Answer:
y = 3/4x - 1
Step-by-step explanation:
4x + 3y = 7
3y = -4x + 7
y = -4/3x + 7/3
The slope of the given line is -4/3 so the slope of a line perpendicular to it is 3/4 (negative reciprocal).
y = 3/4x + b
Substitute x = 4 and y = 2:
2 = 3/4(4) + b
2 = 3 + b
b = -1
Thus the final equation is y = 3/4x - 1
2. Mike Williams, an electrician, is single, claims 1 allowance, and earns $425 per week. Find the federal tax withheld each week
The federal tax withheld each week for Mike Williams is given as follows:
$37.
How to obtain the amount he pays in taxes?Mike Williams salary is given as follows:
$425 a week.
The range that contains the salary, from the table given at the end of the answer, is given as follows:
Between $420 and $430.
The number of allowances that he claims is given as follows:
One allowance.
Hence the federal tax withheld each week is given by the 4th column of the interval between 420 and 430, as he claims one allowance, and the numeric value of this tax is given as follows:
$37.
(which is the weekly amount that he pays in taxes).
Missing InformationThe table with the tax information is given by the image shown at the end of the answer.
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Answer!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
if a person is not a hockey player, they are not a prof athlete
if a person is a hockey player, they are a prof athlete
if a person is not a prof athlete, then they r not a hockey player
Solve the inequality and graph the solution.
k/2 – 20 ≥ –18
To draw a ray, plot an endpoint and select an arrow. Select an endpoint to change it from closed to open. Select the middle of the ray to delete it.
The graph of the inequality is attached below.
What is inequality?
In mathematics, inequalities describe the relationship between two values that are not equal. Equal means to be equal, not. The "not equal symbol (≠)" is typically used to indicate that two values are not equal. But different inequalities are used to compare the values to determine whether they are less than or greater than.
Consider, the given inequality
K/2 - 20 ≥ -18
Add 20 on both sides,
K/2 - 20 + 20 ≥ -18 + 20
K/2 ≥ 2
Multiply both sides by 2,
K/2 x 2 ≥ 2 x 2
K ≥ 4
Now to graph the inequality.
The graph of the inequality is attached below.
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Find the product of -1.5x and -0.25x.
O 0.375x²
O-1.75x²
O 0.375x
O -1.75x
Step-by-step explanation:
(-1.5)x × -0.25x = 0.375x²
remember, -×- = +
compute the integral
integral 2x+11/x^2-x-2 dx
The Integral value of (2x+11)/(x²-x-2) is[tex]2(\frac{1}{3} log|x+1|+\frac{2}{3} log|x-2|)-\frac{11}{3} (log|\frac{2}{3} x+\frac{2}{3}|-log|\frac{2}{3} x-\frac{4}{3}|)+c[/tex]
What is Integration?An integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data.
The given integral is [tex]\int\dx \frac{2x+11}{x^{2} -x-2} dx[/tex]
By partial fractions we divide the integral
Apply the sum rule:
∫f(x)±g(x)dx=∫f(x)dx±∫g(x)dx
[tex]=\int\dx \frac{2x}{x^{2} -x-2} dx+\int\dx \frac{11}{x^{2} -x-2} dx[/tex]
Let us calculate the first integral part
[tex]=\int\dx \frac{2x}{x^{2} -x-2} dx[/tex]
Let us use the partial fraction of [tex]\frac{x}{x^{2} -x-2} dx:\frac{1}{3(x+1)} +\frac{2}{3(x-2)}[/tex]
[tex]\int\dx \frac{2x}{x^{2} -x-2} dx=2\int\dx \frac{1}{3(x+1)} dx+ \frac{2}{3(x-2)} dx[/tex]
[tex]\int\dx \frac{2x}{x^{2} -x-2} dx=2(\frac{1}{3} log|x+1|+\frac{2}{3} log|x-2|)[/tex]
Now let us integrate second term.
[tex]\int\dx \frac{11}{x^{2} -x-2} dx=11\int\dx \frac{1}{x^{2} -x-2} dx[/tex]
We can write denominator as x²-x-2= (x-1/2)²-9/4
[tex]=11\int\dx \frac{1}{(x-\frac{1}{2}) ^{2} -\frac{9}{4}} dx[/tex]
We apply u substitution method
[tex]\int\dx \frac{11}{x^{2} -x-2} dx=-\frac{11}{3} (log|\frac{2}{3} x+\frac{2}{3}|-log|\frac{2}{3} x-\frac{4}{3}|)[/tex]
[tex]=2(\frac{1}{3} log|x+1|+\frac{2}{3} log|x-2|)-\frac{11}{3} (log|\frac{2}{3} x+\frac{2}{3}|-log|\frac{2}{3} x-\frac{4}{3}|)+c[/tex]
Hence, [tex]2(\frac{1}{3} log|x+1|+\frac{2}{3} log|x-2|)-\frac{11}{3} (log|\frac{2}{3} x+\frac{2}{3}|-log|\frac{2}{3} x-\frac{4}{3}|)+c[/tex] is the integral value of of (2x+11)/(x²-x-2).
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The figure below is reflected over x-axis. What are the coordinates of the image of point Y after this transformation?
The coordinates of point y after the transformation is (-6,5).
What is coordinates of point ?A pair of numbers that use the horizontal and vertical separations from the two reference axes to define a point's location on a coordinate plane. typically expressed by the x-value and y-value pair (x,y). a group of variables that accurately depict a stance. The first number on a graph represents the distance along, while the second number represents the distance up or down. For instance, the point (12,5) is located 12 units down and 5 units up.Firstly , we need to get the coordinates of the point y before the transformation
The coordinates are
(-6,-5)
By reflecting over the y-axis, we have the following change;
(x,y) becomes (-x,y)
So we have;
(6,-5)
Then we are to rotate at an angle of 180 degrees counterclockwise
The operation here will be;
(x,y) to (-x,-y)
So we have;
(6,-5) to (-6,5)
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NO LINKS!! Help me with these 2 column proofs 7aa
Here is the two column proof:
Statement Reason
Diagram GivenOS ≅ OS Reflexive property of congruence Proved===================================================
Statement Reason
Diagram Given∠C ≅ ∠C Reflexive property of congruence ProvedCan you please help me
Answer:
The Answer is B/2/middle option
Step-by-step explanation: im great at math
A store pays $70 for a bicycle. The percent of markdown is 20%. What is the selling price?
Answer: $56
Step-by-step explanation:
20% of 70=14
70-14=56
Ahmad will spend at most $34 on gifts. So far, he has spent $21 . What are the possible additional amounts he will spend?
Use c for the additional amount (in dollars) Ahmad will spend.
Write your answer as an inequality solved for c .
The additional amount Ahmad will spend if Ahmad will spend at most $34 on gifts. So far, he has spent $21 is c = 13.
What is inequality?An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. It is most frequently used to compare the sizes of two numbers on the number line.
Given:
Ahmad will spend at most $34 on gifts,
He spent = $21,
c = additional amount
The total amount he can spend now = total amount - he spent
c = 34 - 21
c = 13
Therefore, the additional amount Ahmad will spend, if Ahmad will spend at most $34 on gifts. So far, he has spent $21 is c = 13.
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94.36 rounded tenths
Answer:
94.4
Step-by-step explanation:
What is the value of the expression
4(2+y)
______
2y-x
when x = 2 and y = 47
Answer:
Step-by-step explanation:
I got 196/90
I got this by plugging in 47 for y so I got 4(2+47) and got 196 when I solved it. The bottom one I did 2(47-2) and got 90...( I don't know if it's right though, if wrong I'm sorry)
Alex came home after school one day and found that his mother had left a plate of cookies. Alex ate 1/4 of the cookies. When his sister Bernice came home, she ate 1/3 of the remaining cookies, and when Carla came home, she ate 1/2 of the cookies on the plate. When their mother came home, there were 5 cookies on the plate. How many did each child eat?
Answer: Children ate 15 cookies and 5 each because Alex ate 1/4 and bernice ate 1/3 and carla ate 1/2
and 5 were left
5 into 3 is 20
and 5 are left so
20-5 is 15
15 divide by 3 is 5
Frame calculation process in your words but the final answer is each child ate 5 cookies.
Two bells P and Q ring at intervals of 3hours and 4hours respectively. After how many hours will the two bells first ring simultaneously (at the same time)
Answer:
12 hours
Step-by-step explanation:
4 / 2
2/2
1
4 = 2²
2² x 3 = 4 x 3 = 12
Please help me on this.
Enter the number that belongs in the green box
Mr. Rooks' bank pays 4-% interest per year. He has $17,000 in the bank. How much interest would he receive in 3 years?
Mr. Rooks would receive $2,040 in interest in 3 years.
The interest rate is given as 4%, which means that for every $100 Mr. Rooks has in the bank, he will receive $4 in interest per year.
To find the total interest Mr. Rooks will receive in 3 years, we need to multiply the annual interest rate by the number of years, and then multiply that result by the amount of money Mr. Rooks has in the bank.
In this case, the calculation would be as follows:
Annual interest rate × number of years × amount in the bank = total interest
(4 / 100) × 3 × $17,000 = $2,040
Therefore, Mr. Rooks would receive $2,040 in interest in 3 years.
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Forty-five year old Jim Wiseman just got a new job earning $60,000 per year. He will save 10% of his income each year for his retirement at age 55. He must decide whether to invest his savings in Big Sky Bank which offers 20% compounded semi-annually or Valley Bank which offers 8% compounded quarterly. What compounded amount would he earn he chooses to invest his savings in Big Sky Bank? What compounded amount would he earn if he chooses to invest his savings in Valley Bank?
The compounded amount earned in Big Sky Bank is $40,365.00.
The compounded amount earned in Valley Bank is $13,248.24.
What is compound interest?It is the interest we earned on the interest.
The formula for the amount earned with compound interest after n years is given as:
A = P [tex](1 + r/n)^{nt}[/tex]
P = principal
R = rate
t = time in years
n = number of times compounded in a year.
We have,
P = 10% of 60,000
P = 6000
t = 10 years
Big sky Bank:
r = 20%
n = 2 (semiannually)
A = 6000 [tex](1 + 0.1)^{20}[/tex]
A = 6000 x [tex]1.01^{20}[/tex]
A = $40,365.00
Valley Bank:
r = 8%
n = 4 (quarterly)
A = 6000 [tex](1 + 0.02)^{40}[/tex]
A = 6000 x [tex]1.02^{40}[/tex]
A = $13,248.24
Thus,
Big Sky Bank compounded amount is $40,365.00.
Valley Bank compounded amount is $13,248.24.
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According to a weather report, there is a 53% chance it will
rain tomorrow. What is the probability that it will not rain
tomorrow?
Answer:
47% or .47
Step-by-step explanation:
Solve for the variable
m/9-1=-2
Answer:
m = -9
Step-by-step explanation:
m/9 - 1 = -2
m/9 = -1
m = -1 × 9
m = -9
------------------------------
check
-9/9 -1 = -2
-2 = -2
the answer is good
What is the slope of the line that passes through the points (2, 3) and (0,11)?
:)):))):)/):)::!:&’s
The congruent reason for 5 is (c) ASA
How to determine the congruent reason for 5?From the question, we have the following parameters that can be used in our computation:
Triangles = VWX and ZYX
The ASA similarity theorem implies that the corresponding angles of the triangles in question are similar and the sides between these angles are congruent
From the question, we can see that the following corresponding angles on the triangles:
Angles W and Y
Angles X and X
This implies that these angles are congruent angles
For the triangle to be congruent by ASA, the following sides must also be congruent
WX must be congruent to YX
This is indicated in the table of values at (3)
Hence, the additional information on the similarity of the triangles is (d) ASA
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50 POINTSSSSSS ASAP!!!! 50 POINTSSSSSS ASAP!!!! 50 POINTSSSSSS ASAP!!!!
Quadrilateral RUST has a vertex at T (5, 2).
An image displaying a quadrilateral RUST.The vertex of R is R of 1 comma 5.
What are the coordinates of T' after the translation (x, y) → (x – 1, y + 2), followed by a dilation by a scale factor of 2, centered at the origin?
A.
(8, 8)
B.
(6, 2)
C.
(4, 4)
D.
(10, 4)
Answer:
A) (8, 8)-------------------------------
Apply the rules to point T.
Translation:
T(5, 2) → T'(5 - 1, 2 + 2) = T'(4, 4)Dilation:
T'(4, 4) → T''(4*2, 4*2) = T''(8, 8)The matching choice is A.
The width of a rectangular table top is 2 1/2 feet shorter than 3 times it’s length. If the perimeter of the table is 43 feet, what is the length, L, of the table
Answer: length=6 feet
Step-by-step explanation:
For this you need to create one equation from the question and use the equation for perimeter.
equation 1 is 2W+2L=P where perimeter is 43.
equation 2 is w=3L-2.5
-Now you want to take equation two and plug it into equation 1 for w to find L
It will be 2(3L-2.5)+2L=43 and you want to solve for L
distribute the 2 2(3L-2.5)+2L=43
add up the Ls 6L-5+2L=43
add 5 to each side 8L-5=43
divide each side by 8L=48
Then you get L=6
Now use L=6 to plug into equation two to get W(width)
w=3(6)-2.5=18-2.5=15.5
Now plug in both W and L into equation 1 to make sure you get 43
P=2(15.5)+2(6)=32+12=43 this means that w and l are correct and you get the perimeter given. So length (L) is 6.
A line passes through the point (3,2) and has a slope of 4
The equation of the line that passes through the point (3,2) and has a slope of 4 is; y = 4x - 10
What is the Point-slope form?The equation of the straight line has its slope and given point.
If we have a non-vertical line that passes through any point(x1, y1) and has a gradient m. then general point (x, y) must satisfy the equation
y-y₁ = m(x-x₁)
Which is the required equation of a line in a point-slope form.
Point (3,2)
Then Slope m = 4
Now Write the equation as;
y - 2 = 4(x - 3)
y = 4x - 10
Hence, The equation of the line is; y = 4x - 10
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10. The perimeter of the table shown is 16 feet. Write an equation in
the form px + q=r to solve for x.
the value of x is 5 feets and p = 2, q = 6 and r = 16.
What is a rectangle?
Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral,
Area of rectangle is A = a*b
Perimeter = 2(a+b)
given in the question that the perimeter is 16 feet.
p= 2(3+x)
p = 6+2x
p = 2
q = 6
r = 16
2x = 10
x =5 feet.
Hence, the value of x is 5 feets.
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What are the possible rational zeros of f(x) = x^4+2x^3-3x^2-4x-12
The solution of the function f(x) = (x - 2)(x + 6)(x² + x + 2) will be 2, -3, - 1/2 + (√7/2)i, and - 1/2 - (√7/2)i.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The function is given below.
f(x) = (x⁴ + 2x³ - 3x² - 4x - 12)
Factorize the expression, then we have
f(x) = (x⁴ + 2x³ - 3x² - 4x - 12)
f(x) = x⁴ - 2x³ + 4x³ - 8x² + 5x² - 10x + 6x - 12
f(x) = x³(x - 2) + 4x²(x - 2) + 5x(x - 2) + 6(x - 2)
f(x) = (x - 2)(x³ + 4x² + 5x + 6)
f(x) = (x - 2) (x³ + 3x² + x² + 3x + 2x + 6)
f(x) = (x - 2)[x²(x + 3) + x(x + 3) + 2(x + 3)]
f(x) = (x - 2)(x + 6)(x² + x + 2)
The zeroes of the function are given as,
f(x) = 0
(x - 2)(x + 3)(x² + x + 2) = 0
x = 2, -3, - 1/2 + (√7/2)i, - 1/2 - (√7/2)i
The solution of the function f(x) = (x - 2)(x + 6)(x² + x + 2) will be 2, -3, - 1/2 + (√7/2)i, and - 1/2 - (√7/2)i.
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Given 2x + 3 is the hypotenuse, use the Pythagorean
Theorem to find the length of the side labeled x.
Answer:
24
Step-by-step explanation:
Given right triangle sides x, 2x-3, and 2x+3, you want to know the length of the side labeled x.
Pythagorean theoremThe Pythagorean theorem tells you the square of the hypotenuse is equal to the sum of the squares of the other two sides.
(2x +3)² = (2x -3)² +x²
4x² +12x +9 = 4x² -12x +9 +x²
x² -24x = 0 . . . . . subtract 4x² +12x +9
x(x -24) = 0 ⇒ x = 0 or 24
The length of the side labeled x is 24 units.
__
Additional comment
The triangle is an 8-15-17 triangle scaled up by a factor of 3.
Teena bought a bicyhcle for $528 after getting a discount of 12% taken off its normal price. Find the normal price of the bicycle.
Answer:
Originally $600.
Step-by-step explanation:
[tex]\frac{528}{88} =\frac{y}{100}[/tex]
88 · y = 528 · 100
88y = 52800
y = 600
Originally $600.
1/2 times 4/5 what’s the answer
Answer:
2/5.
Step-by-step explanation:
1/2 times 4/5 is equal to (1/2) * (4/5), which simplifies to 4/10. Since 4/10 can be simplified to 2/5, the answer is 2/5.
Answer:
the answer is 2/5 or as a decimal 0.4