Answers
Answer:
A
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k ) = (2, - 1), thus
y = a(x - 2)² - 1
To find a substitute (5, 8) into the equation
8 = a(5 - 2)² - 1
8 = 9a - 1 ( add 1 to both sides )
9 = 9a ( divide both sides by 9 )
a = 1
Thus
y = (x - 2)² - 1 → A
Related Questions
The sum of two numbers is -36. One number is 106 less than the other. Find the numbers.
Answers
Answer:
71 and -35
Step-by-step explanation:
so with this we can set up a system of equations
x+y=36
and
x-y=106
now we can add these equations together to eliminate y
x+y=36 plus
x-y=106 equals
2x=142
divide both sides by 2
x=71
now we can plug that in
71+y=36
subtract 71 from both sides
y=-35
Answer:
-71 and
35
Step-by-step explanation:
Let the numbers be x and y
x + y = -36
x = y - 106
Substitute y - 106 or x in the first equation
We have
x + y = -36
y - 106 + y = -36
y + y - 106 = -36
2y - 106 = -36
Add 106 to both sides to eliminate -106 on the left side
2y - 106 + 106 = -36 + 106
2y = 70
Divide both sides by 2
2y/2 = 70/2
y = 35
Substitute 35 for y in either equation to get x
Using the second equation, we have
x = y - 106
x = 35 - 106
x = -71
The numbers are 35 and -71
Check
x + y = -36
-71 + 35 = -36
-36 = -36
Can someone help me with this question?
Answers
Answer:
C). 30 I just learned about this!
Step-by-step explanation:
If the smaller diamond is 12 and the bigger one is 36 then its times 3 and whatver you do to the top you do to the bottom so it would be 10 times 3 which would equal 30! (:
Answer:
C - 30
Step-by-step explanation:
Since one side of the smaller diamond is 12 and the side on the bigger diamond is 36 it is 3 times the perimeter on each side so since the side on the small diamond is 10 then you would times it by three to get the perimeter of the side on the bigger diamond , which is 30 .
The Seattle Mariners baseball team wishes to determine the equilibrium price for seats for each of the next two seasons
Answers
Answer:
Price Qd1 Qd2 Qs
25 75000 60000 45000
30 60000 55000 45000
35 45000 50000 45000
40 30000 45000 45000
45 15000 40000 45000
[Find the attachment for the graph]
Final answer:
The equilibrium price for the Seattle Mariners baseball team's seats can be found using economic principles of supply and demand, taking into account factors that influence ticket demand, marginal revenue, and costs.
Explanation:
The question involves determining the equilibrium price for Seattle Mariners baseball team seats. This can be addressed using principles from Economics, specifically the supply and demand model. To determine the equilibrium price, one would need to establish the demand curve, which includes factors such as the population and income of the home city, the team's standing, and the number of superstars on the team. As economists such as Ferguson et al. suggest, the marginal cost for sports teams is often assumed to be zero due to the fixed costs of stadium operations. Therefore, the profit-maximizing quantity of seats sold is where marginal revenue is zero. This can be calculated and visualized with a graph showing both demand and marginal revenue curves. Additionally, adjustments such as the addition of new seats or external fees like licensing can affect the equilibrium dynamics, thus changing the equilibrium price and the total revenue.
Find the equation of the line. Use exact numbers.
y = __x + __
Answers
Answer:
y = 3x+3
Step-by-step explanation:
We know the y intercept since it crosses the y axis at (0,3) and we know the x intercept since it crosses the x axis at (-1,0)
We can fidn the slope
m = (y2-y1)/(x2-x1) (0,3) (-1,0)
=(0-3)/(-1-0)
= -3/-1
=3
The equation for the line is in the form
y = mx +b where m is the slope and b is the y intercept
y = 3x+3
the vertical asymptote is at x =
Answers
Answer:
x=8
Step-by-step explanation:
The vertical asymptote is where the denominator goes to zero
3(x-8) =0
Divide by 3
(x-8) =0
Add 8 to each side
x-8+8=0+8
x=8
The vertical asymptote can be find by solving the 0 of the denominator.
3(x - 8) = 0
3x - 24 = 0
3x - 24 + 24 = 0 + 24
3x = 24
3x/3 = 24/3
x = 8
Besr of Luck!
The base of a triangular prism is an isosceles right triangle with a hypotenuse of 72−−√ centimeters. The height of the prism is 7 centimeters. Find the surface area of the triangular prism. Round your answer to the nearest tenth.
Answers
Answer:
Step-by-step explanation:
Surface area = lateral area + 2(area of base)
Lateral area = perimeter of base * height.
Because it is a isosceles right triangle, both sides are equal.
[tex]x^{2} +x^{2}[/tex] = 72
2[tex]x^{2}[/tex] = 72. Divide both sides by 2
[tex]x^{2}[/tex] = 36. Square both sides.
x = 6.
So the perimeter of the base = 6 + 6 +[tex]\sqrt{72}[/tex] = 20.485281374239
Lateral area = 20.485281374239 * 7 = 143.397 [tex]cm^{2}[/tex]
Area of base is (1/2)base * height.
(1/2)(6)(6) = 18
Using the surface area formula
surface area = 143.397 + 2(18) = 179.4 [tex]cm^{3}[/tex]
Final answer:
The surface area of the triangular prism can be calculated by finding the areas of the two triangular bases and the three rectangular sides. After calculations, the total surface area of the prism is found to be 2304 square centimeters.
Explanation:
The question asks us to find the surface area of a triangular prism whose base is an isosceles right triangle with a hypotenuse of √72 centimeters and a height of 7 centimeters. We'll use various formulas for geometry, area, and volume to solve this problem.
First, we need to find the legs of the isosceles right triangle which form the base of the prism. Since it is a right triangle, and the legs (a) are equal, we can use Pythagoras' theorem where [tex]a^2 + a^2 = (72)^2[/tex]
Solving this gives us each leg as 36 cm.
The area of the base triangle is then found using 1/2 × base × height, which gives us-
1/2 × 36 × 36 = 648 square centimeters
The prism has two such triangular bases, so their combined area is 2 × 648 = 1296 square centimeters.
For the three rectangular sides, we calculate their areas by using the formula for the area of a rectangle (length × width). Each side has a length of 7 cm (the height of the prism). The widths are equal to the sides of the triangular base: 36 cm, 36 cm, and √(362 + 362) = √2592 = 72 cm. Thus, the total area of these sides is-
2(36 × 7) + (72 × 7) = 504 + 504 = 1008 square centimeters.
The total surface area of the prism is the sum of the areas of the bases and the rectangular sides, which is 1296 + 1008 = 2304 square centimeters.
What is g+1 when g= -9
Answers
Answer:
-8
Step-by-step explanation:
plug in -9 as g
(-9) + 1 = -8
Answer:
-8Step-by-step explanation:
If g = -9
Then g + 1 = -9 + 1
-9 + 1 = -8
I hope this helped you!
Ms. Joseph is saving money for a trip to Zearnland over 12 weeks. She starts with 1 dollar. In the second week, she adds 2 dollars. Each week she adds 1 more dollar than she did the week before. For how many weeks will Ms. Joseph be saving money?
Answers
Ms. Joseph saves money for 12 weeks, starting with $1 and increasing the amount by $1 each week. By the 12th week, she adds $12. Therefore, she saves money for a total of 12 weeks.
To determine how many weeks Ms. Joseph is saving money, we need to look at the pattern of her savings. Each week, she adds one more dollar than the previous week:
Week 1: $1Week 2: $2Week 3: $3...Week 12: $12We can see that this is an arithmetic sequence where the first term (a) is $1 and the common difference (d) is $1. The nth term of an arithmetic sequence can be found using the formula: aₙ = a + (n-1)d.
For 12 weeks, the amount saved each week would be: a₁₂= 1 + (12-1) ×1 = 12. Ms. Joseph adds $12 in the 12th week. Finally, the total weeks she saves money is 12 weeks.
Mya's lunchbox is shown. What is the volume of the lunchbox? Round to the nearest tenth if necessary.
Answers
There is no picture but the fomula for volume is lengthxwidthxheight for a square or rectangle
If a club consists of 11 members, how many different arrangements of president, vice-president, and secretary are possible?
Answers
There are 990 different arrangements of president, vice-president, and secretary
The number of arrangementsThe given parameters are:
Club members, n = 11
Members to arrange, r = 3
The number of arrangements is calculated using the following permutation equation
Ways = nPr
This gives
Ways = 11P3
Evaluate
Ways = 990
Hence, there are 990 different arrangements of president, vice-president, and secretary
Read more about permutation at:
https://brainly.com/question/12468032
Final answer:
To find the number of different arrangements of president, vice-president, and secretary in a club of 11 members, we use the concept of permutations. Using the formula for permutations of distinct objects, we calculate P(11,3) = 990. Thus, there are 990 different arrangements possible.
Explanation:
To find the number of different arrangements of president, vice-president, and secretary, we can use the concept of permutations. Since the positions have different roles and can only be assigned to one person each, we use permutations. The number of permutations can be found using the formula for permutations of distinct objects: P(n,r) = n! / (n-r)!.
In this case, we have 11 members and need to assign them to 3 different positions (president, vice-president, and secretary). So, the number of arrangements is P(11,3) = 11! / (11-3)! = 11! / 8! = 11 x 10 x 9 = 990.
Therefore, there are 990 different arrangements of president, vice-president, and secretary possible.
what is x+4x+6x= simplify
Answers
Answer:
11x
Step-by-step explanation:
Find the area of the parallelogram below.
Image result for area and perimeter of parallelograms
Answers
Answer:32 cm2
Step-by-step explanation:Use the formula A=BH, The 7 does not count because it isn't base or height. Use 4 times 8 which will make 32 cm2.
Area of the parallelogram is 32 cm²
Area of the parallelogram:Given that;
Base of parallelograms = 8 cm
Height of parallelograms = 4 cm
Find:
Area of the parallelogram
Computation:
Area of the parallelogram = l × b
Area of the parallelogram = 8 × 4
Area of the parallelogram = 32 cm²
Find out more information about 'Parallelogram'.
https://brainly.com/question/1563728?referrer=searchResults
Can someone word out the equation 3 1\4+7\8 ?ANY RANDOM ANSWER WILL GET REPORTED
Answers
Answer:
13/8
Step-by-step explanation:
Answer:
Three and one fourth plus seven eigths
Step-by-step explanation:
3% percent of the students at Lincoln High School are in orchestra, 5%
are in band and 1% are in both. If a student is selected at random, what is
the probability that the student is in orchestra OR band?
Answers
Answer:
The probability of a student to be in the orchestra or the band is 0.07 or 7%.
Step-by-step explanation:
The probability of a student to be in the orchestra or the band is given by the following formula:
p(orchestra or band) = p(orchestra) + p(band) - p(orchestra and band)
p(orchestra or band) = 0.03 + 0.05 - 0.01
p(orchestra or band) = 0.08 - 0.01
p(orchestra or band) = 0.07
The probability of a student to be in the orchestra or the band is 0.07 or 7%.
Final answer:
The probability that a student is in orchestra or band is 7%.
Explanation:
To calculate the probability that a student at Lincoln High School is in either orchestra or band, we will use the formula for the probability of the union of two events, P(A ∪ B) = P(A) + P(B) - P(A ∩ B), where P(A) is the probability of being in orchestra, P(B) is the probability of being in band, and P(A ∩ B) is the probability of being in both orchestra and band.
In this case, we have been given that 3% of students are in orchestra, 5% are in band, and 1% are in both.
Therefore, we have:
P(orchestra) = 0.03 (3%)P(band) = 0.05 (5%)P(both orchestra and band) = 0.01 (1%)Applying the formula:
P(orchestra OR band) = P(orchestra) + P(band) - P(both orchestra and band) = 0.03 + 0.05 - 0.01 = 0.07
Therefore, the probability that a student is in either the orchestra or the band is 7%.
What is X if Y is 12.8 and Z is 16 in the right triangle below?
Answers
Answer:
Im 90% sure its H.
Step-by-step explanation:
Answer:
H) 9.6
Step-by-step explanation:
Use the pythagorean theorem to solve for a right triangle.
Pythagorean Theorem: a^2 + b^2 = c^2
So, 16^2= 12.8^2 + x ------> 256= 163.84 + x^2 (subtract 163.84 from both sides of the equation) -----> x^2= 92.16 (square root) -----> x=9.6
This is my first answer so I hoped it helped! :)
Use the graph of f(x) to explain the relationship between the real zeros of f(x) and its intercept(s). f(x) has one real zero at –2 because the graph of the function has an intercept at (0, –2). f(x) has two real zeros at –4 and –2 because the graph of the function has intercepts at (–4, 0) and (0, –2). f(x) has no real zeros because the graph of the function does not pass through (0, 0). f(x) has one real zero at –4 because the graph of the function has an intercept at (–4, 0).
Answers
Answer:
f(x) has one real zero at –4 because the graph of the function has an intercept at (–4, 0).
Step-by-step explanation:
Zeros of a function f(x) are those points where f(x) = 0. Then, zeros coordinates have the form (x1, 0), (x2, 0), et cetera. In the graph, a zero is seen as the interception of f(x) with the x-axis.
Answer:
D on Edge 2020
Step-by-step explanation:
what does a subtraction sign mean
Answers
Answer:
If you take a number and 'subtract" it with another number, it means that you take your second number and remove that amount from the first number
If this helped, say thanks on my profile ;)
Answer:
Definition of subtraction sign. : a mathematical symbol used to indicate that a particular quantity is to be subtracted from another to which it is joined by the symbol : a symbolic representation of the relation of subtrahend and minuend —symbol −
Step-by-step explanation:
i need help solving 5x= -7x+6
Answers
Answer:
x=1/2
Step-by-step explanation:
1.). add 7x to both sides
12x=6
2.) divide by 12 to get x by itself.
x=6/12
3.) simplify the fraction and you get the answer!
x=1/2
Choose 1 answer:
A. Vertical angles
B. Complementary angles
C.Supplementary angles
D. None of the above
Answers
Answer:
A
Step-by-step explanation:
vertical are always opposite each other
complementary are 180
supplementary are 90
can i please know the answer
Answers
Answer:
3840 cubic inches
Step-by-step explanation:
10*24 = 240 in
240*16 = 3840 cubic in
find the area of the shaded region
Answers
Answer:
[tex]x^{2} \\[/tex]+3x
Step-by-step explanation:
2x(2x+1)
x(x+1)
2[tex]x^{2}[/tex]+2x-[tex]x^{2}[/tex]+x
=[tex]x^{2}[/tex]+3x
select all that are true for the graph that represents the function f(x)=5(3)^x
Answers
Answer:A. The graph is increasing by a common ratio of 3
C. As x increases, y increases
F. As x decreases, y approaches 0
Step-by-step explanation:
The true statements are:
A. The graph is increasing by a common ratio of 3
C. As x increases, y increases
F. As x decreases, y approaches 0
Information regarding the function:The graph should be rise by ratio of 3. Since x increased so y should also rises. Also, x reduced so y should be 0.Therefore, the option A, C and F is correct. And the other options are incorrect.Find out more information about the graph here: https://brainly.com/question/14375099?referrer=searchResults
A bookshelf contains 9 mysteries, 7 biographies, and 4 science fiction books. A book is randomly selected, not replaced, then another is selected. Find the probability of selecting a biography then a mystery.
Answers
Answer:
63/380
Step-by-step explanation:
Initially,
# of Mysteries, M = 9
# of Biographies, B = 7
# of Sci. Fiction, S = 4
Total number of books = 9 + 7 + 4 = 20 books
P (first book selected is biography) = 7/20
After selecting 1 biography book,
# of Mysteries, M = 9
# of Biographies, B = 7 - 1 = 6
# of Sci. Fiction, S = 4
Total number of books remaining = 9 + 6 + 4 = 19 books
P (second book selected is a mystery) = 9/19
Hence (P first book is biography and 2nd book is mystery)
= (7/20 )(9/19)
= 63/380
The probability of selecting a biography then a mystery is 0.14.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.
Given that, a bookshelf contains 9 mysteries, 7 biographies, and 4 science fiction books.
Total number of outcomes = 9+7+4
= 20
The probability of selecting a biography = 7/20
The probability of selecting a mystery = 9/20
Probability of an event = 7/20 × 9/20
= 56/400
= 0.14
Therefore, the probability of selecting a biography then a mystery is 0.14.
To learn more about the probability visit:
https://brainly.com/question/11234923.
#SPJ3
The table represents the function f (x) = 5 x. A 2-column table with 4 rows. Column 1 is labeled x with entries negative 1, 0, 1, 2. Column 2 is labeled f (x) with entries blank, 0, 5, 10. Which value goes in the empty cell? –51 –5 5 51 Mark this and return
Answers
Final answer:
To find the value that goes in the empty cell, we need to multiply each value of x by 5. So, when x = -1, f(x) = 5*(-1) = -5. Therefore, the value that goes in the empty cell is -5.
Explanation:
The table represents the function f(x) = 5x. In the first column, we have the values of x, which are -1, 0, 1, and 2. In the second column, we have the values of f(x), which are blank, 0, 5, and 10. To find the value that goes in the empty cell, we need to multiply each value of x by 5. So, when x = -1, f(x) = 5*(-1) = -5. Therefore, the value that goes in the empty cell is -5.
13. Jake earns 15% commission on the total amount he sells. If he sells $545 worth of items, how much commission
does Jake earn? A. $21.33 B. $36.33 C. $54.50 D. $81.75
Answers
Answer:
Option D - $81.75
Step-by-step explanation:
Given : Jake earns 15% commission on the total amount he sells. If he sells $545 worth of items.
To find : How much commission does Jake earn?
Solution :
Using the commission formula,
[tex]\text{Commission}=\text{Sales}\times \text{Percentage}[/tex]
[tex]\text{Commission}=\$545\times 15\%[/tex]
[tex]\text{Commission}=545\times \frac{15}{100}[/tex]
[tex]\text{Commission}=81.75[/tex]
Therefore, commission does Jake earn is $81.75.
So, option D is correct.
A swimming pool had 2.5 million liters of water in it. Some water evaporated, and then the pool only had 2 million liters of water in it.
What percent of the water evaporated?
Answers
25 % of the water had evaporated.
Answer:
20%
Step-by-step explanation:
Since the total amount of water is 2.5 million
And 2 million evaporated,
To determine the amount left,it will be total amount- evaporated
2.5-2=0.5
To determine the% of evaporated water
It will be evaporated/total amount ×100
0.5/2.5 × 100
50/2.5
20%
So the percentage of the evaporated water is 20%
Solve the equation using the quadratic formula.
-x^2+27 = 6x
x=-3, X=9
X=-3X=3
x=-9,f=3
x=-9, x=3
Answers
The value of x is -9 and 3.Option D.
Step-by-step explanation:
Given,
[tex]-x^{2} +27 = 6x[/tex]
To find the value of x.
We will apply middle term factor formula.
The given equation can be written as,
[tex]x^{2} +6x-27 = 0[/tex]
or, [tex]x^{2}[/tex]+(9-3)x-27 = 0
or, x²+9x-3x-27= 0
or, x(x+9)-3(x+9)=0
or, (x+9)(x-3) = 0
So, x = -9 and x = 3
Hence,
The correct option is Option D.
What is the product? 4,3,-1,-1 x -3,1,-2,2
Answers
Answer:
B. [tex]\left[\begin{array}{ccc}-18&10\\5&-3\end{array}\right][/tex]
Step-by-step explanation:
The question is off edg. it is supposed to be [tex]\left[\begin{array}{ccc}4&3\\-1&-1\end{array}\right] * \left[\begin{array}{ccc}-3&1\\-2&2\end{array}\right][/tex] with multiple options. I just used the matrix calculator on edg.
What is 5u+1 when u=3
Answers
The dimensions of a garden are shown.
Write an expression to find the perimeter.
Answers
Answer:
P=3x-14
Step-by-step explanation:
P=2(x+1/2 x-7)
=2x+x-14
or P=3x-14
The perimeter of the garden will be;
⇒ 3x - 7/2
What is mean by Rectangle?
A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
The garden is shown in figure.
Width of garden = 1/2x - 7
Length of garden = x
Now,
Since, Width of garden = 1/2x - 7
Length of garden = x
Hence, The perimeter of garden = 2 (Length + Width)
⇒ The perimeter of garden = 2 (x + 1/2x - 7)
⇒ The perimeter of garden = 2 (3/2x - 7)
⇒ The perimeter of garden = 3x - 7/2
Thus, The perimeter of the garden will be;
⇒ 3x - 7/2
Learn more about the rectangle visit:
https://brainly.com/question/25292087
#SPJ2