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Related Questions
write the equation for a parabola with a focus at (6,-4)(6,−4)left parenthesis, 6, comma, minus, 4, right parenthesis and a directrix at y
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The equation of the parabola is (x - 6)² = 6(y + 5.5).
Given that, a focus at (6,-4) and a directrix at y= -7.
We need to find the equation for a parabola.
What are focus and directrix?Parabolas are commonly known as the graphs of quadratic functions. They can also be viewed as the set of all points whose distance from a certain point (the focus) is equal to their distance from a certain line (the directrix).
The standard form of the equation of the parabola is (x - h)² = 4p(y - k), where
The vertex of the parabola is (h , k)
The focus is (h, k + p)
The directrix is at y = k - p
∵ The focus of the parabola is at (6, -4)
The coordinates of the focus are (h, k + p)
∴ h = 6
∴ k + p = -4 ⇒ (1)
∵ The directrix of the parabola is at y = -7
The directrix is at y = k - p
∴ k - p = -7 ⇒ (2)
Solve the system of equations to find k and p
Add equations (1) and (2) to eliminate p
∴ 2k = -11
Divide both sides
∴ k = -5.5
Substitute the value of k in equation (1) to find p
∵ -5.5 + p = -4
Add 5.5. to both sides
∴ p = 1.5
∵ The form of the equation is (x - h)² = 4p(y - k)
Substitute the values of h, k, and p in the form
∴ (x - 6)² = 4(1.5)(y - -5.5)
∴ (x - 6)² = 6(y + 5.5)
Therefore, the equation of the parabola is (x - 6)² = 6(y + 5.5).
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Your question is incomplete, probably the complete question/missing part is:
Write the equation for a parabola with a focus at (6,-4) and a directrix at y= -7
solve (x-3)(x+8)+(2x-x^2)
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The required solution of the given expression is 7x-24.
What is expression?
An expression is a set of terms combined using the operations +, – , x or ÷. An expression is a number, a variable, or a combination of numbers and variables and operation symbols. An expression is in simplest form when no terms can be combined.
Given:
The given expression is
[tex](x-3)(x+8)+(2x-x^{2} )[/tex]
According to given question we have
By the expansion theorem we have
The expression is
[tex](x-3)(x+8)+(2x-x^2)\\\\=x^{2} +8x-3x-24+2x-x^{2} \\\\=7x-24[/tex]
Therefore, the required solution of the given expression is 7x-24.
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Please help with problem 19
Algebra 1
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The expression for r is n(4t-v) and the expression for the width is (P-2l)/2
Subject of formulaThis is a way of representing a variable with another variable.
Given the expression below:
r/n + t = 4v
Making r the subject
r/n = 4v - t
r =. n(4t-v)
Hence the expression for r is n(4t-v)
For the expression
P = 2l + 2w
P - 2l = 2w
2w = P - 2l
w = (P-2l)/2
Hence the expression for the width is (P-2l)/2
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find the area of the polygon with the given points A (-5,-2) B (4,-2) C (4, -7) D (-5, -7)
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Step by step
It’s a rectangle!
9 units long (x axis) by 5 units tall (y axis)
= 45 units squared
HELP HELO
HELPPPPPP ASAP
On average, Leah's car gets 31.4 miles on every gallon of gasoline. If she fills up her tank for $2.18 per gallon, how much will it cost her to drive
358 miles?
Answers
Answer:
Step-by-step explanation:
Car drive 31.4 miles/gallon
for 358 miles, Leah needs 358/31.4 =~ 11.40 gallons
since it cost $2.18 / gallon, it will cost Leah 2.18 * 11.4 = $24.85
write equation in the standard form then identify the terms and the values of a,b and c
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7. Which statements about the values of 7.055
and 70.55 are true? Select all that apply.
7.055 is 10 of 70.55.
7.055 is 100 of 70.55.
70.55 is 10 times 7.055.
70.55 is 100 times 7.055.
7.055 is 10 times 70.55.
Answers
The statement which is true to the values of 7.055 and 70.55 are true is:
70.55 is 10 times 7.055. is true.
Given, the values are 7.055 and 70.55
statement A.
7.055 is 10 of 70.55
= 70.55×1/10
= 705.5
⇒ 705.5 ≠ 7.055
Statement B.
7.055 is 100 of 70.55.
= 70.55×1/100
= 0.7055
⇒ 0.7055 ≠ 7.055
Statement C.
70.55 is 10 times 7.055.
= 10 × 7.055
= 70.55
⇒ 70.55 = 70.55
hence true.
Statement D.
70.55 is 100 times 7.055.
= 100 × 7.055
= 705.5
⇒ 705.5 ≠ 70.55
Statement E.
7.055 is 10 times 70.55.
= 10 × 70.55.
= 705.5
⇒ 705.5 ≠ 70.55
hence the correct option is 70.55 is 10 times 7.055.
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Joel is buying packs of baseball cards to add to his collection. He wants to have at least 65 total. He already has 15 and each pack has 5 cards, c, in it. How many packs will Joel need to buy in order to have at least 65 total cards?
Answers
Answer:
10 cards
Step-by-step explanation:
In order to find how many packs Joel needs to buy we need Make an equation
Equation = 5c + 15 = 65
where,
c = cards5c+15=65
Step 1: Subtract 15 from both sides.
5c+15−15=65−15
5c=50
Step 2: Divide both sides by 5.
5c/5 = 50/5
c=10
Therefore, Joel need to buy total of 10 cards in order to have at least 65 total cards
In a food court there are people eating hamburgers, burritos & pizza. P(h) = 0. 38 and P(b) = 0. 31. If there are 35 people eating pizza, what is the total number of people in the food court?
Answer should be rounded to the nearest WHOLE NUMBER
Answers
The total number of people in the food court eating pizza, burritos, and hamburgers is 113 (Approximate) or (Whole number)
People eating hamburger P(h) =0.38
People eating burritos P(b) = 0.31
Number of people eating pizza = 35
Let's suppose the total number of people is 1
So,
By adding the total number of people eating hamburgers and burritos
= 0.38+0.31
= 0.69
The ratio of the total number of people eating pizza = 1.00 - 0.69
= 0.31
So total number of people eating pizza = 0.31 = 35
By solving :
1 = 35 / 0.31
= (35*100)/31
= 3500/31
= 112.9 (we have to write it down in the nearest whole number)
Here we writing the approximate value of 112.9 = 113 (Approximate)
Hence, the total number of people in the food court in the nearest whole number is 113
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Use the diagram shown to answer the question. What
are the sine and cosine values of a 60° angle?
Answers
Answer: sin(60°)= [tex]\frac{\sqrt{3}} 2[/tex] and cos(60°)=[tex]\frac{1} 2[/tex]
Step-by-step explanation:
sine means opposite/hypothenus (SOH)
opposite=[tex]\frac{\sqrt{3}} 2[/tex] and hypothenus is 1
sin(60°) = [tex]\frac{\sqrt{3}} 2[/tex] ÷ [tex]\frac{1} 1[/tex]
= [tex]\frac{\sqrt{3}} 2[/tex] × [tex]\frac{1} 1[/tex]
= [tex]\frac{\sqrt{3}} 2[/tex]
cosine means adjacent/hypothenus (CAH)
adjacent= [tex]\frac{1} 2[/tex] and hypothenus is 1
cos(60°) = [tex]\frac{1} 2\\[/tex] ÷ [tex]\frac{1} 1[/tex]
= [tex]\frac{1} 2[/tex] × [tex]\frac{1} 1[/tex]
= [tex]\frac{1} 2[/tex]
If m∠j=91 m∠l=16 and m∠k=73 list the sides of ∆JLK in order from smallest to largest
Answers
Answer:
ikj
Step-by-step explanation:
In a triangle:
The shortest side is opposite the smallest angle.The longest side is opposite the biggest angle.When labeling angles and sides of triangles, it is convention to label the side opposite an angle with the same letter but in lower case.
Therefore in ∆JLK:
Side j is opposite angle J.Side l is opposite angle L.Side k is opposite angle K.As 16 < 73 < 91
⇒ m∠I < m∠K < m∠J
As the angles of ∆JLK in order from smallest to largest are IKJ, then the sides of ∆JLK in order from smallest to largest are ikj.
Pls help me quickly!
Answers
Answer:
Step-by-step explanation:
answer number 3
is the answer
set up the equation relating the new ratio of broth to solution to the new percentage of broth to solution. 25/60
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The new percentage of broth to solution 25/60 is 41.67
Broth, also known as bouillon is a savory liquid made of water in which meat, fish or vegetables have been simmered for a short period of time .It can be eaten alone, but it is most commonly used to prepare other dishes, such as soups.
Commercially prepared liquid broths are available, typically chicken, beef, fish, and vegetable varieties. Dehydrated broth in the form of bouillon cubes were commercialized beginning in the early 20th century.
Broths have been used as a nutrition source for the sick in Great Britain since at least the early 1700s, such as for dysentery patients
Let,
60 represents the 100% of the broth to solution
25 represents the x percentage of the broth to solution
Now,
Solving for the 25 which represents the x percentage of the broth to solution.
25/100 = x/100*
25/60 = x/100*x
25(100) = 60x
x = 2500/60
x = 41.67
Therefore,
25 represents the 41.67 percentage of the broth to solution.
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Answer:
a) 25/60=x/100
Step-by-step explanation:
in a bowl containing 10 marbles, 5 are blue and 5 are pink. if 2 marbles are picked randomly, what is the probability that the 2 marbles will not both be pink?
Answers
Answer:from least to greatest:
1) g (x)
2) f (x)
3) h (x)
Step-by-step explanation:
Answer:
For f (x):
f (x) = (x + 3) ^ 2 - 2
For x = -1
f (-1) = (-1 + 3) ^ 2 - 2
f (-1) = (2) ^ 2 - 2
f (-1) = 4 - 2
f (-1) = 2
For x = 3
f (3) = (3 + 3) ^ 2 - 2
f (3) = (6) ^ 2 - 2
f (3) = 36 - 2
f (3) = 34
AVR = ((34) - (2)) / ((3) - (- 1))
AVR = 8
For g (x):
linear graph with and intercept of negative 3 over 2 and x intercept of 3
y = mx + b
b = -3/2
For me we have:
0 = m (3) - 3/2
3m = 3/2
m = 1/2
The function g (x) is:
g (x) = (1/2) x - 3/2
For x = -1
g (-1) = (1/2) (- 1) - 3/2
g (-1) = -1/2 - 3/2
g (-1) = -4/2
g (-1) = -2
For x = 3
g (3) = (1/2) (3) - 3/2
g (3) = 3/2 - 3/2
g (3) = 0
AVR = ((0) - (- 2)) / ((3) - (- 1))
AVR = 1/2
For h (x):
Using the table we have:
AVR = ((62) - (14)) / ((3) - (- 1))
AVR = 12
Step-by-step explanation:
A librarian's salary was $25000 in 2000 and $30500 in 2006. the librarians alary follow a linear growth pattern. What will the salary be in 2025
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y=47,916.666 dollar after 25 years
librarian salary =25000 dollar in 2000
librarian salary=30500 dollar in 2006
in 6 years increment is 30500 - 25000= 5500dollar
in one year increment is 5500/6= 916.666
m= 916.666 each year
b= 25000
y=mx+b
y=916.666*25+25000 given x=25
y=47,916.666 dollar after 25 years
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What is x if f(x) = -2
Answers
in that function x would be -2
mav is older than justin. Their ages are consecutive integers find mavs age if the product of their age is 42
Answers
Answer:
7
Step-by-step explanation:
hope this works :)
consecutive numbers means 2 numbers next to eachother like 8 and 9 or 3 and 4
product means basically the result of numbers multiplying together, e.g. the product of 8×9 = 72
so if you use trial and error you will find 6 × 7 = 42 and since mav is older she must be 7 years old
Answer:
mav is 7
Step-by-step explanation:
let justin's age be n then mav is n + 1 and the product is
n(n + 1) = 42
n² + n = 42 ( subtract 42 from both sides )
n² + n - 42 = 0 ← in standard form
(n + 7)(n - 6) = 0 ← in factored form
equate both factors to zero and solve for n
n + 7 = 0 ⇒ n = - 7
n - 6 = 0 ⇒ n = 6
since n > 0 then n = 6
mav is n + 1 = 6 + 1 = 7
How much weeks would I need to save up to get to $1000 if I get 35 one week, then 45 the next week (Every week for chores I get 35 and 45 every other week)
Example: week 1: +35
Week 2: + 45
Week 3: +35
Week 4: + 45
Answers
Answer:
12.857 aa 35 +12.222 as 25
Answer:
26 weeks (6 months)
Step-by-step explanation:
$35x + $45y = $1000
I don't know how to show the work but it would take 26 weeks to reach $1,040. That's exactly 6 months, so half a year.
how do i solve -8 - -4 as an integer problem??
will give 30 points + brain
Answers
Answer:
-8 - (-4) = - 8 + 4
Because negative times a negative is positive
How to convert 7/18 into a decimal number using long division
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The conversion of 7/18 into a decimal number using long division would be 7/18 = 0.39
In this question, we have been given a fraction.
We need to convert given fraction into a decimal number using long division.
Given fraction: 7/ 18
Consider the long division of 18 ÷ 7
0.388
_________
18 ) 7
- 0
__________
70
- 54
__________
160
- 144
__________
160
- 144
___________
16...
This means, the 7/18 = 0.3888...
If we round the number 0.3888... to two decimal places then it would be, 0.39
Therefore, the conversion of 7/18 into a decimal number using long division would be 7/18 = 0.39
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Evaluate.
Quickly please!
Answers
Answer:
819,200
Step-by-step explanation:
First start by raising all the numbers to the power indicated:
5^4 = 625
8^5 = 32768
2^9 = 512
5^2 = 25
Then divide the numerators by the denominators:
625 / 8 = 78.125
32768 / 64 = 512
512 / 25 = 20.48
Finally, multiply all the numbers together
78.125 * 512 * 20.48 = 819200
Divide. 5/6 ÷ −2/3
−5/4
negative fraction 5 over 4
−5/9
, negative fraction 5 over 9,
5/9
5 over 9
5/4
5 over 9
Answers
Answer:
[tex] \frac{ - 5}{4} [/tex]
Step-by-step explanation:
[tex] \frac{5}{6} \div \frac{ - 2}{3} [/tex]
When dividing two fractions, we turn the second fraction upside-down and multiply two expressions instead.
[tex] \frac{5}{6} \times \frac{ - 3}{2} = \frac{ - 15}{12} [/tex]
Now simplify the fraction by dividing it with biggest common divisor which is 3 in this case.
[tex] \frac{ - 5}{4} [/tex]
is the final result.
The sum of the squares of two consecutive integers is 25 find the integers
Answers
Explanation:
For this problem, we know that we need two consecutive integers and the sum of the squares is equivalent to 25.
So what is the square root of 25?
5
So with this, we know that our two numbers need to be less than 5, but greater than -5.
Consider the following squares:
(1)^2 = 1
(2)^2 = 4
(3)^2 = 9
(4)^2 = 16
Which of the following sums to 25?
9 + 16 = 25
So one pair of numbers is 3 and 4.
Consider that we have the set of integers. Well, the square values of the negative integers are as follows:
(-1)^2 = 1
(-2)^2 = 4
(-3)^2 = 9
(-4)^2 = 16
Notice, the sum of the squares of the consecutive integers -4 and -3 also equals 25.
Hence another pair is -4 and -3.
So there are two pairs that satisfy the stated query.
3 and 4
-4 and -3
Cheers.
After watching baking shows on T.V., Latrell signs up for a cake-decorating class. To practice
his new skills, he decorates a batch of cupcakes with sugar flowers. Latrell puts 4 sugar
flowers on each cupcake. In all, Latrell puts 32 sugar flowers on the cupcakes.
Which equation can you use to find the number of cupcakes c Latrell decorates?
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Please help me!!! In calculus
Answers
Answer::
:i
Step-by-step explanation:
.
the following are like terms and can be combined together through addition: 5x and 3y question 2 options: true false brainly
Answers
It is false that 5x and 3y are like terms. They can not be combined together through addition.
Like terms are those who encompass the same variables raised to the identical power. The most effective difference is within the numerical coefficients. only we are able to integrate like terms in an expression. To make algebraic formulation simpler to work with, we integrate like phrases to shorten and simplify them.to combine like phrases, upload the coefficients while retaining the variables consistent.We integrate like terms to form one term.in contrast to terms are algebraic words that don't have the equal coefficients and can't be raised to the identical strength.An algebraic expression with unlike phrases is 5x + 3y as it consists of wonderful variables, x and y, and they're not raised to the same power.To learn more about like terms, visit :
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What is the scale factor from the drawing to the actual airplane
the scale factor is _
Answers
Answer: 2
Step-by-step explanation: I just did this lesson
A scale factor is a ratio between the scale of the original object in an actual sense and the prototype figure of the same object.
If the height of the actual airplane is 20m and the in the scale drawing the height is 10m.
The scale factor of the airplane is 200.
What is a scale factor?A scale factor is a ratio between the scale of the original object in an actual sense and the prototype figure of the same object.
We have
The height of the plane in scale drawing:
= 10 cm
The height of the plane in an actual airplane.
= 20 m
The scale factor of the height of the airplane:
= 20m / 10 cm
[ 1 m = 100 cm ]
= (20 x 100) cm / 10 cm
= 200
Thus,
The scale factor of the airplane is 200.
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Determine the values of x in the equation x2 = 64.
x = ±32
x = 32
x = ±8
x = −8
Answers
Answer:
32 or +-8 depending on question
Step-by-step explanation:
If question is 2x = 64, then x= 32
If question is x^2 = 64, then x= +-8
Reorganize os termos
2x=64
Divida ambos os membros
Solução
x=32
HELP I LITTERALLY DO NOT UNDERSTAND
Answers
Answer: what are the options tho?
Step-by-step explanation:
25 points plus brainliest
Answers
Answer:
x = -7
Let the first integer be x.
Given the next two integers are consecutive, it would be: x+1, x+2
The problem states: "4 more than the smaller number plus twice the 3rd number is 7 less than the 2nd number."
Translating English to Algebra, you'll get:
(x + 4) + 2(x + 2) + 7 = x + 1
x + 4 + 2x + 4 + 7 = x + 1
3x + 15 = x + 1
2x = -14
x = -7
That would be the third option.