Answer: x-6, x+3, x-3
Step-by-step explanation;
Split the equation into two.
x2(x-6)-9(x-6)
(x-6) is seen as one of the tiles. Now work on x2-9
x2-9 is a difference of squares meaning the last two are (x+3) and (x-3).
What is the independent variable in this function?
Answer:
p.
Step-by-step explanation:
p is the independent variable.
The dependent one is h.
The value of h depends on the value of p.
Are these lines perpendicular, parallel, or neither based off their slopes?
6x - 2y = -2
y = 3x + 12
Answer:
parallel
Step-by-step explanation:
//
Answer: these lines are parallel.
Step-by-step explanation:
[tex]\displaystyle\\\left \{ {{6x-2y=-2} \atop {y=3x+12}} \right. \\\\ \left \{ {{6x-2y+2=0} \atop {y=3x+12}} \right. \\\\ \left \{ {{6x+2=2y\ |:2} \atop {x=2}} \right. \\\\\left \{ {{3x+1=y} \atop {y=3x+12}} \right.\\ \\\left \{ {{y=3x+1} \atop {y=3x+12}} \right. \\So,\ these\ lines\ are\ parallel.[/tex]
The sum of five consecutive positive integers is 2020. Find the largets of these numbers.
The largest integers of the numbers is 406.
How to find the five consecutive positive integers?The sum of five consecutive positive integers is 2020.
Therefore,
let
the first positive integer = x
Hence,
x + x + 1 + x + 2 + x + 3 + x + 4 = 2020
5x + 10 = 2020
5x = 2020 - 10
5x = 2010
x = 2010 / 5
x = 402
largest integer = 402 + 4 = 406
Therefore, the largest integers of the numbers is 406.
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What is the sign of s^67/t^9 when s < 0 and t > 0?
possible answers:
. positive
. negative
. zero
Answer:
negative
Step-by-step explanation:
[tex]s^{67}<0 \\ \\ t^9>0 \\ \\ \implies \frac{s^{67}}{t^9}<0
[/tex]
Answer:
negativeStep-by-step explanation:
The sign of a product or quotient cannot be determined by the positive number (t), so we can ignore it. The sign of the expression will be negative if and only if there are an odd number of negative factors.
Here, there are 67 (an odd number) negative factors, so the expression will be negative.
City community college plans to increase its enrollment capacity to keep up with an increasing number of student applicants. the college currently has an enrollment capacity of 2200 students and plans to increase its capacity by 70 students each year. what will the enrollment capacity be 3 years from now? a. 2480 b. 2410 c. 2340 d. 2240 please select the best answer from the choices provided a b c d
The correct option is B.
The enrollment capacity be 3 years from now is 2410
What is arithmetic sequence?A series of integers in which the difference between succeeding words is always the same is referred to as an arithmetic sequence or arithmetic progression. For instance, the difference in the arithmetic series 1, 5, 9, 13, 17,... is always 4. The common difference is what we refer to as.
How do you find arithmetic sequence?The formula for determining the nth term is used to locate a specific term in an arithmetic sequence. Step 1: An = a + (n - 1)d determines the nth term of an arithmetic series. Add the variables a = 2 and d = 3 to the formula in order to find the nth term.
According to the given information:At = a1 + (n - 1) x d is an equation that can be used to express the number of applications each year.
N equals 4 based on the information provided above. This corresponds to the term, which begins in three years.
At = 2200 + (4 - 1) x 70 = 2410
Thus, 2410 students could enroll at one time.
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A girl get n cedis pocket money money each week. she saves her money for five weeks and buys a present for her mother which cost gh 7900 i. write an expression for the amount of the money left ii.what is the minimum amount she needs to save each week to be able to afford the gift
An expression for the amount of the money left = (5n-7900) cedis
The minimum amount she needs to save each week to be able to afford the gift: n = 7900/5.
What is a word problem?The term "word problem" refers to a type of math question where the answer is written as one or more sentences and asks students to use their mathematical understanding to solve a problem from "real world."
What is the first step in solving word problem?Read the problem in its full to get a clear understanding of what you need to do in order to solve it before you start. Following reading it, you may choose which components of the issue need to be resolved the most and which ones are not.
According to the given data:She gets n cedis a week.
she will get n x 5 cedis for 5 wks =5n cedis.
She buys a present worth 7900.
An expression for the amount of the money left = (5n-7900) cedis.
The minimum amount she needs to save each week to be able to afford the gift.
5n-7900 = 0
n = 7900/5.
7900/5 = ____ per week
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piecewise function f (x) is defined by f of x is equal to the piecewise function of 3 to the power of the quantity x minus 1 end quantity minus 4 for x is less than or equal to 3 and the quantity negative x squared plus 3 times x plus 4 end quantity over the quantity x squared minus 7 times x plus 12 end quantity for x is greater than 3 Part A: Graph the piecewise function f (x) and determine the range. (5 points) Part B: Determine the asymptotes of f (x). Show all necessary calculations. (5 points) Part C: Describe the end behavior of f (x). (5 points)
The range of the function f(x) is (-∝, 3]
Part A: Graph the piecewise functionThe function definition is given as:
[tex]f(x) = \left[\begin{array}{cc}3^{x-1}-4&x\le 3\\ \frac{-x^2 + 3x + 4}{x^2 - 7x + 12}&x > 3\end{array}\right[/tex]
There are two sub-functions and the domains in the above definition.
Each function would be plotted alongside its domain.
See attachment for the graph of the function f(x)
From the graph of the function, we have the following range of f(x)
Minimum = Negative Infinity
Maximum = 5
Hence, the range of the function f(x) is (-∝, 3]
The asymptotes of f(x)We have the domains to be
x <= 3 and x > 3
This means that the asymptote of f(x) is x = 3
The end behavior of f(x)From the graph, we have:
f(x) increases as x increasesf(x) decreases as x decreasesThis means that the end behavior of f(x) is as x approaches +∝, the function approaches +∝ and as x approaches -∝, the function approaches -∝
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Complete question
A piecewise function f (x) is defined by
[tex]f(x) = \left[\begin{array}{cc}3^{x-1}-4&x\le 3\\ \frac{-x^2 + 3x + 4}{x^2 - 7x + 12}&x > 3\end{array}\right[/tex]
A company needs to package 7,560 beads. A wooden container shaped like a rectangular prism can hold 180 beads. A plastic cylindrical container can hold 126 beads. The wooden container costs the company $0.70, while the plastic container costs $0.40.
Which container should the company use to minimize cost? Explain.
The wooden containers should be used because it will cost $5.40 more to use the plastic containers.
The plastic containers should be used because it will cost $5.40 more to use the wooden containers.
The wooden containers should be used because it will cost $16.20 more to use the plastic containers.
The plastic containers should be used because it will cost $16.20 more to use the wooden containers.
The plastic containers should be used by the company to minimize the cost because it will cost $5.40 more to use the wooden containers.
What are word problems in mathematics?A mathematical word problem is a question that is stated as one or more sentences and calls on students to use their understanding of arithmetic operations to solve a "real-life" problem.
As you are aware, word problems can include almost any operation, including addition, subtraction, division, and even many operations at once.
From the given information:
If the company uses a wooden container shaped-liked rectangular prism, the will need to use (7560/180) containers.
= 42 containers of wooden containers.
If the company uses a plastic cylindrical container, they will need to use (7560/126) containers.
= 60 containers of plastic containers.
To determine the container that the company should use that will minimize the cost:
If the company decided to use the wooden container, then they will spend = 42 × $0.70 = $29.4If the company decided to use the plastic container, then they will spend = 60 × $0.40 = $24Therefore, we can conclude that the company should use plastic containers because it will cost $5.40 more to use wooden containers.
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Answer:
B. The plastic containers should be used because it will cost $5.40 more to use the wooden containers.
Step-by-step explanation:
Draw a diagram to show that the square root of 121 is 11.
Answer:
i think this may help you
The diagram to show that the square root of 121 is 11 attached below
What is a perfect square?A perfect square is a number system that can be expressed as the
square of a given number from the same system.
Assume that x-a be the closest perfect square less than x,let x+b be the closest perfect square more than x, then we get: x-a < x < x+b (no perfect square in between x-a and x+b, except possibly x itself).
Then, we get:
[tex]\sqrt{x-a} < \sqrt{x} < \sqrt{x+b}[/tex]
Thus, [tex]\sqrt{x-a} and \sqrt{x+b}[/tex] are the closest integers, less than and more than the value of {x}. (assuming x is non-negative value).
Herewe are given the number as 121
It is perfect root then ;
√121 = 11
The solution that show that the square root of 121 is 11 attached below
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1. The accompanying table shows the number of movie theaters showing a popular film and the film's weekly gross earnings, in millions of dollars. Use the table to answer the questions 1), 2).
Number of Theaters (x)
443
456
493
530
569
657
723
1,054
Gross Earnings (y)
(millions of dollars)
2.57
2.65
3.73
4.05
4.76
4.79
5.15
9.63
1). Write the linear regression equation for this set of data, rounding values to five decimal places. Using this linear regression equation, find the approximate gross earnings, in millions of dollars, generated by 610 theaters. Round your answer to two decimal places.
2). Find the minimum number of theaters that would generate at least 7.65 million dollars in gross earnings in one week.
2. A real estate agent plans to compare the price of a cottage, y, in a town on the seashore to the number of blocks, x, the cottage is from the beach. The accompanying table shoes a random sample of sales and location data. Write a linear regression equation that relates the price of a cottage to it's distance from the beach. Use the equation to predict the price of a cottage, to the nearest dollar, located three blocks from the beach.
Number of Blocks
from the Beach
(x) Price of a Cottage
(y)
5 $132,000
0 $310,000
4 $204,000
2 $238,000
1 $275,000
7 $60,800
3. The table below represents a chart kept by a pediatrician tracking the circumference of babies heads at various months of age.
Age
(in months) Circumference
(in cm)
1 35.8
2 36.6
5 38.5
6 39.1
4 38.9
13 40.1
7 39.1
15 40.3
10 39.9
2 36.8
18 40.6
1). Determine the regression model that best fits the data, rounding all values to the nearest thousandth. Then predict the size of a baby's head at 24 months old. Round your answer to the nearest tenth.
2). The pediatrician measured a newborns head and found the circumference to be 35.1cm. Can he add the pair (0, 35.1) to the data set to calculate a new regression? Justify your answer.
The regression equation of this group of data is given as ŷ = 0.0108X - 1.98123.
How to solve for the amount generated by the theaterŷ = 0.0108X - 1.98123
x = 610
= 0.0108*610 - 1.98123
= 4.61 million dollars
2. the minimum number of theaters that would generate at least 7.65 million dollars in gross earnings in one week.
7.65= 0.0108x-1.98123
take like terms
x = 892
2. correlation coefficient of X and Y is r = -0.987
This shows a negative relationship
b)Linear Regression Equation =
Y = 313309 - 34740x
c) Y = 313309 - 34740x
Y = 313309 - 34740 * 3
209089
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What is the range of this function? (negative infinity, infinity) left-bracket negative 1, infinity) (negative 1, infinity) (0, infinity)
The range of the function [tex]f(x) = -2(6)^{x} +3[/tex] discovered using exponential function is ( -∞, 3).
What is the range?The difference between the greatest and smallest numbers is called the range.What is an exponential function?
The following equations represent an exponential function: [tex]y=ab^{x} +c[/tex]In which:
a is the initial value.b is the rate of change.c is the vertical shift.As for the range, we have:
If a > 0, the range is (c,∞).If a < 0, the range is (-∞,c).In this problem, the function is given by: [tex]f(x) = -2(6)^{x} +3[/tex]
The coefficients are a = -2 0, b = 6, and c = 3, and the range is (-∞,3).
Therefore, the coefficients are a = -2 0, b = 6, and c = 3, and the range is (-∞,3).
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The complete question is given below:
What is the range of the function f(x) = –2(6x) + 3? (negative infinity, negative 2 Right-bracket (negative infinity, 3) Left-bracket negative 2, infinity) Left-bracket 3, infinity)
Answer:B
Step-by-step explanation:edge lolololololololloll
3 rhombi are connected at a point, side by side. All sides are congruent.
Juan is making a model out of rhombi. Each rhombus will be connected to the one before it. Each rhombus will be 6 inches tall and 4 inches wide.
How much paper does he need for each rhombus?
square inches
If his wall is 11 feet long, how much paper does he use?
square inches
a. The amount of paper that he is going to need would given as 12 square inches.
b. If it is 11 inches what is needed to cover the wall is given as 396
a. How to solve for the amount of paper neededWe have the area of a rhombus to be given as
0.5 *d1 * d2
We have d1 = 6 inches
d2 = 4 inches
then area would be
0.5 * 6 * 4
= 12 inches
b. The amount of paper used as length is 11 feet long
1 ft = 12 inches
then 11 feet = 11 * 12
= 132
Number needed = 4
132/4 = 33
Then the area would be 33 * 12 inches to cover the wall
= 396
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Answer:
12 and 396
Step-by-step explanation:
william bougght canned goods at 2.40 per can.he wants to increase the price per can so that he makes a 25% profit. what will the selling price per can be?
Answer:
The answer is 3
Step-by-step explanation:
25% of 2.40 equals 0.6
so 3 will be the total price and he will get 0.6 profit.
William bought canned goods at 2.40 per can. he wants to increase the price per can so that he makes a 25% profit, the selling price per can be, 3.00
What is the percentage?The percentage is a mathematical term, which means a number or a ratio which is represented in fractions of 100. We use the '%' symbol to represent the percentage.
Formula for percentage;
Percentage = (present quantity/whole quantity)×100
Given that,
William bought canned goods at 2.40
He wants to increase the price per can so that he makes a 25% profit
The selling price per can be =?
Percentage = Amount he wants to increase/previous amount×100
25 = x/2.40×100
x = 0.60
new selling price = 2.40+0.60
= 3.00
Therefore, The new selling price is 3.00 per can
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Use the laplace transform to solve the given initial-value problem. y' + y = (t − 1), y(0) = 5
Using the Laplace transform, the value of y' + y = (t − 1), y(0) = 5 is y(t) = 5e ^ -t + u (t - 1)e^(1-t)
Laplace rework is an critical rework approach that is in particular useful in fixing linear normal equations. It unearths very huge applications in regions of physics, electrical engineering, control optics, arithmetic and sign processing.
y' + y = (t − 1)
y (0) = 5
Taking the Laplace transformation of the differential equation
⇒sY(s) - y (0) + Y(s) = e-s
⇒(s + 1)Y(s) = (5+ e^-s)/s + 1
⇒y(t) = L^-1{5/s+1} + {e ^-s/s + 1}
⇒y(t) = 5 e^-t + u(t -1)e^1-t
The Laplace remodel method, the feature within the time area is transformed to a Laplace characteristic within the frequency domain. This Laplace feature will be inside the shape of an algebraic equation and it can be solved easily.
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the slope of the line p is__and the slop of the line q is__
Answer:
The slope of line p is 3 and the slope of line q is -3.
In the student council elections, five students are running for president, two are running for vice president, two are running for treasurer and three are running for secretary. How many different possible student council teams could be elected from these students?
Using the Fundamental Counting Theorem, it is found that 60 different possible student council teams could be elected from these students.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
Considering the number of options for president, vice president, treasurer and secretary the parameters are:
n1 = 5, n2 = 2, n3 = 2, n4 = 3.
Hence the number of different teams is:
N = 5 x 2 x 2 x 3 = 60.
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1. Find the midpoint of the line segment with endpoints (-7, 3) and (3,-7).
Step-by-step explanation:
the coordinates of a midpoint are
x = (x1 + x2)/2
y = (y1 + y2)/2
with (x1, y1) and (x2, y2) being the endpoints.
so, our midpoint here is
((-7 + 3)/2, (3 + -7)/2) = (-4/2, -4/2) = (-2, -2)
A skateboard halfpipe is being designed for a competition. the halfpipe will be in the shape of a parabola and will be positioned above the ground such that its focus is 40 ft above the ground. using the ground as the x-axis, where should the base of the halfpipe be positioned? which equation best describes the equation of the halfpipe?
The equation of the halfpipe is Option A , (0, 20); Y equals one over eighty times x squared plus 20.
The equation of the halfpipe is Y = X²/80 +20.
What is parabola ?
A parabola is the set of points in a plane that are the same distance from a given point and a given line in that plane. The given point is called the focus, and the line is called the directrix. The midpoint of the perpendicular segment from the focus to the directrix is called the vertex of the parabola.The equation of parabola is given by
(X-h)² = 4p(Y-k)²
In this case h = 0
So we get
Y = X²/4P +k
Focus point is (h, p+k) , (p+k) = 40
Hence h, k = (0,20)
P = 40-k = 20
Equation Y = X²/80 +20
Therefore, the equation of the halfpipe is Y = X²/80 +20
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The complete question is -
A skateboard halfpipe is being designed for a competition. The halfpipe will be in the shape of a parabola and will be positioned above the ground such that its focus is 20 ft above the ground. Using the ground as the x-axis, where should the base of the halfpipe be positioned? Which equation best describes the equation of the halfpipe?
(0, 20); y equals one over eighty times x squared plus 20
(0, 20); y equals one over eighty times x squared minus 20
(0, 10); y equals one over forty times x squared plus 10
(0, 10); y equals one over forty times x squared minus 10
Three divers went scuba diving in the ocean for a couple of hours. The table shows how much oxygen they had left in their oxygen tanks.
Diver Oxygen (liters)
Alexis seventy nine over eighth
Dante 9.3
Sofia nine and eight over fifteenth
Place the divers in order from least to greatest based on the number of liters left in their oxygen tank.
Sofia, Dante, Alexis
Alexis, Sofia, Dante
Dante, Alexis, Sofia
Dante, Sofia, Alexis
The divers in order from least to greatest based on the number of liters left in their oxygen tank will be Alexis, Dante, and Sofia. The correct answer is B.
What is ascending order?In mathematics, placing numbers in ascending order refers to doing so from least to largest from left to right. When numbers are arranged in ascending order, they are done so from least to largest.
Given that three divers went scuba diving in the ocean for a couple of hours. The table for the oxygen requirement is given below:-
Diver Oxygen (liters)
Alexis Seventy nine over eighth
Dante 9.3
Sofia Nine and eight over fifteenth
The Numbers are:-
Alexis ( Seventy nine over eighth) = 79 / 9 = 8.78
Dante = 9.3
Sofia ( Nine and eight over fifteenth ) = 9(9/15} = 9.6
The arrangement from least to highest will be Alexis, Dante, and Sofia.
The correct options are given below:-
Sofia, Dante, Alexis
Alexis, Dante, and Sofia.
Dante, Alexis, Sofia
Dante, Sofia, Alexis
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Answer:
Dante, Alexis and Sofia
Step-by-step explanation:
please tell me if I'm wrong but I'm positive its Dante, Alexis and Sofia
ANSWER ASAP!
what is the value of a₁₇ if a₁₃=26 and the recursive form of a geometric sequence is aₙ=1/2aₙ₋₁
please answer with atleast some detail
The 17th term of the geometric sequence given in the problem is:
[tex]a_{17} = \frac{13}{8}[/tex]
What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
As a function of the mth term, the nth term can also be given as follows:
[tex]a_n = a_mq^{n - m}[/tex]
In this problem, we have that:
[tex]a_{13} = 26, q = \frac{1}{2}[/tex]
Hence the 17th term is:
[tex]a_{17} = a_{13}q^{4}[/tex]
[tex]a_{17} = 26 \times \frac{1}{16}[/tex]
[tex]a_{17} = \frac{13}{8}[/tex]
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I need help with this pls
The given expression gives the complex number:
N = 1 + 0i
How to add and subtract complex numbers?Here we want to simplify the expression:
N = -4i + (1/4 - 5i) - (-3/4 + 8i) + 17i
Where i is the complex number, now we can just separate the terms with i and the terms without i.
N = -4i + (1/4 - 5i) - (-3/4 + 8i) + 17i
= (1/4 + 3/4) + (-4i - 5i - 8i + 17i)
= ( 1) + (-4 - 5 - 8 + 17)i
= 1 + 0i
That is the complex number that comes out of the given expression.
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Answer:
huh
Step-by-step explanation:
Graph y=8.5x PLS VERY URGENT ANSWER QUICKLY!!!!!!!!!!!!!!!!
The slope of the line is 8.5 and the y-intercept is at the origin as shown in the graph below.
Graph of a linear functionA linear function is a function that has a leading degree of 1. The standard equation for a linear function is expressed as:
y = mx + b
where
m is the slope which is equal to the rate of change of y coordinate to x-coordinates.
b is the y-intercept
Given the following equation
y=8.5x
The slope of the line is 8.5 and the y-intercept is at the origin as shown in the graph below.
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What is the independent variable in the following function?
The independent variable in the function f(c) = 2c + 9 is c whereas the dependent variable is f.
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.
The independent variable in the function f(c) = 2c + 9 is c whereas the dependent variable is f.
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Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2, and the profit on every wrap is $3. Sal made a profit of $1,470 from lunch specials last month. The equation 2x + 3y = 1,470 represents Sal's profits last month, where x is the number of sandwich lunch specials sold and y is the number of wrap lunch specials sold.
1.Change the equation to slope-intercept form. Identify the slope and y-intercept of the equation. Be sure to show all your work.
Answer:
[tex]y = -\frac{2}{3}x + 490[/tex]
gradient = = [tex]-\frac{2}{3}[/tex]
y-intercept = [tex]490[/tex]
Step-by-step explanation:
• The slope-intercept form of an equation takes the general form:
[tex]\boxed{y = mx + c}[/tex],
where:
m = slope,
c = y-intercept.
• We are given the equation:
[tex]2x + 3y = 1470[/tex]
To change this into the slope-intercept form, we must make y the subject:
[tex]3y = -2x + 1470[/tex] [subtract [tex]2x[/tex] from both sides]
⇒ [tex]y = -\frac{2}{3}x + \frac{1479}{3}[/tex] [divide both sides by 3]
⇒ [tex]y = -\frac{2}{3}x + 490[/tex]
• Comparing this equation with the general form equation, we see that:
m = [tex]-\frac{2}{3}[/tex]
c = [tex]490[/tex].
This means that the gradient is [tex]\bf -\frac{2}{3}[/tex], and the y-intercept is [tex]\bf 490[/tex].
In the diagram below, if < A = 97 °, < B = 46 °, < D = 97 ° and < F = 37 °, we can say that
The two triangles are similar by AA
There is not enough information to tell
The two triangles are not similar
Answer:
(a) The two triangles are similar by AA
Step-by-step explanation:
Similar triangles have congruent corresponding angles and proportional corresponding side lengths.
Third angleThe third angle in triangle ABC is found using the fact that the sum of angles is 180°.
∠C = 180° -∠A -∠B
∠C = 180° -97° -46° = 37°
Two of the angles, A and C, match the measures of two of the angles in triangle DEF. The matches are ...
∠A = ∠D = 97°
∠C = ∠F = 37°
The two triangles are similar by AA.
__
Additional comment
The similarity statement can be ΔABC ~ ΔDEF.
A 7. 12×10−4mol sample of koh is dissolved in water to make up 50. 0ml of solution. what is the ph of the solution at 25. 0∘c? round the answer to three significant figures
The pH of the solution is 12.2.
Molarity (kon) = No. of moles of FoH x 1000
Mckor, 7:12 × 10-4 moles x Looo 50.0 mL.
Volume of solution (m²), McKong = 1.424x102M, [on] =1.424×102M POH = -log [on] pOH =
-log [1.424x102] pon = 1.85.
pH + pOH = 14
PH = 14-pOH = 14-1.85 pH = 12.15.)
12.2.
pH is a measure of the concentration of hydrogen ions in water. Specifically, pH is the negative logarithm of the hydrogen ion (H+) concentration (mol/L) in an aqueous solution. pH = -log10(H+) This term indicates the basicity or acidity of a solution from 0 to 14 where pH 7 is neutral.
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PLEASE HELP IM STUCK PLS
Answer:
The slope between these two points is m=-4.
Step-by-step explanation:
Greetings !
[tex]the \: equation \: for \: slope \: m \: is \\ m = \frac{Y₂-Y}{X₂-X₁}..substitute \: known \: values \\ m = \frac{ (-11 - 9) }{(3 - ( - 2)} \\ m = \frac{ - 20}{5} \\ m = - 4[/tex]
The sum of 10 consecutive integersstarting with 11, equals the sum of 5 consecutive integers, starting with
(A) 22
(B) 29
(C) 31
(D) 33
Answer: [tex]\large\boxed{29}[/tex]
Step-by-step explanation:
The sum of 10 consecutive integersstarting with 11
= 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 = 155
Lets try 29:
29 + 30 + 31 + 32 + 33 = 155
Therefore our answer is:
[tex]\large\boxed{29}[/tex]
if you double the side length of a cube how does it effect the volume
Step-by-step explanation:
Volume of the cube = Side
Since,
All the sides of the cube are equal
Then if the length of a side of the cube is
increased
So, the side of the cube becomes
Side of the cube = 2 × Side
Assume
Side of the cube be ‘s’
Side of the cube = 2s
Now,
Volume of the cube = 2s × 2s × 2s
Volume of the cube = (2s)
Volume of the cube = 8s
To find how many times the volume of the cube is
increased
Geometry: ASAP!!! Complete this proof
Answer:
1. ∠1 ≅ 6 : Given
2. ∠3 ≅ ∠ 4 : Vertical Angles Congruence Property
3. ∠2 ≅ ∠5 : Corollary III of Theorem 19 : If two angles of two triangles are congruent, then the third angle of both triangles are congruent.
Step-by-step explanation: For ∠3 ≅ ∠4, the angles are in a diagonal placement, meaning they are vertical angles. Vertical angles are always congruent.
Lookimg at one of the problems you posted earlier, the Corollary III of Theorem 19 given, states that if two angles are congruent in both triangles, then the third angle is congruent in both triangles. Since we have 2 angles already congruent to 2 other angles, ∠2 and ∠5 must be congruent.
Hope this helped!
