Answer:
first we will multiply -3/10 and 60,
-3/10 x 60 = -18
(one-tenth of 60 is 6, and because we are multiplying -3/10 and not -1/10 we can multiply 6 by -3 to get 18.)
then multiply the exponents
x(x) = x^2
y(y^6) = y^7
we can then multiply all terms together to form one single term
-18(x^2)y^7=-18x^2y^7
our final answer is:
-18x^2y^7
The answer to the given question is [tex]\[ \boxed{-18x^2y^7} \][/tex]
First, we need to multiply the numerical coefficients and the literal coefficients (variables) separately. The numerical coefficients are -3 and 60, and the literal coefficients are 1/10, x, y, x, and [tex]y^6[/tex].
Multiplying the numerical coefficients:
[tex]\[ -3 \times 60 = -180 \][/tex]
Multiplying the literal coefficients (variables):
[tex]\[ \frac{1}{10} \times x \times y \times x \times y^6 \][/tex]
Since we have two x's and one y to the power of 6, we can simplify this as:
[tex]\[ \frac{1}{10} \times x^2 \times y^7 \][/tex]
Now, we combine the numerical and literal coefficients:
[tex]\[ -\frac{180}{10} \times x^2 \times y^7 \][/tex]
Simplifying the numerical fraction:
[tex]\[ -18 \times x^2 \times y^7 \][/tex]
Therefore, the final simplified expression is:
[tex]\[ -18x^2y^7 \][/tex]
The answer is: [tex]-18x^2y^7[/tex].
Sue wants to buy a video that costs $24.95. She has $3 in her pocket and a piggy bank full of quarters,x. Which inequality can be used to represent the number of quarters sue needs to buy the game?
Given
Sue wants to buy a video that costs $24.95.
She has $3 in her pocket
a piggy bank full of quarters x
Find out the inequality can be used to represent the number of quarters sue needs to buy the game.
To proof
As given in the question
Sue wants to buy a video that costs = $24.95.
She has $3
The value of quaters in the piggy bank = x
1 $ = 4 quaters
First convert $24.95 in the quaters form
= 4 × 24.95
= 99.8 quaters
convert $3 in the quaters form
= 3 × 4
= 12 quaters
The equation become in the form
[tex]12 + x \geq 99.8[/tex]
x = 87.8 quaters
quarters sue needs to buy the game is 87.8 quaters.
Hence proved
On a recent day 8 euros were worth $9 and 24 euros were worth $27 write an equation of the form y equals kx to show the relationship between the number of euros and the value in dollars.
Answer:
y=8x/9
Step-by-step explanation:
Given that 8 euros were worth $9 and
24 euros were worth $27.
Let y represent the number of Euros and x no of dollars.
Given that the relation is of the form y = kx+C
When x=0 y =0,
i.e. C =0
Hence equation is of the form y = kx
Substitute x=8 and y =9
We get 9 = 8k
Or k =8/9
Hence relation is y=8x/9 is the relation between x and y.
WE can verify this for 27 dollars worth 24 euros.
24 =8/9(27) is true.
Thus equation is verified.
HELP PLEASE??
Drag and drop the answers into the boxes to correctly complete the statement.
A sequence of transformations that maps △ABC to △A′B′C′ is a _____________ followed by a _____________.
- reflection across the y-axis
- rotation of 180° about the origin
- translation 2 units right
- rotation of 90° counterclockwise about the origin
Answer:
(1) Rotation of 90° counterclockwise about the origin (2) Translation 2 units right .
Step-by-step explanation:
We have been asked to determine a sequence of transformations that maps △ABC to △A′B′C'.
To map △ABC to △A′B′C′ first of all we have to rotate △ABC 90° counterclockwise (positive rotation) about the origin. After rotating △ABC 90° our new coordinates will be A(-3,-4), B(-3,-1) and C (-1,-2).
We can see that distance between A and origin is [tex]\sqrt{5}[/tex] and distance between A' and origin is also [tex]\sqrt{5}[/tex]. Distance between A and A' is [tex]\sqrt{10}[/tex], which forms a right triangle.
To map △ABC to △A′B′C′ completely we will translate our △A′B′C' 2 units right. After translation our coordinates will be A'(-1,-4), B'(-1,-1) and C'(1,-2).
Therefore, a sequence of transformations that maps △ABC to △A′B′C′ is (1) rotation of 90° counterclockwise about the origin and (2) translation 2 units right.
Final answer:
The sequence of transformations is a rotation followed by a translation, which can map one triangle to another in the Euclidean plane.
Explanation:
A sequence of transformations that maps △ABC to △A′B′C′ can be described as a combination of basic transformations such as rotations, reflections, and translations. Based on the options given, the correct sequence to map △ABC to △A′B′C′ is a rotation followed by a translation. For example, if △ABC were rotated 90 degrees counterclockwise about the origin and then translated 2 units to the right, it could be mapped to a new position as △A′B′C′. It is important to note that the order of transformations can affect the outcome, and transformations are done in sequence.
1750932 x 2355435 x Y= ? 50pts
Simplify as much as possible
1,750,932 x 2,355,435 = 4,124,206,515,420
4,124,206,515,420 x Y cannot be simplified anymore, therefore,
4,124,206,515,420 x Y is your answer
~Rise Above the Ordinary, Senpai
All we need to do here is simplify, since there is no given answer to y. The numbers you've provided are quite large, so I'd suggest just using a calculator, unless they're supposed to be decimals. The simplified answer to this is 412,320,615,420y.
What is the slope of the line shown below?
Answer C, aka 3 is that line's slope.
Answer:
the slope of the line is 3
Step-by-step explanation:
Hello, I think I can help you with this
if you have two points of a line
[tex]P1=(x_{1},y_{1})\\ and\\P2=(x_{2},y_{2})[/tex]
you can find the slope using
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\[/tex]
Step 1
Let
P1( 1, 3) and P2(3,9)
put the values into the equation
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\m=\frac{9-3}{3-1}\\m=\frac{6}{2}\\ m=3[/tex]
the slope of the line is 3
I hope it helps,Have a great day.
You wish to have $3000 in 2 years to buy a fancy new stereo system. How much should you deposit each quarter into an account paying 8% compounded quarterly?
Answer:
Deposit each quarter = $342.68
Step-by-step explanation:
Formula use in this problem:
[tex] FV=C\times \left [ \frac{(1+i)^n-1}{i} \right ]\times (1+i) [/tex]
Where,
FV is future value, FV=$3000
C is cash flow quarterly( need to find),C=?
I is rate of interest ( divide by 4), i=[tex] \frac{0.08}{4}=0.02 [/tex]
N number of cash flow, n=8
Substitute all these values into formula to solve for C
[tex] 3000=C\times \left [ \frac{(1+0.02)^8-1}{0.02} \right ]\times (1+0.02) [/tex]
[tex] C=\frac{3000\times 0.02}{[(1+0.02)^8-1]\times (1+0.02)}[/tex]
So, C=$342.68
Final answer:
To achieve $3000 in 2 years in an account with 8% interest compounded quarterly, you should deposit $364.11 each quarter.
Explanation:
To find out how much you need to deposit each quarter to have $3000 in 2 years in an account that pays 8% interest compounded quarterly, you would use the future value of a series formula given by:
S = R [((1 + i)^n - 1) / i]
Where:
S = the future value of the series (in this case, $3000)
R = the regular deposit amount per period (what we're solving for)
i = the interest rate per period (8% per year or 0.08 divided by 4 for quarterly = 0.02)
n = the total number of compounds over the period (2 years * 4 quarters/year = 8 compounds)
Plugging in our values:
$3000 = R [((1 + 0.02)^8 - 1) / 0.02]
$3000 = R * [((1.02)^8 - 1) / 0.02]
$3000 = R * 8.2432
So, solving for R, we get:
R = $3000 / 8.2432 = $364.11
Therefore, to have $3000 in 2 years with an account that pays 8% interest compounded quarterly, you need to deposit $364.11 at the start of each quarter.
Which transformation shows a translation of 3 units to the right?
It is the transformation shown in (B)
(look at one point of the letter P and how it moves precisely 3 units. Also there is only the move, no flipping of the figure)
Answer is B.
B shows a translation of 3 units to the right
Jim drove 436 miles using 16 gallons of gas. At this rate, how many limes would he drive using 14 gallons of gas?
the second longest bridge in the world, the tianjin grand bridge, is 373,000 feet long. Its length is 167,700 feet less than the length of the longest bridge in the world. What is the length of the longest bridge? Show your work.
The length of the longest bridge in the world is found by adding the length of the second longest bridge namely the Tianjin Grand Bridge, and the stated difference between the two bridges' lengths. After calculation, the length of the longest bridge in the world is found to be 540,700 feet.
Explanation:To find the length of the longest bridge in the world, we should add the length of the Tianjin Grand Bridge (the second longest in the world) and the difference between the two bridges. In this case, the length of the Tianjin Grand Bridge is 373,000 feet and it's stated that this is 167,700 less than the length of the longest bridge.
So, we have to do the following calculation: 373,000 feet (length of the Tianjin Grand Bridge) + 167,700 feet (difference in length) = 540,700 feet.
So, the length of the longest bridge in the world is 540,700 feet.
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What is the value of x, given that Line of PQ║line BC?
A. 26
B. 15
C. 13
D. 11
The value of x is option C. 13.
What is Triangle Proportionality Theorem?The triangle proportionality theorem states that if a line is drawn inside the triangle which is parallel to any side of the given triangle, then the line intersects other two sides at two different points. Then the division of the other two sides of the triangle will be in the same ratio.
Given is a triangle ABC.
A line PQ is drawn which is parallel to the line BC.
We have to find the value of x, which is the length of AQ.
Using the triangle Proportionality theorem,
AP / PB = AQ / QC
Substituting the values,
6 / 12 = x / 26
Cross multiplying,
12x = 6 × 26
x = 156 / 12
x = 13
Hence the value of x is 13.
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What conclusion can you draw about the relative frequency of these results?
A) If you are a boy in this group, you are more likely not to eat cereal for breakfast than to eat cereal.
B) If you are a girl in this group, you are more likely to eat cereal for breakfast than not.
C) If you eat cereal for breakfast, you are a boy.
D) Knowing if a person eats cereal will help determin gender.
B) If you are a girl in this group, you are more likely to eat cereal for breakfast than not.
please help me with this problem. image attached.
The answer is D, (3, -4)
Jeff has a rain gauge that shows 1 3/4 inches of rain. After it rains, the gauge shows 5 1/4 inches of rain. How much rain fell between the two readings?
A) 4 1/2 in.
B) 3 1/2 in.
C) 2 1/2 in.
D) 2 1/4 in.
That is 5 1/4 - 1 3/4
= 21/4 - 7/4
=14/4
= 3 1/2 inches
For which situation is the use of approximate numbers most appropriate?
A) preparing your yearly taxes
B) ordering programs for a high school musical
C) paying a cashier for a meal at a fast food restaurant
D) the maximum number of basketball players allowed on the court at a time
The graph shows a car's value as a function of its age.
What was the value of the car in Year 2?
Enter your answer in the box. Do NOT enter a dollar sign or a comma in your answer.
If John ran a 5 km marathon how long What is that in meters
The perimeter of the triangle is 70cm the area of the triangle is a squared what is a squared
Does This Table Represent a function? Why Or Why Not?
Yes, this table represents a function.
Step-by-step explanation:Function--
It is a set of ordered pair of the type: (x,y) in which each input variable i.e. x is mapped to a single output i.e. y.
i.e. each of the value of x is mapped to a single y.
Here after looking the table we observe that each of the value of the independent variable i.e. Hours of training is mapped to a single value of the dependent variable i.e. monthly pay.
Bank card is charging 1.4% monthly interest on credit card charges. If you charged a $175 pair of running shoes on the card and did not pay it off this month, what would be the interest for the shoe charge? $2.45 $245 $4.90 $24.50
Answer:
Option A : the interest for the shoe charge is $2.45.
Step-by-step explanation:
As given, Bank card is charging 1.4% monthly interest on credit card charges.
This amount is charged on $175.
We have the interest value as :
[tex]0.014\times175=2.45[/tex] dollars
Hence, the interest for the shoe charge is $2.45.
Given the graph of a line y=−x. Write an equation of a line which is perpendicular and goes through the point (8,2).
When a line is perpendicular to another line, the slope is the negative reciprocal of the other line's slope. So in this case, the slope would be 1, since the negative reciprocal of -1 is 1/1 which is 1.
To find the y-intercept, you have to substitute the point (8,2) into y = mx + b
2 = 1(8) + b
b = -6
The equation is y = x - 6
The equation of the line which is perpendicular and goes through the point (8,2) is y = x - 6
The equation of the required line in slope-intercept form is expressed as:
y-y0 = m(x-x0) where:
m is the slope(x0, y0) is the point on the lineGiven the equation of the line as y = -x
Get the slope of the line
mx = -x
m = -1
Since the required line is perpendicular to this line, the required slope will be 1 (M = -(-1/1))
Get the required equation
Recall that;
y-y0 = m(x-x0)
y - 2 = 1(x-8)
y - 2 = x - 8
y = x - 8 + 2
y = x - 6
Hence the equation of the line which is perpendicular and goes through the point (8,2) is y = x - 6.
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Use the following information for problems 1 – 3. Suppose you sign a contract for an annual salary of $50,000 with a guaranteed raise of 5% each year.
1. Write your salary for the next n years as a geometric sequence in explicit form.
2. What will your salary be in year 5?
3. How much will you have earned in total salary by the end of your 10th year?
Initial salary = $50,000 .
Rate of raise = 5% each year.
Therefore, each next year salary would be 105% that is 1.05 times.
5% of 50,000 = 0.05 × 50000 = 2500.
Therefore raise is $2500 each year.
According to geometric sequence first term 50000 and common ratio 1.05.
Applying geometric sequence formula
[tex]a_n = ar^{n-1}[/tex]
1) [tex]a_n = 50000(1.05)^{n-1}[/tex]
2) In order to find salary in 5 years we need to plug n=5, we get
[tex]a_5 = 50000(1.05)^{5-1}= 50000(1.05)^4[/tex]
= 50000(1.21550625)
=$60775.3125.3) In order to find the total salary in 10 years we need to apply sum of 10 terms formula of a geometric sequence.
[tex]S_n = \frac{a(1-r^n}{1-r}[/tex]
Plugging n=10, a = 50000 and r= 1.05.
[tex]S_10 = \frac{50000(1-(1.05)^{10}}{1-1.05}[/tex]
[tex]S_10 = \frac{50000(0.050)^{10}}{0.05}[/tex]
= 628894.62678.
Therefore , you will have earned $ 628894.62678 in total salary by the end of your 10th year.find m ∠RPS
(Image below)
∠RPS=___
RPS is 90 degrees because of the vertical line theorem... opposite angles are always congruent.
Answer: RPS is 90 degrees
Step-by-step explanation:
Please help me
10 points
1. 4x = 7(x - 3) 1.Given
4x = (7)(x) + (7)(-3)
2. 4x = 7x - 21 2.Distributive property
4x - 7x = 7x - 7x - 21
3. -3x = -21 3.Subtraction property of equality
-3x : (-3) = -21 : (-3)
4. x = 7 4.Division property of equality
IF WORK IS SHOWN YOU'LL BE MARKED BRAINLIEST
row #of students
1 4
2 7
3 10
4 13
Which formula can be used to find the number of students seated in any given row?
a. an= 4n
b. an= 4n – 1
c. an= n + 3
d. an= 3n + 1
I believe its asking you the formula to find the rows numbers moving forward
Examle row 5 will be 16, I believe that is B. 4n - 1
please help asap 25 pts
your answer is A
hope this helps :)
A = [tex]\frac{1}{2}[/tex]bh
[tex]\frac{1}{2}[/tex] × (bh) = A
[tex]\frac{bh}{2}[/tex] = A
bh = A × 2
bh = 2A
b = [tex]\frac{2A}{h}[/tex]
The answer is a: b= [tex]\frac{2A}{h}[/tex]
the ratio of boys to girls at the beach cleanup was 7:8. If there were 43 boys, how many girls were there?
In a factory, a certain machine needs 10 min to warm up. it takes 15 min for the machine to run a cycle. the machine can operate for as long as 6 h per day including warm up time. Draw a graph showing the total time the machine operates during 1 day as a function of the number of cycles it runs.
-What domain and range are reasonable?
-Is the function a linear function?
Answer:
[tex]y =\frac{1}{6} + 0.25x[/tex]
[tex]0 \leq x \leq23.33[/tex]
[tex]0 \leq y \leq 6[/tex]
Step-by-step explanation:
The machine always takes 10 minutes (or 1/6 hours) to warm up and performs each cycle in 15 minutes, or 0.25 hours.
The maximum amount of daily hours that the machine can work is 6 hours.
Therefore we can represent this situation by means of an equation of the form:
[tex]y =\frac{1}{6} + 0.25x[/tex]
Where
y = daily amount of hours the machine works.
x = number of daily cycles performed.
This equation is a linear function. Because it has the form y = ax where a is a real number
The graph of this equation is shown in the attached image, where the gray shaded area represents the domain of the function.
The domain of the function is:
[tex]x\geq 0[/tex] (because you can not perform less than zero cycles a day)
[tex]x \leq23.33[/tex]. Because the machine can not exceed 6 hours per day, then it can not do more than 23.33 cycles.
So:
[tex]0 \leq x \leq23.33[/tex]
The range of the function is:
[tex]y \geq 0[/tex] (because you can not work less than 0 hours a day)
[tex]y \leq 6[/tex] (because the machine can not work more than 6 hours a day)
So
[tex]0 \leq y \leq 6[/tex]
What’s the answer? (SOMEONE PLEASE HELP ME)
x = - [tex]\frac{7}{4}[/tex] or x = 0
take out a common factor 2x
2x(4x + 7 ) = 0
equate each factor to zero and solve for x
2x = 0 ⇒ x = 0
4x + 7 = 0 ⇒ x = - [tex]\frac{7}{4}[/tex]
Amina used the quadratic formula to solve an equation. Her result shows two solutions that are complex numbers with imaginary parts. Which expression could be Amina's result?
The expression that could be Amina's result is [tex]x = \dfrac{12 \pm \sqrt{-8}}{4}[/tex]
Which expression could be Amina's result?
From the question, we have the following parameters that can be used in our computation:
The list of options
Also, we have that
Her result shows two solutions that are complex numbers with imaginary parts
This can be expressed as
[tex]x = \dfrac{a \pm i\sqrt{b}}{c}[/tex]
From the list of options, the expresion that are of the above form are
[tex]x = \dfrac{12 \pm \sqrt{-8}}{4}[/tex]
hence, the expression that could be Amina's result is [tex]x = \dfrac{12 \pm \sqrt{-8}}{4}[/tex]
Question
Amina used the quadratic formula to solve an equation. Her result shows two solutions that are complex numbers with imaginary parts. Which expression could be Amina's result?
find dy/dx by implicit differentiation. 5+4x=sin(xy^2)
To find dy/dx by implicit differentiation, differentiate both sides of the equation with respect to x. The derivative of sin(xy^2) with respect to x is cos(xy^2) * (y^2 * dx/dx + x * d(y^2)/dx). Simplify the expression to find dy/dx.
Explanation:To find dy/dx by implicit differentiation, we will differentiate both sides of the equation with respect to x.
We have the equation 5+4x=sin(xy^2). Taking the derivative of both sides, the left side will be 0 since it is a constant. On the right side, we use the chain rule.
The derivative of sin(xy^2) with respect to x can be written as cos(xy^2) * (y^2 * dx/dx + x * d(y^2)/dx).
Simplifying further, dy/dx = (cos(xy^2) * (2xy^2 + x * 2y * dy/dx)) / (1 - x * 2y^2 * cos(xy^2)).