Answer: Since AFGH is a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. We can use this property, known as the triangle inequality theorem, to determine the angles of AFGH in order from largest to smallest.
We are given that the perimeter of AFGH is 87, so we know that:
FG + GH + FH = 87
6x + 7 + 8x - 5 + 10x - 11 = 87
24x + 1 = 87
24x = 86
x = 3.5
Now that we know that x = 3.5, we can use the given lengths of the sides to find the values of the sides:
FG = 6x + 7 = 6(3.5) + 7 = 23
GH = 8x - 5 = 8(3.5) - 5 = 25
FH = 10x - 11 = 10(3.5) - 11 = 29
We can now use these values to determine the angles of AFGH in order from largest to smallest.
We can use the triangle inequality theorem to determine that:
FH>FG+GH
29>23+25
Therefore, the angle that is opposite to side FH is the largest angle in the triangle, and the angles opposite to FG and GH are the smaller angles.
So, the angles in the triangle AFGH are ordered from largest to smallest:
The angle opposite to side FH, angle A, is the largest.
The angles opposite to side FG and GH are the smaller angles.
Step-by-step explanation:
Two car leave from the ame location but travel in the oppoite direction. The firt car travel an average of 50 mi/hr and leave 15 min before the econd car, which travel an average of 55 mi/hr. How long will each car travel before they are 200 mi apart?
The first car will travel for 38.2 hours and the second car will travel for 38 hours before they are 200 miles apart.
Let x = time in hours for the first car and y = time in hours for the second car. Since the two cars are traveling in opposite directions, we know that the rate of the cars' combined travel is the difference between their two rates. So, we can create the expression:
50x - 55y = 200
We can also create a second expression using the amount of time that passed between the two cars:
x - y = 0.25
We can solve this system of equations with substitution. Let's substitute the second equation into the first:
50x - 55(x - 0.25) = 200
Simplifying, we have:
5.25x = 200.25
Now, we can isolate x:
x = 200.25/5.25 ≈ 38.2 hours
We can use this value to find y. We know that x - y = 0.25, so we have:
y = x - 0.25 = 38.2 - 0.25 = 38 hours
Therefore, the first car will travel for 38.2 hours and the second car will travel for 38 hours before they are 200 miles apart.
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grace tiene 240 en el banco ella quiere compre tantos videojuegos de 15 como sea posible ¿Cuantos videojuego podria comprar si ¿Queria mantener al menos 120 en el banco? Ayudenme porfa
Grace can buy 8 video games of price $15 each if she wants to save $120 from $240.
Grace puede comprar 8 videojuegos si quiere ahorrar $120 de $240
What does pricing mean?Pricing is the procedure of determining the value that a manufacturer will receive in the exchange of goods and services. To make the cost of the producer's products suitable for both the manufacturer and the customer, a pricing method is used. Pricing is determined by the firm's average prices as well as the consumer's estimation of an item's value in relation to that of similar goods from rival companies.
The remainder must be $12, so
(El resto debe ser $12, entonces)
240 - 120
= $120
Number of video games she could buy with $120
(Número de videojuegos que podría comprar con $120)
⇒ 120/15
= 8
Therefore, Grace can buy 8 video games if she wants to save $120 from $240.
Por lo tanto, Grace puede comprar 8 videojuegos si quiere ahorrar $120 de $240
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Translated question:
Grace has $240 in the bank. She wants to buy as many $15 video games as possible. How many video games could she buy if she wanted to keep at least $120 in the bank? help me please
CONNECTING CONCEPTS Find the value of x such that the quadrilateral is a parallelogram. Then find the perimeter of the parallelogram. Explain.
The value of 'x' must be 4 units such that the quadrilateral is a parallelogram and the perimeter of the parallelogram is 40 square units.
What is a parallelogram?A basic quadrilateral with two sets of parallel sides is known as a parallelogram. In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size.
The area of a parallelogram is base multiples by height as two triangles form a parallelogram.
We know the opposite sides of a parallelogram are equal.
Therefore, 3x - 1 = x² - 5 and 2x + 1 = x² - 7.
x² - 5 - 3x - 1 = 0.
x² - 3x - 4 = 0, solving for x we have x = 4.
And,
2x + 1 = x² - 7.
x² - 7 - 2x - 1 = 0.
x² - 2x - 8 = 0, solving for x we have x = 4
(Negative values are inadmissible).
The perimeter of the parallelogram is 2×(the sum of the opposite sides).
= 2(3x - 1 + 2x + 1).
= 2(5x).
= 2×5×4.
= 40 square units.
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A walker notes that a monument is due North and 7.5 Km from him. He then walks on a bearing of 041. Calculate how far he is from the monument at this point to 2 decimal places.
In a case whereby walker notes that a monument is due North and 7.5 Km from him. He then walks on a bearing of 0.41 the distance from the monument at this point is 5.63km
How can the the distance be calculated?The concept that will be use is bearing. A bearing is the angle, measured in degrees clockwise from north, in mathematics. In most cases, bearings are specified as three-figure bearings. For instance, the standard notation for 30° clockwise from north is 030°.
From the diagram we can see that the interpretation gave us a triangle and from trigonometry,
Cos θ= adjacent / hypothenus
Then Cos 41 = XY/XM
Cos 41 = XY/7.5
0.75 = XY/7.5
0.75 *7.5 =5.63km
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a culture of yeast doubles in size every 20 minutes. the size of the culture is now n0. find its size in 12 hours. how do you solve these problems? sugar is put in a large quantity of water and the mixture is stirred. after 2 minutes, 50% of the sugar has dissolved. how much longer will it take until 90% of the sugar has dissolved?
How much longer will it take until 90% of the sugar has dissolved can be obtained by the equation t = -(log(1-0.9))/(log(0.5)) + 2
1. To find the size of a yeast culture after 12 hours, you can use the formula: size = n0 * 2^(t/20), where t is the time in minutes. In this case, t = 12*60 = 720, so the size of the culture after 12 hours would be n0 * 2^(720/20) = n0 * 2^36.
2. To find how long it takes for 90% of the sugar to dissolve, you can use the formula: t = -(log(1-x))/(log(0.5)), where x is the percentage of sugar dissolved and t is the time in minutes. In this case, x = 0.9 and we know that 50% of the sugar has dissolved in 2 minutes, so we can find t by plugging in the values and solving for t: t = -(log(1-0.9))/(log(0.5)) + 2.
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Drag each equation to show if it could be a correct first step to solving the equation 2(x+7)=36
Answer: x = 11
Step-by-step explanation:
2(x+7) = 36
x + 7 = 18 <-- dividing both sides by two
x = 11
There are multiple different paths you can take in order to get this answer, all equally simple. You could open up the bracket, move to one side, and then divide, however if you were to have the answer in the most efficient and least amount of steps I would suggest doing this.
Here is a rectangle with length 5 units and width 2 units.
1. What is the area of the rectangle?
2. Dilate rectangle ABCD from point A by a scale factor of 2. Calculate the area of the image.
3. Dilate rectangle ABCD from point A by a scale factor of 3. Calculate the area of the image.
This refers to the ratio between the scale of a given original object and a new object. It is its representation but of a different size (bigger or smaller). For example, if we have a rectangle of sides 2 cm and 4 cm, we can enlarge it by multiplying each side by a number, say 2.
Solving for the area and scale factor we have:
L= 5 units
W = 2 units
The area of the rectangle =L * WA = (5 x 2)
A = 10 square units.
If the rectangle is dilated from point A by a scale factor of 2, the area of the image:A= (Scale factor of L * W)* L * W
= (2 x 2 x 5 x 2)
A = 40 square units.
If the rectangle is dilated from point A by a scale factor of 3, the area of the image is:A= (Scale factor of L * W)* L * W
= (3 x 3 x 5 x 2)
A= 90 square units
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what is the remainder when 5x-3 is divided by x-4
Answer:
The answer is 4
answer mine
What are two additional questions that would be meaningful to drill down into with this same dataset, given what you've seen so far?
The two additional questions that would be meaningful to drill down into with this same dataset is that What type of variation occurs within my variables? and What type of covariation occurs between my variables?.
The term data set is defined as a collection of related sets of information that is composed of separate elements but can be manipulated as a unit by a computer.
Here we need to find the two additional questions that would be meaningful to drill down into with this same dataset,
As per the definition we have know that the question that need to be asked over the data set are listed as follows:
They are type of variation occurs within my variables and the type of covariation occurs between my variables.
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interpret the quote never confuse the size of your paycheck with the size of your talent
Note that the quote given above simply means that an employee or worker should never equate how much they earn to how much they are actually worth. This can take on different meanings depending on whether you want to assign a positive connotation to it or a negative one.
What is a quote in Literature?A quote is a verbatim reproduction of someone else's words that is generally surrounded by quotation marks and attributed to the original author or speaker.
Quoting implies paraphrasing someone else's remarks and citing the source. You must ensure the following when quoting a source:
The quoted content is surrounded by quotation marks or shown as a block quote.The original author is properly credited.The wording is exactly the same as the original.Learn more about Quotes:
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explain briefly how the statistic can be used to make inferences about the parameter to test the claim
In statistics, we use samples to make inferences about population
That is the great advantage of the whole role of distribution. Once you know a particular situation or experiment, that you can associate to one specific distribution and compute parameters, you can obtain from a relative smaller quantity of data and with good approximation, inferences about the whole population.
Statistical inference is the method of using data analysis to infer characteristics of a probability distribution.
Inferential statistics is the branch of statistics that uses sample statistics to estimate a population parameter or test a hypothesis about such a parameter.
statistics
Statistics is the science concerned with developing and studying methods for collecting, analyzing, interpreting and presenting empirical data.
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while walking in the country, you count 28 heads and 78 feet in a field of pigs and chickens. how many of each animal are there?
Answer:
There are 11 pigs and 17 chickens.
Step-by-step explanation:
Lets let
p = number of pigs
c = number of chickens
Assuming each animal has only one head, then
p + c = 28
And assuming that pigs have four feet and chickens have two feet:
pig feet = 4p
that is, 4 feet for each pig, and
chicken feet = 2c
right? two feet per chicken.
All the feet are:
4p + 2c = 78
Now we have two equations and two unknowns, so we can solve this "system of equations". You can use substitution or elimination method (or even graphing or matrices) I will run through elimination method.
Multiply p+c=28 times -2.
-2p + -2c = -56
then add the whole equation to the other equation. Do this adding vertically, from top to bottom.
-2p + -2c = -56
4p + 2c = 78
_____________
2p = 22
Divide by 2 to solve
p = 11
There are 11 pigs.
Remember,
p + c = 28
11 + c = 28
subtract 11
c = 17
There are 17 chickens.
there were x quarts of liquid in a con-tainer. first, 3 4 of the liquid in the container was removed. then another 1 2 quart was poured into the container. write an expression in terms of x for the number of quarts of liquid in the container at the end. then write another equivalent expres-sion.explain
The another equivalent expression of total liquid is (x+2)/4.
Expressions that perform similarly but differ in appearance are said to be equivalent expressions. When the same value for the variable is entered, two algebraic expressions that are equivalent will have the same result.
x quarts liquid in the container 3/4 part of liquid is removed
Then remaining liquid in container = X - [tex]\frac{3}{4}X[/tex]
Then remaining liquid in container = x/4quarts
Another 1/2 quart is poured into container
Then total liquid = [tex]X-\frac{3}{4}X+\frac{1}{2}[/tex] quarts
total liquid = [tex]\frac{X+2}{4}[/tex] quarts
So, then the another equivalent expression of total liquid is (x+2)/4.
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how much money will it cost you to drive 100.0 miles if your car gets 25.70 miles per gallon and gas costs $3.309/gallon?
It will cost $12.87 for driving 100 miles.
Based on the given problem, we have identified the given information as follows:
25.70 miles per gallon100 miles as the distance traveled by car$3.309 as the cost of gasoline per gallonThen, we identify the unknown quantity which is the total cost of gasoline, and represent this as C. Now, this can be solved by using the formula
[tex]C = \frac{distance traveled by car}{25.70 miles per gallon} * Cost of gasoline per gallon[/tex]
By substituting the given to the variable given in the formula above, we have,
[tex]C = \frac{100}{25.70} * 3.309[/tex]
C = $ 12.87
The obtained value of C is $12.87, therefore, we can conclude that it costs 12.87 dollars for driving 100 miles.
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Pre-Quiz th Percent - Item 35684 Guided Learning Practice A baseball team played 55 games this year. They won 33 games and lost 22 games. What percent of games did they lose? Po
The percentage of games they lose is 40%.
How do you calculate percentage in different ways?The most basic approach is to divide a number by the total and then multiply by 100. For example, if you have 10 out of a total of 25, you would divide 10 by 25 to get 0.4, and then multiply by 100 to get 40%.
Another way to calculate percentage is to use proportion. This involves setting up a proportion with the given numbers and the percent you want to find on one side and 100 on the other side. For example, if you have 10 out of 25 again and want to find the percent, you would set up the proportion 10/25 = x/100. Solve for x and you get 40%.
Another method is to use a percentage calculator. This is a simple tool that allows you to enter two numbers and it will automatically calculate the percentage for you.
Finally, if you need to calculate the difference between two percentages, you can subtract the smaller percentage from the larger one. For example, if you have 10 out of 25 and 15 out of 30, you would subtract 40% from 50% to get 10%.
All of these methods can help you calculate percentages quickly and easily.
Total number of games team played = 55 games
number of games they won = 33
number of games they lose = 22
The percentage of games they lose = 22/55 x 100 = 40%
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Name each angle in four ways. Then classify the angle as acute, right, obtuse, or straight
Classification of all the angles in four different ways along with name are:
1. ∠ABC, ∠CBA, ∠B, ∠1 and the name is right angle.
2. ∠DEF, ∠FED, ∠E, ∠2 and the name is obtuse angle.
3. ∠LMN, ∠NML, ∠M, ∠3 and the name is straight angle.
4. ∠XYZ, ∠ZYX, ∠Y, ∠4 and the name is acute angle.
5. ∠KLM, ∠MLK, ∠L, ∠5 and the name is acute angle.
6. ∠RST, ∠TSR, ∠S, ∠6 and the name is obtuse angle.
Figure is attached.
Classification of the all the angles in the attached figure in four different ways with their names are:
1. Different name of the angles : ∠ABC, ∠CBA, ∠B, ∠1 .
Measure of the angle is 90°, it is right angle.
2. Different name of the angles : ∠DEF, ∠FED, ∠E, ∠2
Measure of the angle is more than 90°, it is obtuse angle.
3. Different name of the angles : ∠LMN, ∠NML, ∠M, ∠3
Measure of the angle is 180°, it is straight angle.
4. Different name of the angles : ∠XYZ, ∠ZYX, ∠Y, ∠4
Measure of the angle is less than 90°, it is acute angle.
5. Different name of the angles : ∠KLM, ∠MLK, ∠L, ∠5
Measure of the angle is less than 90°, it is acute angle.
6. 2. Different name of the angles : ∠RST, ∠TSR, ∠S, ∠6
Measure of the angle is more than 90°, it is obtuse angle.
Therefore, as per the classification of the given angles different ways to represent them are:
1. ∠ABC, ∠CBA, ∠B, ∠1 , right angle.
2. ∠DEF, ∠FED, ∠E, ∠2 , obtuse angle.
3. ∠LMN, ∠NML, ∠M, ∠3 , straight angle.
4. ∠XYZ, ∠ZYX, ∠Y, ∠4, acute angle.
5. ∠KLM, ∠MLK, ∠L, ∠5 , acute angle.
6. ∠RST, ∠TSR, ∠S, ∠6 ,obtuse angle.
The above question is incomplete , the complete question is :
Name each angle in four ways. Then classify the angle as acute, right, obtuse, or straight.
Attached figure.
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question is in the picture below
Answer:
C
Step-by-step explanation:
A colony of 100 bacteria doubles in size every 60 hours what will the population be 189 hours from now
By evaluating an exponential equation, we will see that the population after 189 hours will be 888 bacteria.
What will be the population in 189 hours from now?We know that initially we have a total of 100 bacteria, and it doubles in size every 60 hours, then the population can be modeled with the exponential equation.
p(x) = 100*(2)^x
Where x is groups of 60 hours, we can rewrite:
x = t/60h
Where t is the amount of hours, and rewrite the equation as:
p(t) = 100*(2)^(t/60h)
The population in 189 hours from now willbe:
p(189 h) = 100*(2)^(198 h/60h) = 887.7
The population is 888 (where we rounded the value)
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What is the value of x? enter your answer in the box. x = cm
The value of x in the given equation will be 2/5
From the data,
We have to determine the value of x.
The given equation is: 18x-16=-12x-4
For determining the value of x, we will first shift the like terms on one side of the equation.
So, for solving the value of x we will shift the terms containing x and the constant on both sides of the equation.
So, shifting -12x from the right-hand side of the equation to the left-hand side of the equation,
We will get it as:
18x+12x = -4+16
30x=12
Now for solving the value of x we will shift x from the left side of the equation to the right side of the equation.
So, the value of x will be = 12/30 = 2/5
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The correct question may be:
What is the value of x
18x-16=-12x-4
Enter your answer in the box.
The equation P = 2(l + w) can be used to find the perimeter P of a rectangle with length l and width w. Solve the equation for w to produce a formula for finding the width of a rectangle given its perimeter and length.
The formula is w =
Answer:
[tex]w = \frac{P - 2l}{2}[/tex]
Step-by-step explanation:
In this case, we will just simplify the given formula of the perimeter and re-arrange it to get the value of w.
[tex]P = 2(l + w)\\P = 2l + 2w\\P - 2l = 2w\\\frac{P - 2l}{2} = w[/tex]
4^{x} = 2^{x-3}[/tex]
Answer:
X 3y 2
Step-by-step explanation:
Simplify 2h+3h^2−4g^4+5f^2+11g^4−4h+f^2
Answer:3h^2 + 7g^4 + 5f^2 - 4h - 4g^4
Step-by-step explanation:To simplify the expression 2h+3h^2−4g^4+5f^2+11g^4−4h+f^2, we can follow these steps:
Group together like terms:
2h + (-4h) = -2h
3h^2 + f^2 = 3h^2 + f^2
-4g^4 + 11g^4 = 7g^4
This gives us the expression: -2h + 3h^2 + 5f^2 + 7g^4
Combine the constants:
3h^2 + 5f^2 + 7g^4 = 3h^2 + f^2 + 7g^4
Combine the like terms:
-2h + 3h^2 + f^2 + 7g^4 = 3h^2 + f^2 + 7g^4 - 2h
So, the simplified expression is: 3h^2 + 7g^4 + 5f^2 - 4h
After simplifying, the expression we'll get, 2h+3h^2+7g^4+6f^2-4h.
To simplify these algebraic expressions, we need to group the like terms. Like terms can be defined as terms that contain the same variables raised to the same power. Only the numerical coefficients are different.
After grouping like terms, perform the required operations. Here we have two operations i.e addition and subtraction. So group the like terms which need to add and those which need to subtract.
For example, Here -4g^4+11g^4 are like terms and 5f^2+f^2 are like terms. So we'll subtract 4 from 11, we'll get 7 and the variable will remain the same that is g^4. Similarly, we'll add 5 and 1, we'll get 6 and the variable will remain the same that is f^2.
Other terms will remain as it is.
2h+3h^2+(-4g^4+11g^4)+(5f^2+f^2)-4h
2h+3h^2+7g^4+6f^2-4h
Therefore the answer is, 2h+3h^2+7g^4+6f^2-4h
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PLSSS HELP IF YOU TURLY KNOW THISSS
Answer:
x = 2
Step-by-step explanation:
18/9=2
9x2=18
os this scam orrr.... what?
Answer:
x=2
Step-by-step explanation:
9x=18
To solve for X we need to have just X on one side. We can do this by dividing each side by 9. Which is equal to the original because we are dividing by the same thing on both sides.
9x/9=18/9
This simplifies to x=2
We can check by putting 2 back into the equation:
9(2)=18
And that is true so we know we have a correct answer.
(6n+ 3)(6n- 4) find each product
The product of the two expressions is equal to 36n²-6n-12
What Is Distributive Property?According to this property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.
Given here: The expression (6n+ 3)(6n- 4)
Using the distributive property of multiplication we get
(6n+ 3)(6n- 4)
6n(6n-4)+3(6n-4)
Now arranging the like terms and again applying the distributive property we get
36n²-24n+18n-12
36n²-6n-12
Hence, The product of the two expressions is equal to 36n²-6n-12
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pls solve this I will give Brainly
Answer:
42
Step-by-step explanation:
(2x + 3) = 7
7x7=49
note:the other 7 is from the exponent 2
49-7=42
a 16 pound bag of kitty kibbles is . an -pound bag of feline flavor is . which statement about the unit prices is true?
If a 16 pound bag of Kitty Kibbles is $20.80 and 8-pound bag of Feline Flavor is $11.20 then the true statement about the unit price is (D) Kitty Kibbles has a lower unit price of $1.30/pound .
the cost of the 16 pound bag of Kitty Kibbles is = $20.80 ;
So , the cost of 1 pound bag of Kitty Kibbles is = $20.80/16
= $1.3 ;
the cost of 8 pound bag of Feline Flavor is = $11.20 ;
So , cost of 1 pound bag of Feline Flavor is = 11.20/8 ;
= $1.4 ;
on comparing both the unit prices , we get that the per unit cost of Kitty Kibbles is lower and the price is $1.3 ;
Therefore , the true statement is (D) Kitty Kibbles has a lower unit price of $1.30/pound .
The given question is incomplete , the complete question is
A 16-pound bag of Kitty Kibbles is $20.80. An 8-pound bag of Feline Flavor is $11.20. Which statement about the unit prices is true ?
A. Feline Flavor has a lower unit price of $1.40/pound.
B. Feline Flavor has a lower unit price of $1.30/pound.
C. Kitty Kibbles has a lower unit price of $1.40/pound.
D. Kitty Kibbles has a lower unit price of $1.30/pound.
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on a certain hot summer day 128 people used the public swimming pool. the daily prices are $1.50 for children and $2.00 for adults. the receipts for admission totaled $223.00. How many children and how many adults swam at the public pool that day?
The number of children and adults that swam in the pool that day is given as follows:
Children: 66.Adults: 62.How to obtain the number of children and adults?The variables to the system of equations are given as follows:
Variable x: number of children.Variable y: number of adults.128 people used the public swimming pool, hence:
x + y = 128.
x = 128 - y.
The receipts for admission totaled $223.00, hence:
1.5x + 2y = 223.
We have that x = 128 - y, hence the number of adults is obtained as follows:
1.5(128 - y) + 2y = 223
0.5y = 31
y = 62.
Then the number of children is obtained as follows:
x = 128 - 62
x = 66.
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A square has a diagonal that is 22 m long. What is the area of the square?
If necessary, round your answer to the nearest whole number.
NUMber 5
If you eplain how you didi it I put you as brianliest
Answer:
y=1/2x+2
Step-by-step explanation:
given the 2 equations, you know the following:
when x=2, you get a value of 3, let's call it Y
same with the next equation: when x=6, Y = 5
so the slope will be the diff b/w ys and then divided by diff of x's
so 5-3=2 is the diff of y
6-2=4 is the diff of x
divide 2/4 = 1/2 so the slope is 1/2
then you know the equation would be something like y=1/2 x but then you need to decide the intercept
1/2 of x when x=6 is 3, but Y =5
so you know the intercept is 2..
so the linear f(x) would be y=1/2x+2
done
You spend $7.50 on a pair of gloves. Now you have $8.00 how much money did u have originally
Answer:
15.50$
Step-by-step explanation:
7.5+8= 15.5