Answer:
x³ - x² + 4x - 7
Step-by-step explanation:
(x³ + 2x - 3) - (x² - 2x + 4)
remove first parenthesis and distribute second parenthesis by - 1
= x³ + 2x - 3 - x² + 2x - 4 ← collect like terms
= x³ - x² + 4x - 7 ← in standard form
Three solid shapes a, b and c are similar.
the volume of shape a is 27 cm
the volume of shape b is 64 cm
the ratio of the surface area of shape b to the surface area of shape c is 8:15
work out the ratio of the height of shape a to the height of shape c.
The ratio of the height of shape A to the height of shape C is [tex]\frac{3}{10}[/tex]
Calculations and Parameters:First step:Recall that similar figures have the same scale factor squared due to the ratio of its surface area.
Hence,
We would make:
z-----> the scale factorx----> surface area shape Ay----> surface area shape B[tex]z^2 = x/y\\z= 2/5[/tex]
Therefore, the ratio of the height of shape A to the height of shape B is = [tex]\frac{hA}{hB} = \frac{2}{5}[/tex]
Next step:To find the ratio of the height of shape B to the height of shape C, we would perform a similar operation which is:
[tex]z^3 = 27/64\\z= 3/4[/tex]
The ratio is:
[tex]\frac{hB}{hC} = \frac{3}{4}[/tex]
Final step:To find the ratio of the height of shape A to the height of shape C would be:
[tex](\frac{hA}{hB}) (\frac{hB}{hC} )= \frac{hA}{hC}[/tex]
= 6/20
= 3/10
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Find the value of (8 × 10³)²
Answer:
64 × [tex]10^{6}[/tex]
Step-by-step explanation:
(8 × 10³)² = (8 × 10³)(8 × 10³)
= 8 × 10³ × 8 × 10³
= 64 × [tex]10^{6}[/tex]
Answer:
64000000Step-by-step explanation:
Find the value of (8 × 10³)²
(8 × 10³)² =
(8 × 1000)² =
8000² =
64000000
Factor quadratic trinomials
Complete the table for each function. Then answer the questions that follow.
a=
; b =
; c =
; d =
;
e =
; f =
; g =
Answer:
[tex]a= 4\\\\b= 4\\\\c= 8 \\\\d=16\\\\e= 12\\\\f=36\\\\g=64[/tex]
Step-by-step explanation:
[tex]a= 4(1^2) = 4\\\\b = 4^1 = 4\\\\c=4(2) = 8\\\\d=4^2 = 16\\\\e = 4(3) = 12\\\\f=4\cdot 3^2 = 4(9) = 36\\\\g = 4^3 = 64[/tex]
On Monday, 56 biographies were
checked out at the library. This is 8 less
than twice the amount of fiction books
checked out that day. How many fiction
books were checked out on Monday?
Jaxon has a bag of marbles. He draws one marble from the bag. Before drawing another marble from the bag, what could Jaxon do to ensure that the events are independent of each other?
keep the marble he initially drew from the bag
return the marble he initially drew from the bag
add more marbles to the bag
remove all marbles that are the same color as the first one
Answer:
Return the marble he initially drew from the bag
Step-by-step explanation:
Help me please !!!!!!!!!
Answer:
A
Step-by-step explanation:
The solution matrices shown are the result of reducing the augmented coefficient matrix to "reduced row-echelon form". Many calculators and spreadsheets have functions specifically for that purpose.
The attachment shows the result of a TI-84 work-alike calculator's reduction of the coefficient matrix. It matches the first choice.
__
Additional comment
When the equations are written in the form shown here, with the variables in the same order, and the constant on the right side of the equal sign, the augmented matrix is simply the matrix of the numbers. It is shown as the argument of the RREF function in the attachment.
The left-right order of the variables on the left side of the equal sign matches the top-down order of the solution values in the rightmost column of the reduced matrix. That is, ...
a = 2, b = -2, c = 0.
If 7 is added to the product of 7 and 3 what is the answer
Answer:
28
Step-by-step explanation:
[tex]7+7\times 3 = 7(1+3)= 7 \times 4 = 28[/tex]
Answer:
28
Step-by-step explanation:
When we find the product of 2 or more numbers, we multiply them.
so
product of 7 and 3 = 7 x 3 = 21
7 + 21 = 28
Hope this helps. I attempted to make it as simple as possible.
- profparis
Wendy had 35 coins in pennies and nickels.She had $1.03.3Which system of equations could be used to determine the number of coins she has?
Wendy had 35 coins in pennies and nickels.She had $1.03.3Which system of equations could be used to determine the number of coins she has?
A..01p +.05n = 35 B. 1p +5n = 1.03
p+ n =1.03 p + n = 35
C .01p + .05 n = 1.03 D. .05p + .01n = 1.03
p + n = 35 p + n = 35
Answer: c. p+n=35, 0.01p+ 0.05n = 1.03
Step-by-step explanation: p= number of pennies, n = number of nickels. Given the total number of coins is 35, we have the equation p+n = 35.
She has total of $1.03. The equation for that would be 0.01p + 0.05n = 1.03
Solve both the equations to get the answer.
Which represent geometric sequences? check all that apply.
a. 3/16, 3/8, 3/4, 3/2, . . .
b. 13/20, 10/20, 7/20, 4/20, . . .
c. 2, 4, 6, 8, . . .
d. 3, 9, 27, 81, . . .
e. f(x) = x/4 -9
f. f(x) = -4(4/9)^x
g. f(x) = -4/9x^4
Only three are geometric sequences, a which is 3/16, 3/8, 3/4, 3/2, d which is 3,9,27,81 and f which is -4(4/9)^x
What is a geometric sequence?A geometric sequence is a sequence of numbers or functions in which successive member differ by a constant term called the common ratio.
Analysis:
For a, the first term is 3/16, second term is 3/8. if we divide the second term by the first we have 2. If we do same with the third and second we still have 2. so this is a geometric sequence
For d, if we divide 9 by 3 we have 3, if we divide 27 by 9 we have 3. so this is a geometric sequence.
For f, if we make x equal to a nonzero integer, we have first term as -16/9, second term as -64/81 and third term as -256/729. if we divide the second term by the first we have -4/9, if we divide the third by the second we have-4/9.
In conclusion, Only three are geometric sequences, a which is 3/16, 3/8, 3/4, 3/2, d which is 3,9,27,81 and f which is -4(4/9)^x
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Factorise 2x^2 + x - 6
[tex] \rm \: {2x}^{2} + x - 6[/tex]
[tex] \rm \: {2x}^{2} + 4x - 3x - 6[/tex]
[tex] \rm \: {2x} \times (x + 2)- 3x \times (x + 2)[/tex]
[tex] \rm \: (x + 2) \times (2x - 3)[/tex]
A translation maps A(1,2) onto A'(-1,3). What are the coordinates of the image of the origin under the same translation?
Using translation concepts, it is found that the coordinates of the image of the origin under the same translation are given by:
3. (-2,1).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
A translation maps A(1,2) onto A'(-1,3), hence the rule is given by:
(x,y) -> (x - 2, y + 1).
Then the image of the origin (0,0) is given by:
(0,0) -> (0 - 2, 0 + 1) = (-2,1)
Which means that option 3 is correct.
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A 6.1 foot tall camper is standing on a 98 foot cliff looking down at his tent. The tent is 65 feet from the base of the
cliff, find the angle of depression to the nearest tenth.
Answer:
58.0 degrees
Step-by-step explanation:
Let the angle of depression be x.
tan x=104.1/65
x=58.0 degrees
Answer:
the angle of depression is 32°
Step-by-step explanation:
What is the exact value of X
Answer:
[tex]6\sqrt{2}[/tex]
Step-by-step explanation:
Select the correct answer from each drop-down menu. What polygon is obtained by graphing the given system of inequalities? What is the area of the polygon bounded by the inequalities? y ≥ 1 x ≥ 1 y ≤ 4 x ≤ 6 The polygon obtained by graphing the system of inequalities is a . The area of the polygon bounded by the inequalities is square units.
Which equation represents a nonlinear function? x(y – 5) = 2 y – 2(x 9) = 0 3y 6(2 – x) = 5 2(y x) = 0
The equation that represents a nonlinear function is x(y – 5) = 2
How to determine the equation?Nonlinear functions are functions that do not have a uniform slope.
A linear function is represented as:
y = mx + b
This means that all other forms are nonlinear function.
From the list of given options, x(y – 5) = 2 is a nonlinear function
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Answer:
A
Step-by-step explanation:
A grocery store sells a bag of 6 oranges for $3.60. If Jeriel spent $2.40 on oranges, how many did he buy?
Answer:
he bought 4 oranges
because you need to divide
Graph the equations to find the solution(s) to the system.
y=x+3y=13(x+5)(x−1)
Use the Line tool to graph the line.
Use the Parabola tool to graph the parabola. Choose maximum or minimum point first and then a point on the parabola.
By graphing both equations, we see that the solutions of the system of equations are (1.05, 4.05) and (-4.97, - 1.97)
How to solve the system of equations?Here we have the system of equations:
y = x + 3
y = 13*(x + 5)*(x - 1).
To solve this system graphically, we need to graph both equations and see where the curves intercept.
The graph of the two equations can be seen below.
There are two solutions, one is (1.05, 4.05) and the other is (-4.97, - 1.97)
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Which equation represents a line that passes through (5’1) and has a slope of 1/2?
Answer:
third one passes through the slope .
Answer:
Step-by-step explanation:
y - 1 = 1/2(x - 5)
y - 1 = 1/2x - 5/2
y - 2/2 = 1/2x - 5/2
y = 1/2x - 3/2
Option 3
The length of a rectangle is four feet more than twice the width of the rectangle. The area of the rectangle is 240 square feet. What, in feet, are the length and width of the rectangle
A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. The width of the rectangle is 10ft , while the length of the rectangle is 24ft.
What is a rectangle?A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but the reverse statement may or may not be true.
Let the width of the rectangle be represented by x.
The length of the rectangle is (2x+4), therefore, the area is,
Area = x(2x+4)
240 ft² = 2x² + 4x
2x² + 4x - 240 = 0
x² + 2x - 120 = 0
x = -12, 10
Since the width can not be negative, the width of the rectangle is 10, while the length of the rectangle is 24.
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Which points in a scatterplot or outliners select each correct answer PLEASE HELP!
Answer:
F and D
Step-by-step explanation:
there 2 out of the other lead
Find the volume of the pyramid
Step-by-step Explanation:
the volume of a pyramid is:
volume = (1/3) • base_area • height
(area = length • width)
(area) • (height) = (volume)³
Example:
area = 12cm² (12 cm squared)
height = 4cm
12 • 4 = 48cm³ (48 cm cubed)
Answer:
area: 6 • 8 = 48(1/2) = 24cm²
height: 12
volume: 24 • 12 = 288cm³(1/3) = 96cm³
Help me please!!!
M
What is m
Answer
in the m∠C it means measure of C
Step-by-step explanation:
Hope this helps!
If not, I am sorry.
According to the line of best fit, about how many words would a person remember after being distracted by 7 text messages? 4 5 6 7
Using the line of best fit, it is found that a person would remember 5 words after being distracted by 7 text messages.
What does the line of best fit states?Researching the problem on the internet, it is found that it states that the number of words a person remembers after being distracted by x text messages is given by a linear function.
Looking at the line, it is found that when x = 7, N(x) = 5, hence a person would remember 5 words after being distracted by 7 text messages.
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There are 12 apples in a basket. Out of these, 3 apples are rotten. Find the probability of choosing a good apple.
Help me out pls
Answer:
the probability is 3/4
Step-by-step explanation:
probability = possible outcome/total outcome
Possible outcome= 12-3=9
Total outcome = 12
Probability = 9/12 = 3/4
So the chance of u getting a good apple is 3/4
Choose the equation that represents the fraction 1/12
Answer:
1/24 + 1/24 = 1/12
Step-by-step explanation:
1/24 + 1/24 = 1/12 I think it’s this.
I don’t have any options though so I just thought of that.
What is the measure of 1, 2 and 3?
Answer:
angle 1= 59 degree, angle 2= 61 degree and angle 3 = 119 degree
Step-by-step explanation:
because in the figure angle 2 and 61 degree are alternative angle so they are equal
The equation of a circle is given below:
x squared minus 4 x plus y squared minus 6 y minus 7 equals 0
Identify the center and radius of the circle.
Group of answer choices
Center: left parenthesis 2 comma 3 right parenthesis
Radius: 20
Center: left parenthesis 4 comma minus 6 right parenthesis
Radius: 2 square root of 5
Center: left parenthesis negative 4 comma 6 right parenthesis
Radius: 20
Center: left parenthesis 2 comma 3 right parenthesis
Radius: 2 square root of 5
Given:
The equation of the circle is
We need to determine the center and radius of the circle.
Center:
The general form of the equation of the circle is
where (h,k) is the center of the circle and r is the radius.
Let us compare the general form of the equation of the circle with the given equation to determine the center.
The given equation can be written as,
Comparing the two equations, we get;
(h,k) = (0,-4)
Therefore, the center of the circle is (0,-4)
Radius:
Let us compare the general form of the equation of the circle with the given equation to determine the radius.
Hence, the given equation can be written as,
Comparing the two equation, we get;
Thus, the radius of the circle is 8
$75 before tax. Disc: 10% Tax: 7%, Tip: 20% what’s the total?
Answer:
$102.75
Step-by-step explanation:
Given the following question:
We are given a cost of 75 dollars and are being asked to find the total cost after adding a tip, tax, and disc to the cost. To find this answer we will use the formula to calculate percentages making sure we use 75 as our base for each addition to our total cost.
Formula to calculate percentages:
[tex]\frac{p\times n}{100}[/tex]
First the disc:
[tex]\frac{10\times 75}{100}[/tex]
[tex]10\times75=750[/tex]
[tex]750\div100=7.5[/tex]
[tex]=7.5[/tex]
Next the tax:
[tex]\frac{7\times75}{100}[/tex]
[tex]7\times75=525[/tex]
[tex]525\div100=5.25[/tex]
[tex]=5.25[/tex]
Last but not least the tip:
[tex]\frac{20\times75}{100}[/tex]
[tex]20\times75=1500[/tex]
[tex]1500\div100=15[/tex]
[tex]=15[/tex]
Finally add:
[tex]75+7.50+5.25+15=102.75[/tex]
[tex]=102.75[/tex]
The total cost after adding the disc, tax, and the tip will be "$102.75."
Hope this helps.
Part E
Use the table showing Manuel's and Gretchen's data to determine the mean, median, standard deviation, and
interquartile range for each data set. Use this information to complete the second table. Use the graphing tool to
determine the value of standard deviation.
The mean, median, standard deviation, and interquartile range for each data set is given below.
What is the definition of Interquartile Range (IQR)?When arranged from lowest to highest, the IQR represents the central 50% of values.
Find the median (middle value) of the lower and higher half of the data to get the interquartile range (IQR).
These are the quartile 1 (Q1) and quartile 3 (Q3) values (Q3). The difference between Q3 and Q1 is the IQR.
What are the measures of central tendency for Manuels Data?Using the statistical tool, the following were arrived at:
Standard Deviation = 3.13961Mean = 8Median = 8IQR = Q3-Q1 = 10 - 6 = 4What are the measures of central tendency for Grethcen's Data?Using the statistical tool, the following were arrived at:
Standard Deviation = 4.68737.Mean = 9.6Median = 9IQR = IQR = Q3-Q1 = 12 - 7 = 5.See the respective Histograms attached.
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