Answers
Answer:
s = -24
Step-by-step explanation:
This is a 2-step linear equation, so can be solved the way all 2-step equations are solved.
SolutionStep 1
Identify the constant term on the side of the equation with the variable term, and add its opposite to both sides.
[tex]7 = \dfrac{1}{6}s+11\qquad\text{given}\\\\7-11=\dfrac{1}{6}s+11-11\qquad\text{add $-11$ to both sides}\\\\-4=\dfrac{1}{6}s\qquad\text{simplify}[/tex]
Step 2
Multiply both sides by the inverse of the coefficient of the variable.
[tex](6)(-4)=(6)\left(\dfrac{1}{6}s\right)\qquad\text{multiply both sides by 6}\\\\\boxed{-24=s}\qquad\text{simplify}[/tex]
Alternate solutionOften, when equations contain fractions, you are advised to "eliminate fractions" as a first step. That generally means you multiply both sides of the equation by a suitable common denominator.
Here, the only denominator is 6, so the fraction can be eliminated by multiplying both sides of the equation by 6.
[tex]7=\dfrac{1}{6}s+11\qquad\text{given}\\\\6(7)=6\left(\dfrac{1}{6}s+11\right)\qquad\text{multiply both sides by 6}\\\\42=s+66\qquad\text{simplify}\\\\42-66=s+66-66\qquad\text{add the opposite of 66 to both sides}\\\\\boxed{-24=s}\qquad\text{simplify}[/tex]
You will note this requires the same number of steps, but you don't have to mess with fractions after the first step.
CheckThe value we found for the variable can be checked in the original equation.
[tex]7=\dfrac{1}{6}(-24)+11\\\\7=-4+11\qquad\text{true}[/tex]
Related Questions
Choose the best answer. the diagonals of a square bisect each other at ___ angles.
Answers
right angles. .... . . . . ......
Please help
Find the area in square units of ABC△ plotted below.
Answers
Answer:
Use the distance formula on both points AC and AB.
Distance formula is this:
\begin{gathered}d=\sqrt{(x2-x1)^2+(y2-y1)^2} \\\\d=\sqrt{(1--5)^2+(8--7)^2} \\\\d=\sqrt{(6)^2+(15)^2} \\\\d=\sqrt{36+225} \\\\d=\sqrt{261} \\\\\end{gathered}d=(x2−x1)2+(y2−y1)2d=(1−−5)2+(8−−7)2d=(6)2+(15)2d=36+225d=261
Distance for AC is 16.16
Now do the same with the numbers for AB and get the distance of 5.39
2. To get the area, use the formula 1/2 x base x height
AB is the base and AC is the height.
1/2 x 16.16 x 5.39 = 43.55
the answer is 43.5
Find sin() and cos(), tan() and cot(), and sec() and csc(). webassign plot (a) sin() and cos() (b) tan() and cot() (c) sec() and
Answers
The values of the trigonometry functions are sin(α) = 4/7, cos(β) = 4/7, tan(α) = 4/√33, cot(β) = 4/√33, sec(α) = 7/√33 and sec(β) = 7/√4
How to evaluate the trigonometry functions?The figure that completes the question is added as an attachment
From the figure, we have the third side of the triangle to be
Third = √(7^2 - 4^2)
Evaluate
Third = √33
The sin(α) is calculated as:
sin(α) = Opposite/Hypotenuse
This gives
sin(α) = 4/7
The cos(β) is calculated as:
cos(β) = Adjacent/Hypotenuse
This gives
cos(β) = 4/7
The tan(α) is calculated as:
tan(α) = Opposite/Adjacent
This gives
tan(α) = 4/√33
The cot(β) is calculated as:
cot(β) = Adjacent/Opposite
This gives
cot(β) = 4/√33
The sec(α) is calculated as:
sec(α) = Hypotenuse/Adjacent
This gives
sec(α) = 7/√33
The csc(β) is calculated as:
sec(β) = Hypotenuse/Opposite
This gives
sec(β) = 7/√4
Hence, the values of the trigonometry functions are sin(α) = 4/7, cos(β) = 4/7, tan(α) = 4/√33, cot(β) = 4/√33, sec(α) = 7/√33 and sec(β) = 7/√4
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If the graph of y = |x| is translated so that the point (1, 1) is moved to (4, 1), what is the equation of the new graph?
a.) y = | x - 3|
b.) y = | x + 3|
c.) y = | x| - 3
d.) y = | x| + 3
Answers
Answer:
A
Step-by-step explanation:
the answer is A because it is absolute so it would actually be x + 3
Ashley has two equations that she found to be valuable models for her research. She thinks that if she can find the intersection of the two graphs, she will be able to identify a key point to her studies. At what point do these equations intersect?
4y –x = 9
y = 2x − 3
(3,3)
(3,-3)
(-3,-3)
(-3,3)
Answers
The equations intersect at the point (3 ,3 ).
Linear FunctionAn equation can be represented by a linear function. The standard form for the linear equation is: ax+b , for example, y=2x+7. Where:
a= the slope
b=constant term that represents the y-intercept.
System of Linear EquationsSystem of linear equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point at which the lines intersect.
The question gives:
4y –x = 9 (1)
y = 2x − 3 (2)
You should replace the variable y of equation 1 to equation 2. Then, you will have:
4*(2x-3)-x=9
8x-12-x=9
8x-x=9+12
7x=21
x=3
If x=3, from equation 2 you can find the value of y. Thus, y=2*3-3=6-3=3
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The table represents the amount of storage space, in megabytes, used by music files on Zayd’s computer.
A 2-column table with 5 rows titled Zayd's Music Storage. The first column is labeled Number of Files with entries 10, 20, 30, 40, 50. The second column is labeled Space Used (Megabits) with entries 15, 30, 45, 60, 75.
Which statement best describes the relationship between storage space and number of music files?
As the number of files remains constant, the storage space used decreases.
As the number of files remains constant, the storage space used increases.
As the number of files increases, the storage space used decreases.
As the number of files increases, the storage space used increases.
Answers
Answer:
As the number of files increases, the storage space used increases.
HELPPP There are 30 pencils in a box (15 pairs). 2 pair(s) are yellow,
3 pairs are brown, and the rest are tan. What is the probability of
pulling out a brown pencil on the first draw?
Write your answer as a reduced fraction.
Answers
Answer:
1/10
Step-by-step explanation:
Probability= number of brown pencil/number of pencil in the box
3/30
=1/10
Answer: 1/5
Step-by-step explanation:
30/15 pairs is 2 pencils per pair. That means there are 4 yellow pencils, 6 brown pencils, and the rest are tan.
30-10=20. There are 20 tan pencils.
6/30 is the probability of a brown pencil being pulled out.
This simplifies to 1/5.
What is the simplified form of the following expression?
2√27+√12-3√3-2√12
O√3
O 9√3
O 11 √3
O 15√3
Answers
Answer:
[tex] \sqrt{3} [/tex]
Step-by-step explanation:
27 is 3×3×3 from square root we can take 3 out as 3^2 elimate square root and remaining 3 is under root
help needed with this one
Answers
Based on the given parameters, the length of the missing length in the triangle is 12 units
How to determine the length of the missing side?The given triangle is an scalene triangle
Scalene triangles are triangles that have unequal three sides
The missing side is x, and the value of x is calculated using the following equivalent ratios
We have
4 : 8 = 6 : x
Express the above equation as a fraction
4/8 = 6/x
Evaluate the quotient
0.5 = 6/x
Solve for x
x = 6/0.5
Evaluate the quotient
x = 12
Hence, the length of the missing length is 12 units
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Jan has $30. Brenda has $66. How many DVDs can they buy with their total amount if one DVD costs $12?
Answers
Answer: they can buy about 8 dvds
Step-by-step explanation:
this is because 30 + 66 = 96 and if you do 96 divided by 12 it gives you 8
The square below has an area of x2 + 4x + 4 square meters.
What expression represents the length of one side of the square?
Perfect Squares
Write your answer without any spaces. Ex. x+3
Answers
Answer:
The side length of a square is the square root of its area. We know that:
x2 + 4x + 4 = (x + 2)2
Therefore, the side length of the square is x + 2
30. You want to simulate an experiment to draw cards out of a deck. You
plan to draw 35 cards (with replacement), and list which card you drew. How
many times would you expect to draw a face card?
6
8
12
10
Answers
Using the binomial distribution, you would expected to draw a face card 8 times.
What is the binomial probability distribution?It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The expected value of the binomial distribution is:
E(X) = np
For this problem, the parameters are given as follows:
n = 35, as the experiment will be repeated 35 times.p = 12/52, as of the 52 cards, there are 12 faces, hence this is the probability of a success on a single trial.Then the expected value is found as follows:
E(X) = np = 35 x 12/52 = 420/52 = 8.
Thus, you would expected to draw a face card 8 times.
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Solve for P : p/10 = 7.2/3
Answers
P/10 = 7.2/3
P = 7.2x10/3
P=72/3
P= 24
please help!!! i just need this one
Answers
Answer:
[tex]p = x \\ r = 6\% \\ t = 2yrs[/tex]
[tex]p = 1600[/tex]
please see the attachment
Answer:
P = $1600
Step-by-step explanation:
We have to use the equation:
[tex]\boxed{I = Prt}[/tex] .
We know that:
• I = $192
• P = ?
• r = 6% = 0.06
• t = 2 years
Substituting these values into the equation:
[tex]192 = P \times 0.06 \times 2[/tex]
Solving for P:
[tex]P = \frac{192}{0.06 \times 2}[/tex]
[tex]P = \bf \$1600[/tex]
Please help me urgently
Answers
Answer:
A=36°
B=54°
C=90°
a=7
b=9.6
c=11.9
Step-by-step explanation:
Upper case A,B,C are angles. B and C are given. Calculate A because the three angles in a triangle add up to 180°. See image.
Lower case a,b, and c are side lengths.
a is given. You need to use trigonometry and a calculator to find b or c or both. Or you can find one and use the Pythagorean Theorem to find the other. See image.
The product of three consecutive integers is 210. What is their sum?
Answers
Answer:
3 consecutive no.s are
5×6×7=210
sum of them is= 5+6+7
=18
So, I hope. it helps !!
Three times my age in 5 years is 54. How old am i now.
a.10
b.11
c.12
d.13
e.14
Answers
Answer:
D. 13
Step-by-step explanation:
54 ÷ 3 = 18 (your age in 5 years)
18 - 5 = 13 (your age now)
54/3=18
18-5=13
This is correct
The graphs below are both quadratic functions. The equation of the red graph
is fx) = ». Which of these is the equation of the blue graph, g(x)?
Answers
Answer:
A. y = 1/3x^2
Step-by-step explanation:
The red graph is stretched horizontally by a factor 1/3 to give the blue graph
In 2021, the Internal Revenue Service (IRS) decreased the deductible mileage cost to 56 cents from 57.5 cents. Find the percent decrease. (Round to the nearest hundredth of a percent)
Answers
The deductible mileage cost has reduced by 2.16%
What is a percentage change?
A percentage change compares the difference between the new amount and the old amount to the old amount.
I mean the percentage change is the new deductible mileage cost minus the old deductible mileage cost divided by the old deductible mileage cost
New deductible mileage cost= 57.5 cents
Old deductible mileage cost= 56 cents
percentage decrease=(56-57.5)/57.5
percentage decrease=-2.61%
The negative sign in -2.61% means that there was a percentage decrease in deductible mileage cost by 2.61%
In essence, the deductible mileage cost has been reduced by 2.16%
Hundredth of a percent means two decimal places.
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A container contains 20 liters of milk and another container contains 20 liters of syrup. One liter was taken from each vessel and poured into another vessel. After doing this twice, determine the ratio of milk and syrup in the two types of mixture.
Answers
Answer:
Step-by-step explanation:
20 liters -1 liter = 19 liters of milk
20 liters -1 liter = 19 liters of syrup
This was done twice so therefore;
19 liters -1 liter = 18 liters of milk
19 liters -1 liter = 18 liters of syrup
Therefore the ratio comes to 18:18
18 goes into 18 1 and the same for the other 18. Therefore the ratio comes to ;
1:1
Your final answer is 1:1
PLease helppppppppp!!!
Answers
Answer:
437.068 28.019
Step-by-step explanation:
Not sure how to explain this one....it is what it is
7 ones = 7
3 tens = 30
4 hundreds = 400 added = 437
No tenths = 0
6 hudredths = .06
8 thousandths = .008 added to = 437.068
280 tenths = 280 * 1/10 = 28
19 thousandths = .019 summed = 28.019
from your scale drawing, find the actual distance between the opposite corners of the school ball
Answers
The actual distance between the opposite corners of the school hall is; 10√34 m
How to use a Scale Drawing?The scale drawing showing the corners of the hall has been drawn and attached.
Now, from the attached scale drawing it was drawn with the scale;
1 cm to represent 5 m.
Now, the distance between the opposite corners of the hall measuring 50 m and 30 m is indicated as D on the scale drawing. Thus, to find the distance between the opposite corners, we will use Pythagoras theorem to get;
D² = 30² + 50²
D² = 900 + 3500
D² = 4400
D = √4400
D = 10√34 m
Thus, the actual distance between the opposite corners of the school hall is; 10√34 m
Complete question is;
Make a scale drawing of a rectangular school hall which is 50 m long and 30 m wide using a scale of 1 cm to 5 m. From your scale drawing, find the actual distance between the opposite corners of the hall.
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In a grade 11 class there are 30 learners. 16 of them are girls. there are 7 girls and 6 boys with blue eyes. a student is selected at random tone the class monitor what is the probability that the class monitor is a girl
Answers
Answer:
8/15
Step-by-step explanation:
possibilities/ sample size=16 girls/30 "learners"=8/15
quien me hace una canción de ley de los cosenos de C por favor le doy 100 estrellas y corona
Answers
Answer:
Step-by-step explanation: all oof it equals to = 2c c2 = b1
Find the output, h, when the input, x, is -18.
h = 17+
=
I
6
Answers
The value of output, h, when the input, x, is -18 for the given equation is 14
Solving an equationFrom the given question, we are to determine the value of the output, h, when the input x is -18
The given equation written properly is
h = 17 + x/6
Now, to determine the value of output, h, we will put in the value of x into the equation
h= 17 + x/6
The given value of x is -18
Thus, putting the given value of x into the equation, we get
h= 17 + x/6
h= 17 + -18/6
h = 17 + -3
h = 17 - 3
NOTE: + × - = -
h = 14
∴ h is 14 when x is -18
Hence, the value of output, h, when the input, x, is -18 for the given equation is 14
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Simplify: 7^x+1 + 7^x / 2×7^x
Answers
The simplified form of the expression 7^x+1 + 7^x / 2×7^x as given in the task content follows from the laws of indices and is equal to; 4.
What is the simplified form of the expression 7^x+1 + 7^x / 2×7^x?It follows from the task content that the expression whose simplified form is to be determined is given as; 7^x+1 + 7^x / 2×7^x.
On this note, it follows from the law of indices that; 7^x+1 = 7× 7^x.
Hence, we have; 7^x(7+1 ) / 2×7^x.
And upon simplification, we have; 8/2 = 4.
Consequently, we may conclude that the simplified form of the expression as given in the task content is; 4.
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help with math and explain plsss
Answers
Step-by-step explanation:
cotθcosθ=1tanθ⋅1cosθ
(06.04) it costs $100 to rent the bowling alley, plus $4 per person. the cost for any number (n) of people can be found using the expression 100 4n. the cost for 15 people equals $ ___. (input whole number only.) numerical answers expected! answer for blank 1:
Answers
The cost for 10 people equals to $ 140.
What is cost simple word?
Cost is a value of money that a company had to spend to produce its goods or services. It is calculated as the amount that company spends in order to produce a certain unit of a product. In simple words – it is the money that a company spends on things such as labor, services, raw materials, and more.Cost of renting bowling alley = $ 100
Additional cost of renting bowling alley per person = $ 4
⇒ Total Cost for n no. of people = 100 + 4 × n
So, Cost for 10 people = Fix $100 for bowling alley + $4 for each 10
people
= 100 + 4 × 10
= 100 + 40
= 140
Therefore, The cost for 10 people equals to $ 140.
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In the expansion of (2a + 3b)8, which of the following are possible variable terms? Explain your reasoning.
a2b3; a5b3; ab8; b8; a4b4; a8; ab7; a6b5
Answers
The possible variable terms are a^5b^3, b^8, a^4b^4, a^8, ab^7
How to determine the possible variable term?The expression is given as:
(2a + 3b)^8
The power of the above expression is 8
When expanded, the sum of powers on each variable must be 8.
Using the above explanation, we have the following possible variable terms:
a^5b^3, b^8, a^4b^4, a^8, ab^7
This is because the sum of powers equals 8
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Choose the equation that represents a line that passes through points (−1, 2) and (3, 1).
4x − y = −6
x + 4y = 7
x − 4y = −9
4x + y = 2
Answers
Answer:
x + 4y = 7
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 1, 2 ) and (x₂, y₂ ) = (3, 1 )
m = [tex]\frac{1-2}{3-(-1)}[/tex] = [tex]\frac{-1}{3+1}[/tex] = - [tex]\frac{1}{4}[/tex] , then
y = - [tex]\frac{1}{4}[/tex] x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (- 1, 2 )
2 = [tex]\frac{1}{4}[/tex] + c ⇒ c = 2 - [tex]\frac{1}{4}[/tex] = 1 [tex]\frac{3}{4}[/tex] = [tex]\frac{7}{4}[/tex]
y = - [tex]\frac{1}{4}[/tex]x + [tex]\frac{7}{4}[/tex] ← in slope- intercept form
multiply through by 4 to clear the fractions
4y = - x + 7 ( add x to both sides )
x + 4y = 7 ← equation in standard form
equation of line in two point form is needed here.
(y - y1) = [ (y2 - y1)/(x2-x1) ] (x - x1)y - (2) = [ (1 - 2)/(3 - (-1)) ] (x - (-1))y - 2 = [ -1/4 ] (x + 1)y = -(x/4) -1/4 + 2y = -x/4 + 7/44y = -x + 7x + 4y = 7