Answer:
See explanation
Step-by-step explanation:
A. Let x represent the original test scores.
(1) The teacher will give a 10-point bonus, then the score will be x + 10. Hence,
[tex]f(x)=x+10[/tex]
(2) The teacher will increase everyone's grade by 9% of their score, then the score will be x + 0.09x = 1.09x. Hence,
[tex]g(x)=1.09x[/tex]
B. If [tex]f(x)=x+10[/tex] and [tex]g(x)=1.09x,[/tex] then
[tex]f(g(x))=g(x)+10=1.09x+10[/tex]
Meaning: the teacher increased by 9% the score and then increased the result by 10 points.
[tex]f(g(75))=1.09\cdot 75+10=91.75[/tex]
C. If [tex]f(x)=x+10[/tex] and [tex]g(x)=1.09x,[/tex] then
[tex]g(f(x))=1.09f(x)=1.09(x+10)[/tex]
Meaning: the teacher increased by 10 points the score and then increased the result by 9%.
[tex]g(f(75))=1.09(75+10)=92.65[/tex]
D. [tex]g(f(x))\neq f(g(x))[/tex] because [tex]1.09(x+10)\neq 1.09x+10[/tex]
The number of deer to
hunters is 17:3. Altogether
deer and hunters is 740.
How many deer and how
many hunters on the ranch?
The given ratio problem can be solved by converting the ratio to an algebraic equation and solving that equation. The total of deer and hunters on the ranch is 629 deer and 111 hunters.
Explanation:The given ratio is of deer to hunters is 17:3, and their total sum is given as 740. We solve such problems by converting ratio to equation i.e., 17x + 3x = 740, where 'x' is a constant multiplier.
Adding 17x and 3x gives us 20x = 740. By dividing both sides by 20, we calculate the value of 'x' which is 37.
Substitute the value of 'x' in 17x and 3x, we get the number of deer and hunters as 629 and 111 respectively.
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rewrite equation to solve for m 4n-6m=-2
Answer:
Step-by-step explanation:
4n - 6m = - 2 Subtract 4n from both sides.
4n-4n - 6m = -2-4n
-6m = - 2 - 4n Divide by - 6
-6m/-6= -2/-6 -4n/-6 Do the division
m = 1/3 + 2n/3
The signs change because each term has 2 minus signs. 2 minus signs make a plus. Or both minus signs cancel.
Solve -3 |2x+3| -4 = 1
Answer: x = 1.5
Step-by-step explanation:
First, we need to isolate the absolute value.
+ 3 to each side.
|2x + 3| - 4 = 4
Then, add 4 more to each side.
|2x + 3| = 8
Subtract 3 from each side.
|2x| = 5
Divide each side by 2
|x| = 1.5
Answer:
no solutions
Step-by-step explanation:
[tex]-3|2x+3|-4=1[/tex]
[tex]-3|2x+3|=1+4[/tex]
[tex]-3|2x+3|=5[/tex]
[tex]{\left|2x+3\right|}=\frac{5}{-3}[/tex]
The absolute value of a number is always positive or zero.
solve the equation 7-y-y=-1
Answer: y=4
Step-by-step explanation:
7-y-y=-1
Combine like terms
7-2y=-1
Subtract seven on both sides of the equation
7-7-2y=-1-7
-2y=-8
Divide both sides by -2
-2y/-2=-8/-2
y=4
Check the answer by plugging 4 back in the equation for y.
7-4-4=3-4=-1
The final answer is y=4
Which choice is equivalent to the product below? Square root of 3/16 • Square root of 3/9
Answer:
3/12
Step-by-step explanation:
it was right on, you know, where its from
The product Square root of 3/16 • Square root of 3/9 = 3/12 = 1/4.
What is square root?The root is figuring out what number accelerated by way of itself is the same as the variety under the square root image. So: √9= 3, due to the fact 3² $ -3² = 9
square root, in mathematics, a component of a variety of that, while accelerated by way of itself, gives the authentic quantity. for example, each 3 and –3 are square roots of 9.
The square root of 3/16 • Square root of 3/9
⇒[tex]\sqrt{\frac{3}{16} }[/tex]×[tex]\sqrt{\frac{3}{9} }[/tex]
⇒3/4*3
⇒1/4.
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HELP PLZ!!!
In an equilateral triangle, all 3 sides are equal length, and the perimeter of an equilateral triangle is 3 times the length of one side. If one side measures 9 + 3x, and the measure of another side is 5x – 5, what is the perimeter of the equilateral triangle?
Check the picture below.
Answer:
The perimeter of the equilateral triangle is 90 units.
Step-by-step explanation:
Let the side of the triangle be = s
So, perimeter of equilateral triangle = [tex]s+s+s=3s[/tex]
One side measures 9+3x and the measure of another side is 5x-5.
Both are equal, so we get the sides as:
[tex]9+3x=5x-5[/tex]
[tex]3x-5x=-5-9[/tex]
[tex]-2x=-14[/tex]
x = 7
We get the sides as :
First side [tex]9+3(7)[/tex]
= 30
OR
Second side [tex]5(7)-5[/tex]
= 30
And the third side will also be 30 as it is equilateral triangle.
Hence, the perimeter is = [tex]30+30+30=90[/tex] units
Therefore, the perimeter of the equilateral triangle is 90 units.
This table shows the distance traveled by a car and the car’s average speed on different days. A three column table with six rows. The first column, Day, has the entries 3, 4, 5, 6, 7. The second column, Average Speed in miles per hour, has the entries, 55, 58, 63, 65, 68. The third column, Distance in miles, has the entries, 495, 660, 825, 990, 1,155. Given that the days are the independent variable, which dependent variable has a constant rate of change? What is the constant rate of change?
The Dependent variables are Average speed and Distance and the rate of change in distance is constant.
Day ____ Average Speed __ Distance
3 __________ 55 __________ 475
4 __________ 58 __________ 660
5 __________ 63 __________ 825
6 __________ 65 __________ 990
7 __________ 68 __________ 1155
The dependent variables are Average speed and Distance.
The rate of change is the change in the dependent variable per change in the independent variable.
Average speed :
The rate of change in speed for the different days is not constant.
Between Day 4 and 3 :
58 - 55 = 3
Between Day 5 and 4 :
63 - 58 = 5
Distance in miles :
Rate of change in distance for the different days is constant
Between Day 4 and 3 :
660 - 475 = 165
Between Day 5 and 4 :
825 - 660 = 165
Between Day 6 and 5 :
990 - 825= 165
Between Day 7 and 6 :
1155 - 990 = 165
Therefore, the rate of change in distance per day is 165 for days 3 to 7.
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Answer:
Distance and 165
Step-by-step explanation:
got it right
Write three numbers that are between -3 and -4
Answer:
-3.3, -3.5, -3.7
13. A reflection of the rectangle over which line will map the rectangle onto itself?
a. y = 0 b. y=2_c. y=x d. y = 2x
Answer:
Step-by-step explanation:
Y=2
Reflection of a rectangle over the x-axis (y = 0) will generally cause it to map onto itself. The other given lines (y = 2, y = x, and y = 2x) will not typically have this result, unless the rectangle is specifically located on the plane.
Explanation:In geometry, a shape maps onto itself under reflection when it is reflected over a line that bisects it symmetrically. With a rectangle, this can occur when it is reflected over the x-axis or y-axis, assuming the rectangle's sides are parallel to the axes. From the given options, only y = 0 (x-axis) could create this type of reflection.
Reflection over the line y = 0 will leave a rectangle in the same position if its height is evenly distributed above and below the x-axis. For lines like y = 2, y = x, and y = 2x, they would not bisect a rectangle symmetrically unless the rectangle is specifically positioned, so they will not generally result in the rectangle mapping onto itself.
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Find the 15th term for the arithmetic sequence -3,3,9,...
Answer:
your adding 6 each time so just find the 15th term
Step-by-step explanation:
-3 + 6= 3 and 3+6 = 9
What the answer fast
To solve this problem, first let x=0.933333(repeating). Then, you want to multiply both sides by 10 to get 10x = 9.33333 (repeating). Next, take equation 2 and minus equation 1 from it giving you 9x = 8.4. Finally, multiply both sides by 10 and you will get 90x = 84. Divide both sides by 90 giving x=84/90. Answer is 84/90. 84/90 can reduce to 14/15.
Ms.Sinnott has 7/12 m of string and she cuts the string into eight pieces how long are the new piece of string
Answer:
7/96 m
Step-by-step explanation:
7/12 ÷ 8 = 7/96
Help ASAP please!
The figure shows three quadrilaterals on a coordinate grid:
A coordinate grid is shown from positive 8 to negative 8 on the x-axis and from positive 8 to negative 8 on the y-axis. An image of a rectangle labeled A is shown on ordered pair 1, 1 and 3, 1 and 3, 2 and 1, 2. Another image of a rectangle labeled B is shown on ordered pair 2, 2 and 6, 2 and 6, 4 and 2, 4. Another image of a rectangle labeled C is shown on ordered pair negative 1, 1 and negative 1, 2, and negative 3 , 2 and negative 3, 1.
Which of the following statements is true about the three quadrilaterals? (5 points)
a
A and B are similar but not congruent.
b
A and C are similar but not congruent.
c
A and B are similar and also congruent.
d
B and C are similar and also congruent.
9514 1404 393
Answer:
(a) A and B are similar but not congruent
Step-by-step explanation:
All of the rectangles have sides in the ratio of 2:1, so are all similar. Only the rectangles that are the same size are congruent: A and C.
A and B are similar, but not congruent.
Which is the most accurate measurement of 1 mile (Remember, there are 1760 yards in a mile
Answer: 1755 yards
Step-by-step explanation:
apex
Hank started the month with $531.49 in his bank account. He deposited 2 paychecks during the month into his bank account. One for $240.42 and the other for $281.67. During the month he ended up spending $275.66 on food, $48.29 on gas, and $107.64 and on his phone. He then bought a new iPad which cost him $429.81. How much money was in Hank's account at the end of the month?
Answer:
$192.18
Step-by-step explanation:
$531.49+$240.42+281.67
$1053.58-$275.66-$48.29-$107.64-$429.81
=$192.18
A rectangular prism measures 2 2/5 inches by 3 1/5 inches by 2 inches
How many cubes with edge length 1/5 inch fit in the prism?
Total 1920 cubes can fit in the given prism.
Given that:Dimensions of prism are: [tex]2\dfrac{2}{5} = \dfrac{12}{5}[/tex] , [tex]3\dfrac{1}{5} = \dfrac{16}{5}[/tex], and 2 inches respectively.
Size of a side of given cube = 1/5 inch
To find:Number of cubes that can fit in given prism.
Calculations and explanation:This problem is all about spaces. Only that number of cube will fit, which the prism will allow to. The given prism has got some space in it(The volume), and the cubes have some size (their volume).
Since prism is a cuboid(which is mistakenly written as rectangular in the question), thus we have:
Volume of prism = multiplication of lengths of its sides = [tex]\dfrac{12}{5} \times \dfrac{16}{5} \times 2 = \dfrac{384}{25}[/tex] cubic inches
Volume of the cube = cube of its one side's length = [tex](\dfrac{1}{5})^3 = \dfrac{1}{125}[/tex] cubic inches
We will divide the total space with space amount each cube take so as to find number of cubes allowed by prism to be fitted in it.
Thus:
[tex]\text{Number of cubes} = \dfrac{\dfrac{384}{25}}{\dfrac{1}{125}} = 1920 \: \rm cubes[/tex]
Thus, in total, there can be 1920 cubes fitted in the prism.
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The rectangular prism can hold 1920 cubes with edge lengths of [tex]\frac{1}{5}[/tex] inch. This is calculated by finding the volume of the prism and dividing it by the volume of one small cube.
To find how many cubes with an edge length of [tex]\frac{1}{5}[/tex] inch fit into a rectangular prism with dimensions [tex]2\frac{2}{5}[/tex] inches, [tex]3\frac{1}{5}[/tex] inches, and 2 inches, we follow these steps:
Convert the dimensions of the prism into improper fractions:
[tex]2\frac{2}{5}[/tex] inches = [tex]\frac{12}{5}[/tex] inches[tex]3\frac{1}{5}[/tex] inches = [tex]\frac{16}{5}[/tex] inches2 inches = [tex]\frac{10}{5}[/tex] inchesCalculate the volume of the prism:
Volume = [tex]\frac{12}{5} \times \frac{16}{5} \times \frac{10}{5} = \frac{1920}{125}[/tex] cubic inchesDetermine the volume of one small cube:
Edge length of a small cube = [tex]\frac{1}{5}[/tex] inch → Volume = [tex]\left(\frac{1}{5}\right)^3[/tex] = [tex]\frac{1}{125}[/tex] cubic inchesFind the number of small cubes by dividing the volume of the prism by the volume of one small cube:
Number of cubes = [tex]\frac{1920/125}{1/125} = 1920[/tex]Thus, 1920 cubes with an edge length of [tex]\frac{1}{5}[/tex] inch can fit into the given rectangular prism.
Corrected question:
A rectangular prism measures [tex]2\frac{2}{5}[/tex] inches by [tex]3\frac{1}{5}[/tex] inches by 2 inches
How many cubes with edge length [tex]\frac{1}{5}[/tex] inch fit in the prism?
Can someone explain to me how to do questions 6-8 because I understand how to do 3-5 now. Can you explain to me how you do this please ? I have a test tomorrow
Answer: 6. 4,2
7. 3,2
8. 5,2
please forgive me if i am incorrect.
Answer:
see explanation
Step-by-step explanation:
Using the midpoint formula to equate the x and y coordinates of the endpoints to the x and y coordinates of the midpoint, that is
(6)
let ( x, y ) be the coordinates of the required endpoint, then
x → [tex]\frac{x+6}{2}[/tex] = 2 ( multiply both sides by 2 )
x + 6 = 4 ( subtract 6 from both sides )
x = - 2 and
y → [tex]\frac{y+2}{2}[/tex] = 0 , thus
y + 2 = 0 ( subtract 2 from both sides )
y = - 2
Coordinates of the other endpoint = (- 2, - 2)
(7)
x → [tex]\frac{x-4}{2}[/tex] = - 1 ( multiply both sides by 2 )
x - 4 = - 2 ( add 4 to both sides )
x = 2 and
y→ [tex]\frac{y+3}{2}[/tex] = - 1 ( multiply both sides by 2 )
y + 3 = - 2 ( subtract 3 from both sides )
y = - 5
Coordinates of the other endpoint = (2, - 5)
(8)
x → [tex]\frac{x+7}{2}[/tex] = 2 ( multiply both sides by 2 )
x + 7 = 4 ( subtract 7 from both sides )
x = - 3 and
y → [tex]\frac{y+3}{2}[/tex] = 1 ( multiply both sides by 2 )
y + 3 = 2 ( subtract 3 from both sides )
y = - 1
Coordinates of the other endpoint = (- 3, - 1)
When Spencer was 5, he was 28 inches tall. Today he is 5 feet 3 inches tall. What is the percent increase in Spencer’s height?
I appreciate any help! Thank you!
Answer:
The percentage increase in Spencer’s height is 125 %
Solution:
[tex]\begin{array}{l}{\text { Percentage increase }=\frac{\text { change in height }}{\text { initial height }} \times 100 \%} \\\\ {\text { percentage increase }=\frac{\text { increased height - initial height }}{\text { initial height }} \times 100 \%}\end{array}[/tex]
Initial height of spencer = 28 inches
Increased height of spencer = 5 feet 3 inches
= 5 feet + 3 inches
(5 feet = 5 ×12=60 inches)
= 60 + 3
[tex]\begin{array}{l}{\text { Increased height }=63 \text { inches }} \\ {\text { Percentage increase }=\frac{63-28}{28} \times 100 \%} \\\\ {=\frac{35}{28} \times 100 \%} \\\\ {=1.25 \times 100 \%} \\ {\text { percentage increase in height of spencer }=125 \%}\end{array}[/tex]
Weighs 600 grams how much will it way in pounds
The absolute value of -5 and 5 are ?
Hey!
---------------------------
Absolute Value - the enormity of a number regarding its sign.
|-5| = 5
|5| = 5
---------------------------
Hope This Helped! Good Luck!
Find the two roots of 4 49 A) 2 and 7 B) 2 7 and - 2 7 C) 2 and -7 D) -2 and -7
Answer:
the answer should be 2, -2, 7, -7
What is the perimeter of the figure
Answer:
68 1/2 yd or 68.5 yd
Step-by-step explanation:
You need to add all of the sides (of the figure) to find out what the perimeter is.
Answer:
B
Step-by-step explanation:
Andrew bought a computer for $650, a printer for $135.89, and two printer cartridges for
$28.79 each.
How much did Andrew spend in all?
Answer:
814.68
Step-by-step explanation:
[tex]650+135.89+28.79=814.68[/tex]
Answer:
$843.47
Step-by-step explanation:
First off I added 650 to 135.89 to get 785.89. Then I added 57.58 because Andrew bought 2 cartridges. Add 57.58 to 785.89, and you get your answer.
Which of the following represents a combination? Select all that apply.
the PIN for a bank or credit card
a committee consisting of three members with the same role
a committee consisting of a president, vice president, and secretary
final standings in a professional sports league
m selecting two sandwiches from a menu of 10
Answer:
Combinations:
A committee consisting of three members with the same role
Selecting two sandwiches from a menu of 10
Step-by-step explanation:
A combination is a selection of items from a collection, such that the order of selection does not matter.
A permutation is a selection of items from a collection, such that the order of selection matters.
A. The PIN for a bank or credit card - order matters → permutation
B. A committee consisting of three members with the same role - order does not matter → combination
C. A committee consisting of a president, vice president, and secretary - order matters → permutation
D. Final standings in a professional sports league - order matters → permutation
E. Selecting two sandwiches from a menu of 10 - order does not matter → combination
Given that y is directly proportional to x^2 and that y=2 when x=3 find the value of y when x=6
Answer:y=4/3
y is directly proportional to x^2 is written as
[tex]y \alpha {x}^{2} [/tex] introducing a constant,
y=kx^2
but from the question, when y=2 , x=3 . putting it in the formula to get the value of k
[tex]2 = {3}^{2} \times k[/tex]
2=9k . dividing through by 9 to get the value of k
[tex] \frac{2}{9} = \frac{9k}{9} [/tex]
[tex]k = \frac{2}{9} [/tex]
putting it in the general expression
[tex]y = \frac{2}{9} x[/tex]
the value of y when x=6
[tex]y = \frac{2}{9} \times 6[/tex]
[tex]y = \frac{4}{3} [/tex]
therefore the value of y when x=6 is
4/3
please help and find the missing side x
[tex]\text{Hello there!}\\\\\text{A simple way to find the value of x is to find the scale factor}\\\\\text{When you flip the shapes to make it look exactly the same,}\\\text{you would see that the numbers are divisible to it}\\\\\text{Side 21 is congruent to side 3}\\\\\text{Divide 21 by 3 and you'll get 7 (1/7 sine we're going to a smaller shape)}\\\\\text{The x side is congruent to the 91 side}\\\\\text{Divide 91 by 7}\\\\91\div7=13\\\\\large\boxed{x=13}[/tex]
Solve for x. Round your answer to the nearest hundredth.
13.48X – 200 < 256.12
x> 33.84
x< 33.84
x < 4.16
x>4.16
Step-by-step explanation:
13.48x - 200 < 256.12
+200 +200
13.48x < 456.12
divide by 13.48 on both sides
x < 33.84
so your answer is the second one
Answer:
ik im late sry
Step-by-step explanation:
13.48x - 200 < 256.12
+200 +200
13.48x < 456.12
divide by 13.48 on both sides
x < 33.84
so your answer is the second one
The pass a quiz students need a score of at least 32 points out of a total of 40 points at least what percent do the students need to pass a quiz
Answer:
80%
Step-by-step explanation:
To find the percentage, we have to take 32 over 40 and multiply it by 100
32/40 * 100 = 80%
Therefore the students need 80% to pass a quiz :)PLEASE DO MARK ME AS BRAINLIEST IF MY ANSWER IS HELPFUL :)
Translate 4n-5 To verbal statement
The algebraic expression 4n-5 translates verbally to 'four times a number minus five.'
Explanation:To translate the algebraic expression 4n-5 into a verbal statement, consider the components of the expression. The '4n' part indicates four times a number 'n', and '-5' signifies that five is subtracted from the product of four and the number. Thus, the verbal statement of the expression is 'four times a number minus five.'
The complete question is:Translate 4n-5 To verbal statement
The algebraic expression 4n - 5 translates to "Five subtracted from the product of 4 and a number."
In Mathematics, an algebraic expression is a type of mathematical equation which is typically used for showing the relationship existing between two (2) or more variables, numerical quantities (constants), accompanied with the use of different mathematical operations.
Generally speaking, the variable x is typically used for denoting an independent variable.
Based on the given algebraic expression 4n - 5, a word problem that represents the expression can be written as "Five subtracted from the product of 4 and a number."
I need to know what this table is cause I need the answer
Answer:
f(- 2) = 1
Step-by-step explanation:
f(- 2) means what is the value of f(x) when x = - 2
From the table we can see that when x = - 2 f(x) = 1
Hence
f(- 2) = 1
Answer:
f(-2) = 1
Step-by-step explanation:
Actually, you need to know how to use this table to find the value of the function defined by the table when x = -2.
Look in the first column of the table for x = -2. When x = -2, f(x) = 1. This is the desired result ("What is f(-2)?")