ok
Total money = $300
money spend = $15
300 ---------------------- 100
15 ---------------------- x
x = (15 x 100)/300
x = 1500/300
x = 5
Jennie spent 5% of her money
To solve it, use a rule of three. $300 is 100%, so we need to calculate which percent is $15 of the total amount.
In a rule of three, it's necessary to use cross multiplication and then division.
That's why I multiplied 15 by 100 and then I divided by 300.
15 is 5% of $300
Does the following equation represent a growth of a decay of an exponential function? What isthe rate of the growth/decay?y = 1/2(1.5)^x
It represents a growth
The growth rate is 1.5
Which equation represents a line which is parallel to the line y = 1/3x +6x+3y=243y-x=-183y−x=−183x-y=73x−y=73x+y=-83x+y=−8
Recall that two lines are parallel if they have the same slope.
Now, the given equation is in the form
[tex]y=mx+b,[/tex]where m is the slope. Therefore, the slope of the given line is
[tex]\frac{1}{3},[/tex]and it has to be the slope of the parallel line.
Taking the options to their slope-intercept form, we can determine which equation represents a parallel line to the given line.
Answer: An equation of the form:
[tex]y=\frac{1}{3}x+b\text{.}[/tex]Where b is a constant.
Complete the function table.Input (n) Output (n + 5)-242
Answer
To complete the table, you need to substitute the values of the inputs (n) given into the output (n+5) given.
do the following which line segments with the given lengths form a right triangle9.40,4111.60,6248.55,73
From the Pythagorean Theorem, if a, b and c are the sides of a right triangle, with c being the longest side, then:
[tex]a^2+b^2=c^2[/tex]Or, equivalently:
[tex]a^2+b^2-c^2=0[/tex]Find the corresponding values of the second expression for each case. If the result is equal to 0, then those are the sides of a right triangle:
9, 40 and 41
[tex]\begin{gathered} 9^2+40^2-41^2=81+1600-1681 \\ =1681-1681 \\ =0 \end{gathered}[/tex]Then, these are the sides of a right triangle.
11, 60 and 62
[tex]\begin{gathered} 11^2+60^2-62^2=121+3600-3844 \\ =3721-3844 \\ =-123 \end{gathered}[/tex]Then, these are not the sides of a right triangle.
48, 55 and 73
[tex]\begin{gathered} 48^2+55^2-73^2=2304+3025-5329 \\ =5329-5329 \\ =0 \end{gathered}[/tex]Then, these are the sides of a right triangle.
Therefore, from the given sets of numbers, the ones that correspond to lengths of sides of a rigtr triangle, are:
[tex]\begin{gathered} 9,40,41 \\ 48,55,73 \end{gathered}[/tex]Which of the following illustratesthe associative property ofmultiplication?Enter a, b, c, d, or e.(a + b)(cd) =a. acd + bcdb. (b + a)(cd)c. (ac + bc)d d. [(a + b)c]de. (cd)(a + b)
The associative property of multiplication states that
[tex](a\cdot b)\cdot c=a\cdot(b\cdot c)[/tex]Given that (a+b)(cd), then its associative counterpart is
[tex](a+b)\mleft(cd\mright)=\lbrack(a+b)c\rbrack d[/tex]In this figure, the curve y= 3x+2-2x^2 cuts the x-axis at two points A and B, and the y-axis at the point C. Find the coordinates of A, B and C
To find the x-coordinates of A and B, find the zeroes of the equation (set y=0 and solve for x).
[tex]y=3x+2-2x^2[/tex]If y=0 then:
[tex]0=3x+2-2x^2[/tex]Writing this quadratic equation in standard form, we get:
[tex]2x^2-3x-2=0[/tex]Use the quadratic formula to find the solutions for x:
[tex]\begin{gathered} \Rightarrow x=\frac{-(-3)\pm\sqrt[]{(-3)^2-4(2)(-2)}}{2(2)} \\ =\frac{3\pm\sqrt[]{9+16}}{4} \\ =\frac{3\pm\sqrt[]{25}}{4} \\ =\frac{3\pm5}{4} \\ \Rightarrow x_1=\frac{3+5}{4}=\frac{8}{4}=2 \\ \Rightarrow x_2=\frac{3-5}{4}=\frac{-2}{4}=-\frac{1}{2} \end{gathered}[/tex]Then, the x-coordinate of A is -1/2, and the x-coordinate of B is 2. Both the y-coordinate of A and B are 0.
On the other hand, to find the y-coordinate of C, which is the point where the graph crosses the Y-axis, replace x=0:
[tex]\begin{gathered} y=3(0)+2-2(0)^2 \\ =2 \end{gathered}[/tex]Therefore, the coordinates of A, B and C are:
[tex]\begin{gathered} A(-\frac{1}{2},0) \\ B(2,0) \\ C(0,2) \end{gathered}[/tex]
Solve for y:2x-17y=13
The given equation is:
[tex]2x-17y=13[/tex]Step 1. Add 17y to both sides:
[tex]\begin{gathered} 2x-17y+17y=13+17y \\ \\ 2x=13+17y \end{gathered}[/tex]Step 2. Subtract 13 from both sides:
[tex]\begin{gathered} 2x-13=13-13+17y \\ \\ 2x-13=17y \end{gathered}[/tex]Step 3. Isolate y by dividing both sides by 17 and simplify:
[tex]\begin{gathered} \frac{2x-13}{17}=\frac{17y}{17} \\ \\ \text{ Simplify }\frac{17}{17}=1 \\ \\ \frac{2x-13}{17}=1*y \\ \\ \text{ Reorder terms} \\ y=\frac{2x-13}{17} \end{gathered}[/tex]As we don't have an x-value, we let y in terms of x, as in the equation above.
A sales person is given a choice of two salary plants plan one is a weekly salary of 800 plus 3% commission of sales. plan 2 is a straight commission of 11% of sales. how much in sales must she make in a week for both plans to result in the same salary
SOLUTION:
Let us represent the amount in sales that we are to calculate with "x".
For both plans to result in the same salary, we have;
Plan 1 = Plan 2
[tex]800\text{ + 3 \% of x = 11 \% of x}[/tex][tex]\begin{gathered} 800\text{ + 0.03x = 0.11x} \\ 800\text{ = 0.11x - 0.03x} \\ 800\text{ = 0.08x} \\ \\ \frac{0.08x}{0.08}\text{ = }\frac{800}{0.08} \\ \\ x\text{ = 10,000} \end{gathered}[/tex]The amount in sales she must make in a week for both plans to result in the same salary is 10,000
Find the measures of angles `CFE` and `DEF.` Explain or show your answer.
We can put a circle on quadrangle only if :
So,
A bicycle tire with a 16-inch radius has an angular speed of 328(pi) radians per minute. Find the linear speed of the tire in feet per second. Round to the nearest tenth.
SOLUTION
The relationship between linear and angular speed is given as
[tex]\begin{gathered} v=rw \\ \text{Where } \\ v=l\text{inear sp}eed=? \\ r=\text{ radius = 16-inch} \\ w=\text{ angular sp}eed\text{ = 328}\pi\text{ radians } \end{gathered}[/tex]Substituting the values into the equation we have
[tex]\begin{gathered} v=rw \\ v=16\times\text{328}\pi \\ v=16487.07825 \end{gathered}[/tex]An amusement park sold ride tickets in the ratio shown in the diagrams
as shown in the diagram.
Every 3 A tickets sold, B tickets were sold 5. Thus:
for A. it should be 8 tickets sold ----> false
for B. This is A + B = 3 + 5 = 8, so it should be 5:8 ----> false
for C. 3 A tickets sold, B tickets were sold 5, so its 3 to 5 -----> true
for D. A tickets sold, B tickets were sold 5, so -----> true
for E. 6 ride A tickets were sold, it should be 10 ride B tickets sold, so ----> false
for F. the ratio of 30 to 50 is 3 to 5 so, ----> true
answer: C, D and F
I need help with my math
Answer
5².2÷10 + 3.2 - 1 = 10
Explanation
To solve this, we will use the order of operation mnemonic to solve it.
PEMDAS explains that we solve the expression with power first, then multiplication, division and then the addition and then subtraction
5².2÷10 + 3.2 - 1
= (25.2÷10) + (3.2) - 1
= (50÷10) + 6 - 1
= 5 + 6 - 1
= 11 - 1
= 10
Hope this Helps!!!
Find the factors of f(x), given that x = 4 is a zero.f(x) = x3 − 7x2 + 2x + 40.
Answer:
Explanation:
Here, we want to get the factors of the given polynomial
From what we have:
[tex]\begin{gathered} x\text{ = 4} \\ \text{ Then x-4 is a factor} \end{gathered}[/tex]To get other factors, we have to divide the polynomial by the first factor obtained
Mathematically, we have that as follows:
[tex]\frac{x^3-7x^2\text{ + 2x +40}}{x-4}=x^2-9x\text{ + 20}[/tex]What we finally have to do is to factorize what was obtained
We have that as:
[tex]\begin{gathered} x^2-9x+20=x^2-4x-5x+20 \\ =x(x-4)-5(x-4) \\ =\text{ (x-5)(x-4)} \end{gathered}[/tex]So, we have the factors as (x-5)(x-4)(x-4)
An equation is shown below:5(2x − 3) = 5Part A: How many solutions does this equation have? (4 points)Part B: What are the solutions to this equation? Show your work.
Part A
The given equation is
[tex]5(2x\text{ -3\rparen=5}[/tex]as there is only one variable, the equation either has 1 solution or no solution. However, note that on the left we have a polynomial of degree 1 (a line), whenever we make it equal to a constant, we always have a solution. So in this case the solution is 1.
Part B
Now, to solve this equation first we divide both sides by 5. So we get
[tex]2x\text{ -3=1}[/tex]Then, we add 3 on both sides to get
[tex]2x=1+3=4[/tex]Finally we divide both sides by 2 to get
[tex]x=\frac{4}{2}=2[/tex]so the unique solution of the equation is x=2
Which statements about angles ABC and angles DEF is true
First, we identify the corresponding sides in the triangles. In the following image we can see corresponding sides in the same color:
For the triangles to be similar, there must a proportion between the corresponding sides.
A proportion is a number by which you multiply the sides of 1 triangle to get the sides of the other triangle. In this case, we can see that between the red sides there is a proportion of 2:
Also, between the blue sides there is a proportion of 2:
But, between the green sides, this proportion of 2 is not true, because 6x2 will be 12 and we have 14,
thus, the answer is:
They are not similar because corresponding sides are not proportional
Football game admission is $2.00 for general admission and $6.50 for reserved seats . The receipts were $3953.00 for 1297 paid admissions .How many of each ticket were sold? (round to the nearest intergar if necessary .) ___ general admission tickets sold .____reserved seating tickets sold.
Let x represent the number of general admission tickets sold.
Let y represent the number of reserved seating tickets sold.
We were told that general admission ticket costs $2 each and reserved seating ticket costs $6.50 each. This means that the cost of x general admission tickets and y reserved seating tickets would be
2x + 6.5y
The total amount received was $3953. It means that
2x + 6.5y = 3953
Also, the total number of tickets sold was 1297. It means that
x + y = 1297
x = 1297 - y
Substituting x = 1297 - y into 2x + 6.5y = 3953, it becomes
2(1297 - y) + 6.5y = 3953
2594 - 2y + 6.5y = 3953
- 2y + 6.5y = 3953 - 2594
4.5y = 1360
y = 1360/4.5
y = 302.22
Rounding to the nearest integer,
y = 302
x = 1297 - y = 1297 - 302
x = 995
995 general admission tickets were sold .
302 reserved seating tickets were sold
the equation 0 -b=-b is an example of which property
Recall that the identity property of addition states that:
[tex]0+x=x+0=x\text{.}[/tex]Answer: Third option.
Each side of a square is increased 5 inches. When this happens, the area is multiplied by 9. How many inches in the side of the original square?
The side of the original square is 2.5 inches
Define square.In geometry, a square is a flat shape with four equal sides and four right angles (90°). A square is an unique sort of parallelogram as well as an equilateral rectangle (an equilateral and equiangular one).
Let side of a square be x
The area of this square will be [tex]x^{2}[/tex]
The second square has a side that has 5 more,
Therefore, side of second square= x+5
The area of second square= [tex](x+5)^{2}[/tex]
Thee area of the second square which is 9 times the original square =
[tex](x+5)^{2}[/tex]= 9([tex]x^{2}[/tex])
use foil to multiply (x+5)(x5) = [tex]x^{2}[/tex]+10x+25 = 9[tex]x^{2}[/tex]
That is, 0 = 8[tex]x^{2}[/tex]-10x-25
Factoring quadratic expressions
0= (4x+5)(2x-5)
0 = 4x+5 or 0=2x-5
Therefore, x= -5/4 or x= 2.5.
Reject -5/4 as length cannot be negative and accept the value 2.5.
That is side of the original square x=2.5 sq in
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You leave your house and run 6 miles due west followed by 3.5 miles due north. At that time, what is your bearing from your house?
N 60° W
Explanation
Step 1
draw the situation
we have a right triangle, so we can use a trigonometric function to find the missing angle,
then
Let
[tex]\begin{gathered} \text{opposite side= 3.5 m} \\ \text{adjacent side=6 mi} \end{gathered}[/tex]so, we need a function that relates those values
[tex]\tan \alpha=\frac{opposite\text{ side}}{\text{adjacent side}}[/tex]replace
[tex]\begin{gathered} \tan x=\frac{3.5}{6} \\ \text{ Inverse tan in both sides} \\ \tan ^{-1}(\tan x)=\tan ^{-1}(\frac{3.5}{6}) \\ x=30.25 \\ \text{rounded } \\ x=30\text{ \degree} \end{gathered}[/tex]so, the direction is
N 60° W
13. SHOPPING You go to the hardware store for some building materials. You purchase 7fans (f) for a house you are remodeling and $8 worth of other materials. You return 2fans (f) that were not working properly. Write an expression that represents yourshopping. After writing your expression, simplify the expression.
The function of the situation would be:
[tex]\begin{gathered} 7\cdot f+8-2\cdot f \\ 5\cdot f+8 \end{gathered}[/tex]therefore, the expression is:
5*f + 8
7. Consider the line below.A. Find two points on this line with whole number coordinates.B. Find an equation for this line in point slope form.C. Find the equation for this line in slope intercept form. Be sure to show your work-550-5
Let take the x-intercept and the y-intercept.
• From the graph, the x-intercept (x-axis cutting point) is >>>
[tex](x_1,y_1)=(1,0)[/tex]• The y-intercept (y-axis cutting point) is >>>
[tex](x_2,y_2)=(0,-1)[/tex]Now, let's find the point slope and slope intercept form of the line.
B.Point Slope Form
[tex]y-y_1=m(x-x_1)[/tex]Where m is given by the formula,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]So, let's substitute the the points and find the point slope form:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \\ y-0=\frac{-1-0}{0-1}(x-1) \\ y-0=\frac{-1}{-1}(x-1) \\ y-0=1(x-1) \end{gathered}[/tex]Thus, the point-slope form is
[tex]y-0=1(x-1)[/tex]C.The slope intercept form is given by
[tex]y=mx+b[/tex]Where
m is the slope and b is the y-intercept
Just re-arranging the point slope form will give us the slope intercept form. Shown below:
[tex]\begin{gathered} y-0=1(x-1) \\ y=1(x-1) \\ y=x-1 \end{gathered}[/tex]The slope intercept form is
[tex]y=x-1[/tex]About 102 baby boys are born for every 100 baby girls. What is the simplified ratio of girls to boys?
Answer: 51/50
Step-by-step explanation: 102/100 = 51/50
because you divide both by 2 which is the answer
The following equations are givenEquation #1 3x+z+y=8Equation #2 5y-x=-7Equation #3 3z+2x-2y=15Equation #4 4x+5y-2z=-3a. is it possible to solve for any of the variables using only Equation #1 and Equation #27 Explain your answer. If possible, solve for the variables using only equations #1 and #2b. is it possible to solve for any of the variables using only Equation #1, Equation #2, and Equation #37 Explain your answer if possible, solve for the variables using only equations #1, #2, and #3c. if you found solutions in part b, do these solutions also hold for Equation #4?
Solution
(a). For any number of equations to be solved simultaneously, the number of equations, must be same as number of variables.
Hence, Equation (1) & (2) can't be solved simultaneously, because, only two equations are given to solve for 3 variables.
(b) From the explanation above, it is obvious that, Equation (1), (2), and (3), can be solved simultaneously, because, we have 3 variables (x, y, z), with 3 equations to solve with.
Next we do is to solve Equation (1), (2), and (3) simultaneously using substitution method.
[tex]\begin{bmatrix}3x+z+y=8\\ 5y-x=-7\\ 3z+2x-2y=15\end{bmatrix}[/tex]From the Equation 2, make y the subject of formula
[tex]\begin{gathered} 5y-x=-7 \\ 5y=-7+x \\ y=\frac{-7+x}{5} \end{gathered}[/tex]We substitute, for y in equation (1), and (3).
[tex]\begin{bmatrix}3x+z+\frac{-7+x}{5}=8\\ 3z+2x-2\cdot \frac{-7+x}{5}=15\end{bmatrix}[/tex]Simplifying,
[tex]\begin{bmatrix}z+\frac{-7+16x}{5}=8\\ 3z+\frac{14+8x}{5}=15\end{bmatrix}[/tex]make z the subject of formula
[tex]z=8-\frac{-7+16x}{5}[/tex]Substitute z in the second equation,
[tex]\begin{gathered} \begin{bmatrix}3\left(8-\frac{-7+16x}{5}\right)+\frac{14+8x}{5}=15\end{bmatrix} \\ simplifying \\ \begin{bmatrix}-8x+31=15\end{bmatrix} \\ simplifying \\ -8x=15-31=-16 \\ x=\frac{-16}{8}=-2 \end{gathered}[/tex]Now, we have the value of x, remaining y, and z, and we substitute the value of x = -2, in the equation above for z.
[tex]\begin{gathered} z=8-\frac{-7+16x}{5} \\ z=8-\frac{-7+16(2)}{5}=\frac{-7+32}{5} \\ z=\frac{25}{5}=5 \end{gathered}[/tex][tex]\begin{gathered} y=\frac{-7+x}{5}=\frac{-7+2}{5}=\frac{5}{5}=1 \\ y=1 \end{gathered}[/tex]Hence, x = -2, y = 1, z = 5
(c)
Next, we proof for the values of x, y, and z in equation (4)
Substitute, x = -2, y = 1, z = 5 in equation (4)
[tex]\begin{gathered} 4x+5y-2z=-3 \\ 4(-2)+5(1)-2(5)=-8+5-10=-13\ne-3 \\ \end{gathered}[/tex]Hence, the solution doesn't hold for the equation (4).
I need help on this pleasefirst blank: a geometric, an arithmetic
This is geometric sequence and the common ratio is equal to 1/10
Explanation:The sequence: 200, 20, 2, ....
For the sequence to be arithmetic, we must have a common difference
For the sequence to be geometric. we msut have a common ratio
common difference = next term - previous term
when next term = 20, previous term = 20
common difference = 20 - 200 = -180
when next term = 2, previous term = 20
common difference difference = 2 - 20 = -18
The common difference are not the same. Hence, it is not an arithmetic sequence
common ratio = next term/previous term
when next term = 20, previous term = 200
common ratio = 20/200 = 1/10
when next term = 2, previous term = 20
common ratio = 2/20 = 1/10
Common ratio is the same.
Hence, it is a geometric sequence.
Completing the statement:
This is geometric sequence and the common ratio is equal to 1/10
PLEASE HELP ME
Describe the transformation that was performed on parallelogram EFGH to create parallelogram E’F’G’H’. Show or explain how you got your answer.
The transformation of (x,y) from EFGH to E'F'G'H' is (x + 4, y - 2).
We can see that the coordinates of E are (3,6) and the coordinates of E' are (7,4)
Hence, we can see that,
x coordinate is increased by 3 and y-coordinate is decreased by 2.
Also, the coordinates of F are (5,6) and the coordinates of F' are (9,4).
Here also, x coordinate is increased by 3 and y-coordinate is decreased by 2.
This is happening in all vertices of the parallelogram.
Hence,
The transformation of (x,y) from EFGH to E'F'G'H' is (x + 4, y - 2).
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What is the y-intercept of function f? f(x)={-3x-2, -infinity
======================================================
Explanation:
The y intercept always occurs when x = 0.
Visually this is where the function curve crosses or touches the vertical y axis.
The input x = 0 fits into the interval [tex]-2 \le \text{x} < 3[/tex] since [tex]-2 \le 0 < 3[/tex] is a true statement. This means we'll go for the second piece of the piecewise function.
Plug x = 0 into this middle piece to get...
f(x) = -x+1
f(0) = -0+1
f(0) = 1
Tell whether the ordered pair is a solution of y=-2x+1.
the expression is,
y = -2x + 1
a)
the point is (-4,9)
put x = -4 and y = 9
9 = -2(-4) + 1
9 = 8 + 1
9 = 9
both values are same
so this pair is satisfying the equation.
b) the point is (0.5,0)
put x = 0.5 and y = 0
0 = -2(0.5) + 1
0 = -1 + 1
0 = 0
so this pair is satisfying the equation.
c)
the point (1,3)
put x = 1 and y = 3
3 = -2(1) + 1
3 = -2 + 1
3 = -1
so this pair is not satisfying the equation.
On the coordinate plane, rectangle WXYZ has vertices W(–
3,–
7), X(3,2), Y(6,0), and Z(0,–
9).
What is the area of rectangle WXYZ? If necessary, round your answer to the nearest tenth.
The area of rectangle WXYZ is 39 units sq.
What is the distance between two points?Distance between two points is the length of the line segment that connects the two given points and is find by formula
√ (x2 -x1)² + (y2-y1)²
Given that, On the coordinate plane, rectangle WXYZ has vertices W(-3,-7), X(3,2), Y(6,0), and Z(0,-9).
In the given rectangle, WX = YZ
Area of rectangle = length*width
Here, length = XY and width = WX
XY = √(6-3)²+(0-2)² = √13 units
WX = √(3+3)²+(2+7)² = √117 units
Area = XY*WX = √13*√117 = 39 units sq.
Hence, the area of rectangle WXYZ is 39 units sq.
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The landscaper recommended a mix of 3 pounds of rye grass seed with 44 pound of blue grass.seed. If the lawn needs 544 pounds of rye grass seed; how many pounds of blue grass seed would that be?
Let's use a rule of three:
Therefore,
[tex]\begin{gathered} x=\frac{544\cdot44}{3} \\ \Rightarrow x=7978.67 \end{gathered}[/tex]We would neeed 7978.67 lb of blue grass seed.
The value of the expression -2xy for x = -4.7 and y = 0.2 is _____.
-1.88
-18.8
18.8
1.88
Answer:
answer: 1.88
Step-by-step explanation:
if X=4.7 and if Y=0.2 then the expression should look like this.
-2 × -4.7 × 0.2 = -1.88
the value that x and y was assigned will be used in the expression for instance if I said Y is equal to 5 then that means that Y and 5 is used to replace Y in the equation.
Example:
X•Y= ?
when
Y=5
and
X=4
that means.
4•5=20
.
Answer:
d) 1.88
Step-by-step explanation:
Given that,
→ x = -4.7
→ y = 0.2
The given expression is,
→ -2xy
Now the required value is,
→ -2xy
→ -2(-4.7) × 0.2
→ 9.4 × 0.2 = 1.88
Hence, the value is 1.88.