Answer:
(2 (y - 2 x^2 + 5))
Step-by-step explanation:
Simplify the following:
2 y - x^2 - 3 x^2 + 10
Grouping like terms, 2 y - x^2 - 3 x^2 + 10 = 2 y + (-x^2 - 3 x^2) + 10:
2 y + (-x^2 - 3 x^2) + 10
-x^2 - 3 x^2 = -4 x^2:
2 y + -4 x^2 + 10
Factor 2 out of 2 y - 4 x^2 + 10:
Answer: (2 (y - 2 x^2 + 5))
Answer:
(2 (y - 2 x^2 + 5))
parallel to 3y – 2x = – 2, passes through (3, –3)
y = 2/3x -6
Conditions for Lines to be parallel
If two straight lines are cut by a transversal, the pair of alternate angles are equal, then two straight lines are parallel to each other. the pair of interior angles on the same side of traversals is supplementary, then the two straight lines are parallel.
Given line
3y – 2x = – 2
passes through (3, –3)
The slope-intercept form is
y =mx+b,
where m is the slope and
b is the y-intercept.
y = mx+b
Divide each term in
3y – 2x = – 2 by -2 and simplify.
-3/2y +x =1
Reorder terms.
y = -(2/3)(x+1)
Using the slope-intercept form, the slope is
2/3.m=2/3
To find an equation that is parallel, the slopes must be equal. Find the parallel line using the point-slope formula.
Use the slope
2/3 and a given point (3, –3)
to substitute for
x1 and y1
in the point-slope form
y−y1=m(x−x1)
which is derived from the slope equation
m=(y2−y1)x2−x1.
y−(-3)=2/3⋅(x−(3))
Simplify the equation and keep it in point-slope form.
y+4=2/3⋅(x-3)
y = 2/3x -6
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What are the square roots of 8,100?
40 POINTS!
Simplify 3x * 1/x^-4 * x^-3
3x
3x2
3
3x−2
Answer:
[tex]\sf {3x}^{2} [/tex]
Step-by-step explanation:
[tex] \rightarrow \sf 3x(\frac{1}{{x}^{-4}}) {x}^{-3} [/tex]
[tex] \rightarrow \sf \frac{ {3x}^{5} }{ {x}^{3} } [/tex]
[tex] \rightarrow \sf {3x}^{2} [/tex]
A, B and C are the vertices of a triangle.
A has coordinates (4, 6)
B has coordinates (2,-2)
C has coordinates (-2,-4)
D is the midpoint of AB.
E is the midpoint of AC.
Prove that DE is parallel to BC.
According to the solving it is proved that DE is parallel to BC.
What do we mean by coordinates?Coordinates are numerical lengths or angles that uniquely identify points on two-dimensional (2D) or three-dimensional (3D) surfaces ( 3D ). Mathematicians, physicists, and engineers employ a variety of coordinate systems.
What does a parallel mean?In-parallel refers to something that is the same distance as well as the direction away from something else. Two lines of individuals standing straight across from each other is an example of in-parallel. noun. 1. In-parallel means traveling the same direction and distance as something else.
According to the given data:To obtain the coordinates of each midpoint, use the midpoint formula.
(x, y) = (½ (x₁ + x₂), ½(y₁ + y₂))
Coordinates of D:
(x, y) = (½ (4 + 2), ½(6 + -2))
(x, y) = (3, 2)
Coordinates of E:
(x, y) = (½ (4 + -2), ½(6 + -4))
(x, y) = (1, 1)
Slope of DE:
m = Δy / Δx
m = (2 − 1) / (3 − 1)
m = 1/2
Slope of BC:
m = Δy / Δx
m = (-2 − -4) / (2 − -2)
m = 1/2
Therefore, DE is parallel to BC.
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At a used book sale, 5 books cost $15.
1. What is the cost per book?
2. At this rate, how many books can you buy for 21$
Answer:
the cost per book is 3$. you can buy 7 books for 21$.
Step-by-step explanation:
15 divided by 5 is 3, so they cost 3 each. 21 divided by 3 is 7.
A pharmacist wishes to mix a solution that is 8% Minoxidil. She has on hand 100 of a 2% solution and wishes to add some 10% solution to obtain 8% how much 10% solution should she add
Answer:
300 units
Step-by-step explanation:
What is the price, in dollars, of an iPhone that has been marked down 18
percent from its original price of 1200 dollars?
Answer:
If 100%=1200 what about 100%-18%.
You get 984$
Each day Donna and Mary toss a coin to see who buys the other person coffee ($1.73 a cup). One tosses and the other calls the outcome. If the person who calls the outcome is correct, the other buys the coffee; otherwise the caller pays. Assume that an honest coin is used, that Mary tosses the coin, and that Donna calls the outcome. Find Mary's expected payback. Is this a fair game?
Mary's expected payback based on the information illustrated is 0.865. This isn't a fair game.
How to calculate the probability?Based on the information, the chances of Donna winning will be 1/2.
It was also stated that each day Donna and Mary toss a coin to see who buys the other person coffee ($1.73 a cup).
Therefore, Mary's expected payback will be:
= (0 × 1/2) + (1.73 × 1/2)
= 0 + 0.865
= 0.865.
Therefore, Mary's expected payback based on the information illustrated is 0.865. This isn't a fair game.
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under her cellphone plan, makayla pays a flat cost of $47.50 per month and $5 per gigabyte. She wants to keep her bill at $70.50 per month. How many gigabytes of data can she use while staying within her budget?
Answer:
15 Gigabites
Step-by-step explanation:
The closest you can can get to is $70, so by adding five in the times tables it gets you up to 15 x 5 which is 70.
What are the steps in order to solve this?
Since m(n(x)) = n(m(x)) = x, then m(x) and n(x) are inverse functions
What is the inverse of a function?The inverse of a function is a function that can reverse into another function.
If we have function f and g, and f f(x) = y, then g is the inverse of f if and only if g(y) = x
Also, if f is a function f⁻¹ is the inverse of x and ff⁻¹(x) = f⁻¹f(x) = x
How to show that the composite fucntions are inverses?Given the functions m(x) = x³ - 5 and n(x) = ∛(x + 5)
If m(x) and n(x) are inverse, then m(n(x)) = n(m(x)) = x
So, we proceed as follows
m(x) = x³ - 5
m(n(x)) = (∛(x + 5))³ - 5
m(n(x)) = x + 5 - 5
m(n(x)) = x + 0
m(n(x)) = x
Also,
n(x) = ∛(x + 5)
n(m(x)) = ∛(x³ - 5 + 5)
n(m(x)) = ∛(x³ - 0)
n(m(x)) = ∛(x³)
n(m(x)) = x
Since m(n(x)) = n(m(x)) = x, then m(x) and n(x) are inverse functions
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Evaluate 4(b + 1)² if b = 4.
Answer:
68
Step-by-step explanation:
4(4 + 1)²
4(16 + 1)
64 + 4
68
chapter 8
2.Find the volume of each figure. Round your answers to the nearest hundredth, if necessary.
The volume of the given figure is 267.95 mi³.
What is the volume?The given object is a sphere. A sphere is a three-dimensional object that has all its surface points at equal distances from the center. A sphere is round in shape.
The volume of an object is the amount of space in the three-dimensional object. The radius of a sphere is a straight line from the circumference of the sphere to the center of the sphere.
Volume of a sphere = 4/3 × π × r³
Where:
π = pi = 22/7
r = radius = 4
4/3 x 22/7 x 4³ = 267.94667 mi³
267.95 mi³
To round off to the nearest hundredth, if the thousandth digit is equal to 5 or greater than 5, add 1 to the hundredth digit and change all the digits after the hundredth digit to 0.
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. Write down the first five terms of the AP with first term 7 and common difference 7.
The arithmetic sequence is 7,14,21,28,35,48
In an arithmetic progression (AP) sequence of numbers, the difference between any two consecutive integers is always the same. It is also known as an arithmetic sequence.
There are two definitions for an arithmetic sequence. Each term in an arithmetic sequence is created by adding a predetermined number (positive, negative, or zero) to its preceding term. It is a "series where the differences between every two following terms are the same."
Given,
first term, a = 7
common difference d = 7
n = 2
a+(n-1)d = 7+( 2 - 1 )7
= 7 + 7
= 14
n = 3
a+(n-1)d = 7+(3-1) 7
= 7+14
= 21
n = 4
a+(n-1)d = 7+(4-1) 7
= 7+ (3)7
= 28
n = 5
a+(n-1)d = 7+( 5-1 ) 7
= 7+ (4)7
= 35
n = 6
a+(n-1)d = 7+( 6-1 ) 7
= 7+ (5)7
= 42
the five terms are 7,14,21,28,35,48.
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Jordan bought 4 shirts
that each cost the same
amount and I pair of
jeans
that cost $40.
The items he bought cost
a total of $180 before
tax. What was the cost of
each shirt in an equation.
Answer:
Each shirt costs $35.00
Step-by-step explanation:
1 jeans = $40
4 shirts =$180 - $40 = $140.00
1 shirt = $140 ÷ 4 = $35.00
Is 4x-6=y linear or nonlinear
There are 713 identical plastic chips number one through 713 in a box what is the probability of reaching into the box and randomly drawing the chip number to 564 express your answer as a simplified fraction or decimal rounded to four decimal places
The probability of randomly drawing the chip number 564 is 1 / 713 or 0.0014
What is the probability?
Probability is used to determine the odds that a random event would happen. The odds that the event would happen is a distribution that lies between 0 and 1.
If it is certain that the event would occur, the probability value would be 1. If it is certain that the event would not occur, the probability value would be 0. If it is equally likely that the event would happen or not happen, the probability value would be 0.5.
The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.
The probability of randomly drawing the chip number 564 = number of chips numbered 564 / total number of chips
1 / 713 = 0.0014
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The following angles are supplementary to each other.
mzA= (3x + 21)° and mzB = (6x - 21)°
Determine x.
A10
B20
C36
D60
Answer: 20
Step-by-step explanation: I can help with am explanation if you dm me:)
Please help asap Geometry
Answer:
x=4
Step-by-step explanation:
22x-3+35+60=180
add like numbers.
22x+92=180
180-92=88
22x=88
88 divided by 22
x=4
check work=
22(4)-3+35+60=180
If y varies directly with x and y=36 when x=6, find the value of y when x=4.
6
12
24
-18
If y varies directly with x and y=36 when x=6, the value of y is 24 when x=4.
What is direct variation?
The mathematical relationship between two variables that can be expressed by an equation in which one variable is equal to a constant times the other. It is a linear function defined by an equation of the form
y = kx when x is not equal to zero.
Given:
If y varies directly with x and y=36 when x=6
According to given question we have
we can write direct variation equation as
y= k*x
where k is constant
y = 36 when x=6,
36 =k(6)
k=6
So, by putting the value of x=4 we get,
y =kx
y=6*4
y=24
Therefore, If y varies directly with x and y=36 when x=6, the value of y is 24 when x=4.
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Y+2=1/3(x-8) what is the slope
The slope of the equation of the line described is equal to 1/3.
What is a slope?A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.
How to calculate the slope of a line?Mathematically, the slope of any straight line can be calculated by using this formula;
[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
Mathematically, the standard form of the equation of a straight line is given by;
y = mx + c
Where:
x and y are the points.m is the slope.c is the intercept.y + 2 = 1/3(x-8)
y + 2 = 1/3x - 8/3
y = 1/3x - 8/3 - 2
y = 1/3x - 2/3
Therefore, the slope of the equation of the line described is equal to 1/3.
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What is the solution set for the following equations:
y = 5x -7 and y = 2x + 5
(3,12)
(4, 13)
(-7,5)
(2,5)
please help!
Answer:
(4,13)
Step-by-step explanation:
Set the 2 equations equal to each other and solve for x.
5x - 7 = 2x + 5 Subtract 2x from both sides
3x - 7 = 5 Add 7 to both sides
3x = 12 Divide both sides by 3
x = 4
Now plug 4 back into either of the original 2 equations to find y.
y = 5x -7
y= 5(4) -7
y = 20 -7
y= 13
To prepare one bowl of salad, 3 3/4 pounds of vegetables are required. How many pounds of vegetables are required to prepare one-third bowl of salad?
Applying the knowledge of fractions, the number of pounds of vegetables required to prepare 1/3 bowl of salad is: 1¼ pounds.
How to Solve Fractions?In solving this problem, we would apply our knowledge of fractions as explained below.
One bowl of salad needs 3¾ pounds of vegetables
Let the number of pounds if vegetables needed for ⅓ bowl be represented as x. Therefore, we would have the following proportion:
1 bowl = 15/4 pounds of vegetables [i.e. 3¾]
⅓ bowl = x
Thus:
1/15/4 = ⅓/x
1/1 × 4/15 = 1/3 × 1/x
4/15 = 1/3x
Cross multiply
4(3x) = 1(15)
12x = 15
Divide both sides by 12
12x/12 = 15/12
x = 15/12
x = 5/4
x = 1¼ pounds
Therefore, applying the knowledge of fractions, the number of pounds of vegetables required to prepare 1/3 bowl of salad is: 1¼ pounds.
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Given g(a) = 5x - 3, find g(-2)
Answer:
-13
Step-by-step explanation:
Plug in -2 to x:
5(-2) - 3
Multiply 5x-2:
-10 - 3
Because two negatives make a positive, add -10 and -3:
-13
Rubin has 6 rolls of pennies containing 50 coins each, 5 rolls of nickels
containing 40 coins each, 4 rolls of dimes containing 50 coins each, and 3
rolls of quarters containing 40 coins each. How much money does he have?
A. $63.00
B. $17.50
C. $68.40
D. $8.20
Answer:
$63
Step-by-step explanation:
Penny = $0,01
Nickel = $0.05
Dime = $0.1
Quarter= $0.25
Number of pennies = 6*50 = 300
Number of nickels = 5*40= 200
Number of dimes = 4*50= 200
Number of quarters = 3*40 = 120
The total amount of money:
300*0.01+ 200*0.05 + 200*0.1 + 120*0.25 = $63
A statue is 6 feet tall and weighs about 145 pounds. A second model statue is 4 feet tall.
Assume that the two statues have similar shape.
a) What is the linear scale factor for going from first to second statue?
b) How much does the second statue weigh?
The linear scale factor for going from first to second statue will be 2/3 and the weight of the second statue will be 96 2/3 pounds.
How to illustrate the information?It should be noted that the statue is 6 feet tall and weighs about 145 pounds and second model statue is 4 feet tall.
Therefore, the linear scale factor for going from first to second statue will be:
= 4/6
= 2/3
Therefore, the weight of the second statue will be:
= 2/3 × 145
= 96 2/3 pounds.
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subtracting linear expressions 30 points
Answer:
1) -2a + 2
2) x + 1
3) -5x + 5
Step-by-step explanation(1):
[tex]\left(7a+4\right)-\left(9a+2\right)\\=7a+4-\left(9a+2\right)\\=7a+4-9a-2\\=7a-9a+4-2\\=-2a+4-2\\=-2a+2[/tex]
Step-by-step explanation(2):
[tex]\left(2x+5\right)-\left(x+4\right)\\=2x+5-\left(x+4\right)\\=2x+5-x-4\\=2x-x+5-4\\=x+5-4\\=x+1[/tex]
Step-by-step explanation(3):
[tex]\left(2x+4\right)-\left(7x-1\right)\\=2x+4-\left(7x-1\right)\\=2x+4-7x+1\\=2x-7x+4+1\\=-5x+4+1\\=-5x+5[/tex]
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Out of 340 racers who started the marathon, 311 completed the race, 25 gave up, and 4 were disqualified. What percentage did not complete the marathon?
replace the ? with a number to make it correct 9-5=6-?
PLEASE HELP!
When purchasing a new music Plan you are given two pay options
With Plan A, you can pay 25 cents per minute. This can be represented by the equation
c = 0.25m
With Plan B, you can pay 19 cents per minute plus a flat fee of $6.00. This can be represented by the equation c = 0.19m + 6.00
Complete the following steps to determine how many minutes you would need to use for
Plan B to be less expensive than Plan A
Write an inequality that represents Plan B < Plan A
Inequality: ____ <_____
Solve the inequality and use your answer to complete the following sentence:
Plan B is less expensive than Plan A when you use at least ______
Plan B is less expensive than Plan A when you use at least 25
What is an inequality?Inequalities can simply be defined as mathematical expressions in which both or two sides of the expression are not equal.
From the information given, we have that;
Plan A = c = 0. 25mPlan B = c = 0. 19m + 6. 00Now, let's write the inequality that represents Plan B < Plan A
If Plan B < Plan A
Then,
0. 19m + 6. 00 < 0. 25m
Let's simply the inequality
6. 00 < 0. 25m - 0. 19m
0. 06m < 6. 00
Make 'm' the subject
m < 6. 00/ 0. 06
m < 100
Thus, Plan B is less expensive than Plan A when you use at least 25
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Kaleigh's aunt drives for Wheels Around Town, an app-based ride sharing service, to make extra money for her family. The table below shows the relationship between miles driven and money earned. Is the relationship between miles and money earned proportional
Based on the money earned by Kaleigh's aunt from Wheels Around Town, the relationship between miles and money earned is proportional.
How to find a proportional relationship?In a proportional relationship, the rate of increase or decrease in x should be equivalent to the rate of increase or decrease in y. This rate should be constant through the entire distribution.
The equation of the line should take the form:
y = mx
There should be no y-intercept.
The slope is:
= (48 - 72) / (120 - 180)
= -24 / - 60
= 2/5
Every value of y has to be 2/5 of x.
= 160 x 2/5 = 64
= 200 x 2/5 = 80
The relationship is therefore proportional.
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