Answer:
Step-by-step explanation:
there are two ways to solve systems of equations, elimination or substitution, this looks like elimination would work quickly
x= 25 -y
x + y = 25 (eq 1)
5x + y = 10 (eq 2)
subtract 2 from 1
x + y = 25
-(5x + y = 10)
-4x + 0y = 15
-4x = 15
x = - 15/4
now plug in x into either starting equations and solve for y
-15/4 + y = 25
y = 25 + 15/4
y = 100/4 + 15 /4
y = 115 /4
y = 28 3/4
we have solved it :)
Answer:
5x+ y = 10 ---(eq1)
x = 25 - y ---(eq2)
substituting (eq2) in (eq1)
5(25 - y) + y = 10
125 - 5y + y = 10
125 - 4y = 10
-4y = 10 - 125
-4y = -115
4y = 115
y = 115/4 = 28.75
substituting value of y in (eq2)
x = 25 - 28.75
x = -3.75
Solve for x in the equation 4 = 32x.
*
Answer:
Your answer is in the Step by Step
Step-by-step explanation:
4=32x
We move all terms to the left:
4-(32x)=0
We move all terms containing x to the left, all other terms to the right
-32x=-4 x=-4/-32 x=1/8
Answer:
the answer is x=1/8
in the decimal form, it's x=0.125
Step-by-step explanation:
isolate the variable by dividing each side by a factor that doesn't contain the variable
hope this helps.
may I please get a brainliest:)
Graph the line x = 3.
Answer: this my graph
Step-by-step explanation:
Please give me the correct answer
Answer:
m∠4 = m∠1 + m∠3
Step-by-step explanation:
The measure of an exterior angle of a triangle is equal to the sum of its two opposite interior angles
Now, examining the given triangle, we can note that:
∠4 is an exterior angle
∠1 and ∠3 are its two opposite interior angles
Based on the givens and the above theorem, we can conclude that:
m∠4 = m∠1 + m∠3
Hope this helps :)
Answer:
her answer is correct please
If a rectangle has length x and width x+3, what is the perimeter of the rectangle in terms of x?
Answer:
[tex]4x+6[/tex] units
Step-by-step explanation:
Skills needed to solve: Order of Operations, Distributive Property, Perimeter Formula, Like Terms
1) To solve this problem, you need to understand the perimeter formula, and that is:
--> [tex]P = 2(L+W)[/tex]
P = Perimeter
L = Length
W = Width
2) Based on that, we are given that:
[tex]L = x[/tex] (since the length is x)
[tex]W = x+3[/tex] (since the width is x+3)
3) After that, we substitute in the values:
[tex]P = 2(L+W)[/tex]
[tex]P = 2(x+(x+3))[/tex]
[tex]x + (x+3) = x+x+3 = 2x+3[/tex] (with like terms and addition)
so: [tex]P=2(2x+3)[/tex]
Use distributive property, which is [tex]a(b+c) = ab+ac[/tex]
get: [tex]2(2x+3) = 2(2x) + 2(3)[/tex]
[tex]2(2x) = 4x[/tex]
[tex]2(3) = 6[/tex]
So: [tex]P = 4x+6[/tex]
Hope this helps and have a nice day!! :) :]
simplify the following 6(1/2+1/3)
Answer:
5
Step-by-step explanation:
use the distributive property
6 * 1/2 = 3
6 * 1/3 = 2
3 + 2 = 5
Hope this helped! Have a nice rest of ur day! Plz mark as brainliest!!!
-Lil G
Which of the following is NOT a linear factor of the polynomial function?
f (x) = x^3 – 5x^2 - 4x + 20
F. (x + 5)
G. (x - 2)
H. (x - 5)
J. (x + 2)
Answer:
Among the four choices, [tex](x + 5)[/tex] is the only one that is not a linear factor of this polynomial function.
Step-by-step explanation:
Let [tex]a[/tex] denote some constant. A linear factor of the form [tex](x - a)[/tex] is a factor of a polynomial [tex]f(x)[/tex] if and only if [tex]f(a) = 0[/tex] (that is: replacing all [tex]x[/tex] in the polynomial [tex]f(x) \![/tex] with the constant [tex]a\![/tex] would give this polynomial a value of [tex]0[/tex].)
For example, in the second linear factor [tex](x - 2)[/tex], the value of the constant is [tex]a = 2[/tex]. Verify that the value of [tex]f(2)[/tex] is indeed [tex]0[/tex]. (In other words, replacing all [tex]x[/tex] in the polynomial [tex]f(x) \![/tex] with the constant [tex]2[/tex] should give this polynomial a value of [tex]0\![/tex].)
[tex]\begin{aligned}f(2) &= 2^3 - 5\times 2^2 - 4 \times 2 + 20 \\ &= 8 - 20 - 8 + 20 \\ &= 0 \end{aligned}[/tex].
Hence, [tex](x - 2)[/tex] is indeed a linear factor of polynomial [tex]f(x)[/tex].
Similarly, it could be verified that [tex](x - 5)[/tex] and [tex](x + 2)[/tex] are also linear factors of this polynomial function.
Rewrite the first linear factor [tex](x + 5)[/tex] in the form [tex](x - a)[/tex] for some constant [tex]a[/tex]: [tex](x + 5) = (x - (-5))[/tex], where [tex]a = -5[/tex].
Calculate the value of [tex]f(5)[/tex].
[tex]\begin{aligned}f(5) &= (-5)^3 - 5\times (-5)^2 - 4 \times (-5) + 20 \\ &= (-125) - 125 + 20 + 20 \\ &= -210\end{aligned}[/tex].
[tex]f(5) \ne 0[/tex] implies that [tex](x - (-5))[/tex] (which is equivalent to [tex](x + 5)[/tex]) isn't a linear factor of this polynomial function.
Find the volume of the cone th=20 in and r=8 in. Solve in terms of pi and round off the decimal to the
nearest tenths.
Answer:
426.7pi
Step-by-step explanation:
V = 1/3 pi r2h
1/3 × 22/7× 8 × 8 × 20
426.7 pi
If computers sell for $1020 per unit and hard drives sell for $118 per unit, the revenue from x computers and y hard drives can be represented by
Answer:
Revenue = 1020x + 118y
Step-by-step explanation:
Revenue = 1020x + 118y
This is an important question to understand. You will use it very shortly when you try and solve 2 equations with 2 unknown. Just to show you what that means, Suppose the revenue is
Revenue = 5808
and 11 items total were sold
x + y = 11 Total number of items sold
1020x + 118y= 5808 Revenue
is the kind of problem you will be solving.
Step-by-step explanation:
a computer sell for $1020
x computer will sell for $1020x
a hard drive sell for $118
y hard drive will sell for $118y
The revenue equals $1020x + $118y
You had a bag of fruit snacks that you shared with 4 friends. Each of you got 175 or fewer fruit snacks. The inequality x÷4≤175 models this situation. Solve the inequality to find the number of fruit snacks that were in the bag.
Answer:
Step-by-step explanation:
It’s 20
A real estate agent has 17 properties that she shows. She feels that there is a 50% chance of selling any one property during a week. The chance of selling any one property is independent of selling another property. Compute the probability of selling less than 3 properties in one week. Round your answer to four decimal places.
Answer:
0.0011 = 0.11% probability of selling less than 3 properties in one week.
Step-by-step explanation:
For each property, there are only two possible outcomes. Either they are sold, or they are not. The chance of selling any one property is independent of selling another property. This means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
A real estate agent has 17 properties that she shows.
This means that [tex]n = 17[/tex]
She feels that there is a 50% chance of selling any one property during a week.
This means that [tex]p = 0.5[/tex]
Compute the probability of selling less than 3 properties in one week.
This is
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{17,0}.(0.5)^{0}.(0.5)^{17} \approx 0[/tex]
[tex]P(X = 1) = C_{17,1}.(0.5)^{1}.(0.5)^{16} = 0.0001[/tex]
[tex]P(X = 2) = C_{17,2}.(0.5)^{2}.(0.5)^{15} = 0.0010[/tex]
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0 + 0.0001 + 0.0010 = 0.0011[/tex]
0.0011 = 0.11% probability of selling less than 3 properties in one week.
Triangle A'B'C' is the image of ABC under a dilation with a scale factor of 2.
What length of segment A'B?
The length of segment A'B' from the triangle A'B'C' is 6 units.
Given that, triangle A'B'C' is the image of ABC under a dilation with a scale factor of 2.
In the given triangle ABC, AB=3 units
The basic formula to find the scale factor of a figure is expressed as,
Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.
2=Dimensions of the new shape/3
Dimensions of the new shape=6 units
Therefore, the length of segment A'B' from the triangle A'B'C' is 6 units.
To learn more about the scale factor visit:
https://brainly.com/question/22312172.
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Solve 7x – 9 = 28 + 4(x – 1).
given that f(x)=2x-5, find the value of x that makes f(x)=15
Answer:
x = 10
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
FunctionsFunction NotationStep-by-step explanation:
Step 1: Define
f(x) = 2x - 5
f(x) = 15
Step 2: Solve for x
Substitute in f(x) [Function]: 15 = 2x - 5[Addition Property of Equality] Add 5 on both sides: 20 = 2x[Division Property of Equality] Divide 2 on both sides: 10 = xRewrite: x = 10.A boat can travel 280 miles on 56
gallons of gasoline. How much
gasoline will it need to go 110 miles
Answer:
22 gallons
Step-by-step explanation:
280 miles / 56 gallons = 5 miles per gallon
110 miles/5 mpg = 22 gallons
A square has a side of 10x. Write and simplify an expression for the perimeter of the square. Then calculate the perimeter of the square if
X=12
Answer:
Step-by-step explanation:
perimeter = 4(10x) = 40x units
if x = 12, perimeter = 480x units
A jury pool has 18 people that are married and 22 people that are not married, from which 12 jurors will be selected. Assuming that each person is equally likely to be chosen and that the jury is selected at random, find the probability that the jury consists of the following. (Give answer as a fraction or a decimal out to at least 4 places. If your answer is very small use scientific notation out to 4 decimal places for example 3.3421E-6.)
Find the volume of the composite figure. First, find the volume of the triangular prism. Triangular prism Volume = [?] ft 8 ft Rectangular prism Volume = [ ] ft 10 ft Total Volume of Composite Figure = [ ] ft 14 ft 10 ft
Answer:
1440ft^3
Step-by-step explanation:
Answer:
120
Step-by-step explanation:
i already did it
Find the lettered angles.
Tanisha is graphing the function f(x) = 25(Three-fifths)x. She begins by plotting the point (1, 15). Which could be the next point she plots on the graph?
(2, 9)
(2, –10)
(2, 14Two-fifths)
(2, 5)
The next point she plots on the graph is (2,9)
How to determine the next point?The function is given as:
f(x) = 25(Three-fifths)^x
Rewrite properly as:
f(x) = 25(3/5)^x
The first point has an x value of 1.
So, the next would be x = 2
This gives
f(2) = 25(3/5)^2
Evaluate the product
f(2) = 9
So, we have:
(2, 9)
Hence, the next point she plots on the graph is (2,9)
Read more about exponential functions at:
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Which table of values is defined by the function y = 5x + 4?
Answer:
Graph using a table of values.
x y
-2 -6
-1 -1
0 4
1 9
2 14
Step-by-step explanation:
Answer:
Step-by-step explanation:
Hey niy
The function f(x) = -(x + 5)(x + 1) is shown.
What is the range of the function?
10
8
O all real numbers less than or equal to 4
O all real numbers less than or equal to -3
O all real numbers greater than or equal to 4
O all real numbers greater than or equal to -3
6
2
-10
-8
4
-2
2
4
8
8
10
X
4
-6
8
-10
Answer:
a
Step-by-step explanation:
f(x)=-(x+5)(x+1)=-(x²+6x+5)=-(x²+6x+9-9+5)
=-(x+3)^2+4
Range: all numbers ≤4
I really need this please
[tex](2^{\frac{1}{2}})^n=\frac{2^x}{2^{3y}}\\2^{\frac{1}{2}n}=2^{x-3y}\\\frac{n}{2}=x-3y\\n=2x-6y[/tex]
im super confused pls help
What is the solution to this system?
2x + 6y = -2
5x - 3y = 31
Answer:
2x+6y=-2 x is -3y-1 and 5x-3y=31 x is 3y+31/5
Step-by-step explanation:
5x−3y=31
Add 3y to both sides.
5x=31+3y
The equation is in standard form.
5x=3y+31
Divide both sides by 5.
5
5x = 5
3y+31
Dividing by 5 undoes the multiplication by 5.
x= 5
3y+31
Please helpppp!!!! Thanks
Answer:
I think it would be the first choice however I may be wrong
Step-by-step explanation:
You measure the sides of a pool and find that it is 20 yards wide and 60 yards long.
30 points!
Approximately, how far would it be diagonally between corners of the pool?
63 yards
55 yards
67 yards
72 yards
Answer:
63
Step-by-step explanation:
Answer: 63
Step-by-step explanation:
Help me please please help me
The mean electrix bill for family C is approximately: $33., $21., $28., and $25. greater than the mean electric bill for family A. This difference is about 2 1/2 times, 3 1/2 times, 2 times, or 1 1/2 times. (part A: choices r $33, $21, $28, & $25. Part B: choices r 2 1/2, 3 1/2, twice, or 1 1/2 times. I still need the answer as well. mean of family C electric bill is $1,339.60 and family A: $943.00. )
As the student council treasurer, you prepare the budget for your class rafting trip. Each large raft
costs $100 to rent and each small raft costs $40 to rent. You have $1,600 to spend. Write and
solve a linear equation to find the number of small rafts you can rent if you rent 12 large rafts.
Answer:
10 small rafts
Step-by-step explanation:
(1600- 1200) / 40 = 10
1600- 1200 = 400
400 / 40 = 10
12 large rafts costs $1200 so subtract that amount from you budget. If you do that you will have $400 left. So I divided $400 by the amount of money each small raft cost whitch was $40 per small raft so i got the quotient of 10.
Sorry if i worded that weirdly but you get the point.
P.s sorry if it isn't comlety correct but i did my best so... ya
Solve. -x < 20
Graph on a number lin
Answer:
x > -20
Step-by-step explanation:
-x < 20
When dividing by negative numbers, flip the inequality.
x > -20
inclusive -> open circle
greater than -> to the right
open circle at -20 going to the right