Answer:
y = -5x + 32
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
Step 1: Write in known variables
slope m = -5
y = -5x + b
Step 2: Find b
7 = -5(5) + b
7 = -25 + b
b = 32
Step 3: Write linear equation
y = -5x + 32
Answer:
y - 7 = -5(x - 5)
Step-by-step explanation:
Pre-SolvingWe are given that a line has a slope of -5 and contains the point (5,7).
We want to write the equation of this line.
The equation of this line can be written in three ways:
Point-slope form, which is [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1,y_1)[/tex] is a point.Standard form, which is ax+by=c, where a, b, and c are free integer coefficients. Slope-intercept form, which is y=mx+b, where m is the slope and b is the value of y at the y intercept.Either one of these ways works, but let's use point-slope form, as that form is the easiest.
SolvingWe can immediately substitute the values into the formula to get the equation.
We can start with the slope; replace m with -5 in the formula.
[tex]y-y_1=m(x-x_1)[/tex] => [tex]y-y_1=-5(x-x_1)[/tex]
Now, we can replace [tex]x_1[/tex] and [tex]y_1[/tex] with 5 and 7 respectively to get:
y - 7 = -5(x - 5)
If g(x) = x^2 – 2x – 6 and h(x) = 2x^2 – 5x + 2 find (h – 9) (-2)
Answer: (h-g)(-2)=18
Step-by-step explanation:
(h – g) (-2) means the same as subtracting h(-2) and g(-2). Since we are given h(x) and g(x), we can use them to solve. There are two ways to solve. One is to find h(-2) and g(-2), and then subtract them. Another way is to do (h-g)(x), then plug in x=-2. I will show both methods.
Method 1
h(-2)=2(-2)²-5(-2)+2 [exponent]
h(-2)=2(4)-5(-2)+2 [multiply]
h(-2)=8+10+2 [add]
h(-2)=20
g(-2)=(-2)²-2(-2)-6 [exponent]
g(-2)=4-2(-2)-6 [multiply]
g(-2)=4+4-6 [add then subtract]
g(-2)=2
(h-g)(-2)=20-2 [subtract h(-2) and g(-2)]
(h-g)(-2)=18
--------------------------------------------------------------------------------------------------------
Method 2
(h-g)(x)=2x²-5x+2-(x²-2x-6) [distribute -1]
(h-g)(x)=2x²-5x+2-x²+2x+6 [combine like terms]
(h-g)(x)=x²-3x+8
(h-g)(-2)=(-2)²-3(-2)+8 [plug in x=-2, exponent]
(h-g)(-2)=4-3(-2)+8 [multiply]
(h-g)(-2)=4+6+8 [add]
(h-g)(-2)=18
--------------------------------------------------------------------------------------------------------
Now, we know that (h-g)(-2)=18. We confirmed this with both methods.
5. A real estate agent earns 3.5% commission on the selling price of a home. Find the commission
earned on the sale of a $300,000 home.
$10,500
$5,500
$9,500
$3,500
Joshua is going kayaking with a group during one of his vacation days. In his vacation planning, he budgeted $50 for a kayak rental. How can Joshua determine the number of hours he can rent a kayak for himself?
Answer: Divide Kayak budget by rental rate
Step-by-step Explanation:
As Joshua is renting for himself alone, the two available options would be the Single Kayak and the Single Sea Kayak.
He can determine the number of hours to rent a Kayak for by dividing his Kayak Budget by the rental rate per hour of the 2 options available to him.
Single KayakBudget available = $50
Rental rate = $15 per hour
Hours he can rent = 50/15
= 3.33 hours
Single Sea KayakBudget available = $50
Rental rate = $18 per hour
Hours he can rent = 50/18
= 2.78 hours
Use the simple interest formula to determine the missing value. p =$1325, r =?t=2 years I=$37.10 r=?% (Do not round until the final answer. Then round to one decimal place as needed.)
Answer:
r = 1.4 %
Step-by-step explanation:
given p(principle) is 1,375$, r(interest rate) is unknown, t(time in years) is 2, and I(Interest / final balance) is 37.10$. The simple interest formula: I = prt can be rewritten as: r = I/pt to solve for r. 37.1 / ( 1325 × 2 ) = 37.1 / 2650 = 0.014 = ( 0.014 * 100 ) % = 1.4 %
Find the slope of the line that passes through each
pair of points. Express as a fraction in simplest
form. (-2,6), (1,15)
Answer:
m = 3/1
Step-by-step explanation:
m = (y2 - y1)/(x2 - x1) = (15 - 6)/(1 - (-2)) = 9/3 = 3/1
Sam hss 100 cheese slices to make sandwiches. The equation below can be used to find s, the number of sandwiches he can make based on c, the number of cheese slices per sandwich.
s=100/c
Which equation is the same when solved for c in terms of s?
F. C=100/c
G. C=s/100
H. C=100-s
J. C= s-100
h c=100-s thats the cooreect answer
Answer:
G
Step-by-step explanation:
ion kno how to explain♀️♀️
How much is 5 divided by 3/10?
Answer:
16.6666666667
Step-by-step explanation:
Answer:
16 2/3
Step-by-step explanation:
Step 1:
5/1 ÷ 3/10
Step 2:
5/1 × 10/3
Step 3:
50/3
Answer:
16 2/3
Hope This Helps :)
Hello, please help with this question. Thanks.
Answer:
x = 17
Step-by-step explanation:
4x +22 = 90
4x = 68
x = 68/4
x = 17
What the square root of 50/ 250 (rounded to 2 decimal places)? * 0.45 0.44 0.47 0.46
Answer:
[tex]Root = 0.44[/tex]
Step-by-step explanation:
Required
Determine the square root of [tex]\frac{50}{250}[/tex]
Start by simplifying the fraction
[tex]Digit = \frac{50}{250}[/tex]
Divide the numerator and denominator by 50
[tex]Digit = \frac{1}{5}[/tex]
Next, determine the square root;
[tex]Root = \sqrt{\frac{1}{5}}[/tex]
Split the squarer root
[tex]Root = \frac{\sqrt{1}}{\sqrt{5}}[/tex]
[tex]Root = \frac{1}{\sqrt{5}}[/tex]
Rationalize
[tex]Root = \frac{1}{\sqrt{5}} * \frac{\sqrt{5}}{\sqrt{5}}[/tex]
[tex]Root = \frac{\sqrt{5}}{5}[/tex]
[tex]Root = \frac{2.2360679775}{5}[/tex]
[tex]Root = 0.4472135955[/tex]
[tex]Root = 0.44[/tex] --- Approximated
What is the perimeter of the rectangle with length of 2x + 3 and width of 5x – 5? Explain your process to find the perimeter.
Answer:
14x-4
Step-by-step explanation:
length:2x+3
width:5x-5
perimeter of rectangle:2(l+b)
:2(2x+3+5x-5)
:2(7x-2)
:14x-4
•••The perimeter of rectangle(p)=14x-4
Translate and solve: 24.67 is what percent of 129? Rounded to the nearest tenth of a percent.
Answer:
31.8
Step-by-step explanation:
24.67x129
=>31.82
=>31.8
Lauren has dimes and nickels in her purse. The number of dimes is three more than seven times the number of nickels. Let n represent the number of nickels. Write an expression for the number of dimes.
Answer:
X = 7n + 3
Step-by-step explanation:
x= dimes
n=nickels
X = 7n + 3
Karen is working on a project that is due in 8 days.
So far, she has spent 3 2/5 hours on it and figures that she is about 4/8 done.
How many more hours will she need to spend on this project?
Express your answer as a decimal, rounded to the nearest hundredth
Given :
Karen spent 3 2/5 hours on it and figures that she is about 4/8 done.
To Find :
How many more hours will she need to spend on this project .
Solution :
Simplifying time spend in normal fraction .
[tex]t=3\dfrac{2}{5}=\dfrac{(3\times 5)+2}{5}\\\\\\t=\dfrac{17}{5}\ hours[/tex]
Now , time taken to complete full project .
[tex]x=\dfrac{17}{5} \times \dfrac{8}{4}\\\\x=6.8\ hours[/tex]
Therefore , hours required to complete the project is 6.8 hours .
Hence , this is the required solution .
Make up your own “which one doesn’t belong” example:
a. 8x^3-64
b. x^6+27y^3
c. 27-x^9
d. -x^3-8
Una prueba de resistencia se realiza en un circuito de 1.54 km.¿Cuántos kilómetros recorre el corredor si da 6 vueltas?
PORFAVOR AYUDA EN MENOS DE 15 MINUTOS
Answer:
La corredora correría 9 kilómetros y 24 pies.
Step-by-step explanation:
multiplique la longitud de una vuelta (1.54) por cuántos de ellos corrieron (6) para obtener cuántos kilómetros corrieron (9.24)
Julie made 25 international long-distance phone calls to London last month. The scatterplot below shows the length and cost of each phone
call she made.
Cost of International
Long Distance Phone Calls
3
Cost of Call (dollars)
.
N
.
.
0
6 12 18 24
Length of Call (minutes)
Which conclusion is best supported by the scatterplot?
Answer:b
Step-by-step explanation:
Answer:d there is no relationship time and cost varies
Step-by-step explanation:
its conman sense
Jade had $520 to spend on extra items this month. She spent .15 on art supplies, 1 10 was spent at the book store, 3 5 was spent at Chicka-fila. How much did she have left of her extra money?
Answer:
515.25 is what she got left
Step-by-step explanation:
What is 75% of 35 feet?
Answer:
26.25 feet
Step-by-step explanation:
A percentage is simply a ratio of the whole. If we assume 35 feet to be 100%, or the whole, then we can say the following:
0.75 * 35 == 26.25
Hence, 75% of 35 feet is 26.25 feet.
Cheers.
Two angles are supplementary if their sum is 180 degrees. The larger angle is 6 degrees more than five times the measure of the smaller angle. Let
x
represent the measure of the smaller angle and these two angles are supplementary, find the measure of each angle.
Answer:
Step-by-step explanation:
x+y=180
y=5*x+6
so
x+5x+6=180
6x=180-6
6x=174
x=174/6
x=29 degrees
y=29*5+6
y=145+6=151
y=151 degrees
-2times(3+8divided4)2
Answer:
20
Step-by-step explanation:
Answer:-20
Step-by-step explanation: 8/4+3=5 then -2*5 =-10*2 =-20
(I need help again)
Which number is farthest to the right
A. —15
B. —1
C. 0
D. 1
Find -5
A. -5
B. 5
C. 1/5
D. -1/5
Answer:
5
Step-by-step explanation:
on a graph all of the regular numbers are on the left
Tell which set or sets the number below belongs to: natural numbers, whole numbers, integers, rational numbers, irrational numbers, or real numbers. 8/9
Answer:
Rational numbersStep-by-step explanation:
A rational number is a number that can be written as a ratio of two integers. The are expressed as fractions. Given the value 8/9, this value is a fraction and is written as a ratio of two integers 8 and 9.
The value is neither a real number, nor an integer because integers and whole numbers are not expressed as fractions.
Natural numbers are also whole numbers starting from 1 and above. Hence 8/9 is not a natural number as well.
Note that irrational numbers are also classified as real numbers and they can not be written as a ratio of two integers.
Conclusively, 8/9 is only classified as a rational number
7. a. Use the distributive property to rewrite the equation.
Enter the new equation as your answer.
2 (x - 1) - 3 = 5
Enter your answer
8.b. Combine any like terms to rewrite the equation that you entered as an answer in part a.
Enter the new equation as your answer.
Enter your answer
9.c Use addition or subtraction to rewrite the equation that you entered as an answer in part b.
Enter the new equation as your answer.
Enter your answer
10.d. Use multiplication or division to rewrite the equation that you entered as an answer in part c.
Enter the new equation as your answer."
Answer:
Hey there!
a.
2(x-1)-3=5
2x-2-3=5
b.
2x-5=5
c.
2x=10
d.
x=5
Let me know if this helps :)
Give the next three terms in each Arithmetic Sequence and the common difference
Answer:
A) Sequence: -5, -10, -15, -20, -25, -30, -35, -40 cd = -5
B) Sequence: -1, 2, 5, 8, 11, 14, 17, 20 cd = 3
C) Sequence: 17, 19, 21, 23, 25, 27, 29, 31 cd = 2
D) Sequence: 11, 16, 21, 26, 31 , 36, 41, 46 cd = 5
E) Sequence: -9, -6, -3, 0, 3, 6, 9, 12 cd = 3
Step-by-step explanation:
A) Sequence: -5, -10, -15, -20, -25
The common difference (cd) - which is the number that we need to add to each term in order to get the next - is -5
and the next three terms are: -30, -35, -40.
B) Sequence: -1, 2, 5, 8, 11,
The common difference is 3, cd = 3
so the next three terms in the sequence are; 14, 17, 20
C) Sequence: 17, 19, 21, 23, 25,
the common difference is 2, cd = 2
so the next three terms in the sequence are: 27, 29, 31
D) Sequence: 11, 16, 21, 26, 31
the common difference is 5, cd = 5
so the next three terms of the sequence are: 36, 41, 46
E) Sequence: -9, -6, -3, 0, 3,
the common difference is 3, cd = 3
so the next three terms in the sequence are: 6, 9, 12
two consecutive integers who sum of 111
Answer:
55 and 56
Step-by-step explanation:
Let the first number = k
the second number = k + 1
k + k + 1 = 111
2k + 1 = 111
2k = 111 - 1
2k = 110
k = 110/2
k = 55
The two numbers are 55 and 56
How do you do this question?
Step-by-step explanation:
F(x) = ∫ₓᵃ sin(2t) dt
Use the identity:
-F(x) = ∫ₐˣ sin(2t) dt
Take derivative using fundamental theorem of calculus.
-F'(x) = sin(2x)
F'(x) = -sin(2x)
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.
y = 5√49 − x2
y = 0
x = 2
x = 4
Answer:
V = 4316.75 π
Step-by-step explanation:
Given that:
[tex]y = 5 \sqrt{49 -x^2}[/tex] y = 0, x = 2, x = 4
[tex]V = \pi \int \limits ^{x=4}_{x=2} y^2 \ dx[/tex]
where;
y² = 25 (49 - x²)
[tex]V = 25 \pi \int \limits ^4_2 (49-x^2) dx[/tex]
[tex]V = 25 \pi [ (49x-\dfrac{x^3}{3}]^4_2[/tex]
[tex]V = 25 \pi [ 49\times 4 -\dfrac{4^3}{3} - 2][/tex]
[tex]V = 25 \pi [ 196-21.33 - 2][/tex]
[tex]V = 25 \pi [ 172.67][/tex]
V = 4316.75 π
how many is 18 thousands x 10
Solve x[tex]x^{2} = 225[/tex]
Hi there!
~
Let's solve your equation step-by-step.
[tex]x^{2} =\ 255[/tex]
Step 1: Take square root.
[tex]x =[/tex] ± [tex]\sqrt{255}[/tex]
[tex]x = \sqrt{255}[/tex] or [tex]= - \sqrt{255}[/tex]
Hope this helped you!
CAN SOMEONE PLEASE HELP ME ASAP PLEASEEEE!!!
Answer:
11.4
Step-by-step explanation:
So we know that Triangle ACB is similar to Triangle EFD.
This means that their sides are proportional to each other.
We want to find x or side AB. To do so, we can set up a proportion.
The proportional side to AB is ED. Let's also use BC since we know its value. The proportional side to BC is DF. Thus:
[tex]\frac{AB}{ED}=\frac{BC}{DF}[/tex]
Substitute x for AB, 3.8 for Ed, 15 for BC, and 5 for DF. Thus:
[tex]\frac{x}{3.8}=\frac{15}{5}[/tex]
Reduce the right:
[tex]\frac{x}{3.8}=\frac{3}{1}[/tex]
Cross multiply:
[tex]x=11.4[/tex]
So, the value of x is 11.4
And we're done!