Answer:
1/2
Step-by-step explanation:
A line passes through the points (–5, 2) and (10, –1). Which is the equation of the line?
a. y= -1/5x+1
b. y= 1/5x+3
c. y= -5x-23
d. y= 5x+27
Answer:
a. y= -1/5x+1
Step-by-step explanation:
If we have 2 points , we can find the slope using the formula
m = (y2-y1)/(x2-x1)
= (-1-2)/(10--5)
=(-1-2)/(10+5)
= -3/15
= -1/5
The slope if -1/5
We can use the point slope form of a line to write an equation
y-y1= m(x-x1)
y-2 = -1/5(x--5)
y-2 =-1/5(x+5)
Distribute the -1/5
y-2=-1/5x -1
Add 2 to each side
y-2+2 = -1/5x -1+2
y = -1/5x+1
Step-by-step explanation:
Use this formula: Y2 - Y1
X2 -X1
Then, use point slope form: y - Y1 = m (x - X1)
m is the slopeY1 & X1 is a point on the lineThe form allows you to identify the slope & the point on the lineFinally, it'll reveal your answer!!! :)
A wood stove burns 4 same-sized logs in 2 hours.How many logs does the stove burn in 8 hours?
Answer:
16 logs
Step-by-step explanation:
4 logs in 2 hours
8 logs in 4 hours
12 logs in 6 hours
16 logs in 8 hours
Answer:
16
Step-by-step explanation:
16 Because 2 divided by 8 equals 4 then 4x4=16
PLEASE HELP AND EXPLAIN!
The table below shows how much it costs to use a music website. How much will it cost you to use website for 6 months?
Month Cost
First Month .................. Free
Second month .............. $8.50
Each additional month .... $5.25
Answer:
$29.50
Step-by-step explanation:
the artist goes to the store to buy brushes and small cans of paint. he pays $94. he buys 8 brushes that cost $5 each. the rest of the money is used for the 6 cans of paint. each can of paint cost the same amount. how much does each can of paint cost?
Answer:
$9
Step-by-step explanation:
The artist buys 8 brushes that cost $5 each, then all brushes cost
[tex]\$5\cdot 8=\$40.[/tex]
He pays $94 for all brushes and cans of paint, then all cans of paint cost
[tex]\$94-\$40=\$54.[/tex]
If he buys 6 cans of paint, then one can of paint costs
[tex]\$54:6=\$9.[/tex]
A drum and burgle corps rents instruments to members. Each burgle rents for $10 per month and each drums rents for $5 per month. Find the monthly income I if members rent 7 burgled and 9 drums. Then find the monthly income if members rent 9 burgled and 7 drums.
Answer:
Case I
$115
Case II
$125
Step-by-step explanation:
Bugles rent for $10 per month
Drums rent for $5 per month
Case I
7 bugles and 9 drums
7 * bugle cost per month + 9 * drum cost per month
7 * 10 + 9* 5
70 + 45
$115
Case II
9 bugles and 7 drums
9 * bugle cost per month + 7 * drum cost per month
9 * 10 + 7* 5
90 + 35
$125
A restaurant freezes a cherry and lime juice mixture to create slushes. Cherry juice costs $5 per quart, and lime juice costs $3 per quart. Each day, the restaurant spends a total of $36 on 8 quarts of juice. The restaurant manager organizes the information in the table below.

Which equation can be used to determine the amount of cherry juice in each mixture?
5c + 3(8 – c) = 36
5c + 3(8 – c) = 8
c + (8 – c) = 8
c + 5 = 5c
Answer:
Step-by-step explanation:O would say the first answer choice
Answer:
The first one.
Step-by-step explanation: Well it is simple, the total has to be 36, none of the other ones show 36 as the total.
Solve 3[-x + (2x +1)] =x-1
Answer:
x=-2
Step-by-step explanation:
Remove parenthesis 3(-x+(2x+1))=x-1
Collect the like terms 3(-x+2x+1)=x-1
Multiply parenthesis by 3 3(x+1)=x-1
Move terms 3x+3=x-1
Collect the like terms and calculate 3x-x=-1-3
Divide both sides by 2 2x=-4
Answer: x=-2
Step-by-step explanation:
your network wants to cut your expenses per episode. thry have given you a budget of $85,134 for the next 6 episode. how much do you have to spend per episode?
Evaluate the expression for x = 5, y = 3, and z = 14 . 5x−6y+20z / 4yz
Substitute the values of x, y and z to the expression:
[tex]x=5,\ y=3,\ z=14\\\\\dfrac{5x-6y+20z}{4yz}=\dfrac{(5)(5)-(6)(3)+(20)(14)}{(4)(3)(14)}=\dfrac{25-18+280}{(12)(14)}\\\\=\dfrac{7+280}{168}=\dfrac{287}{168}=1\dfrac{119}{168}=1\dfrac{119:7}{168:7}=1\dfrac{17}{24}[/tex]
please help!!! MAX POINTS I CAN DO//// it’s in math because i trust the math people more
i can help you with points if you would like
pls consider it i have alot
HEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEELLLLLLLLLLLPPPPPPPPPPPPP
The system results in a false statement
Please Help Quick!!!
Answer:0.16 and 6%
Step-by-step explanation:
John has 630 baseball cards he sorts the cards into stacks of 30 how many stacks can we make
Answer:21
Step-by-step explanation:
Divide 630 by 30. 30 goes into 630 21 times
Answer:
21 stacks
Step-by-step explanation:
Divide 630/30
21 stacks
Enjoy!
write the expression in terms of sine and cosine, and then simplify so that no quotients appear in the final expression. sec beta - cos beta.
A.1-cos^2beta
B.sin^2beta
C.cos^2beta
D.1
E.sin beta tan beta
Answer:
E
Step-by-step explanation:
The expression given is: sec β - cos β ( i will write "beta" instead of the symbol β)
We know that [tex]sec(x)=\frac{1}{cos(x)}[/tex]
Substituting this into the the expression and doing some algebra manipulation, we have:
[tex]sec(beta)-cos(beta)\\=\frac{1}{cos(beta)}-cos(beta)\\=\frac{1-cos^{2}(beta)}{cos(beta)}[/tex]
Using the identity [tex]cos^{2}(x)+sin^{2}(x)=1\\[/tex] (also [tex]sin^{2}(x)=1-cos^{2}(x)[/tex]), we can now write:
[tex]\frac{1-cos^{2}(beta)}{cos(beta)}\\=\frac{sin^2(beta)}{cos(beta)}\\=\frac{sin(beta)*sin(beta)}{cos(beta)}\\=\frac{sin(beta)}{cos(beta)}*sin(beta)[/tex]
We know [tex]tan(x)=\frac{sin(x)}{cos(x)}[/tex], substituting this, we have:
[tex]\frac{sin(beta)}{cos(beta)}*sin(beta)\\=tan(beta)*sin(beta)[/tex]
Answer choice E is the right answer.
The expression sec β - cos β in terms of sine and cosine simplifies to sin2 β. This is achieved by knowing that secant is the reciprocal of cosine and using the Pythagorean identity in trigonometry.
Explanation:To write the expression in terms of sine and cosine, we start by remembering that secant is the reciprocal of cosine, so sec β = 1/cos β. So, the expression sec β - cos β is equivalent to 1/cos β - cos β.
However, to remove the quotient from the expression, we multiply through by cos β to get 1 - cos2 β. So the expression sec β - cos β simplifies to 1 - cos2 β.
But remember, based on the Pythagorean identity in trigonometry, 1 - cos2 β is also equivalent to sin2 β. So that's our final simplified expression in terms of sine and cosine.
Learn more about Sine and Cosine here:https://brainly.com/question/22649800
#SPJ3
what is indicated by arrowheads on a line?
Arrows on a line mean that the line continues forever in that direction. If there are two arrows in both directions along a line, then you have a geometric line. If you only have one arrow, then it is a ray. Having no arrows indicates a segment.
use the graph to find the value of y = sin theta for the value of theta.
1/4pi radians
a. -0.7
b. 0.7
c. -0.9
d. 0.9
Answer:
y ≈ 0.7
Step-by-step explanation:
locate [tex]\frac{\pi }{4}[/tex] on the x-axis, move up the vertical line until meeting the graph then the horizontal reading gives y ≈ 0.7
what is the square root of 120
Answer: [tex]2\sqrt{30}[/tex]
Step-by-step explanation:
120
∧
12 10
∧ ∧
3 4 2 5
∧
2 2
[tex]\sqrt{120}[/tex]
= [tex]\sqrt{2*2*2*3*5}[/tex]
= [tex]2\sqrt{2*3*5}[/tex]
= [tex]2\sqrt{30}[/tex]
Please help.............
Answer:
A. -4
Step-by-step explanation:
J= Jake's Number
A= Amy's Number
2j = 3j+2
-j = 2
j = -2
check: 2(-2) = 3(-2)+2
-4 = -6+2
-4 = -4 (correct)
Jake's number is -2. Amy's is -4
Given X(4, -7). What are the coordinates of X" if
X"=R----
A. (-4, 7)
B. (0,9)
C.(-4,9)
D.(0,-7)
B. (0, 9)
Step-by-step explanation:Reflection across x=a is represented by the transformation ...
... (x, y) ⇒(2a-x, y)
Reflection across y=b is represented by the transformation ...
... (x, y) ⇒ (x, 2b-y)
The double reflection, across x=2, y=1 will result in the transformation ...
... (x, y) ⇒ (2·2-x, y) ⇒ (4-x, 2·1-y) ⇒ (4-x, 2-y)
For (x, y) = X(4, -7), the transformed point is ...
... X''(4-4, 2-(-7)) = X''(0, 9)
The double reflection across x=2 and y=1 transforms the point X(4, -7) to X''(0, 9), illustrating the sequential application of reflection transformations (4-x, 2-y).
The correct answer is option B.
A reflection across the vertical line x=a is represented by the transformation (x, y) ⇒ (2a-x, y). Similarly, a reflection across the horizontal line y=b is represented by the transformation (x, y) ⇒ (x, 2b-y). The double reflection, across x=2 and y=1, can be expressed by applying these transformations sequentially.
Starting with the point (x, y), the first reflection across x=2 yields (2·2-x, y), and then, the reflection across y=1 gives (4-x, 2·1-y). Combining these transformations, the double reflection is represented by the transformation (x, y) ⇒ (4-x, 2-y).
Now, applying this double reflection to the given point X(4, -7), we get X''(4-4, 2-(-7)) = X''(0, 9). Therefore, the transformed point after the double reflection is X''(0, 9) making option B the correct option.
Learn more about Transformations here:
https://brainly.com/question/37212834
#SPJ6
solve the system of linear equations by elimination 2x+7y=1 2x-4y=12
[tex]\left\{\begin{array}{ccc}2x+7y=1\\2x-4y=12&\text{change the signs}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}2x+7y=1\\-2x+4y=-12\end{array}\right}\qquad\text{add both sides of equations}\\.\qquad\qquad11y=-11\qquad\text{divide both sides by 11}\\.\qquad\qquad \boxed{y=-1}\\\\\text{Put the value of y to the first equation:}\\\\2x+7(-1)=1\\2x-7=1\qquad\text{add 7 to both sides}\\2x=8\qquad\text{divide both sides by 2}\\\boxed{x=4}\\\\Answer:\ \boxed{x=4\ and\ y=-1\to(4,\ -1)}[/tex]
Melinda starts with $22 and saves $10 each week. George starts with $10 and saves $13 each week. After how many weeks will they have the same amount saved?
Answer: 4
Step-by-step explanation:
Melinda: y = 10x + 22
George: y = 13x + 10
13x + 10 = 10x + 22
-10x -10x
3x + 10 = 22
-10 -10
3x = 12
÷3 ÷3
x = 4
Lets say Y is the amount they will save.
So Melinda's savings could be described by the equation Y=22+10X, where X is the number of weeks. The same goes to George, but his equation would be Y=10+13X.
To save the same amount, their equations must match:
22+10X = 10+13X
Solving this, one gets
12 = 3x
=> 4=x
So the answer is 4 weeks.
Translate the sentence into an equation.
Three times the sum of a number and 9 is 4.
Use the variable b for the unknown number.
Answer:
3* (b+9) = 4
Step-by-step explanation:
b is the unknown number
Three times the sum of a number and 9 is 4.
3* (b+9) = 4
To translate 'Three times the sum of a number and 9 is 4' into an equation, you represent the unknown number by 'b' and write the equation as 3(b + 9) = 4. Solve for 'b' by distributing the 3 and then isolating 'b' to get b = -23/3.
Translating the sentence 'Three times the sum of a number and 9 is 4' into an equation involves identifying the phrases that represent mathematical operations and the variable represented by b. The sentence describes a two-step mathematical process: finding the sum of a number (b) and 9, and then multiplying that sum by 3 to get 4. This can be written as an equation: 3(b + 9) = 4.
To solve for the unknown, which in this case is b, we first distribute the 3 inside the parentheses: 3b + 27 = 4. Then we isolate the b on one side by subtracting 27 from both sides of the equation: 3b = 4 - 27, which simplifies to 3b = -23. Finally, we divide both sides by 3 to get b on its own: b = -23/3.
translate each of the following into a variable expression
the product of mask (m) and acceleration(a)
Solve for x: 5x > -20
The answer is x > -4
To get this answer, you divide both sides by 5. This is to undo the multiplication that happens to the 'x' in '5x'. Note that 5x means 5*x or 5 times x, where x is just a placeholder for some unknown number.
Saying x > -4 means you can pick any number larger than -4.
The parabola has a focus at (−3, 0) and directrix y = 3. What is the correct equation for the parabola? x2 = −12y x2 = 3y y2 = 3x y2 = −12x
Answer:
[tex]x^2+6x+6y=0[/tex]
Step-by-step explanation:
The distance between the parabola focus and the directrix is 3, then
[tex]p=3.[/tex]
Parabola vertex is placed on the perpendicular line to the directrix and this perpendicular line passes trough the focus. Its equation is x=-3 and parabola vertex coordinates are (-3,1.5).
Branches of the parabola go in negative y-direction, then the equation of the parabola is
[tex](x-(-3))^2=-2\cdot 3(y-1.5),\\ \\(x+3)^2=-6(y-1.5),\\ \\x^2+6x+9=-6y+9,\\ \\x^2+6x+6y=0.[/tex]
Answer:
y2=-12x
Step-by-step explanation:
if f(x) = -4^x - 8 and g(x) = 5x + 6, find (f+g)(x)
Answer:
(f+g)(x) = -4^x + 5x - 2
Step-by-step explanation:
if f(x) = -4^x - 8 and g(x) = 5x + 6,
(f+g)(x) = f(x) + g(x)
= -4^x - 8 + 5x + 6
= -4^x + 5x - 2
Answer:
-4^x + 5x - 2
Step-by-step explanation:
By the additive property of function, (f+g)(x) = f(x) + g(x)
Given f(x) = -4^x - 8 and g(x) = 5x + 6
(f+g)(x) = f(x) + g(x)
= -4^x - 8 + 5x + 6
= -4^x + 5x - 2
In a parking lot of 240 red and blue cars, the ratio of red cars to blue is 3:5
How many red cars are there?
Answer:
There would be 144 red cars.
Step-by-step explanation:
3:5 is equal to 3/5
240 * (3/5) = 144
Answer:
90 red cars
Step-by-step explanation:
sum the parts of the ratio 3 + 5 = 8 parts
divide 240 by 8 to find one part of the ratio
240 ÷ 8 = 30 ← 1 part of the ratio
3 parts = 3 × 30 = 90 ← number of red cars
5 parts = 5 × 30 = 150 ← number of blue cars
A water park offers a season pass for $64 per person which includes free
admission and free parking. Admission for the water park is $14.50 per person. Parking is normally $5 for those without a season pass.
a. How many visits to the water park would you have to use for
the season
pass to be a better deal?
b. What would the total cost be for 3 visits with and without a season pass?
Answer:
Part a) The number of visits mus be greater than or equal to [tex]4[/tex]
Part b)
with season pass
The total cost is [tex]\$64[/tex]
without season pass
The total cost is [tex]\$58.5[/tex]
Step-by-step explanation:
Let
x---> the number of visit to the water park
y---> the total cost to visit the water park per person
we know that
[tex]y=(14.50+5)x=19.5x[/tex]
so
Part a) How many visits to the water park would you have to use for the season pass to be a better deal?
For [tex]y=\$64[/tex]
Substitute the value of y in the equation and solve for x
[tex]64=19.5x[/tex]
[tex]x=64/19.5=3.28\ visits[/tex]
therefore
The number of visits mus be greater than or equal to [tex]4[/tex]
Part b) What would the total cost be for 3 visits with and without a season pass?
with season pass
The total cost is [tex]\$64[/tex]
without season pass
The total cost for [tex]x=3\ visits[/tex] is
[tex]y==19.5(3)=\$58.5[/tex]
I need help with numbers 7-9 please
Answer:
7. n = 5r + 10
9. [tex] 28.50j + 18s \le 100 [/tex]
Step-by-step explanation:
7.
The table gives you these values
2 20
4 30
6 40
8 50
The left side goes up by 2 each time while the right side goes up by 10 each line.
Using that pattern, fill in a few extra lines. I did it below in bold.
0 10
1 15
2 20
4 30
6 40
8 50
The line 0, 10 shows you that b in y = mx + b is 10. Also from the fist line to the second line, as x goes from 0 to 1, a difference of 1, y goes from 10 to 15, a difference of 5. The slope is difference in y over difference in x, so
slope = m = 5/1 = 5.
The equation is
y = mx + b
y = 5x + 10
The problem uses n instead of y and r instead of x, so you get
n = 5r + 10
9.
One pair of jeans costs $28.50. j is the number of jeans. j number of jeans cost 28.50j.
One shirt costs $18. s is the number of shirts. s number of shirts cost 18s.
The total cost is the cost of the jeans plus the cost of the shirts.
The total cost is 28.50j + 18s.
She can spend up to $100. The total cost of the jeans and shirts can be less than $100 or exactly $100, but it cannot be more than $100.
cost of jeans and shirts must be less than or equal to $100
[tex] 28.50j + 18s \le 100 [/tex]
2x^2 + 5x - 12 solve this expression
Answer:
x=3/2, x=-4
Step-by-step explanation:
2x^2 + 5x - 12
First lets see if we can factor this
(2x ) ( x )
-12 = -1*12 1*-12
- 2*6 2 * -12
- 3*4 3 * -4
2 * one of these pairs - the other pair = +5
2*4 -3 = 5
Put the -3 in the first spot and the 4 in the second spot
(2x-3) ( x+4)
Using the zero product property
2x-3 =0 x+4=0
2x=3 x=-4
x = 3/2