Parallel lines have equivalent slopes, so as the slope of the given line is 1, the slope of the line we want to find is also 1.
Substituting into point-slope form and rearranging into slope-intercept form,
[tex]y-2=1(x+6)\\\\y-2=x+6\\\\\boxed{y=x+8}[/tex]
f(x)=x^3+10x^2+31x+30
The factors of the given polynomial will be ( x + 2 ), ( x + 5 ) and ( x + 3 ).
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
The given expression will be solved as:-
f(x) = x³ + 10x² + 31x + 30
f(x) = ( x³ + 7x² + 10x + 3x² + 21x + 30
f(x) = ( x² + 7x + 10 ) ( (x + 3 )
f(x) = ( x²+ 5x + 2x + 10 ) ( x + 3 )
f(x) =[ x ( x+ 5 ) +2 ( x+ 5) ] ( x + 3 )
f(x) = ( x + 5 ) ( x + 2 ) ( x + 3 )
Therefore factors of the given polynomial will be ( x + 2 ), ( x + 5 ) and ( x + 3 ).
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Multiply by this number to make the coefficient of the variable 1
Multiply by 9/25 to make the coefficient of the variable 1 the answer is 9/25.
What is a linear 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.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have a given linear equation.
After solving the linear equation we get:
[tex]\rm \dfrac{25}{9}x = 25[/tex]
To make the coefficient of the variable 1
Multiply by 9/25 on both sides.
[tex]\rm \dfrac{9}{25}\times\dfrac{25}{9}x = 25\times \dfrac{9}{25}[/tex]
x = 9
Thus, multiply by 9/25 to make the coefficient of the variable 1 the answer is 9/25.
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Answer: the answer is 9/25
Step-by-step explanation: Multiplying both sides of the equation by 9/25 isolates x
A camper lights an oil lantern at 12 noon and lets it burn continuously. Once the lantern is lit, the lantern burns oil at a constant rate each hour. At 2 p.m., the amount of oil left in
the lantern is 63 ounces. At 5 p.m., the amount of oil left in the lantern is 61 ounces.
Based on the average rate of oil burning per hour, how much oil, in ounces, was in the
lantern at 12 noon?
SHOW WORK!
Answer:
09
Step-by-step explanation:
09
Unit rate is the quantity of an amount of something at a rate of one of another quantity.
The rate at which the oil burns.
1 hour = 2/3 ounce
At 12 noon = 193/3 = 64.33 ounces
At 2 pm = 63 ounces
At 5 pm = 61 ounces
The amount of oil at 12 noon is 64.33 ounces.
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
A camper lights an oil lantern at 12 noon and lets it burn continuously. Once the lantern is lit, the lantern burns oil at a constant rate each hour.
At 2 p.m., the amount of oil left in the lantern is 63 ounces.
At 5 p.m., the amount of oil left in the lantern is 61 ounces.
This means,
Amount of oil burnt in the lantern from 2 pm to 5 pm.
= 63 ounces - 61 ounces
= 2 ounces
Now,
3 hours = 2 ounces
2 hours = 1.33 ounces
1 hour = 0.67 ounces
Now,
The number of hours from 12 noon to 2 pm.
= 2 hours
So,
The amount of oil at 12 noon.
= 63 + 4/3
= (189 + 4) / 3
= 193/3 ounces
Thus,
The amount of oil at 12 noon is 65 ounces.
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If you are given the graph of a line in an xyplane and its corresponding equation, you can be sure that the coordinates of every point on that line will satisfy the equation.
If the graph of a line in an x y plane and its corresponding equation is given then , all the coordinates of every point on that line will satisfy the equation is a true statement.
What is the equation for a straight line ?An equation of a straight line is given by
y = mx+c
where m is the slope and c is the intercept on y axis.
If the graph of a line in an x y plane and its corresponding equation is given then , all the coordinates of every point on that line will satisfy the equation .
Even for a scatter plot the line of the best fit is drawn and every point on the line will satisfy the equation.
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find the slope of the line that passes through the points (2,1) and (-7,4)
Answer:
[tex]-\frac13[/tex]
Step-by-step explanation:
Just the slope, so we can simply apply the definition, as variation in y over the variation in x
[tex]m= \frac{\Delta y}{\Delta x} = \frac{1-4}{2-(-7)} = \frac {-3}{9} = -\frac13[/tex]
Answer:
0.222
Step-by-step explanation:
Y2-Y1 ÷ X2-X1
4-2 ÷ -7-2
2÷-9
0.222
x2 +kx+12
What are two numbers that k could be so that each expression could be factored??
Answer:
K could be 7 or 8
Step-by-step explanation:
If K was to be 7, the equation would be x^2 + 7x + 12 = (x+3)(x+4)
If K was to be 8, the equation would be x^2 + 8x + 12 = (x + 2)(x + 6)
The function f(x) = x2 + 6x +7 is graphed below.
Drag the correct word and the the appropriate value to the box with each given interval to indicate whether the function is increasing or decreasing on that interval
The function f(x) = x² + 6x + 7 is increasing over the interval x > -3 and decreasing over the interval x < -3.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the function f(x) = x² + 6x + 7. This is a quadratic equation,that is of degree two.
The function f(x) = x² + 6x + 7 is increasing over the interval x > -3 and decreasing over the interval x < -3.
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d) Suppose you pick one marble from the bag at random. Find the expected value of its number.
(c) Suppose you pick 9 marbles from the bag at random with replacement. Find the probability that you pick at least one purple marble.
C) The probability that you pick at least one purple marble is 98%.
ProbabilityThe question is incomplete, since the number of marbles of each color in the bag is missing: 3 blue, 5 green, and 2 purple marbles.
Now, to answer the questions, the following calculations must be done:
C) 100 - (2/9x9) = X100 - 2 = X98 = XLearn more about probability in brainly.com/question/27656131
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Answer:C) The probability that you pick at least one purple marble is 98%.
Step-by-step explanation:
IMPORTANT, PLEASE HELP QUICKLY! 40 POINTSS
Answer the following questions given that Angles A and B are the acute
angles found in a right triangle.
1. If tan (A) = 3/4, then tan (B) equals?
2. If tan (B) = 2/7, then tan (A) equals?
3. Based on the information in #2, which angle would be bigger, A or B?
Use a diagram to help justify your answers.
Answer:
[tex]\sf 1. \quad \tan(B)=\dfrac{4}{3}[/tex]
[tex]\sf 2. \quad \tan(A)=\dfrac{7}{2}[/tex]
[tex]\sf 3. \quad \angle A[/tex]
Step-by-step explanation:
Acute angle: an angle less than 90°
Tan trigonometric ratio
[tex]\sf \tan(\theta)=\dfrac{O}{A}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleA is the side adjacent the angleQuestion 1
Refer to the first attached diagram.
If tan(A) = 3/4 then the side opposite ∠A is 3 units, and the side adjacent ∠A is 4 units.
Therefore:
[tex]\implies \sf \tan(B)=\dfrac{4}{3}[/tex]
Question 2
Refer to the second attached diagram.
If tan(B) = 2/7 then the side opposite ∠B is ,and the side adjacent ∠B is 7.
Therefore:
[tex]\implies \sf \tan(A)=\dfrac{7}{2}[/tex]
Question 3Angle A would be bigger (see second attachment).
Find the time diffrence.
If u click there will be pic (very easy im just lazy lol)
Step-by-step explanation:
2 hours and 45 minutes.
8:45am + 2 hours = 10:45am
10:45am + 45 minutes = 11:30 am
Which of the following polynomials is in standard form?
A. F(x)=-3x+6x²-1+7x
B. F(x)=7x+6x² -1-3x4
C. F(x)=-3x4 -1+6x² +7x
D. F(x)=-3x +6x² +7x-1
Answer:
d
Step-by-step explanation:
Question Content Area
If fixed costs are $281,000, the unit selling price is $33, and the unit variable costs are $21, the break-even sales (units) if fixed costs are reduced by $38,400 is
a.16,173 units
b.20,217 units
c.24,260 units
d.30,325 units
The correct answer is option b which is the break-even quantity will be 20217 units.
What is the break-even point?
The point at which the company will not have any profit and loss on the products they manufactured they only get the amount they invested in manufacturing the product is called the break-even point.
Given that:-
If fixed costs are $281,000, the unit selling price is $33, and the unit variable costs are $21, the break-even sales (units) if fixed costs are reduced by $38,400.
The formula for calculating break-even quantity will be given as:-
[tex]BEQ = \dfrac{FC}{SP-VC}[/tex]
Here,
FC = Fixed cost = $281000
SP = Selling price = $33
VC = Variable cost = $21
The fixed cost is reduced by $38400 so the fixed cost now:-
FC = $281000 - $38400
FC = $242600
[tex]BEQ = \dfrac{242600}{33-21}[/tex]
BEQ = 20217 units
Therefore the correct answer is option b which is the break-even quantity will be 20217 units.
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If Jenny walks 2 miles in 40 minutes, then Jenny will walk how far in 100
minutes if she walks at the same speed the whole time? If necessary, round
your answer to the nearest tenth of a mile.
Answer:
Five miles
Step-by-step explanation:
if 2=40 then 1=20 so 5=100
What are the possible values of xin 8x² + 4x=-1?
Answer:
hey
Step-by-step explanation:
4
Answer:
(-½,0)
Step-by-step explanation:
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You damage your car and it will cost $2,700 to repair. You have a $500 deductible. How much will the insurance company pay? A.$500 b.$2,200 c.$2,700 D.$0 e.$1,000
Answer:
After finding the money we were short with, we find that Option-b, that is, $2200 is the correct option.
Step-by-step explanation:
Given that the cost to repair the damaged car is $2700. We have $500.
Insurance company is a company that gives the payment of someone's valuable items when they are lost or get damaged. For example, home insurance, car insurance, life insurance and much more.
Here we can see that we are short with $2700 - $500 = $2200.
So, to complete the payment, insurance company will pay $2200.
Clearly, the correct option is Option-b.
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It takes to complete 200 rotations in 1 minute. How long does it take to complete 300 rotations? How many times does it rotate in half minute?
Answer:
1.5 min
100 rotations
Step-by-step explanation:
to find 300 rotations time duration use the half-minute,
to find half of a minute divide the amount in one minute (200) by 2
200/2 = 100
then mutiply the 100 times 3 to find the time
100 * 3 = 300
therefore 30 sec (100 rot.) and 3 (3 times)
30 * 3 = 90
90 seconds minus 60 (one minute) is 30
so then it is equal to 1.5 minutes aka 1 min. 30 sec.
How long does it take to complete 300 rotations? 1.5 minutes (1 min. 30 sec.)
How many times does it rotate in a half minute? 100 rotations
hope this helps:)
meijun had some money. she used 1/3 of it on a watch and 1/9 of it on a gift. the watch and the gift cost $144 altogether. how much money did she have at first?
Answer:
$324
Step-by-step explanation:
let x be the amount of money she had at first , then
[tex]\frac{1}{3}[/tex] x + [tex]\frac{1}{9}[/tex] x = 144 ( multiply through by 9 to clear the fractions )
3x + x = 1296
4x = 1296 ( divide both sides by 4 )
x = 324
she had $324 at first
3. How many more paintings,
sculptures, and photographs would
the artist need to sell to make
another $500?
answer
Step-by-step explanation:
there are only one
painting, sculpture and photograph.
i need help can someone give me answers
Answer:
Step-by-step explanation:6 type
5/25=1/5=20%
1-1/5=4/5=80%
The types of candles are 6. And the probability of a small pink candle and NOT a small pink candle will be 0.20 and 0.80, respectively
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the probability is given as,
P = (Favorable event) / (Total event)
The table is given below.
Small Medium Large Total
White 9 3 5 17
Pink 5 2 1 8
Total 14 5 6 25
The types of candles are given as,
⇒ 2 x 3
⇒ 6
The probability of a small pink candle is as,
P = 5/25
P = 0.20
The probability of NOT a small pink candle is as,
Q = 1 - P
Q = 1 - 0.20
Q = 0.80
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what is the formula for equations.
A formula is a fact or rule that uses mathematical symbols. It will usually have: an equals sign (=) two or more variables (x, y, etc) that stand in for values we don't know yet.
Example: The formula for finding the volume of a box is:
x = 2y - 7 Formula (relating x and y)
a2 + b2 = c2 Formula (relating a, b and c)
The price p in dollars that a store sets for an items is given by the equation p=c + 1/10c where c dollars is the stores cost for the items if the store sets a price of $55 for an ideal what is the cost for the item
The cost of the item whose price $ 55 is $ 50.
What is Cost Price?The cost price is the price paid by an individual to buy an item or any other commodity. Or this can also be taken as the total amount of money spent by the manufacturer to assemble a product or deliver a service.
Here, Price equation in terms of cost
P = C + C/10
P = (10C+C)/10
P = 11C/10
C = 10P /11
For P = $ 55, the cost will be
C = 10 X 55 / 11
C = 10 X 5
C = $ 50
Thus, the cost of the item whose price $ 55 is $ 50.
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The number of measles cases increased 36.5% to 193 cases this year. What was the number of cases prior to the increase? The number of measles cases increased 36.5 % to 193 cases this year . What was the number of cases prior to the increase ?
Answer:
70.445
Step-by-step explanation:
you have to subtract 36.5 by 193.
Find the slope of a line perpendicular to a line through the given points. E(5, 7), F(3, 1)
Answer: -1/3
Step-by-step explanation:
The slope of the given line is [tex]\frac{7-1}{5-3}=\frac{6}{2}=3[/tex].
Thus, since perpendicular lines have slopes that are negative reciprocals of each other, the answer is -1/3
Name the marked angle in 2 different ways.
W
T
V
U
The marked angle can be named in two different ways as: ∠HFG and ∠GFH.
How to Name an Angle?To name an angle, the letter representing the vertex would always be at the middle.
Given the angle marked in the image below, where F is the vertex, we can name the marked angle in two different ways with F at the center as:
∠HFG and ∠GFH
Thus, the two different ways to name the marked angle are:
∠HFG and ∠GFH.
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What is the probability if a penny lands on heads 30 times after being tossed 50 times?
The probability will be equal to 60%.
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
The best thing to do here is to put it into a fraction. as 30 landed heads up, 20 (50-30) must be tails.
You can then put this into a fraction, which becomes 20/50.
To turn this into a decimal, you can then divide 1 by 50
1/50= 0.02
As you've got 22 lots of this, you then need to multiply 0.02 by 20.
0.2x20= 0.40
To find the percentage, you've then got to multiply the decimal by 100.
100x0.40= 40.
Therefore, 40% of the tosses would be tails
As you've found what one percentage is, you simply need to take this number away from 100 to find the other, rather than having to go through the process again.
100-40= 60
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Randy invested $850 in a regular savings account that paid compound interest at a rate of 3.75% per year, compounded quarterly. How much
was his investment worth in three years? a.$881.88 b.$950.71 c.$100.71 d.$95.63 e. $945.63
Answer:
the answer is a.
Step-by-step explanation:
In ΔFGH, FH = 9 ft, FG = 11 ft, and m∠F = 65°. Find m∠G. Round your answer to the nearest tenth.
The value of m∠G = 48.6° .
What is a Triangle ?A triangle is a polygon with three sides , angles and vertices.
It is given that
In ΔFGH, FH = 9 ft, FG = 11 ft, and m∠F = 65°
m∠G = ?
well, using the law of cosines,
GH ² = 9² + 11² - 2(9)(11) cos65°
f = 10.88 ft
now, using the law of sines,
sinG/9 = sin65°/10.88
m∠G = 48.6°
Therefore the value of m∠G = 48.6° .
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The admission fee at a local zoo is $1.50 for children and $5.00 for adults. On a certain day, 3000 people enter the zoo and $9, 400.00 is collected. How many children and how many adults attended?
1600 children and 1400 adults attended
How to determine the number of adults?Let the children be x and adult be y.
So, we have the following equations:
x + y = 3000
1.5x + 5y = 9400
Make x the subject in x + y = 3000
x = 3000 - y
Substitute x = 3000 - y in 1.5x + 5y = 9400
1.5(3000 - y) + 5y = 9400
Expand
4500 - 1.5y + 5y = 9400
Evaluate the like terms
3.5y = 4900
Divide both sides by 3.5
y = 1400
Substitute y = 1400 in x = 3000 - y
x = 3000 - 1400
Evaluate
x = 1600
Hence, 1600 children and 1400 adults attended
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3
cky has a board that is 2 feet long. She needs to cut the board into 11 pieces of equal length. How long
ould each piece be?
0.223 feet
0.25 feet
0.5 feet
0.75 feet
ase select the best answer from the choices provided
A
В
C
D
Answer:
0.223 is the answers for the question but I got this answer 0.181
Step-by-step explanation:
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Use the Pythagorean Theorem to find the length of the leg in the triangle shown below.
The figure shows a right triangle with one leg marked 12. The hypotenuse is marked 15.
Answer:
9
Step-by-step explanation:
a^2+b^2=c^2
a^2+12^2=15^2
a^2=225-144
a=sqrt(81)
a=9
