1) Solve for x (11 - 2*) 7 = 21
Answers
ok done. Thank to me :>
Related Questions
isha's art club has $250. They sell 6 paintings for $16 each. They buy 9 sketchbooks that cost $13 each. Aisha says they now have about $280. Is Aisha’s estimate reasonable? Aisha’s estimate is not reasonable. They earned about $120 and spent about $120 so they should have the same amount of money as they started with. Aisha’s estimate is not reasonable. They earned about $100 and spent about $120 so they should have about $20 less than they started with. Aisha’s estimate is reasonable. They earned about $100 and spent about $130 so they should have about $30 more than they started with. Aisha’s answer is reasonable. They earned about $60 and spent about $90 so they should have about $30 less than they started with.
Answers
Answer:
Step-by-step explanation:
Aisha’s estimate is not reasonable.
They earned about $100 and spent about $120 so they should have about $20 less than they started with.
The following are water temperatures at various beaches in San Diego:
58° 61° 68° 65° 58°
What is the mode of the data set?
Answers
Answer:
Mode is 58 degrees
Step-by-step explanation:
You buy a serving spoon for $4.05 and a bread knife for $3.99. What is the total cost of your purchase?
A. $8.94
B. $7.04
C. $7.94
D. $8.04
Correct answer on gradpoint is D: $8.04
Answers
Answer: d. $8.04
Step-by-step explanation:
$4.05 + $3.99 = $8.04
Answer:
d. 8.04
Step-by-step explanation:
4.05+3.99=8.04
Connor gets one hour of lunch and recess every day at school. He eats lunch first, and then gets to go outside for recess. He begins lunch at 11:15am. Based on this information, select All of the statements that are correct. a. If it takes Connor 25 minutes to eat lunch, he can go outside for recess at 11:40am. b. If it takes Connor 35 minutes to eat lunch, he will have 20 minutes left for recess. c. If it takes Connor 20 minutes for lunch, he can go outside for recess before 11:45am. d. If it takes Connor 25 minutes for lunch, he will still have at least 40 minutes left for recess. Vle. If it takes Connor 45 minutes for lunch, he can go out to recess at 12:00pm.
Answers
Answer: B ( sorry if im wrong )
Step-by-step explanation:
if Conner begins lunch at 11:15am then we need to find out what it'll be in +60 minutes, which is . . . 12:15pm
so it's not A, C, E - which now leaves us B and D
( I used a time calculator btw )
the answer is D because B is 25 minutes for recess
What is m% of n? Also what is m% of p% of n?
Answers
That would become mn/100.
Which is..
mn%.
Then for the part for m%*p%*n, you would do
M/100 * p/100 * n
=
mpn/100000.
It could be wrong, because i have not learned this before. But i am only using the methods i know to solve the problem. Good luck
Answer:
mnp/10000
Step-by-step explanation:
Same reasoning as above, but 100*100 is 10000 so there you go
A nut mixture of peanuts and macadamia nuts at a small fair is $1.00 per pound of peanuts and $3.26 per pound of macadamia nuts. Over the
entire day, 131 pounds of the nut mixture were sold for $248.52. If p is the number peanuts and n is the number of macadamia nuts, then the
system of equations that models this scenario is:
p+n=131
P+3.26n = 248.52
ANSWER CHOICES:
(Please help it would mean everything to me. I’d give brainliest <3)
Answers
Answer:
D
Step-by-step explanation:
You can infer to the solution of this problem by looking at the choices. Hope this helped :)
James is observing the population of the fish he put into a pond. He built a pond and
populated it with 700 fish. The population of the fish doubles every year.
Answers
The exponential equation is given by y = 700(2)ˣ
An exponential function is given by:
y = abˣ
where y, x are variables, a is the initial value of y and b is the multiplier.
Let y represent the population of fish after x hours.
Given that he starts with 700 fishes, hence
a = 700
The population of the fish doubles every year, hence:
b = 2
The exponential equation becomes:
y = 700(2)ˣ
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2) Oil with ρ= 876 kg/m3 and μ= 0.24 kg/m · s is flowing through a 1.5 cm diameter pipe that discharges into the atmosphere at 88 kPa. The absolute pressure 15 m before the exit is measured to be 135 kPa. Determine the flow rate of oil through the pipe if the pipe is (a) horizontal, (b) inclined 8° upward from the horizontal, and (c) inclined 8° downward from the horizontal.
Answers
The pressure in a fluid flowing with laminar flow through a pipe is given by
Hagen-Poiseuille equation.
The correct responses are;
(a) If the pipe is horizontal, the flow rate is approximately 1.622 × 10⁻⁵ m³/s(b) If the pipe is inclined 8° upwards, the flow rate is approximately 1.003 × 10⁻³ m³/s(c) If the pipe is inclined 8° downwards, the flow rate is approximately 2.24 × 10⁻⁵ m³/sReasons:
When the flow is a steady incompressible flow through pipe, the flow rate
can be derived from the Hagen-Poiseuille equation as follows;
[tex]\displaystyle \dot V = \mathbf{\frac{\left[\Delta P - \rho \cdot g \cdot L \cdot sin\left(\theta \right) \right] \cdot \pi \cdot D^4 }{128 \cdot \mu \cdot L}}[/tex]
ΔP = 135 kPa - 88 kPa = 47 kPa
The density of the oil, ρ = 876 kg/m³
μ = 0.24 kg/(m·s)
L = 15 m
The diameter of the pipe, D = 1.5 cm = 0.015 m
(a) When the pipe is horizontal, we have;
θ = 0°
Which gives;
[tex]\displaystyle \dot V = \mathbf{\frac{\left[47 \times 10^3 - 876 \, kg/m^3 \times 9.81 \, m/s^2 \times 15 \, m \cdot sin\left(0^{\circ} \right) \right] \times \pi \times (0.015 \, m)^4 }{128 \times 0.24 \, kg/(m \cdot s) \times 15 \, m}}[/tex]
[tex]\displaystyle \dot V = \frac{\left[47 \times 10^3\, Pa - 128903.4\, Pa \cdot sin\left(0^{\circ} \right) \right] \times \pi \times (0.015 \, m)^4 }{128 \times 0.24 \, kg/(m \cdot s) \times 15 \, m}[/tex]
[tex]\displaystyle \dot V = \frac{\left[47 \times 10^3\, Pa - 128903.4 \, Pa \cdot sin\left(0^{\circ} \right) \right] \times \pi \times (0.015 \, m)^4 }{128 \times 0.24 \, kg/(m \cdot s) \times 15 \, m} =\frac{0.002379357\cdot \pi}{460.8}[/tex]
[tex]\displaystyle \dot V=\frac{0.002379357\cdot \pi}{460.8} = \mathbf{1.622 \times 10^{-5}}[/tex]
The flow rate when the pipe is horizontal, [tex]\displaystyle \dot V[/tex] = 1.622 × 10⁻⁵ m³/s(b) When the pipe is inclined 8°, we have;
[tex]\displaystyle \dot V = \mathbf{\frac{\left[47 \times 10^3\, Pa - 128903.4\, Pa \cdot sin\left(8^{\circ} \right) \right] \times \pi \times (0.015 \, m)^4 }{128 \times 0.24 \, kg/(m \cdot s) \times 15 \, m}} = 1.003 \times 10^{-5} \, m^3/s[/tex]
The flow rate of oil through the pipe if the pipe is inclined 8° upwards from the horizontal, [tex]\displaystyle \dot V[/tex] = 1.003 × 10⁻⁵ m³/s(c) If the pipe is inclined 8° downward from the horizontal, we have;
[tex]\displaystyle \dot V = \frac{\left[47 \times 10^3\, Pa - 128903.4\, Pa \cdot sin\left(-8^{\circ} \right) \right] \times \pi \times (0.015 \, m)^4 }{128 \times 0.24 \, kg/(m \cdot s) \times 15 \, m} = 2.24\times 10^{-5} \, m^3/s[/tex]
If the pipe is inclined 8° upwards from the horizontal, the flow rate of oil through the pipe is, [tex]\displaystyle \dot V[/tex] = 2.24 × 10⁻⁵ m³/sLearn more about flow through pipes here:
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Write 762.238 correct to 2 decimal places
Answers
Answer:
762.24
Step-by-step explanation:
Rounded to the hundredth place
The probability that an 80-year-old male in the U.S. will die within one year is approximately 0.069941. If an insurance company sells a one-year, $12,000 life insurance policy to such a person for $495, what is the company's expectation
Answers
The company's expectation is $486.26.
Since the probability that an 80-year-old male in the U.S. will die within one year is approximately 0.069941, to determine, if an insurance company sells a one-year, $ 12,000 life insurance policy to such a person for $ 495, what is the company's expectation, the following calculation must be performed:
(12000 x 0.069941 / 100) + (495 x (100 - 0.069941) / 100) = X -8.39292 + 494.65379205 = X 486.26 = X
Therefore, the company's expectation is $486.26.
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A curve has equation y=4x^3 -3x+3. Find the coordinates of the two stationary points. Determine whether each of the stationary points is a maximum or a minimum.
Answers
Answer:
There are two stationary points
Local max = (-0.5, 4)Local min = (0.5, 2)Note that 1/2 = 0.5
==========================================================
How to get those answers:
Stationary points occur when the derivative is zero, when the graph is neither increasing nor decreasing (i.e. it's staying still at that snapshot in time).
Apply the derivative to get:
f(x) = 4x^3 - 3x + 3
f ' (x) = 12x^2 - 3
Then set it equal to zero and solve for x.
f ' (x) = 0
12x^2 - 3 = 0
12x^2 = 3
x^2 = 3/12
x^2 = 1/4
x = sqrt(1/4) or x = -sqrt(1/4)
x = 1/2 or x = -1/2
x = 0.5 or x = -0.5
----------------------
Let's do the first derivative test to help determine if we have local mins, local maxes, or neither.
Set up a sign chart as shown below. Note the three distinct regions A,B,C
A = numbers to the left of -0.5B = numbers between -0.5 and 0.5; excluding both endpointsC = numbers to the right of 0.5The values -0.5 and 0.5 are not in any of the three regions. They are the boundaries.
The reason why I split things into regions like this is to test each region individually. We'll plug in a representative x value into the f ' (x) function.
To start off, we'll check region A. Let's try something like x = -2
f ' (x) = 12x^2 - 3
f ' (-2) = 12(-2)^2 - 3
f ' (-2) = 45
The actual result doesn't matter. All we care about is whether if its positive or negative. In this case, f ' (x) > 0 when we're in region A. This tells us f(x) is increasing on the interval [tex]-\infty < x < -0.5[/tex]
Let's check region B. I'll try x = 0.
f ' (x) = 12x^2 - 3
f ' (0) = 12(0) - 3
f ' (0) = -3
The result is negative, so f ' (x) < 0 when [tex]-0.5 < x < 0.5[/tex]. The f(x) curve is decreasing on this interval.
The change from increasing to decreasing as we pass through x = -0.5 indicates that we have a local max here.
Plug x = -0.5 into the original function to find its paired y coordinate.
f(x) = 4x^3 - 3x + 3
f(-0.5) = 4(-0.5)^3 - 3(-0.5) + 3
f(-0.5) = 4
The point (-0.5, 4) is a stationary point. More specifically, it's a local max.
Side note: This is the same as the point (-1/2, 4) when written in fraction form.
----------------------
Let's check region C
I'll try x = 2
f ' (x) = 12x^2 - 3
f ' (2) = 12(2)^2 - 3
f ' (2) = 45
The positive outcome tells us that any number from region C does the same, and f ' (x) > 0 when [tex]0.5 < x < \infty[/tex]. The function f(x) is increasing on this interval.
Region B decreases while C increases. The change from decreasing to increasing indicates we have a local min when x = 0.5
Plug this x value into the original equation
f(x) = 4x^3 - 3x + 3
f(0.5) = 4(0.5)^3 - 3(0.5) + 3
f(0.5) = 2
The local min is located at (0.5, 2) which is the other stationary point.
The graph and sign chart are shown below.
The local min is located at (0.5, 2) which is the other stationary point.
How to Determine whether each of the stationary points is a maximum or a minimum?Stationary points occur when the derivative is zero, when the graph is neither increasing nor decreasing.
Apply the derivative to get:
f(x) = 4x^3 - 3x + 3
f ' (x) = 12x^2 - 3
Then set it equal to zero and solve for x.
f ' (x) = 0
12x^2 - 3 = 0
12x^2 = 3
x^2 = 3/12
x^2 = 1/4
x = 1/2 or x = -1/2
x = 0.5 or x = -0.5
The first derivative test to help determine if we have local mins, local maxes, or neither.
A = numbers to the left of -0.5
B = numbers between -0.5 and 0.5 excluding both endpoints
C = numbers to the right of 0.5
Thus, The values -0.5 and 0.5 are not in any of the three regions. They are the boundaries.
Let's try something like x = -2
f ' (x) = 12x^2 - 3
f ' (-2) = 12(-2)^2 - 3
f ' (-2) = 45
In this case, f ' (x) > 0 when we're in region A.
Let's check region B x = 0.
f ' (x) = 12x^2 - 3
f ' (0) = 12(0) - 3
f ' (0) = -3
The result is negative, so f ' (x) < 0 when f(x) curve is decreasing on this interval.
The change from increasing to decreasing as we pass through x = -0.5 indicates that we have a local max here.
Substitute x = -0.5 into the original function to find its paired y coordinate.
f(x) = 4x^3 - 3x + 3
f(-0.5) = 4(-0.5)^3 - 3(-0.5) + 3
f(-0.5) = 4
The point (-0.5, 4) is a stationary point, it's a local max.
Let's check region C x = 2
f ' (x) = 12x^2 - 3
f ' (2) = 12(2)^2 - 3
f ' (2) = 45
The positive outcome tells us that any number from region C does the same, and f ' (x) > 0 when The function f(x) is increasing on this interval.
Susbtitute this x value into the original equation
f(x) = 4x^3 - 3x + 3
f(0.5) = 4(0.5)^3 - 3(0.5) + 3
f(0.5) = 2
Hence, The local min is located at (0.5, 2) which is the other stationary point.
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help i dont know what this means
The youth group is going on a trip to the state fair. The trip costs $64. Included in that price is $12 for a concert ticket and the cost of 2 passes, one for the rides and one for the game booths. Each of the passes costs the same price. Write an equation representing the cost of the trip, and determine the price of one pass. Solve your equation by showing your work and steps.
Answers
Answer:
12+26x=64
Step-by-step explanation:
64-12=52
52/2=26
$26 per pass
equation 12+26x=64
x=2 in this case x is representing the number of passes
12 is the ticket
and 64 is total cost
A recipe calls for 3/4 of a cup of flour to make 5/8 of a pound of bread
dough. How many cups of flour are needed to make 1 pound of dough?
Show your work and write your answer in simplest form.
Answers
Answer:
[tex]\huge\boxed{\sf 1 \ pound \ of \ dough = 1\frac{1}{5} \ cup \ of \ flour}[/tex]
Step-by-step explanation:
[tex]\displaystyle \underline{Given \ that:}\\\\\frac{5}{8} \ pound \ of \ dough = \frac{3}{4} \ cup\ of \ flour\\\\Multiply \ 8 \ to \ both \ sides\\\\5 \ pounds \ of \ dough = \frac{3}{4} \times 8 \ cup \ of \ flour\\\\5 \ pounds \ of \ dough = 3 \times 2 \ cup \ of \ flour\\\\5 \ pounds \ of \ dough = 6 \ cups \ of \ flour\\\\Divide \ both \ sides \ by \ 5\\\\1 \ pound \ of \ dough = \frac{6}{5} \ cup \ of \ flour\\\\\boxed{1 \ pound \ of \ dough = 1\frac{1}{5} \ cup \ of \ flour}\\\\[/tex]
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807Which equation could possibly represent the graphed function?
OA. f(x) = (x-4)(x + 2)(x + 4)
OB. f(x) = (x-4)^2(x - 2)
OC. f(x) = (x+4)^2(x+2)
OC. f(x) = (x-4)(x-2)(x+4)
Answers
Answer:
A
Step-by-step explanation:
You're looking for x-intercepts
From the graph you know that the x-intercepts are as follows:
x = -4, x = -2, x = 4
And this is when y or f(x) = 0
so you can rewrite each x-intercept as an equation
0 = x + 4
0 = x + 2
0 = x - 4
Now you know each of the terms
f(x) = (x-4)(x+2)(x+4)
Answer:
A choice.
Step-by-step explanation:
If you notice, you see the graph having x-intercepts which are x = 4, -2 and -4.
Because the graph passes through x = 4, -2 and -4, we have to find the function that satisfy x-values when f(x) = 0.
Finding x-intercepts, let f(x) = 0.
A choice
f(x) = (x-4)(x+2)(x+4)
Let f(x) = 0 to find x-intercepts.
0 = (x-4)(x+2)(x+4)
Then solve the equation like linear.
Hence, x = 4,-2,-4
Since the x-intercepts are (4,0),(-4,0) and (-2,0), it satisfies the graph and therefore A is correct.
If an eight-pound bag of rice cost $9.60, what is the cost of 1 pound of rice?
Answers
Answer:
$1.20 for one pound of rice
Step-by-step explanation:
$9.60 ÷ 8 = $1.20
I hope this helps!
van is watching the birds in his backyard, of the birds he watched 9 of them or 45% are sparrows, how many birds are in his backyard
Answers
Rewrite the expression using the
distributive property.
3(a + 2) + 4a
3a + 6 + 4a
Now combine like terms.
[?]a + [
Enter
Answers
Answer:
Step-by-step explanation:
Answer:
7a + 6
Step-by-step explanation:
Expand the brackets and then collect like terms. 4a + 3a = 7a
Please help me asap!
Answers
Answer:
Step-by-step explanation: I think it is c
what is most likely to be represented by the number -40
Answers
Answer:
You tell me the question properly and i will edit this and put answer
Step-by-step explanation:
Until then bye
Answer:
Read Explanation Below
Step-by-step explanation:
So... I didn't know what you were referencing nor did I see a paper, so I came up with a scenario that I thought would represent this number. (also, if you could send a picture so I know what you're referencing, that would be awesome)
1. When James took a nap at 3pm, he saw that the temperature outside was 70 degrees. However, when he woke up at 8pm, he checked the weather and it was 30 degrees. How much did the temperature change during his nap.
How many minuteds does it take to make one balloon sculpture? How many balloons are used in one sculpture
Answers
Answer:
It will take 5 minutes to make one balloon structure. 7 balloons are used in 1 sculpture For part b the answer would be: Tom's unit rate for balloons used per minute would be 1.4
Step-by-step explanation:
PLEASE HELP MEEE!!!!
5. Jared visited his family doctor after suffering for days with a rash that appeared on his ankles and calves as soon as he arrived home from camp. Jared's doctor asked him several questions about his activities during the past week, including the places he'd been and the kind of clothing he wore. Then the doctor announced that Jared had a nasty case of polson Ivy.
What kind of reasoning did Jared's physician use to make a diagnosis? Explain how you you were able to tell what kind of reasoning was used.
Answers
Answer:
I would say Inductive reasoning.
Step-by-step explanation:
Inductive reasoning is defined as "A method of reasoning in which a body of observations is synthesized to come up with a general principle." and this is exactly what the doctor did to come up with his diagnosis.
Hope this helps you out a bit.
Answer:
Deductive reasoning
Step-by-step explanation:
Deductive reasoning, he was given some simple information and any person could simply assume he had poison ivy, as it was made clear he had most likely been around it. And deductive reasoning is basically reasoning based off a few questions from which you can draw a conclusion from.
How much interest will you earn if you deposit
$4000 into an account compounded semi-annually
at 2.8% for 5 years?
Answers
Answer:
45215.31
Step-by-step explanation:
$596.6 is the interest will you earn if you deposit $4000 into an account compounded semi-annually at 2.8% for 5 years.
What is compounding?
Compounding is the process whereby interest is credited to an existing principal amount as well as to interest already paid. Compounding thus can be construed as interest on interest—the effect of which is to magnify returns to interest over time, the so-called “miracle of compounding.”
According to question,$4000 into an account compounded semi-annually at 2.8% for 5 years.
We have to find interest rate.
Formula for compound interest is [tex]P[(1+i)^n-1][/tex]
Since compounding is semi-annually,
[tex]i=\frac{0.028}{2}[/tex][tex]=0.014[/tex] (since compounding is semi-annually)
[tex]n[/tex]=number of years=[tex]5[/tex] ×[tex]2=10[/tex] years (since compounding is semi-annually)
So, compound interest
[tex]=[/tex][tex]P[(1+i)^n-1][/tex]
[tex]=4000((1+0.014)^{10} -1))[/tex]
[tex]=4000[/tex]×[tex]0.1491[/tex]
[tex]=596.6[/tex]
Hence we can conclude that,$596.6 is the interest will you earn if you deposit $4000 into an account compounded semi-annually at 2.8% for 5 years.
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The number of gold fish that can live in a small tank is at most 6.
Let g be the number of goldfish that can live in the tank.
Which inequality represents this situation?
g<6 g≥6 g>6 g≤6
Answers
Answer:
g≤6
Step-by-step explanation:
g≤6 inequality represents the given situation of at most.
What is inequality?" Inequality means an algebraic expression which represents the relation between two situation or values with the sign of > , < , ≥, ≤."
Term used
At most means 'less than to equals to' ( ≤ )
According to the question,
Given'
'g' represents the number of gold fish live in the tank
As per condition of inequality given,
Number of gold fish can live in small tank at most 6
Represent as the term used we get,
Inequality is
g ≤ 6
Hence, g≤6 inequality represents the given situation of at most.
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references on kinetic energy will give brainlist! in own words NO PLARISM!!!!!!!!!!!
Answers
Answer:
See below
Step-by-step explanation:
Kinetic energy is basically energy that an object has while it moves. For example, a ball rolling down a hill will have kinetic energy as it rolls, or a bullet shot out of a gun.
For how many positive integers n is it possible to have a triangle with side lengths five, 12, and n
Answers
Step-by-step explanation:
you know, a single side cannot be longer than the other 2 sides combined.
otherwise, the triangle cannot "close".
so, it starts with 12 cannot be longer than 5 + n.
therefore, n must be at least 7.
and n cannot be longer than 5+12 = 17
7 and 17 I would normally rule out a well, because in these cases the triangle would just be a flat line, when the 3rd side is as long as the other 2 combined.
so, in reality for a real, visible triangle, the range of valid values is 8 .. 16.
that is 9 positive integer values.
Tony’s birthday his mother is making cupcakes for his friends at his daycare that the recipe calls for 3 1/3 of flour I make 2 1/2 dozen cupcakes.Call me she’ll ask flower two dozen of cupcakes
Answers
Answer:
No, there is no enough flour for each of his friends to get a cupcake
Step-by-step explanation:
Let us use the ratio method to solve the question
∵ This recipe makes 2 dozen cupcakes
∵ Each dozen contain 12 cupcakes
∴ The number of cupcakes can the recipe make = 2 × 12
∴ The number of cupcakes can the recipe make = 30 cupcakes
∵ The recipe calls for 3 cups of flour
→ That means 3 cups of flour can make 30 cupcakes
∴ 3 cups of flour makes 30 cupcakes
∵ Anthony’s mother has only 1 cup of flour
→ By using the ratio method
→ flour : cupcake
→ 3 : 30
→ 1 : x
→ By using cross multiplication
∵ 3 × x = 1 × 30
∴ 3 x = 30
→ Divide both sides by 3
∴ x = 9
∵ x represents the number of cupcakes
∴ Anthony’s mother can make 9 cupcakes with 1 cup of flour
∵ Anthony has 12 friends at his daycare
∵ The number of the cupcakes = 9
∴ The number of cupcakes is not enough for each of his friends to
get a cupcake
Step-by-step explanation:
Answer:
Tony’s birthday his mother is making cupcakes for his friends at his daycare that the recipe calls for 3 1/3 of flour I make 2 1/2 dozen cupcakes.Call me she’ll ask flower two dozen of cupcakes
Step-by-step explanation:
-5+i/2i ????
please help!
Answers
[tex]-5+\frac{i}{2i} = -5+\frac{1}{2}=-\frac{9}{2} =-4.5[/tex]
ok done. Thank to me :>
Solve this by elemination thx.
5x-4y=16
3y+2x=-12
And explain.
Answers
Answer:
10x-8y=32
10x+15y=-60
-23y=92
y=-92/23
make as brainleast
Which value of y makes the equation y+4.2=21 true?
I NEED THE ANSWER ASAP I ONLY HAVE 20 MINS TO COMPLETE
A. y = 16.8
B.y=17.2
C.y=17.8
D=25.2
Answers
Answer:
A: 16.8
Step-by-step explanation:
4.2 and 16.8 both have decimal place values. If you line up the decimals when you add them, then you get 21.
The quotient of 2 numbers, p and q.
Answers
Answer:
p/q = x
Step-by-step explanation: