The Distance between line ℓ and the point j (-5,-1) is 8units.
The distance between a point PP and a line LL is the shortest distance between PP and LL; it is the minimum length required to move from point PP to a point on LL. In fact, this path of minimum length can be shown to be a line segment perpendicular to LL. The distance d can then be defined as the length of the line segment that has PP as an endpoint and is perpendicular to LL.
We know that the distance d between a point (x1,y1) and a line having equation in form of ax+by+c=0 can be expressed as,
[tex]d = \frac{|ax1+by1+c|}{\sqrt{(a^2+b^2)} }[/tex]
So, we have given that equation of line
y = 7
y-7=0
Point j = (-5,-1)
So, Distance between point j and line = d
d = [tex]\frac{|0(-5)+1(-1)-7|}{\sqrt{(0^2+1^2)} }[/tex]
d = [tex]\frac{8}{\sqrt{1} }[/tex]
d = 8 units
Therefore, The point j is at a distance of 8 units from the line ℓ.
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A group of friends wants to go to the amusement park. They have no more than $170 to spend on parking and admission. Parking is $7.25, and tickets cost $23.25 per person, including tax. Write and solve an inequality which can be used to determine
x, the number of people who can go to the amusement park.
Answer:
7 People is they all go in the same car and pay only for 1 parking space.
Step-by-step explanation:
23.25x + 7.25 ≤ 170 Subtract 7.25 from both sides of the equation
23.25x ≤ 170 Divide both sides by 23.25
x ≤ 7
At Silver Gym, membership is $20 per month, and personal training sessions are $45 each. At Fit Factor, membership is $90 per month, and personal training sessions are $35 each. In one month, how many personal training sessions would Sarah have to buy to make the total cost at the two gyms equal?
Sarah would have to buy _____ personal training sessions to make the total cost at the two gyms equal.
Answer: 7
Step-by-step explanation:
Let the number of sessions be x. Then,
[tex]20+45x=90+35x\\\\10x=70\\\\x=7[/tex]
-2 3/7 - 1 2/3 show ur work!please
Answer:
-4 2/21
Step-by-step explanation:
-2 3/7 - 1 2/3
Change to improper fraction
-2 3/7 = -17/7
- 1 2/3 =-5/3
-17/7-5/3
L.C.M=21
-51-35/21
= -86/21
= -4 2/21
Hope it helps..
Please mark brainliest
hey! i will give a lot of pts for the answers to these!!
Answer:X squared =4/9 is c
X to the third power is a
X squared =81/46 is b or d
X to the third power is d or b
Find the area of the circle. Use 3.14 for T. d = 4 m A = [?] m² A = πr² Enter
Step-by-step explanation: I hope this helps.
Answer:
1) Mrs. Martins deposits $2,650 into a savings account. The account earns 6%
interest per year, and the interest is not compounded. How much amount will
be in the account after 9 years?
The amount in the savings account of Mrs. Martins after 9 years will be $4081.
According to the question,
We have the following details:
The amount deposited in the savings account or the principal amount = $2,650
Interest per year = 6%
Time = 9 years
(It is given that the interest is not compounded.)
Now, using the formula of simple interest, we will first find the total interest after 9 years,
Simple Interest (S.I.) = (Principal * Rate * Time)/100
S.I. = (2650*6*9)/100
S.I. = (2650*54)/100
S.I. = 143100/100
S..I. = $ 1,431
Now, the total amount in the savings account would be the sum of the principal amount and the total interest.
So, we have:
Total amount = Principal + S.I.
Total amount = $ (2,650+1,431)
Total amount = $ 4,081
Hence, the total amount in Mrs. Martins's savings account is $ 4,081.
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3x^2 +16x−10=6x−2 algebra 2
Answer:
x= 2/3 or x= −4
Explanation:
3x2+16x−10=6x−2
Step 1: Subtract 6x-2 from both sides.
3x2+16x−10−(6x−2)=6x−2−(6x−2)
3x2+10x−8=0
Step 2: Factor left side of equation.
(3x−2)(x+4)=0
Step 3: Set factors equal to 0.
3x−2=0 or x+4=0
x=2/3 or x= −4
Question 6 (Yes/No Worth 1 points) (02.01 LC) Is the following relation a function? x y 1 −2 1 −3 2 1 3 −2 Yes No
This is not a function, we know this because the input x = 1 is mapped into two different outputs.
Is the following relation a function?A relation maps elements from one set, the domain, into elements from another set, the range. A relation is only a function if each element of the domain is mapped into only one element of the range.
In this case, we have the relation:
x: 1, -2, 1, -3
y: 2, 1, 3, -2
The input x = 1 is mapped into two different values, y =2 and y = 3.
Thus, the relation is not a function.
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Select all diagrams that have expressions in corresponding angles.
Answer:
1, 2, 8
Step-by-step explanation:
Corresponding angles lie on the same side of the parallel lines and on the same side of the transversal.
1, 2, and 8 are corresponding angles.
Given m n, find the value of x.
m
(5X-11)°
(6x-7)°
Answer:
x = 18
Step-by-step explanation:
the angles pictured are supplementary angles.
supplementary angles are angles whose sum equals 180°
ex: <1 + <2 = 180°
[tex]5x - 11 + 6x - 7 = 180[/tex]
[tex]11x - 18 = 180[/tex]
[tex]11x = 198\\x = 18[/tex]
Answer:
[tex]\boxed{\sf{x=18}}[/tex]
Step-by-step explanation:
To find the value of x, you have to use the supplementary angles which is equal to 180°.
Supplementary angles = 180°
5x-11+6x-7=180
Combine like terms.
[tex]\sf{5x+6x-11-7=180}[/tex]
5x+6x=11x
[tex]\sf{11x-11-7=180}[/tex]
Subtract the numbers from left to right.
-11-7=-18
[tex]\sf{11x-18=180}[/tex]
You have to add by 18 from both sides.
11x-18+18=180+18
Solve.
Add the numbers from left to right.
180+18=198
11x=198
Divide by 11 from both sides.
11x/11=198/11
Solve.
198/11=18
[tex]\rightarrow \boxed{\sf{x=18}}[/tex]
Therefore, the final answer is x=18.
The cost of a mobile set is Rs 18000. If Mrs Sharma purchased it with 13% VAT,how much did she pay for it.
To purchase a mobile set with the cost of Rs 18000 and VAT 13% , Mrs Sharma needs to pay Rs 20,340.
As given in the question,
Cost of the mobile set Mrs Sharma purchase = Rs 18000
VAT added on purchasing a mobile set is equal to 13%
Amount of VAT on mobile set is equal to
= 13% of 18000
= (13/100) × 18000
= 13 ×180
= Rs 2340
Mrs Sharma needs to pay amount to purchase a mobile set
=18000 + 2340
= Rs 20,340
Therefore, to purchase a mobile set with the cost of Rs 18000 and VAT 13% , Mrs Sharma needs to pay Rs 20,340.
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SHOW YOUR WORK FOR BRAINLIEST
Find the length of the segment indicated. Round your answer to the nearest tenth if necessary.
The answer is 16.4
Answer:
x = 16.4
Step-by-step explanation:
From the diagram, we can see that the radius of the circle is 19.4 as the line labelled 19.4 goes from the centre to the edge of the circle.
Therefore the length of the line marked in green is also 19.4 units, as it is also a radius of the circle.
Now we can simply use the Pythagorean Theorem to calculate the value of [tex]x[/tex]:
[tex]19.4^2 = x^2 + 10.3^2[/tex]
⇒ [tex]x^2 = 19.4^2 - 10.3^2[/tex]
⇒ [tex]x = \sqrt{19.4^2 - 10.3^2}[/tex]
⇒ [tex]x = \bf 16.4[/tex]
Therefore the length of the indicated segment is 16.4 units.
Consider this function f(x) = x -4
The inverse of the given function is f-1(x)= x²+4.
What is inverse of a function?A function that "undoes" another function in mathematics is known as an inverse. In other words, if f(x) produces y, then y entered into the inverse of f produces x. An invertible function is one that has an inverse, and the inverse is represented by the symbol f-1.
To calculate the inverse of a function:
Consider f(x)=y
And interchange the variables.
So given f(x)= √x-4 becomes
y=√x-4 ⇒ x=√y-4
Now on squaring both sides we get,
x²= y-4
⇒ y = x²+4
Replace y by f-1(x)
So the equation becomes,
f-1(x) = x²+4
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Martin earned $8.75 an hour plus another $18 in tips. Lawrence earned $9.25 an hour and spent $2 on a soda. Lawrence had more money than Martin. Let x represent the number of hours worked.
If Martin earned $8.75 an hour plus another $18 in tip and Lawrence earned $9.25 an hour and spent $2 on a soda, then the inequality represents the situation is 8.75x+18 < 9.25x-2
The payment of Martin per hour = $8.75
The addition tip he got = $18
The payment of Lawrence per hour = $9.25
The amount he spend for soda = $2
x represents the number of hours worked
Lawrence had more money than Martin
Then the inequality will be
8.75x+18 < 9.25x-2
Hence, if Martin earned $8.75 an hour plus another $18 in tip and Lawrence earned $9.25 an hour and spent $2 on a soda, then the inequality represents the situation is 8.75x+18 < 9.25x-2
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Solve the inequality. Graph the solution. 3x≤−54
[tex]x\leq -18[/tex]
Graph Displayed Below
Hope this helps!
The solution to the given inequality [tex]3x \leq -54[/tex] is [tex]x \leq \frac{-54}{3}[/tex] .
Inequality is a fine statement that compares two values, showing if one is lower than, lesser than, or simply not equal to another value. Inequalities are frequently used to represent connections between amounts, similar to the relationship between the height and weight of a person, or the relationship between the speed and time of an object in stir.
We first divide the inequality [tex]3x \leq -54[/tex] by 3 on both sides to obtain:
[tex]x \leq \frac{-54}{3}[/tex] .
Then, we plot the line [tex]x = \frac{-54}{3}[/tex] on the graph. The region left to the line thus obtained is the solution of the given question.
Thus, the line [tex]x \leq \frac{-54}{3}[/tex] is plotted in the graph.
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You earn $100 per month and want to save 10% in a savings account.
How much will your monthly contribution be? (Do not include the $ sign in your
response) PLEASE HELPP
Math easy will give brainly and points
A large container is being filled with water at the rate of 2 3/4 per minute
Answer:
5 minutes and 20 seconds
Step-by-step explanation:
basically your equation is: (rate of filling container) x (time to fill container)
- (minus)
(rate of leaking from container) x (time to fill container)
=
(the size of the container in gallons)
--------------------
step 1 - so t = the time in minutes to fill14 gallon container
step 2 - convert 2 3/4 to quarters so:
2 • 4 = 8 and it’s in quarters so 8/4 then
8/4 + remaining 3/4 = 11/4
step 3 - so then you fill in the equation:(11/4)•t - (1/8)•t = 14
step 4 - multiply both sides of the equation by 8:
(11/4) = 2.75 • 8 = 22
(1/8) = 0.125 • 8 = 114 • 8 = 112
so the equation is:
22t - t = 112
step 5 - divide both sides of the equation by 22:
22t / 22 = t
112 / 22 = 5.333
so t = 5.333
step 6 - convert
so 5.333 has a repeating decimal of 0.3 which is 1/3. so to convert that to seconds, take 1/3 of 60:
60 / 3 = 20
so it takes 5 minutes and 20 seconds to fill the 14 gallon container
hope this helps :)
Need help on finding the domain and range
The domain and the range of the graph are x >= 1 and -∝ < y < ∝, respectively
What is the domain of a function?The domain of the function is the set of input values of the graph
What is the range of a function?The range of a function is the set of output values of the graph.
How to determine the domain and the range?The domain
On the graph of the function, we can see that:
The x values start from 1 and it extends indefinitely to the right
This means that the domain is x >= 1
The range
On the graph of the function, we can see that:
The y values extend indefinitely on all sides of the coordinate plane
This means that the range is -∝ < y < ∝
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Find all horizontal asymptotes of the following function.
f(x) =3x² - 48/2x+8
The given function f(x) =3x² - 48/2x+8 has no Horizontal asymptote.
A horizontal asymptote may be defined as a horizontal line at which the graph of the function will appear to meet but will not actually meet. It is a tool to determine the end behavior of the function. We are given the function f(x) = 3x² - 48/2x+8. Now to find horizontal asymptote of this function we first find lim ₓ→∞ f(x) that is
lim ₓ→∞ (3x² - 48)/(2x + 8)
lim ₓ→∞ 3/2(x - 4) = ∞
Now, we calculate lim ₓ→-∞ f(x) that is
lim ₓ→-∞ (3x² - 48)/(2x + 8)
lim ₓ→-∞ 3/2(x - 4) = -∞
Since, both the limits are different therefore function does not have any horizontal asymptote.
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solve the inequlaity 2(4x+1)<3(2x-3)
The solution to given inequality 2(4x + 1) < 3(2x - 3) is x < -11/2
In this question, we have been given an inequality 2(4x + 1) < 3(2x - 3)
We need to solve given inequality.
2(4x + 1) < 3(2x - 3) ..............(Given inequality)
8x + 2 < 6x - 9 .............(simplify both sides of the inequality)
8x + 2 - 6x < 6x - 9 - 6x ............(subtract 6x from both the sides)
2x + 2 < -9
2x + 2 - 2 < -9 - 2 ............(subtract 2 from each side)
2x < -11
2x/2 < -11/2 ................(Divide each side by 2)
x < -11/2
Therefore, the solution to given inequality 2(4x + 1) < 3(2x - 3) is x < -11/2
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Subtract 8 1/6-4 5/6. Simplify the answer and write as a mixed number.
In the following equation, what would be the most logical first step when solving for z.
Answer:
Multiply 5/2 to both sides
Step-by-step explanation:
Doing so 'cancels' out the coefficient of (z+1) on the left-hand side.
Find AC (why do questions have to be at least 20 characters LOL)
Answer:
Step-by-step explanation:
21
Answer: 21
Step-by-step explanation: To solve for AC, you will need to add segments AB and BC together. So, 9+12=21
If the area of a square shaped rug is 81 in², what is the
measurement
of ONE SIDE of the rug?
Answer: 9 inches
Step-by-step explanation:
We know that the area of a square can be solved with the following formula when s is the length of one side. We will plug in our known values and solve:
a = s²
(81) = s²
[tex]\sqrt{81}[/tex] = s
9 in = s
One side of the rug is equal to 9 inches.
ANSWER PLEASE IM GONNA DIE
PLEASE HELP, I will give brainliest! due soon thank you so much and please give explanation
question 1,2 and 3 thank you
Answer:
8.368, 156.8, 2.52$
Step-by-step explanation:
0.8% of 1,046 is 8.368
to get this first find 80% of 8.368 so you can get 836.8 and then you move it back 2 places to get 8.368
160% of 98 will be 156.8
first split it up into 2 problems for it to be easier
100% of 98
and 60% of 98
100% of 98 = 98
60% of 98 = 9.8*6 = 58.8
98+58.8 = 156.8
For the 3rd one it will be 2.52$ srry gtg soon so can't explain
EASY POINTS WILL GIVE BRAINLIST TO BEST ANSWER
Determine if the sequence is arithmetic. If it is, find the common difference, the 21st term, the explicit rule, the recursive rule, and the three terms in the sequence after the last one given.
-2, 8, 18, 28
Answer:
The sequence is arithmetic.
-2 , 8 , 18 , 28 , 38 , 48 , 58 , 68 , 78 , . . .
21st term value is 198.
Step-by-step explanation:
Is -√225 rational or irrational?
Answer:
Rational
Step-by-step explanation:
- √225 = -15
State the degree and end behavior of f(x)=8x³+2x⁴-5x²+9. Explain or show your reasoning.
Examining the given polynomial we arrive at the various parameters
the polynomial is degree 4The end behavior is x → ∞ f(x) → ∞, x → - ∞ f(x) → ∞How to find the degree of a polynomialThe degree refers to the maximum power to which the equation is raised. We can see that the term 2x⁴ bears the maximum power and it is 4 hence the equation is degree 4
How to find the end behavior of a polynomialThe end behavior refers to how the equation relates at the extremes. The extremes a big positive value and big negative value.
Big positive value say x = 1000
f(x)=8x³+2x⁴-5x²+9
f(1000) = 2.008x10^12
Big negative value say x = -1000
f(x)=8x³+2x⁴-5x²+9
f(-1000) = 1.992x10^12
comparing the two values shows that the value is increasing in both positive and negative, hence we write the end behavior as x → ∞ f(x) → ∞, x → - ∞ f(x) → ∞
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The parallelogram had an area of 20 square inches
Answer:
b = 4.472 and h = 4.472
Step-by-step explanation:
Area of a parallelogram is A = bh
Find b and h where the area is 20 square inches
So, to find the equal value of both b and h take square root of 20
➟ √20
➟ 4.472
So, b = 4.472 and h = 4.472
Checking
A = 4.472 × 4.472
A = 19.9 ≈ 20