Answer:
Step-by-step explanation:
Find the Parabola with Focus (7,0) and Directrix x=-7 (7,0) x=-7. (7,0) ( 7 , 0 ) x=−7 x = - 7. Since the directrix is horizontal, use the equation of a parabola that opens left or right. ... Find the distance from the focus to the vertex. ... Substitute in the known values for the variables into the equation (y−k)2=4p(x−h) ( y - k ) 2 = 4 p ...
Using the distance formula, the equation of a parabola with directrix y=7 and focus (0,−7) is [tex]x^2 = -28y[/tex]
The focus = (0, -7)
The directrix: y = 7
The distance formula is given as:
[tex](x - a)^2+(y-b)^2= r^2[/tex]
From the focus (0, -7)
a = 0, b = -7
r = y - 7
Substitute a = 0, b = -7 and r = y - 7 into the equation above:
[tex](x - 0)^2 + (y +7)^2 = (y - 7)^2\\\\x^2 + y^2+14y + 49= y^2-14y+49\\\\x^2 = y^2-y^2-14y-14y+49-49\\\\x^2 = -28y[/tex]
Using the distance formula, the equation of a parabola with directrix y=7 and focus (0,−7) is [tex]x^2 = -28y[/tex]
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Of two consecutive integers, four times the smaller is 30 more than three times the larger. Find both integers,
Answer:
33 and 34
Step-by-step explanation:
Let the integers be x and x+1 respectively.
4x = 3(x+1) + 30
x = 33
therefore, the integers are 33 and 34
This is a question on forming and solving algebraic equations. If you wish to venture further into it/understand this topic better, you may want to follow my Instagram account (learntionary), where I post some of my own notes on certain topics and also some tips that may be useful to you :)
A license plate is made of three letters and three numbers. How many different license plates are possible? (Recall there are 26 letters in the alphabet and 10 single digit numbers 0-9).
Using the permutations formula, it is found that: 11,232,000 different license plates are possible
----------------------------------------------------
The order in which the letters and the numbers appear is important(123ABC is a different plate than A123BC), which means that the permutations formula is used to solve this question.
----------------------------------------------------
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
----------------------------------------------------
In this question:
3 letters from a set of 26.3 digits from a set of 10.Thus:
[tex]T = P_{26,3}P_{10,3} = \frac{26!}{23!}\times\frac{10!}{7!} = 11,232,000[/tex]
11,232,000 different license plates are possible
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A chef locates a pre-made tuna salad that is nearly identical to the one she makes from scratch in her sandwich shop. To make it from scratch, an $8.25/hour employee needs 20 minutes to prepare the tuna salad. The ingredients cost $12.18 and yield 10 four-ounce servings. The chef can purchase the pre-made tuna salad at $26.99 for a 5# tub. Calculate the cost per portion for the scratch-made and the premade versions. If cost were the only factor, should the chef make or buy this product?
Correct question
A chef locates a pre-made tuna salad that is nearly identical to the one she makes from scratch in her sandwich shop. To make it from scratch, an $8.25/hour employee needs 20 minutes to prepare the tuna salad. The ingredients cost $12.18 and yield 10 four-ounce servings. The chef can purchase the pre-made tuna salad at $26.99 for a 5 pound tub. Calculate the cost per portion for the scratch-made and the premade versions. If cost were the only factor, should the chef make or buy this product?
Answer:
If cost were the only factor, the chef should not make version of the tuna salad from scratch because it is expensive that the premade version
Step-by-step explanation:
For tuna: Made from scratch
The ingredients cost $12.18 and yield 10 four-ounce servings.
10 servings = $12.18
1 serving = x
10 × x = 1 × $12.18
x = $12.18/10
x = $1.218
Hence, 1 four ounce serving cost $1.218
The chef can purchase the pre-made tuna salad at $26.99 for a 5# tub.
5 pound tub salad = $26.99
1 pound tub of tuna salad = x
5 × x = 1 × $26.99
x = $26.99/5
x = $5.398 per pound
Converting to ounces
0.0625 pound = 1 ounce
5 pound = x
x = 5/0.0625
x = 80 ounces
80 ounces of tuna salad = $5.398
4 ounces of tuna salad = x
80 × x = 4 × $5.398
x = 4 x 5.398/80
x = $0.2699
Hence, 1 4 ounce pre made tuna salad cost = $0.2699
Hence, the cost per portion for the scratch-made is $1.218 per 4 ounces servings and the premade versions is $0.2698 per 4 ounce servings
If cost were the only factor, the chef should not make version of the tuna salad from scratch because it is expensive that the premade version
question in the picture!!
looking for the answer of 3) and 4) !!
<3
Answer:
3(percent): 75% 3(decimal): .75
4(percent):60% 4(fraction): 6/10 or 3/5, depending on wether or not you choose to simplify.
if a triangular sail has a vertical height of 83 ft and horizantal length of 40 ft, what is the area of the sail?
Answer:
A = 1660 [tex]ft^{2}[/tex]
Step-by-step explanation:
Area of the sail or a triangle is base times height
A = [tex]\frac{1}{2}[/tex](b x h)
Base is 40 ft (horizontal length)
Height is 83 ft (vertical height)
A = [tex]\frac{1}{2}[/tex](b x h)
A = [tex]\frac{1}{2}[/tex](40 x 83) = [tex]\frac{1}{2}[/tex](3320) = 1660 [tex]ft^{2}[/tex]
What operation is being done to the variable in the equation -5m = -40?
It's being multiplied by -5.
It's being divided by -5.
It's being multiplied by -40.
It's being divided by -40.
Answer:
it is A
Step-by-step explanation:
Which of the following is equivalent to 8^(1/3)?
Option 1
Option 2
Option 3
Option 4
(look at photo for answers)
the answer is option 2....
Answer:
Option 2
Step-by-step explanation:
when the power appears as a fraction, take the root of the number based on the denominator of the fraction when numerator is equal to 1
This is my sister's work, please help. will give brainliest. DON'T GIVE STUPID ANSWERS, I WILL REPORT
A wire 45 meters long is cut into two pieces, One piece is 5 meters longer than the other. What is the length of the two pieces? Create an equation and solve .
Given:
A wire 45 meters long is cut into two pieces
One piece is 5 meters longer than the other.
To find:
The length of the two pieces.
Solution:
Let length of one piece be x.
One piece is 5 meters longer than the other. So,
Length of another piece = x+5
Total length of wire is 45. So,
[tex]x+(x+5)=45[/tex]
[tex]2x+5=45[/tex]
Subtract 5 from both sides.
[tex]2x=45-5[/tex]
[tex]2x=40[/tex]
Divide both sides by 2.
[tex]x=\dfrac{40}{2}[/tex]
[tex]x=20[/tex]
Now,
Length of one piece = 20 meters
Length of another piece = 20 + 5
= 25 meters
Therefore, the length of two pieces are 20 and 25 meters.
Please help me with this
Answer:
The answer is s = 1.
Step-by-step explanation:
Opposite sides of a parallelogram are equal so,
3s + 19 = s + 21
3s - s = 21 - 19
2s = 2
s = 1
next,
s + 21 =? 3s + 19
1 + 21 equal to (?) 3(1) + 19
22 = 22
so the answer is correct
Answer:
is the answer you add 19 + 21 give you 40
40
Rachel has $1,800 to spend on renting a venue for a party. The available locations to rent for the party cost between $660 and $2,500. This cost includes a base cost, plus a set-up fee that is one-fifteenth of the base cost. The total cost can be modeled by the function shown below, where c represents the base cost of renting a venue.
f(c)=c+1/5c
State the domain of values that represents the base cost for the venues Rachel can afford.
Answer:
618.75 to 1687.50
Step-by-step explanation:
an equation of the line with a slope of 2/3 and y-intercept of −8.
Answer:
y = 2/3x - 8
Step-by-step explanation:
Use the slope intercept form, y = mx + b, where m is the slope and b is the y intercept
Plug in the slope and y intercept:
y = mx + b
y = 2/3x - 8
So, y = 2/3x - 8 is the equation of the line.
Esteban stands on a dock 1.25 yd above the water. A fish swims below Esteban at -4.61 yd from the surface of the water. How many yards apart are Esteban and the fish?
Answer:
3.36 yards
Step-by-step explanation:
✓From the question, Esteban stands on a dock 1.25 yd above the water which means the distance of Esteban above the water is 1.25 yd
✓A fish swims below Esteban at -4.61 yd from the surface of the water which means the distance of the fish away from the surface is 4.61 yd in opposite direction of Esteban
NOTE: The negative sign only signify direction of the fish which is opposite of Esteban
✓then the distance in yards apart of Esteban and the fish is
=4.61-1.25
=3.36 yards
Enter an equation in standard form to model the linear situation. A bathtub that holds 23 gallons of water contains 13 gallons of water. You begin filling it, and after 5 minutes, the tub is full.
Answer:
2x - y = -13
Step-by-step explanation:
The function g(x) is a transfomation of the function f(x). If g(x) = 2(x – 3) 2
f(x) = 2(x + 4) then what translation describes the change from f (x) to g(x)?
2
1
Answer:
881 (-6x)
Step-by-step explanation:
please need this asap!! will give brainliest and a thanks to fast answers :)
Answer:
15 days
Step-by-step explanation:
Answer:
27 days
Step-by-step explanation:
The total bill of a meal at a restaurant is 25x – 115. Five
friends agree to split the cost of the meal equally. What
could you do to find the amount that each person must
pay? Explain.
Answer: Divide the whole equation by 5
Step-by-step explanation: You could divide the whole equation by 5 since there are 5 friends. Once you do that you end with the equation 5x - 23, which is what each friend would pay.
Answer:
Sample response: Factor the GCF of five out of the total bill. Divide both terms of the expression by 5. The result is 5x – 23, which is the expression that can be used to find the amount each person pays.
Step-by-step explanation: (you may want to reword it)
Juan rented a chainsaw from Steve's Tools. It cost $19 plus $6 per hour. If Juan paid
$49, then he rented the chainsaw for how many hours?
Answer:
2 hours
Step-by-step explanation:
if you do 19x2 then that is 38 and then you have to add 6 dollars per hour so that would be 2 hours
. When 12 is subtracted from 4 times a number, the result is 24. Which equation can be used to find the number?
Answer:
12 + 24 divided by 4
Step-by-step explanation:
12 + 24 is 36, so divide that by 4, that gives you the answer, which is 9
The equation that represents the situation is 12 - 4x = 24. Then the solution of the equation will be negative 3.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
When 12 is subtracted from 4 times a number, the result is 24.
Let the number be 'x'. Then the equation is given as,
12 - 4x = 24
Simplify the equation, then we have
12 - 4x = 24
- 4x = 24 - 12
- 4x = 12
4x = - 12
x = - 12 / 4
x = - 3
The equation that represents the situation is 12 - 4x = 24. Then the solution of the equation will be negative 3.
More about the solution of the equation link is given below.
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Steph makes and sells birthday cakes. Each cake costs £54 to make.
She makes a profit of 15% on each cake.
What is the selling price of Steph's birthday cakes?
(2 marks)
£=
The selling price of Steph's birthday cakes such that the profit is 15% will be £62.1.
What is the percentage?The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
The percentage is also called the indicating hundredths. Thus, 2% is two-hundredth, which means 2%=2/100=0.02.
As per the given,
Cost per cake = £54
15% of £54 = 0.15 x 54 = £8.1
Selling price = £54 + £8.1 = £62.1
Hence "The selling price of Steph's birthday cakes such that the profit is 15% will be £62.1".
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Which equation below would be best solved by using the addition property of equally?
1-23-45
231-45
f. 23-45
1-23 - 45
Answer:
D
Step-by-step explanation:
Edge 2020 :)
Answer:
the answer is D
Step-by-step explanation:
Can someone please explain to me how I got this wrong? The other options in the image are the ones under the questions and I'm rlly confused. Could anyone fully explain it please?
Answer: [tex]-\frac{p}{8}[/tex]
This is the fraction -p/8
====================================================
Explanation:
When we divide by -16, we're really multiplying by -1/16. Fractions and division are very similar ideas.
So we can say,
[tex]2p \div -16 = 2p \times \frac{-1}{16}\\\\2p \div -16 = \frac{2p}{1} \times \frac{-1}{16}\\\\2p \div -16 = \frac{2p(-1)}{1*16}\\\\2p \div -16 = \frac{-2p}{16}\\\\2p \div -16 = \frac{-2p}{2*8}\\\\2p \div -16 = -\frac{p}{8}\\\\[/tex]
The second to last step has a pair of '2's divide and cancel out.
-------------
Another way to think of it is to consider
[tex]\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}[/tex]
The flip from division to multiplication has us apply the reciprocal of the second fraction. In this problem, we have a = 2p, b = 1, c = -16 and d = 1. The steps will be very similar if not identical to what is shown above.
2(-6m - 3) =6(5m - 1) please show work what is m ?
Answer: m=0
Step-by-step explanation: simplify each individual expression first. The left side of the equation is equal to -12m-6, and the right side is equal to 30m-6. Then together, it equals to -12m-6=30m-6. The -6 cancel each other out. M=0
Does anyone know how to do it?
Answer:
x = -7º
x+59 = 52º
x+51 = 44º
Step-by-step explanation:
84 + (x+59) + (x+51) = 180º
180 - 84 = 96
x+59 + x+51 = 96
2x + 110 = 96
2x = -14
x = -7
proof:
-7+59 = 52º
-7+51 = 44º
the sum of angles in a triangle must be 180º so:
84 + 52 + 44 = 180
Answer:
∠A = 44°Step-by-step explanation:
84 + x + 59 + x + 51 = 180
2x = 180 - 84 - 59 - 51
x = -14/2
x = -7
∠A = x + 51
∠A = -7 + 51
∠A = 44°
f(x) = 2x + 1
h(x) = one-halfx – one-half
h(x) = one-halfx + one-half
h(x) = one-halfx – 2
h(x) = one-halfx + 2
January 30,2019 was the coldest day in minieapolis-St. Paul in over 20 years. The lowest tempeauture recorded that day was -28F. The warmest temperature was 15 higher
Answer:
The warmest temperature was -13FStep-by-step explanation:
We are expected to compute the warmest temperature recorded at Minneapolis
Step one:
We are told that on January 30th of 2019 was the coldest day at Minneapolis
hence the temperature reading= -28F------this is like 28 points away from 0 on the number line
Step two:
We are given that the warmest temperature recorded is 15F higher.
since the -ve sign represent cold or snowy weather, the warm temperature
is gotten by adding 15F to the negative temperature
=-28+15
= -13F
The warmest temperature was -13F
What is the value of f(3) ?
Answer:
f(3)=-60
Step-by-step explanation:
f(3)=5*(3^2)-7(4*3 + 3)
f(3)=5*9 - 7*15
f(3)=45-105
f(3)=-60
Answer: -60
Step-by-step explanation:
f(3) means that you replace the input function of x with 3; So, your equation would look something like this:
5(3)^2 - 7(4(3) +3)
= 5(9) - 7(15)
= 45 - 105
= -60
Fihding the Selling Price for a Given Profit
Soccer ball profit
y = -6x2 + 100x – 180
Suppose the store wants to earn a daily profit of
$150 from the sale of soccer balls. To earn this
profit, what price should the store charge for each
soccer ball? Explain how to solve this problem.
DONE
) Intro
6 of 8
Answer:
2.05 and 14.61
Step-by-step explanation:
On Edg
PLEASE HELP
PART A
Diego deposited $10,000 for 4 years at a rate 6% simple interest. find the amount of interest Diego earned after 4 years.
PART B
If Diego closes his account after the 4 years, how much money will he have total?
Total Amount=
Answer:
Part A=2,400 Part B=12,400
Step-by-step explanation:
The amount of interest Diego earned after 4 years is 2400 and the money Diego have after 4 years is 12400.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
Diego deposited $10,000 for 4 years at a rate 6% simple interest
We need to find the interest earned by Diego after 4 years.
Let us find what is 6% of 10000
Convert 6% to decimal value by dividing with 100.
6/100=0.06
Now multiply zero point zero six with 10000
0.06×10000
600
Noe for four years she earned
4×600
2400
2400 is the amount of interest Diego earned after 4 years.
Now let us find the money Diego have after 4 years.
Which is 10000+2400
12400
Hence the amount of interest Diego earned after 4 years is 2400 and the money Diego have after 4 years is 12400.
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Claire's car averages 21 miles per gallon of gas. At that rate, how far would it go on 21 gallons? *
Answer:Claire car will go 441 miles on 21 gallons
Step-by-step explanation: 21×21=441