x=5 is the value of the x that is the solution of the given inequality.
Define inequality.Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
What are types of inequality.>,< and not equal to are types of inequality.
x=5 is the value of the x that is the solution of the given inequality.
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Which functions have an axis of symmetry of x = –2? Check all that apply.
f(x) = x2 + 4x + 3
f(x) = x2 – 4x – 5
f(x) = x2 + 6x + 2
f(x) = –2x2 – 8x + 1
f(x) = –2x2 + 8x – 2
The quadratic functions that have an axis of symmetry at x = -2 are given as follows:
f(x) = x² + 4x + 3.f(x) = -2x² - 8x + 1.How to obtain the axis of symmetry of a quadratic function?The standard definition of a quadratic function is given by the rule presented as follows:
y = ax² + bx + c, in which a is different of zero.
The axis of symmetry is given by the x-coordinate of the vertex, hence it's equation is defined as follows:
x = -b/2a.
Meaning that the correct options are given by the first and by the fourth options in this problem.
For the first function, we have that:
a = 1, b = 4.
Hence the axis of symmetry is obtained as follows:
x = -4/2 = -2.
For the fourth function, we have that:
a = -2, b = -8.
Hence:
x = -8/4 = -2.
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What is the product of 3p and 4p² 5p 7?
The product of 3p, 4p² and 5p 7 is 120p⁹.
What is product?Product is an item or thing that is created or produced by a business. It can refer to both physical and intangible items, such as machines, food, software, intellectual property, or services. The concept of a product is used in many different industries, including manufacturing, retail, technology, and finance. Products are typically sold in exchange for money, but can also be given away or traded. Products are an essential part of any business, as they are what generate income for a company.
This can be calculated by multiplying 3p (3 x p) with 4p² (4 x p²) and 5p 7 (5 x p x 7). The result of this multiplication is 120p⁹ (3 x 4 x 5 x p x p² x 7).
To understand this calculation better, we can break it down into its component parts.
The 3p component is 3 x p, which gives us 3p. The 4p² component is 4 x p², which gives us 4p². The 5p 7 component is 5 x p x 7, which gives us 5p 7. When these three components are multiplied together we get 3 x 4 x 5 x p x p² x 7,which is equivalent to 120p⁹.
In conclusion, the product of 3p, 4p² and 5p 7 is 120p⁹.
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You are filling up a water balloon at a rate of 30pi cm^3sec. How fast is the radius of the balloon increasing when the radius is 2cm
The fast of the radius of balloon increasing is 480 cm³ / sec.
How do you calculate speed?If you know how far something has travelled and how long it took to get there, you can calculate its average speed. Speed is calculated as follows: speed = distance * time.When figuring out test problems, the triangle might help you recall the formula more quickly. You may recall the three formulae with the aid of the triangle: Speed is calculated as Distance x Time.The result will be expressed in miles per hour (mph, mi/h), and so on for km/h, m/s, etc., if the distance was measured in miles and the duration in hours.Simple division of time by distance yields the equation for speed. To calculate speed, divide the distance travelled (say, 3 metres) by the passing time (say, three seconds) (one metre per second)Given data :
V = [tex]\frac{4}{3}[/tex] π r³
we know [tex]\frac{dr}{dt}[/tex] = 30 cm/ sec
we want [tex]\frac{dV}{dt}[/tex] when r = 2cm
Differentiate V = [tex]\frac{4}{3}[/tex] π r³ implicitly with respect to t
[tex]\frac{dV}{dt}[/tex] (V) = [tex]\frac{dr}{dt}[/tex] ( [tex]\frac{4}{3}[/tex] π r³ )
[tex]\frac{dV}{dt}[/tex] = [tex]\frac{4}{3}[/tex] π x 3r² [tex]\frac{dr}{dt}[/tex] = 4 π r² [tex]\frac{dr}{dt}[/tex]
Plug in what you know and solve for what you don't know.
[tex]\frac{dV}{dt}[/tex] = 4π ( 2 )² ( 30 / sec ) =
= 120 x 4 .π cm³ / sec
= 480 cm³ / sec
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Solve each system of inequalities. SHOW WORK.
[tex]\left \{ {{0.7x-2.1\ \textless \ 0} \atop {\frac{2}{3} x\ \textgreater \ 1}} \right.[/tex]
Answer:
Solve linear or quadratic inequalities with our free step-by-step algebra calculator. ... Example 1 Solve for x and check: x + 5 = 3. Solution.
Missing: [tex 0.7x-2.1\ \textless \atop \textgreater tex]
A=?cm
What is the total area of the tiles Felix needs to buy?
Therefore , the solution of the given problem of surface area comes out to be Felix is required to purchase 10 parallelogram-shaped tiles for an area totaling 80cm2.
Definition of surface areaIts surface area is a gauge of the space it takes up overall. A three-dimensional shape's entire environment is considered part of its surface area. Surface area is the total area of a thing. By adding up the faces on each of its six rectangle sides, a cuboid's volume of water can be calculated. The following formula could be used to calculate the dimensions of the box: Surface is the same for 2lh, 2lw, and 2hw (SA). The muti shape's surface area serves as a representation of the entire region.
Here,
Given: One parallelogram-shaped tile has a base of 4 cm and a height of 2 cm.
4 x 2 cm is the area of a single parallelogram-shaped tile.
8 cm2 is the size of one parallelogram-shaped tile.
The total area of the five black and five white tiles is 10 8cm2.
Total tile area is 80cm2 for the 5 black and 5 white tiles.
Felix is therefore required to purchase 10 parallelogram-shaped tiles for an area totaling 80cm2.
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What is the percent change from 15.5 to 70?
Answer:
First, you need to calculate your grade in percentages. The total answers count 70 - it's 100%, so we to get a 1% value, divide 70 by 100 to get 0.70. Next, calculate the percentage of 15: divide 15 by 1% value (0.70), and you get 21.43% - it's your percentage grade.
Step-by-step explanation:
help need answered today PLEASE
first answer thats correct will get brainly crown
Answer:
2/3
Step-by-step explanation:
Slope = rise / run = 2 / 3
Because points A, B, C, and D are collinear (meaning on the same line), the slope for line segment AB is the same as the slope for segment DC.
Answer:
2/3.
Step-by-step explanation:
The 2 triangles are similar so their corresponding sides are in same ratio.
The sides BA and CD are collinear so theire slopes are the same.
Slope of BA = rise/run = 2/3 so slope of DC is also 2/3.
Coconut palm trees can reach heights of up to 100 feet. Suppose you are lying on the beach at a distance of 74 feet from a 58-ft tall palm tree. What is the angle of elevation from your position to the top of the tree?
The angle of elevation of the coconut palm tree from me is [tex]38\x^{o}[/tex].
What is angle of elevation ?The angle of elevation is the angle created between the line of sight and the horizontal. The angle created is an angle of elevation if the line of sight is upward from the horizontal line.
the angle of elevation is defined as "the angle created between the horizontal line and the line of sight when an observer looks upwards." It is always higher than the observer and at a larger angle. When a person stares downward, they create an angle of depression, which is the opposite of an elevation angle. When studying heights and distances in trigonometry, it is crucial to understand the angle of elevation and depression. Angles, horizontal lines, and line of sight are the three main terms related to the angle of elevation.
Height of the palm tree is 58 ft
Distance at which I am standing from the tree is 74 ft
As per sum
[tex]tan \theta = \frac{58}{74}[/tex]
[tex]\theta = tan\x^{-1} (\frac{58}{74})[/tex]
[tex]\theta\\[/tex] = [tex]38\x^{o}[/tex]
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A commuter wants to determine the average price of gas in the area. Which is the best method of collecting a population sample so that the commuter can answer this question? Responses: A. Check gas prices at several gas stations near the commuter’s house. B. Find the gas prices over the past several years at a single particular gas station in the area. C. Look up a number of randomly selected gas stations in the area to find out gas prices. D. Survey friends on social media to see how much people are paying for gas.
The best method of collecting a population sample so that the commuter can answer this question is C. Look up a number of randomly selected gas stations in the area to find out gas prices.
What is the population?The entire group about which you want to draw conclusions is referred to as a population. The particular group from which you will gather data is known as a sample. The sample size is always smaller than the total population size.
A sample is characterized as a more manageable and compact version of a larger group. a smaller population that possesses the traits of a larger population. When the population size is too large to include all participants or observations in the test, a sample is used in statistical analysis.
This method would be the most representative of the entire population of gas stations in the area, and therefore the most likely to produce an accurate average price.
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Find the missing values in the ratio table then write the equivalent ratios in the order they appear in the table 3/4 1/3 2/3 3 1
The missing values in the ratio table are given as follows:
8 meters -> 1/3 minutes.4 meters -> 1/6 minutes.6 meters -> 1/4 minutes.10 meters -> 5/12 minutes.Hence the equivalent ratios are given as follows:
8 : (1/3).4 : (1/6).6 : (1/4).10 : (5/12).What is a proportional relationship?A proportional relationship is a linear function with an intercept of zero modeled as follows:
y = kx.
In which k is the constant of proportionality.
The input and output variables for this problem are given as follows:
Input: time.Output: meters.Hence the constant of proportionality is obtained as follows:
k = 8/(1/3) = 24.
Hence the equation is given as follows:
y = 24x.
The time for 4 meters is given as follows:
4 = 24x
x = 4/24
x = 1/6.
The distance for 1/4 minutes is given as follows:
y = 24 x 1/4
y = 6 meters.
The distance for 5/12 minutes is given as follows:
y = 24 x 5/12
y = 120/12
y = 10 meters.
The equivalent ratios for each case are given as follows:
y = y : x.
Missing InformationThe problem is given by the image presented at the end of the answer.
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The number of rats living in an abandoned building increases each year. The total number of rats can be described by this sequence: 2, 6, 18, 54, 162, ...
What is the explicit formula?
What is the recursive formula?
Please help with the recursive formula the most if you can!
Answer: The explicit formula for this sequence is given by the expression a_n = 3^n, where n is the position in the sequence (starting from n=1 for the first term).
The recursive formula for this sequence is given by the expression a_n = 3a_(n-1), where n is the position in the sequence (starting from n=1 for the first term) and a_(n-1) is the previous term in the sequence.
Here's how you can use the recursive formula to find the terms of the sequence:
a_1 = 2
a_2 = 3a_1 = 3 * 2 = 6
a_3 = 3a_2 = 3 * 6 = 18
a_4 = 3a_3 = 3 * 18 = 54
a_5 = 3a_4 = 3 * 54 = 162
and so on.
To find the explicit formula, you can try to find a pattern in the terms of the sequence. For example, you might notice that each term is simply the previous term multiplied by 3. This pattern can be expressed using the recursive formula a_n = 3a_(n-1). To find the explicit formula, you can then solve for a_n in terms of n:
a_n = 3a_(n-1)
a_n / 3 = a_(n-1)
a_n / 3 = (3a_(n-2)) / 3
a_n / 3 = 3^(n-2)
a_n = 3^n
Therefore, the explicit formula for this sequence is a_n = 3^n.
Step-by-step explanation:
Use logarithmic table to evaluate 40.79÷0.003949
Answer:
1.033×10⁴
Step-by-step explanation:
You want the quotient 40.79÷0.003949 using log tables.
Log of quotientThe log of a quotient is the difference of logs:
log(a/b) = log(a) -log(b)
Log valuesIt can work well to start by writing the numbers in scientific notation:
log(40.79) = log(4.079×10¹) = 1 +log(4.079) = 1.6106
log(0.003949) = log(3.949×10⁻³) = -3 +log(3.949) = -3 +0.5965
Log of quotientThen the log of the quotient is ...
log(40.79/0.003949) = 1.6106 -(-3 +0.5965) = 4.0141
AntilogThe antilog of this number will be ...
antilog(4.0141) = 10⁴ × antilog(0.0141) ≈ 1.033×10⁴
With our 4-digit log tables, 4 significant figures is the best we can expect.
The quotient is about 1.033×10⁴.
__
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The spinner is spun 75 times. What is the experimental probability of spinning the given result? Round your answer to the nearest hundredth if necessary. Outcome A B C D Frequency 20 11 14 30 B or C
The experimental probability of spinning of B or C is 1/3.
In the given question, the spinner is spun 75 times.
We have to find the experimental probability of spinning of B or C.
The given data is:
Outcome A B C D
Frequency 20 11 14 30
Total frequency = 20 + 11 + 14 + 30
Total frequency = 75
The probability of spinning B = Frequency of B/Total Frequency
The probability of spinning B = 11/75
The probability of spinning C = Frequency of C/Total Frequency
The probability of spinning C = 14/75
Now the experimental probability of spinning of B or C;
P(B or C) = P(B) + P(C)
P(B or C) = 11/75 + 14/75
P(B or C) = (11 + 14)/75
P(B or C) = 25/75
P(B or C) = 1/3
Hence, the experimental probability of spinning of B or C is 1/3.
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[Please help me on this- I will give you brainlist!!]
Write the terms in standard form. Then state the degree of the polynomial and the leading coefficient (LC).
For the polynomial 9, 3x², 8x; the degree is 2 and the leading coefficient is 3
What is an equation?An equation is used to show the relationship between numbers and variables.
Polynomial is an expression composed of variables, constants and exponents using mathematical operations such as addition, subtraction, multiplication and division
The degree is the highest exponent of variable for the polynomial. The polynomial with degree of 2 is known as a quadratic polynomial
Given the polynomial:
9, 3x², 8x
Writing in standard form is done by rearranging from highest exponent of variable to least. This is:
3x², 8x, 9
Hence the degree is 2 and the leading coefficient is 3
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aleris is sending a fancy organic fruit basket to her grandma for her birthday. apples cost $3 and oranges cost $2. Aleris can spend no more than $24 on the gift. write an inequality that describes the situation
The inequality when apples cost $3 and oranges cost $2 and Aleris can spend no more than $24 on the gift is 3a + 2o ≤ 24.
How to illustrate the inequality?Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.
In this case, Aleris is sending a fancy organic fruit basket to her grandma for her birthday. apples cost $3 and oranges cost $2 and Aleris can spend no more than $24 on the gift.
Let apple = a
Let orange = o
Therefore, the inequality will be:
3a + 2o ≤ 24.
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Caculate the total amount from a simple interest account
Principal $300
interest rate 7%
Time 2
Answer:
$42.00
Step-by-step explanation:
Interest = principle x rate x time
Interest = 300 x .07 x 2
Interest = 42
1. The accuracy of a pool thermometer is the positive difference between the temperature
reading on the thermometer t and the actual temperature of the pool p. Write two absolute
value expressions equivalent to the accuracy of a pool thermometer.
The two absolute value expressions equivalent to the accuracy of a pool thermometer are |t - p| and |p - t|
How to write absolute value expressions for the accuracy of the thermometer?Absolute value means to remove any negative sign in front of a number and to think of the number as positive. This is indicated by the vertical lines | |
Any expression that contain the vertical lines is called absolute
value expression
Since the accuracy of a pool thermometer is the positive difference between the temperature reading on the thermometer t and the actual temperature of the pool p.
We can write:
accuracy = | t - p|
OR
accuracy = | p - t|
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Answer:
It-pI
Step-by-step explanation:
A painting, square in shape, is placed in a wooden frame with width of 10% of the length of the side of the paining. The painting was enlarged by 10%. By what percent is the new frame bigger than the original frame if the width of the frame remains the same?
PLEASE HELP
The percent that the new frame is bigger than the original frame if the width of the frame remains the same is 9.1%.
How to illustrate the percentage?From the information, the painting, square in shape, is placed in a wooden frame with width of 10% of the length of the side of the paining. The painting was enlarged by 10%.
Let the length be Illustrated as 10cm.
Width = 10% × 10cm
= 1cm
New Length = 10cm + (10% × 10cm)
= 11cm
The old perimeter will be:
= 2(1 + 10)
= 22cm
New perimeter will be:
= 2(1 + 11)
= 24cm
The percentage increase will be:
= (24 - 22) / 22 × 100
= 2/22 × 100
= 9.1%
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Sara had 222 dollars to spend on 9 books after buying then she had 15 dollars how much did each book cost
Answer:
each book cost=222-15=207/9=22.88 dollar
Chelsea wants to determine the number of people in her school who read news reports on the Internet daily. She asks five people in her language arts class. Which improvements could Chelsea make to her sample to increase the validity of the results
The three choices are increase the sample size, pick individuals from various grade levels and in all language arts classes, pick the fourth student.
what is sample size?
The number of observations utilized to calculate estimates for a given population is referred to as the sample size. From the population, a sample size was chosen. The term "sample size" describes the number of subjects or observations that make up a study. n is typically used to represent this number.
The three choices are increase the size of the sample, pick individuals from various grade levels and in all language arts classes, pick the fourth student.
It's important to take into account the following data:
The sample size should be raised in order to boost the result validity, The students should be chosen from among the various grade levels and For all language kinds, a student should be chosen every fourth student.
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kiran wants to make a larger scale drawing of the same classroom which of these aclales could he use
htx
Kiran would choose scale of 1 to 50.
What is Scale Factor?To adjust the size of a figure without altering its shape, a scale factor is a number or conversion factor that is utilised. It is employed to change the size of an object. If the original figure's dimensions and the dilated (increased or lowered) figure's dimensions are known, the scale factor can be determined.
Given:
As, The scale “1 inch to 6 feet” is equivalent to the scale “1 to 72,” because there are 72 inches in 6 feet.
The scale “1 to 100” would make a scale drawing that is smaller than the scale “1 to 72,” because each inch on the new drawing would represent more actual length.
The scale “1 to 50” would make a scale drawing that is larger than the scale “1 to 72,” because Kiran would need more inches on the drawing to represent the same actual length.
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The options are as follow:
1 to 50
1 to 72
1 to 100
The sum of ages of a woman and her daughter is 46 years. In 4 years time, the ratio of their ages will be 7:2. Find their present ages?
Step-by-step explanation:
Given ,The sum of the ages of a woman and her daughter is 46 years.In 4 years time,the ratio of their ages will be 7:2.To Find : Their present ages
Solution :Consider,
Present age of woman = x yearsPresent age of Daughter = y yearsAccording to the 1st condition :-The sum of the ages of a woman and her daughter is 46 years.[tex]x + y = 46\\x = 46 -y[/tex]
According to the 2nd condition :-In 4 years time,the ratio of their ages will be 7:2.After 4 years,Age of woman = (x+4) yearsAge of daughter = (y+4) years→ (x+4) : (y +4) = 7:2
→ x+4/y+4 = 7/2
→ 46-y+4/y+4 = 7/2
→ 50-y/y+4 = 7/2
→7y +28 = 100-2y
→ 7y +2y = 100 -28
→ 9y = 72
→ y = 8
Present age of Daughter = 8 yearsNow put y = 8 in eq(1) .
→ x = 46 - y
→ x = 46 - 8
→ x = 38
Present age of woman = 38 years.Mark Me Brainliest
A company is loading recliners and sofas onto a trailer that has a volume of about 3800 cubic feet. Each recliner takes up about 40 cubic feet and each sofa takes up about 80 cubic feet. The company wants the shipment to have at least 30 recliners and more than 25 sofas. Identify and interpret the ordered pair in the solution region.
The ordered pair that would be needed by the company for shipment can be loaded in the trailer as the pair will take only 3200ft³ of the volume of the trailer which is 3800 cubic feet.
How to calculate the ordered pair for shipment?The total volume of the trailer = 3800 cubic feet
The volume of each recliner = 40 cubic feet
The volume of each sofa = 80 cubic feet
The number of recliner needed = 30
The number of sofas needed = 25
The volume that the sofa will cover = 25 × 80 = 2000
The volume that the recliner will cover= 30 × 40 = 1200
Therefore the total volume both will take = 3200 cubic feet.
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find the output, g, when the input, r is 3
g= -5 + 13
The output of function g(r) = -5x + 13 when r is 3 is -2.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
g(r) = -5r + 13
Input r = 3
g(3)
= -5 x 3 + 13
= -15 + 13
= - 2
Thus,
The output is -2.
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In the figure, mzEDF = 42°. Which other angle must have the same measure?
OA. ZGDF
B. ZEGF
OC. ZDEG
D.
LEGD
D
42°
C
E
IL
In the quadrilateral, ∠GEF will be same as angle ∠EDF=42°°
A quadrilateral shape is what?A polygon with four sides, four angles, and four vertices is called a quadrilateral. The Latin words quadri, which means four, and latus, which means side, were combined to create the English word quadrilateral. A quadrilateral is shown in the above image as an example.
A parallelogram is a trapezoid, right?A parallelogram has two pairs of parallel sides, whereas a trapezoid only has one pair. Consequently, a parallelogram is a trapezoid.
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Answer:
EGF
Step-by-step explanation:
Got it right on plato.
L)
express the given in terms os sin x or cos x
sin ( 4pi - x )
how
The value of sin(4π-x) is -sinx
What are trigonometric functions?The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
Given that, express the given in terms of sinx or cosx sin (4π-x)
sin(4π-x) = sin(2π+2π-x)
We know, that, sin(a+b) = sina·cosb+sinb·cosa
Here, a = 2π and b = 2π-x
Therefore,
sin(2π+2π-x) = sin2πcos(2π-x)+sin(2π-x)cos2π
Now, sin2π = 0 and cos(2π) = 1
Therefore,
sin2πcos(2π-x)+sin(2π-x)cos2π
= sin(2π-x)
As we know that, sin(2π-x) = -sinx
Hence, sin(4π-x) = -sinx
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After getting new carpet installed, Antonio noticed that the door would not close. He decided to trim 1/16 of an inch off the bottom of the door to see if it would help. After doing this three more times, the door finally closed. If the door was originally 84 5/8 inches tall, how tall was it after he trimmed it?
After he trimmed it, it was [tex]84\frac{3}{8}[/tex] inches tall. This can be solved using expression.
What is an expression?A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. Any one of the following mathematical operations can be used i.e. addition, subtraction, multiplication, or division.
There are three different expression types:
There is just one arithmetic value that an arithmetic expression may produce.A character expression evaluates to just one character value.One logical value is produced by the evaluation of a logical or relational statement.The expression becomes:
= [tex]84\frac{5}{8} - [{4 * (\frac{1}{16})][/tex]
= [tex]84\frac{5}{8} - [\frac{1}{4}][/tex]
= [tex]84\frac{3}{8}[/tex]
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BUILD PERSEVERANCEA
a. What is the x-coordinate of the centroid of A ABC?
0
x +
ABC has vertices A(-3, 3), B(2, 5), and C(4, -3).
(3)
The x-coordinate of the centroid of the triangle ABC with vertices
A(-3, 3), B(2, 5), and C(4, -3) is 1.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
The centroid of a triangle is the common intersection point of all the medians of the triangle.
When vertices of a triangle is given the co-ordinate of the centroid are
(x₁ + x₂ + x₃)/3 and (y₁ + y₂ + y₃)/3.
Given, ΔABC has vertices A(-3, 3), B(2, 5), and C(4, -3).
Therefore, The x-coordinate of the centroid is,
Gₓ = (- 3 + 2 + 4)/3.
Gₓ = 3/3.
Gₓ = 1.
So, The x-coordinate of the centroid is 1.
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The town librarian bought a combination of new-release movies on DVD for $20 and classic movies on DVD for $8. Let
x represent the number of new releases, and let y represent the number of classics. If the librarian had a budget of
$500 and wanteho purchase as many DVDs as possible, which values of x and y could represent the number of new
release and classie movies bought?
O x= 8, y = 45
O x= 10, y = 22
O x = 16. Y = 22
Ox= 18, y=18
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The Correct answer is option (C) x = 16. Y = 22 . number of new-release movies on DVD is 16 and the number of classic movies on DVD is 22 .
What is linear equation?An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.
Given,
To find the values of X and Y,
Let x = number of new releases
Let y = number of classics.
The equation to solve the question is ,
20x + 8y = 500
When x= 16 and y = 22
= 20x + 8y
= 20(16) + 8(22)
= 320 + 176
= 496
Therefore, the number of new-release movies on DVD is 16 and the number of classic movies on DVD is x= 16, y = 22
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Why is the longest side of a triangle always opposite the largest angle?
The longest side of a triangle is always opposite to the largest angle because the endpoints of the lines on either side are going to be further apart if the angle is wider .
What is Triangle ?
The triangle can defined as a three-sided polygon that consists of three edges and three vertices.
Let the angle opens up to its opposite side.
So , the larger the angle, the wider will be it's opening. which means that the endpoints of lines on either side of the angle are going to be further apart if angle is wider.
If the endpoints are further apart, then the line connecting them, which makes up the side opposite will be going to be more longer.
So , the longest side will always be opposite to the largest angle
Similarly , the smallest angle will result in shortest side opposite side for the same reasons.
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