There are 37 students in drama club and 27 students in yearbook club.
And the system of equations will be 1.x + 1.y = 64.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
Given that,
Total number of students in drama club and yearbook club = 64,
Also, there is a yearbook club. Students in drama club has 10 more than yearbook club,
If x represents the number of students in the drama club and y represents the number of students in yearbook club.
According to given condition,
x+ y = 64 (1)
and x = y + 10
Substitute the value of x in equation (1),
y + 10 + y = 64
2y = 54
y = 27
And x = 27 + 10 = 37
The required system of equations,
1.x + 1.y = 64
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Use the image below to answer the next two questions.
ABCD pictured below is a square.
Categorize the angles as either 45° or 90°.
The measure of angle ABC is 90° and the the measure of angle BDC is 45°.
Square ABCD is given.
What is a square?A square is a quadrilateral with four equal sides. There are many objects around us that are in the shape of a square. Each square shape is identified by its equal sides and its interior angles that are equal to 90°.
Diagonals bisects the angles in square and intersect each other at right angle.
Now, ∠ABC=90°
∠AED=90°
∠BAC=45°
∠DBC=45°
∠BDC=45°
Hence, the measure of angle ABC is 90° and the the measure of angle BDC is 45°.
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Write an equation for a rational function with:
Vertical asymptotes at x = 6 and x = 3
x intercepts at x = 1 and x = -1
y intercept at 5
Answer:
Making a fraction is the easiest way to do this.
The x-intercepts give solutions to a problem that equals zero.
The vertical asymptotes are values x cannot be, in a fraction the denominator can not be zero.
Horizontal asymptotes are the values y approaches. This can be accomplished by making the leading term have a coefficient of 6
Step-by-step explanation:
Simplify to create an equivalent expression.
2(-n -3) -7(5+2n)
Answer:
-16n-41
Step-by-step explanation:
Christian went into a movie theater and bought 8 drinks and 10 candies, costing a total of $94. Dianelys went into the same movie theater and bought 9 drinks and 6 candies, costing a total of $79.50. Write a system of equations that could be used to determine the price of each drink and the price of each candy. Define the variables that you use to write the system.
The cost of each drink is $5.5
The cost of each candy is $5
What is elimination method ?Using the elimination method, you may either add or subtract the equations to produce an equation in one variable. To eliminate a variable, add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are in equality.
According to the given information
Let number of drinks = x
Let number of candies = y
Christian bought 8 drinks and 10 candies and it costed $94
So the equation becomes
8x + 10 y = $94
Other guy bought 9 drinks and 6 candies and it costed $79.50
So the equation becomes
9x + 6y = $79.50
By applying elimination method
9x + 6y = $79.50
Dividing by 2
3x + 2y = $26.5
multiplying the above equation by 5
15x + 10y = $132.5
8x + 10 y = $94
Subtract the following equation
7x = 38.5
x = 5.5
substituting the value of x in above one equation we get
y = 5
So the cost of each drink is $5.5
the cost of each candy is $5
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Answer:
D = the price of each drink
C = The price of each candy
One drink costs d. So 8 drinks cost 8d. Same thing with candies except a different variable. One candy costs c. Therefore 10 candies cost 10c. So the first equation here would be :
8d + 10c = 94
Same thing with the second equation but with different numbers :
9d + 6c = 79.50
If you're also looking for a solution to this answer. You use a process called the elimination method.
Let me know if you have any questions ! <3
With the recent launch of Artemis there has been a new initiative to send manned missions to the Moon in hopes of one day colonizing it. The newly founded International Space Agency has decided to select one lucky person from the general population to join this venture. Instead of choosing people at random, however, they decide to administer a 50-question multiple-choice test to everyone who applies. Each question has only two choices (A or B) and only one correct answer. Answer the questions below and explain the steps you used to arrive at your answers (e.g., give calculations when applicable):
a) What is the probability that random guessing will lead to a passing (70% or higher) score?
b) Imagine that the Agency decided that 50 questions was too difficult and shortened the test to just 25 questions. To balance this out, they also changed the questions so they each have four options (A, B, C, and D), but still only one possible correct answer. What is the probability that random guessing will lead to a perfect score?
c) Based on the results, do you think the first or second version of the test is safer against examinees guessing to achieve a passing score? Explain your answer.
a) The probability that random guessing will lead to a passing score is of: 0%.
b) The probability that random guessing will lead to a perfect score is of: 3.35 x 10^-18.
c) The first version of the test is safer against examinees guessing to achieve a passing score.
What is the binomial distribution formula?The mass probability formula, giving the probability of x successes, is presented as follows:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.For item a, considering that for 50 questions, all are guessed among five answer, the values of these parameters are given as follows:
n = 50, p = 1/5 = 0.2.
The probability of passing is given as follows:
P(X ≥ 35).
Using a binomial distribution calculator, with the given parameters, we have that:
P(X ≥ 35) = 0%.
For item b, the parameters are given as follows:
n = 25, p = 1/4 = 0.2.
Hence the probability of a perfect score is given as follows:
P(X = 25) = 0.2^25 = 3.35 x 10^-18.
For item c, we have that the first version is safer against examinees guessing to achieve a passing score, as:
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Find a polynomial f(x) of degree 4 with real coefficients and the following zeros. 1 (multiplicity 2) , 1+2i
Answer:
Factorization
Step-by-step explanation:
(a) Solve the given inequality 3 (x +2) ≥ 5 (x + 1).
(b) Find the greatest possible value of x, if it is;
1. a rational number
2. an integer
3. a prime number
213. Sandy has 1 quart and 1 pint of soda.
How many cups can she divide this
amount into?
The chart shows the average time spent reading per day for students in an 8th grade class.
The line plot is titled minutes of reading per day, and the horizontal axis is labeled minutes of reading per day. There are 5 dots at 30, 1 dot at 33, 5 dots at 35, 1 dot at 36, 1 dot at 37, 3 dots at 40, 1 dot at 44, one dot at 46, 1 dot at 47, and 1 dot at 50.
Which of the following describes this data set?
Categorical and bivariate
Categorical and univariate
Numerical and bivariate
Numerical and univariate
This data collection may be characterized as numerical and univariate.
How do you define numerical and univariate?If the collection of all potential values for a numerical univariate data is finite or countably infinite, the data is discrete. Usually, discrete univariate data are used in counting (such as the number of books read by a person). If the range of all potential values is a set of numbers, then a numerical univariate data is continuous.
Categorical data – what is it?Categorical variables represent different sorts of data that may be categorized. Race, sex, age group, and educational level are some examples of categorical variables.
Data types that may be kept and recognized based on the names or labels assigned to them are referred to as categorical data. Numerical data refers to the data that is in the form of numbers, and not in any language or descriptive form. Also known as qualitative data as it qualifies data before classifying it.
Over here we have the data for the average time spent reading per day for students in an 8th grade class.
Average Time is a numerical data
Bivariate data deals with two variables
univariate data, which is one variable data
we have numerical data and one variables so its
Numerical and univariate
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Where does the line f(x) = x-1 cross the parabola g(x) = (x+2)^2-9?
Answer:
The line and the parabola cross at x = -4 and x = 1
Step-by-step explanation:
Set f(x) = g(x)
[tex]x-1 = (x+2)^2-9\\x - 1 = x^2+4x+4-9\\x = x^2 + 4x - 4\\0 = x^2 + 3x - 4\\Factor\\0 = (x - 1) (x + 4)\\x = 1, -4[/tex]
A employee must create 140 gallons of slash burn fuel that must have a ratio of 8 parts diesel to 2 parts gas. How much diesel and gas are needed to create this mixture?
The amount of diesel required to create slash burn fuel is = 112 gallons
The amount of gas required to create slash burn fuel = 28 gallons
What is Proportion?
The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
Given data ,
The total amount of slash fuel = 140 gallons
The ratio of diesel to gas in slash fuel is = 8 : 2
Let the amount of diesel required to create slash burn fuel be = 8x
Let the amount of gas required to create slash burn fuel be = 2x
So , the equation of proportion is given by
Total amount of slash fuel = amount of diesel required to create slash burn fuel + amount of gas required to create slash burn fuel
Substituting the values in the equation , we get
Total amount of slash fuel = 8x + 2x
8x + 2x = 140
10x = 140
Divide by 10 on both sides of the equation , we get
x = 14 gallons
Substituting the value of x in the above expressions , we get
Amount of diesel required to create slash burn fuel = 8x
Amount of diesel required to create slash burn fuel = 8 x 14
Amount of diesel required to create slash burn fuel = 112 gallons
And ,
Amount of gas required to create slash burn fuel = 2x
Amount of gas required to create slash burn fuel = 2 x 14
Amount of gas required to create slash burn fuel = 28 gallons
Hence ,
The amount of diesel required to create slash burn fuel is = 112 gallons
The amount of gas required to create slash burn fuel = 28 gallons
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There is a fee to enter the county fair, plus a fixed amount to play each game. The
line shows the money spent at the fair, y, when a games are played.
Money Spent at the Fair
Money Spent ($)
y
Write an equation for the line in slope-intercept form.
Drag a number into each box to write the equation.
Y
An equation for the line in slope-intercept form is y=(6/5)x+8
What is a slope?The same number is given for every two different points on the same line when the ratio is stated as a quotient ("rise over run"). On a falling line, there is a negative "rise." In a diagram that depicts a roof or a road as a description or a design, the line may be practical as established by a road surveyor.
The steepness, incline, or grade of a line can be approximated by the slope's absolute value. The slope of a line determines how steep it is.
From the graph,
The line passes through the points (0,8) and (5, 14)
Slope m=(14-8)/(5-0)
m=6/5
(0, 8) passes through the line y=mx+c
So, 8=6(0)/5+c
Then, c=8
An equation for the line in slope-intercept form is y=(6/5)x+8.
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Write an inequality with x isolated on the left side that is equivalent to the given inequality.
Fx+Wy>R; Assume F > 0.
The equivalent inequality with x isolated on the left side is
Need help asap
The inequality Fx + Wy > R written with x isolated to the left sides is
x > (R - Wy) / FHow to write the inequality with x isolated to the left hand sideInequality refers to a way of representing relationships between variables at the left hand side of equation to the variables to the right hand side of an equation.
The signs used in inequality are of 4 types namely
less thangreater thanless than or equal togreater than or equal toThe given inequality in the problem has greater than sign and it is written as Fx + Wy > R
rearranging the inequality gives
Fx + Wy > R
Fx > R - Wy
divide through by F
Fx / F> R/F - Wy/F
x > (R - Wy) / F
isolating x to the left side gives x > (R - Wy) / F
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Output(y) 8 less than 3 times x
Answer:
y = 3x - 8
Step-by-step explanation:
John asks why the last step of Pólya's four-step problem solving process, looking back, is necessary since he has already given the answer. What can you tell him?
Select all the possible reasons the last step, looking back, is necessary below.
A. Looking back allows a student to check that the answer is correct.
B. Looking back allows a student to determine the best strategy to find the solution.
C. Looking back allows a student to understand the problem.
D. Looking back allows a student to check that the answer makes sense in context of the problem.
The reason why looking back is important in mathematical answers is that; Option D: Looking back allows a student to check that the answer is correct and makes sense in context of the problem.
How to confirm mathematical answers?We know that in mathematics, every problem has steps to solve it whether algebra, proportion, trigonometry, calculus, congruency, angles, logarithms, e,t,c
Now, since we know that every Maths problem has steps to solve them, then we can say that, in some instances, we definitely have to look back to be sure that the answer actually makes sense when we consider the solution being required.
Now, if we have to look back to check that the answer is actually correct and properly portrays the solution being demanded, then we can say that the appropriate option for looking back her is option D.
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A quality inspector visits two factories. She measures statistics for the mass of screwa produced at each factory.
- The screws from which factory have grealer mass?
Overall, the screws from Factory A have greater mass.
- Find the difference in means between the factories:
25.1-24.9=0.2
Find the ratio of the difference in means to the MAD of Factory A: 0.2/0.2=1 Find the ratio of the difference in means to the MAD of Factory B: 02/0.3}=0.67 Are the screws produced by the two factories substantially different?
The required percentage is 95% data lies between the given data.
What is percentage?
A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.Let X be the lengths of screws.
X~ Normal (μ = 5.5, σ = 0.1)
P[5.3 < X < 5.7]
= P[(5.3-5.5)/0.1 < (X-μ)/σ < (5.7-5.5)/0.1]
= P[-2 < Z < 2] Z is a standard normal variable.
= 2*P[Z < 2] - 1
= 2*0.97725 - 1, from standard normal table.
= 0.9545
P[5.3 < X < 5.7] = 0.95
Hence, the required percentage is 95% data lies between the given data.
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A football club sells, on average, 23000 tickets per match. In one season they play, on average, 46 matches.How many tickets do they sell, on average, each season?
Answer:
On average, the football club sells 1,058,000 tickets per season.
Step-by-step explanation:
[tex]23000[/tex] × [tex]46 = 1058000[/tex]
The following information matrices shows how many of each Video Game Consoles that each
electronics store sold during one weekend and the price that is charged for each gaming console at all
3 stores.
Micro Middle store sold the least number of video game consoles.
What is a 2D matrix?The two dimensions of a matrix are represented by rows and columns. The row index and the column index are the two subscripts that each element is specified by.
The rows and columns in a matrix stand in for the two dimensions. The row index and the column index serve as two subscripts that each define an element. A 2D matrix is expanded into a multidimensional array, which uses additional subscripts for indexing.
The total no. of consoles sold by each store is:
Game Go = 53+21+48 = 122
Better Buy = 65+34+70 = 169
Micro Middle = 18+11+15 = 44
The least number of consoles were sold by Micro Middle(44).
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Given BC ║ AD and BC ≅ AD
Proof m∠ BAC ≅ m∠ DCA
What is parallelogram side theorem?
The parallelogram side theorem simply means that the opposite sides of a parallelogram are equal and also parallel to each other.
Proof: We have AD || BC [Opposite sides of parallelogram ABCD]
∠BAC= ∠ACD …(i) [Alternate angles with transversal AC]
Now, AB || CD [Opposite sides of parallelogram ABCD]
∠DAC = ∠ACB …(ii) [Alternate angles with transversal AC]
In ΔABC and ΔACD, we have
∠1 = ∠3 [From (i)]
∠2 = ∠4 [From (ii)]
and AC = CA [Common]
∴ ΔABC≅ ΔCDA [By ASA Congruence]
Hence Proved.
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ΔABC≅ ΔCDA By ASA Congruence, therefore m∠ BAC ≅ m∠ DCA, hence proved using parallelogram side theorem.
What is parallelogram side theorem?
The parallelogram side theorem simply means that the opposite sides of a parallelogram are equal and also parallel to each other.
Proof: We have AD || BC [Opposite sides of parallelogram ABCD]
∠BAC= ∠ACD …(i) [Alternate angles with transversal AC]
Now, AB || CD [Opposite sides of parallelogram ABCD]
∠DAC = ∠ACB …(ii) [Alternate angles with transversal AC]
In ΔABC and ΔACD, we have
∠1 = ∠3 [From (i)]
∠2 = ∠4 [From (ii)]
and AC = CA [Common]
∴ ΔABC≅ ΔCDA [By ASA Congruence]
Hence Proved.
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Question
the third term of GP is 4 the product of its first 5 term is
please solve it
Don't Spam
[tex] \huge{ \bold{ \color{purple}{Solution }}}[/tex]
Let a be the first term and r be the common ratio
Now,
[tex] \large{ \sf{T _3 = 4}}[/tex]
[tex] \large{ \sf{ {ar}^{2} = 4}}[/tex]
[tex]\large{ \sf{ \therefore \: product \: of \: first \: 5 \: term \: = a _1 \times a_2 \times a_3 \times a_4 \times \: a _5}}[/tex]
[tex] \large{ \sf{ = a(ar)( {ar}^{2} )( {ar}^{3} )( {ar}^{4} ) = {a}^{5} r {}^{10} }}[/tex]
[tex] \large{ \sf{ \red{(ar {}^{2} ) {}^{5} = {4}^{5} }}}[/tex]
[tex] \rule{150pt}{5pt}[/tex]
b is the midpoint of segment ac. a has coordinates (-3, 4) and b has coordinates (-1 1/2, 1). find the coordinates of c
The coordinates point C of the given line segment AC is C(0, -2) whose midpoint is at B.
How to calculate a midpoint of a line segment?To calculate the midpoint of a line segment, find the average for the coordinates of the endpoints of the line segment. I.e.,
Consider a line segment AC, B is its midpoint.
So, the coordinates of B are (Where we have A(x1, y1) and C(x2, y2))
B(x, y) = [tex](\frac{x1+x2}{2}, \frac{y1+y2}{2})[/tex]
Calculation:It is given that, B is the midpoint of a line segment AC.
Where A has coordinates as (-3, 4) and B has coordinates as (-1 1/2, 1).
So, the coordinates of the other end point C of the given line segment are calculated as
B(x, y) = [tex](\frac{x1+x2}{2}, \frac{y1+y2}{2})[/tex]
⇒ (-1.5, 1) = [tex](\frac{-3+x2}{2}, \frac{4+y2}{2})[/tex]
⇒ -1.5 = (-3 + x2)/2 and 1 = (4 + y2)/2
⇒ -3 = -3 + x2 and 2 = 4 + y2
⇒ x2 = 0 and y2 = 2 - 4 = -2
Therefore, point C has coordinates as (0, -2).
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Find the volume of the solid. When appropriate, use 3.14 and round to the nearest hundredth.
Answer:
904.32 cm³
Step-by-step explanation:
Assuming 12cm is the diameter.
The given solid is a sphere, we must find the volume.
Given radius:
[tex]6[/tex]6
Use the equation [tex]v=\frac{4}{3} \pi r^3[/tex] to find the volume of the sphere.
[tex]\frac{4}{3} \times\pi\times6^3[/tex]
≈ 904.77868
Rounding, 904.32 cm³
27 students are learning to make ballon animals. There are 172 ballooons to be shared equally among the students.
Question 5 id points
Do not round or enter wards, use a decimal answer.
You are playing a carnival game. You will spin the two spinners below.
Rule 1: To win the grand prize, you need to spin an "A" and a "1". What is the probability that you win a bōsic prize?
Answer:
Rule 2: To win you a basic prize, you need to spin an "A" or a "1". What is the probability that you win a basic prize?
Probability of winning a grand prize is 1/10
Probability of winning a basic prize is 11/20
What is the probability of two independent events?
If A and B are two independent events, then P(A and B) = P(A) * P(B).
If Events A and B are independent, the probability that either Event A or Event B occurs is: P(A or B) = P(A) + P(B) - P(A and B).
Solution:
P(A) = no. of A / total possibility
= 4/10
P(B) = no. of 1's/total possibility
= 3/12
= 1/4
Now,
To win a grand prize you need an "A" and "1" .
∴ P(A and B) = P(A) × P(B)
= 4/10 × 1/4
P(A and B) = 1/10
Now ,
To win a basic prize you need to spin an "A" or a "1"
∴ P(A or B) = P(A) + P(B) - P(A and B)
= 4/10 + 1/4 - 1/10
= 3/10 + 1/4
∴ P(A or B)= 11/20
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Probability of winning a grand prize is 1/10
Probability of winning a basic prize is 11/20
What is the probability of two independent events?If A and B are two independent events, then P(A and B) = P(A) * P(B).
If Events A and B are independent, the probability that either Event A or Event B occurs is: P(A or B) = P(A) + P(B) - P(A and B).
Evaluating :P(A) = no. of A / total possibility
= 4/10
P(B) = no. of 1's/total possibility
= 3/12
= 1/4
Now,
To win a grand prize you need an "A" and "1" .
∴ P(A and B) = P(A) × P(B)
= 4/10 × 1/4
P(A and B) = 1/10
Now ,
To win a basic prize you need to spin an "A" or a "1"
∴ P(A or B) = P(A) + P(B) - P(A and B)
= 4/10 + 1/4 - 1/10
= 3/10 + 1/4
∴ P(A or B)= 11/20
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A standard queen bed hotel room at the Posh Inn is currently priced at $ 135 a day, after a 17 % markup to offset inflation costs. What was the daily charge for the room before the increase?
the regular daily charge is "x", oddly enough that's the 100%.
so the new charge is 17% up, that means the new charge is 100% + 17% = 117%, and we know that's $135, so
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 135& 117 \end{array} \implies \cfrac{x}{135}~~=~~\cfrac{100}{117} \\\\\\ 117x=13500\implies x=\cfrac{13500}{117}\implies x=\cfrac{1500}{13}\implies x=115\frac{5}{13}[/tex]
plssss helpppp right answers only and explaintion.
The equivalent of the expression 2³/2⁷ using the law of indices is (a) 1/2⁴
How to determine the equivalent expression?From the question, we have the following parameters that can be used in our computation:
2³/2⁷
The above expression can be solved using the law of indices
When the law of indices is applied, we have the following representation
2³/2⁷ = 2(³ ⁻ ⁷)
Remove the bracket in the above expression
So, we have the following representation
2³/2⁷ = 2³ ⁻ ⁷
Evaluate the difference
This gives
2³/2⁷ = 2⁻⁴
Rewrite as
2³/2⁷ = 1/2⁴
Hence, the solution is (a) 1/2⁴
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The lengths of the legs of an isosceles right triangle are x and [tex]\sqrt{6x+16}[/tex]
a. Find the length of the hypotenuse, in terms of x, in simplest radical form
b. Find the length of all three sides of the triangle, in simplest radical form.
Check the picture below. Let's recall is an isosceles, so it has twin sides and is a right-triangle.
[tex]x^2+(\sqrt{6x+16})^2\implies \sqrt{x^2+6x+16}\qquad \impliedby hypotenuse \\\\[-0.35em] ~\dotfill\\\\ x~~ = ~~\sqrt{6x+16}\implies \stackrel{\textit{squaring both sides}}{x^2=6x+16}\implies x^2-6x-16=0 \\\\\\ (x-8)(x+2)=0\implies x= \begin{cases} 8 ~~ \textit{\LARGE \checkmark}\\\\ -2 ~~ \bigotimes \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\underset{\textit{length of each side}}{\stackrel{\sqrt{(8)^2 + 6(8) + 16}}{{\Large \begin{array}{llll} 8\sqrt{2} \end{array}}}\hspace{5em}\stackrel{x}{\text{\Large 8}}\hspace{5em}\stackrel{\sqrt{6(8) - 16}}{\text{\Large 8}}}[/tex]
now, let's notice, the negative value is a legitimate value, however for this case is invalid since the lengths of the triangle can't be negative.
simplify the expression: 5(1+2m)
Answer:
Hi!
The answer would be: 5 + 10m
I hope this helped you! :)
Answer:
[tex]\bf 5+10m[/tex]
Step-by-step explanation:
[tex]\bf 5\left(1+2m\right)[/tex]
Apply the distributive law:-
[tex]\bf 5\left(1+2m\right)=5\times \:1+5\times\:2m[/tex]
[tex]\bf 5\times\:1+5\times \:2m[/tex]
[tex]\bf 5+10m[/tex]
___________________
Hope this helps!
Have a good one!
Which of the following graphs shows a dilation of the triangle from a fixed point?
The graph that shows a dilation among the given graphs is; Graph F.
What is dilation?Dilation in graphs simply means each side is multiplied by the same
scale factor. What this means is that the ratio of each dilated side to their respective old sides before dilation must be the same scale factor.
We can see that the pre-dilated image has 2 units along the y - axis and 4 units across the x-axis. After dilation, it now has 4 units along the y - axis and 8 units across the x-axis. This means the scale factor in both axis are; 4/2 = 2 and 8/4 = 2. They are both the same scale factors and as such this graph shows a dilation.
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wn measures (Example 1)
B 8 in.
2.
85%
12 in.
A 35°
14 in.
60°
C
Z
42 in.
t
S
Y
36 in.
Answer:
The answer is A
Step-by-step explanation:
took the test.