Answers
The vertex of the parabola y = x² - 16x + 24 will be at (8, -40). Then the correct option is D.
What is the equation of the parabola?Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.
Then the equation of the parabola will be given as,
y = a(x - h)² + k
The equation is given below.
y = x² - 16x + 24
Convert the equation into vertex form, then we have
y = x² - 16x + 24
y = x² - 2·8·x + 8² - 8² + 24
y = (x - 8)² - 64 + 24
y = (x - 8)² - 40
The vertex of the parabola y = x² - 16x + 24 will be at (8, -40). Then the correct option is D.
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Related Questions
-6x-4/2
2. Select all the expressions that are equivalent to
2
A.-3x - 2
B. 3x + 2
С. - 6х+4
2
D.-1/-
2 (6x+4)
E. 1/2 (-3x-2)
Answers
The expressions that are equivalent to -6x-4/2 are: -6x-4/2 and 1/2 (-3x-2)
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers
According to the given option, the required solution would be as:
A. -3x - 2 (if you multiply both sides of the equation -6x - 4 = 2 by -1/2, you get -3x - 2 = 1)
E. 1/2 (-3x-2) (if you multiply both sides of the equation -6x - 4 = 2 by 1/2, you get -3x - 2 = 1, and then divide both sides by -1 to get 1/2 (-3x-2) = -1/2)
Hence, the correct answer would be options (A) and (E).
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Solve the inequality for z.
z - 3 > 11
Simplify your answer as much as possible.
Answers
Answer: z > 14
Step-by-step explanation:
Move 3 to the right
Change= +
M>14
Triangle ABC is a right triangle, with right angle B. Side AC has a
length of 13. Side AB has a length of 5. Find the length of side
CB.
Answers
The length of side BC is approximately 10.928.
What is the right triangle?
In a right triangle, the side opposite the right angle is called the hypotenuse. In triangle ABC, side AC is the hypotenuse, and sides AB and BC are the other two sides.
To find the length of side BC, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
We can use the given information to write the Pythagorean theorem in the form:
AC^2 = AB^2 + BC^2
Substituting the given lengths, we get:
13² = 5² + BC²
Solving for BC, we get:
BC = √(13² - 5²)
= √(144 - 25)
= √(119)
= approximately 10.928
Therefore, the length of side BC is approximately 10.928.
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Find the simple interest on a loan of $9,000 at 7.6% interest for 9 months.
Anyone know the answer ??
Only answer if you know, any other answers will be reported !
Answers
Answer:
P= RS. 9000
R=7.6%
T= 9 months
Simple Interest (SI}=?
By using formula,
SI= PTR/100
= 9000* 7.6* 9/ 100* 12
= 615600/1200
= 513
Or
Bill write 4 page per hour. I the total number of page written proportional to the number of hour pent writing?
Answers
Equation used to represent the relation between the number of pages written to the number of hours used with constant of proportionality is
x = 4y.
As given in the question,
Let us consider number of pages write by Bill be 'x'
And number of hours represented by 'y'
Number of hours used by Bill to write 4 pages = 1 hour
Number of pages written by Bill in 1 hour = 4
Given :
Number of pages is proportional to the number of hours
⇒ x ∝ y
⇒ x = ky
Where 'k' is the constant of proportionality.
When x = 4 , y = 1
substitute the value in the equation,
4 = k(1)
⇒ k = 4
Now the required equation with the constant of proportionality k = 4 is:
x = 4y
Therefore, the required equation to represent the relation between number of pages written to the number of hours used with constant of proportionality is equal to x =4y.
The complete question is:
Bill enjoys writing in his spare time. He writes 4 pages per hour. The proportional relationship between the number of pages written to the number of hours is represented by the equation ______. Write the equation in standard form with a constant of proportionality.
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Question 6(Multiple Choice Worth 2 points)
(Two-Column Tables MC)
The table below shows the ratios of black to white keys on pianos of various sizes.
Black A 18 45 72
White 13 B 65 C
Determine which table has the correct values for A, B, and C.
Answers
The correct values for A, B and C are given as follows:
A = 9.B = 26.C = 104.How to obtain the correct values for A, B and C?The table shows the ratios of black to white keys on pianos of various sizes, and these ratios are constant, meaning that the following proportional relationship is established:
A/13 = 18/B = 45/65 = 72/C
Then the value of A can be obtained as follows:
A/13 = 45/65
Applying cross multiplication, we have that:
65A = 13 x 45
A = 13 x 45/65
A = 9.
The value of B can be obtained as follows:
18/B = 45/65
Applying cross multiplication, we have that:
45B = 18 x 65
B = 18 x 65/45
B = 26.
Finally, the value of C can be obtained as follows:
72/C = 45/65
Applying cross multiplication, we have that:
45C = 72 x 65
C = 72 x 65/45
C = 104.
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Which is an equation of the line through the origin and (-5, 6)?
Answers
The equation of line through the origin and (-5, 6 ) is y = [tex]-\frac{6}{5}x[/tex]
What is slope?The slope of a line is the ratio of the amount that y increases as x increases some amount. Slope tells you how steep a line is, or how much y increases as x increases. The slope is constant (the same) anywhere on the line.
the coordinates of the origin is (0, 0) and h other coordinates are (-5, 6)
at x = 0 and y = 0
using the equation of straight line y = mx + c
0 = 0(m) + c
so c = 0
at x = -5, y = 6
6 = -5m +c
but c = 0
6 = -5m
m = -6/5
Equation of line becomes y = -6/5x
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Find the values of x and y.
Answers
Answer:
x = 90 , y = 43
Step-by-step explanation:
Since AB and AC are congruent , then Δ ABC is isosceles with base angles congruent , that is
∠ ABD = ∠ ACD = 47°
AD is the perpendicular bisector of BC , so
∠ ADB = x = 90
the sum of the 3 angles in Δ ABD = 180° , then
y = 180° - (90 + 47) = 180 - 137 = 43
An engineer looks up at the top of a cell tower. The engineer stands 30 meters from the center of the tower with a line of sight of 37° from the horizontal. The engineer's eyes are 2
meters above the ground.
Answers
The value of the tangent of angle 37° is 3/4. Then the height of the cell tower will be 24.5 meters.
What is trigonometry?Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
A specialist gazes toward the highest point of a cell tower. The specialist stands 30 meters from the focal point of the pinnacle with a view of 37° from the level. The designer's eyes are 2 meters over the ground.
Let 'h' be the height of the tower. Then we have
tan 37° = (h - 2) / 30
Simplify the equation, then we have
tan 37° = (h - 2) / 30
3/4 = (h - 2) / 30
4h - 8 = 90
4h = 98
h = 24.5 meters
The level of the cell pinnacle will be 24.5 meters.
The diagram is given below.
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What inequality represents the graph? 4 . -8-40 48 x <= - 8; x < - 8; x > - 8; x < 8
Answers
Option 1 : x < = - 8 represents the given graph of inequality.
What is inequality?In mathematics, an inequality displays the connection between two values in an unbalanced algebraic expression. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signs.
Depending on which way the inequality sign is pointing, a sign can be greater or less than. When the open portion of the sign is facing left, >, the value on the left side of the sign is greater than the value on the right. When it is turned to the right, the left value is less than the right value.
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The lines 5x + 2y = 14 and y = –5x + 9 are A. parallel b.perpendicular c.neither
Answers
Answer:
parallel
Step-by-step explanation:
same slope
You sell TV's at a local store and they pay you 4% commission for whatever you sell. At the end of the month you sold $9,000 worth of TV's. How much money in commission did you receive?
Answers
Answer:
360 in commission.
Step-by-step explanation:
If you received a 4% commission on the TVs you sold, and you sold $9,000 worth of TVs, then you would have received 4/100 * $9,000 = $<<4/100*9000=360>>360 in commission.
The amount of time a certain brand of light bulb lasts is normally distribued with a
mean of 1900 hours and a standard deviation of 45 hours. Out of 670 freshly installed
light bulbs in a new large building, how many would be expected to last more than
1890 hours, to the nearest whole number?
Answers
To calculate the area under the normal distribution curve, we first need to standardize the value 1890 hours. This means we need to convert it to a z-score, which represents the number of standard deviations above or below the mean a value is. To standardize a value, we use the following formula:
z = (x - mean) / standard deviation
In this case, we have x = 1890, mean = 1900, and standard deviation = 45, so the z-score is:
z = (1890 - 1900) / 45 = -0.22
We can now use this z-score to look up the corresponding area under the normal distribution curve using a table of the standard normal distribution. This table gives the area under the curve between the mean and a given z-score. Since our z-score is negative, we need to look up the area to the left of the mean. In this case, the area is 0.4162.
We can now multiply this probability by the total number of light bulbs, 670, to find the number of light bulbs that are expected to last more than 1890 hours. This is:
0.4162 * 670 = 278.29
Rounded to the nearest whole number, this is 278 light bulbs. So we would expect about 278 out of 670 freshly installed light bulbs in the new large building to last more than 1890 hours.
The answer is 278 light bulbs.
Need help:
given that M∠QRT=105, find M∠QRS and M∠SRT
Answers
Answer:
m∠QRS = 30°
m∠SRT = 75°
Step-by-step explanation:
Given;m∠QRT = 105°m∠QRS = (6x)°m∠SRT = (14x + 5)°To Find;m∠QRS and m∠SRTNow,
The sum of m∠QRS and m∠SRT is equal to m∠QRT which is 105°
So,
m∠QRS + m∠SRT = m∠QRT
(6x)° + (14x + 5)° = (105)°
6x + 14x + 5 = 105
20x + 105 - 5
20x = 100
x = 100/20
x = 5
Thus, The value of x is 5°
Now,
m∠QRS = (6x)° = 6 × 5 = 30°
m∠SRT = (14x + 5)° = 14(5) + 5 = 70 + 5 = 75°
Find the perimeter of the triangle.
Answers
Answer:
39 inches
Step-by-step explanation:
All of the sides are the same length because all of the angles are equal
21 - x = 2x - 3 Set two sides equal to each other and solve for x. Add x to both sides
21 = 3x - 3 Add 3 to both sides
24 = 3x Divide both sides by 3
x = 8
Substitute in 8 for x to find the value of a side
2x - 3
2(8) - 3
16 - 3
13
Each side length is 13
3 x 13 = 39
Two shoppers bought meat at a supermarket deli. The first shopper bought 3 pounds of meat for $9.87. The second shopper bought 4 pounds of a meat that cost $1 more per pound than the meat the first shopper bought. How much did the second shopper pay?
Answers
Answer: $17.16 dollars
Step-by-step explanation:
first, you divide 9.87 by three which equals $3.29
then you add 1 which is $4.29
Finally, multiply it by 4 which is $17.16
Answer:$17.16
Step-by-step explanation:
A class is planning a trip to the local City Museum of Art. There are 22 people going on this trip.
There are four drivers and two types of vehicles, cars and trucks. The cars set four people,
including the driver and the truck seats six people again including driver. How many trucks and
cars doe the class need for this trip? Write a system of equations to solve.
12/24
Answers
A class is planning a trip to the local City Museum of Art. The class needs 3 trucks and 1 car to transport all 22 people on the trip.
What is the system of equations?Generally, To solve this problem, we can set up a system of equations using the information given. Let C be the number of cars needed and T be the number of trucks needed.
The first equation will represent the number of people that can be transported in the cars: 4C + 6T = 22
The second equation will represent the number of drivers: C + T = 4
Now we can solve this system of equations using elimination or substitution.
Using elimination, we can multiply the first equation by 2 and the second equation by 4 to get: 8C + 12T = 44 4C + 4T = 16
Then we can subtract the second equation from the first equation to get: 4C + 8T = 28
Then we can divide both sides by 4 to get: C + 2T = 7
Then we can substitute this value for C in the second equation to get: 7 - 2T = 4 T = 1.5
Since T represents the number of trucks, which must be a whole number, this solution is not possible.
Using substitution, we can solve for C in the second equation and substitute it into the first equation: C = 4 - T 4(4 - T) + 6T = 22 16 - 4T + 6T = 22 2T = 6 T = 3
Substituting this value for T into the second equation, we get: C = 4 - 3 C = 1
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Please HELP WITH CHEM
Answers
The ratio of Oats to Maple syrup for 36 cookies is 192 grams: 816 grams. So the answer is Option C. 192 grams: 816 grams.
What is Ratio:Comparing two amounts of the same units and determining the ratio tells how much of one quantity is in the other.
when evaluating the relationship between two quantities or numbers. In general, x: y, which can be interpreted as "x is to y," is used to denote a ratio between two quantities.
Here we have
15 Cookies need 80g Oats
=> Amount of Oats for 1 cookie = 80g/15 gms
So the amount Oats for 36 Cookies = 80g/5 × 36 = 192 grams
15 Cookies need 340 grams of Maple syrup
=> Amount of Maple syrup for 1 cookie = 340/15 gram
So the amount of Maple syrup for 36 cookies = (340/15)×36 = 816 grams
By the above calculations,
For 36 Cookies we need 192 grams of Oats and 816 grams of Maple syrup
The Ratio of Oats to Maple syrup = 192 gram: 816 gram
Therefore,
The ratio of Oats to Maple syrup for 36 cookies is 192 grams: 816 grams. So the answer is Option C. 192 grams: 816 grams.
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You deposit $600 in a savings account. After 18
months, you check your statement and see that
you have earned $31.50 in interest. What is the
interest rate for your account?
Answers
Answer:
To calculate the interest rate for your account, you will need to use the formula for simple interest:
Interest = Principal x Rate x Time
In this case, the principal is the amount of money you deposited, or $600. The time is the number of months the money was in the account, or 18 months. And the interest is the amount of money you earned, or $31.50.
Plugging these values into the formula, we get:
$31.50 = $600 x Rate x 18
To solve for the rate, we can divide both sides of the equation by $600 and 18:
Rate = $31.50 / ($600 x 18)
Simplifying this expression gives us:
Rate = 0.01625
So, the interest rate for your account is approximately 1.625%.
work out the area of this triangle
height=2.5cm
base=4.6cm
Answers
Answer:
5.75
Step-by-step explanation:
So first you would multiply 2.5*4.6 which is 11.5
Next you would divide 11.5/2 because a triangle is half of a square.11.5/2 is 5.75
Urgent help:
please look at the image
will mark brainliest for correct answer
Answers
[tex]\sqrt[4]{256x^{6}y^{10} }[/tex]will be 4[tex]x^{3/2} y^{5/2}[/tex]
What is the fourth root?The number that, when multiplied four times by itself, yields the original number is the fourth root of a number. In other words, the square root of the square root of an integer equals the number's fourth root.
eg:
eg: [tex]\sqrt[4]{81}[/tex] = 3
We are asked
x> 0 and y> 0then
[tex]\sqrt[4]{256x^{6}y^{10} }[/tex] = 4 [tex]x^{3/2} y^{5/2}[/tex]
As 4 multiplied by 4 , 4 times given 256 and x to the power 6 and root 4 so that will be x to the power 3/2 and y to the 10 and root 4 will give 5/2
thus
[tex]\sqrt[4]{256x^{6}y^{10} }[/tex] will be equivalent to 4 [tex]x^{3/2} y^{5/2}[/tex]
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Dora says that only one triangle can be constructed with two given side lengths and one given angle measure. Is Dora correct? Explain.
Answers
How many solutions does this equation have?
-2-y=-y
no solution
one solution
infinitely many solutions
Answers
Answer:
No solution
Step-by-step explanation:
-2-y=-y
clt
-2=-y+y
-2=0
:ans is -2=0 making it with no solution
A rectangular room is 2 meters longer than it is wide, and its perimeter is 20 meters. Find the dimension of
the room. Length and width
Answers
Answer:
Hope this helps good luck :)
see explanation
Step-by-step explanation:
Find relationship of length(L) and width(w)
Perimeter = L + W + L + W
[tex]20. = (w+2) + w + (w+2) +w 20. = 4w + 4 -4. -4 16 = 4w 16. = 4w 4. 4 4. = w w = 4 L. = w+2 = 4 +2 L = 6[/tex]
Answer width is 4 meters and length is 6 meters.
3(4x+2)=(?)x+( )
Enter the number that goes in the green box
Answers
3*4x = 12x 3*2= 6
Darrel spent $383 on 21 presents for his grandchildren. Which expression uses compatible numbers to estimate the amount he spent on each?
Answers
$18.24
Step-by-step explanation:How do I find out the answer to this?You can find the answer to this by simply dividing the two numbers:
$383 ÷ 21 = $18.24
I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!
ok so i did this twice but got wrong answer need help with this one rq
Answers
By solving an inequality, we will see that option a is cheaper for more than 60 miles.
For what number of miles is option A better?We know that option A charges $25 per day plus $0.15 per mile, so the cost for x miles is given by the linear equation:
A(x) = $25 + $0.15*x
While for option B the fixed cost is $10 and the cost per mile is $0.40, so the cost equation is:
B(x) = $10 + $0.40*x
The cost of option a will be smaller when:
$25 + $0.15*x < $10 + $0.40*x
$25 - $10 < $0.40*x - $0.15*x
$15 < $0.25*x
$15/$0.25 < x
60 < x
So for 60 miles the cost is the same, for x > 60 miles the cost of option a will be smaller (because the slope is smaller).
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answer the question linked
Answers
If we distribute the X in Tony’s equation, it would be the same as Mai’s.
Ms. patels gym class is practicing soccer. Ms. pedal has 18 soccer balls and three teams of students. She gives the same number of bars to eat student. How many balls does Ms. patel give each team
Answers
Answer
6
Step-by-step explanation:
There are 3 teams and 18 soccer balls. For each team to have the same number of soccer balls you need to do 18 divided by 3 to get 6. Each time will have 6 soccer balls.
To earn a "C" in Probability, Sam must get a grade average of at least 70%.
Sam's test scores are 62, 71, and 65. His final exam score counts as 3 test
scores in the average. What is the minimum score Sam needs to get on his
final exam to get a "C" in the course?
Answers
The minimum score Sam needs to get on his final exam to get a "C" in the course is 82.
What is a probability?
A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
Given that, Sam's test scores are 62, 71, and 65.
The total score in three test is (62 + 71 + 65) = 198
Assume that, he scored x in the final test.
Total score of Sam is 198 + x.
He needs to score 70% means he needs to score 70 out of 100.
According to question,
(198 + x)/ 400 ≥ 70/100
Multiply both sides by 100:
(198 + x)/ 4 ≥ 70
Multiply both sides by 4
198 + x ≥ 280
x ≥ 280 - 198
x ≥ 82
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