Answer:
f'(x)=-(x+42)/5
Step-by-step explanation:
Rewrite f(x) as y:
y=-5x-42
Flip x and y and solve for y:
x=-5y-42
x+42=-5y
(x+42)/-5=y
So the inverse function is f'(x)=-(x+42)/5 (note that f' means inverse)
How many plastic cubes can fit into the box?
Option D:
160 plastic cubes can fit into the box.
Solution:
Convert mixed fraction into improper fraction.
Length of the box = 4 ft
Width of the box = [tex]2\frac{1}{2}=\frac{5}{2}[/tex] ft
Height of the box = 2 ft
Volume of the box = length × width × height
[tex]$=4\times\frac{5}{2} \times2[/tex]
= 20 ft³
Volume of the box = 20 ft³
Length of the plastic cube = [tex]\frac{1}{2}[/tex] ft
Volume of the cube = length × length × length
[tex]$=\frac{1}{2} \times\frac{1}{2} \times\frac{1}{2}[/tex]
[tex]$=\frac{1}{8} \ \text{ft}^3[/tex]
Volume of the cube = 0.125 ft³
[tex]$\text{Number of plastic cubes}=\frac{\text{Volume of box}}{\text{Volume of cube}}[/tex]
[tex]$=\frac{20}{0.125}[/tex]
= 160
Number of plastic cubes = 160
Hence 160 plastic cubes can fit into the box.
Option D is the correct answer.
What is 60% of 76???
Answer:
45.6
Step-by-step explanation:
0.60 x 76 = 45.6
Answer:45.6
Step-by-step explanation:
60/100*76
0.6*76
45.6
2x + 5
rewrite each expression as the product of a constant and a sum of terms
Answer:
= 2(x+[tex]\frac{5}{2}[/tex] )
Step-by-step explanation:
2x + 5
= 2(x+[tex]\frac{5}{2}[/tex] )
When:
2 is the constant
(x+[tex]\frac{5}{2}[/tex] ) is a sum of terms
Hope it will find you well.
The expression 2x + 5 can be written as the product of 1 and the sum 2x + 5. Therefore, it's 1(2x + 5).
Step 1:
Factor out the greatest common factor.
In the expression 2x + 5, there is no common factor other than 1 since both terms do not share any common factors.
Step 2:
Rewrite as the product of a constant and a sum of terms.
We rewrite 2x + 5 as the product of 1 and the sum of 2x and 5: [tex]\(1 \times (2x + 5)\).[/tex]
Step 3:
Perform the multiplication.
Multiplying 1 by the sum (2x + 5) gives us [tex]\(1 \times (2x + 5) = 2x + 5\)[/tex].
Step 4:
Interpret the result.
The expression [tex]\(2x + 5\)[/tex] represents the original expression 2x + 5 as the product of the constant 1 and the sum of terms 2x and 5. This expression is now in the form requested.
Brandon had $500. He spent 47% of his money on a tablet computer. How much did his computer cost?
Answer:
453
Step-by-step explanation:
Since Brandon spent 47 % of his money you Will subtract 500-47.
Work out the angle of CDA?
Answer:
32.3°
Step-by-step explanation:
Sqrt(7.5² - 6²) = 4.5
Tan(D) = 6/(24-10-4.5)
= 6/9.5
D = 32.3
what are some equivalent expressions for :
120.5y + 80.5y + 65.5y
Answer:
266.5y
Step-by-step explanation:
120.5y+80.5y+65.5y
201y+65.5y
266.5y
Solve for a
7a - 20 = 52m
Answer:A=52M/7+20/7
Step-by-step explanation:
Three friends bought ¼ kg of trail mix to share. How many kg will each friend receive?
Answer:
1/12 kg
Step-by-step explanation:
1/4(1/3)=1/12
x+1+2/x add the two radical expressions
Answer:
[tex]\frac{ \sqrt{ {x}^{2} + x} + 2}{ \sqrt{x} } [/tex]
Step-by-step explanation:
If you are talking about radical expressions, then the two equations should be something like
[tex] \sqrt{x + 1} + \frac{2}{ \sqrt{x} } [/tex]
Assuming this is the intended expression, then:
[tex] \frac{ \sqrt{x \times } \sqrt{x + 1} + 2}{ \sqrt{x} } [/tex]
We then simplify by collecting LCM to obtain:
[tex]\frac{ \sqrt{ {x}^{2} + x} + 2}{ \sqrt{x} } [/tex]
What is the center of a circle whose equation is x2 + y2 – 12x - 2y + 12 = 0?
(-12, -2)
O (-6, -1)
(6, 1)
O (12, 2)
Solution:
Given equation of circle is:
[tex]x^{2} +y^{2} -12x-2y+12=0[/tex]
Move the constant to other side
[tex]x^{2} +y^{2} -12x-2y = -12[/tex]
Group the equation
[tex](x^{2} -12x)+(y^{2}-2y)=-12[/tex]
Add 36 and 1 from both sides
[tex](x^{2} -12x +36)+(y^{2}-2y + 1)=-12 + 36 + 1\\\\(x^{2} -12x + 36)+(y^{2}-2y + 1)= 25[/tex]
Which is simplified as:
[tex](x - 6)^2 + (y-1)^2 = 25[/tex] --------- eqn 1
The equation of circle is given as:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
Where, r is radius and (h, k) is center
Compare eqn 1 with above general equation
(h, k) = (6, 1)
Thus the center of a circle is (6, 1)
Answer:
the center the circle is (6,1)
Step-by-step explanation:
How did the graph of f(x) = x^2 and g(x) = 3/4 x^2 relate?
g(x) = [tex]\frac{3}{4} f(x)[/tex] or g(x) is 3/4 times of f(x) , F(x) and g(x) have common solution or intersecting point in the graph parabola at x=0 i.e. in origin and x = [tex]\frac {4}{3}[/tex].
Step-by-step explanation:
We have a function f(x) = [tex]x^{2}[/tex] and another function , g(x) = [tex]\frac{3}{4} x^{2}[/tex]. In the graph of y = [tex]x^{2}[/tex] , the point (0, 0) is called the vertex. The vertex is the minimum point in a parabola that opens upward. In a parabola that opens downward, the vertex is the maximum point.
Graphing y = (x - h)2 + k , where h = 0 & k = 0
Function g(x) can be formed with compression in function f(x) by a factor of 3/4 , i.e. g(x) = [tex]\frac{3}{4} f(x)[/tex] or g(x) is 3/4 times of f(x).Domain and range of f(x) and g(x) are same ! Although structure of both functions is same the only difference is g(x) is compressed vertically by a factor 3/4. Both are graph of a parabola with vertex at (0,0). Also, F(x) and g(x) have common solution or intersecting point at x=0 i.e. in origin.
4 1/4 - 3 3/4 is you get this you will have 11 points
Answer:Exact Form: 1/2
Step-by-step explanation:
Complete the statement. Round to the nearest tenth if necessary. 3 km per minute = __ mi per hour?
3 km per minute is approximately equal to 111.8 miles per hour.
To convert 3 km per minute to miles per hour, we can use the conversion factors:
1 kilometer = 0.621371 miles 1 hour = 60 minutes
First, let's convert 3 km per minute to km per hour:
3 km/min * 60 min/hour = 180 km/hour
Now, let's convert km per hour to miles per hour:
180 km/hour * 0.621371 miles/km = 111.84757 miles/hour
Rounding to the nearest tenth, we get:
3 km per minute is approximately equal to 111.8 miles per hour.
Which would all these equal in value on the number line 0366145 A is 0 and 2 is 6 I need the others
A = 0, B = 6, C = 3, D = 6, E = 4, F = 5 and G = 1.
Solution:
Starting line is [tex]\frac{0}{6}=0[/tex].
First line is [tex]\frac{1}{6}[/tex].In the number line, all the denominators are same.
Second line is [tex]\frac{2}{6}[/tex].Third line is [tex]\frac{3}{6}[/tex].Fourth line is [tex]\frac{4}{6}[/tex].Fifth line is [tex]\frac{5}{6}[/tex].Sixth line is [tex]\frac{6}{6}=1[/tex].If we match this to the given number line, we get
A = 0, B = 6, C = 3, D = 6, E = 4, F = 5 and G = 1.
solve for x: picture included
Answer:
9
Step-by-step explanation:
because diameter never change or if it is radius the first half is 9 so, the second half would be 9 too.
so, x=9
The points (5, 3), (3, -4), (10, 3), and (8, -4) are the vertices of a polygon. What type of polygon is formed by these points?
Answer:
Parallelogram
Explanation:
Since there are four points, this is a quadrilateral.
There is a slope during the points. Therefore it could not be a rectangle nor square. The sides are still parallel though.
The length is not equal too, so it could not be a rhombus.
If you plot these points to the graph and connect them, it would form a parallelogram.
Answer:
a parallelogram
Step-by-step explanation:
When the points are connected to form a convex polygon, that polygon is a parallelogram.
Graph the image of triangle ABC after a reflection across the x-axis. The vertices of the image will be called A” B” , and C” .
For the graph, the image of triangle ABC after a reflection across the x-axis, the vertices of the image will be called A” B” , and C” are respectively, (-3, 4), (-3, 1), (-1, 1)
What is "reflection about the axis" ?Reflection about the axis is a transformation in geometry where a figure is flipped across a line or plane, producing a mirror image of the original figure. The line or plane across which the figure is reflected is called the axis of reflection.
Given that,
A graph, having triangle ABC
The reflection points, A', B', C' = ?
All the vertices and their mirror image will be at equal distance from the x-axis
So, y-coordinate will be equal in magnitude but different in sign for all the vertices and their mirror image
x-axis is axis of reflection,
there will be no change in x-coordinates
So, x-coordinates will be same in magnitude and in sign as well
Now, Mirror image points can be written as,
A' = (-3, 4)
B' = (-3, 1)
C' = (-1, 1)
Hence, the points are (-3, 4), (-3, 1), (-1, 1)
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What is the order least to greatest -3,0,-1/2,1,-3 1/3,6,5,-1,21/5,4
Answer: -31/3,-3,-1,-1/2,0,1,4,21/5,5,6
Determine the slope and y-intercept of the line.
y = -69x - 346
Answer:
Step-by-step explanation:
Compare y = mx + b to
y = -69x - 346.
Here the slope, m, equals -69 and the y-intercept, b, equals -346 (Answer C)
Answer:
Trust him (:
Step-by-step explanation:
Andre says that 10x + 11 and 5x + 11 are equivalent because they both equal 16 when x is 1. do you agree with Andre?
Answer: No
Step-by-step explanation:
10x + 11 when x= 1 is equal to 21
While 5x + 11, when x=1 is equal to 16
Jane is considering a 7/23 balloon mortgage with an interest rate of 4.15% to
purchase a house for $197,000. What will be her monthly payment for the first
7 years of the balloon mortgage?
O A. $945.98
O B. $933.64
O c. $900.00
O D. $957.62
Answer:
957.62
Step-by-step explanation:
Given the house price, P=$197,000, [tex]n=12\times 30=360, i=0.0415/12[/tex], the monthly payments, M, can be calculated as:
[tex]M=P[\frac{i(1+i)^n}{(1+i)^{360}-1}]\\\\M=[\frac{\frac{0.0415}{12}(1+\frac{0.0415}{12})^360}{(1+\frac{0.0415}{12})^{360}-1}]\\\\M=957.62[/tex]
Hence, the monthly payment of the baloon mortgage is $957.62
What is 6 multiplied by 8
Answer:
48
Step-by-step explanation:
Step 1: Convert words into an expression
What is 6 multiplied by 8
6 * 8
Step 2: Multiply
6 * 8
48
Answer: 48
On a very cold morning, it was -8°F. As the day went on the temperature rose 2
degrees each hour. Which equation shows the temperature over time?
ERO
CLEAR
CHECK
y = -2x + 8
VE 1.2x
y = 2x + 8
Langu
ENG
1:33 PM
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Type here to search
gf
2/12/2020
Answer:
The temperature in °F after x hours will be given by, y = - 8 + 2x.
Step-by-step explanation:
The temperature in the morning was - 8°F. Now, as the day went on the temperature rose 2°F each hour.
So, after x hours the temperature will rise by 2x°F.
Therefore, the temperature in °F after x hours will be given by, y = - 8 + 2x. (Answer)
78/17 round to the nearest 10
Answer:
0
Step-by-step explanation:
78/17 gives 4.588
In rounding up numbers, 1 to 4 is rounded up to zero, while numbers 5 to 9 will be rounded up to 1.
In the question above, we are asked to round up to the nearest 10. And then 78/17 gives 4.588
This number is between 0 and 10.
The whole number there is 4. Therefore, 4 will be rounded up to Zero.
If the question and us to round up to the nearest whole number, as we have 4.588
The number before the whole number 4 is 5 (the tenth digit), and then 5 will be rounded up to 1. That 1 will hence be added to 4.
4+1= 5. To nearest whole number, it is 5 but to nearest ten, it is 0
Find the 97th term of the arithmetic sequence
25
,
29
,
33
,
.
.
.
25,29,33,...
Step-by-step explanation:
The given sequence is 25, 29, 33, ....
The sequence represents arithmetic progression
In an AP, the first term is a1 = 25
The difference between two terms, d = 29 - 25 = 4
To find the 97th term,
By formula, [tex]a_{n} = a_{1} + (n - 1) d[/tex]
Substituting the values in the above equation, we get
[tex]a_{97} = 25 + (97 - 1) 4[/tex]
= 25 + (96 * 4)
= 25 + 384
= 409
The 97 th term in the given sequence is 409.
The 97th term of the arithmetic sequence 25,29,33,... can be calculated using the formula: a+(n-1)*d. In this case, the 97th term equals 409.
Explanation:The subject of your question is arithmetic sequences. In an arithmetic sequence, every term is a certain amount greater than the previous term. This difference is known as the common difference. In your question, the sequence is 25, 29, 33, ..., indicating the common difference is 29-25, which equals 4.
To calculate the 97th term of an arithmetic sequence, we can use the formula: a + (n-1) * d where 'a' is the first term, 'n' is the term you're looking for, and 'd' is the common difference.
So, for your question, we input the necessary values and calculate: 25 + (97-1)*4 = 25 + 96*4 = 25 + 384 = 409.
Therefore, the 97th term of the arithmetic sequence you provided is 409.
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A farm is 350 acres .72% of the farm is suitable for farming. How many acres can be used to farm?
Answer:
252
Step-by-step explanation:
Multiply 350 by the decimal form of 72%. To find the decimal form of 72%, divide 72 by 100 or move every number two places to the right:
72/100 = 0.72
Then multiply 350 by 0.72:
350 x 0.72 = 252
I hope this helps!
Help with 16 and 17 please
Answer:
16) b and 17) C
Step-by-step explanation:
Use a metric prefix to write 3,100 grams in kilograms
Answer:
3.1 kg
Step-by-step explanation:
3100 × 10^-3 = 3.1
Find the volume of the cone
Enter and exact answer in terms of pi or use 3.14 for pi and round your answer to the nearest hundredth
Answer:
Find 6.75% of 260
Step-by-step explanation:
Hi
To find the volume of a cone, you use the formula 1/3πr²h, substituting in the radius for r and the height for h. For an example cone with a radius of 4 and a height of 9, the volume would be 48π or approximately 150.72 after rounding to the nearest hundredth.
Explanation:The student is asked to find the volume of a cone. The formula to find the volume of a cone is 1/3πr²h, where r is the radius of the base of the cone and h is the height of the cone.
If the student is given the radius and the height, they would just need to substitute the values into the formula. For example, if the radius of the cone is 4 and the height is 9, the volume would be 1/3 * π * (4)² * 9 = 48π. If the student prefers a decimal approximation, they can substitute pi with 3.14 to get 150.72, rounded to the nearest hundredth.
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