Answer:
a) -3p +4q
b) -6x +3y
Step-by-step explanation:
Use the distributive property to eliminate parentheses. Use the properties of arithmetic to combine the numbers.
__
a)The order of operations tells you to start with the inner parentheses and work outward.
[tex]-\dfrac{1}{3}(6(p+q)-3(p-2(p-3q)))=-\dfrac{1}{3}(6(p+q)-3(p+(-2)(p) +(-2)(-3q)))\\\\=-\dfrac{1}{3}(6(p+q)-3(p-2p+6q))=-\dfrac{1}{3}(6(p+q)-3(-p+6q))\\\\=-\dfrac{1}{3}((6)(p)+(6)(q)+(-3)(-p)+(-3)(6q))=-\dfrac{1}{3}(6p+6q+3p-18q)\\\\=-\dfrac{1}{3}(9p -12q)=(-\dfrac{9p}{3})+(-\dfrac{-12q}{3})=\boxed{-3p+4q}[/tex]
__
b)Same deal for the second expression: use the distributive property and combine like terms.
[tex]y-\dfrac{2}{3}(9x-3y)=y+(-\dfrac{2\cdot9x}{3})+(-\dfrac{2(-3y)}{3})\\\\=y-6x+2y=\boxed{-6x+3y}[/tex]
30 points pls helppp
Select the equation of the line that passes through the point (2, –1) and has slope 3 in point-slope form.
(y + 1) = 3(x – 2)
(y – 1) = 3(x + 2)
(x + 2) = 3(y – 1)
(x – 2) = 3(y + 1)
Answer:
(y + 1) = 3( x +2)
Step-by-step explanation:
from equation,
y - y1 = m( x - x1)
given x1=2, y1= -1
m = 3 (slope)
substitute
y - (-1) = 3( x - 2)
ans: y+1= 3(x+2)
The tank of a car holds 10 gallons of gas.
How many liters does the tank hold? Round to the nearest tenth.
Answer:
37.9 liters
Step-by-step explanation:
Multiply the number of gallons by 3.785 to convert to liters
Multiplying by ten moves the decimal point over to the right
3.785 * 10 = 37.85
The tenths place is where the 8 is, and since 5 is [tex]\geq[/tex] (greater than or equal to) 5 that makes the 8 round up to a 9
resulting in...
10 gallons = 37.9 liters
hope this helps:)
A notebook costs £1.60, a pen costs 37p, a pencil costs 21p and a sharpener costs 86p.
Remi buys 3 pencils, 2 pens, 3 sharpeners and some notebooks.
He pays with £8 and receives 85p change.
How many notebooks did he buy?
notebooks
Answer:
2
Step-by-step explanation:
£1 = 100p
3*21p+2*37p+3*86p+x*160p (x is the number of notebooks)
63p+74p+258p+x*160p = 395p+x*160p
He paid £8 so he paid 800p
800p-395p = 405p
405p-85p = 320p
320p:160p = 2
He bought 2 notebooks
27
5
to a mixed number
a
decimal.
Answer: 5.4 and 5⅖
Step-by-step explanation:
27/5 to a mixed number 5⅖
Decimal 5.4
Can you please help me really quick I need help with this
Check the picture below.
PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
c
Step-by-step explanation:
because 3 x 3 = 9
1 x 5 = 5
simplest form will be 1 4/5
6. A rectangle with a length of 15 feet has a
diagonal that measures 17 feet. Find the
perimeter of the rectangle.
Answer:
46 feet
Step-by-step explanation:
it is a 8-15-17 Pythagorean Triple (or you can use the Pythagorean theorem)
P=8+8+15+15=46
The perimeter of the rectangle with a length of 15 feet and has a diagonal that measures 17 feet is: A. 46 feet.
What is the Perimeter of a Rectangle?To find the perimeter of the rectangle, we need to know the width of the rectangle. Let's call the width of the rectangle W.
In a rectangle, the diagonal, length, and width are related by the Pythagorean theorem:
Diagonal² = Length² + Width²
In this case, the diagonal (D) is 17 feet, and the length (L) is 15 feet. So we have:
17² = 15² + W²
289 = 225 + W²
Now, let's solve for W:
W² = 289 - 225
W² = 64
W = √64
W = 8 feet
Now that we know the width is 8 feet, we can calculate the perimeter (P) of the rectangle:
Perimeter = 2 * (Length + Width)
= 2 * (15 + 8)
= 2 * 23
Perimeter = 46 feet
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‼️⚠️⚠️‼️ HELP PLEASE WILL GIVE POINTS
Answer:
m∠ABC=42°
Step-by-step explanation:
m∠ABD=70°
⇒m∠ABD=m∠ABC+m∠CBD
⇒70°=(3x+33°)+(5x+13°)
70°=8x+46°
70°-46°=8x
24°=8x⇒x=3°
x=3°
Then,
m∠ABC=3x+33°
put x=3°, we get
m∠ABC=3×3°+33°=9°+33°
m∠ABC=42°
Draw a right trapezoid with bases of 8 and 10 cm
Answer:
Here is a picture of a right trapezoid with bases of 8 and 10 cm
Sally's soccer team played 25
games this season and lost 9 of
those games. What percent of the
games did the team win?
Answer:
64%
Step-by-step explanation:
25 - 9 = 16, so 16 of the games were won by Sally's team.
16/25 = 64% of the games were won
Solve the following inequalities, if it is known that the function g is decreasing on its domain. g(5-x^2)≤g(3x-5), Dg=(-∞,4)
For the following inequalities, if it is known that the function g is decreasing on its domain. g(5-x^2)≤g(3x-5) the solution is mathematically given as
1 ≤ x < 6
What is the following inequalities g(5-x^2)≤g(3x-5)?
Generally, the equation for the inequalities is mathematically given as
g(5-x^2)≤g(3x-5)
therefore,
x^2<5x+6
-1< x <6
In conclusion, the solution to the inequalities are
1 ≤ x < 6
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Find the area of the sector of the circle.
A)40π
B)200π
C)60π
D)300π
Answer:
the answer is D) 300 π
Step-by-step explanation:
Formula for Area of sector is:
θ/360° * π * (r)^2
here,
θ= 30° and radius= 60 in
so, after we substitute, we get:
30/360* π* 60*60 after simplifying we get:
= 1/12* π* 5*60
=300π
Hope it helps.
Answer:
D
Step-by-step explanation:
area of sector=
[tex] \frac{theta}{360} \times \pi \: r {}^{2} \\ \\ \frac{30}{360} \times \pi \: (60) {}^{2} \\ \\ 300\pi[/tex]
360
Whats 38240 divided by 4
Answer:
9560
Step-by-step explanation:
Use a calculator or do long division.
You can also divide by 2 twice.
38240/2 = 19120
19120/2 = 9560
Answer: 9560
Answer:
9560
Step-by-step explanation:
30000÷4=7500
8000÷4=2000
200÷4=50
40÷4=10
0÷4=0
7,500+2,000+50+10+0=9,500+60=9,560
f x + 12 ≤ 5 − y and 5 − y ≤ 2(x − 3), then which statement is true?
A vending machine that takes only dimes and
quarters contains 30 coins, with a total value of
$4.20. How many of each coin are there?
please solve for x 3x + 22
Answer:
The x intercept is [tex](-\frac{22}{3} ,~0)[/tex]
The y intercept is [tex](0,~22)[/tex]
What's the range of f(x)=x+6 if x ∈(-4,-1)
Answer:
the range of is (2 , 5)Step-by-step explanation:
f(x)=x+6
f is an increasing function then the range of is
f(-4,-1) = (f(-4) , f(-1))
f(-4) = -4 + 6 = 2
f(-1) = -1 + 6 = 5
Therefore
the range of is f(-4,-1) = (2 , 5)
Tisha and her scout troop are heading to the Swing Time zipline park. They plan to purchase
the group package. With the package, the cost per person is $5 less than the normal cost for
an individual. There are 12 scouts in Tisha's troop. Her troop leader called ahead and found
that the total cost for the group will be $150. What is the normal cost for an individual?
Answer:
$17.5
Step-by-step explanation:
divide 150 by 12 to get 12.5. 12.5 is what they paid per-person with the discount. add 5 to get 17.5 and that is the on-discounted price
The normal cost for an individual is $17.50.
Let's denote the normal cost for an individual as "N."
According to the given information, with the group package, the cost per person is $5 less than the normal cost for an individual. So, the cost for each scout in Tisha's troop is "N - $5."
There are 12 scouts in Tisha's troop, so the total cost for the group is given as $150.
We can set up an equation based on the total cost:
Total Cost = Cost per Person × Number of People
$150 = (N - $5) × 12
Now, let's solve for the normal cost for an individual (N):
$150 = 12N - $60
12N = $150 + $60
12N = $210
N = $210 / 12
N = $17.50
So, the normal cost for an individual is $17.50.
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The graph of a linear function is shown on the grid.
Which equation is best represented by this graph?
Answer:
C
Step-by-step explanation:
Because thats the answer
Brady dilates an oblique prism by a scale factor of 2/3. Determine the scale factors for perimeter, area, and Volume. (Answer as a fraction)
Using proportions, it is found that:
The scale factor for the perimeter is of [tex]\frac{2}{3}[/tex].The scale factor for the area is of [tex]\frac{4}{9}[/tex].The scale factor for the volume is of [tex]\frac{8}{27}[/tex].What is a proportion?A proportion is a fraction of a total amount.
For the perimeter, as it is given in units, the scale factor is the same, hence it is of [tex]\frac{2}{3}[/tex].
For the area, as it is given in units squared, the scale factor is squared, hence:
[tex]\left(\frac{2}{3}\right)^2 = \frac{4}{9}[/tex]
For the volume, as it is given in cubic units, the scale factor is eleveted to the third power, hence:
[tex]\left(\frac{2}{3}\right)^3 = \frac{8}{27}[/tex]
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Last year the depth of the river was 4.2 feet deep. This year it dropped 9% Find the depth of the river this year
Answer: 3.822
Step-by-step explanation: 9/100 × 4.2 = 0.378
Deduct from 4.2
Which equation represents the graphed function? –3x 2 = y –x 2 = y x – 3 = y 2x – 3 = y
Answer:
C) 3/2x-3=y
Step-by-step explanation:
-3 because that is the Y- intercept and 3/2 is the slope of the line. Y= mx +b is the formula and m is the slope and b is the y intercept.
I’m confused please help!
Answer:
See below
Step-by-step explanation:
c will be tha same as the labelled angle = 99 degrees
then c + b = a straight line = 180
99 + b = 180
b = 81 degrees
A sample of students is taken from the school's A honor roll. The school
estimates that there are 360 students on the A honor roll. Using this sample,
how many students on the A honor roll are 8th graders?
Answer:
There are 126 8th grade A honor roll students.
Step-by-step explanation:
Look at the image for the instructions! I need this asap! I will give points, 5 stars and brainliest ((:
(This is an essay)
Answer:
1. one is smaller by 5 cm and one is larger by 5 cm
2. well they are similar to each other, but one is dilated and isn't
In 2010, Cameron invested $10,000 in an account that earns 8. 5% interest compounded monthly. How much money would Cameron have gained by 2025?
Answer:
Step-by-step explanation:
First, we need to calculate how many years will earn percent.
2010---->2025= 15 years elapsed. Now we have our time, we need to plug it in our compound interest formula=
Principal(rate+1)^time or A=P(1+R)^t
10,000(0.085+1)^15
=$33,997.43
To calculate how much Cam earned, you need to subtract from original amount.
=$33,997.43-10,000=
---->$23997.43
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P is a rectangle with length 40 cm and width x cm. Q is a rectangle with width y cm. P The length of Q is 25% more than the length of P. The area of Q is 10% less than the area of P. Work out the ratio x : y x cm Give your answer in its simplest form. 40 cm Q y cm
From rectangle P and Q, the ratio of x to y is 25/18
What is an equation?An equation is an expression used to show the relationship between two or more numbers and variables.
Area of P = 40 * x = 40x cm²
Area of Q = y * (1.25 * 40) = 50y cm²
Given that area of Q = 90% if P = 0.9(40x) = 36x cm²
50y cm² = 36x cm²
x/y = 50/36 = 25/18
From rectangle P and Q, the ratio of x to y is 25/18
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Don't Send links, don't Write random things and get the points for free.
Answer:
2,714in^3
Step-by-step explanation:
V = pi*r^2*h
V = 3.14*6^2*24
V = 3.14*36*24
V = 2,714
The volume of the cylindrical fish tank is 2,714 inches cubed.
Answer:
Option A, [tex]2714\ in^3[/tex]
Step-by-step explanation:
Step 1: Determine the volume of the cylinder
[tex]V=\pi r^2h[/tex]
[tex]V=\pi *(12\ in/2)^2*24\ in[/tex]
[tex]V=\pi *(6\ in)^2*24\ in[/tex]
[tex]V=\pi * 36\ in^2 *24\ in[/tex]
[tex]V = \pi *864\ in^3[/tex]
[tex]V=2,714\ in^3[/tex]
Answer: Option A, [tex]2714\ in^3[/tex]
Bob has 30 coins, which are all dimes and quarters. If the total amount of money he has
is $4.80, how many of each coin does he have?
Answer:
that means he will have 25.2
what is the median in 72 77 75 72 70 69 71 78 75 68 62 69 65 63 68 53 57 79 77 75 80 73 71 64 71 64 50 50 55 55
Answer:
The median is 69.5
Step-by-step explanation:
The median is also known as the middle value. To find the median, you first arrange your data in numerical order.
Numerical order:
50, 50, 53, 55, 55, 57, 62, 63, 64, 64, 65, 68, 68, 69, 69, 70, 71, 71, 71, 72, 72, 73, 75, 75, 75, 77, 77, 78, 79, 80
There are 30 numbers, which means that the median is between the 15th and 16th value (69 and 70).
69 + 70 = 139
139/2 = 69.5
Therefore, the median of this data set is 69.5
Hope this helps!