Answer:
There were 24 cookies in the jar at the beginning.
Step-by-step explanation:
There is 1 cookie left add the one susan took that is two. Two is 1/4 of 8. Eight is 2/3 of 12. Twelve is 1/2 of 24. 24 is the answer. You can also check it by going back.
For
f(x) = 4x
and
g(x) = x10,
find the following.
(a)
(f + g)(x)
(b)
(f − g)(x)
(c)
(f · g)(x)
(d)
(f/g)(x)
,
x ≠ 0
The addition, subtraction, multiplication and division of the two functions are 4 · x + x¹⁰, 4 · x - x¹⁰, 4 · x¹¹ and 4 / x⁹, respectively.
How to determine the expression resulting from operations between functions
In functions there are two fundamental operations (addition, multiplication) and two derivate operations (subtraction, division). In this problem we must look for the following definitions:
Addition
(f + g)(x) = f(x) + g(x)
Subtraction
(f - g)(x) = f(x) - g(x)
Multiplication
(f · g)(x) = f(x) · g(x)
Division
(f / g)(x) = f(x) / g(x), for x ≠ 0.
If we know that f(x) = 4 · x and g(x) = x¹⁰, then the expression behind the operations are, respectively:
Addition
(f + g)(x) = 4 · x + x¹⁰
Subtraction
(f - g)(x) = 4 · x - x¹⁰
Multiplication
(f · g)(x) = (4 · x) · x¹⁰ = 4 · x¹¹
Division
(f / g)(x) = (4 · x) / x¹⁰ = 4 / x⁹
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Two splice plates are cut from a piece of sheet steel that has an overall length of 18 3/4 in. The plates are 10 1/2 in. and 6 15/16 in. long. How much material remains from the original piece if each saw cut removes 1/16 in.?
Total material remains from original piece if overall length of sheet is
[tex]18\frac{3}{4}[/tex] in and two plates are cut of length [tex]10\frac{1}{2}[/tex] in and [tex]6\frac{15}{16}[/tex] in ,two saw of length 1/16 in is 35 / 16 in.
As given,
Overall length of steel sheet=[tex]18\frac{3}{4}[/tex] in
=(75 /4) in
=(300 /16)in
Length of two plates is [tex]10\frac{1}{2}[/tex] in and [tex]6\frac{15}{16}[/tex] in
Total length of two plates=[tex]10 \frac{1}{2} + 6\frac{15}{16}[/tex]
=(21 /2) +(95/16)
=(168 +95)/16
=263 /16
Total length of saw cut=(1/16) +(1/16)
=2/16
Material remains from original piece=(300/16) - (263/16 +2/16)
= 35 /16
Therefore, total material remains from original piece if overall length of sheet is [tex]18\frac{3}{4}[/tex] in and two plates are cut of length [tex]10\frac{1}{2}[/tex] in and [tex]6\frac{15}{16}[/tex] in ,two saw of length 1/16 in is 35 / 16 in.
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Based on the information below, what are the values of x and y of the solution to the system of equations used to
create the information?
38
141-14 |Ax|- 2141-
26
x = -5, y = 2
x = -0.2, y = 0.5
x=0.5, y = -0.2
x = 2, y = -5
38
8 26
The values of x and y of the solution to the system of equations are 2 and -5, respectively.
We are given three matrices. The matrices are A, Ax, and Ay.
The determinant of the matrix A is [(4*-2)-(-6*8)] = 40.
The determinant of the matrix Ax is [(38*-2)-(-6*26)] = 80.
The determinant of the matrix Ay is [(4*26)-(38*8)] = -200.
We need to find the values of x and y of the solution to the system of equations.
The value of x is |Ax|/|A| = 80/40 = 2.
Hence, the value of "x" is 2.
The value of y is |Ay|/|A| = -200/40 = -5.
Hence, the value of "y" is -5.
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Scatter Graphs
The best description of a scatter graph does the following:
“tells the story” of the graph from left to right giving specific values and dates for the first data point, the last data point, any relevant high points and low points
explains the overall trend seen on the graph
includes at least one relevant calculation (absolute change, percent change, ratio, etc) to better describe the data, the trends, or changes in the data
ends with some meaningful conclusion or “take away”
uses terminology correctly
1. Write a thorough description of this scatter graph using the guidelines above. [3 pts]
A specific type of graphic or mathematical diagram known as a "scatter plot" employs Cartesian coordinates to display values for typically two variables for a group of data.
A scatter graph, scatter chart, scattergram, or scatter diagram are other names for it.
If the points are color-, shape-, or size-coded, a second variable can be displayed. Each point's location on the horizontal axis is determined by the value of one variable, while its location on the vertical axis is determined by the value of the other. The data is shown as a series of dots.A scatter plot can be used when both continuous variables are independent of one another or when one continuous variable is in the researcher's control and the other one depends on it.The scatter graph can be represented by the line of best fit which is calculated by taking the average of all the x -coordinates and the y-coordinates.
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What is the solution to this equation?
x+8 = -3
OA. x = -5
OB. x = 5
OC. x = 11
OD. x=-11
[tex]x + 8 = - 3 \\ x = -3 - 8 \\ x = - 11[/tex]
OPTION (D) SUITS ..IT IS THE SOLUTION.
What is the horizontal shift of y = cos(0 – ³7) + 3?4A. noneOB.-37OC. 3rD. 3Reset Selection
The horizontal shift will be the term that is subtracting the angle, in this case: -3pi/4= B .
If an object is shot upward with an initial velocity, vo, in feet per second (ft/s), the velocity, v, in ft/s is given by the
formula
v = vo -32t, where t is time in seconds. Find the initial velocity of an object if the velocity after 4 seconds is 41 ft/s.
-
What is the surface area of the prism?
77.25 cm2
154.5 cm2
225 cm2
309 cm2
The surface area of the prism represented by the net diagram is 154.5 cm^2
What are areas?The area of a shape is the amount of space on the shape
For most regular quadrilaterals, you multiply the side lengths to determine the area
How to determine the surface area of the prism?The given parameter is in the figure
In the figure, we have the net of a rectangular prism
From the net of a rectangular prism, we have the following dimensions
Length = 8 1/2 cm
Width = 4 1/2 cm
Height = 3 cm
The surface area of the prism is then calculated as
Surface area = 2 * (Length * Width + Length * Height + Width * Height)
Substitute the known values in the above equation
So, we have the following equation
Surface area = 2 * (8 1/2 * 4 1/2 + 8 1/2 * 3 + 4 1/2 * 3)
Evaluate the products
So, we have the following equation
Surface area = 2 * (38 1/4 + 25 1/2 + 13 1/2)
Evaluate the sum
So, we have the following equation
Surface area = 2 * 77 1/4
Evaluate the products
So, we have the following equation
Surface area = 154.5
Hence, the surface area of the prism is 154.5 cm^2
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I’m begging help me out with this, please
For given function f(x)=8/(x+2) , g(x)=4x² +2 then evaluation of the composition of function (fog)(-1) =1.
As given in the question,
Given function:
f(x) = 8 / (x+2)
g(x) = 4x² +2
Evaluation of the composition of function f(x) and g(x) we get,
(fog)(x)
= f(g(x))
Substitute g(x) = 4x² + 2
= f(4x² +2)
= 8/(4x² +2+2)
= 8/(4x²+4)
= 2/(x²+1)
Substitute x =-1 in the above function
(fog)(-1) = 2/ ((-1)² +1)
= 2/ 2
=1
Therefore, for given function f(x) = 8/ (x+2) , g(x) = 4x² +2 then evaluation of the composition of function (fog)(-1) =1.
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Calculate the cone: 1) volume; 2) the area of the lateral surface; 3) the total surface area;for AB = 14, SO = 24.
Given:
AB = 14
SO = 24
To find:
a) the volume
b) the area of the lateral surface
c) the total surface area
a) To find the volume of the cone, we will use the formula:
[tex]Volume\text{ of a cone = }\frac{1}{3}πr²h[/tex]r = radius
diameter = AB = 14
diameter = 2(radius)
radius = diameter/2 = 14/2
radius = 7
height = SO = 24
let π= 3.14
[tex]\begin{gathered} Volume\text{ of the cone = }\frac{1}{3}\times3.14\times7^2\times24 \\ Volume\text{ of the cone = 1230.88 unit}^3 \end{gathered}[/tex]b) To get the lateral surface, we will apply the formula:
[tex]\begin{gathered} lateral\text{ surface of the cone = \pi rl} \\ where\text{ l = }\sqrt{h^2+r^2} \end{gathered}[/tex][tex]\begin{gathered} Lateral\text{ surface of the cone = 3.14 }\times7\times\sqrt{7^2+24^2} \\ \\ Lateral\text{ surface area of the cone = 549.5 units}^2 \end{gathered}[/tex]c) The total surface area formula:
[tex]\begin{gathered} Total\text{ surface area of cone = Area of base + lateral surface area} \\ \\ Total\text{ surface area = \pi r}^2\text{ + \pi rl} \\ \\ Total\text{ surface area = \lparen3.14 }\times\text{ 7}^2)\text{ + 549.5} \end{gathered}[/tex][tex]Total\text{ surface area of cone = 703.36 unit}^2[/tex]my aunt's food budget is R 3500 . She save 1/5 of her budget. How much money did she save?
The money she saved is 700.
What are fractions?Simply put, a fraction shows us how many pieces of a whole we have. The slash that is printed between the two numbers indicates that the numbers are a fraction. We have two numbers: the numerator at the top and the denominator at the bottom. The number is represented mathematically as a quotient, where the numerator and denominator are split.Given:
Aunt's food budget = 3500
Fraction of the budget she saved = 1/5
So, the total money she saved = 1/5 of the food budget
= 1/5 × 3500
= 700
Therefore, the money she saved is 700.
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Whats the solution to this formula?Tan^-1 ( 7 / 420) =
Okay, here we have this:
Considering the provided expression, we are going to solve it, so we obtain the following:
[tex]\begin{gathered} tan^{-1}(\frac{7}{420}) \\ =arctan(\frac{7}{420}) \\ =arctan(\frac{1}{60}) \\ =0.95° \end{gathered}[/tex]Finally we obtain that the expression is equal to 0.95°.
hi can you please help me
The area of the kitchen will be:
[tex]\begin{gathered} A=w\cdot l \\ \text{where:} \\ w=\text{width}=36-24=12ft \\ l=\text{length}=8ft \\ A=12\cdot8 \\ A=96ft^2 \end{gathered}[/tex]The number f of miles a helicopter is from its destination x minutes after takeoff is given by f(x)=60−1.5x. The number f of miles a commercial jet is from its destination x minutes after takeoff is shown in the graph below.
The distance of each flight is 60 miles and the time taken is 40 minutes.
Distance is the total path covered by an object or species in a particular time period.
At x = 0 minutes after takeoff,
f(x)=60−1.5x (given)
= 60-1.5*0 (at 0 minutes)
= 60 miles (distance between the helicopter and destination)
So, the distance of the flight is 60 miles.
When the helicopter reaches the destination, distance left is 0 miles
Thus, f(x) = 0 in x minutes.
Putting the above data in the equation, we get
0 = 60 - 1.5x
1.5x = 60 (bringing unlike terms on different sides)
x = 60/1.5
x = 40 minutes
Therefore, the distance of each flight is 60 miles and the time taken is 40 minutes.
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Consider the following function.
f(x) = (x − 3)2, x ≥ 3
Find the inverse function
f −1.
The inverse equation of the function is f'1(x) = 3 + √x
What are inverse functions?Inverse functions are the opposite of an original equation. This means that for a function f(x), the inverse of the function f(x) is f-(x)
How to determine the inverse function?The function f(x) is given as
f(x) = (x - 3)^2, x ≥ 3
As a general rule, we start by writing f(x) as a variable (say f(x) = y).
So, the equation of the function becomes
y = (x - 3)^2
The next step is to switch/swap the positions of x and y in the equation
The equation becomes
x = (y - 3)^2
Make y the subject of the formula in the equation
The equation becomes
y = 3 + √x
Express as an inverse function
f'1(x) = 3 + √x
Hence, the equation of the inverse function is f'1(x) = 3 + √x
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Julie is solving the equation 3x² + 5x + 15 = 0 and notices that the discriminant b^2 - 4ac has a value of -155. This
tells her that the equation has
A one real roots.
B one imaginary root.
C two real roots.
D two imaginary roots
Answer: i think b
Step-by-step explanation:
Question 1 (1 point)Given the graph below, is this relation a function?MathMLXBlarSubmit
To be a function, a relation can't have more than 1 value of 'y' for the same value of 'x'
For example, if you have points (3,7) and (3,-6) does not represent a function but points (3,7) and (-3,7) does.
In this problem, none of the graphed pairs have 2 or more values of 'y' for a single value of 'x'. They are all different, so yes, this relation is a function
factor of the following expression:
81x^4-16y^2
Answer:
See below
Step-by-step explanation:
(9x^2 - 4 y ) * (9x^2 + 4 y )
Estimate the product of 653.2×4.6
Answer: 3004.72
Step-by-step explanation: i used a calculator
Betsy's Bakery packages muffins in boxes of one dozen. If Besty bakes 1,152 muffins on Saturdays, how many boxes are ready to sell?
Answer:
96 boxes of muffins
Step-by-step explanation:
so how you would get to this answer would be 1152÷12
12 is equal to a dozen and so that is why you divide it by 12
the answer would be 96
Bill and ross are twins, their brother mark was born on the same day as twins but is three year older. if mark was born in 1990, in what year did the three boys get total age 21
Step-by-step explanation:
x = age of one of the twin boys
when they had together 21 years of age,
Bill was x years old
Ross was x years old
Mark was x+3 years old
so, we have
x + x + (x + 3) = 21
3x + 3 = 21
3x = 18
x = 6
Bill and Ross were 6 years old.
Mark was 6+3 = 9 years old.
Mark was born in 1990.
1990 + 9 = 1999
so, it was 1999 when they had together 21 years of age.
Which of the following linear equations represents the data chart?
Answer:
y = -x + 7
Step-by-step explanation:
let's use the first numbers as an example.
x=1 and y=6
now to get this we need to find the difference between the two numbers and we can do this by simply doing - 1 + 7 = 5
therefore making the answer y = -x + 7
Conscider this absolute value function.f(x) = (x – 5)How can function fbe written as a piecewise function?
f(x) = lx – 5l
x-5, if x-5 ≥ 0, x ≥5
-(x-5) = -x + 5 if x-5<0, x < 5
Gavin has a smart phone data plan that costs $20 per month that includes 6
GB of data, but will charge an extra $10 per GB over the included amount.
How much would Gavin have to pay in a month where he used 2 GB over the
limit? How much would Gavin have to pay in a month where he used went
over by x GB?
Total cost when over by 2 GB:
Total cost when over by x GB:
Total cost is given by the function $(20 + 10x)
What is a function?
A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The set X is referred to as the function's domain, and the set Y is referred to as the function's codomain. Al-Biruni and Sharaf al-Din al-Tusi, two Persian mathematicians, are responsible for the earliest known treatment of the concept of function. Initially, functions represented the idealised relationship between two varying quantities. A planet's position, for instance, depends on time. In the past, the idea was developed with the infinitesimal calculus at the end of the 17th century, and the functions that were taken into consideration until the 19th century were differentiable (that is, they had a high degree of regularity).
Total cost is given by the function $(20 + 10x)
Total cost when over by 2 GB = $(20 + 10x2) = $(20+20) = $40
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Correct each of the following errors by circling the error, describing what is wrong, entering what should be there instead, and entering the correct answer.-the equation is in the photo
As given by the question
There are given that expression:
[tex]4a^2\times3a^5[/tex]Now,
First, multiply the numbers:
[tex]4a^2\times3a^5=(4\times3)a^{2+5}[/tex]In the given solution of the question, there are perform addition, so this is the first error.
Now,
[tex](4\times3)a^{2+5}=12a^7[/tex]Hence, the correct answer is :
[tex]12a^7[/tex]During a sleepover, Carissa played karaoke with her friends. Her song was 6 minutes long. She had already sung for 4 minutes. Which equation could be used to see how much longer she will have to sing?
x + 2 = 6
x + 4 = 10
x + 4 = 6
x − 4 = 6
Brett has a box of colored pencils. He uses 78 pencils and has 120 pencils left in the box. Write an equation showing how many pencils are in the box before he starts drawing.
78 + p = 120
p − 78 = 120
120 + p = 78
p = 120 − 78
Answer:
for the first one it is x + 4 = 6
for the second one it is 78 + p = 120
Step-by-step explanation:
i hoped this helped!!!
Answer:
x+4=6
Step-by-step explanation:
x represents the missing number 4 represents the time she had already sang and 6 is the total
he figure on the left represents a scale drawing of the figure on the right.
pls help its due in 10 min
The scale of the drawing is expressed as, 1 inch : 2.5 yards.
What is a Scale Factor?A scale factor describes to what size an original image has been reduced or enlarged. If the scale factor of an enlargement is 2, it means every side lengths of the original image is increased times two to get the new image after enlargement.
On the other hand, if the reduction was done using a scale factor of 0.5 or 1/2, it means the size of the original image was reduced by half to get the new side lengths of the new image.
How to Find the Scale Factor of a Scale Drawing?The scale factor of a scale drawing = dimension of new image/corresponding dimension of original image.
The figure by the right is the original figure, while the one on the left is the scale drawing which is the new figure.
Scale of the drawing = 1 inches to 5/2 yards
Scale = 1 inch : 2.5 yards.
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help plssssss I really need help genuinly
What are the coordinates of the vertices of the image triangle after a 90 clockwise rotation about the origin? :
A'(1, 3) B'(-3, 4) C'(-2,-3)
A'(3, 1) B'(4,-3) C'(-3,-2)
A'(3,-1) B'(4, 3) C'(-3, 2)
A'(1,-3) B'(-3,-4) C'(-2, 3)
A'(-3, 1) B'(-4,-3) C'(3,-2)
Before carrying out rotation transformation, the coordinates of the vertices of the pre-image are;
A (3, -6)
B(1, 2)
C (7, -1).
What is the effect of clockwise rotation transformation?We are given the coordinates of the transformed image as:
A'(6, 3),
B'(–2, 1),
C'(1, 7).
We need to find the coordinates of the pre-image A, B and C.
The rule for rotation of 90° about the origin is (x,y) ---> (-y,x).
But we need to find the coordinates of the vertices of the pre-image.
So, we need to apply rule (-y,x) ---->(x,y).
Applying the 90 degrees clockwise rotation rule,
A'(6, 3) -----> A (3, -6)
B'(–2, 1) -----> B(1, 2)
C'(1,7) -----> C (7, -1).
Therefore, coordinates of the vertices of the pre-image are
A (3, -6)
B(1, 2)
C (7, -1).
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Complete question is;
After a rotation of 90° about the origin, the coordinates of the vertices of the image of a triangle are A'(6, 3), B'(–2, 1), and C'(1, 7). What are the coordinates of the vertices of the pre-image?
7x+12=x-6
I need help!!!!
Answer:
x = -3
Step-by-step explanation:
You have to isolate x:
7x + 12 = x - 6
7x = x - 6 - 12 = x - 18
6x = -18
x = -3