Answer:
y = -3x - 3.
Step-by-step explanation:
Find the slope of the line JK:
Slope = (6-4)/(3- (-3))
= 2 / 6
= 1/3.
Therefore the slope of the line perpendicular to it is - 1 / 1/3
= -3.
Now we use the point-slope form of a line to get the required equation:
y - y1 = m(x - x1)
Here m = -3 and (x1, y1) = (3, -12) so we have
y - (-12) = -3(x - 3)
y + 12 = -3x + 9
y = -3x + 9 - 12
y = -3x - 3 is the answer.
Which expression is equivalent to 1/2b -15?
A. -1/2 (b + 30)
B. -1/2 (b - 30)
C. 1/2 (b - 30)
D. 1/2 (b + 30)
The expression 1/2b -15 is equivalent to, 1/2(b-30), So option C is correct
What are expressions?An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.
For example, 2x+3
Given that,
An expression, 1/2b -15
The expressions are equivalent = ?
So now, we can take 1/2 common from the expressions
⇒ 1/2b -15(2/2)
⇒ 1/2(b -15×2)
⇒ 1/2(b - 30)
Hence, the equivalent expression is, 1/2(b - 30)
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f(x) = 4/9x + 7
linear or nonlinear?
Answer:
linear. :)
Step-by-step explanation:
Answer:
It depends on what you meant. See below.
Step-by-step explanation:
What you wrote means this:
[tex] f(x) = \dfrac{4}{9}x + 7 [/tex]
This is linear.
If you meant this
[tex] f(x) = \dfrac{4}{9x} + 7 [/tex]
or this
[tex] f(x) = \dfrac{4}{9x + 7} [/tex]
then it's non-linear.
An x in the denominator makes a function non-linear.
What is the LCM of 10 and 12?
Answer:
The LCM of 10 and 12 is 60
Step-by-step explanation:
Hope this helped! :)
Answer:
i think its 60
Step-by-step explanation:
Find the area of a regular octagon with an apothem of 8.45 cm and a side length of 7 cm. (round to the nearest whole number) A) 59 cm2 B) 118 cm2 C) 237 cm2 D) 473 cm2
Answer:
237
Step-by-step explanation:
The area of the regular octagon is 237 cm^2
How to determine the area?The given parameters are:
Apothem (a) = 8.45
Side length (s) = 7
Number of sides (n) = 8
The area of the regular octagon is then calculated as:
A = 0.5 * a * n * s
This gives
A = 0.5 * 8.45 * 8 * 7
Evaluate the product
A = 236.6
Approximate
A = 237
Hence, the area of the regular octagon is 237 cm^2
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helpppp meeee plz...
Answer:
3 coefficient po
Step-by-step explanation:
sana maka tulong
which of the given values will make the inequality n-93>175 true?
n=82
n=105
n=268
n=300
n=312
Answer:
n = 300 and n = 312
Step-by-step explanation:
n - 93 > 175
n > 175 + 93
n > 268
Therefore only the two last answers are are possible n values (n has to be more than 268, not equal)
The two numbers 300 and 312 will make the inequality n-93>175 true which are correct option (D)300 and (E)312.
What is inequality?Inequality is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is not equal.
Given inequality as:
n - 93 > 175
n > 175 + 93
n > 268
Therefore, n must be greater than 268 and not equal.
Hence, the two numbers 300 and 312 will make the inequality n-93>175 true.
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What is the slope-intercept equation for the
graph shown below?
A. y = 1/2x - 1
B. y = -1/2x - 1
C. y = -1/2 + 1
D. y = 2x - 1
what do you observe about the form of the equation of any circle whose center is at the point of origin
Ce clasă ești sa văd daca te pot ajuta
How do I write a phrase in words as an algebraic expression for 8/d?
Answer:
The quotient of 8 and d.
Step-by-step explanation:
I hope this helps you have a wonderful day! :D
What is the maximum volume in cubic inches of an open box to be made from a 10- inch by 20-inch piece of cardboard by cutting out squares of equal sides from the four corners and bending up the sides? Your work must include a statement of the function and its derivative.
Answer:
192.5 in³
Step-by-step explanation:
The cardboard is 10 by 20 before removing a square from each end. Assuming that the square is x inches wide. Therefore, the 20 in side gets reduced by x inches on both sides, or say it becomes 20 - 2x inches. On the other hand, the 10 in side is also reduced by 2x. The x value we get happens to be the height of the box when the sides are folded up.
Thus the volume V = lbh =
V = (20-2x)*(10-2x)*(x)
V = 4x³ - 60x² + 200x
On differentiating, we have dv/dx to be
dv/dx = 12x² - 120x + 200
Using general formula to find the roots of this equation, we can solve that x = 7.886 and x = 2.113
This roots we got are possible values of x, the square we cut. Since 7.886 * 2 = 15.772 inches, this is more than the 10 inch side, henceforth x = 2.113 inches.
You cut 2.113 inches from each corner to obtain the maximum volume.
The sizes of the cubes are
20 - (2 * 2.113) = 15.774
10 - (2 * 2.113) = 5.774
2.113
The volume of the cube is 15.774 * 5.774 * 2.113 = 192.5 cubic inches.
What additional information would you need to prove
Answer:
A
Step-by-step explanation:
We use the Hypotenuse Leg Theorem
When we know the hypotenuse and a leg of a triangle.
We know The Hypotenuse (TO) so we need to know A leg of the triangle which the only leg is TM and OR.
‘Find the value and figure of B’
Answer:
b = 12 in
Step-by-step explanation:
Use the Pythagorean theorem.
a^2 + b^2 = c^2
b^2 + 9^2 = 15^2
b^2 = 225 - 81
b^2 = 144
b = 12
Answer: b = 12 in
2/3z=-6
Help please!!
Answer:
z = -9
Step-by-step explanation:
Station A and Station B are 120 miles apart. A train traveling from station A to station B travels exactly 1/3 of the distance when it is held up and stops for 16 minutes. When the train continues its journey, the engineer increases its average speed by 15 mph so that the train will arrive at station B on schedule. Find the average speed of the train before it stopped for 16 minutes.
Answer:
60
Step-by-step explanation:
60
The average speed of the train was 80mph.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Here, Given that, Station A and Station B are 120 miles apart.
And, a train traveling from station A to station B travels exactly 1/3 of the distance when it is held up and stops for 16 minutes.
Let, its average speed was x mph.
Then, Total time if didn't stop = 120/x h
Now, before stop it took time =( 1/3×120)/x h =40/x h
After stop it took time = 80/(x+15) h
i.e. 40/x +16/60+ 80/(x+15) = 120/x
⇒80/(x+15)+8/30= 80/x
⇒80(1/x-1/(x+15))=8/30
⇒10×(15/x^2+15x)=1/30
⇒x^2+15x=10×15×30
⇒x^2+15x-450=0
⇒x^2+75x-60x-450=0
⇒(x+75)(x-60)=0
⇒x=60 or, x= -75
Hence. the required speed was 60mph.
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Decide if the ansewer to 7/5x11 is less than greater than or equal to 11. A.greater than B.less than C.equal to
Answer:
The answer to 7/5x11 is 15.4, so A. Greater than.
Step-by-step explanation:
7/5= 1.4, 1.4x11=15.4.
There are (2^6)^3• 2^0bacteria in a sample. What is the total number of bacteria in the sample?
Answer:
262,144
Step-by-step explanation:
2^0 = 1
(2^6)^3 = 2^18 = 262,144
Answer: 262,144.
Step-by-step explanation: (26)3(20)
=(643)(20)
=262144(20)
=(262144)(1)
=262144
At her most recent race, Sue finished in 272 minutes. That is 15% less time than the previous race. What was her time in the previous race?
Answer:
320 minutes was her time on the previous race
Step-by-step explanation:
Let the time spent on the previous race be x minutes.
Given that at her most recent race, Sue finished in 272 minutes which is 15% less time than the previous race then
x - 15% * x = 272
x - 0.15x = 272
0.85x = 272
x = 272/0.85
x = 320 minutes
Which expression has a value closest to 1? (Use 3.14 as the value of 1.)
A.
77
V10
B. 75-V74
O C.
V37-V26
3V5 – V20
D.
Answer:
C: √37 - √26
Step-by-step explanation:
√37 = 6.083
√26 = 5.1
6.083 - 5.1 = 0.983
Answer:
C
Step-by-step explanation:
the length of a room is 2 m longer than its breadth .if the area of its floor is 63 sq.m.calculate the length and the breadth of the room
Answer:
Given :-the length of a room is 2 m longer than its breadth .if the area of its floor is 63 sq.m.calculate the length and the breadth of the room
To Find :-Length and breadth
Answer :-Let the length and breadth be l + 2 and l
Now,
[tex] \large \sf \: Area = l + 2 \times l [/tex]
[tex] \large \sf \: 63 = l + 2 \times \: l[/tex]
[tex] \large \sf \: 63 = 2l + {l}^{2} [/tex]
[tex] \large \sf \: {l}^{2} + 2l - 63 = 0[/tex]
[tex] \large \sf \: {l}^{2} (9l - 7l) - 63 = 0[/tex]
[tex] \large \sf \: l(l + 9) - 7(l + 9)[/tex]
Either
[tex] \large \sf \: l = - 9[/tex]
or,
[tex] \large \sf \: l = 7[/tex]
Length can't be negative,
So,
L = 9
B = 7
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d) What would be the total cost of purchasing the number of shirts needed to use your coupon—after your coupon is applied and a 7.5% sales tax is charged on the purchase?
Answer: Multiply 7.5% by the price after subtracting the coupon's value.
Step-by-step explanation:
Let's assume that the cost of the shirts is x. So the coupon would subtract y from x so that's x-y which gives us z. Then to find z, on a calculator just put in 7.5% x z. I used variables since I don't know the value of the coupon or the original price of the shirts.
pls help me it is important to me
Answer:
no
Step-by-step explanation:
01:53:18
Which inequality represents the sentence below?
Two more than a number is less than 14.
2 + n less-than-or-equal-to 14
2 + n less-than 14
2 + n greater-than-or-equal-to 14
2 + n greater-than 14
Answer: It's the second option
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
edge 2020-2021 <3
Charmaine has 17 cars available to rent. Let C be the number of cars she would have left after renting R of them.
Answer:
C = 17 - R
Step-by-step explanation:
In this scenario, 17 cars would be the initial starting point. While C would be the final number of cars, meaning that our equation would have to equal C. If she rents R number of cars then this number is being subtracted from the initial number of cars because Charmaine would no longer have them in his/her possession. Therefore, it is being subtracted. Using this information we can create the following equation.
C = 17 - R
Find the area of the inner and the outer circles, shown in the figure below. Use 3.14 for pi.
please help me with this
Answer:
D. [tex]\sqrt{250}[/tex]
Step-by-step explanation:
First, use prime factorization of 250 to get [tex]\sqrt{2*5^3}[/tex]
Then apply the exponent rule, [tex]a^{b+c} =a^{b}*a^{c}[/tex]
=[tex]\sqrt{2*5^2*5} }[/tex]
Apply radical rule: [tex]\sqrt{ab}= \sqrt{a} \sqrt{b}, a\geq 0, b\geq 0[/tex]
=[tex]\sqrt{5^{2}} \sqrt{2*5}[/tex]
Apply radical rule: [tex]\sqrt{a^{2}} =a, a\geq 0[/tex]
=5[tex]\sqrt{2*5}[/tex]
=5[tex]\sqrt{10}[/tex]
Answer:
D. I did the math on my calculator
If you borrow $491 for one year at an interest rate of 9%, how much interest will you pay?
Answer:
44.19
Step-by-step explanation:
419*0.09=44.19
Mary ate x pounds of cherries. Leslie ate LaTeX: \frac{6}{9}6 9 more. Write an expression to represent how many pounds of cherries Leslie ate.
Answer:
The expression to represent number of cherries Leslie ate = ( x + [tex]\frac{6}{9}[/tex] ) pound.
Step-by-step explanation:
As given,
Mary ate cherries = x pound
And
Leslie ate [tex]\frac{6}{9}[/tex] more.
⇒Leslie ate cherries = ( x + [tex]\frac{6}{9}[/tex] ) pound.
Solve the inequality.
Step-by-step explanation:
subtract the value by placing it in the right side and multiply with 4.
someone solve please
Convert the following quadratic equation to vertex form. 2) 3x2 - 12x - 5
Answer:
3(x - 2)² - 17
Step-by-step explanation:
The equation of a quadratic in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Using the method of completing the square.
Given
3x² - 12x - 5 ← factor out 3 from the first 2 terms
= 3(x² - 4x) - 5
To complete the square
add/subtract ( half the coefficient of the x- term)² to x² - 4x
= 3(x² + 2(- 2)x + 4 - 4 ) - 5
= 3(x - 2)² - 12 - 5
= 3(x - 2)² - 17 ← in vertex form
