Mitch needs to do his laundry. It takes him 75 minutes to do each load
when he washes and dries the load. It takes him 43 less minutes if he
hangs up his laundry to dry. He decides to hang up one load of laundry
to dry.
Mitch writes the equation 75r -43 = 332, where x is the number of loads
of laundry he needs to do in order to determine how long it is going to
take him.
The next step Mitch wrote to solve the equation is shown here: 75r = 375
Which property did he use to get to this step?
A
addition property of equality
B
distributive property
C
subtraction property of equality
D
combining like-terms
Answer: [A] addition property of equality
Step-by-step explanation:
Mitch used the addition property of equality because he added 43 to both sides of the equation.
75r - 43 = 332
43 + (75r - 43) = (332) + 43
75r = 375
Learn more about some different properties used when solving equations here:
https://brainly.com/question/26092220
The Candle Factory is producing a new candle. It has a radius of 3 inches and a height of 5 inches. How much wax is needed to make the candle? Use 3.14 for Pi. Round to the nearest whole cubic inch.
A cylinder with a radius of 3 inches and height of 5 inches.
Recall the formulas S A = 2 pi r squared + 2 pi r h and V = pi r squared h.
141 cubic inches
236 cubic inches
443 cubic inches
565 cubic inches
Answer:
141 cubic inches
Step-by-step explanation:
The candle can be modeled as a cylinder.
To find how much wax is needed to make the candle, calculate the volume of the cylinder.
[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]
Given:
r = 3 inh = 5 inπ = 3.14Substitute the given values into the formula and solve for V:
[tex]\implies \sf V=3.14 \cdot 3^2 \cdot 5[/tex]
[tex]\implies \sf V=3.14 \cdot 9 \cdot 5[/tex]
[tex]\implies \sf V=28.26 \cdot 5[/tex]
[tex]\implies \sf V=141.3\:in^3[/tex]
Therefore, the amount of wax needed to make the candle is 141 cubic inches (nearest whole cubic inch).
Fill in the blank. In the triangle below, y=? Round your answer to two decimal places.
Answer:
z= 38°
Step-by-step explanation:
z= 90(from right angle)+52=142
180-142=38°
g(x)=f(x)-3 which statement best describes the graph of g(x) with the graph of f(x)
Answer: The graph of g(x) is the graph of f(x) shifted 3 units down.
Which equation has a constant of proportionality equal to 1/2
Choose 1 answer:
How much is Bob's net salary for the week? Question 32
Answer:
A. $152.00
Step-by-step explanation:
I'm 99% sure the net salary is just the 220 (gross salary) minus everything else taken away which is (42 + 7 + 15 + 4) = 68. 220 - 68 = 152 so Bob's net salary would be 152
Four students were asked to write an expression which has terms that have a greatest common factor of ab. The
expressions provided by the students are shown below.
Olivia
20ab-14abc
Michelle
16a+3b
Michelle
Naomi
Which student wrote the correct expression?
O Olivia
O Peyton
Naomi
18abc-13abc
Peyton
15abc+ 14ab
Answer: Peyton
Step-by-step explanation:
Michelle: Greatest common factor is 1
Naomi: Greatest common factor is abc
Olivia: Greatest common factor is 2ab
Peyton: Greatest common factor is ab
3+7=6-|-x|
Solve for x.
Thanks :)
Answer:
no solution
Step-by-step explanation:
| | is a notation for absolute value, which is the distance that a number is from 0.
you can think of this as the "positive version" of a number
so, |-x| will become: x
We can plug this into the equation, and solve like we would for any variable
3 + 7 = 6 - |-x| {simplify}
3 + 7 = 6 - x {simplify}
10 = 6 - x
Now, we can isolate x (isolate = get it alone)
10 = 6 - x
-6 - 6 {subtract 6 from both sides}
4 = -x {multiply both sides by -1 to get positive x}
·-1 ·-1
- 4 = x
{check solution:}
3 + 7 = 6 - | -4 |
10 = 6 - 4
10 = 2
FALSE
because this solution has been found to be false, there is no possible value for x
we write this as: no solution
[tex]3+7=6-|-x|\\10=6-|x|\\|x|=-4\\x\in\emptyset[/tex]
Consider a student loan of $12, 500 at a fixed APR rate of 9% for 25 years.
a. Calculate the monthly payment
b. Determine the total amount paid over the term of the loan
c. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest.
The monthly payment is; $104.9; The total amount paid over the term of the loan is; $31470
How to calculate APR?
We are given;
Loan principal = $12,500
Interest rate = 12%
Number of payments per year = 12 payments per year.
Loan term = 25 years.
Formula for monthly payment is;
PMT = (p * APR/n)/[1 - (1 + APR/n)^(-nY)]
Where;
p is principal
APR is interest rate
n is number of payments per year
Y is loan term
Thus;
PMT = (12500 * 0.09/12)/[1 - (1 + 0.09/12)^(-12 * 25)]
PMT = 93.75/(1 - 0.106288)
PMT = $104.9
B) Total amount paid over the loan term is;
A = PMT * m * n
where;
m is number of months in a year,
n is number of years
A = 104.9 * 12 * 25
A = $31470
C) The principal as a percentage of the loan is;
P/A = 12500/31470
P/A = 39.72%
Percentage paid for interest is = 100% - 39.72% = 80.28%
Read more about APR at; https://brainly.com/question/24703884
#SPJ1
please answer me please
Step-by-step explanation:
please mark me as brainlest
Please solve these questions with an explanation
Answer:
Step-by-step explanation:
DRaw the graph of f (x) = 1/2 x² -2x where -2 < x < 4
Answer:
Graphs Attached Below
Step-by-step explanation:
Hello!
Standard form of a quadratic: [tex]ax^2 + bx + c= 0[/tex]
From our Equation:
a = 1/2b = -2c = 0There are several values that are needed to drawing a parabola:
y - interceptAxis of Symmetry (AOS)Vertexx - interceptsY-interceptStandard form of a quadratic: [tex]ax^2 + bx + c= 0[/tex]
The y-intercept is the "c" value. Given that our equation has a "c" value of 0, the y -intercept is 0.
Axis of SymmetryA parabola is always symmetrical vertically. The line in which the fold happens is the Axis of Symmetry.
To calculate the AOS, we use the formula [tex]AOS = \frac{-b}{2a}[/tex], from the values of the equation.
Calculate
[tex]AOS = \frac{-b}{2a}[/tex][tex]AOS = \frac{-(-2)}{2(0.5)}[/tex][tex]AOS = \frac{2}{1}[/tex][tex]AOS = 2[/tex]The Axis of Symmetry is a vertical line, so the AOS is the line x = 2.
VertexThe vertex is the highest or lowest point on the graph of a parabola. It resides on the AOS of the graph.
To calculate the vertex, we simply have to find the y-value, given that we have the x-value from the AOS. We can find the y-value by plugging in the AOS for x in the original equation.
Calculate
[tex]f(x) = \frac12x^2 - 2x[/tex][tex]f(x) = \frac12 (2)^2 - 2(2)[/tex][tex]f(x) = 2 - 4[/tex][tex]f(x) = -2[/tex]The y-value is -2. The vertex is (2, -2).
X-interceptsThe x-intercepts are the points where the graph intersects the x-axis (y = 0).
Solve by Factoring
[tex]f(x) = \frac12 x^2 - 2x[/tex][tex]0 = \frac12x(x - 4)[/tex][tex]x = 0, x = 4[/tex]The roots are (0,0) and (4,0).
GraphNow we just draw the y-intercept, vertex, AOS, and the x-intercepts, and draw a curved line between them.
Image Attached
Domain RestrictionsThe Domain (x-values) are being restricted to all x-values that are greater than or equal to -2 and less than 4.
That means we remove the parts of the line that don't belong in that domain.
Image Attached
Find an equation for the line that passes through the point P(-5,-3) and is parallel to the line
7x + 4y
10. Use exact values.
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{y = -1.75x - 11.75}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{Goes through (-5, -3) and parallel to 7x + 4y = 10}[/tex]
Find: [tex]\textsf{The equation in slope-intercept form}[/tex]
Solution: We need to first solve for y in the equation that was provided so we can determine the slope. Then we plug in the values into the point-slope form, distribute, simplify, and solve for y to get our final equation.
Subtract 7x from both sides
[tex]\textsf{7x - 7x + 4y = 10 - 7x}[/tex][tex]\textsf{4y = 10 - 7x}[/tex]Divide both sides by 4
[tex]\textsf{4y/4 = (10 - 7x)/4}[/tex][tex]\textsf{y = (10 - 7x)/4}[/tex][tex]\textsf{y = 10/4 - 7x/4}[/tex][tex]\textsf{y = 2.5 - 1.75x}[/tex]Plug in the values
[tex]\textsf{y - y}_1\textsf{ = m(x - x}_1\textsf{)}[/tex][tex]\textsf{y - (-3) = -1.75(x - (-5))}[/tex]Simplify and distribute
[tex]\textsf{y + 3 = -1.75(x + 5)}[/tex][tex]\textsf{y + 3 = (-1.75 * x) + (-1.75 * 5)}[/tex][tex]\textsf{y + 3 = -1.75x - 8.75}[/tex]Subtract 3 from both sides
[tex]\textsf{y + 3 - 3 = -1.75x - 8.75 - 3}[/tex][tex]\textsf{y = -1.75x - 8.75 - 3}[/tex][tex]\textsf{y = -1.75x - 11.75}[/tex]Therefore, the final equation in slope-intercept form that follows the information that was provided is y = -1.75x - 11.75
if the relationships below are given in the form(input, output) which paring always describes a function
The function among the given option is height of a building in feet, height of the building in inches , Option B is the correct answer.
What is a Function ?
A function is a law that relates a dependent and an independent variable.
The options mentioned below needs to be studied to determine which forms a function.
Option A , C and D doesn't really form a function ,
For two variables need to be a function then they have to be dependant on each other and have only one output for a given input.
height of a building in feet, height of the building in inches
Height of building in feet = (height of building in inches/12)
so this is a function
Therefore Option B is the right answer.
The missing options are
If the relationships below are given in the form (input, output), which pairing always describes a function?
A) (number of doors in a car, number of cup holders in the car)
B) (height of a building in feet, height of the building in inches)
C) (beverage charge on a bill, total meal charge on the bill)
D) (distance from home during a trip, time elapsed during the trip)
To know more about Function
https://brainly.com/question/12431044
#SPJ1
Britney sells mattresses at a furniture store. She makes a 9.75% commission on each mattress she sells. Last week, Britney sold four mattresses. The sale price of each mattress is shown in the table.
How much did Britney earn last week?
Enter your answer in the box.
$
Mattress sale Amount
Mattress 1 $2400
Mattress 2 $3200
Mattress 3 $1900
Mattress 4 $800
Answer:
$809.25
Step-by-step explanation:
→ Find the sum of the sales amount
2400 + 3200 + 1900 + 800 = 8300
→ Find the amount that s commission
( 9.75 × 8300 ) ÷ 100 = $809.25
please help me i am struggling
The Equation is represented as [tex]\rm F = \dfrac{9}{5} (K -273.15 ) +32[/tex]
Option B is the answer.
What is an Equation ?An equation is am mathematical statement formed when an algebraic expression is equated by an equal sign with another algebraic expression or a constant.
A Equation is given in the question
[tex]\rm K = \dfrac{5}{9}(F -32) +273.15[/tex]
where K denotes temperature in Kelvins and F denotes Fahrenheit .
To convert the equation in terms of K it can be rewritten as follows
[tex]\rm K = \dfrac{5}{9}(F -32) +273.15\\\\K -273.15 = \dfrac{5}{9}(F -32) \\\\\dfrac{9}{5} (K -273.15 ) = F - 32\\\\F = \dfrac{9}{5} (K -273.15 ) +32[/tex]
Therefore Option B is the right answer.
To know more about Equation
https://brainly.com/question/10413253
#SPJ1
Immediate help needed please.
Can you answer and explain please
The possible values of k are k < - 1.868 or k > 0.535 in which the inequality is true.
What is a quadratic equation?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
We have a quadratic equation:
(k - 1)x² + (4k)x + k -3 = 0
Here,
a = k - 1
b = 4k
c = k - 3
As we know for distinct real roots:
D > 0
[tex]\rm {b^2-4ac}} > 0[/tex]
(4k)² - 4(k-1)(k-3) > 0
[tex]\rm 16k^2-4\left(k-1\right)\left(k-3\right) > 0[/tex]
[tex]\rm 12k^2+16k-12 > 0[/tex]
[tex]\rm 3k^2+4k-3 > 0[/tex]
[tex]\rm 3\left(k+\dfrac{2}{3}\right)^2-\dfrac{13}{3} > 0[/tex]
[tex]\rm 3\left(k+\dfrac{2}{3}\right)^2 > \dfrac{13}{3}[/tex]
[tex]\rm \left(k+\dfrac{2}{3}\right)^2 > \dfrac{13}{9}[/tex]
[tex]\rm k < \dfrac{-\sqrt{13}-2}{3}\quad \mathrm{or}\quad \:k > \dfrac{\sqrt{13}-2}{3}[/tex]
or
[tex]\rm k < -1.868 \quad \mathrm{or}\quad \:k > 0.535[/tex]
Thus, the possible values of k are k < - 1.868 or k > 0.535 in which the inequality is true.
Learn more about quadratic equations here:
brainly.com/question/2263981
#SPJ1
If f(x)=5x-2 and g(x)=2x1 find (f+g)(x)
Answer:
D
Step-by-step explanation:
5x-2+2x+1
5x+2x+1-2
7x-1
2 ft
4.5 ft
6 ft
A) 38 cubic feet
B) 54 cubic feet
C)
66 cubic feet
D) 125 cubic feet
What is the volume?
Answer:
B
Step-by-step explanation:We know Volume = (a*b*c)
Answer:
B) 54 cubic feet
Step-by-step explanation:
Which of the following best describes a tessellation?
O A. An arrangement of repeating shapes with spaces between the
shapes and overlapping shapes
B. The point about which an image is rotated in rotational symmetry
C. An arrangement of repeating shapes with no spaces or overlaps
between them
D. The axis about which an image is rotated in reflectional symmetry
The statement that best describes a tessellation is an arrangement of repeating shapes with no spaces or overlaps between them. Option C
What is tessellation?
A tessellation can be defined as a pattern of geometric shapes that fill a two-dimensional space without gaps and overlaps
It is also known to repeat infinitely in all directions.
Thus, the statement that best describes a tessellation is an arrangement of repeating shapes with no spaces or overlaps between them. Option C
Learn more about dimensional shapes here:
https://brainly.in/question/273952
#SPJ1
Find f(-4) for f(x)=9(3)^x
Answer:
[tex] f(-4) = \dfrac{1}{9} [/tex]
Step-by-step explanation:
[tex] f(x) = 9(3)^x [/tex]
[tex] f(-4) = 9(3)^{-4} [/tex]
[tex] f(-4) = 3^2 \cdot 3^{-4} [/tex]
[tex] f(-4) = 3^{-2} [/tex]
[tex] f(-4) = \dfrac{1}{9} [/tex]
Answer:
1/9
-------------
file attached belowfile attached below
a dog is moving at a constant speed of 8 m/s. what is the dog’s acceleration
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: Acceleration_{dog} = 0[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
A dog is moving at a constant speed of 8 m/s, that concludes that there's no change in its speed with respect to time.
And Acceleration is define as rate of change in velocity, but since velocity/speed is constant. change in velocity = 0
Henceforth, Acceleration of dog is 0 as well.
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Answer: Acceleration = 0 ✅
Step-by-step explanation:
Hii, let me help you out! (:
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Part 1Acceleration means "change in speed (which is also known as velocity, V, in physics) per a specific amount of time.
Part 1 is Successfully completed!
↪
Part 2Our Dog ProblemNow let's focus on finding the acceleration of the dog.
Like I said above, [tex]\sf Acceleration=change\;in\;speed\;per\;a\;specific\;amount\;of\;time[/tex]
Well, we are provided with the information that the dog's speed is constant. This means that it doesn't change. So the dog keeps on moving at a speed of 8 m/s. This means that its speed doesn't change, so the change in speed is 0. And this means that its acceleration is 0.
Voila! There's our answer, cheers! (:
___________________Hope I helped! Best wishes.
Reach far. Aim high. Dream big.
[tex]\underbrace[/tex]
the probability that Luis will pass his test is 0.82. find the probability that he will fail his statistic test
The probability of failure for Luis will be 0.18.
What is probability?
Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
The probability of passing is = 0.82
We know that the maximum probability of happening any event is 1 or 100 per cent if the probability of passing of the person is 0.82 then the probability of failure will be calculated as:-
Probability of failing = 1 - probability of passing
Probability of failing = 1 - 0.82
Probability of failing = 0.18
Therefore the probability of failure for Luis will be 0.18.
To know more about probability follow
https://brainly.com/question/24756209
#SPJ1
In your own words, explain the discriminant test. Use the discriminant test to decide whether the equation represents a parabola, ellipse or a hyperbola and explain why you know this is true. x^2 − 4xy + 3x + 25y − 6 = 0
A discriminant test is one that tells whether a formula has one, two or no solutions.
The equation represents a parabola because the discriminant of a parabola has either x or y squared and not the both.
What is a discriminant test?A discriminant test is a test that tells whether there are one, two or no solutions for a formula.
The discriminant is the part of the quadratic formula underneath the square root symbol: b²-4ac.
The discriminant of a quadratic equation is given as ax2 + bx + c = 0
A discriminant is said to be a parabola either x or y is squared and not both unlike that of an eclipse and a hyperbola.
With the given equation, x^2 − 4xy + 3x + 25y − 6 = 0, only x is squared and not both x and y.
Thus, the equation represents a parabola because the discriminant of a parabola has either x or y squared and not the both.
Learn more about discriminant test here:
https://brainly.com/question/4220311
#SPJ1
1.) I can find my Vulome if the vulome of cylinder is multiplied by 4/3 who am i?
2.)The Vulome is 1/3 that of a cylinder that has the same base and height with me. Who am I?
If the volume of a cylinder is multiplied by 4/3, it would become the volume of a sphere. Thus, you're a sphere.
How to calculate the volume of a cone?Mathematically, the volume of a cone can be calculated by using this formula:
V = 1/3 × πr²h
Where:
h is the height.r is the radius.How to calculate the volume of a sphere?Mathematically, the volume of a sphere can be calculated by using this formula:
V = 4/3 × πr³
Similarly, the volume of a cylinder can be calculated by using this formula:
V = πr²h
In this context, we can infer and logically deduce that if the volume of a cylinder is multiplied by 4/3, it would become the volume of a sphere. Also, multiplying the volume of a cylinder by 1/3 would produce the volume of a sphere.
Read more on volume of a sphere here: https://brainly.com/question/20394302
#SPJ1
(X+p)(x+q) what part of the trinomial will equal the product of p and q?
The part of the trinomial that will equal the product of p and q is the constant part
How to determine the part?The expression is given as:
(x + p)(x + q)
From the expression, p and q are both constants.
When a constant is multiplied to another, the result is a constant
This means that:
pq = constant
Hence, the part of the trinomial that will equal the product of p and q is the constant part
Read more about trinomial at:
https://brainly.com/question/1538726
#SPJ1
Expand each expression A ( x+1)^2 B(x-3)^2. C ( x+4)^2 D (x-1/2)^2
The expanded expressions are shown below:
(x + 1)² = x² + 2 · x + 1(x - 3)² = x² - 6 · x + 9(x + 4)² = x² + 8 · x + 16(x - 1/2)² = x² - x + 1/43 · (x - 5)² = 3 · (x² - 10 · x + 25) = 3 · x² - 30 · x + 75(1/2) · (x - 2)² = (1/2) · (x² - 4 · x + 4) = (1/2) · x² - 2 · x + 2How to expand perfect square trinomials
Perfect square trinomials are polynomials of grade 2 with the form (a + b)² = a² + 2 · a · b + b². In this case, we have to expand six perfect square trinomials:
a) (x + 1)² = x² + 2 · x + 1
b) (x - 3)² = x² - 6 · x + 9
c) (x + 4)² = x² + 8 · x + 16
d) (x - 1/2)² = x² - x + 1/4
e) 3 · (x - 5)² = 3 · (x² - 10 · x + 25) = 3 · x² - 30 · x + 75
f) (1/2) · (x - 2)² = (1/2) · (x² - 4 · x + 4) = (1/2) · x² - 2 · x + 2
To learn more on perfect square trinomials: https://brainly.com/question/385286
#SPJ1
A student survey his classmates to determine their favorite movies
Answer:
The answer is C. Hope it helps
se the distributive property to remove the parentheses.
-(-3v-4w+1)
Hii!
[tex]\leadsto\parallel\boldsymbol{Answer.}\parallel\gets[/tex]
_________________________________________________________
3v+4w-1
__________________________________________________________
[tex]\leadsto\parallel\boldsymbol{Explanation.}\parallel\gets[/tex]
We use the distributive property to "distribute" the minus sign.
[tex]\sf -(-3v-4w+1)=-1\cdot(-3v)+(-1)\cdot(-4w)+(-1)\cdot1}[/tex].
Simplify!
[tex]\sf 3v+4w-1}[/tex]. Which is our final answer.
Hope that this helped! Best wishes.
[tex]\textsl{Reach far. Aim high. Dream big.}[/tex]
[tex]\boldsymbol{-Greetings!-}[/tex]
_________________________________________________________
