What is 7.5 as a fraction ?
The sum of nine times a number and fifteen is less than or equal to the sum of twenty-four and ten times the number
What is 20% of 300 EXPLAIN ...?
Carlon plans to evaporate a number of gallons of water from 90 gallons of a 15% salt solution to make a 25% salt solution. Which equation can he use to find x, the number of gallons that should be evaporated?
the options are
1. 13.5/90-x = 25/100
2. 13.5/x =25/100
3. 13.5(90-x) = 0.25
4. 13.5(90-x) = 25
A
first option is correct
5 1/3 * (-3 9/18) Simplify and Show your work
Which of these terms does not describe polygon A'B'C'D ?
A) rotation
B) image
C) preimage
D) transformation
Answer:
Hence, Option: C is correct.
The term that does not describe polygon A'B'C'D' is:
Pre-image.
Step-by-step explanation:
Clearly we could observe that the polygon A'B'C'D' is the image that is obtained by the applying some transformation to the polygon ABCD.
The transformation that is applied to ABCD to obtain A'B'C'D' is:
Rotating the figure anticlockwise 90° and then translating it 7 units to the left and 1 unit downward.
Hence, Polygon A'B'C'D' is not a pre-image.
Since it is an image which is formed or obtained by applying required transformation to the pre-image ABCD.
The correct option is C) preimage. Polygon [tex]\(A'B'C'D'\)[/tex] is the image of the transformation, not the preimage.
To determine which term does not describe polygon [tex]\(A'B'C'D'\)[/tex], we need to understand the definitions of each term in the context of transformations in geometry:
Rotation : This is a type of transformation that turns a figure around a fixed point at a certain angle. Polygon [tex]\(A'B'C'D'\)[/tex] could be a result of rotating polygon [tex]\(ABCD\)[/tex]
Image : The image is the result of applying a transformation to a figure. [tex]A'B'C'D'\)[/tex] is the image of [tex]\(ABCD\)[/tex] after some transformation.
Preimage : The preimage is the original figure before a transformation is applied. In this context, [tex]\(ABCD\)[/tex] is the preimage, not [tex]\(A'B'C'D'\)[/tex]
Transformation : This is a general term that refers to any operation that moves or changes a figure in some way to produce a new figure. The process that produced [tex]\(A'B'C'D'\)[/tex] from [tex]\(ABCD\)[/tex] is a transformation.
From these definitions, the term that does not describe polygon [tex]\(A'B'C'D'\)[/tex] is preimage.
Factor 9x3 + 18x2 – x – 2
...?
To factor the polynomial 9x^3 + 18x^2 − x − 2, group terms to factor out common factors and then factor further if possible. The factored form is (x + 2)(3x + 1)(3x - 1).
Explanation:To factor the polynomial 9x3 + 18x2 − x − 2, we look for common factors and use techniques such as grouping. First, we can try to group the terms in pairs and factor out the greatest common factor from each pair.
Let's group the first two terms and the last two terms separately:
(9x3 + 18x2) − (x + 2)From the first group, we can factor out 9x2 and from the second group, we can factor out -1:
9x2(x + 2) - 1(x + 2)We now have a common factor of (x + 2) that we can factor out:
(x + 2)(9x2 - 1)The expression 9x2 - 1 is a difference of squares, which can be factored further:
(x + 2)(3x + 1)(3x - 1)So, the fully factored form of the given polynomial is (x + 2)(3x + 1)(3x - 1).
The polynomial 9x^3 + 18x^2 - x - 2 can be factored by grouping and by recognizing the difference of squares, resulting in the factors (x + 2)(3x + 1)(3x - 1).
Explanation:The student has asked to factor the polynomial 9x3 + 18x2 - x - 2. Factoring polynomials is a process of expressing a polynomial as a product of its factors, which can involve numbers, variables, or both. This can make the expression simpler or more useful for further mathematical operations such as solving equations.
To begin factoring 9x3 + 18x2 - x - 2, we look for a common factor in each term. Here, there is no common factor, so we attempt to factor by grouping. We group terms that can potentially have common factors or that can be factored further.
Let's separate the polynomial into two groups:
First group: 9x3 + 18x2Our two groups now look like this:
First group: 9x2(x + 2)Second group: -1(x + 2)Because the (x + 2) is a common factor in both groups, we can factor it out:
(x + 2)(9x2 - 1)
The second term, 9x2 - 1, is a difference of squares which can be factored as (3x + 1)(3x - 1).
Finally, the completely factored form of the given polynomial is:
(x + 2)(3x + 1)(3x - 1)
A side length of the base is 6 inches, and the apothem of the base is 4 inches. The height of the prism is 18 inches. What is the area of a cross-section of the prism? What is the volume of the prism?
A) 12 in2; 216 in3 B) 24 in2; 432 in3 C) 60 in2; 1080 in3
D) 120 in2; 2160 in3
Answer:
Area and volume of pentagonal prism is 660 inches² and 1080 inches³
Step-by-step explanation:
Given : A pentagonal prism having side length of the base is 6 inches, and the apothem of the base is 4 inches. The height of the prism is 18 inches.
We have to calculate
1) area of a cross-section of the prism
2) the volume of the prism
1) Area of cross section of pentagonal prism =5ab +5bh
Where a = apothem
b - base length
h = height.
For the given pentagon
apothem = 4 inches
base = 6 inches
Height = 18 inches
Area of cross section of pentagonal prism =5 ×4 × 6 + 5× 6 × 18
Area of cross section of pentagonal prism = 120 + 540
Area of cross section of pentagonal prism = 660 inches²
2) Volume of pentagonal prism = [tex]\frac{AP}{2} \times H[/tex]
Where, A = apothem
P is perimeter of base
H= height
Perimeter of pentagon is 5b = 30 inches
Volume of pentagonal prism = [tex]\frac{4\times 30}{2} \times 18[/tex]
Volume of pentagonal prism = 1080 inches³
Thus, Area and volume of pentagonal prism is 660 inches² and 1080 inches³.
Find the missing coefficient in the equation of the line that passes through the given point. ...?
Which best explains whether a triangle with side lengths 2 in., 5 in., and 4 in. is an acute triangle? The triangle is acute because 22 + 52 > 42. The triangle is acute because 2 + 4 > 5. The triangle is not acute because 22 + 42 < 52. The triangle is not acute because 22 < 42 + 52.
Let
[tex]a=2\ in\\b=4\ in\\c=5\ in[/tex]
we know that
If [tex]c^{2} =a^{2}+b^{2}[/tex] -----> is a right triangle
If [tex]c^{2} > a^{2}+b^{2}[/tex] -----> is an obtuse triangle
If [tex]c^{2} < a^{2}+b^{2}[/tex] -----> is an acute triangle
so
substitute the values
[tex]5^{2} > 2^{2}+4^{2}[/tex] ------> is an obtuse triangle
therefore
the answer is
The triangle is not acute because [tex] 2^{2}+4^{2}< 5^{2}[/tex]
Answer: The correct option is
(C) The triangle is not acute because 2² + 4² < 5².
Step-by-step explanation: We are to select the statement that best explains the type of the triangle having lengths of three sides as 2 inch, 5 inch and 4 inch.
We know that a triangle with side lengths a, b and c (c > a, b)is
(i) an acute-angled if a² + b² > c², and
(ii) an obtuse-angled if a² + b² < c².
For the given triangle,
a = 2 inch, b = 4 inch and c = 5 inch.
So, we have
[tex]a^2+b^2=2^2+4^2=4+16=20,\\\\c^2=5^2=25.[/tex]
Since,
[tex]20<25\\\\\Rightarrow a^2+b^2<c^2,[/tex]
so the given triangle is not acute, but obtuse.
Thus, the triangle is not acute because 2² + 4² < 5².
Option (C) is correct.
A = a+b+c / 3
Solve for b.
A.) 3A - a - c = b
B.) -c / 3 = b
C.) A - c / 3 = b
C.) -3 - c = b ...?
To solve for b in the equation A = (a + b + c) / 3, multiply both sides by 3 and then subtract a and c from both sides. The correct answer is A) 3A - a - c = b.
Explanation:To solve for b in the equation A = (a + b + c) / 3, you need to isolate the variable b.
First, multiply both sides of the equation by 3 to eliminate the denominator:
3A = a + b + c
Then, subtract a and c from both sides to get b by itself:
3A - a - c = b
So, the correct answer is:
A) 3A - a - c = b
Write the point-slope form of the equation of the line that passes through the point (1, 3) and has a slope of 2. Include your work in your final answer
If F(x) = x² + 5x and G(x) = 2x + 1, find F(5) + G(6).
How many feet are in 30 yards?
__ ft
On a map the length of a river is 4.75 in. The actual length is 247mi. What's the scale of the map?
What is 1.2 divided by 9?
Patrick hit his neighbor's car while backing his vehicle out and caused $700 worth of damage. The insurance company paid for $300 of the damage while Patrick had to pay the remaining $400. The amount Patrick paid was his _____.
Trent is 25 years old and works for a company that matches his 401(k) contribution up to 5%. The interest rate for his 401(k) is 7.3%. If he puts away 10% of his $32,000 salary every year, how much would he have saved in 10 years? Round your answer to the nearest cent.
Answer:
The answer is : $67,266.16
Step-by-step explanation:
This question is a future value question.
As given, Trent puts away 10% of his $32,000 every year and the company will put half amount of $1,600. So, total amount becomes =[tex]3200+1600=4800[/tex] each year.
Formula for future value or FV is Fv = Pmt (1 + r/n)^(nt) – 1 / (r/n)
Where, Fv = Future Value , Pmt = repeated payments , R = interest rate ,N = total number of payment periods
Putting the values in the formula,
Fv = 4800 (1 + 0.073/1)^(1x10) – 1 (0.073/1)
Fv = $67266.16
Hence, the answer is $67266.16
The amount saved in 10 years is [tex]\boxed{\$ 67266.20}.[/tex]
Further Explanation:
Annuity is a series of payment that is made after equal interval of time.
Future value of annuity of payment P for n year if the return is i can be expressed as,
[tex]\boxed{{\text{Future Value}} = {\text{P}} \times \frac{{{{\left( {1 + \frac{i}{n}} \right)}^{nt}}}}{{\frac{i}{n}}}}[/tex]
Given:
Total salary is [tex]\$ 32000.[/tex]
The interest rate is [tex]7.3\%.[/tex]
Trent save [tex]10\%[/tex] of his salary every year.
Company puts [tex]5\%[/tex] of salary every year.
Calculation:
The [tex]10\%[/tex] of [tex]\$32000[/tex] can be calculated as follows,
[tex]\begin{aligned}{\text{Amount}}&= \frac{{10}}{{100}} \times 32000\\&= \$ 3200\\\end{aligned}[/tex]
The amount that company put can be obtained as follows,
[tex]\begin{aligned}{\text{Company Amount}} &= \frac{5}{{100}} \times 32000\\&= \$ 1600\\\end{aligned}[/tex]
The total amount can be calculated as follows,
[tex]\begin{aligned}{\text{Amount}} &= 3200 + 1600\\&= \$ 4800\\\end{aligned}[/tex]
The future value can be obtained as follows,
[tex]\begin{aligned}{\text{FV}} &= 4800 \times \frac{{{{\left( {1 + 0.073} \right)}^{10}} - 1}}{{0.073}} \\ &= 4800 \times 14.014\\&= \$ 67266.20\\\end{aligned}[/tex]
Hence, the amount saved in 10 years is [tex]\boxed{\$ 67266.20}.[/tex]
Learn more:
Learn more about inverse of the function https://brainly.com/question/1632445 Learn more about range and domain of the function https://brainly.com/question/3412497 Learn more about profit and loss https://brainly.com/question/2479097
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Investment and return
Keywords: Trent, 25 years old, works, company, matches, 401(k), 7.3%, 10%. $32000, salary, every year, 10 years, amount, 5%, nearest cent.
What is the length of a picture frame whose width is 3 inches and whose proportions are the same as a 9-inch wide by 15-inch long picture frame?
What is the total interest on a 10 year 6.1% loan with a principle of 32,000
F = 32,000 (1+ 0.061*10)
F = 51,520
That makes the total interest equal 51,520 -32,000 = 19, 520.
if a rubik's cube has a volume of 384 cubic centimeters, how long is one side of the cube? (recall that the volume of a cube is calculated by L3, where L is the length of one side.
To determine the side length of a Rubik's cube with a volume of 384 cubic centimeters, take the cube root of 384 to find that each side is approximately 7.24 centimeters long.
To find the length of one side of a cube when given the volume, you can use the formula for the volume of a cube, which is V = L³, where V is the volume and L is the length of a side of the cube.
In this case, the volume is 384 cubic centimeters, so we need to find the cube root of 384 to find the length of one side.
The calculation is as follows:
L³ = 384 cm³L = ∛384 cm³L ≈ 7.24 cmTherefore, each side of the Rubik's cube is approximately 7.24 centimeters long.
Train A and train B leave a central station at the same time. They travel the same speed, but in opposite directions, with train A heading towards station A, and train B heading towards station B. Train A reaches station A after 212212 h. Train B reaches station B after 4 h. Station A and B are 585 mi apart.
What is the rate of the trains?
Answer:
90 mph
Step-by-step explanation:
Let speed of both train=x mph
Time taken by train A to reach station A=[tex]2\frac{1}{2}[/tex] hr=\frac{5]{2} h[/tex]
Time taken by train B to reach station B=4 h
Distance between two trains=585 miles
We know that
Distance=[tex] speed\times time[/tex]
Distance covered by train A=[tex]\frac{5}{2} x[/tex]
Distance covered by train B=[tex]4x[/tex]
When two trains travel in opposite direction then total distance
[tex]\frac{5}{2}x+4x=585[/tex]
[tex]\frac{5x+8x}{2}=585[/tex]
[tex]\frac{13}{2}x=585[/tex]
[tex]x=585\times \frac{2}{13}=90 mph[/tex]
Hence, the rate of both trains=90 mph
The table below shows the distance d(t) in feet that an object travels in t seconds.
t d(t)
(second) (feet)
1 15
2 60
3 135
4 240
What is the average rate of change of d(t) between 2 seconds and 4 seconds and what does it represent?
A) 50 m/s; it represents the average speed of the object between 2 seconds and 4 seconds
B) 90 m/s; it represents the average speed of the object between 2 seconds and 4 seconds
C) 90 m/s; it represents the average distance traveled by the object between 2 seconds and 4 seconds
D) 50 m/s; it represents the average distance traveled by the object between 2 seconds
Answer:
Option B is correct
The average rate of change of d(t) between 2 second and 4 second is; 90 ft/s
and it represents the average speed of the object between 2 seconds and 4 seconds.
Step-by-step explanation:
Average rate of change of function is defined as the ratio of the difference in the function f(x) as it changes from a to b to the difference between a and b. Then, the average rate of change is denoted as A(x).
[tex]A(x) =\frac{f(b)-f(a)}{b-a}[/tex]
As per the given statement, the distance d(t) is in feet and t is the time in second.
To find the average rate of change of d(t) between 2 seconds and 4 seconds.
From the table we have;
at t = 2 , d(2) = 60
and
at t =4 , d(4) = 240.
Then, by the definition of average rate of change ;
[tex]A(t) = \frac{d(4)-d(2)}{4-2}[/tex] = [tex]\frac{240-60}{4-2} =\frac{180}{2}[/tex]
Simplify:
[tex]A(t) = 90 ft/s[/tex]
therefore, the average rate of change of d(t) between 2 second and 4 second is; 90 ft/s and it represents the average speed of the object between 2 seconds and 4 seconds.
Polar coordinates of a point are given. Find the rectangular coordinates of the point. (2.1 ; 2pi/9)
A. (-1.6, -1.3)
B. (1.6, 1.3)
C. (1.3, 1.6)
D. (-1.3, -1.6)
Dakota has $5.38 in her savings a count. Each week she adds $2.93. How much money does Dakota have after 5 weeks? After N weeks?
a childrens book has dimensions 20cm by 24cm what scale factor should be used to make a enlarged version that has dimensions 25cm by 30cm
Final answer:
To find the scale factor for enlarging a children's book from 20 cm by 24 cm to 25 cm by 30 cm, divide the enlarged dimension by the original corresponding dimension, resulting in a scale factor of 1.25.
Explanation:
We are asked to find the scale factor used to enlarge a children's book from dimensions of 20 cm by 24 cm to a larger version with dimensions of 25 cm by 30 cm. To find the scale factor, we need to divide one dimension of the enlarged book by the corresponding dimension of the original book. We can take either the length or the width to find the scale factor.
Let's use the width for this example:
Original width = 20 cm
Enlarged width = 25 cm
Scale factor = Enlarged width / Original width
Scale factor = 25 cm / 20 cm
Scale factor = 1.25
Therefore, a scale factor of 1.25 should be used to enlarge the book from the original dimensions to the new dimensions.
What are the x-intercept and y-intercept of the graph of
y=1/3 x−6
x:
Y:
The scale factor of the blueprint of a gymnasium to the actual gymnasium is 1in/15ft. The area of the flow on the blueprint is 114in2.
What is the area of the actual gymnasium?
B) 25, 650 ft^2
If the ratio is 1:15, then the measurements of each side of the actual gym are 15 times greater than the scale's. So the areas would have a ratio of 1:225. 114 times 225 is equal to 25, 650
Isabel earned 350 points wile she was playingblastibg robot.isaabels mom earned 3 times as many then isabel. how many points did isabels mom earn
For the following pair of lines, identify the system by type.
A) consistent
B) equivalent
C) inconsistent
Answer:
Option (c) is correct.
The system is Inconsistent.
Step-by-step explanation:
Given : A pair of lines.
We have to identify the system by type.
Consider the given system of pairs of lines.
Since, the graph shows two parallel lines.
1) Consistent : A system of linear equation is said to be consistent if the graph of equation either intersect at a single point or two lines overlap each other.
that is a unique solution or infinite many solution.
2) equivalent : When two system of equations have same solution then the two system are said to be equivalent.
3) Inconsistent : A system of linear equation is said to be inconsistent if the graph of equation are parallel to each other.
Thus, the given graph shows parallel lines,
Hence, The system is Inconsistent