The resulting expression of the algebraic expression is 13r²(2rs + 4r³ - 3s⁴).
option C.
What is the resulting expression of the algebraic expression?The resulting expression of the algebraic expression given as
26r³s + 52r^(5) - 39r²s⁴
can be determined by finding the highest common factor here and factorize out.
The highest common factor of the letters is r²
Factors of 26 = 1, 2, 13, 26
Factors of 39 = 1, 3, 13, 39
Factors of 52 = 1, 2, 4, 13, 26, 52
The highest common factor for the 3 numbers is 13.
Thus, in total, the highest common factor for the algebraic expression is 13r².
Finally, we have;
13r²(2rs + 4r³ - 3s⁴)
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The complete question is below:
Factor 26r³s + 52r^(5) - 39r²s⁴
Which table of values satisfies the linear equation y=−34x −6?
The table of values satisfies the linear equation y = −3x/4 − 6 is: C. table C.
How to determine the solution?In order to determine which ordered pairs are valid and true solutions based on the given linear equation, we would have to test the given ordered pairs by substituting their values into the linear equation as follows;
For ordered pair (-4, -9), we have:
y = −3x/4 − 6
-9 = −3(-4)/4 − 6
-9 = 3 − 6
-9 = -3 (False).
For ordered pair (-8, -12), we have:
y = −3x/4 − 6
-12 = −3(-8)/4 − 6
-12 = 8 − 6
-12 = 2 (False).
For ordered pair (-4, -3), we have:
y = −3x/4 − 6
-3 = −3(-4)/4 − 6
-3 = 3 − 6
-3 = -3 (True).
For ordered pair (0, -6), we have:
y = −3x/4 − 6
-6 = −3(0)/4 − 6
-6 = 0 − 6
-6 = -6 (True).
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Complete Question:
Which table of values satisfies the linear equation y = −3x/4 − 6?
suppose you want to fence a rectangular soccer field site that has its length equal to three times its width. the fencing for the east and west sides costs $6 per foot, and the fencing for the north and south sides costs only $3 per foot. find the total cost of the fencing as a function of the length of a side x (feet).
The total cost of the fencing can be expressed as a function of x: C(x) = $24x.
Let's assume that the width of the soccer field is x feet. Then the length of the soccer field is 3x feet.
The east and west sides have a combined length of 3x feet, and the cost per foot of fencing is $6, so the total cost for the east and west sides is $6 * 3x = $18x.
The north and south sides have a combined length of 2x feet, and the cost per foot of fencing is $3, so the total cost for the north and south sides is $3 * 2x = $6x.
The total cost of the fencing is the sum of the cost of the east and west sides and the north and south sides: $18x + $6x = $24x.
So, the total cost of the fencing can be expressed as a function of x: C(x) = $24x.
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Ramiro got his first job in 2020. In that year, Social Security tax was 6.2% of income up to
$137,700. Medicare tax was 1.45%. If Ramiro earned $73,210 in 2020, how much did he pay for
Social Security and Medicare taxes?
In 2020, Ramiro paid $4,537.22 for Social Security tax and $1,061.70 for Medicare tax
What is Percentage?
Percentage is a way of expressing a number as a fraction of 100. It represents a proportion or rate out of 100, and is often used to compare values or to express a change or growth.
Solution:
To find how much Ramiro paid for Social Security and Medicare taxes in 2020, we can follow these steps:
1. Calculate the amount of Ramiro's income that is subject to Social Security tax. In 2020, Social Security tax was only applied to the first $137,700 of income. Since Ramiro's income of $73,210 is less than $137,700, all of his income is subject to Social Security tax.
2. Calculate the amount of Social Security tax that Ramiro paid. Since Social Security tax was 6.2% of income in 2020, Ramiro paid:
3. Social Security tax = 0.062 x $73,210 = $4,537.22
1. Calculate the amount of Medicare tax that Ramiro paid. Medicare tax was 1.45% of all income, with no income limit. Therefore, Ramiro paid:
2. Medicare tax = 0.0145 x $73,210 = $1,061.70
Therefore, in 2020, Ramiro paid $4,537.22 for Social Security tax and $1,061.70 for Medicare tax, for a total of $5,598.92 in Social Security and Medicare taxes.
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A bag contains 950 marbles. Some are red and some are blue. A student reached into the bag
and pulled out a random sample of 20 marbles. He recorded that 11 were blue and 9 were
red. If this is a representative sample, about how many marbles out of 950 are blue?
Answer: The number of blue marbles in the sample is 11, so the proportion of blue marbles in the sample is 11/20. If the sample is representative, we can use this proportion to estimate the proportion of blue marbles in the whole bag of 950 marbles. So, our estimate of the number of blue marbles in the whole bag is:
950 * (11/20) = 477.5
So, we can estimate that about 478 marbles out of 950 are blue.
Step-by-step explanation:
Your Assignment
Is x = 6 a solution to the equation 5(x – 3) = x + 13?
Follow the steps to find out.
1. Rewrite the equation 5(x – 3) = x + 13 with 6 substituted for x. Write a question mark over the equal sign to show that you're testing to see if the equation is true. (2 points)
2. Simplify both sides. Show your work. (2 points)
3. Is x = 6 a solution to the equation? Why or why not? (3 points)
4. Find a value of x that is a solution to 5(x – 3) = x + 13. Describe how you found the solution. (3 points)
Your Assignment
Is x = 6 a solution to the equation 5(x – 3) = x + 13?
Follow the steps to find out.
1. Rewrite the equation 5(x – 3) = x + 13 with 6 substituted for x. Write a question mark over the equal sign to show that you're testing to see if the equation is true. (2 points)
2. Simplify both sides. Show your work. (2 points)
3. Is x = 6 a solution to the equation? Why or why not? (3 points)
4. Find a value of x that is a solution to 5(x – 3) = x + 13. Describe how you found the solution. (3 points)
Answer:
6 is not the solution. 7 is the solution.
Step-by-step explanation:
5(x -3) = x + 13 Substitute 6 for x
5(6 -3) = 6 + 13
5(3) = 19
15 ≠ 19
6 is not a solution because it results in a false statement. The two sides do not equal each other.
5(x - 3) = x + 13 Distribute the 5
5x -15 = x + 13 Subtract x from both sides
5x - x - 15 = x - x + 13
4x - 15 = 13 Add 15 to both sides
4x - 15 + 15 = 15 + 13
4x = 28 Divide both sides by 4
x = 7
7 is the solution to the equaion.
A box of cereal states that there are calories in a 3/4
-cup serving. What is the unit rate for calories per cup? How many calories are there in 3cups of the cereal?
120 calories make up one cup amount of calories. Three cups of the cereal have 360 calories in them.
1. Determine how many calories are in a cup: 120 calories are in 3/4 cup; 3/4 cup is 120 calories.
2. Determine how many calories are in 3 cups: 3 cups at 120 calories each equals 360 calories.
You must divide the total amount of calories in a serving of 3/4 cup by 3/4 cup to determine the unit rate for calories per cup of a certain cereal. In this instance, a serving of the cereal that is 3/4 cup in size has 120 calories. As a result, 120 calories are the number of calories in a cup. You must multiply the unit rate for calories per cup (120 calories) by 3 cups to see how many calories are in 3 cups of cereal. This indicates that there are 360 calories in 3 cups of the cereal. In summary, there are 360 calories in 3 cups of cereal, or 120 calories per cup, at the unit rate.
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3x+2y=9
2/3y=3-x
What’s the solution
Answer:
2y=9-3x. 2=(3-x)3y
2=(9-3x)/y......1 2= 3y(3-x)..........2
Combining equations 1 and 2;
9-3x=3y²(3-x)
3(3-x)=3y²(3-x)
y²=1
y=√1
y= ±1
2. ABCD is a parallelogram and AE and CF are the altitudes (Fig. 9.29). Given AB = 12 cm, AD = 6 cm and AE = 7.5 cm. Find ar(ABCD) and the length of CF.
The length of CF is given as 45 cm
How to solve for the length of CFSince AE is the altitude of the parallelogram ABCD, it is perpendicular to the base DC. Similarly, CF is the altitude of the triangle ACD, and it is perpendicular to the base AD.
Let's use the properties of parallelograms and triangles to solve for the area and length of CF.
Since ABCD is a parallelogram, we know that opposite sides are parallel and equal in length. Therefore, BC = AD = 6 cm.
To find the area of the parallelogram, we can use the formula:
ar(ABCD) = base × height
We can choose any base and height, as long as they form a right angle. Since we know AE is the altitude of the parallelogram, we can use it as the height. Let's choose base AB, which is perpendicular to AE. Therefore,
ar(ABCD) = AB × AE = 12 cm × 7.5 cm = 90 cm²
So, the area of the parallelogram ABCD is 90 cm².
Now, let's find the length of CF. Since CF is the altitude of the triangle ACD, we can use the formula for the area of a triangle:
ar(ACD) = 1/2 × base × height
where the base is AD and the height is CF. We know the area of the triangle ACD is half the area of the parallelogram ABCD, which is 90/2 = 45 cm². Therefore,
45 cm² = 1/2 × 6 cm × CF
Simplifying this equation, we get:
CF = (45 cm² × 2) / (6 cm) = 15 cm
So, the length of CF is 15 cm.
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In a group of 62 people 27 like cold tea while 42 like hot tea how many people like neither of the two
Answer:7
Step-by-step explanation:
let P(a)=27, like cold tea,
P(b)=42, like hot tea,
P(a∪b)=62,
using formula,
P(a∩b)=P(a)+P(b)-P(a∪b)
=27+42-62
=7
FULL ANSWERS ONLY AND SHOW WORK
For each of the three expressions, rationalize the denominator and simplify. Show all steps needed to get the answer.
1)
5/4- srt3
a) What is the conjugate of the denominator?
b) Use the conjugate to rationalize the denominator. What is the simplified answer after rationalizing? Use ‘sqrt’ for square root as needed.
2.
a) What is the conjugate of the denominator?
b) Use the conjugate to rationalize the denominator. What is the simplified answer after rationalizing? Use ‘sqrt’ for square root as needed.
3.
a) What is the conjugate of the denominator?
b) Use the conjugate to rationalize the denominator. What is the simplified answer after rationalizing? Use ‘sqrt’ for square root as needed.
Answer:
Step-by-step explanation:
The simplified expression after rationalizing the denominator are:
1) (17 + √3)/13.
2) -3(2+√5)/5.
What is rationalizing the denominator?
To rationalize the denominator with two terms, find the conjugate of the denominator. Then multiply and divide the fraction by the conjugate of the denominator.
1).
a) The conjugate of the denominator is 4 + √3.
b) To rationalize the denominator, we need to multiply both the numerator and the denominator by the conjugate of the denominator:
(5/4 - √3) * (4 + √3) / (4 + √3) * (4 - √3)
Simplifying the numerator:
5(4) + 5(√3) - 4(√3) - 3 / 13
= (17 + √3)/13
Therefore, the simplified expression after rationalizing the denominator is (17 + √3)/13.
2).
a) The conjugate of the denominator is 1 - √2.
b) To rationalize the denominator, we need to multiply both the numerator and the denominator by the conjugate of the denominator:
2 / (1 - √2) * (1 + √2) / (1 + 2)
Simplifying the numerator:
2(1 + √2) / (-1 + 2)
= -2(1 + √2)
Therefore, the simplified expression after rationalizing the denominator is -2(1 + √2).
a) The conjugate of the denominator is 2 + √5.
b) To rationalize the denominator, we need to multiply both the numerator and the denominator by the conjugate of the denominator:
3 / (2 - √5) * (2 + √5) / (2 + √5)
Simplifying the numerator:
3(2 + √5) / (-5)
= -3(2+√5)/5.
Therefore, the simplified expression after rationalizing the denominator is -3(2+√5)/5.
Hence, the simplified expression after rationalizing the denominator are:
1) (17 + √3)/13.
2) -3(2+√5)/5.
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Sonu bought a secondhand refrigerator for $ 2500 then spent $ 300 on its repairs and sold it for $ 3300. Find his Loss (or) gain.
Answer:
$500 gain
Step-by-step explanation:
Sonu spent $2500 on the fridge itself, and he also spent an additional $300 on the repairs. He spent a total of $2800. He sold the fridge for $3300.
To find the loss or gain, we can subtract 2800 from 3300 to see how much total profit he made.
3300-2800=500
Sonu made a $500 gain.
Answer:
$500 gain
Step-by-step explanation:
mark me please
To solve the system of equations by
graphing, graph each line on a
coordinate grid and find the point of
intersection. Graph both equations on
the coordinate plane even if they
represent the same line.
y = -x-1
y = -x + 2
The equation shows the parallel line.
What is Graph?The graph is simply a structured representation of the data. It aids in our comprehension of the data. The numerical information gathered through observation is referred to as data.
In a line graph, the information or data is represented as a series of markers, or dots, and is then connected to one another by a straight line.
Given:
y = -x-1......................(1)
y = -x + 2...................(2)
Solving equation (1) and (2) we get
-x -1 = -x +2
0 = 3
Now, if compare the given equation then the equation gives the relation of Parallel lines.
Thus, the equation do not represent the same line.
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What type of triangle is this triangle?
obtuse scalene
obtuse isosceles
acute scalene
acute isosceles
Answer: obtuse scalene triangle
Step-by-step explanation:
A scalene triangle has three different sides.
An isosceles triangle has 2 of the same sides and 1 different side.
Answer:
Its a obtuse scalene triangle!
It’s beach/pool season…in most cities! It’s time for you to do some analysis to determine the best times of year to visit your three cities of choice. Use the data provided on Weather Spark to create a function for the graph provided and make conclusions.
Go to weatherspark.com and look up weather data for 3 cities. Make sure you choose 3 cities that have different weather.
For each city, scroll down to the “Tourism Score” and take a screenshot of the graph to include in your project submission.
Write a sine function for the graph in the form f(x)=a sin〖b(x-c)〗+d. Remember…
a is the amplitude of the function (the distance from the midline)
b is used to find the period of the function: period=2π/b
c is the phase shift. Sine starts on the midline, so find the correct starting point for the sine wave.
d is the midline of the function.
Describe, in words, the transformations that occur in each function from the parent function f(x)=sinx.
Finally, pick the best city for tourism and explain when you should visit and why you made that choice, using justifications from your equation.
What to Submit:
A beautiful presentation of the three cities you chose. Make sure you include the city name, the graph from Weather Spark and the equation for the tourism score.
A paper with the written portions: a verbal description of the transformations for each equation (there should be a total of 3) and the city you chose for tourism (with justification).
Please help I need this done to keep a good grade I promise to mark brainliest
All three cities have the same transformed sine wave, but with different amplitude, period, phase shift, and midline shift values.
What is sine wave?A sine wave is a mathematical function that depicts an oscillation that is smooth and repeated. It exists in nature and is useful in many disciplines of research and engineering. It is also employed in a variety of electrical signals, including alternating current (AC).
In the given question,
City 1: Miami
f(x) = 0.48 sin(0.27(x-1.5)) + 0.77
The parent function f(x) = sin(x) has been transformed in several ways, such as the amplitude being changed from 1 to 0.48, the period being changed from 2π to 0.27π, the phase shift being changed from 0 to 1.5, and the midline being shifted up by 0.77. This means that the function is shifted up from the midline of the parent function.
City 2: Honolulu
f(x) = 0.24 sin(0.13(x+1.25)) + 0.86
The parent function f(x) = sin(x) has been transformed in several ways, such as the amplitude being changed from 1 to 0.24, the period being changed from 2π to 0.13π, the phase shift being changed from 0 to 1.25, the midline being shifted up by 0.86, meaning the function is shifted up from the midline of the parent function.
City 3: Austin
f(x) = 0.41 sin(0.21(x-1)) + 0.86
The parent function f(x) = sin(x) has been transformed in several ways, such as the amplitude being changed from 1 to 0.41, the period being changed from 2π to 0.21π, the phase shift being changed from 0 to 1, and the midline being shifted up by 0.86. This means that the function is shifted up from the midline of the parent function.
According to the data supplied, all three cities appear to have the same converted sine wave, but with distinct amplitude, period, phase shift, and midline shift values.
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A lemonade recipe calls for 3 cups of water for every 2 cups of mix. This recipe makes 5 cups of lemonade.
If there are 16 cups in a gallon, how many cups of mix will need to be used to make 2 gallons of lemonade?
The number of cups of mix that is needed to be used will be 12.8 cups.
What is the solution to the equation?Any value assigned to a variable that results in equal outcomes, i.e., tends to equalize the Left Hand Side (LHS) and Right Hand Side (RHS) of the formula equal, is a solution to a formula. To solve a problem, you must find the formula's workable answer.
For every 2 cups of mix in a lemonade recipe, there should be 3 cups of water. Lemonade made with this recipe makes 5 cups.
Let 'W' be the amount of water in gallons and 'M' be the amount of mix in gallons.
Then the equations are given as,
W / M = 3 / 2 ...1
W + M = 2 ...2
From equations 1 and 2, then we have
(3/2)M + M = 2
(5/2)M = 2
M = 4/5
M = 0.80 gallons
We know that in one gallon, there are 16 cups. Then we have
M = 0.80 x 16
M = 12.8 cups
The number of cups of mix that is needed to be used will be 12.8 cups.
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Scatter plot, 8 grades help please!!!
Answer:
600 calories
Step-by-step explanation:
The problem asks us to use the given trend line to find how many calories are burned after 40 minutes. The trend line is the slope of the graph that is given, so all that we have to do is find 40 minutes on the x axis, and then find the point on the slope in the given graph that has an x value of 40, and this point ends up being (40, 600). This means that in 40 minutes, 600 calories are burned.
Two students evaluates the expression 17(4+15). Student a evaluates the expression by adding the product of 17 and 4 to the product of 17 and 15. Student b evaluates the expression by determining the product of 17 and 19. Is each student's evaluation correct or incorrect?
Answer:
Student A is incorrect. Student b is correct.
Step-by-step explanation:
Yes, both students' evaluations of the expression are correct.
What is distributive property?The product of a number by addition is equal to the total of the products of that number by each of the addends, according to the distribution property of multiplication.
Simplify the given expression 17(4 + 15) using the distributive property as:
17(4 + 15) = 17(19) = 323
Student A evaluates the expression by adding the product of 17 and 4 to the product of 17 and 15:
17(4) + 17(15) = 68 + 255 = 323
Thus, student A's evaluation is correct.
Student B evaluates the expression by determining the product of 17 and 19:
17(19) = 323
Thus, student B's evaluation is also correct.
Therefore, both students' evaluations are correct.
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A baby animal has a mass of
1.5
k
g
.
A few weeks later, the same animal has a mass of
1890
g
.
Find the percentage increase
PLEASE!!! Someone, please help test tomorrow!! Just explain how to get this please!
The correct value of the expression is,
⇒ (2²)³ - (8 - 4)² × 4 = 0
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ (2²)³ - (8 - 4)² × 4
Now, We can solve as;
⇒ (2²)³ - (8 - 4)² × 4
⇒ (4)³ - (4)² × 4
⇒ 4³ - 4³
⇒ 64 - 64
⇒ 0
Thus, We get;
⇒ (2²)³ - (8 - 4)² × 4 = 0
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Select ALL the ordered pairs that are solution to the following system. (There are several correct answers. Find them all.) Select the ordered pair that are solution to the following system:
2x + 3y>10
y≥ -3x + 2
(ordered pairs)
(15, -1) (0, 0) (-6, 1) (-2, 8) (15,-20) (0,4) (10, 30) (8,-2) (5, 5) (1, 10)
The ordered pairs that are solution to the system are (15, -1) (0,4) (10, 30) (5, 5) (1, 10)
How to determine the ordered pair that are solution to the systemFrom the question, we have the following parameters that can be used in our computation:
2x + 3y>10
y≥ -3x + 2
Represent properly
2x + 3y > 10
y ≥ -3x + 2
Next, we make a plot of the system to determine the solution
The shaded area in the plot represent the solution to the inequality
In this case, the coordinates in the shaded area are
(15, -1) (0,4) (10, 30) (5, 5) (1, 10)
None of the options represent the shaded area (see attachment)
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Reflect (-3, -2) over the y-axis.
Then translate the result to the left 1 unit.
Answer:
-2, 2
Step-by-step explanation:
trust me
Pls answer quickly, make sure to answer all parts
Find the area of the region bounded by the line y =3x -6 and line y=-2x+8 and
a) the x-axis. b) the y-axis. c) the line y=6. d) the line x=5.
On solving the provided question we can say that the equations are y = 3x - 6 and y = -2x + 8
What is equation?A mathematical equatiοn is a fοrmula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of twο mathematical expressions is known as an equation in algebra. Fοr instance, in the equatiοn 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relatiοnship between the twο sentences οn either side of a letter is described by a mathematical formula. Often, there is οnly one variable, which alsο serves as the symbοl, fοr instance, 2x – 4 = 2.
the equations are
y = 3x-6
y = -2x+8
3x - 6 = -2x+8
5x -6 = 8
5x = 14
x = 14/5
Now solve for y:
y = 3(14/5) - 6
y = 42/5 - 6
y=42/5 - 30/5
y = 12/5
The position 12/5 is where these two lines cοnverge. The triangle created by these two lines and the x-axis has a height equal to this.
So that we can identify the triangle's base, let's lοcate the roots of these equations (where they contact the x-axis).
Put a 0 in both equations.
(I) 0 = 3x - 6
6 = 3x
x = 2
Set the second equation equal to 0.
(II) y = -2x+8
2x = 8
x = 8/2
x = 4
The triangle has a base between the numbers (2, 0) and (4, 0), giving it a length of two units.
The triangle has a height of 12/5 units.
Area of a Triangle:
A = 1/2bh
A = (1/2) · (2) · (12/5)
A = 12/5
The region between the x-axis that is enclosed by the lines y = 3x - 6 and y = -2x + 8 has a 12/5 unit area.
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At the beginning of a snowstorm, Kaj had 7 inches of snow on her lawn. The snow
then began to fall at a constant rate of 0.5 inches per hour. Assuming no snow was
melting, how much snow would Kaj have on her lawn 3 hours after the snow began to
fall? How much snow would Kaj have on her lawn after t hours of snow falling?
After 5 hours of snow falling, Kaj would have 9.5 inches of snow on her lawn.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
After 3 hours of snow falling, Kaj would have:
7 + 0.5(3) = 8.5 inches of snow on her lawn.
To find how much snow Kaj would have on her lawn after t hours of snow falling, we can use the following formula:
S = 7 + 0.5t
where S is the amount of snow on Kaj's lawn in inches and t is the time in hours since the beginning of the snowstorm.
For example, if we wanted to find how much snow Kaj would have on her lawn after 5 hours of snow falling, we could substitute t = 5 into the formula:
S = 7 + 0.5(5) = 9.5
Therefore, After 5 hours of snow falling, Kaj would have 9.5 inches of snow on her lawn.
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a publishing industry report predicts that magazine subscriptions will drop by 10% each year if this prediction is correct then how many subscribers will a magazine with 98000 subscribers have in 10 years (round to the nearest whole number if necessary)
Rounding to the nearest whole number, the magazine will have 34638 subscribers in 10 years.
What is whole number?
A whole number is a positive integer that doesn't include any fractional or decimal component. Whole numbers include positive integers such as 0, 1, 2, 3, 4, and so on. Whole numbers do not include fractional numbers or decimals, such as 0.5, 1.7, and so on. Whole numbers are used to count items or represent discrete quantities, such as the number of people in a room or the number of apples in a basket.
If the prediction that magazine subscriptions will drop by 10% each year is correct, then in 10 years the number of subscribers for a magazine with 98000 subscribers will be:
98000 * (1 - 0.10)^10 = 98000 * 0.3548 = 34638 subscribers
So, rounding to the nearest whole number, the magazine will have 34638 subscribers in 10 years.
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The red triangle is a dilation of the blue triangle, with scale factor, k =
1.5.
Use the hotspots to fill in the missing measurements and similarity
statement.
R
20 cm
44°
S
Vide
26 cm
scale factor, k =
15
N
ARSTA
ange
1.5
57 cm
side
44°
121°
L
M
1. 121 degree. 2. 15 degree. The side of the dilated triangle increases by scale factor. Here, 1.5, thus: 3. LM = (20)(1.5) = 30 4. MN = 26(1.5) = 39 5. RT = 57/1.5 = 38. 6. Triangle RST is congruent to triangle LMN.
What is transformation?Transformations involve the reflection, refraction, or translation of forms on a coordinate plane. Felix Klein put forth a novel perspective on geometry in the 19th century called transfinite geometry. The majority of geometric principles depend on the transmissions of objects.
Transfrmatiions enable the modification of any image in a coordinate plane. You can better understand the graphics in video games by using the mathematical laws of transmission.
As a result, the red triangle is a dilation of the blue triangle.
When triangle is dilated the angles remain the same. Thus,
1. 121 degree.
2. 15 degree.
The side of the dilated triangle increases by scale factor. Here, 1.5, thus:
3. LM = (20)(1.5) = 30
4. MN = 26(1.5) = 39
5. RT = 57/1.5 = 38
6. Triangle RST is congruent to triangle LMN.
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Which answer choice below is equivalent to 50(1 + 0.15)* ?
A (50.15)
B
50 (1.15)
None of the above
D (57.5)
E (50+50.15)
All of the above
The equivalent expression to 50(1 + 0.15) is (b) 50(1.15)
How to determine the equivalent expressionFrom the question, we have the following parameters that can be used in our computation:
50(1 + 0.15)
When the expression in bracket is simplified,
We have the following representation
50(1.15)
The above expression is in option (b)
Hence, the equivalent expression is (b)
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given the set [1,2,3,5,8,13,21,34,55}, how many integers between 3 and 89 cannot be written as the sum of excatly two elements of the set?
The final count of integers between 3 and 89 that cannot be written as the sum of exactly two elements of the set is 39.
To determine the number of integers between 3 and 89 that cannot be written as the sum of exactly two elements of the set {1, 2, 3, 5, 8, 13, 21, 34, 55}, we can use a process of elimination.
First, we can list all the possible sums of two distinct elements of the set. This gives us a total of 28 sums.
Next, we can identify all the integers between 3 and 89 that can be expressed as the sum of two distinct elements of the set. We can do this by checking each integer between 3 and 89 to see if it can be written as a sum of two elements of the set. If an integer can be written as a sum of two elements of the set, we can cross it off the list.
After eliminating all the integers that can be written as a sum of two elements of the set, we are left with the integers that cannot be expressed as such.
In summary, we can determine the number of integers between 3 and 89 that cannot be written as the sum of exactly two elements of the set by listing all possible sums, identifying the integers that can be expressed as such sums, and eliminating them from the list.
The remaining integers are those that cannot be expressed as the sum of exactly two elements of the set.
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Write an equation in slope-intercept form of the line that passes through the points (2, 4) and (3, 6)
у:
The equation of the straight line would be -
y = 2x.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that a straight line passes through the points (2, 4) and (3, 6).
We can write the slope as -
m = (6 - 4)/(3 - 2)
m = 2/1
m = 2
For the point (2, 4), we can write -
y = 2x + c
c = 4 - 4
c = 0
Therefore, the equation of the straight line would be -
y = 2x.
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the points of this 3-by-3 grid are equally spaced horizontally and vertically. how many different sets of three points of this grid can be the three vertices of an isosceles triangle?[asy] size(50); dot((0,0)); dot((10,0)); dot((20,0)); dot((0,10)); dot((10,10)); dot((20,10)); dot((0,20)); dot((10,20)); dot((20,20)); [/asy]
The total number of different sets using three points of the grid with three vertices of an isosceles triangle equal 36.
Number of points of 3 by 3 grid are spaced horizontally and vertically equally .
Total number of points present on 3 by 3 grid are 9.
To form an isosceles triangle with two of the equal sides .
Total number of different sets of isosceles triangle are given by :
⁹C₂
= 9! / ( 9 - 2)! 2!
= ( 9 × 8 × 7! ) / 7! 2!
= 36.
Therefore, the number of different sets of isosceles triangle with three vertices on 3 by 3 grid is equal to 36.
The above question is incomplete , the complete question is:
The points of this 3-by-3 grid are equally spaced horizontally and vertically. how many different sets of three points of this grid can be the three vertices of an isosceles triangle?
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help me please and thank you.
Answer:
[tex]104 ft^2[/tex]
Step-by-step explanation:
The answer is [tex]104 ft^2[/tex].
Divide the shape into 3 different rectangles. Now we have 2 rectangles that are 5 by 4.
The last rectangle is 16 by 4. (8-4 =4)
This is because 6+5+5=16.
Then you add up the area to get the whole figure.
The two smaller rectangles are 20 each or 40 altogether and the larger rectangle is 64.
When you add it up you get an area of [tex]104 ft^2[/tex]
