount of fruit. There are 5 apples, 10 oranges, 5 strawberries and 10 grapes. How much will each person get?
Find the absolute maximum and minimum values of f on the set
d. f(x, y) = 9 + xy − x − 2y, d is the closed triangular region with vertices (1, 0), (5, 0), and (1, 4)
For the function f(x, y) = 9 + xy - x - 2y in the triangular region, the maximum value is 9 at point (1,0), and the minimum value is 1 at point (1,4). The critical point does not lie within the triangle region.
Explanation:To find the absolute maximum and minimum values of the multivariate function f(x, y) = 9 + xy − x − 2y on the triangular region with vertices (1, 0), (5, 0), and (1, 4), we first locate the critical points within the region by solving the system of first order partial derivative equations.
∂f/∂x = y - 1 = 0, which means y = 1∂f/∂y = x - 2 = 0, which means x = 2
Notice that (2,1) is not in the triangle region, so there's no critical point in the interior of the triangle. The maximum and minimum must occur somewhere on the boundary, i.e., the lines connecting (1, 0), (5, 0), and (1, 4).
After using these points in the function, we get the following:
F(1,0) = 9F(5,0) = 4F(1,4) = 1
The maximum value is 9 when (x,y) are (1,0) and the minimum value is 1 when (x,y) are (1,4).
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A circle has a diameter of 9 inches. What is the approximate ratio of the circumference of the circle to its diameter?
A) 22/7
B)7/22
C)1/2
D)2/1
4 minus the product of one and a number x
Hattie jumps rope 57 times in 3 minutes. If Hattie jumps at a constant speed, how many times does she jump per minute?
Answer: Hattie Can jump 57 times in 3 minutes so therefore she jumps 19 times per minute. Because if do 57/3 it would give you 19.
Hope this helped!
if a/4 = b/7, what is the value of a-b/b ?
By what percent will a fraction increase if its numerator is decreased by 30% and its denominator is decreased by 50%?
40 percent of a fraction increase if its numerator is decreased by 30% and its denominator is decreased by 50%.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Given that, numerator is decreased by 30% and its denominator is decreased by 50%.
Let x/y be the original fraction.
Then, the new fraction is (x-30% of x)/(y-50% of y)
= 0.7x/0.5y
Now, difference = 0.7x/0.5y-x/y
= 0.7x/0.5y - 0.5x/0.5y
= 0.2x/0.5y
Percentage increase = 0.2x/0.5y ÷ x/y
= 0.2/0.5 ×100
= 40%
Therefore, 40 percent of a fraction increase if its numerator is decreased by 30% and its denominator is decreased by 50%.
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What's the radius of a circle with an area of 64 square feet?
Answer:
4.51
Step-by-step explanation:
What integer is equivalent to 9 3/2
The distribution of the baggage weights for passengers using a particular airline has a mean of 19.4 lbs and a standard deviation of 5.3 lbs. what is the probability that for (a random sample of) 100 passengers … the total luggage weight is less than 2,100 lbs?
Answer:
0.9987
Step-by-step explanation:
Given that X, The distribution of the baggage weights for passengers using a particular airline has a mean of 19.4 lbs and a standard deviation of 5.3 lbs.
For a sample of size 100, we have
n=100
Hence std deviation of sample = [tex]\frac{SD}{\sqrt{n} } =0.53[/tex]
To find the probability that X>2100/100 lbs
=P(X<21[tex]\frac{21-19.4}{0.53} =3.019[/tex]) =P(Z<3.019)
=0.5+0.4987
0.9987