Answers
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
Related Questions
Samantha and Kylee are bakers. If Samantha can decorate a cake in 5 hours and Kylee 8 hours to decorate a cake, how long will it take if they worked together. Explain each step in solving this equation.
Answers
Answer:
3 1/13 hours
Step-by-step explanation:
Lets create a variable:
Samantha and Kylee together (NOT the answers) = [tex]T_{SK}[/tex]
Now lets create an equation:
[tex]1/T_{SK} = 1/T_{S} +1/T_{K}[/tex]
Let's look at the time Samantha and Kylee takes to decorate the cake by themselves:
Samantha: 5 hours
Kylee: 8 hours
Let's create an equation to find the answer now:
[tex]1/T_{SK} = 1/5 + 1/8[/tex]
Note that now that's its basically algebra, change the variable to [tex]x[/tex] like this:
[tex]1/x = 1/5 +1/8[/tex]
Now let's find the LCM (Lowest Common Multiple) of 5, 8, and [tex]x[/tex] which is 40[tex]x[/tex].
[tex]40 = 8x + 5x[/tex]
[tex]40 = 13x[/tex]
[tex]13x = 40[/tex]
[tex]x = 40/13[/tex]
[tex]x[/tex] = 3 1/13 hours
Please note that the step where it swapped 13[tex]x[/tex] and 40 is only my way, it is not necessary, it's just my own comfort.
Divide and simplify as much as possible: -20v^7 x^7 + 12v^4 x^7 / 4v^5 x^4
Answers
[tex]\dfrac{-20v^7x^7+12v^4x^7}{4v^5x^4}=\dfrac{-20v^7x^7}{4v^5x^4}+\dfrac{12v^4x^7}{4v^5x^4}=-5v^{7-5}x^{7-4}+3v^{4-5}x^{7-4}\\\\=\boxed{3v^{-1}x^3-5v^2x^3}[/tex]
Used
[tex]\dfrac{a^n}{a^m}=a^{n-m}[/tex]
Other method:
[tex]\dfrac{-20v^7x^7+12v^4x^7}{4v^5x^4}=\dfrac{4v^4x^4(-5v^3x^3+3x^3)}{4v^4x^4(v)}=\dfrac{3x^3-5v^3x^3}{v}[/tex]
Kristin is swimming in the ocean and notices a coral reef below her. The angle of depression is 35∘ and the depth of the ocean, at that point is 250 feet. How far away is she from the reef? Round your answer to the nearest tenth of a foot if necessary.
Answers
Answer:
Distance: 435.9 ft
Step-by-step explanation:
This is a right triangle shown in the picture.
To solve for [tex]x[/tex], we can use trigonometry.
The 35° angle's opposite side is 250 ft and the hypotenuse of the triangle is [tex]x[/tex] (what we are seeking to find).
The ratio that relates opposite and hypotenuse is sine.
We know that,
[tex]sin(angle)=\frac{opposite}{hypotenuse}[/tex]
Thus we can write:
[tex]sin(35)=\frac{250}{x}[/tex]
Cross multiplying and solving for [tex]x[/tex] gives us:
[tex]sin(35)=\frac{250}{x}\\x=\frac{250}{sin(35)}\\x=435.9[/tex]
Second answer choice is right: 435.9 ft
An electrician charges $40 to come to your house. She also charges $55 for each hour that she works.The electrician charges you a total of $190. How many hours does the electrician work at your house? Use h for the number of hours
Answers
Answer:
your answer is h=2.65 hours
How do you solve this? (#11/#12)
Answers
[tex]\text{If}\ x_1,\ \text{and}\ x_2\ \text{are zeros of a polynomial function, then the function}\\\text{has equation}:\\\\f(x)=a(x-x_1)(x-x_2).\\----------------------------\\\\11.\ \text{We have the zeros}\ 3\ \text{and}\ i:\\\\f(x)=(x-3)(x-i)=(x)(x)+(x)(-i)+(-3)(x)+(-3)(-i)\\\\=x^2-xi-3x+3i=\boxed{x^2-(3+i)x+3i}\\\\12.\ \text{We have the zeros}\ -2\ \text{and}\ 2i:\\\\f(x)=(x-(-2))(x-2i)=(x+2)(x-2i)\\\\=x^2-(2i)^2=x^2-2^2i^2=x^2-4(-1)=\boxed{x^2+4}\\\\\text{used}\\\\(a-b)(a+b)=a^2-b^2\\\\i=\sqrt{-1}\to i^2=-1[/tex]
Which transformation are needed to change the parent cosine function to y=3cos(10(x-pi))
Answers
Answer:
Step-by-step explanation:
First, we can transform y = cos(x) to y = 3*cos(x) by stretching the graph vertically by a factor of 3. At x = 0, the y value would now be 3 * 1 = 3 instead of 1 (the stretching would cause all new y-values to be 3 times their original values for any given x).
Now transforming y = 3*cos(x) to y = 3*cos(10*x) will stretch the graph horizontally by a factor of 10 (for any given y value, the new x value corresponding to it is 10 times the original x value).
Finally, to transform y = 3*cos(10*x) to y = 3*cos(10(x-pi)), shift the graph to the right by pi.
Answer:
It's B or C
Step-by-step explanation:
what is the solution to −1/4(d+1)<2
Answers
Answer:
[tex] d > -9 [/tex]
Step-by-step explanation:
[tex] -\dfrac{1}{4}(d + 1) < 2 [/tex]
First, multiply both sides by -4. You must also change the inequality sign since you are multiplying both sides by a negative number.
[tex] -4 \times \left(-\dfrac{1}{4}\right)(d + 1) > 2 \times (-4) [/tex]
[tex] d + 1 > -8 [/tex]
Subtract 1 from both sides.
[tex] d + 1 - 1 > -8 - 1 [/tex]
[tex] d > -9 [/tex]
Shawn has a budget of $50 per month to spend on bus fare. He made a table showing the total amount of bus money he will have left after the given number of rides.
Number of rides 0 9 18 27
Total amount of bus money left ($) 50 41 32 23
Which equation, in standard form, represents the relationship between the number of bus rides, x, and the amount of bus money Shawn will have left, y?
50x = y
x + y = 50
50y = x
Answers
Answer:
x+y = 50
Step-by-step explanation:
We can find the slope of the line
m = (y2-y1)/(x2-x1)
= (50-41)/(0-9)
= 9/-9
=-1
We can use the point slope form of the equation to make an equation for a line
y-y1 = m(x-x1)
y-50 = -1(x-0)
y-50 = -x
To get it in standard from, subtract y from each side
y-y-50 = -x-y
-50 = -x-y
Multiply each side by -1
50 = x+y
x+y = 50
The equation representing the relationship between the number of bus rides and the amount of bus money is [tex]\( x + y = 50 \)[/tex]. The option (a) is correct.
The amount of bus money Shawn will have left is [tex]y[/tex].
Representing the relationship between the number of bus rides [tex]\( x \)[/tex] .
We can see that for every 9 rides, Shawn's remaining bus money decreases by $9.
This suggests that the cost of each ride is $1 (since $9 divided by 9 rides equals $1 per ride).
We know that Shawn starts with $50 and each ride costs $1.
So, after [tex]\( x \)[/tex] rides, Shawn will have spent [tex]\( x \)[/tex] dollars.
So, the equation is :
[tex]\[ y = \text{Initial amount} - \text{Cost per ride} \times \text{Number of rides} \][/tex]
[tex]\[ y = 50 - 1 \times x \][/tex]
[tex]\[ y = 50 - x \][/tex]
This equation can be rearranged to standard form, which is [tex]\( Ax + By = C \)[/tex] , where [tex]\( A \), \( B \), and \( C[/tex] are constants.
For our equation,[tex]\( A = -1 \), \( B = 1 \) , and \( C = 50 \)[/tex] , so in standard form, it is :[tex]\[ -x + y = 50 \][/tex] .
We can multiply the entire equation by -1 to get :
[tex]\[ x - y = -50 \][/tex]
[tex]\[ x + y = 50 \][/tex]
This is the equation in standard form that represents the relationship between the number of bus rides, [tex]\( x \)[/tex], and the amount of bus money Shawn will have left, [tex]\( y \)[/tex].
Therefore, the correct answer is [tex]\( x + y = 50 \)[/tex] .
The complete question is:
Shawn has a budget of $50 per month to spend on bus fare. He made a table showing the total amount of bus money he will have left after the given number of rides.
Which equation, in standard form, represents the relationship between the number of bus rides, x, and the amount of bus money Shawn will have left, y?
a) x+y = 50
b) 50x + 50y = 1
c) 50y = x
d) 50x = y
I need help on this question.
Answers
Let's go:
The centroid of a triangle is the point of intersection of its medians. The distance from de centroid to some vertex of triangle to which it belongs is equal to 2/3 of the length of its median:
BM = 18/3 = 6
I hope I helped you.
Haylee opened a savings account with $440 in Week 1. Each week after this, she deposited $65 in her account. How much money will Haylee have in her savings account after Week 25?
Answers
Answer:
$2,000
Step-by-step explanation:
Since she has $440 dollars and adds $65 dollars a week, the equation will be 440+65(24)=X
Answer:
2000
Step-by-step explanation:
Jodi is cutting out pieces of paper that measure 8 1/2ninches by 11 inches from a large sheet of paper that has a area of 1,000 square inches
Answers
Answer:
93.5 in^2
Step-by-step explanation:
we know that
Jodi is cutting out pieces of paper that measure inches by inches
The area of each piece that jodi is cutting out is equal to the area of a rectangle
jada has 12 library books checked out and han has
[tex] \frac{1}{3} [/tex]
less than that .how many books does han have checked out
Answers
Answer: Hello there!
We know that Jada has 12 books checked out, and Han has one third less than that.
one-third of a number is equal to the number divided by 3, in this case, we have the number 12, so a third of 12 is: 12/3 = 4
then if Han has a third less than 12, Han has 12 - 4 = 8 books checked out.
Barrett is comparing the membership fees for two museums. The art museum charges a one-time fee of $8.25 plus $2.25 per month. The science museum charges a one-time fee of $10.75 plus $3.50 per month. How much does Barrett save by joining the art museum instead of the science museum? Enter your answers in the boxes.
Answers
The savings that Barret makes by joining the art museum instead of the science museum is $2.50 + $1.25m.
The one time fee charged by the art museum is $8.25 and the one charged by the science museum is $3.50. The saving here is:
= 10.75 - 8.25
= $2.50
The savings made per month is:
= Amount charged per month by science - Amount charged per month by art
= 3.50 - 2.25
= $1.25
In conclusion, the savings per month is $2.50 + $1.25 per month.
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What is the perfect square of 289
Answers
Answer:
17²
Step-by-step explanation:
to find the perfect square take the square root of 289
[tex]\sqrt{289}[/tex] = 17 ⇒ 17² = 289
Answer:
17
Step-by-step explanation:
The defenition of a perfect square is "the product of a rational number multiplied by itself."
If you multiply 17 by itself you get 289, so the answer is 17.
Find the area of the shaded region in the figure below.
Answers
Area of the triangle=> (b•h)/2= (8•3)/2= 24/2= 12 in²
Area of the shadowed surface is 40-12= 28 in²
The formula of an area of a triangle:
[tex]A_{\triangle}=\dfrac{1}{2}bh[/tex]
b - base
h - height
We have b = 8in and h = 3in. Substitute:
[tex]A_{\triangle}=\dfrac{1}{2}(8)(3)=(4)(3)=12\ in^2[/tex]
The formula of an area of a rectangle:
[tex]A_{\boxed{\ }}=lw[/tex]
l - length
w - width
We have l = 8in and w = 5in. Substitute:
[tex]A_{\boxed{\ }}=(8)(5)=40\ in^2[/tex]
The area of a shaded region:
[tex]A=A_{\boxed{\ }}-A_{\triangle}\\\\A=40\ in^2-12\ in^2=28\ in^2[/tex]
Answer: 28 in²Sierra left $4.50 as a tip for a waiter. This was 18% of the bill before the tip. How much was her total bill before the tip? Enter your answer in the box.
Answers
Answer: $20.5
Step-by-step explanation:
Let x denotes the amount for total bill.
We are given that , Sierra left $4.50 as a tip for a waiter.
This was 18% of the bill before the tip.
We can write 18% = 0.18. [To convert percent into decimal we divide it by 100.]
Then, the tip amount = 0.18 x Total bill
[tex]\Rightarrow\ 4.5=0.18x\\\\\Rightarrow\ x=\dfrac{4.5}{0.18}=25[/tex]
So, the total bill amount = $25
Hence, her total bill before the tip= Total bill amount - Tip amount
= $25- $4.50=$20.5
Thus ,her total bill before the tip= $20.5
To find Sierra's total bill before the tip, an equation can be created where the tip amount ($4.50) is 18% of the total bill. Solving the equation provides that Sierra's total bill before the tip was $25.
Explanation:To solve this problem, you want to figure out the original bill amount before the tip was added. We know that the tip amount, $4.50, represents 18% of the original bill. Therefore, we can set up an equation to find the total bill before the tip was included.
The equation is as follows: 0.18x = $4.50, where 'x' stands for the total bill before the tip. By dividing both sides of the equation by 0.18, we can find 'x' which represents the initial bill.
So, x = $4.50 / 0.18 and calculating this gives us x = $25. Therefore, Sierra's total bill before the tip was $25.
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The system of equations y=2x+5 and y=-3y-15 is shown on the graph below
According to the graph what is the solution to this system of equations
A(-4,-3)
B(-3,-4)
C(-5,5)
D(5,-5)
Answers
Answer:
A
Step-by-step explanation:
because -4 is x and -3 is y
Answer:
A
Step-by-step explanation:
the solution to a system of equations graphically is the point of intersection of the 2 lines.
The point of intersection = (- 4, - 3) → A
A sweater is on sale for 30% off the ticketed price of $84. How much will the sweater cost after the discount?
Answers
Or if you want to do it the long way you can calculate the actual discount (your savings from this purchase first then subtract it from the original price of $84. It`s just easier to figure out what is left (which is 70% of $84).
To find the discounted price of the sweater, multiply the original price $84 by 30% to get the discount amount of $25.20. Subtract this from the original price to find that the sweater will cost $58.80 after the discount.
To calculate the cost of a sweater that is on sale for 30% off its ticketed price of $84, you will need to find 30% of $84 and then subtract that amount from the original price.
Determine the discount amount by converting the percentage to a decimal and multiplying by the original price: 30% = 0.30, so 0.30 x $84 = $25.20.Subtract the discount from the original price: $84 - $25.20 = $58.80.Therefore, after a 30% discount, the sweater will cost $58.80.
Solve the equation
4x−2·(3x−2)=3x
Answers
Answer: [tex]x=\frac{4}{5}[/tex]
Step-by-step explanation:
To solve this problem you must apply the proccedure shown below:
1. You have the following equation given in the problem above:
[tex]4x-2(3x-2)=3x[/tex]
2. Apply the Distributive property:
[tex]4x-6x+4=3x[/tex]
4. Now, you must add like terms:
[tex]4=3x-4x+6x\\4=5x[/tex]
5. Solve for [tex]x[/tex], then the result is:
[tex]x=\frac{4}{5}[/tex]
X-4y=28 2x+y=2 Elimination
Answers
[tex]\left\{\begin{array}{ccc}x-4y=28\\2x+y=2&\text{multiply both sides by 4}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}x-4y=28\\8x+4y=8\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad9x=36\qquad\text{divide both sides by 9}\\.\qquad\boxed{x=4}\\\\\text{Put the value of x to the second equation:}\\\\2(4)+y=2\\8+y=2\qquad\text{subtract 8 from both sides}\\\boxed{y=-6}\\\\Answer:\ \boxed{x=4\ and\ y=-6\to(4,\ -6)}[/tex]
What percent of 88 is 154?
Answers
Answer:
It Is 175% Of 88.
Step-by-step explanation:
154 ÷ 88 = 1.75
To Convert A Decimal Into Percent, You Multiply By 100.
1.75 · 100% = 175%
Therefore, The Answer Is 175%.
The answer is 57.14%
What are percentages?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”
Given here 88/154 and therefore in percentage terms it is 88/154 × 100
= 57.14%
Hence, The answer is 57.14%
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if a particle moves along a straight line according to s(t)= t^4 -4t^3 +6t^2 -20, find the maximum and minimum acceleration on 0 less or equal to t less or equal to 3
Answers
so we have s(t), namely the positional equation for the particle.
now, let's recall that the derivative of s(t) will be v(t), namely the derivative of the positional equation will be the velocity, and the derivative of the velocity will be the acceleration.
s'(t) = v(t) and s''(t) = a'(t) <--- acceleration
so we need the 2nd derivative of s(t) firstly, and then we can check for any critical values and find its extrema.
[tex]\bf s(t)=t^4-rt^3+6t^2-20\implies \stackrel{\textit{velocity}}{s'(t)=4t^3-12t^2+12t} \\\\\\ \stackrel{\textit{acceleration}}{s''(t)=12t^2-24t+12}\implies \stackrel{\textit{derivative of acceleration}}{s'''(t)=24t-24} \\\\[-0.35em] ~\dotfill\\\\ 0=24t-24\implies 24=24t\implies \cfrac{24}{24}=t\implies 1=t[/tex]
now, if we run a first-derivative test on that acceleration derivative, namely s'''(t), let's say we test s'''(0) and that gives us a negative value, and then test s'''(2) and that gives us a positive value, so the test goes like in the picture below, clearly, 1 = t is a minumum, and is between [0, 3].
s'''(0) = -24
s'''(3) = 48
so clearly the maximum happens at the s'''(3) endpoint, when t = 3.
What is the common ratio between successive terms in the sequence? 27, 9, 3, 1, , , , ... –3 – 3
Answers
Answer:
1/3
Step-by-step explanation:
To determine the common ration, we take the second term and divide it by the first term
9/27 = 1/3
We verify this by taking the third term and diving by the second term
3/9 = 1/3
The common ratio is 1/3
Answer:
1/3
Step-by-step explanation:
Divide a term by the previous term.
For example, divide 1 by 3 to get 1/3.
Libby sold $60 worth of vegetables at the farmer's market. Jess sold 3/4ths of what Libby sold. Stephanie sold 1/3rd of what Jess sold. How much did they all sell together?
Answers
Answer:
$120.
Step-by-step explanation:
We have been given that Libby sold $60 worth of vegetables at the farmer's market.
Jess sold 3/4th of what Libby sold. Let us find 3/4 of 60.
[tex]\text{Jess sold}=60\times \frac{3}{4}[/tex]
[tex]\text{Jess sold}=15\times 3[/tex]
[tex]\text{Jess sold}=45[/tex]
Therefore, Jess sold $45 worth of vegetables.
We are told that Stephanie sold 1/3rd of what Jess sold. So let us 1/3rd of 45.
[tex]\text{Stephanie sold}=45\times \frac{1}{3}[/tex]
[tex]\text{Stephanie sold}=15[/tex]
Therefore Stephanie sold $15 worth of vegetables.
Now let us add amounts of money earned by Libby, Jess and Stephanie to get the total money earned by all.
[tex]\text{The total money earned by Libby, Jess and Stephanie}=60+45+15[/tex]
[tex]\text{The total money earned by Libby, Jess and Stephanie}=120[/tex]
Therefore, they all sell $120 worth of vegetables together.
Answer:
As per the statement: Libby sold $60 worth of vegetables at the farmer's market.
⇒ Libby sold vegetables at the farmers market = $60
Jess sold 3/4th of what Libby sold.
⇒ Jess sold = [tex]\frac{3}{4} \times 60 = \$45[/tex]
Also, Stephanie sold 1/3rd of what Jess sold.
⇒ Stephanie sold = [tex]\frac{1}{3} \times 45 = \$15[/tex]
To find how much did they all sell together.
Together they all sell together = Libby sold + Jess sold + Stephanie sold
=$60 + $45+$15 = $120
Therefore, they all sell together is, $120
The diameter of a circle is 6 units. What is the radius of the circle?
Answers
6/2=3
r=3
Answer:
The radius of the circle is 3 unit.
Step-by-step explanation:
Given : The diameter of a circle is 6 units.
To find : What is the radius of the circle?
Solution :
The radius of the circle is [tex]r=\frac{d}{2}[/tex]
Where, d is the diameter d=6 units
Substitute the value,
[tex]r=\frac{6}{2}[/tex]
[tex]r=3[/tex]
Therefore, the radius of the circle is 3 unit.
which of the following best explains why cos 2 pie/3 does not equal cost 5 pie/3
Answers
Answer:
Hope this helps, sorry for my horrible handwriting. If you have any questions feel free to ask me!
Step-by-step explanation:
Which graph is defined by the function given below? y=(x+2)(x+7)
Answers
We can determine the x-intercepts from the equation. X-intercepts are x=-2 and x=-7 which is what Graph A shows.
Answer:
Graph A.
Step-by-step explanation:
The given graph in the question is y = (x + 2) (x + 7)
or y = x² + 2x + 7x + 14
= x² + 9x + 14
Now we convert this equation of parabola in vertex form
[tex]y=(\frac{x+9}{2})^{2}-\frac{81}{4}+14[/tex]
[tex]=(x+4.5)^{2}-6.25[/tex]
This equation is in the form of y = (x-h)² + k where (h,k) is the vertex.
So in the given equation y = (x + 4.5)² - 6.25
Vertex should be (-4.5, 6.25) which lies in third quadrant.
Therefore, option A. is the graph.
A set of rules used to determine the proper order for performing operations in an expression that involves more than one operation is a(n) ___.
proportion
order of operations
output
equation
Answers
A set of rules used to determine the proper order for performing operations in an expression that involves more than one operation is a(n) order of operations.
What is proportion?The number or amount of a group or part of something when compared to the whole is called proportion.
What is order of operations?The order of operations is a rule that tells the correct sequence of steps for evaluating a math expression.
What is output?Something produced as a result of some input is called output.
What is an equation?An equation is a mathematical statement which equate two algebraic expressions. An equation has an equal to (=) sign in between the expression.
How to know the what the given set of rules called?Output of operations is the set of rules used to determine the proper order for performing operations in an expression that involves more than one operation
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how many solutions does this equation have 3x-2x+4=2+x+2
Answers
[tex]x + 4 = x + 4[/tex]
so X can technically be any number
QUESTION!!!! WHEN TRYING TO PROVE SIMILER TRIANGLES, IF YOUR USINF THE ANGLE ANGLE SIMILARITY POSTUALET HOW MANY ANGLES DO YOU NEED TO PROVE IN YOUR STATEMENTS? AND IS THERE A WAY TO MAKE SURE THAT THE WAY YOU PROVED YOUR TRIANGLES SIMILAR IS RIGHT?
Answers
Answer: 2 pairs of angles
As the name "angle angle" suggests, we need 2 pairs of angles proven congruent in order to prove that two triangles are similar. Each "angle" refers to a pair of angles between the two triangles, which are corresponding angles. We could use the third pair, but it's extra unnecessary work. This theorem is often written as "AA similarity" or something along those lines.
One way to check for similar triangles is to compare the ratios of the sides. If the corresponding sides divide to the same value, then you have similar triangles. This method only works of course if you know the side lengths.