Randy's initial money = $12
Randy's earnings per week = $6
Becky's initial money = -$6 (she owes )
Becky's earnings per week = $7
Number of weeks: x
The equation for each:
• Randy:
50 = 12 + 6x
• Becky:
50 = -6 + 7x
Solve each for x:
Randy:
50= 12 + 6x
50-12 = 6x
38 = 6x
38/6=x
x= 6.3
Becky:
50= -8 + 7x
50+8 =7x
58=7x
58/7=x
x= 8.28
Randy will take 6.33 weeks and Becky 8.28 weeks.
Answer:
A. Randy
Identify the Terms, Constants, Coefficients and Variables in the following equation
13x + 5y - 2 = 3
13x
From the given equation 13x + 5y - 2 = 3, we can tell that;
Variables are; x and y
Coefficients are; 13 and 5
Constants are; -2 and 3
What are the properties of the Equation?
We are given the equation;
13x + 5y - 2 = 3
A variable is a term that is subject to change and is not fixed. Thus, in our expression, the variables are x and y.
Now, the constants are terms that a single without a variable attached to them. Thus, in our expression, the constants are -2 and 3
The coefficients are basically the numbers that are attached to the variables. Thus, the coefficient of x is 13 and the coefficient of y is 5.
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The quadrilateral RSTU is inscribed in the circle shown below. S R U Jake wants to prove the theorem that says that the measure of the quadrilateral's opposite angles add to 180°. He knows that the measure of angle Ris half the measure of are STU and that the measure of angle T is half the measure of arc SRU. Which of the following is an appropriate step to prove that ZR + ZT =180°?
Arc STU and arc SRU can form the complete circle. Therefore
[tex]Therefore,[tex]\begin{gathered} 2R+2T=360^0 \\ \text{factorize left hand side} \\ 2(R+T)=360^0 \end{gathered}[/tex]Dividing both sides by 2, we have
[tex]Hence, the appropriate steps are: Assume that the measure of arcs STU and SRU add up to 360 degreesAlso, substitute 2 m
pick yes in options 2 and 3
pick no in options 1 and 4
Number 6. Find the missing measure and round to nearest 10th
Note that Cosine law can be used if three sides of the triangle are given in order to get the angles.
For example, in getting the measurement of angle C
[tex]\cos C=\frac{a^2+b^2-c^2}{2ab}[/tex]Then take the arccos to get the angle C.
From the problem, we have :
We need to find the measurement of angle F using the same formula above.
[tex]\begin{gathered} \cos F=\frac{16^2+12^2-18^2}{2(16)(12)} \\ \cos F=\frac{19}{96} \end{gathered}[/tex]Taking the arc cosine :
[tex]\begin{gathered} \angle F=\arccos (\frac{19}{96}) \\ \angle F=78.58 \end{gathered}[/tex]The answer rounded to the nearest 10th is
Describe a series of transformations Matt can perform to device if the two windows are congruent
Congruent shapes are produced by combining the three different transformations—rotations, reflections, and translations. Actually, by combining one or more of these three transformations, any pair of congruent shapes can be matched to one another.
What are transformations?A point, line, or geometric figure can be transformed in four different ways, each of which alters the shape and/or placement of the object. While Image refers to the position and ultimate shape of the object, Pre-Image refers to the shape of the thing as it was before alteration.
Given Data
We now understand that the size and shape of the figures are preserved during stiff transformations (reflections, translations, and rotations). The pre-image and the actual image concur all the time.
The following Matt's transformational skills:
Reflection
Since the reflection maintains its original shape, The line of reflection remains the same distance away from comparable points from the pre-image to the image.
As a Congruence Transformation, rotations
Rotating a figure causes it to twist. Even though the figure is the same size and shape as before, it appears to have toppled over. A clock is a fantastic example of how the earth actually rotates. Every hour or every day, the clock's connecting arms revolve around their axis. A rotation's degree determines what it is, and common rotations include 90, 180, and 270 degrees. Before going back to its original position, the figure rotates a full 360 degrees. the direction of a rotation, whether it is counterclockwise or clockwise. It is possible to determine the degree, amount, and the revolution's direction.
Transformation based on translational congruence
When an object or shape is transported from one location to another without changing its size, shape, or orientation, the movement is referred to as a translation. During a translation, also known as a slide, every point on an object or shape is moved by the same amount and in the same direction.
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#3 TV Aspect RatioUsing your knowledge of aspect ratios, find the difference between the actualscreen size or area of an older style TV with an aspect ratio of 4:3 and a newer TVwith an aspect ratio of 16:9. Assume that both TV's are 52 inches in height. Whatis the difference in the areas of the two TV's? (show all work and justify youranswer) (8 points)
3:4 ratio
height: 52 in
width: height * 4/3 = 52*4/3 = 208/3 in
Area of the TV: height*width = 52*208/3 = 3605 1/3 square inches
9:16 ratio
height: 52 in
width: height * 16/9 = 52*16/9 = 832/9 in
Area of the TV: height*width = 52*832/9 = 4807 1/9 square inches
Then, the difference in the areas is: 4807 1/9 - 3605 1/3 = 1201 7/9 square inches
please help me out fr
Christian, this is the solution to the problem:
p = 2l + 2w
Solving for l, we have:
2l = p - 2w
Dividng by 2 at both sides:
2l/2 = (p - 2w)/2
l = (p - 2w)/2
The correct answer is D.
Write the value of 17 tens in three different ways. Use the largest unit possible.
Answer:
1 and 7 and 0
Step-by-step explanation:
white ratio as a rate with a denominator of 1 2,400 copies in 3 minutes
Answer
Rate = 800 copies per minute
Explanation
Work = rate x time
Work = 2400 copies
Time = 3 minutes
Rate = work / time
Rate = 2400 / 3
Rate = 800 copies per minute
Therefore, rate is 800 copies per minute
What shape is generated when SABC is rotated around the vertical linethrough B and C?4ABA. PrismB. PyramidC. CylinderD. Cone
A triangle, when rotated about one of its sides will generate a solid in a form of a Cone.
The cone could be a hollow one or a solid-filled one, depending on the properties of the triangle being rotated.
Therefore, the shape generated is a cone.
Answer: D.
plsssssss i need hdelpppppp plss 20 points on the line
Answer:d is the correct answer.
Step-by-step explanation:
HELP ASAP I NEED ANSWER NOWW IT'S MISSING PLEASE HELP 50 POINTS
Answer:
Let [tex]g[/tex] equal the number of games.
Let [tex]r[/tex] equal the number of rides
System of Equations
[tex]2.50g+4r=52.50[/tex]
[tex]r=2g[/tex]
Step-by-step explanation:
One game costs $2.50, so [tex]g[/tex] games cost [tex]2.50g[/tex]. One ride costs $4.00, so [tex]r[/tex] rides cost [tex]4r[/tex]. The total [tex]2.50g+4r[/tex] equals $52.50: [tex]2.50g+4r=52.50[/tex]
Since Stella's number of rides she went on is twice the number of games she played, there are two times the number of games for her number of rides. [tex]r=2g[/tex]
p and q are both prime numbers. They are each less than 22 Give an example where p + q is odd but not prime. You must only write the two numbers in the answer box. Type here to search O RI e Total ma
Answer:
See below
Step-by-step explanation:
2 + 7 = 9 2 and 7 are prime the answer is odd but not prime
I dont know how to solve this , I am not familiar with it and am confused.
a) We have to calculate the total reimbursement.
We can list the types of lunches and reimbursements for each:
0. Free lunches: the school served 29,000 free lulnches and will receive $2.68 for each one.
,1. Reduced-price lunches: the school served 19,000 reduced-price lunchs and will receiv $2.28 for each one.
,2. Full price lunches: the school seved 51,000 regular-price lunches and will receive $0.25 for each one.
Then, we can calculate the total reimbursement as:
[tex]\begin{gathered} R=29000\cdot2.68+19000\cdot2.28+51000\cdot0.25 \\ R=77720+43320+12750 \\ R=133790 \end{gathered}[/tex]The lunch reimbursement should be $133,790.
b) The milk reimbursement can be estimated as $0.035 per lunch, so it can be calculated as:
[tex]\begin{gathered} M=(29000+19000+51000)\cdot0.035 \\ M=99000\cdot0.035 \\ M=3465 \end{gathered}[/tex]The milk reinbursement is $3,465.
c) We can calculate the total reinbursement as the sum of the lunch reinbursement and the milk reinbursement:
[tex]R+M=133790+3465=137255[/tex]The total reinbursement is $137,255.
d) We can calculate the average reinbursement per lunch dividing the total reinbursement by the number of lunches:
[tex]\frac{T}{L}=\frac{137255}{99000}\approx1.39[/tex]The average reinbursement is $1.39 per lunch.
Help need please!!!!!!!factorize 36a-12b-60c
Solution:
Given:
[tex]36a-12b-60c[/tex]The greatest common factor (GCF) is factored out of the expression.
The GCF is 12.
Hence,
[tex]36a-12b-60c=12(3a-b-5c)[/tex]Therefore, the factorization of the given polynomial 36a - 12b - 60c is;
[tex]12(3a-b-5c)[/tex]PLS HELP!!!!!
TRUE OR FALSE:
A single cube with a side of 1cm has the same surface-to-volume ratio as a structure containing 8 cubes with sides that equal 1cm (remember that surface of a cube with a side A is 6A2cm2 and the volume is A3cm3).
Answer:
the answer is true
Step-by-step explanation:
Here’s the question to solve. Just do the question that has the chart
Step 1:
Write the equation
[tex]x^4-x^3+3x^2\text{ - 9x }-\text{ 54 = 0}[/tex]Step 2:
Use trial and error to find one the the factor
x - 3 is a factor
Because when you substitute x = 3, the result is zero
Hence, 3 is zero of the polynomial
Step 3
Use the long division
How to solve it and how to calculate the gst and pst
Given:-
Given amount is $50.
Price of article is $24.
GST is 7%.
PST is 7%.
To find:-
The remaining amount.
The GST amount is,
[tex]\begin{gathered} 24\times\frac{7}{100}=0.24\times7 \\ \text{ =1.68} \end{gathered}[/tex]The PST amount is,
[tex]\begin{gathered} 24\times\frac{7}{100}=0.24\times7 \\ \text{ =1.68} \end{gathered}[/tex]So the total tax amount is,
[tex]1.68+1.68=3.36[/tex]Now the total amount of the article is,
[tex]24+3.36=27.36[/tex]So the remaining amount is,
[tex]50-27.36=22.64[/tex]So the remaining amount is $22.64
Out of 250 tickets in a raffle, one ticket will win a $980 prize, one ticket will win a $680 prize, and one ticket will win a $470 prize. The other tickets will win nothing. If you have a ticket, what is the expected payoff?
The expected value is given as:
[tex]E(x)=\sum ^{}_{}xP(x)[/tex]then in this case we have:
[tex]\begin{gathered} E(x)=980(\frac{1}{250})+680(\frac{1}{250})+470(\frac{1}{250}) \\ =8.52 \end{gathered}[/tex]therefore the expected payoff is $8.52
What is the volume, in cubic inches, of a rectangular prism with a height of 19in, a width of 8in, and a length of 17in?
The volume of a rectangular prism is given by
[tex]V=L\times W\times H[/tex]Where L is the length, W is the width, and H is the height of the rectangular prism.
For the given case, we have
Length = 17 in
Width = 8 in
Height = 19 in
Let us substitute these values into the above formula
[tex]\begin{gathered} V=L\times W\times H \\ V=17\times8\times19 \\ V=2584\: in^3 \end{gathered}[/tex]Therefore, the volume of the given rectangular prism is 2584 cubic inches.
jermey wants to buy a new computer the sales woman says that he can make a down payment and then pay for the computer in installments here is the formula for this scex=t-yzx= amount down y=money each month z=number of months t= total price rewrite the formula to solve for the total price of the computer
ANSWER:
[tex]t=x+yz[/tex]STEP-BY-STEP EXPLANATION:
We have the following formula for the statement
[tex]x=t-yz[/tex]They ask us to rewrite this formula solving for the total price of the computer, it would be like this:
[tex]\begin{gathered} t-yz=x \\ t-yz+yz=x+yz \\ t=x+yz \end{gathered}[/tex]will give brainlist
Which graph represents the solution to one half m is greater than or equal to negative seven elevenths?
number line with closed circle on point negative 14 over 11 and arrow shaded to the right
number line with closed circle on point negative 7 over 22 and arrow shaded to the right
number line with closed circle on point negative 14 over 11 and arrow shaded to the left
number line with closed circle on point negative 7 over 22 and arrow shaded to the left
The solution to the inequality is m ≤ -14/11 which is the correct answer would be option (C).
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
If it is "> or," the shaded arrow is drawn to the right of the inequality graph; if it is "or," it is drawn to the left.
Given the inequality, -1/2m ≥ 7/11,
Which represents the solution to one-half m is greater than or equal to negative seven elevenths
Solve for m:
⇒ -1/2m(-2) ≥ 7/11(-2)
m ≤ -14/11 [Because we are multiplying both sides by a negative value, the sign shifts]
The solution to the inequality is m ≤ -14/11 which the graph is attached below for m ≤ -14/11.
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what is 1,235,721 + 9,576,345,123
The sum of the two numbers 1,235,721 and 9,576,345,123 is 9,577,580,844 after applying the arithmetic operation.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that is +, -, ×, and ÷.
It is given that:
= 1,235,721 + 9,576,345,123
The above number expression is representing the sum of two big numbers.
After applying the arithmetic operation on the number expression:
1,235,721 + 9,576,345,123 = 9,577,580,844
Thus, the sum of the two numbers 1,235,721 and 9,576,345,123 is 9,577,580,844 after applying the arithmetic operation.
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Given that f ( x ) = 3 x − 6 f ( x ) = 3 x - 6 and g ( x ) = 2 − x 2 g ( x ) = 2 - x 2 , calculate
If it is given f(x) = 3x− 6 and g(x) = 2- x² then f(g(x)) = -6x².
To solve this problem we have to know more about mathematical functions.
What is a mathematical function?
A mathematical function is a such type of mathematical device as it establishes a special type of relation which provides an output concerning an input.
Example: f(x) = x²+ 2 where f(x) is a function of x where x is the input. If x = 3 then the output value of f(x) = 3²- 2 = 9-2 = 7.
Here we have to calculate, f(g(x)) where f is a function of g(x) and g(x) is a function of x.
g(x) = 2- x².
f(x) = 3x - 6.
Therefore,
f(g(x)) = 3( 2- x² ) - 6. [where g(x) = 2- x²]
So, f(g(x)) = 3( 2- x² ) - 6 = 6 -6x² -6 = -6x²
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The complete question:
Given that f(x) = 3x − 6 and g(x) = 2 - x² , calculate f(g(x))
Victor earns 19% commission as a salesperson. He sold a microscope that cost $368.84. How much commission did Victor earn? Round your answer to the nearest cent: $
Victor earns 19% commission
He sold a microscope that cost $368.84.
so, the commission = 19% of $368.84 = 0.19 * 368.84 = 70.0796
Rounding to the nearest cent
So,
the commission = $70.08
What do we call the total area of all exposed surfaces of a geometric solid?
The total area of all exposed surfaces of a geometric solid is called surface area .
What does it mean by surface area of geometric solid ?The area is the entire amount of space filled by flat or two-dimensional objects. In other words, the number of square units that cover the surface of a closed figure is used to represent its area.
It is quantified in square inches, or square units. The area only has length and width since 2-dimensional shapes can be measured using them.
The area is a two-dimensional measurement of the size of a flat surface, whereas surface area is a measurement of a solid shape's exposed surface (three-dimensional).
The main distinction between area and surface area is this. However, both amounts are expressed in square units, which is the same for both. Learn the distinction between area and volume as well.
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Which of the following statements is false?A. In the ordered pair (3, 7), 3 is the x-coordinateB. The point (0,5) is on the y-axis.OC The horizontal distance between the point located at (3,7) and the point located at (6, 7) is 3unitsOD. In the ordered pair (9.7), 7 is the x-coordinate,
Answer:
D. In the ordered pair (9,7), 7 is the x-coordinate
Explanation:
The ordered pairs have the form (x, y) where the first number is the x-coordinate and the second number is the y-coordinate. So, in the ordered pair (9, 7), 7 is the y-coordinate. This makes the last statement false and the answer is
D. In the ordered pair (9,7), 7 is the x-coordinate.
Model the following problem with a quadratic equation. Then solve.Find the length of a side of a square with an area of 50 ft?.Model the problem with a quadratic equation. Let x be the length of a side of the square.
The area of a square is equal to the squared of one side.
[tex]A=x^2[/tex]Using the given data, we can have the quadratic equation of
[tex]x^2\text{ -50 = 0}[/tex]We can solve for x in 2 ways
[tex]\begin{gathered} x^2\text{ = 50} \\ x\text{ = }\sqrt[]{50}\text{ = 7.07} \end{gathered}[/tex]Or by using the quadratic formula
[tex]undefined[/tex]Suppose that the functions p and q are defined as follows.
p(x)=x² +6
q(x)=√x+1
Find the following.
(q. p) (3)=
(p.q) (3)=
The most appropriate choice for function can be given by
q[tex]o[/tex]p(3) = [tex]\sqrt{15}+1[/tex]
p[tex]o[/tex]q(3) = [tex]2\sqrt{3} + 10[/tex]
What is function?
A function from A to B is a rule that maps to each element of A a unique element of B.
A is called the domain of the function and B is called the co domain of the function.
We can do addition, subtraction, multiplication, division and composition on functions.
Let f and g be two functions
f[tex]o[/tex]g(x) = f(g(x)) and g[tex]o[/tex]f(x) = g(f(x))
This is known as composition of function.
Here,
[tex]p(x) = x^2 + 6\\q(x) = \sqrt{x} +1[/tex]
q[tex]o[/tex]p(x) = q(p(x))
=[tex]q(x^2+6)[/tex]
= [tex]\sqrt{x^2+6}+1[/tex]
q[tex]o[/tex]p(3) = [tex]\sqrt{3^2+6}+1[/tex]
= [tex]\sqrt{15}+1[/tex]
p[tex]o[/tex]q(x) = p(q(x))
= p([tex]\sqrt{x}+1[/tex])
= [tex](\sqrt{x}+1)^2+6[/tex]
= [tex]x + 1 + 2\sqrt{x} + 6[/tex]
= [tex]x + 2\sqrt{x} +7[/tex]
p[tex]o[/tex]q(3) = [tex]3 + 2\sqrt{3} +7[/tex]
[tex]2\sqrt{3} + 10[/tex]
[tex]2\sqrt{3} + 10[/tex]
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Pls help I really need this!!!
For what values of x is the function
positive?
y = |x +4|-1
Answer: x > -3 or x < -5
Step-by-step explanation:
The function is positive when y > 0.
So if we make this function into an inequality, we can solve for the values of x.
0 < |x + 4| -1
1 < | x + 4 |
Absolute values make the answer always positive despite the sign so now we have to solve for x when x + 4 > 1 and when x + 4 > -1.
x = 1 - 4 = -3
x = -1 -4 = -5
So for the function to be positive,
x > -3 or x < -5
write the coordiantes of twrite the coordinates of the vertices after a rotation 270 degrees counterclockwise around the origin D( 1,5) D'( )E (1,10) E' ( )F ( 10,10) F' ( ) G ( 10,5) G' ( )
A rotation of 270 degrees counterclockwise is the same as a rotation 90 degrees clockwise.
This rotation will make a point from the first quadrant go to the fourth, from the second to the first, from third to second and from fourth to third.
If the point goes from the first quadrant to the fourth, we change the signal of the x-coordinate.
If the point goes from the second quadrant to the first, we change the signal of the y-coordinate.
If the point goes from the third quadrant to the second, we change the signal of the x-coordinate.
If the point goes from the fourth quadrant to the third, we change the signal of the y-coordinate.
Also, in all those rotations, we need to switch the x and y coordinates between themselves.
So we have that:
[tex]\begin{gathered} D(1,5)\to1st\text{ quadrant}\to D^{\prime}=(1,-5) \\ E(1,10)\to1st\text{ quadrant}\to E^{\prime}=(1,-10) \\ F(10,10)\to1st\text{ quadrant}\to F^{\prime}=(10,-10) \\ G(10,5)\to1st\text{ quadrant}\to G^{\prime}=(10,-5) \end{gathered}[/tex]