Three consecutive integers can be represented as followed.
X → first integer
X + 1 → second integer
X + 2 → third integer
Since the sum of our three consecutive integers is 135, we can set up an equation to represent this.
X + X + 1 + X + 2 = 135
-Simplify on the left-
3x + 3 = 135
-3 -3
3x = 132
÷3 ÷3 ← divide both sides by 3
X = 44
X + 1 = 45
X + 2 = 46
Therefore, the three consecutive integers are 44, 45, and 46.
Find b given that p(b,2) is equidistant from a(5,4) and b(2,5)
Please help me with this graphing problem
Enid got a job through an employment agency that charges a fee equal to 40% of the first five weeks’ pay. The job pays $315 per week. How much does Enid have to pay the employment agency?
The coordinate plane below represents a town. Points A through F are farms in the town.Part A: Using the graph above, create a system of inequalities that only contains points D and E in the overlapping shaded regions. Explain how the lines will be graphed and shaded on the coordinate grid above. (5 points) Part B: Explain how to verify that the points D and E are solutions to the system of inequalities created in Part A.
(3 points)
Nonstandard dice can produce interesting distributions of outcomes. you have two balanced, six-sided dice. one is a standard die, with faces having 1, 2, 3, 4, 5, and 6 spots. the other die has three faces with 0 spots and three faces with 6 spots. what are the possible values for the total number of spots y on the up-faces when you roll these two dice?
When rolling a standard die and another die with faces having either 0 or 6 spots, the possible total values y range from 1 to 12, excluding the numbers 5 and 6 twice due to the unique nature of the second die.
Explanation:The question asks about the possible values for the total number of spots y on the up-faces when you roll two nonstandard dice: a standard six-sided die with faces having 1, 2, 3, 4, 5, and 6 spots, and another die with three faces having 0 spots and three faces having 6 spots. To find y, we need to consider all the possible outcomes of rolling these two dice and summing the numbers of spots on the up-faces.
If the standard die shows a 1, y can be 1+0=1 or 1+6=7.If it shows a 2, y can be 2+0=2 or 2+6=8.If it shows a 3, y can be 3+0=3 or 3+6=9.If it shows a 4, y can be 4+0=4 or 4+6=10.If it shows a 5, y can be 5+0=5 or 5+6=11.If it shows a 6, y can be 6+0=6 or 6+6=12.Therefore, the possible values for y are 1, 2, 3, 4, 5, 5, 7, 8, 9, 10, 11, and 12.
Find the area of triangle.
The formula for a trapezoid relates the area A, the two bases, a and b, and the height, h.
Solve for a.
multiply both sides by 2 to get
2A = (a+b)*h
divide both sides by h
to get 2A/h = a+b
subtract b from both sides to get a = 2A/h -b
3rd choice is correct
Option C - a = [tex]$\frac{2A-bh}{h}[/tex] is the correct alternative.
We have the formula for a trapezoid that relates the area - A, the two bases - a and b and the height - h as follows -
[tex]$A=\frac{(a+b)}{2} h[/tex]
We have to solve for ' a '.
Solve for x : x ( 1 + 2 + 3 + .... + n) = πOn solving -
x( 1 + 2 + 3 + .... + n) = π
[tex]\frac{xn(n+1)}{2} =\pi[/tex]
[tex]x =\frac{2\pi }{n(n+1)}[/tex]
According to the question, we have -
[tex]$A=\frac{(a+b)}{2} h[/tex]
2A = (a + b)h
2A = ah + bh
2A - bh = ah
a = [tex]$\frac{2A-bh}{h}[/tex]
Hence, Option C is the correct alternative.
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P=21+2w the answer is w=p-21/2 I need the work to go along with it
Sammy and David were selling waterbottles to raise money for new football uniforms Sammy sold 5 for every 3 waterbottles David sold together they sold 160 waterbottles how many did each boy sell
Three variable 2x-5y+z=5 3x+2y-z=17 4x-3y+2z=17
What is 4 pi cubed divided by 3
(17+4) + 9 = 17 + (4+9)
Did I do number 2 right?
Brooke buys a toothbrush and toothpaste for 2.95. If the toothbrush costs .65 less than the toothpaste. How much is the toothbrush
Given the information, we can determine that the cost of the toothbrush is $1.15. To arrive at this, we created an equation based on the given information and solved for the unknown, which in this case is the cost of the toothbrush.
Explanation:If Brooke buys a toothbrush and toothpaste for $2.95, and the toothbrush costs $.65 less than the toothpaste, we have to use the information to solve for the cost of the toothbrush.
Let's define the cost of the toothpaste as x. Therefore, the cost of the toothbrush would be x - $0.65 (since the toothbrush costs $0.65 less than the toothpaste).
The combined cost of the toothbrush and toothpaste is $2.95, so we can set up the equation: x + (x - $0.65) = $2.95
If we simplify and solve this equation, we get x = $1.80. That's the cost of the toothpaste. The cost of the toothbrush would therefore be $1.80 - $0.65 = $1.15.
So, the toothbrush costs $1.15.
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-4=g+1
A. g=-4
B. g=4
C. g=-5
D. g=-3
What is 3x-2 if x=-1/3
Givens
x = - 1/3
y = 3x - 2
Problem solve for y
y = 3(-1/3) - 2
but 3 * (1/3) = 1
and 3 * (- 1/3) = - 1
So y = -1 - 2
y = - 3
Think of this as a money question. If you are one dollar in the whole and you spend 2 more, you are not 3 in the whole which is minus 3.
A rectangular rug covers the floor in a living room one of the walls in the same living room is painted blue. Are the rug and the blue wall parallel
What is the equation of a horizontal line passing through the point (−3, 8)?
x = −3
y = 8
x = 5
y = −11
The equation of a horizontal line passing through the point (−3, 8) is y= 8
How to determine the equation of a horizontal line passing through the point (−3, 8)
From the question, we have the following parameters that can be used in our computation:
The point (−3, 8)
The equation of a horizontal line is of the form
y = c, where
c is a constant.
Since the line is horizontal, the value of y is constant for all points on the line.
In this case, the line passes through the point (−3,8), so the equation of the horizontal line is y = 8.
If f(x) = 3x + 2 and g(x) = x2 + 1, which expression is equivalent to (f*g) (x)?
Answer: The required expression is [tex]3x^3+2x^2+3x+2.[/tex]
Step-by-step explanation: We are given the following two functions :
[tex]f(x)=3x+2\\\\g(x)=x^2+1.[/tex]
We are to find the expression equivalent to [tex](f*g)(x).[/tex]
We know that
for any two functions p(x) and q(x), we have
[tex](p*q)(x)=p(x)\times q(x).[/tex]
Therefore, we get
[tex](f*g)(x)\\\\=f(x)\times g(x)\\\\=(3x+2)(x^2+1)\\\\=x^2(3x+2)+1(3x+2)\\\\=3x^3+2x^2+3x+2.[/tex]
Thus, the required expression is [tex]3x^3+2x^2+3x+2.[/tex]
(-7,8)(-9,10)(-6,11) reflected over x-axis What are the new coordinates
Find two consecutive integers whose sum is 101
Four times a number, x, plus 3 times a number, y, equals 75. Five times x minus 3 times y equals 6. Find the numbers by setting up a system of linear equations and solving the system using the elimination method.
Which function below is the inverse of f(x)=x^2-25
f(x) = x^2-25
inverse:
y = x^2-25
x = y^2-25
y = sqrt(5 +25)
Answer is B
Rhinestone Cowboy Dreadlock Holiday MacArthur Park Total Republican B 33 C 90 Democrat A 24 34 E Total 61 D 53 171 Which of the following can be determined from the table above? A. 2004-06-03-06-00_files/i0290000.jpg B. 2004-06-03-06-00_files/i0290001.jpg C. 2004-06-03-06-00_files/i0290002.jpg D. 2004-06-03-06-00_files/i0290003.jpg
B) On e2020 at least
Hope I helped!
The values that can be determined from the table are:
A = 23, B = 38, C = 19, D = 57 and E = 81
What are equations?Equations are expressions that have equal values, and they are represented by the "=" sign
How to determine the values of A to EThe table entries are given as:
Rhinestone Cowboy Dreadlock Holiday MacArthur Park Total
Republican B 33 C 90
Democrat A 24 34 E
Total 61 D 53 171
From the table, we have the following equations
[tex]B + 33 + C = 90[/tex]
[tex]A + 24 + 34 = E[/tex]
[tex]61 + D + 53 = 171[/tex]
The above equations become:
[tex]B + 33 + C = 90[/tex]
[tex]B + C = 57[/tex]
[tex]A + 24 + 34 = E[/tex]
[tex]A + 58 = E[/tex]
[tex]61 + D + 53 = 171[/tex]
[tex]D= 57[/tex]
Also from the table, we have the following equations
[tex]B + A = 61[/tex]
[tex]C + 34 = 53[/tex]
[tex]90 + E = 171[/tex]
Solve for C and E in the above equations
[tex]C + 34 = 53[/tex]
[tex]C = 19[/tex]
[tex]90 + E = 171[/tex]
[tex]E = 81[/tex]
Recall that:
[tex]A + 58 = E[/tex]
So, we have:
[tex]A + 58 = 81[/tex]
[tex]A = 23[/tex]
Recall that:
[tex]B + A = 61[/tex]
So, we have:
[tex]B + 23 = 61[/tex]
[tex]B = 38[/tex]
Hence, the values that can be determined from the table are:
A = 23, B = 38, C = 19, D = 57 and E = 81
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At an annual salary of 55000 per year what is the amount of semi monthly paychecks
What numbers below belong to the solution set of the inequality... x+16>51
38
35
16
80
55
34
I don't know how to do this
2(6-7x) = -8(x+6)
multiply the numbers inside the parenthesis with the numbers outside of them:
12 -14x = -8x-48
add 12 to each side:
-14x =-8x -36
add 8x to both sides
-6x = -36
divide both sides by-6
x = 6
A glacier advanced down a mountain from an elevation of 2010 m to 1780 m in 5 years. what was the glaciers rate of change
Answer:
[tex]-46[/tex] meters per year.
Step-by-step explanation:
We have been given that a glacier advanced down a mountain from an elevation of 2010 m to 1780 m in 5 years.
[tex]\text{Rate of change}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\text{Rate of change}=\frac{1780-2010}{5-0}[/tex]
[tex]\text{Rate of change}=\frac{-230}{5}[/tex]
[tex]\text{Rate of change}=-46[/tex]
Since the glacier is melting down, therefore, the glacier's rate of change would be [tex]-46[/tex] meters per year.
the table shows the annual profits (in thousands of dollars) of a county fair from 2008 to 2012. What must the 2012 profit be (in hundreds of dollars) to break even over the five-year period?
The 2012 profit must be 0.45 thousand dollars is equal to 4.5 hundred dollars to break even over the five-year period.
It is required to find the profit in 2012.
What is break even point?The break-even point is the point at which total cost and total revenue are equal, meaning there is no loss or gain for your small business. It tells an owner the amount of revenue needed to cover all expenses, including fixed costs.
Given:
The break-even point is the point in which a business makes no gain and no loss.
According to given question we have
Let the 2012 profit be x, then
2.5 + 1.75 + (-3.3) + (-1.4) + x = 0
4.25 - 3.3 - 1.4 + x = 0
-0.45 + x = 0
x = 0.45
Therefore, the 2012 profit must be 0.45 thousand dollars is equal to 4.5 hundred dollars to break even over the five-year period.
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Triangle MNO is an equilateral triangle with sides measuring units. What is the height of the triangle? NR units
Answer:24
Step-by-step explanation: