Answer:
1/2
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
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]
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
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]
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]
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?
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.
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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
Please Help Quick!!!
Answer:0.16 and 6%
Step-by-step explanation:
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.
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
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]
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
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:
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
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!!! :)
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!
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.
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
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.
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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:
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.
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]
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.
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]
translate each of the following into a variable expression
the product of mask (m) and acceleration(a)
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
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:
HEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEELLLLLLLLLLLPPPPPPPPPPPPP
The system results in a false statement
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.