Which are the solutions to the quadratic equation 4x^2=64?
A. x=-16 and x=16
B. x=-8 and x=8
C. x=-4 and x=4
D.x=-2 and x=2
Answer: x= -4, 4
Step-by-step explanation:
Using a straightedge draw a random triangle now carefully cut it out next amputate the angles by snipping through adjacents sides now move the angles together so the vertices all touch
It should be noted that a triangle is a polygon with three edges and three vertices.
What is a triangle?A triangle is a simple closed curve or a polygon that is formed by three line segments.
It should be noted that triangles have 180°. In this case, looking at the attached figure, it can be deduced that the addition of the angles equals 180.
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The formula for volume of this rectangular prism is:
V = 2x 3 + 17x 2 + 46x + 40
Find an expression for the missing side length. Show all of your work for full credit.
The volume of a rectangular prism is the product of its dimension.
The missing side length is 2x + 5.
The volume is given as:
[tex]\mathbf{V = 2x^3 + 17x^2 + 46x + 40}[/tex]
Let the missing side be y.
So, we have:
[tex]\mathbf{V = (x + 2) \times ( x + 4) \times y}[/tex]
So, we have:
[tex]\mathbf{(x + 2) \times ( x + 4) \times y = 2x^3 + 17x^2 + 46x + 40}[/tex]
Factorize
[tex]\mathbf{(x + 2) \times ( x + 4) \times y = (x + 2) \times (x + 4) \times (2x +5)}[/tex]
Cancel out common factors
[tex]\mathbf{y = (2x +5)}[/tex]
Remove brackets
[tex]\mathbf{y = 2x +5}[/tex]
Hence, the missing side length is 2x + 5.
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a business analyst makes 20$ an hour for the first 42 hours he works during a week and 28$ an hour for each worked over 42 hours. which piecewise equation models his weekly pay y in dollars as it relates to the number of hours x that he has worked during the week
Answer:
[tex]y=28(x-42)+840[/tex]
Step-by-step explanation:
Let he works for x hours in total.
We are given that he makes 20$ an hour for the first 42 hours
So, he earns in 1 hour = 20
He earns in 42 hours = [tex]20 \times42[/tex]
= [tex]840[/tex]
Now we are given that he earns $28 an hour for each hour worked over 42 hours.
Since he worked for 42 hours out of x hours .
So, remaining hours = x-42 hours
So,he earns for x-42 hours = [tex]28\times(x-42)[/tex]
y denotes his total earning of weekly
So, total earning [tex]y=28(x-42)+840[/tex]
Hence piecewise equation models his weekly pay y in dollars as it relates to the number of hours x that he has worked during the week is [tex]y=28(x-42)+840[/tex]
Part A: Jake rented a kayak at $26 for 3 hours. If he rents the same kayak for 5 hours, he has to pay a total rent of $42. Write an equation in the standard form to represent the total rent (y) that Jake has to pay for renting the kayak for x hours. (4 points)
Part B: Write the equation obtained in Part A using function notation. (2 points)
Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals. (4 points)
Answer:
8x+2
fx= 8x+2
Step-by-step explanation:
Find the area of A cylinder has a volume of 175 cubic units and a height of 7 units. The diameter of the cylinder is
Prism A is similar to Prism B. The volume of Prism A is 2080 cm³.
What is the volume of Prism B?
A.260 cm³
B.520 cm³
C.1040 cm³
D.16,640 cm³
Will give brainliest answer!
Final answer:
Prism B's volume is 8 times larger than Prism A's volume due to the dimensions being twice as large. Given the volume of Prism A as 2080 cm³, the volume of Prism B is 16640 cm³.
Explanation:
The student is asking about the volume of similar prisms. When two prisms are similar, their volumes are proportional to the cube of the ratio of their corresponding linear dimensions. In this case, Prism B is similar to Prism A, and the ratio of the volumes is given in the problem. Specifically, the volume of Prism B is 4 times the volume of Prism A because the dimensions of Prism B are twice that of Prism A, making the volume 23 or 8 times greater. However, you've also provided that the volume of Prism B is 4 times that of Prism A, this seems to be a conflict in the information, and there's an issue with typos in the provided content which makes it inconsistent (2L3 versus 213, 213). Based on the correct proportion which should be 8 times, if the volume of Prism A is 2080 cm3, then the volume of Prism B would be 2080 cm3 multiplied by 8 (8L3/L3), yielding 16640 cm3.
F(x) = x4/5(x − 6)2 find the critical numbers of the function
Final answer:
To find the critical numbers, differentiate the function using the product rule, set the derivative equal to zero, and solve for x. Critical numbers are where the derivative is zero or undefined, provided they are within the domain of the function.
Explanation:
To find the critical numbers of the function f(x) = x4/5(x − 6)2, you need to locate the values of x where the first derivative of the function is either zero or undefined. The first derivative can be calculated using the product rule and the power rule.
First, let's find the derivative:
f'(x) = d/dx [x4/5] * (x - 6)2 + x4/5 * d/dx [(x - 6)2]
After simplifying, you will get a derivative function where you can then set it equal to zero to find the critical points. The points where the derivative is zero are potential local maxima, minima, or points of inflection. Additionally, points where the derivative is undefined can also be critical points, if they are within the domain of the function.
Once you calculate and simplify the derivative, set it equal to zero and solve for x. You might find that you get explicit values of x, which are the critical numbers of the function. If the function's derivative does not exist at some point, that will also be a critical number.
Remember, critical numbers are only relevant if they are within the domain of the original function.
If g(x) is the inverse of f(x) and f(x) = 4x+12 what is g(x)?
Answer:
Inverse function: A function g is the inverse of a function f if whenever y=f(x) then x=g(y).
In other words, we can write this in terms of the composition of f and g as g(f(x))=x.
For any input x, the function corresponding to f spits out the value y=f(x)=4x+12.
Now, we want to find the inverse function g(x)=[tex]f^{-1}[/tex] that takes the value y as an input and spits out x as the output.
In other words, y=f(x) gives y as a function of x and we want to find [tex]x=f^{-1}(y)[/tex] that will give us x as a function of y.
Given,the expression y=4x+12 for y as a function of x and solve for x.
Subtract 12 from both sides we get;
y-12 = 4x+12-12
Simplify:
y-12 = 4x
Divide by 4 to both sides we get;
[tex]\frac{y-12}{4} =\frac{4x}{4}[/tex]
Simplify:
[tex]x=\frac{1}{4}y - 3[/tex]
therefore, [tex]x = f^{-1}(y) = \frac{1}{4}y-3[/tex]
since, g(x) is the inverse of f(x)
⇒[tex] g(x)=\frac{1}{4}x-3[/tex]
Now, verify that g(x) is really the inverse of f(x), we should show that the composition of f and g doesn't do anything to the input.
[tex](g o f)(x) = g(f(x)) = g(4x+12) = \frac{1}{4}(4x+12) -3 = x+3 -3[/tex]
Simplify:
g(f(x)) = x for all x
⇒ g(x) is the inverse of f(x)
Therefore, [tex] g(x)=\frac{1}{4}x-3[/tex]
Using inverse functions, it is found that that:
[tex]g(x) = \frac{x - 12}{4}[/tex]
To find the inverse function, we exchange x and y in the original function, then isolate f.
The function f(x) is given by:
[tex]f(x) = 4x + 12[/tex]
Function g(x) is the inverse of f(x), then:
[tex]y = 4x + 12[/tex]
[tex]x = 4y + 12[/tex]
[tex]4y = x - 12[/tex]
[tex]y = \frac{x - 12}{4}[/tex]
[tex]g(x) = \frac{x - 12}{4}[/tex]
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need help thank thank you
Which expressions are completely factored?
Select each correct answer.
A. 16a^5−20a^3=4^3(4a^2−5)
B. 24a^4+18=6(4a^4+3)
C. 30a^6−24a^2=3a^2(10a^4−8)
D. 12a^3+8a=4(3a^3+2a)
Answer:
B
Step-by-step explanation:
The only thing that you can factor out of B is 6, while the others are not in simplest form. Answer C can still factor out 2 and answer choice D can still factor out a. Answer choice can still be factored further using difference of squares.
ASAP PLEASE:
Segment RS is congruent to segment DF. Which congruence statement is true?
- RS ≅ DF
- RS ≅ SFD
- RS ≅ SF
- RS ≅ RD
Answer:
A. [tex]\text{ Arc RS}\cong \text{Arc DF}[/tex]
Step-by-step explanation:
We have been given a circle and we are told that segment RS is congruent to segment DF.
We can see that segment RS corresponds to arc RS and segment DF corresponds to arc DF.
As both segments are congruent, therefore, both arcs will be congruent as well.
We can represent this information as:
[tex]\text{ Arc RS}\cong \text{Arc DF}[/tex]
Therefore, option A is the correct choice.
which rule describes the translation PQR --> P'Q'R'?
Jacey obtains a 30-year 6/2 ARM at 4% with a 2/6 cap structure in the amount of $224,500. What is the monthly payment during the initial period?
General Idea:
We need to make use of the below formula to find the monthly payment..
[tex] Monthly \; Payment\; =\; \frac{P \times \frac{r}{12}}{(1-(1+\frac{r}{12})^{-m})} \\ \\ Where:\\ P\; is\; Principal\\ r\; is\; rate\; in\; decimal\; form\\ m\; is\; number\; of\; monthly\; payments [/tex]
Applying the concept:
Given:
[tex] P=\$224,500\\ r=4\%=0.04\\ m=30\; year \times 12 \; months/year=360\\ [/tex]
Substituting the given in the formula we will get the monthly payment.
[tex] Monthly\; Payment\; =\; \frac{224500 \times \frac{0.04}{12}}{(1-(1+\frac{0.04}{12})^{-360})} =\frac{\frac{8980}{12}}{(1-0.301796)} =\frac{748.3333}{0.698204} \\ \\ Monthly \; Payment= \$1071.7975 [/tex]
Conclusion:
The monthly payment during the initial period is $1072.
PLEASE HELP
7.06
1. Find the first six terms of the sequence.
a1 = -7, an = 4 • an-1
A) -7, -28, -112, -448, -1792, -7168
B) -28, -112, -448, -1792, -7168, -28,672
C) -7, -28, -24, -20, -16, -12
D) 0, 4, -28, -24, -20, -16
2. Find an equation for the nth term of the arithmetic sequence.
-13, -8, -3, 2, ...
an = -13 x 5(n - 1)
an = -13 + 5(n - 1)
an = -13 + 5(n + 2)
an = -13 + 5(n + 1)
3. Find an equation for the nth term of the arithmetic sequence.
a15 = -53, a16 = -5
A) an = -725 - 48(n - 1)
B) an = -725 + 48(n + 1)
C) an = -725 + 48(n - 1)
D) an = -725 - 48(n + 1)
4. Determine whether the sequence converges or diverges. If it converges, give the limit.
11, 44, 176, 704, ...
A) Diverges
B) Converges; 231
C) Converges; 3751
D) Converges; 935
5. Find an equation for the nth term of the sequence.
-4, -16, -64, -256, ...
A) an = 4 • -4n
B) an = 4 • -4n + 1
C) an = -4 • 4n
D) an = -4 • 4n - 1
6. Find an equation for the nth term of a geometric sequence where the second and fifth terms are -2 and 16, respectively.
A) an = 1 • (-2)n - 1
B) an = 1 • 2n
C) an = 1 • (-2)n + 1
D) an = 1 • 2n - 1
7. Write the sum using summation notation, assuming the suggested pattern continues.
4 - 24 + 144 - 864 + ...
A) summation of four times six to the power of n from n equals zero to infinity
B) summation of four times negative six to the power of n from n equals zero to infinity
C) summation of four times negative six to the power of the quantity n minus one from n equals zero to infinity
D) summation of four times six to the power of the quantity n plus one from n equals zero to infinity
8. Write the sum using summation notation, assuming the suggested pattern continues.
-3 + 6 + 15 + 24 + ... + 132
A) summation of negative 27 times n from n equals 0 to infinity
B) summation of negative 27 times n from n equals 0 to 15
C) summation of the quantity negative 3 plus 9 n from n equals 0 to infinity
D) summation of the quantity negative 3 plus 9 n from n equals 0 to 15
9. Write the sum using summation notation, assuming the suggested pattern continues.
343 + 512 + 729 + 1000 + ... + n3
A) summation of the quantity n minus 1 cubed from n equals 7 to infinity
B) summation of n cubed from n equals 7 to infinity
C) summation of n cubed from n equals 8 to infinity
D) summation of the quantity n plus 1 cubed from n equals 7 to infinity
10. Find the sum of the arithmetic sequence.
3, 5, 7, 9, ..., 21
A) 39
B) 120
C) 20
D) 23
11. Find the sum of the geometric sequence.
4 divided by 3, 16 divided by 3, 64 divided by 3, 256 divided by 3, 1024 divided by 3
A) 1363 divided by 3
B) 1364 divided by 15
C) 1364 divided by 3
D) 1363 divided by 15
12. An auditorium has 20 rows with 10 seats in the first row, 12 in the second row, 14 in the third row, and so forth. How many seats are in the auditorium?
A) 390
B) 580
C) 620
D) 400
13. Use mathematical induction to prove the statement is true for all positive integers n.
10 + 20 + 30 + ... + 10n = 5n(n + 1)
14. A certain species of tree grows an average of 4.2 cm per week. Write an equation for the sequence that represents the weekly height of this tree in centimeters if the measurements begin when the tree is 300 centimeters tall.
LM¯¯¯¯¯¯¯ is the midsegment of trapezoid ABCD . AB=78 and DC=142 . What is LM ?
A telephone pole is perpendicular to the ground. What is the size of the angle between the ground and the telephone pole? How do you know?
Triangle RST is congruent to triangle WXY. If the area of triangle WXY is 20 square inches, then the area of triangle RST is _____.
40 in2
10 in2
20 in2
80 in2
The area of triangle RST is also 20 20 square inches
What are congruent triangles?Triangles having equal side lengths and equal corresponding angles measures are called congruent triangles.
Given that, triangle RST is congruent to triangle WXY, the area of triangle WXY is 20 square inches,
We are asked to find the area of triangle RST,
Since, triangles RST and WXY are congruent, therefore, they will have congruent sides and angles,
That means, they will have equal area also,
ar (Δ RST) = ar (Δ WXY)
Therefore,
ar (Δ RST) = 20 square inches
Hence, the area of triangle RST is also 20 20 square inches
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y=x-8/x^2+4x-5 find any points of discontinuity for the rational function
a. x=5, x=1
b. x=-5, x=1
c. x=8
d. x=5, x=-1
Answer:
x=-5, x=1
Step-by-step explanation:
y=x-8/x^2+4x-5
[tex]y=\frac{x-8}{x^2+4x-5}[/tex]
When denominator becomes 0 in a rational function then there will be a break in the graph
To find any points of discontinuity for the rational function , we set the denominator =0 and solve for x
x^2 + 4x -5 =0
Now we factor x^2 +4x -5
product is -5 and sum = 4
5 * (-1) = -5
5 +(-1) = 4
(x+5)(x-1) =0
set each factor =0 and solve for x
x+5=0 , so x= -5
x-1=0 , so x= 1
x=-5, x=1 are the points of discontinuity for the rational function
Answer:
x=-5 , X=1
Step-by-step explanation:
Which is the formula for the volume of a sphere with diameter d?
A. S= 4πd²
B. S= πd²
C. S= [tex] \frac{4}{3} [/tex]πd³
D. S= [tex] \frac{1}{6} [/tex]πd³
What is the m∠ABC?
1)m∠ABC = 60°
2)m∠ABC = 67°
3)m∠ABC = 120°
4)m∠ABC = 127°
we are given
m∠BCD =67
and m∠BDC=60
we know that
m∠ABC is exterior angle
m∠BCD and m∠BDC are interior angles
exterior angle is sum of interior angles
so, we can write it as
m∠ABC=m∠BCD+m∠BDC
now, we can plug values
and we get
m∠ABC=60+67
m∠ABC=127
so, option-4.........Answer
please help im confused....
which ordered pair is a solution of the inequality?
2y+6<8
a. (4,13)
b. (-5,2)
c.(0,6)
d.(4,8)
helppppppppppppppppppppppp
Find an equation of the line that satisfies the given conditions. through (−1, −3); perpendicular to the line 2x + 7y + 2 = 0
Boyles law involves the pressure and volume of gas in a container. It can be repersented by the formula p sub 1 v sub 1= p sub 2 v sub 2. When the formula is solved for p sub 2, the results is
Boyle's Law can be rearranged to solve for p sub 2 (final pressure) using the formula p sub 2 = p sub 1 v sub 1 / v sub 2. This shows the inverse relationship between pressure and volume of gas at a constant temperature.
Explanation:The question is asking to solve the formula representing Boyle's Law (p sub 1 v sub 1 = p sub 2 v sub 2) for p sub 2. Boyle's Law states that the pressure and volume of a gas have an inverse relationship when temperature is held constant. To solve for p sub 2, you rearrange the formula to be p sub 2 = p sub 1 v sub 1 / v sub 2. This formula means that the final pressure (p sub 2) equals the initial pressure (p sub 1) times the initial volume (v sub 1), all divided by the final volume (v sub 2). Therefore, if the volume increases, the pressure decreases, and if the volume decreases, the pressure increases, keeping the gas's temperature constant.
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Each of the 14 students in the art club needs 4 ounces of paint for a project. The art store sells paint only in 8-ounce bottles. How many bottles of paint does the art club president need to buy for the project?
Answer: The art club president need to buy 14 bottles of paint for the project.
Step-by-step explanation: Given that each of the 14 students in the art club needs 4 ounces of paint for a project. The art store sells paint only in 8-ounce bottles.
We are to find the number of bottles of paint that the art club president need to buy for the project.
We will be using the unitary method to solve the given problem.
Number of bottles filled by 8 ounces of paint = 1.
So, the number of bottles filled by 1 ounce of paint is
[tex]\dfrac{1}{8}.[/tex]
So, the number of bottles filled by 4 ounces of paint will be
[tex]\dfrac{1}{8}\times4=\dfrac{1}{2}.[/tex]
Now, number of bottles of paint needed by 1 student [tex]=\dfrac{1}{2}.[/tex]
Therefore, the number of bottles of paint needed by 14 students will be
[tex]\dfrac{1}{2}\times14=7.[/tex]
Thus, the art club president need to buy 14 bottles of paint for the project.
Find the value of x. The diagram is not drawn to scale.
Answer:
C. [tex]x=99^{\circ}[/tex]
Step-by-step explanation:
We have been given a image. We are asked to find the value of x.
We can see that our given figure is a quadrilateral. We know that all interior angles of a quadrilateral add up-to 360 degrees.
[tex]x^{\circ}+y^{\circ}+125^{\circ}+72^{\circ}=360^{\circ}[/tex]
We can see that y and 116 degrees angles are linear angles, so we can set an equation as:
[tex]y^{\circ}+116^{\circ}=180^{\circ}[/tex]
[tex]y^{\circ}+116^{\circ}-116^{\circ}=180^{\circ}-116^{\circ}[/tex]
[tex]y=64^{\circ}[/tex]
Substitute [tex]y=64^{\circ}[/tex] in the equation:
[tex]x^{\circ}+y^{\circ}+125^{\circ}+72^{\circ}=360^{\circ}[/tex]
[tex]x^{\circ}+64^{\circ}+125^{\circ}+72^{\circ}=360^{\circ}[/tex]
[tex]x^{\circ}+261^{\circ}=360^{\circ}[/tex]
[tex]x^{\circ}+261^{\circ}-261^{\circ}=360^{\circ}-261^{\circ}[/tex]
[tex]x^{\circ}=99^{\circ}[/tex]
[tex]x=99[/tex]
Therefore, the value of x is 99.
Use the rules of significant figures to answer the following question:
67.31 - 8.6 + 212.198
A. 270.9
B. 271
C. 270.908
D. 270
Answer:
A. 270.9
Step-by-step explanation:
We know that the rule of significant figures for addition and subtraction states that 'the number of places after the decimal point in the result is equal to the least number of decimal places in each term.'
So, 67.31 - 8.6 + 212.198 = 67.31 + 212.198 - 8.6 = 279.508 - 8.6 = 270.908
Now, the resultant number is 270.908
Using the rule of significant figures, we get that, the number of places after the decimal point in 270.908 will be equal to the least number of decimal places i.e. 1 ( in 8.6 )
Hence, 67.31 - 8.6 + 212.198 = 270.9
Between the ages of 24 months and 6 years, the average child will gain _____ in height. 1 foot 1.5 feet 8 inches 4 inches
The values √8 and √14 are plotted on the number line.
What is the approximate difference in tenths between the two values?
0.5
0.9
1.1
2.4
Answer:
The correct option is 2.
Step-by-step explanation:
The values √8 and √14 are plotted on the number line.
From the given number line it is clear that
[tex]\sqrt{8}\approx 2.8[/tex]
[tex]\sqrt{14}\approx 3.7[/tex]
We have to find the approximate difference in tenths between the two values √8 and √14.
[tex]\sqrt{14}-\sqrt{8}\approx 3.7-2.8[/tex]
[tex]\sqrt{14}-\sqrt{8}\approx 0.9[/tex]
The approximate difference in tenths between the two values is 0.9.
Therefore the correct option is 2.