Answer:
x = 9
Step-by-step explanation:
Start by dividing both sides by the singular number, 3. We divide by 3 and not 21 because 21 is the result of the equation, not the coefficient.
[tex]\frac{3\left(x-2\right)}{3}=\frac{21}{3}[/tex]
We got 21 over 3 because you cannot divide 3 times an unknown number subtracted by 2 by 3. This is because we do not know the number. So that's where 21 comes in.
Next, simplify this equation by dividing whole numbers.
[tex]\frac{3}{3} = 1[/tex]
[tex]1\left(x-2\right) = \left(x-2\right)[/tex]
[tex]\frac{21}{3} = 7\\= x-2 = 7[/tex]
Lastly, add 2.
[tex]x - 2 + 2 = 7 + 2\\2 + 2 = 4\\7 + 2 = 9\\= x - 4 = 9\\x = 9[/tex]
Why x - 4 is 0: We assume x is always equal to 1, since 4 does not go into 1, the result would be 0. x - 0 = 0. Therefore, the problem became x = 9.
Hope this helps!
Write an equation in slope-intercept form of the line shown. (3,1) (1,-3)
Answer:
[tex]y = 2x - 5[/tex]
Step-by-step explanation:
The first step in finding the equation of a line from a given set of points is to find its slope. The slope of a line is defined by the formula:
[tex]m = \dfrac{\textrm{rise}}{\textrm{run}} = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]
In this problem, we are given two points in the form [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex].
So, we can define the x's and y's as:
[tex]x_1 = 3[/tex], [tex]y_1 = 1[/tex], [tex]x_2 = 1[/tex], [tex]y_2 = -3[/tex].
Hence, the slope of the line can be solved for.
[tex]m = \dfrac{-3 - 1}{1 - 3}[/tex]
[tex]m=\dfrac{-4}{-2}[/tex]
[tex]m = 2[/tex]
So, the slope of the line is 2.
Now, we can plug this into the point-slope equation for a line where (a, b) is a point on the line and m is its slope.
[tex]y - b = m(x - a)[/tex]
I will use the point (3, 1):
[tex]y - 1 = 2(x - 3)[/tex]
and isolate y to put it into slope-intercept form.
[tex]y - 1 = 2x - 6[/tex]
[tex]y = 2x - 6 + 1[/tex]
[tex]y = 2x - 5[/tex]
So, the equation in slope-intercept form for the line that goes through the points (3, 1) and (1, -3) is [tex]y = 2x - 5[/tex].
Please I need help please
The measure of missing angles in the diagram is angle 1 = 88°, angle 2 = 42° and angle 3 = 113° .
In the question ,
a figure is given ,
the labelled diagram is show below .
we can see that the angle ACB and angle ECD are vertically opposite angles ,
we know that, the vertically opposite angles are equal ,
So, angle ACB = m∠2 = 42°
In triangle ABC
By Angle Sum Property Of Triangle ,
angle A + angle B [tex]+[/tex] angle C [tex]=[/tex] 180°
50° + m∠1 + 42° [tex]=[/tex] 180°
92° + m∠1 = 180°
m∠1 = 180° - 92°
m∠1 = 88°
In triangle CDE ,
By Angle Sum Property Of Triangle
angle C + angle D [tex]+[/tex] angle E [tex]=[/tex] 180°
42° + m∠3 + 25° [tex]=[/tex] 180°
m∠3 + 67° = 180°
m∠3 = 180° - 67°
m∠3 = 113°
Therefore , The measure of angle 1 = 88°, angle 2 = 42° and angle 3 = 113° .
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Franchising is a popular way to grow. Subway has about 42,000 franchisees that pay 12. 5% of their annual store revenue ($417,000 average) to subway. About how much does subway collect in franchise fees?.
Total amount that Subway collect in franchise fees = $2,189,250,000
Total number of subway franchisees = 42,000
Average annual store revenue = $417,000
Total paying percentage of franchisees = 12.5%
12.5% of average revenue = (417000×12.5)÷100
= $52,125
Total subway collection in franchise fee= total number of franchisees×amount of fees per franchisees
= 42,000×52,125
= $2,189,250,000
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Since subways has about 42000 franchisees and about $417000 average revenue is earned. Therefore, the total amount that Subway collect in franchise fees is $2,189,250,000.
Subways Franchise operate 16 submarine sandwich shop and they expanded quickly with its long time slogan "East Fresh".
Franchisor gives a franchisee the authority to do business in the franchisor's trade name using its business system it is called franchising.
Subways franchises pay 12.5% every week (gross sales minus the sales tax), 8% goes toward the franchise royalties and 45% gores towards advertising.
The company has the lowest start-up costs compared to many other fast food franchises but does take more royalty and advertising money.
The franchise fee:
A franchise owner pay 12.5% of gross sales minus tax every week. They must pay even if they are losing money.8% of that 12.5% goes toward the franchise royalties and 4.5% is for advertising.Now, according to the question:
Total number of subway franchisees = 42,000
Average annual store revenue = $417,000
Total paying percentage of franchisees = 12.5%
∴ At 12.5% of average revenue = (417000 × 12.5) ÷ 100
= $52,125
Total subway collection in franchise fee
= total number of franchisees × amount of fees per franchises
= 42,000×52,125
= $2,189,250,000
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If you are given the two sides that are not the hypotenuse, which trig function should you use?.
The trigonometric function that can be used when given 2 sides that are not the hypotenuse is tangent.
When two sides are given that is not the hypotenuse, the trigonometric function that can be employed is the tangent.
A right-angle triangle has the following sides:
Hypotenuse
Adjacent side
the opposite side
The following trigonometric ratios can be used to determine the angles in a right-angle triangle:
sin = opposite/hypotenuse
cos = neighboring / hypotenuse
tan = opposite /adjacent
Tangent is the trigonometric function that can be used to determine the angle of a right-angle triangle given two sides other than the hypotenuse.
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Kevin planted ome corn in the back yard and meaure it height regularly. Currently, the talk are 75 inche tall. That i 25% taller than the lat time he checked. How tall were the talk then?
The height of the tree was 56 inches.
We can calculate the percentage of a certain amount by :
Subtracting New - Original / New multiplied by 100
this implies it will be
75 - x / 75 × 100 = 25 %
7500 - 100 x = 1875
this implies 7500 - 1875 = 100 x
5625 = 100 x
Thus , On dividing both sides by 100 we get
56.25 = x
Now on rounding off this number we will get
56 = x
Thus the original height of the corn plant was 56 inches
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150 decreased by 15 percent
Answer:127.5
Step-by-step explanation:
15% of 150 = 22.5
150-22.5=127.5
Answer:
Step-by-step explanation:
the car owner decided to test this by tracking 30 trips. the average mpg the car owner achieved was 24.1 mpg with a standard deviation of 2.1. flag question: question 9 question 92 pts what is the lower estimate (limit) of the 95% confidence interval for the average miles per gallon? (report to 2 decimal places)
The lower limit of the 95% confidence interval for the average miles per gallon is 23.32 mpg.
How to calculate the lower limit of the confidence interval?
Given,
n = 30
mean = μ = 24.1
standard deviation = σ = 2.1
confidence interval = 95%
Since the sample is 30, use t-table. If sample is greater than 30 use z-table.
Level of significance, α = 1 - 0.95 = 0.05
degree of freedom, df = n - 1 = 30 - 1 = 29
t value = 2.045
Lower limit = [tex]\mu-t\frac{s}{\sqrt{n}}[/tex]
= [tex]24.1 - 2.045\frac{2.1}{\sqrt{30}}[/tex]
= 24.1 - 0.784
= 23.316
= 23.32 mpg
Thus, the lower limit of the 95% confidence interval for the average miles per gallon is 23.32 mpg.
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The sum of three times a number and 2 less than 4 times that same number is 15. Which of the followin
equations could be used to find the value of the number, n? Explain how you arrived at your choice.
Answer:
11
Step-by-step explanation:
Three times an unknown number
= 3(n)
Added to
Two less than four times the same unknown number
= 4 - 2(n)
Total
= 3(n) + 4 - 2(n) = 15
= 3n + 4 - 2n = 15
Collect like terms
= 3n - 2n = 15 - 4
n = 11
At first, students might think that the lengths of the sides of a triangle can be any three lengths, but that is not so. The Triangle Inequality says that the length of any side must be less than the sum of the lengths of the other two sides. For the triangle in part (a) to exist, all of these
statements must be true:
?
?
?
5<3+4, 3<4+5, and 4<5+3.
Yes, the triangle with the given side lengths exists because the triangle inequality holds true.
At first, students might think that the lengths of the sides of a triangle can be any three lengths, but that is not so. The triangle inequality says that the length of any side must be less than the sum of the lengths of the other two sides.
We are given a set of three side lengths. The side lengths are 3, 4, and 5. We need to check whether a triangle can be formed using the given three side lengths. We will use the triangle inequality.
The first inequality is 3 + 4 > 5. This inequality holds true because 7 is greater than 5. The second inequality is 4 + 5 > 3. This inequality holds true because 9 is greater than 3. The first inequality is 5 + 3 > 4. This inequality holds true because 8 is greater than 4. The triangle inequality holds true, so a triangle with the given side lengths exists.
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Please, i need help . .
Step-by-step explanation:
b^3 x b^8 / b^5
b^11/b^5
b^(11-5)
b^6
Find the area of the chape giving… pls help me
Answer:
Area = 8 sq cm
Step-by-step explanation:
This shape is a parallelogram. Its like a rectangle that got tipped over. Area is:
base × height.
We don't know the base that is on the bottom of the image as it is shown. But if you turn it sideways, the 4 can be the base and the 2 is the height.
Area = b × h
= 4 × 2
= 8
The area is 8 sq cm.
Please someone help me I need help with this
From the given graph we get, the coordinates of original P are (-6,-6).
So initial x=-6 and y=-6
Also from the graph we can see that the coordinates of transformed point P' are (-1,3)
So now, (-1,3) = (-6+5,-6+9) = (x+5,y+9)
Hence the first and second box are 5 and 9 respectively.
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The tree diagram represents an
experiment consisting of two trials.
P(D) =[?]
Answer:
P(D) = 0.7
Step-by-step explanation:
There are two routes to D:
AD, which is 0.5*0.6BD, which is 0.5*0.7We then add these two probabilities:
AD + BD = (0.5*0.6) + (0.5*0.7) = 0.3 + 0.35 = 0.7
Therefore, P(D) should be 0.7, or 70%
One fifth of a number plus three times the number is equal to twice the number plus 42 . What is the number
The value of the number is 35
What are algebraic expression?Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values.These letters are called variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.
If the number is represented by x then,
1x/5+3x= 2x+42
making the left hand side a single fraction, then,
(x+15x)/5= 2x+42
16x/5= 2x+42
multiply both sides by 5
16x= 10x+210
collect like terms
16x-10x= 210
6x= 210
x=35
therefore the value of the number is 35
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calculate the surface area of box A 6in 6in 7in box B 3in 8in 9in
The surface area of box A is 240in².
the surface area of box B is 246in².
What is Surface area?
This is referred to as the space/ area occupied by a three- dimensional object by its outer, flat surface of an object.
Formular for calculating surface area is:
Surface area, SA=( 2*L*W)+( 2*L*H) +=( 2*W*H)
where
Length, L
Height,H
Width,W
from the Question box A
L= 6in
W= 6in
H= 7in
Hence
Surface area, SA=( 2*L*W)+( 2*L*H) +=( 2*W*H)
=( 2*6*6)+( 2*6*7) +=( 2*6*7)
=72+84+84
= 240in².
from the Question box B
L= 3in
W= 8in
H= 9in
Hence
Surface area, SA=( 2*L*W)+( 2*L*H) +=( 2*W*H)
=( 2*3*8)+( 2*3*9) +=( 2*8*9)
=48+54+144
= 246in².
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Simplify
a9/a5
a^4
1/a^4
4
a^14
Answer:
36a^10
Step-by-step explanation:
Rewrite x4y2 − 3x3y3 using a common factor.
A) 3xy(x3y − x2y)
B) 3xy2(x2 − x2y)
C) x2y(xy − 3xy2)
D) x2y2(x2 − 3xy)
Rewrite [tex]x^4y^2-3x^3y^3[/tex] using a common factor.
A) [tex]3xy(x^3y-x^2y)[/tex]
B) [tex]3xy^2(x2-x^2y)[/tex]
C) [tex]x^2y(xy-3xy^2)[/tex]
D) [tex]x^2y^2(x^2-3xy)[/tex]
option d
HELP ME PLSS THIS IS DUE NOW
Find the equation of a line parallel to 2x + 2y = -12 that passes through the
point (2, -7).
y+7=x-2
y+7=(x - 2)
y-7=x+2
y - 7 = -(x + 2)
The equation of the line parallel to 2x + 2y = -12 that passes through the point (2,-7) is y+7= -(x - 2) , the correct option is (b) .
In the question ,
it is given that ,
the equation of the line is parallel to 2x + 2y = -12 ,
2x + 2y = 12
2y = -2x + 12
Dividing both sides by 2 , we get
y = -x + 6
So , the slope of the line is -1 ,
since the required line is parallel , so the slope of the required line is -1 .
So , the equation of the line passing through the points (2,-7) with slope -1 is
(y - y₁) = m(x - x₁)
(y -(-7)) = -1(x - 2)
y + 7 = -1(x - 2)
y + 7 = -(x - 2)
Therefore , The equation of the line parallel to 2x + 2y = -12 that passes through the point (2,-7) is y+7= -(x - 2) .
The given question is incomplete , the complete question is
Find the equation of a line parallel to 2x + 2y = -12 that passes through the point (2, -7) ?
(a) y+7=x-2
(b) y+7= -(x - 2)
(c) y-7=x+2
(d) y-7= -(x + 2)
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Write the following decimal in standard form:
twelve and eighty-four hundredths
i really need this asap
Answer:
below
Step-by-step explanation:
12 + 84/100 = 12.84
4.a bag contains 4 green and 4 red balls. two balls are drawn one by one. what will be the probability that the first drawing gives green ball and second drawing a red ball, in case the first ball drawn was not replaced before drawing the second one.
The probability that the first drawing gives green ball and second drawing a red ball is 2/7
Number of green balls = 4 green balls
Number of red balls = 4 red balls
Total number of balls in the bag = 4 + 4
= 8 balls
The probability = Number of favorable outcomes / Total number of outcomes
The probability of getting green balls in first draw = 4 / 8
= 1/2
First ball drawn was not replaced before drawing the second one
The probability of getting red ball in second draw = 4 / 7
The probability that the first drawing gives green ball and second drawing a red ball = (4/8) × (4/7)
= 2/7
Hence, the probability that the first drawing gives green ball and second drawing a red ball is 2/7
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A farmer has 180 bushels of wheat to sell at her roadside stand.She sells an average of 14 5/8 bushels each day.Represent the total change in the number of bushels she has for sale after 5 days.
A farmer has 180 bushels of wheat to sell at her roadside stand. She sells an average of 14 5/8 bushels each day.
The total change in the number of bushels she has for sale after 5 days can be represented as [tex]\frac{117}{8} X 5[/tex].
Define average.
The average is defined as the mean value, which is equal to the ratio of the sum of the number of values in a given set to the total number of values present in the set.
In plain English, an average is a single number taken as representative of a list of numbers, typically the sum of the numbers divided by how many numbers are in the list. For instance, the average of the digits 2, 3, 4, 7, and 9 is 5.
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A Jewelry company makes and sells necklaces. For one type of necklace, the company uses clay beads and glass beads. Each necklace has no more than 10 clay beads and at least 4 glass beads. For every necklace, four times the number of glass beads is less than or equal to 8 more than twice the number of clay beads. Each clay bead costs $0.20 and each glass bead costs $0.40. The company wants to find the minimum cost to make a necklace with clay and glass beads and find the combination of clay and glass beads in a necklace that costs the least to make. a. Define the variables and write a system of inequalities. Then write an equation for the cost C. b. Graph the system of inequalities and find the coordinates of the vertices of the feasible region. c. Find the number of clay beads and glass beads in a necklace that costs the least to make.
a. The system of inequalities that models the situation is:
0 ≤ x ≤ 10.y ≥ 4.4y ≤ 8 + 2x.The equation for the cost is: C(x,y) = 0.2x + 0.4y.
b. The graph is given by the image at the end of the answer, and the vertices are (4,4), (10,4) and (10,7).
c. The number of clay beads and glass beads in a necklace that costs the least to make is: 4 clay beads and 4 glass beads.
What is the system of inequalities?The variables for the system are presented as follows:
Variable x: number of clay beads used.Variable y: number of glass beads used.Each necklace has no more than 10 clay beads and at least 4 glass beads, hence the constraints are listed as follows:
0 ≤ x ≤ 10.y ≥ 4.The numbers of each beads are countable amounts, meaning that they cannot assume negative values.
Four times the number of glass beads is less than or equal to 8 more than twice the number of clay beads, hence the final constraint is of:
4y ≤ 8 + 2x.
Each clay bead costs $0.20 and each glass bead costs $0.40, hence the cost function is given as follows:
C(x,y) = 0.2x + 0.4y.
Using the three constraints, the graph is given by the image at the end of the answer, and the vertices are as follows:
(4,4).(10,4).(10,7).The minimum cost is at the vertex with the smallest numeric value of the cost function, hence the numeric values are listed as follows:
C(4,4) = 0.2(4) + 0.4(4) = 2.4. -> minimum cost.C(10,4) = 0.2(10) + 0.4(4) = 3.6.C(10,7) = 0.2(10) + 0.4(7) = 4.8.More can be learned about a system of inequalities at https://brainly.com/question/9195260
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Find the equation of the line passing through the given point and parallel to the given line.
( -1 , -1 ), x + y = 8
( -5 , -2), y + 3x = 10
The equation of the line that passes through (-1, -1) and is parallel to x + y = 8 is x + y = -2
The equation of the line that passes through (-5, -2) and is parallel to y + 3x = 10 is 3x + y = -17
Equation of a lineFrom the question, we are to determine the equation of the line passing through the given points and parallel to the given line.
NOTE: If two lines are parallel, then their slopes are equal
First, we will determine the slopes of the given line
x + y = 8
Write the equation in the slope-intercept form, y = mx + b
Where m is the slope
and b is the y-intercept
x + y = 8 becomes
y = -x + 8
Therefore, m = -1
Now, we will determine the equation of a line that has a slope of -1 and that passes through (-1, -1)
Using the point-slope form of the equation of a straight line,
y - y₁ = m(x - x₁)
y - (-1) = -1(x - (-1))
y + 1 = -1(x + 1)
y + 1 = -x -1
x + y = -1 -1
x + y = -2
Hence, the equation is x + y = -2
Now, we will determine the slope of y + 3x = 10
Express the equation in slope-intercept form
y + 3x = 10
y = -3x + 10
Therefore, m = -3
Now, we will determine the equation of a line that has a slope of -3 and that passes through (-5, -2)
Using the point-slope form of the equation of a straight line,
y - y₁ = m(x - x₁)
y - (-2) = -3(x - (-5))
y + 2 = -3(x + 5)
y + 2 = -3x - 15
3x + y = -15 -2
3x + y = -17
Hence, the equation is 3x + y = -17
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The last time that Dr. Mason, a farm veterinarian, checked, a particular pig weighed 59.8 kilograms. Dr. Mason just weighed the pig again and found out that it weighs 8.1% less now. How much does the pig weigh now
The weight of the pig now is 54.9562 kg.
How to calculate the weight?Given that the farm veterinarian, checked, a particular pig weighed 59.8 kilograms. Dr. Mason just weighed the pig again and found out that it weighs 8.1% less now.
The reduction will be:
= Percentage × Original weight
= 8.1% × 59.8
= 4.8438 kg
Therefore the weight of the pig will be:
= Original weight - Reduction
= 59.8 - 4.8438
= 54.9562 kg
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9/5 ÷ by 2/3 I need a answer for that.
Answer:
Step-by-step explanation:
Exact Form: 6/5
Decimal Form : 1.2
Mixed Number Form : 1 (whole number) 1/5
2 p varies directly as q and the square of r and inversely as s.
a. Write the equation of the relation.
b. Find kif p = 40 when q = 5, r = 4 and s = 6.
c. Find p when q = 8, r= 6 and s= 9.
d. Finds when p= 10, q=5 and r = 2.
The equation for the relation is [tex]p=k \frac{qr^2}{s}[/tex].
The value of k when q = 5, r = 4 and s = 6 is 3.
The value of p when q = 8, r= 6 and s= 9 is 96.
The value of s when p= 10, q=5 and r = 2 is 6.
A connection between two different items is called variation. There are two categories of difference. Direct Variation is the name of the first one. When two variables move in the same direction, direct variation occurs. Additionally, as one variable rises, the other variable rises as well. Inverse Variation is the second kind. When the two variables move in the opposite direction, inverse variation occurs. Additionally, this occurs when one variable rises while the other falls.
Since p varies directly as q and the square of r and inversely as s. So the equation will be [tex]p=k \frac{qr^2}{s}[/tex].
Now, finding the value of k, for p = 40 when q = 5, r = 4 and s = 6,
[tex]p=k \frac{qr^2}{s}\\40=k \frac{5\times4^2}{6}\\k = 3[/tex]
Now, finding the value of p when q = 8, r= 6 and s= 9,
[tex]p=3 \frac{8\times 6^2}{9}\\=96[/tex]
Now, finding the value of s when p= 10, q=5 and r = 2,
[tex]10=3 \frac{5\times 2^2}{s}\\\\10=3\times \frac{20}{s}\\s=6[/tex]
Therefore, the equation for the relation is [tex]p=k \frac{qr^2}{s}[/tex] , the value of k when p = 40 when q = 5, r = 4 and s = 6 is 3, the value of p when q = 8, r= 6 and s= 9 is 96 and the value of s when p= 10, q=5 and r = 2 is 6.
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1) A sales representative earns a 2.5% commission on sales. Find the commission earned when the total sales are $80,500.
Which triangles can be mapped onto one another through a sequence of rigid transformations
Answer:
e and c
Step-by-step explanation:
both are the exact same size, which would allow them to be placed on top of each other without any overlap
Answer:
A, B and E are the correct answers
Step-by-step explanation:
I had that same question on the test too.
a survey carried out recently to find the number of applicants that apply for jobs in three newspaper establishment revealed i-70 applied to the Daily Times 65 applied to the daily graphic and 85 apply to the Punch. 40 applied to the daily times only, 20 applied to the daily graphic only while 45 applied to the punch only. if 15 applied to all the three newspaper establishment, find: I. the number that applied to both the daily times and daily graphic. Ii.the number that applied to the daily times and the punch. III. the number that applied to both the daily graphic and the punch. iv. the number that applied to at least one newspaper establishment.
The values of x= 10; y= 5; z= 20.
Given that
40 applied to the daily times only,
20 applied to the daily graphic only while
45 applied to the punch only.
To find out, if 15 applied to all the three newspaper establishment
I. the number that applied to both the daily times and daily graphic
II. the number that applied to the daily times and the punch.
III. the number that applied to both the daily graphic and the punch.
iv. the number that applied to at least one newspaper establishment.
Given that: DT (marked "T"), 70 & 40 (red circle).
DG (marked "G"), 65 & 20 (green circle).
P, 85 & 45 (blue circle).
x + y + 15 + 40 = 70
y + z + 15 + 45 = 85
x + z + 15 + 20 = 65
==========>
x + y = 15, (1)
y + z = 25, (2)
x + z = 30. (3)
------------------------Add 3 equations ====>
2x + 2y + 2z = 15 + 25 + 30 = 70 ====>
x + y + z = 35. (4)
Subtract (1) from (4): z= 20;
Subtract (2) from (4): x= 10;
Subtract (3) from (4): y= 5.
Hence the answer is the values of x= 10; y= 5; z= 20.
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