To determine the vertices of the hyperbola using the equation[tex](x - 3)^2/9 - (y - 2)^2/16 = 1,[/tex] we can identify the values of a and b, where a represents the distance from the center to the vertices along the x-axis, and b represents the distance from the center to the vertices along the y-axis Therefore the correct option is D.
The given equation can be written as ([tex]x - 3)^2/3^2 - (y - 2)^2/4^2 = 1[/tex], which indicates that [tex]a^2 = 9[/tex] and[tex]b^2 = 16[/tex]. Taking the square root of a^2 and b^2 yields a = 3 and b = 4. The center of the hyperbola is (3, 2), and since the vertices are symmetrical about the center along the x-axis, the vertices can be found by subtracting and adding a from the x-coordinate of the center.
Consequently, the vertices of the hyperbola are (0, 2) and (6, 2). In summary, the vertices of the given hyperbola are located at (0, 2) and (6, 2).
Therefore the correct option is D
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Please help me
Mariah earns $32.75 per week working as a pet sitter. She worked as a pet sitter for 2 weeks. She previously saved $70.99 in allowance money. She spent $12.25 of her total earning to buy video games. Mariah put 1 over 4 of the remaining money in her savings account. Mariah used the following steps to find the total money she put in her savings account:
Step 1: [($32.75 ⋅ 2) + $70.99 − $12.25] ⋅ 1 over 4
Step 2: [$65.5 + $70.99 − $12.25] ⋅ 1 over 4
Step 3: $136.49 − $3.0625 = $133.4275
In which step did Mariah first make an error? Explain, using words, how Mariah can correct her error.
Answer:
1) Step 3: S = $136.49 - $3.0625 × 1/4
2) By completing the operations within the parenthesis in Step 2, before multiplying the result by 1/4
Step-by-step explanation:
1) From the given information, we have;
The amount amount Maria earns as a pet sitter = $32.75
The number of weeks Maria worked as a pet sitter = 2 weeks
The amount Mariah previously saved = $70.99
The amount Maria spent = $12.25
The amount Mariah put in her savings account = 1/4 of the remaining (balance) money
Therefore, we have;
The amount placed in Mariah's savings account, S, is given as follows;
Step 1: S = [($32.75 × 2) + $70.99 - $12.25] × 1/4
Step 2: S = [($65.5 × 2) + $70.99 - $12.25] × 1/4
Step 3: S = [($136.49) - $12.25] × 1/4
Step 4: S = $124.24 × 1/4
Step 5: S = $31.06
The amount Mariah puts in her saving's account = $31.06 and the step Mariah first makes an error is Step 3 where what she put down was as follows;
Step 3: S = $136.49 - $3.0625 × 1/4
2) She can correct the error by completing the calculation of the operation within the parenthesis in Step 2, before multiplying by the factor 1/4.
find the value of x that makes m||n
Answer:
x = 6
Step-by-step explanation:
In order for m to be parallel to n 16x - 6 would have to equal 90. We can demonstrate that using an equation.
16x - 6 = 90
Let's solve for x:
First add 6 to both sides to isolate the 16x:
16x - 6 + 6 = 90 + 6
16x = 96
Now divide both sides by 16 to isolate the x:
16x/16 = 96/16
x = 6
The value of x has to be 6 in order for m to be parallel to n.
Carolina goes to a paintball field that charges an entrance fee of \$18$18dollar sign, 18 and \$0.08$0.08dollar sign, 0, point, 08 per ball. The field has a promotion that says, "Get \$10$10dollar sign, 10 off if you spend \$75$75dollar sign, 75 or more!" Carolina wonders how many paintballs she needs to buy along with the entrance fee to get the promotion.
Let BBB represent the number of paintballs that Carolina buys.
Answer:
18 + 0.08B ≥ 75
Step-by-step explanation:
18 + 0.08 ≥ 75subtract 18 0.08B ≥ 57divide by 0.08 B ≥ 712.5Activity Warren's tape measure is marked in increments of 16 inch, not in decimal numbers. To measure the tiles, he needs to know the side lengths to to incħ. In this activity, you will convert decimal values to fractional values and then calculate the area of the tiles. the nearest Question 1 Part A The length of tile A is about 2.23607inches, which mark on the tape measure is closest to 2.23607inches? Remember, the tape measure is marked in sixteenths of an inch.
Answer:
the fourth mark after 2 inches
Step-by-step explanation:
each tile measures 2.23607 inches long
That means that the mark will be 2 inches and somewhere in between the third and fourth mark. The third mark is equivalent to 0.1875 inches and the fourth mark is equivalent to 0.25 inches. The mark closest to the actual length of the tile would be the fourth mark after 2 inches.
each mark represents 1 / 16 = 0.0625 inches, if we divide 0.23607 by 0.0625 = 3.69072 marks which we can round to 4 marks
The difference between the record high and low temperatures in Charlotte, NC, is 109℉. The record low temperature was −5℉. What was the record high temperature?
Answer:
[see below]
Step-by-step explanation:
The difference between the record high and low temperatures in Charlotte is 109℉. We are given the record low temperature of -5℉.
[tex]h - 5 = 109[/tex]
Let 'h' be the high temperature.
[tex]h-5=109\\\\h-5+5=109+5\\\\\boxed{h=114}[/tex]
Hope this helps.
If The difference between the record high and low temperatures in Charlotte, NC, is 109℉. The record low temperature was −5℉.Then 104 ℉ was the record high temperature.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
The difference between the record high and low temperatures in Charlotte, NC, is 109℉.
The record low temperature was −5℉.
We need to find record high temperature
H-(-5)=109
H+5=109
H=109-5
H=104
Hence the record high temperature is 104.
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The sum of two numbers is 22 and the sum of their squares is 250. Find the numbers
Answer:
9 and 13
Step-by-step explanation:
Answer:
13 and 9
Step-by-step explanation:
sum of num: 13+9 = 22
sum of square: 13²+9² = 250
169+81 = 250
y is directly proportional to x. when x = 8, y = 20. determine the value of y when x = 3
Step-by-step explanation:
y is directly proportional to x
y = kx
k represents the constant of proportionality.
when y = 20 and x = 8:
20 = 8k
Dividing both sides by 8 gives:
k = 2.5
Hence when x = 3.
y = 2.5(3)
y = 7.5 .
The value of y when x=3 is 7.5
What is proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
According to the concept of proportion, two ratios are in proportion when they are equal.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
y is directly proportional to x.
and, when x = 8, y = 20.
So, using proportion
8/20 = 3/y
8y = 60
y= 60/8
y= 7.5
Hence, the value of y is 7.5
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Five years ago, John's age was half of the age he will be in 8 years. How old is he now?
Answer:
Five years ago, John’s age was half of the age he will be in 8 years. How old is he
He is 18
Step-by-step explanation:
Solution:
=x-5 = (x+8)/2
=2[x-5 = (x+8)/2]
=2x-10 = x+8
=2x-x=10+8
=x=18
ANS: x=18
Does this graph represent a function? Why or why not?
10
10
A. No, because it is not a straight line.
B. Yes, because it passes the horizontal line test.
c. Yes because it passes the vertical line test
D. No, because it fails the vertical line test.
Answer:
No because it does no pass the vertical line test
Step-by-step explanation:
find the value of x that would prove y/z State the converse used to support your answer.
Answer:
x=6
alternative exterior angles
Step-by-step explanation:
to prove y and z parallel then the two angles must be equal:
11x-3=4x+39
11x-4x=39+3
7x=42
x=42/7
x=6
Whats the volume of 12yd 15yd and 12yds?
Answer: 2160 cubic yards
Step-by-step explanation:
12*12*15= 2160
2. (i) Find the area of a circle whose circumference
is 52.8 cm
Answer:
A≈8758.26
Step-by-step explanation:
[tex]A\pi r{2}[/tex]=π·52.8[tex]{2}[/tex]
value of pi is approximately 3.14 so
3.14*52.8[tex]{2}[/tex]
≈8758.26
Answer:
[tex]221.8 cm^{2}[/tex]
Step-by-step explanation:
[tex]C=2\pi r\\A=\pi r^{2}[/tex]
[tex]2\pi r=52.8\\r=\frac{52.8}{2\pi }[/tex]
[tex]A=\pi ((\frac{52.8}{2\pi }) ^{2} )[/tex]
[tex]A=\pi (70.61681215)[/tex]
[tex]A = 221.8 cm^{2}[/tex]
Solve the system by substitution 5x+y=-10. 4x-7y=-8
Answer:
x = -2 and y = 0
Step-by-step explanation:
5x + y = -10
4x - 7y = -8
Rearrange the first equation to equal y.
5x + y = -10
y = -10 - 5x
Replace y in the second equation with the first equation.
4x - 7y = -8
4x - 7(-10 - 5x) = -8
4x - (-70 -35x) = -8
4x + 70 + 35x = -8
Rearrange the equation to find x.
4x + 35x = -8 - 70
39x = -78
x = -2
Now that you know x, use the rearranged first equation to find y.
y = -10 - 5x
y = -10 - 5(-2)
y = -10 + 10
y = 0
Dan invests £1500 into his bank account.
He receives 2.5% per year simple interest.
How much will Dan have after 4 years?
Give your answer to the nearest penny where appropriate.
Answer:
1500+500=15500
Step-by-step explanation:
PRT/100
=1500×2.5×4/100
=150
15000+500=£15500
15500×100=1,550,000penny
Answer: 1655.72
Step-by-step explanation:
1500( 1 + 0.025)^4 = 1655.72
First think of two numbers that have a difference of 8.
Type the LARGER of these numbers below.
Given the statement "If there is a lightning storm, then we won’t go swimming,” which is the contrapositive?
If there is not a lightning storm, then we will go swimming.
If there is not a lightning storm, then we won’t go swimming.
If we go swimming, then there will not be a lightning storm.
If we don’t go swimming, then there will be a lightning storm.
What is the length of EF in the right triangle below? E 39 A D 15 F
A. 585
B. 576
C. 1296 D. 24
E. 36
F. 54
Answer:
E. 36
Step-by-step explanation:
You have to do a² + b² = c²
Plug in
15² + b² = 39²
225 + b² = 1521 (subtract 225 on both sides)
√b² = √1296 (square root on both sides)
b = 36
Hope this helps ya!
The length of the EF in the right-angle triangle is 36 units if the length of DF is 15 units the length of DE is 39 units option (E) is correct.
What is a right-angle triangle?It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
We have a right angle triangle shown in the picture.
The length of DF = 15 units
The length of DE = 39 units
As we know, Pythagoras' theorem can be defined as the square of the hypotenuse in a right-angled triangle equal to the sum of the squares of the other two sides.
Applying Pythagoras theorem:
DE² = DF² + EF²
Plug the known values:
39² = 15² + EF²
1521 = 225 + EF²
EF² = 1296
EF = √1296
EF = 36 units
Thus, the length of the EF in the right-angle triangle is 36 units if the length of DF is 15 units the length of DE is 39 units option (E) is correct.
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Write a polynomial function that has the given zeros.
-3,3, 2/3
Answer:
Step-by-step explanation:
y = (x + 3)(x - 3) ( x - 2/3)
y = (x + 3)(x - 3) (3x - 2)
The key point you want to study is that (3x - 2) does give a solution at x = 2/3. That's why I made the graph.
Solve for x
6.5-0.9n=-4.12
Answer:x=11.8
Step-by-step explanation:
fimd the measure of an interior angle polygon with 12 sides
Answer:
150 degrees
Step-by-step explanation:
This image should help. (It was hard to explain, sorry about that ._.)
Plz answer if uk theses answer
find the value of Y in the parallelogram (explain your answer)
Answer:
49 degrees.
Step-by-step explanation:
The interior angles of a triangle always add up to 180 degrees. 180-102-29=49.
Answer:
Answer : 49 degrees
Step-by-step explanation:
exp: 180 - 102- 29 = 49
use a recursive function for the geometric sequence 2, -6, 18, -54,... to represent the 9th term.
f(9) = f(8) • (-3)
f(9) = f(1) • (-3)^8
f(9) = f(1) + -3(8)
f(9) = f(8) + -3(8)
Answer:
f(9) = f(8)·(-3)
Step-by-step explanation:
A recursive function is one where each successive term is calculated using the previous term;
The clear pattern demonstrated in the sequence of terms shown is that each term is multiplied by -3 to give the next one;
Hence, the correct option is the first.
Answer:
The Answer is A. f(9) = f(8) • (−3)
Hope This Helps!
Hey can someone pls help me will give brainliest I will be very grateful thx!!!!
Answer:
17) 4 inches
18) 14 inches
19) 162 inches
20) 30 inches
Step-by-step explanation:
For the first two, you use the formula π× (radius)². Since you have the area, divide it by two then find the square root. For the second two, you just divide the by pi.
Answer:
17) D=4in
18)D=14yd
19)D=162yd
20)D=30yd
Step-by-step explanation:
17)
[tex]d = 2 \times \sqrt{4} = 4[/tex]
Think of a situation when someone would need to make a measurement with
extreme precision. Describe the setting, why the measurement must be so
precise, and some of the consequences that might occur if it were not precise.
Answer:
a
Step-by-step explanation:
aa
A coordinate plane with a line passing through (0, negative 3), (2, 0), and (4, 3).
Which equation represents the graphed function?
–3x + 2 = y
–x + 2 = y
x – 3 = y
2x – 3 = y
Answer:
I don't see the answer but it is 3/2x - 3 = y
Step-by-step explanation:
did it on edge 2020
The equation of the line representing the graphed function is y = ( 3/ 2 ) x - 3. Option E is correct.
What is an equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
The equation is formed by finding the slope using the coordinates ( 0,-3 ),( 2, 0 ) and ( 4, 3 ).
The slope is calculated as,
[tex]m = \dfrac{x_2-x_1}{y_2-y_1}[/tex]
x₁ = 0, y₁ = -3 and x₂ = 2, y₂ = 0.
The equation is given as,
y = mx + c
y = (-3/2)x - 3
Therefore, the equation of the line representing the graphed function is y = ( 3/ 2 ) x - 3.
The complete question is given below;-
A coordinate plane with a line passing through (0, negative 3), (2, 0), and (4, 3).
Which equation represents the graphed function?
–3x + 2 = y
–x + 2 = y
x – 3 = y
2x – 3 = y
y = ( 3/ 2 ) x - 3.
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Select three ratios that are equivalent to 16: 12.
Choose 3 answers:
A
8:6
(в
32:24
4:3
12:8
(E
24:16
Answer:
Step-by-step explanation:
16 : 12 = 4: 3
The answer is B
Anwser:
Step by step explanation: 8:6
32:24
there are 32 radios , 8 of them are out of order. what percent of radios are out of order ?
Answer:
25%
Step-by-step explanation:
8÷32
=0.25 x 100
=25%
Answer:
25%Step-by-step explanation:
[tex]\dfrac{8}{32}\cdot 100\%=\dfrac14\cdot 100\%=25\%[/tex]
PLEASE HELP ME THIS IS MOST OF MY GRADE. I PUT 100 POINTS. SERIOUS ANSWERS ONLY. I WILL GIVE BRAINLIEST
Answer:
Step-by-step explanation:
hehe good luck loser T^T
Answer:
1. Cheese burger, French fries (regular), Ice cream (regular), any of the beverages.
2. Fried Chicken, Macaroni soup, Mango pie, any of the beverages.
3. Cheese burger, French fries (regular), Ice cream (regular), any of the beverages, because, there are going to be 40 guests and that are a lot of people to feed so I would rather spend more money than on some random people who come to my 2 year old son.
4. PhP 222.2 repeated
Step-by-step explanation:
Help ill give brainlist