Answer:
A. x= 2
B. x= 8
Step-by-step explanation:
Solving an equation refers to finding the value of the variable in the equation.
A. 17x +12= 54 -4x
Bring all x terms to one side, constant to the other:
17x +4x= 54 -12
21x= 42
x= 42 ÷21
x= 2
B. 5x -10 +2x= 6(x +1) -x
7x -10= 6x +6 -x
7x -10= 5x +6
Bring all x terms to one side, constant to the other:
7x -5x= 10 +6
2x= 16
Divide both sides by 2:
x= 16 ÷2
x= 8
Hey ! there
Answer:
Value of x in equation A is 2 .Value of x in equation B is 8 .Step-by-step explanation:
In this question we are provided with two equations that are 17x + 12 = 54 - 4x and 5x - 10 + 2x = 6(x + 1) - x . And we are asked to solve the equation that means we have to find the value of x for both the equations .
Solution : -
A)[tex] \longmapsto \qquad \: 17x + 12 = 54 - 4x[/tex]
Step 1 : Subtracting 12 on both sides :
[tex] \longmapsto \qquad \: 17x + \cancel{ 12} - \cancel{12} = \bold{54} - 4x - \bold{ 12}[/tex]
Simplifying it ,
[tex] \longmapsto \qquad \: 17x = 42 - 4x[/tex]
Step 2 : Adding 4x on both sides :
[tex] \longmapsto \qquad \: 17x + 4x = 42 - \cancel{4x} + \cancel{4x}[/tex]
On further calculations, we get :
[tex] \longmapsto \qquad \: 21x = 42[/tex]
Step 3 : Dividing with 21 on both sides :
[tex] \longmapsto \qquad \: \dfrac{ \cancel{21}x}{ \cancel{21} } = \cancel{ \dfrac{42}{21} }[/tex]
We get :
[tex] \longmapsto \qquad \: \red{\underline{\boxed{ \frak{x = 2}}}} \quad \bigstar[/tex]
Henceforth , value of x is 2 .Verifying : -
Now , we are verifying our answer by substituting value of x as 2 in the given equation . So ,
17x + 12 = 54 - 4x 17 ( 2 ) + 12 = 54 - 4 ( 2 )34 + 12 = 54 - 846 = 46L.H.S = R.HSHence , Verified .Therefore , our solution is correct .
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B)[tex] \longmapsto \qquad \: 5x - 10 + 2x = 6(x + 1) - x[/tex]
Step 1 : Adding like terms on left side :
[tex] \longmapsto \qquad \: 7x - 10 = 6(x + 1) - x[/tex]
Step 2 : Solving parenthesis on right side by using distributive property . ( Multiplying 6 with x and 1 both ) :
[tex] \longmapsto \qquad \: 7x - 10 = \bold{6x} + 6 - \bold{x}[/tex]
Step 3 : Solving like terms on right side :
[tex] \longmapsto \qquad \: 7x - 10 = 5x + 6[/tex]
Step 4 : Adding 10 on both sides :
[tex] \longmapsto \qquad \: 7x - \cancel{10} + \cancel{ 10} = 5x + 6 + 10[/tex]
Simplifying it ,
[tex] \longmapsto \qquad \: 7x = 5x + 16[/tex]
Step 5 : Subtracting 5x on both sides :
[tex] \longmapsto \qquad \: 7x - 5x = \cancel{5x }+ 16 - \cancel{5x}[/tex]
On further calculations , we get :
[tex] \longmapsto \qquad \: 2x = 16[/tex]
Step 6 : Dividing with 2 on both sides :
[tex] \longmapsto \qquad \: \dfrac{ \cancel{2}x}{ \cancel{2}} = \cancel{\dfrac{16}{2} }[/tex]
We get :
[tex] \longmapsto \qquad \: \red{\underline{\boxed{ \frak{x = 8}}} } \quad \bigstar[/tex]
Henceforth , value of x is 8 .Verifying : -
Now , we are verifying our answer by substituting value of x as 8 in the given equation . So ,
5x - 10 + 2x = 6(x + 1) - x5 ( 8 ) - 10 + 2( 8 ) = 6 ( 8 + 1 ) - 840 ( - 10 ) + 16 = 6 ( 9 ) - 856 - 10 = 54 - 846 = 46L.H.S = R.H.SHence , Verified .Therefore , our solution is correct.
#Keep LearningConvert to standard form: y=-7x/2-3
Answer:
7x + 2y = −6
Step-by-step explanation:
SAT math scores for a particular year are normally distributed with a mean of 510 and a standard deviation of 80.
What is the probability that a randomly selected score is greater than 590? Enter the numerical answer only (no percent sign).
Using the normal distribution, it is found that there is a 16% probability that a randomly selected score is greater than 590.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.In this problem, the mean and the standard deviation are, respectively, given by [tex]\mu = 510[/tex] and [tex]\sigma = 80[/tex].
The probability that a randomly selected score is greater than 590 is one subtracted by the p-value of Z when X = 590, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{590 - 510}{80}[/tex]
Z = 1
Z = 1 has a p-value of 0.84.
1 - 0.84 = 0.16.
0.16 = 16% probability that a randomly selected score is greater than 590.
More can be learned about the normal distribution at https://brainly.com/question/24663213
I need help guys I got like 1 hour left.
Answer:
Domain: x <= 4
Step-by-step explanation:
The domain is all the x's on the graph or all the x's that can be used in the equation. see image for graph. The graph exists coming from negative infinity (the left side of the graph) and then stops at the point where x is 4. So x must be less than 4 or equal to 4.
Algebraically, if x is bigger than 4, you get a negative number inside the radical (the square root symbol) and that is not allowed. Again we find that x has to be less than or equal to 4.
please b quick
The display on a calculator reads 9.378 E - 5. Which value does this represent?
a. 937,800,000
b. 937,800
c. 0.00009378
d. 0.000009378
Answer: C.0.0009378
Step-by-step explanation:
9.378E-5 is basically 9.378 x 10∧-5. Move the decimal to right 5 times.
URGENT!!! HELP!!!
You spend a $20 per turn on a fair game to win $50 for each win. You lose the first round but win the next two rounds.
What was the net payoff?
$100
-$60
-$30
$40
The net payoff obtained during the game is $40. Option D is the correct answer.
What is net payoff?The term "net payoff" describes the profit or loss realised from a transaction or operation after deducting all costs, charges, and taxes. It is determined by deducting the total cost of the activity or investment from the total income received. A gain is shown by a positive net reward, whereas a loss is indicated by a negative net payoff.
Given that, each round cost $20, and each win gives $50.
Now, for 3 rounds the total cost is:
$20 x 3 = $60
After winning the two round the win amount is:
$50 x 2 = $100
Now, the net payoff is:
$100 - $60 = $40.
Hence, the net payoff obtained during the game is $40. Option D is the correct answer.
Learn more about net payoff here:
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Kristine wants to do hardwood flooring for her room. A floor plan of the room (in feet) is shown. How much hardwood flooring does she need?
Kristine would require at least 116ft of hardwood flooring for her room.
The answer is arrived at by using simple calculations of the area of a square - a polygon.
How do we arrive at the answer above?Note that there are missing portions on the shape of the floor. (See a more elaborate version attached).
The side labeled F = 12ft
The side labeled CDE comprises three sides: 8, 2, and 2 respectively. This is also equal to 12.
With this information, we can calculate the area of the square assuming it was full.
The area of a square is given as:
Length x Breadth or L²;
that gives us: 12 x 12 or 12² = 144ft.
Now we get the total actual area by removing the areas of the missing segments.
Section Ax and Ay is also a square. because the length and the breadth are equal.
hence the area of AxAy = 16ft.
We also have the area of the section labeled D,Dx. This section is a rectangle. The formula for the area of a rectangle is:
Length x Breadth.
Hence, we have
6 x 2 = 12ft.
Total area of missing sections are:
12 + 16 = 28ft.
The total area of the square less the missing areas is:
144 - 28 = 116ft.
Hence the total amount of Hardwood that Kristine would require in square ft is 116ft.
See the attached images and learn more about areas of polygons at:
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Find the slope of the line containing the points (-2, -3) and (-4, 1).
Answer:
- 2
Step-by-step explanation:
Slope, m = (y1-y2)/(x1-x2)
= ( -3 -1)/(-2- -4) =
-4 / ( 2) = - 2
Sloep:-
m=1-(-3)/-4-(-2)m=1+3/-4+2m=4/-2m=-2Answer number 14. It’s very difficult for me and i need some help.
Answer:
1201.2 in (100.1ft)
Step-by-step explanation:
A scale model represents a ratio. All sides must be shrunk or increased based on a constant value. In this case the ratio of the model is 1/13 the size of the original giving us a 1:13 ratio. So each side of your scale model must be multiplied by 13 to find the real value of the side.
First convert all units to inches then divide the width of the real windmill by the width of the scale model (both in inches) you will see the answer is 13. Multiply the inch values of all sides of your model by 13 and this gives you the proportional value of each side of the real windmill in relation to the scale model.
m ∠ 1 = ______ °
m ∠ 2 = ______ °
m ∠ 3 = ______ °
Answer:
M < 1=180
M<2=90
M<3=90
Step-by-step explanation:
M 2 and 3 are both right angles and m1 is a obtuse angle
a ball is dropped from a height of one meter. every time it hits the ground, it rebounds to exactly 2/3 of the previous height. what is the total distance the ball has traveled after its hits the ground for the eigth time?
Answer:69/56 that is your answer did it help
Yo I need to bring up my grade bad so
2x=5+y
(please show it graphed already :D)
Answer:
Step-by-step explanation:
How many solutions does this system of equations have?
Sy=-4x + 3
2x + 8y = 10
Answer:
Step-by-step explanation:
Assuming the s is a typo the answer to this system is x=7/15 and y=17/15
Choose the angle which is vertical to angle BFC in the following figure.
answer A angle CFD
answer B angle DFE
answer C angle AFC
answer D angle EFA
Find x and y
Y 12 x 6
Answer:
Step-by-step explanation:
Coach Morton is going on vacation! He drives 7.5 hours at an average speed of 35mph. How many miles did he travel?
Answer:
4.7m
Step-by-step explanation:
35/7.5
=4.7m
Am sure am correct
Let a represent a positive number and let b represent a negative number. Tell whether each statement is True or False. True False a. The difference (a - b) could be negative. True False b. The difference (b − a) cannot be positive. True False C. The sum (a + b) could be positive. True False d. The sum (b + a) must be negative.
a. False; if b is negative, then -b is positive, so
a - b = a + (-b)
is the sum of two positive numbers, which must be positive.
b. True; the sum of two negative numbers is again negative.
c. True; a + b will be positive as long as a > |b|. (For example, if a = 2 and b = -1, then of course 2 > |-1| = 1, and a + b = 2 + (-1) = 1 > 0.)
d. False; this would contradict the result of part (c). b + a is only negative if a ≤ |b|. (For example, if a = 1 and b = -2, then b + a = -2 + 1 = -1 < 0.)
C is a circle with centre (0,0)
L is a straight line with negative gradient.
The circle C and the line L intersect at the points A and B.
The coordinates of A are (-9,2)
The x coordinate of B is 7
Find an equation of L.
Answer:
Step-by-step explanation:
answeeeer plssssss..
ok well- what time do you need it to be answered by?
An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 22 feet up. The ladder makes an angle of 77^{\circ} ∘ with the ground. Find the length of the ladder. Round your answer to the nearest tenth of a foot if necessary.
Now
[tex]\\ \rm\Rrightarrow sin\theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{22}{H}=sin77[/tex]
[tex]\\ \rm\Rrightarrow H=22/sin77[/tex]
[tex]\\ \rm\Rrightarrow H=22.59ft\approx 23ft[/tex]
The length of the extension ladder that is against the outside wall of the house is 22.58 feet.
What is the length of the ladder?When the ladder lies against a house, a right triangle is formed. The length of the ladder is the hypotenuse. The distance from the base of the ladder to the house is the base. The lenfth off the house is the length.
To find the length of the ladder, Sin would be used:
Sin = opposite / hypotenuse
Sin 77 = 22 / h
h = 22 / 0.9743 = 22.58 feet
To learn more about trigonometry, please check: https://brainly.com/question/22782564
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PLEASEEEEEE HELP ME OUT
Answer:
[tex]x = 135(being \: opposite \: angles \: of \: a \: paralleogram)[/tex]
Step-by-step explanation:
x =135(being opposite angles of a parallelogram)
The radius of a circle is 15 in. Find its area in terms of \piπ
Answer:
Step-by-step explanation:
A = [tex]\pi[/tex]r²
A = [tex]\pi[/tex]15²
A = [tex]\pi[/tex]225
Alex wants to measure lengths of rope for a knot-tying activity at camp What is the best customary unit of measurement for Alex to use to measure the rope? Why?Help I'm stuck. thank u
Answer:
The best customary unit of measurement to measure the lengths of the rope for knot-tying would be:
Inches (in.)
Alex can also use feet, yards, and miles, but Inches are the best measurement to use in this situation.
Step-by-step explanation:
Have a great rest of your day
#TheWizzer
PLEASE HELP WILL GIVE BRAINLIST HURRY PLS
Answer:
we know the trapezoids are similar, so that means all sides are at a ratio, thus
that means from the model to actual, the scale is 1:12, so the large side is 12 times as large.
so for the large trapezoid
EF = 6 * 12 =... 72
EH = 4 * 12 =.. 48
HG = 3 * 12 = ..36
GF = 3 * 12 =...36
72+48+36+36 = 192.
Step-by-step explanation:
find the value of x to the nearest tenth
Answer:
X, to the nearest tenth would be 27.
Step-by-step explanation:
Sin(theta) = adjacent/hypotenuse
Sin64 = x/30
X = sin64 x 30
X= 26.963…
What is the percent if 200 is the total and 150 is the part?
Answer:
75%
Step-by-step explanation:
75% of 200 is 150
Answer:
75% since [tex]50 + 50 + 50 = 150[/tex] which is [tex]3[/tex] quarters of [tex]200[/tex]
Please mark brainliest.
I need help on this please its really hard its due in thirty min
Answer:
L < 5.25yd
Step-by-step explanation:
We can think of Mrs. Klein's composting area as a rectangle, and the formula for finding the area of a rectangle is Base * Height = Area (B*H=A)
Let's just say for the sake of solving the problem that they say that area of the garden had to be exaclty 6 square feet. Because the area must be 6sqft (sqyd = square yards) then we can enter 6 into our formula.
B*H=A now equals B*H=6
They also tell us that the width (which is a stand-in for height) is [tex]1\frac{1}{7}[/tex] so we can enter that in our formula as well
B*H=6 now is [tex]B*1\frac{1}{7} =6[/tex] and now we just have one unknown... the B (base)
And since [tex]B*1\frac{1}{7} =6[/tex] then [tex]6/1\frac{1}{7} =B[/tex]
Thus,
[tex]6yd / 1\frac{1}{7} = 5.25yd[/tex]
And because the question said that the area must be less then 6sqyd, then the length can be anything less then 5.25yd.
Thus,
L < 2.25
Hope that helped... Chow!
Factor x^2−2x. Is this a special product?
Answer:
x(x-2)
Step-by-step explanation:
x^2−2x
Factor out an x
x(x-2)
This is not a special product
Use the drawing tools to form the correct answer on the graph.
Graph this system of equations on the coordinate plane:
y = -3x + 3
y = 1/2x - 4
Answer:
The answer would be (2,3) or you can find the answer in desmos
Step-by-step explanation:
You can input the coordinates in Desmos graphing calculator for the graph
Can someone help me with these I really don’t understand no matter what I try
Answer:
Step-by-step explanation:
This are 3 triangles
One big one, that is divided into 2
Of the 2 triangles one is smaller than the other
So
inside the big trangle we have:
Small triange (Small side = 8/ Median side = y /large side =12
Median triangle(small side = y/ Median side = x/ Large side = z
And then the 2 triangles make a big triangle:
Large triangle (small side=12/ Median side= z/ Large side = 8+x
PLEASE HELP I ILL MARK BRAINLIEST
Answer: 90 dergrees
Step-by-step explanation: 90 dergrees