Answer:
x = -10
Step-by-step explanation:
Order of Operations: BPEMDAS
Step 1: Write out equation
8x - 2(x + 1) = 7x + 8
Step 2: Distribute
8x - 2x - 2 = 7x + 8
Step 3: Combine like terms
6x - 2 = 7x + 8
Step 4: Subtract 6x on both sides
-2 = x + 8
Step 5: Subtract 8 on both sides
-10 = x
Step 6: Rewrite
x = -10
Dave has $11 to spend on a $8 book and two birthday cards (c) for his friends. How much can he spend on each card if he buys the same card for each card
Answer:
$1.50
Step-by-step explanation:
What is negative 300 minus 150
Answer: -450 since negative minus a positive makes it even more negative
Find the Autocorrelation function of the following periodic function: X(t) = A sin(wt +θ) 21 With T=2π/w the period, A, θ, and w are constants.
Answer:
[tex]\mathbf{R(\tau) = \dfrac{A^2}{2} cos (\omega \tau)}[/tex]
Step-by-step explanation:
To find Autocorrelation function of the following periodic function
Given that:
X(t) = A sin(wt +θ)
with the period T=2π/w , A, θ, and w are constants.
The autocorrelation function of periodic function with period and phase θ can be expressed as:
[tex]R(\tau) = \dfrac{1}{T} \int \limits ^{T/2}_{-T/2} x(t) *x(t - \tau) \ dt[/tex]
[tex]R(\tau) = \dfrac{A^2}{T} \int \limits ^{T/2}_{-T/2} \ A sin ( \omega t + \theta)*A sin [ \omega (t- \tau ) + \theta] \ dt[/tex]
where;
[tex]sinAsin B = \dfrac{1}{2}[cos (A-B) -cos (A+B)][/tex]
Then;
[tex]R(\tau) = \dfrac{A^2}{2T} \int \limits ^{T/2}_{-T/2} \ cos ( \omega t- \omega \tau + \theta - \omega t - \theta) - cos (\omega t - \omega \tau + \theta + \omega t + \theta) \ dt[/tex]
[tex]R(\tau) = \dfrac{A^2}{2T} \int \limits ^{T/2}_{-T/2} \ cos ( - \omega \tau ) - cos (2 \omega t - \omega \tau + 2 \theta) \ dt[/tex]
[tex]R(\tau) = \dfrac{A^2}{2T} \int \limits ^{T/2}_{-T/2} \ cos ( - \omega \tau ) \ dt - \dfrac{1}{2T} \int \limits ^{T/2}_{-T/2} cos (2 \omega t - \omega \tau + 2 \theta) \ dt[/tex]
The term 2 is the cosine wave of frequency and the phase = [tex]- w \tau + 2 \theta[/tex]
if we integrate that, the second term in the expansion for R(t) = zero
As such,
[tex]R(\tau) = \dfrac{A^2}{2T} \int \limits^{T/2}_{-T/2} \ cos ( - \omega \tau ) dt[/tex]
where ;
[tex]cos (-\omega \tau )[/tex]is constant
Then :
[tex]R(\tau) = \dfrac{A^2}{2T} cos (-\omega \tau) [t]^{T/2}_{-T/2}[/tex]
[tex]R(\tau) = \dfrac{A^2}{2T} cos (-\omega \tau) \times [\dfrac{T}{2}+ \dfrac{T}{2}][/tex]
[tex]R(\tau) = \dfrac{A^2}{2T} cos (-\omega \tau) \times [\dfrac{2T}{2}][/tex]
[tex]R(\tau) = \dfrac{A^2}{2T} cos (-\omega \tau) \times T[/tex]
[tex]R(\tau) = \dfrac{A^2}{2} cos (-\omega \tau)[/tex]
since [tex]cos (-\omega \tau) = cos (\omega \tau)[/tex]
[tex]\mathbf{R(\tau) = \dfrac{A^2}{2} cos (\omega \tau)}[/tex]
miranda made some cupcakes for the school bake sale. Of the cupcakes 1/2 are choclate and 1/2 are strawberry. Of the strawberry cupcakes, 1/3 are frosted with vanilla frosting, and the rest are frosted with choclate frosting. What portion of the cupcakes are strawberry with chocalate frosting? I also need to be quick and show work
Answer:
2/3
Step-by-step explanation:
half are choclate so the rest is 50% and 1/3 is vanilla so 2/3 are strawberry and chocolate
1/3 portion of the cupcakes are strawberry with chocolate frosting.
What is portion?An individual part or share of something is called as portion.
It also refers to the divide something into parts.
Now it is given that,
Portion of chocolate cupcakes = 1/2
Portion of strawberry cupcakes = 1/2
Of the strawberry cupcakes.
frosted with vanilla frosting = 1/3
frosted with chocolate frosting = 1-1/3 = 2/3
Since, 1/2 portion of all the cupcakes are strawberry cakes and out of 1/2, 1/3 are frosted with vanilla frosting and 2/3 are frosted with chocolate frosting.
strawberry cupcakes frosted with chocolate frosting = 2/3 of 1/2 = 2/6
⇒strawberry cupcakes frosted with chocolate frosting = 1/3
Hence,1/3 portion of the cupcakes are strawberry with chocolate frosting.
Learn more about portions :
https://brainly.com/question/18884319
#SPJ2
-5/2 (3x + 4) < 6 - 3x
Step-by-step explanation:
here is the ans
please check
Find the quotient of 9216 and 150
Answer: 61.44
Step-by-step explanation:
To find the quotient of 9216 and 150, it means to divide.
9216/150=61.44
Which of the following is a rational number
Label each of the triangles illustrated below
Answer:
a. Equilateral
b. Scalene
c. Isosceles
d. Right
e. Obtuse
f. Acute
Step-by-step explanation:
pf
While Abbie is jogging, she moves forward 85 cm every second. How many seconds will Abbie take to jog 8.5 meters?
Thank you very much !!!!!! :D
Answer:
It will take Abbey 10 seconds to move 8.5 meters
Step-by-step explanation:
100 cm makes one meter
So 85 cm=85/100
85 cm. = 0.85 meter
So Abbey travels 0.85 meters every second
One second= 0.85 meters
Let the unknown time be x
X= 8.5 meters/0.85
X= 10 seconds
It will take Abbey 10 seconds to move 8.5 meters
I don’t understand this
Answer: OPTION A
Step-by-step explanation:
The distance between any number is always positive so we should apply the absolute value.
The distance between numbers=number 1-number2 (or vise versa, and that is why we need absolute value)
In your question, the two numbers are 3/4 and 2. Applying to the expression above, the distance between two numbers should be |3/4-2| or |2-3/4|.
The only option in your case is |3/4-2| and this is it.
Hope this helps!! :)
Please let me know if you have any question
{...-3, -2,-1, 0, 1, 2, 3...}
Real Numbers
Whole Numbers
Natural Numbers
Integers
Rational
Answer:
they are integers and also rational numbers
Find the median for the given set of data.
5/8, 3/4, 1&1/8, 1&1/4
A. 15/16
B. 7/8
C. 13/16
What’s the writing in the form of a/b: -16 *
Answer:
-16/1
Step-by-step explanation:
-16 in the form a/b can be written as -16/1.
Is 1/6 rational or irrational
In the 1970s, due to world events, there was a gasoline shortage in the United States. There were often long lines of cars waiting at gas stations. Part A: If there were 41 cars in a line that stretched 388 feet, what is the average car length? Assume that the cars are lined up bumper-to-bumper. Round your answer to the nearest tenth of a foot.
Answer:
Part A: The average car length is 9.1 feet to the nearest tenth foot
Part B: The line would be 9100 feet to contained 1000 cars
Step-by-step explanation:
* Lets explain how to solve the problem
# Part A:
- There were 62 cars in a line that stretched 567 feet
- The cars are lined up bumper-to-bumper
- That means there is no empty spaces between the cars
* To find the average length of the car we will divide the length of
the line by the numbers of the cars
∵ The average car length = length of the line/number of cars
∵ The length of the line is 567 feet
∵ The numbers of the cars is 62 cars
∴ The average car length = 567/62 = 9.1 feet
* The average car length is 9.1 feet to the nearest tenth foot
# Part B:
- There are 1000 cars
- We need to find the length of line which contained the cars
∵ The average car length = length of the line/number of cars
∵ The average of car length is 9.1 feet
∵ The number of the cars is 1000 cars
∴ 9.1 = length of the line/1000
- Multiply both sides by 1000
∴ The length of the line = 9.1 × 1000 = 9100 feet
∴ The line would be 9100 feet to contained 1000 cars
What’s the difference/same with y/x and y1-y2/x2-x1? Are they both the same?
They are both similar but not entirely the same.
The first expression y/x means we divide y over x. We divide two values here and we are not subtracting first before division. This expression is useful for when you want to find the variation constant in the equation y = kx (for direct proportion equations).
The other expression (y2-y1)(x2-x1) is where we first subtract the y values, and do the same for the x values, before we divide. This computes the slope of the line through the two points (x1,y1) and (x2,y2). It's also useful to figure out the average rate of change (one application of slope). For problems involving time versus distance, the average rate of change is the average speed in which the object is moving.
Read the situations in the table below. Then drag a graph and equation to represent
each situation indicate whether each of the relationships is proportional or non-
proportional
Answer:
Step-by-step explanation:
"Tamara runs 5 miles each week"
Let Tamara runs 'x' weeks then equation that represents the total distance covered by Tamara will be,
1). y = 5x
2). Here 'y' is directly proportional to the number of weeks 'x'.
3). And the graph when plotted will start from 0. Therefore, graph (1) will be the graph for the given equation.
"Tamara runs 5 minutes more than she walks each day."
1). If Tamara walks 'x' minutes daily and she runs for y minutes then relation between x and y will be,
y = x + 5
2). y and x are non proportional.
3). Graph will have y-intercept = 5
Answer:
ik somebody answer already n stuff
Step-by-step explanation:
Work the following area application problem.
You wish to paint a storage shed. Its four walls measure 5 ft. high and 8 ft. wide each. If one gallon of paint covers 160
sq. ft., how many gallons of paint will you need?
Gallons of paint required =
a. 1
b. 2
c. 3
d. 4
Answer: a. 1
Step-by-step explanation:
There are 4 walls in total, and each wall measures 5ft high, 8ft wide
5 × 8=40 ft² for each wall
4×40=160 ft² for 4 walls
------------------
stated one gallon cover 160 ft²
160 ÷ 160=1 gallon
Hope this helps!! :)
Please let me know if you have any question
Lexie drives her car 204 miles using 12 gallons of gasHow many miles per gallon does her car get? not include the units in your answer
Answer: 17
Step-by-step explanation: 204/12 = 17
Answer:
204÷12=17
lexie used 17 per miles
Step-by-step explanation:
that if am right lol
Caleb brought groceries and paid $1.60 in sales tax. The sales tax rate is 2.5%. What was the price of caleb’s groceries, before tax?
Answer:
$64
Step-by-step explanation:
We can set up a percentage proportion to find the value Caleb's groceries before tax.
[tex]\frac{1.60}{x} = \frac{2.5}{100}[/tex]
We can cross multiply to find the value of x.
[tex]100\cdot1.60=160\\\\160\div2.5=64[/tex]
So the original cost before tax was $64.
Hope this helped!
Answer:
$1.64
Step-by-step explanation:
We need to find the before tax price so let that be x
100-2.5% = 97.5% (since this is the reduction before the sale)
Turn this percentage into a decimal so 0.975
To find x we must remember this price multiples 0.975 to give us $1.60
x * 0.975 = 1.60
x = 1.60 / 0.975
x = 1.64 (2dp)
for the equation f(x)=x^2-4x+1
f(x+h)-f(x)/h = ?
Answer: f(x)=x2-4x
Step-by-step explanation:
a car manufacturer claims that their car can get 32 miles per gallon minus the speed factor. thus caj be modeled by linear equatioj f (×) =33 -015x where f(×) represents the miles per gallon and x is the mph . what would be the predicted miles per gallon for a car going 60 mph using this equation?
Answer:
f(x) = 24 miles per gallon
Step-by-step explanation:
car manufacturer claims that their car can get 33 miles per gallon minus the speed factor
f (×) =33 -0.15x
For a car going 60 mph
f (×) =33 -0.15x
X=60 mph
f (×) =33 -0.15x
f(x) = 33-0.15(60)
f(x) = 33-9
f(x) = 24 miles per gallon
1) Find an equation of the tangent line at each given point on the curve.x = t2 − 4, y = t2 − 2tat (0, 0)at (−3, −1)at (−3, 3)2) Find the arc length of the curve on the given interval. (Round your answer to three decimal places.)Parametric Equations Intervalx= sqrt1a.gif t y=5t-4 0 ≤ t ≤ 13) Find dy/dx and the slopes of the tangent lines shown on the graph of the polar equation. (If an answer does not exist, enter DNE.)r = 2(1 − sin(θ))
Answer:
1) at ( 0,0) : y = x/2. at(-3-1) : y = -1. at(-3,3) : y = 2x +9
2) DNE ( does not exist )
Step-by-step explanation:
The general equation of tangent line
y - y1 = m( x - x1 )
attached below is the detailed solution on how i derived the answers above
2. If x¹¹+101 is divided by x + 1, then what remainder do we get?
Answer:
Step-by-step explanation:
To get the remainder of (x-(-1)) we need to evaluate for -1,
[tex](-1)^{11}+101=-1+101=100[/tex]
So if this is divided by x+1, it means that we can write
[tex]x^{11}+101=(x+1)P(x)+R\\\\so \ for \ x = -1\\\\(-1)^{11}+101=100=0*P(-1)+R=R\\\\\text{So the remainder is 100 !!}[/tex]
thanks
The dimensions of a rectangular bin are consecutive integers. If the volume of the bin is 4896 cubic inches, what are the dimensions of the bin? a. 12 x 18 x 24 c. 15 x 17 x 19 b. 16 x 17 x 18 d. 17 x 18 x 19
Let's use an equation to solve this problem.
Since they are consecutive integers, if we say that the first number is [tex]x[/tex], then the next two numbers (three dimensions in a rectangular prism) are [tex]x+1[/tex] and [tex]x+2[/tex] respectively.
[tex]x*(x+1)*(x+2)=4896[/tex]
[tex]x*(x+1)=x^2+x[/tex]
[tex](x^2+x)*(x+2)=x^3+2x^2+2x[/tex]
[tex]x^3+3x^2+2x=4896[/tex]
[tex]x^3+3x^2+2x-4896=0[/tex]
[tex]x=16[/tex]
B is the correct answer.
4(7-13)divided by 3 + (-4) times 2 - (6-2)
Answer:
[tex]24[/tex]
Step-by-step explanation:
[tex] \frac{4(7 - 13)}{3 + ( - 4)} \times \frac{2 - (6 - 2)}{1} = \frac{28 - 52}{3 - 4} = \frac{ - 24}{ - 1} = 24[/tex]
Hope this helps ;) ❤❤❤
Answer:
24 (Can I have a brainlist, please?)
Step-by-step explanation:
4(7-13)/3 + (-4)2-(6-2)
First we solve the problems in the paraenthesis:
4(7-13)/3 + (-4)2-(6-2)
4(-6)/3 + -4 × 2 -(4)
Now we multiply the ones that are needed to be multiplied:
4(-6)/3 + -4 × 2 -(4)
-24/3 + -8 -(4)
-24/3 + 32
Now we divide:
-24/3 + 32
-8 + 32
And finally we solve the last:
-8 + 32
= 24
Hope that helped!
Segments AB and CD intersect to form an angle of 88.5° as shown. What is the measure
of <2
Answer:
91.8°
Step-by-step explanation:
180-88.2=91.8°
I need a step by step of this equation please -2(3x+1)=26
Answer:
x = -14/3
Step-by-step explanation:
-2(3x + 1) = 26
Distribute the -2 to the number in the parentheses.
-6x - 2 = 26
Add 2 to both sides of the equation.
(-6x - 2) + 2 = 26 + 2
-6x = 28
Divide both sides of the equation by -6.
(-6x)/-6 = 28/-6
x = -28/6
x = -14/3
I need help I don’t understand
Answer:
A. 1.2 > -6.9
Step-by-step explanation:
The reasoning is because positive numbers are ALWAYS greater than negative numbers, and in this question, 1.2 is higher than -6.9. Hope this helped!
Answer:
1.2> - 6.9
Step-by-step explanation:
1.2 is greater than (>) -6.9
Luke earns $11.00 per hour. He works 32 1/2
hours per week. What is his weekly wage
Answer: 357.50
Step-by-step explanation:
Multiply 11.0 and 32.5 without the decimal points.
It should look like this: 110 × 325
After you solve this equation, count the numbers after the decimal points in 11.0 and 32.5. There is one number after the decimal point in 11.0, and one number after the decimal point in 32.5. In the number 35750, count from the last number and add a decimal point right before the 5.
Hope it helps!!