Which system of inequalities is represented by the graph?
y ≤ –1/2x
y > –1
y ≥ –1/2x
y < –1
y < –1/2x
y ≥ –1
y > –1/2x
y ≤ –1
Answers
ur other line has a y int of (0,0), it has a slope of -1/2 ....it has a dashed line...it is shaded below the line.....so the equation for this line is : y < -1/2x
so ur answer is : y > = -1 and y < -1/2x
the answer is D)y ≥ 2x
y > 1
on ed
just took the test
Related Questions
Suppose a study estimated that 85% of the residents of a town (with an error range of ±12 percentage points at 95% confidence) favor building a new community center. Which of the following percentages of the town's residents may favor building a new community center?
A. 69%
B. 79%
C. 59%
D. 99%
Answers
The confidence interval for a given sample value can be calculated using the following formula:
Confidence interval = Average value ± Margin of error
Which in this case the values are:
Average value = 85%
Margin of error = 12%
Therefore substituting the given values into the equation will give us:
Confidence interval = 85 ± 12
Confidence interval = 73, 97
Therefore the percentage of the residents of the town who are favour of building a new community center ranges from 73% to 97%.
Based from the given choices, only letter B 79% is within this range:
Answer:
B. 79%
Answer:
B. 79%
Step-by-step explanation:
yes
Explain how the GCF helps with the distributive property. Why is it so important to use the GCF when factoring a sum of two numbers?
Answers
GCF is the greatest common factor, that divides two number and the distributive property is that when a number multiplied with each number in the bracket and then perform addition or subtraction etc.
GCF help with distributive property and it is important to use when factoring a sum of two numbers. For example we have to add fractions 2/3 and 4/9, now the GCF is 9
2/3 + 4/9
= 2(3) + 4 (1) / 9
Now 2 is the common factor, so it allow us to use the distributive property.
= 2 (3 + 2) / 9
= 2(5) /9
=10 / 9 is the answer.
The cost to produce a product is modeled by the function f(x) = 5x2 − 70x + 258 where x is the number of products produced. Complete the square to determine the minimum cost of producing this product.
Answers
= 5(x^2 - 14x) + 258
= 5[ ( x - 7)^2 - 49) + 258
= 5 (x - 7)^2 - 245 + 258
= 5(x - 7)^2 + 13
The minimum cost of producing this product is:
13
Step-by-step explanation:The function which is used to represent the cost to produce x elements is given by:
[tex]f(x)=5x^2-70x+258[/tex]
Now, on simplifying this term we have:
[tex]f(x)=5(x^2-14x)+258\\\\i.e.\\\\f(x)=5(x^2+49-49-14x)+258\\\\i.e.\\\\f(x)=5((x-7)^2-49)+258\\\\i.e.\\\\f(x)=5(x-7)^2-5\times 49+258\\\\i.e.\\\\f(x)=5(x-7)^2-245+258\\\\i.e.\\\\f(x)=5(x-7)^2+13[/tex]
We know that:
[tex](x-7)^2\geq 0\\\\i.e.\\\\5(x-7)^2\geq 0\\\\i.e.\\\\5(x-7)^2+13\geq 13[/tex]
This means that:
[tex]f(x)\geq 13[/tex]
This means that the minimum cost of producing this product is: 13
Mary, who is sixteen years old, is four times as old as her brother. how old will mary be when she is twice as old as her brother? explained
Answers
16 ÷ 4 = 4
Now that you have two ages, you can just make a list to find the answer.
16 and 4
18 and 6
20 and 8
22 and 10
24 and 12
which one is it? need help please
Answers
y + 2x = 4
--------------------subtract
-2 1/3x = -14
-7/3x = -14
x = -14 (-3/7)
x = 6
2x + y = 4
2(6) + y = 4
y = 4 - 12
y = -8
(6, -8)
answer
C. (6, -8) (third choice)
25 decreased by 1/5 of a number is 18
Answers
The equation for the student's question is 25 - (1/5)x = 18. Solving for x involves simple algebraic manipulation, resulting in x being equal to 35.
Explanation:The student's question '25 decreased by 1/5 of a number is 18' is a basic algebra problem. We could represent the unknown number as x. So the equation would be 25 - (1/5)x = 18.
To solve the equation 25 decreased by 1/5 of a number is equal to 18, we can set up the equation as 25 - (1/5)x = 18, where x is the unknown number.
To isolate x, we first subtract 25 from both sides of the equation:
- (1/5)x = -7.
Next, we can multiply both sides of the equation by -5 to eliminate the fraction:
x = (-7) * (-5) = 35.
To solve for x, first, add (1/5)x to both sides to get 25 = 18 + (1/5)x.
Then, subtract 18 from both sides to obtain 7 = (1/5)x. Finally, multiply both sides by 5 to find the value of x. Thus, x equals 35.
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Answers for 1.2.1 how can I describe a graph
Answers
Hope this helps!
8x-2y over 10xy if x=4 and y=-7
Answers
The value of the expression 8x-2y over 10xy when x=4 and y=-7 is -0.1643 (rounded to four decimal places).
Explanation:To evaluate the expression 8x-2y over 10xy when x=4 and y=-7, we substitute these values into the expression:
8(4)-2(-7) over 10(4)(-7)
Simplifying further,
32+14 over -280
46 over -280
Therefore, the value of the expression 8x-2y over 10xy when x=4 and y=-7 is -0.1643 (rounded to four decimal places).
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What is the answer to 40-2a squared when a=4?
Answers
40-8
32
Hope that helps
a=4
2(4)=8
40-8=32
32(32)=1024
Use basic identities to simplify the expression. sin2θ + tan2θ + cos2θ
Answers
sin^2 (θ) + tan^2 (θ) + cos^2 (θ)
To be able to simplify this, we need to have knowledge on the different trigonometric identities. These identities are expressions which would relate the different trigonometric functions. For this case, we use two known basic identities. These are
sin^2 (θ) + cos^2 (θ) = 1
1 + tan^2 (θ) = sec^2 (θ)
We simplify as follows:
sin^2 (θ) + tan^2 (θ) + cos^2 (θ) = sin^2(θ) + tan^2 (θ) + cos^2 (θ)
= 1 + tan^2 (θ)
= sec^2
Therefore, the expression sin^2 (θ) + tan^2 (θ) + cos^2 (θ) is equal to sec^2 (θ). Other form that would also be equivalent to the same expression would be sin^2 (θ) + sin^2 (θ) / cos^2 (θ) + cos^2 (θ).
Write an expression for the number of hours in an unknown number of minutes.
Answers
I think this is what u need
$35,485.00 to $50,606.00 per year is equivalent to how much an hour
Answers
assuming it is based on a 40 hour work week, working 52 weeks per year:
35485/52 = 682.40 per week
682.40/40 = 17.06 per hour
50606/52 = 973.19 per week
973.19/40 = 24.33 per hour
so between 17.06 & 24.33 per hour
Hans deposits $300 into an account that pays simple interest at a rate of 2% per year. How much interest will he be paid in the first 5 years?
Answers
answer
interest will $30 in the first 5 years
what ithe distance from (3 1/2,5) to (3 1/2,-12)
Answers
5--12=17
So these two points are 17 units apart.
Hey!
Hope this helps...
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Questions like these are really simple to answer, for one, all you have to know is Rise over Run (or Rise/Run)...
This being:
Rise: the distance from one y value to the other...
Run: the distance from one x value to the other...
Naturally graph points are represented as (x, y).
So, all we need to is do the math....
For Rise: the distance from 5 to -12 is 17...
For Run: the distance from 3.5 (or 3 1/2) to 3.5 is 0, but because the denominator of ANY fraction can never be 0, we will change it to 1...
So, our equation looks like: 17/1 (or 17 over 1)...
And our answer is: The 2 points are EXACTLY 17 units apart...
Why do we state restrictions for rational expression and when do we state the restrictions?
Answers
We state restrictions for rational expressions to ensure that the denominator does not equal zero, as division by zero is undefined in mathematics. The restrictions are the values of the variable that make the denominator equal to zero. We state the restrictions whenever we are simplifying, performing operations with, or solving rational expressions.
A rational expression is an expression that can be written in the form of a fraction, where the numerator and the denominator are polynomials. The denominator of a rational expression cannot be zero because division by zero is not defined in mathematics. Therefore, when working with rational expressions, it is crucial to identify the values of the variable that would make the denominator equal to zero. These values are the restrictions, or domain restrictions, for the rational expression.
For example, consider the rational expression [tex]\(\frac{1}{x-3}\)[/tex]. The denominator is[tex]\(x-3\)[/tex]. To find the restriction, we set the denominator equal to zero and solve for [tex]\(x\)[/tex]:
[tex]\[x - 3 = 0\][/tex]
[tex]\[x = 3\][/tex]
Therefore, the restriction for this rational expression is [tex]\(x \neq 3\)[/tex], meaning that [tex]\(x\)[/tex] can be any real number except 3.
We must state these restrictions whenever we perform operations such as simplifying, adding, subtracting, multiplying, or dividing rational expressions, as well as when we are solving rational equations. This ensures that the operations are valid and that the solutions to the equations do not include any undefined expressions.
In summary, stating restrictions for rational expressions is a critical step in avoiding mathematical errors and ensuring that the expressions and equations we work with are well-defined.
Find the coordinates of point Q that lies along the directed line segment from R(-2, 4) to S(18, -6) and partitions the segment in the ratio of 3:7.
Answers
distance between (x1,y1) and (x2,y2) is
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
so distance between (-2,4) and (18,-6) is
[tex]D=\sqrt{(18-(-2))^2+(-6-4)^2}[/tex]
[tex]D=\sqrt{(18+2)^2+(-10)^2}[/tex]
[tex]D=\sqrt{(20)^2+100}[/tex]
[tex]D=\sqrt{400+100}[/tex]
[tex]D=\sqrt{500}[/tex]
D=10√5
so in ratio 3:7
3+7=10
3/10 of 10√5 is 3√5
I'm thinkin you want R then Q then S such that RQ:QS=3:7
so
distance from R to Q is 3√5
Q is (x,y)
R is (-2,4)
D=3√5
[tex]3\sqrt{5}=\sqrt{(-2-x)^2+(4-y)^2}[/tex]
[tex]3\sqrt{5}=\sqrt{x^2+4x+4+y^2-8y+16}[/tex]
square both sides
[tex]45=x^2+4x+4+y^2-8y+16[/tex]
[tex]45=x^2+y^2+4x-8y+20[/tex]
now, ithas to be on the line that R and S are on
do some simple math
slope is rise/run=-10/20=-1/2
y=-1/2x+b
4=-1/2(-2)+b
4=1+b
3=b
y=-1/2x+b
sub that for y in our other equation ([tex]45=x^2+y^2+4x-8y+20[/tex])
[tex]45=x^2+(\frac{-1}{2}x+3)^2+4x-8(\frac{-1}{2}x+3)+20[/tex]
I'm too lazy to show you expanstion and whatnot so I'll give you the solution
we get (after some manipulation)
0=x²+4x-32
what 2numbers multiply to get -32 and add to get 4?
-4 and 8
0=(x-4)(x+8)
set to zero
0=x-4
4=x
0=x+8
-8=x
but wait, -8 is not between -2 and 18 so it can't be
so x=4
remember, y=-1/2x+3
sub that to get y=-1/2(4)+3=-2+3=1
the point is (4,1)
apologies for mishap
Answer:
(2 2/7, 5 1/3)
Step-by-step explanation:
The coordinates of point Q, lies along R(-2,4) and S(18,-6)
thus, QR and RS, that is in ratio of QR : RS = 3 : 7
Let point Q = (x,y)
Hence, QR = -2 - x; RS = -6 - 4
Thus, QR/RS = 3/7, which is: (-2 - x)/(-6 - 4) = 3/7
7(-2 - x) = -30
-14 - 7x = -30
7x = 16
∴ x = 16/7 = 2 2/7
If x : y = 3 : 7 ( where x = 2 2/7)
Hence, (2 2/7)/y = 3/7
3y = 16
∴ y = 16/3 = 5 1/3
The coordinates of point Q = (2 2/7, 5 1/3)
JL is a common tangent to circles M and K at point J. If angle MLK measures 61ᵒ, what is the length of radius MJ? Round to the nearest hundredth. (Hint: Show that triangles LMJ and LKJ are right triangles, and then use right triangle trigonometry to solving for missing sides of the right triangles.)
Answers
To find the length of radius MJ, we can use right triangle trigonometry. Firstly, we can show that triangles LMJ and LKJ are right triangles. Then, we can use the given angle MLK of 61ᵒ to find the length of radius MJ, using the sine function. The equation to find MJ is MJ = rM * sin(29ᵒ).
Explanation:To find the length of radius MJ, we can use right triangle trigonometry. Firstly, we can show that triangles LMJ and LKJ are right triangles. Since JL is a common tangent, it is perpendicular to the radii of the circles at points J. Therefore, angle LMJ and angle LKJ are right angles. Now, we can use the given angle MLK of 61ᵒ to find the length of radius MJ.
Let's call the radius of circle M rM and the radius of circle K rK. In triangle LMJ, we have the following relationships:
angle LMJ = 90ᵒ (since it is a right triangle)angle MLJ = angle MLK - angle JLK = 61ᵒ - 90ᵒ = -29ᵒ (since angle JLK is a right angle)angle MJL = angle JML = 90ᵒ - angle MLJ = 90ᵒ - (61ᵒ - 90ᵒ) = 119ᵒUsing the sine function, we can find the length of side MJ:
sin(angle MLJ) = length of side MJ / length of side LJ
sin(-29ᵒ) = MJ / rM
Since sin(angle MLJ) = -sin(angle MJL), we can rewrite the equation as:
sin(29ᵒ) = MJ / rM
Now, we can rearrange the equation to solve for MJ:
MJ = rM * sin(29ᵒ)
Since we are not given the values of rM or rK, we cannot find the specific value of MJ. However, we can use this equation to find the length of radius MJ if we are given the values of the radii of the circles and the given angle MLK.
Remember to round the answer to the nearest hundredth as specified in the question.
In a batch of 280 water purifiers, 12 were found to be defective. What is the probability that a water purifier chosen at random will be defective? Write the probability as a percent. Round to the nearest tenth of a percent if necessary
Answers
If 12 were found to be defective out of 280 the experimental probability of a purifier being defective is:
12/280 which is:
4.3% (to nearest tenth of a percent)
Answer:
[tex]\text{Probability}=4.3\%[/tex]
Step-by-step explanation:
Given : In a batch of 280 water purifiers, 12 were found to be defective.
To find : What is the probability that a water purifier chosen at random will be defective? Write the probability as a percent.
Solution :
Total number of batch of purifiers = 280
Number of defective purifiers = 12
The probability that a water purifier chosen at random will be defective is given by,
[tex]\text{Probability}=\frac{\text{Favorable outcome}}{\text{Total outcome}}[/tex]
[tex]\text{Probability}=\frac{12}{280}[/tex]
[tex]\text{Probability}=\frac{3}{70}[/tex]
Converting into percentage,
[tex]\text{Probability}=\frac{3}{70}\times 100[/tex]
[tex]\text{Probability}=4.28\%[/tex]
Round to nearest tenths,
[tex]\text{Probability}=4.3\%[/tex]
Find the X intercepts of the parabola with the vertex (1,-9) and y intercept of (0,-6)
Answers
y=a(x-1)^2-9 and we are given the point (0,-6)
-6=a(-1)^2-9
-6=a-9
3=a
y=3(x-1)^2-9
The x-intercepts occur when y=0 so
3(x-1)^2-9=0 divide both sides by 3
(x-1)^2-3=0
(x-1)^2=3
x-1=±√3
x=1±√3
So the intercepts are the points:
(1+√3, 0) and (1-√3, 0)
The x-intercepts of the parabola with vertex (1,-9) and y-intercept of (0,-6) are of [tex]x = 1 \pm \sqrt{3}[/tex].
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
In this problem, the parabola has vertex (1,-9), hence h = 1, k = -9, and:
y = a(x - 1)^2 - 9.
The y-intercept is of (0,-6), hence when x = 0, y = -6, and this is used to find a.
-6 = a - 9
a = 3.
So the equation is:
y = 3(x - 1)^2 - 9.
y = 3x² - 6x - 6.
The x-intercepts are the values of x for which:
3x² - 6x - 6 = 0.
Then:
x² - 2x - 2 = 0.
Which has coefficients a = 1, b = -2, c = -2, hence:
[tex]\Delta = b^2 - 4ac = (-2)^2 - 4(1)(-2) = 12[/tex]
[tex]x_1 = \frac{2 + \sqrt{12}}{2} = 1 + \sqrt{3}[/tex]
[tex]x_2 = \frac{2 - \sqrt{12}}{2} = 1 - \sqrt{3}[/tex]
The x-intercepts of the parabola are [tex]x = 1 \pm \sqrt{3}[/tex].
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Find the area of a regular hexagon whose side length is 16 in. and the apothem is 8 square root of 3 in
Answers
polygon area = 6 * 16 * 13.8564064606 / 2
polygon area = 665.1075101088 square inches
A rectangular shipping container has a volume of 2500 cubic cm. The container is 4 times as wide as it is deep, and 5cm taller than it is wide. What are the dimensions of the contaner?
Answers
4x = width
4х+5 = height
[tex]x*4x*(4x+5)=2500 \\ 4x^2(4x+5)=2500\\ 16x^3+20x^2-2500 = 0 \ \ |:4 \\ 4x^3 +5x^2-625=0 \\ 4x^3-20x^2+25x^2-625=0 \\ 4x^2(x-5)+25(x^2-25)=0 \\ 4x^2(x-5)+25(x-5)(x+5)=0 \\ (x-5)(4x^2+25(x+5))=0 \\ (x-5)(4x^2+25x+125)=0\\x-5=0 \ \ \ \ \ or \ \ \ 4x^2+25x+125=0 \\ \boxed{x=5} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ D=25^2-4*4*125=-1375 \to \ no \ real \ solutions [/tex]
We got one solution x=5. Let's find the measurements of the container:
depth = x = 5 cm
width = 4x = 4*5 = 20 cm
height = 4x+5 = 4*5+5 = 25 cm
The question asks for the dimensions of a rectangular container with given volume and specific proportional relationships between its dimensions. Setting up and solving the equation 2500 = d × (4d) × (4d + 5) leads us to find the distinct depth, width, and height of the container.
Explanation:The subject matter of the student's question pertains to the mathematics concepts of volume and dimensional relationships of rectangular prisms. Let's represent the depth of the shipping container as d, the width as 4d (since it is four times the depth), and the height as 4d + 5 (since it is 5cm taller than the width). The volume of a rectangular prism (such as our shipping container) is given by the formula Volume = length × width × height. Given the volume is 2500 cubic cm, or 2500 cm³, we can set up the equation 2500 = d × (4d) × (4d + 5).
Solving this equation leads us to find the dimensions of the container, wherein the depth, width, and height are represented by the variables d, 4d, and 4d + 5
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What is the 5th term of an arithmetic sequence if t3 = 10 and t7 = 26?
18
20
22
24
Answers
A Ferris wheel has a diameter of 42 feet. It rotates 3 times per minute. Approximately how far will a passenger travel during a 5-minute ride?
132 feet
659 feet
1,978 feet
3,956 feet
Answers
The diameter is 2r, so we have to divide 42 by two. You get 21 for the radius. We will use 3.14 for the pi.
then you plug it in to the formula
C = 2 (3.14) * 21
The answer is 131.88
Then times that with 3
you get 395.64
but since it has been 5 minutes, then you times it with 5
that's 1,978.2
Approximately 1978 ft a passenger travel during a 5-minute ride and this can be determined by using the formula of the perimeter of a circle.
Given :
A Ferris wheel has a diameter of 42 feet. It rotates 3 times per minute.
The following steps can be used in order to determine the total distance travel by the passenger during a 5 minutes ride:
Step 1 - First determine the perimeter of the circle. The formula of the perimeter of the circle is given by:
[tex]\rm C = 2\pi r[/tex]
Step 2 - Now, substitute the value of known terms in the above formula.
[tex]\rm C=2\pi\times(21)[/tex]
[tex]\rm C= 131.94\;ft[/tex]
Step 3 - In one minute passenger travels:
[tex]\rm =131.94\times 3=395.82\; ft[/tex]
Step 4 - So, in three minutes passenger travels:
[tex]=395.82\times5[/tex]
= 1978 ft
So, approximately 1978 ft a passenger travel during a 5-minute ride.
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Can anyone please help ASAP, will give thanks and all that fun stuff
Answers
(every time i use a in this, i mean a1)
Answer:
The answer is B!!!!
The point (–3, –5) is on the graph of a function. Which equation must be true regarding the function?
f(–3) = –5
f(–3, –5) = –8
f(–5) = –3
f(–5, –3) = –2
Answers
Answer:
Option 1st is correct
[tex]f(-3) = -5[/tex]
Step-by-step explanation:
If any point [tex](x, y)[/tex] is on the graph then we can write the function as:
[tex]y= f(x)[/tex]
where
x is the independent variable and
y is the dependent variable.
As per the statement:
The point (–3, –5) is on the graph of a function.
⇒x = -3 and y = -5
By above definition we have;
[tex]f(-3) = -5[/tex]
Therefore, the equation must be true regarding the function is, [tex]f(-3) = -5[/tex]
just need to check these answers
Answers
Good luck in your next tests.
A doorway is 8 feet high and 4 feet wide. A square piece of plywood needs to be moved through the doorway. The plywood is 10 feet long and 10 feet wide. The door is a rectangle with a height of 8 feet, and a width of 4 feet. A dotted line shows the diagonal.
Will the piece of plywood fit through the door if it is tilted diagonally?
A. No, because the length of the diagonal is close to 9 feet.
B. No, because the height of the door is less than 10 feet.
C. Yes, because the length of the diagonal is close to 11 feet.
D. Yes, because the sum of the height and width of the door is greater than 10 feet.
Answers
d^2=x^2+y^2
d^2=8^2+4^2
d^2=64+16
d^2=80
d=√80
d=4√5 ft
d≈8.944
So
A. No because the diagonal is close to 9 feet.
After calculating the diagonal of the doorway to be approximately 8.944 feet using the Pythagorean theorem, it's clear that the 10-foot square piece of plywood will not fit diagonally through the door. Thus, the correct answer is option (A).
The question is whether a 10-foot square piece of plywood can fit through an 8-foot by 4-foot doorway when tilted diagonally. To determine if the plywood can fit, we need to calculate the diagonal of the doorway using the Pythagorean theorem which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed as c² = a² + b² where c is the hypotenuse, and a and b are the other two sides.
Let's apply the theorem to our doorway:
Height (a) = 8 feet
Width (b) = 4 feet
Diagonal (c) = ?
We calculate the diagonal:
c² = a² + b²
c² = 8² + 4²
c² = 64 + 16
c² = 80
c = sqrt(80)
c = 8.944 feet (approx)
The diagonal of the doorway is approximately 8.944 feet, which is less than the 10 feet length of the plywood. Therefore, the correct answer is:
No, because the length of the diagonal is close to 9 feet.
The option (A) is correct.
Transform (5 square root x^7)^3 into an expression with a rational exponent
Answers
[tex](5 \sqrt{ x^{7} } ) ^{3} [/tex]
First start out by simplfiying the square root of [tex] x^{7} [/tex]
[tex] \sqrt[2]{ x^{7} } [/tex] in fraction form pulls the 2, which is called the index over as the denominator in the exponent, with the 7 being the numerator. So that expression as a square root looks like this as an rational exponent:
[tex] x^{ \frac{7}{2} } [/tex]
But we still have the 5 to content with, so let's add that in there:
[tex][5( x^{ \frac{7}{2} } )] ^{3} [/tex]
not only is the exponent cubed now by multiplication, so is the 5:
[tex]125 x^{ \frac{21}{2} } [/tex]
In order to transform (5 square root x^7)^3 into an expression with a rational exponent, first transform square root x^7 into x^(7/2), then raise entire expression to the power of 3. So, final expression is 125x^(21/2).
Explanation:To transform (5 square root x^7)^3 into an expression with a rational exponent, firstly simplify the expression inside the bracket, then apply the exponent of 3 to the simplified expression.
Inside the brackets, square root of x^7 can be written as x^(7/2). So, the first parenthesis can be transformed into 5x^(7/2). Now, raise this to the power of 3. The rule for powers of powers is to multiply the powers. So, 5 cubed is 125 and (x^(7/2))^3 is x^(21/2).
So, the transformed expression with a rational exponent is 125x^(21/2).
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The domain of the function is given. Find the range.
f(x) = 2x - 1
Domain: {-2, 0, 2, 4}
Answers
So for x = -2, f(x) = 2(-2) - 1 = -5
The range will consist of -5 and the other 3 values of f(x) found for x = 0, x=2 and x=4.
Suppose you buy a CD for $500 that earns 2.5% APR and is compounded quarterly. The CD matures in 3 years. How much will the CD be worth at maturity?
Answers
A=p (1+r/k)^kt
A future value?
P present value 500
R interest rate 0.025
K compounded quarterly 4
T time 3years
A=500×(1+0.025÷4)^(4×3)
A=538.82