Step 1: Calculate the initial number of hospitals. In 2000, there were 5,727 hospitals, so the initial number of hospitals (H0) is 5,727.
Step 2: Calculate the rate of change. From 2014 to 2017, the number of hospitals decreased by 156. Therefore, the rate of change (r) is -156.
Step 3: Calculate the equation. The equation for the number of hospitals H in this country t years since 2000 is H = H0 + rt. Substituting in the values from Steps 1 and 2, this gives us H = 5,727 – 156t.
Therefore, the equation for the number of hospitals H in this country t years since 2000 is H = 5,727 – 156t.
First order equations include linear equations. In the coordinate system, the linear equations are defined for lines. A linear equation in one variable is one in which there is a homogeneous variable of degree 1 (i.e., only one variable). More than one variable may be present in a linear equation.
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Pls help me i need help
all the work in is the picture. lmk if anything is unclear, I'm happy to help
PLS HELP 100 points
A photographic negative is 5.4 cm by 1.35 cm. If you are going to enlarge the image on a 10.2 in by 2.4 in piece of photo paper, what is the largest length and width you can use to keep the photo in proportion to its negative?
Answer:
Step-by-step explanation:
To keep the photo in proportion to its negative, you need to maintain the same aspect ratio, which is the ratio of the width to the height of the image. The aspect ratio of the negative is 5.4 cm / 1.35 cm = 4. To maintain this aspect ratio, the aspect ratio of the enlargement must also be 4.
The aspect ratio of the photo paper is 10.2 in / 2.4 in = 4.25. So, the largest length and width that you can use to keep the photo in proportion to its negative is 2.4 in * 4 = 9.6 in and 9.6 in / 4 = 2.4 in, respectively.
Answer:
Length = 9.6 inWidth = 2.4 inStep-by-step explanation:
Conversion
1 inch ≈ 2.54 cmFirst convert the dimensions of the photo paper to centimeters:
[tex]\implies \sf 10.2\;in=10.2 \times 2.54=25.908\;cm[/tex]
[tex]\implies \sf 2.4\;in=2.4 \times 2.54=6.096\;cm[/tex]
Therefore, the dimensions of the photo paper in centimeters are:
25.908 × 6.096 cm (nearest thousandth)To determine the dimensions of the photo if the image is enlarged to fit on a 25.908 × 6.096 cm piece of photo paper, first calculate the scale factor by dividing the shortest side of the photo paper by the shortest side of the negative:
[tex]\sf Scale\;factor=\dfrac{6.096}{1.35}=4.51555...[/tex]
Multiply this scale factor by the longest side of the negative to determine the proportional length of the photo:
[tex]\implies \sf 4.51555...\times 5.4=24.384\;cm[/tex]
As 24.384 cm is less than the longest side of the photo paper, this scale factor will work to keep the photo in proportion to its negative.
Therefore, the largest length and width you can use to keep the photo in proportion to its negative is:
24.384 × 6.096 cm9.6 × 2.4 inSarah invests £9600 at a simple interest rate of 8% per year.
Work out the value of investment after 3 years.
Pls help or else am dead
The equation of a line is 3y + x - 15 = 0.
What is the equation of a line?
The set of points that make up a line in a coordinate system is represented algebraically by a line's equation. An equation of a line is an algebraic expression that represents the many points that together make up a line in the coordinate axis as a set of variables, x, and y. We may determine whether a given point lies on a line using the equation of any line.
Here, we have
Given: A(0,0), B(1,3)
The slope of AB = (3-0)/(1-0) = 3
The slope of a line perpendicular to AB = -1/3
y-intercept is 5
Equation of a line:
y - 5 = (-1/3)(x-0)
3y - 15 = -x
3y + x - 15 = 0
Hence, the equation of a line is 3y + x - 15 = 0.
Question: Given A(0,0) and B(1,3), find the equation of the line perpendicular to the y-intercept of 5
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URGENT!! WILL MARK BRAINLIEST!!!
The area of the parallelogram BEFD will be 100 square units.
What is the parallelogram area theorem?The area of parallelograms with the same base and corresponding parallels is the same. A parallelogram's area is the same as the area of a rectangle with the same base and height, or between the same parallels.
Given that the sides AB = 15, AD = 15 and the area of the quadrilateral ABCD is 100 square units.
From the theorem, the area of the parallelogram ABCD is equal to the area of the parallelogram BEDF.
Area of quadrilateral BEDF = 100 square units
Therefore, the area of the parallelogram BEFD will be 100 square units.
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I NEED HELP AGAINNNNN
1) Are the triangles ABC and PQR in the diagram congruent? GIVE REASONS for your answer.
2) In a piggy bank, there are x numbers of one dollar bills and 2x number of 50 dollar bills. Find the total amount of money in the piggy bank, in terms of x.
Answer:
no they are not equal just look at the picture carefully and you will realise it's not equal
justify your reasons by determining the postulates, definitions, theorems, and properties used.
The angle 1 and angle 2 are congruent by alternate interior angles.
What is the angle sum property of triangle?The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.
1. Angle1 and angle2 are complementary. angle2 and angle 3 are complementary.
= sum of these angles is 180 degree because they are linear angles
2. m angle1+ m angle2 = 90° m/2+m/3 = 90°
=There sum makes right angle
3. m angle1+ m angle2 = m angle2 + m angle3
= sum of both the sides is 180 degree
4. m angle2 = m angle2
= sum of both the sides is equal
5. m angle1= m angle3
= sum of both the sides is equal
6. angle1 congruent angle3
=They are alternate interior angles.
Therefore, by the triangles properties angle 1 and angle 3 are congruent.
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Shannon dreams of becoming the national spelling bee champion. She can already spell a lot of the words on her study list, but she needs to learn even more. This table shows the relationship between the time (in hours) that Shannon spends studying, x, and the total number of words on the study list that she can spell, y. x (hours) y (words) 1.1 93 1.3 95 1.6 98 1.8 100 According to the values in the table, do x and y have a proportional relationship? yes no
According to the values in the table, no, x and y does not have a proportional relationship. Therefore, the correct answer option is: B. no.
What is a proportional relationship?In Mathematics, a proportional relationship is a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:
y = kx
Where:
x represent the time (in hours).k is the constant of proportionality.y represent the total number of words.Next, we would determine the constant of proportionality (k) for the relationship between the x-values and y-values in this table as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 93/1.1 ≠ 95/1.3 ≠ 98/1.6 ≠ 100/1.8
Since the constant of proportionality (k) for the relationship between the x-values and y-values are different, we can logically deduce that this is not a proportional relationship.
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a certain group of women have a .92% rate of red/green colorblindness. if a woman is randomly selected, what is the probability that she dies not have red/green colorblindness?
The probability that a randomly selected woman does not have red/green colorblindness is 99.08%.
The probability that a randomly selected woman does not have red/green colorblindness is calculated by subtracting the given rate of red/green colorblindness from 100%. The formula for this probability is P(not colorblind) = 100% - .92% = 99.08%. The calculation is 100% - .92% = 99.08%. Therefore, the probability that a randomly selected woman does not have red/green colorblindness is 99.08.
Therefore, The probability that a randomly selected woman does not have red/green colorblindness is 99.08%. This was calculated using the formula P(not colorblind) = 100% - .92%.
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the adjoining figure shows a racing track consisting of two parallel stretches which is 119 M long and 10 metre wide its other two end are semicircular the inner distance between the two parallel Streches is 70 m evaluate and also find the distance around the track along its outer edge and the area of the track
The distance around the track along its outer edge is 740.4 meters and the area of the track is 2514 meter square.
A racing track consisting of two parallel stretches which are of 119 meters long and 10 meters wide.
The other two ends are semicircular the inner distance between the two parallel stretches is 70 m.
Radius of Exterior = ( 70 + 10 ) m = 80 m
The circumference formula is given by:
Circumference = 2πr
= 2 (3.14) (80)
= 2 (251.20)
= 502.4
Now we have to calculate the distance around the track
The Distance Around the Track = Circumference + 2 (Length)
= 502.4 + 2 (119)
= 502.4 + 238
= 740.4 meters
The Area of track = The Area of the outer circle - The Area of the inner circle
= π × R square - π × r square
= 6364 - 3850
= 2514 meter square
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The histogram below shows information about the ages of the paintings in a gallery. 12 of the paintings in the gallery are over 90 years old. Work out an estimate for the number of the paintings that are over 70 years old.
The estimate for the number of the paintings that are over 70 years old is given as follows:
56.
How to obtain the estimate?The histogram shows the number of observations that appear in each range of the data-set.
12 of the paintings in the gallery are over 90 years old, hence the height of each small square is of:
12/(3 x 2) = 2 units.
Then the estimate of those over 70 years old is given as follows:
22 between 70 and 80.22 between 80 and 90.12 over 90.Hence the sum is given as follows:
22 + 22 + 12 = 56.
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G
E
C
D
28. Find x and y if CG=x+2y, EG=4, FG = 3x-y, and
DG=5.
Given the above values relative to the parallelogram, x = 2 and y = 1
What is a parallelogram?A parallelogram is a basic quadrilateral with two pairs of parallel sides in Euclidean geometry. A parallelogram's opposing or facing sides are of equal length, and its opposite angles are of equal measure.
Since the a parallelogram's diagonals are not all the same length, and they connect at the point of junction and have equal sides across the intersection, we can state that:
a
CG = EG and
FG = DG
Thus,
x+2y = 4; .........(1) and
3x-y = 5............(2)
Solving by substitution:
Let's make x the subject of the formula in (1)
x + 2y + (-2y) = 4 + (-2y)
x = -2y + 4 .......................................(3)
Substitute (3) into (2)
Where (2) is 3x-y = 5, thus;
3 (-2y + 4 )-y = 5.
-7y + 12 = 5
-7y + 12 -12 = 5 + -12
-7y = -1 (Divide both sides by -7)
y = 1 .............................(4)
Since y = 1, let's impute this in (1) x+2y = 4
x+2 (1) = 4
x = 4 -2
x = 2
Thus, x = 2, and y = 1
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Full Question;
Quadrilateral DEFC is parallelogram. Find x and y if CG = x + 2y, EG = 4, FG =3x-y, and DG = 5. Show your solution.
See attached image.
Which expression to represents the phrase: "6 times a number plus 3."
6 x 3
6 x 3 + n
6n + 3
6n = 3
how many cubic feet of sand would you need to fill a space that 20 feet wide, 40 feet long, and a 6 inches thick?
The amount of sand needed, we will multiply 400 cubic feet by 1.5, which will give us 600 cubic feet of sand needed to fill the space.
The formula for finding the volume of a space is length x width x height. To find the cubic feet of sand needed to fill the space, we will need to calculate the volume of the space in cubic feet and then multiply it by the amount of sand needed to fill the space. To calculate the volume of the space, we will first convert the 6 inches to feet by dividing it by 12, which will give us 0.5 feet. We can then plug the numbers into the volume formula, which will look like this: 20 feet x 40 feet x 0.5 feet = 400 cubic feet. To find the amount of sand needed to fill the space, we will multiply the volume of the space by the amount of sand needed (which is usually 1.5 to 2 cubic feet per square foot). For this example, we will use 1.5 cubic feet. So to find the amount of sand needed, we will multiply 400 cubic feet by 1.5, which will give us 600 cubic feet of sand needed to fill the space.
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what is 3/50+7/10 for adding and subtracting fractions
Answer:
37/50
Step-by-step explanation:
Step 1) Multiply 7/10 by 5/5 to get 35/50
Step 2) Add 3/50 and 35/50
Step 3) 3/50+ 35/50= 37/50
Write 3 situations where you would use the number -5
In many ways we can use the number -5.
-5 degrees Celsius or -5 degrees Fahrenheit can be used to represent temperatures below freezing. For example, if the outside temperature is -5 degrees Celsius, water will freeze.
Backward Counting: In mathematics, -5 can be used to count backwards from zero. For example, if we subtract 5 from 0, we get -5. This is frequently used when counting down from a starting number, such as in a countdown timer.
Credit Balance: A negative balance or debt owed in a financial account, such as a credit card or loan, can be represented by -5 in accounting. For example, if someone has a -5 dollar credit card balance, it means they owe the credit card company $5. it means they owe the credit card company $5 and have a negative balance on their account.
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WILL GIVE brainliest
Answer:-4/7y+4/7x
Step-by-step explanation:
A gardener will use up to 250 square feet for planting flowers and vegetables. She wants the area used for vegetables to be at least twice the area used for flowers. Let x denote the area (in square feet) used for flowers. Let y denote the area (in square feet) used for vegetables. Shade the region corresponding to all values of x and y that satisfy these requirements.
Answer:
Step-by-step explanation:
We can start by setting up the following system of inequalities to represent the requirements given in the problem:
x + y ≤ 250 (the total area used should not exceed 250 square feet)
y ≥ 2x (the area used for vegetables should be at least twice the area used for flowers)
To graph these inequalities, we can first graph the boundary lines for each inequality:
x + y = 250 (the boundary line for the first inequality, with points (250, 0) and (0, 250))
y = 2x (the boundary line for the second inequality, with points (0, 0) and (125, 250))
Then, we can shade the region that satisfies both inequalities, which is the region below the line x + y = 250 and to the right of the line y = 2x:
|
250-|__________________________
| / |
| / |
| / |
| / |
| / |
| / |
| / |
| / |
| / |
| / |
|/________________________|
0 125 250
The shaded region represents all values of x and y that satisfy the requirements given in the problem, where x is the area used for flowers and y is the area used for vegetables. The x and y values in this region can vary, as long as the total area used is less than or equal to 250 square feet and the area used for vegetables is at least twice the area used for flowers.
Answer:
To plot the region that satisfies the requirements, we can start by setting up the inequalities:
y ≥ 2x (the area used for vegetables is at least twice the area used for flowers)
x + y ≤ 250 (the total area used for planting is at most 250 square feet)
We can plot these inequalities on a coordinate plane to find the shaded region:
First, plot the line y = 2x (Load failedboundary line for the first inequality). This line passes through the origin and has a slope of 2, so we can plot additional points using this information. For example, when x = 50, y = 100 (since 100 is twice 50).
So, the shaded region on the coordinate plane corresponds to all values of x and y that satisfy the given requirements.
a)
3e - 2/4+30-4e/3=6
What does e =?
If the equation be 3e-2/4+30-4e/3=6 then the value of e be -14.1.
What is meant by expressions?A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression in mathematics.
A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. It is possible to multiply, divide, add, or subtract in math. In mathematics, a numerical expression is a mixture of numbers and integers combined using addition, subtraction, multiplication, or division.
Let the given equation be [tex]$3 e-\frac{2}{4}+30-4 \cdot \frac{e}{3}=6$$[/tex]
Subtract [tex]$-\frac{2}{4}+30$[/tex] from both sides
[tex]$3 e-\frac{2}{4}+30-4 \cdot \frac{e}{3}-\left(-\frac{2}{4}+30\right)=6-\left(-\frac{2}{4}+30\right)$$[/tex]
Simplifying the above equation, we get
[tex]$3 e-4 \cdot \frac{e}{3}=-\frac{47}{2}$$[/tex]
Expand [tex]$3 e-4 \cdot \frac{e}{3}= \frac{5 e}{3}$[/tex]
[tex]$\frac{5 e}{3}=-\frac{47}{2}$$[/tex]
Multiply both sides by 3, then
[tex]$\frac{5 e}{3} \cdot 3=-\frac{47}{2} \cdot 3$$[/tex]
Simplifying the above equation, we get
[tex]$5 e=-\frac{141}{2}$$[/tex]
Divide both sides by 5
[tex]$\frac{5 e}{5}=\frac{-\frac{141}{2}}{5}$$[/tex]
Simplifying the above equation, we get
[tex]$e=-\frac{141}{10}$$[/tex]
e = -14.1
Therefore, the value of e be -14.1.
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Which expression(s) are equivalent to 3x + 5y - x + 2 - 5. Choose all equivalent answers.
Question 3 options:
2x + 5y - 3
3x + 5y -3x
Which expression(s) are equivalent to 3x + 5y - x + 2 - 5. Choose all equivalent answers.
The equivalent answer for the expression mentioned in question is 2x + 5y - 3.
Firstly we will solve the mentioned equation followed by checking each answer. Now, rewriting the equation provided in question -
3x + 5y - x + 2 - 5
Solving the values with x variable and without any variable. For this, we will perform subtraction of. the two pairs.
2x + 5y - 3
Now we see that second option is same as the solved part of the first answer. The first option has 3x and - 3x, which will eventually yield 0, further leaving the equation only with y variable. Therefore, it is the correct answer.
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what is wrong with the following statement: boolean y = 12.5;
Answer:
we can not assign a floating-point number to a boolean variable
Step-by-step explanation:
The statement "boolean y = 12.5;" is incorrect or "wrong" because it is attempting to assign a floating-point value (12.5) to a boolean data type, which is a type of data that can only represent two values: true or false.
A boolean data type is a fundamental data type in programming and is commonly used in logic and decision-making structures. It is used to represent conditions that are either true or false, and can be used to control program flow, make decisions, and perform logical operations.
In the statement "boolean y = 12.5;", the value 12.5 is a floating-point value, which is a type of data that represents a decimal number with a fractional component. However, a boolean data type is not capable of representing such values, and can only represent two states: true or false.
In programming, attempting to assign a value of the wrong data type to a variable is known as a "type error" or a "type mismatch." Type errors can cause programs to fail, produce unexpected results, or behave in unintended ways.
To fix the statement "boolean y = 12.5;", the data type of the variable "y" should be changed to a data type that can represent decimal values, such as a floating-point data type like "double" or "float." Alternatively, if the intent of the statement was to assign a boolean value to the variable, the value of 12.5 should be replaced with a boolean expression that evaluates to either true or false.
In summary, the statement "boolean y = 12.5;" is incorrect or "wrong" because it attempts to assign a floating-point value to a boolean data type, which is not a valid data type for the value being assigned. Type errors like this can cause programs to fail, produce unexpected results, or behave in unintended ways, and must be corrected to ensure proper program operation.
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X
y
a) Complete the table of values for
y=x²- 2x + 5
1
2
-2 -1
13
-
b The aranh
0
5
-2
5
io
3
Answer:
See table below.
Step-by-step explanation:
Enter each x value into the equation x^2+2x+5 to find the value of y.
For example, when x = -2:
x^2-2x+5
(-2)^-2(-2)+5 for x = -2
4 + 4 + 5
y = 13
======
In the same manner:
x y
-2 13
-1 8
0 5
1 4
2 5
3 8
Suppose G(x)=2x+3/x-4
find x such that G(x) = -3.
Answer:
I'm not entirely sure but maybe it's -11
Step-by-step explanation:
I'm sorry if it's wrong I tried what I think you need to do
Consider the line 3x+5y=-1 What is the slope of a line parallel to this line? What is the slope of a line perpendicular to this line?
Answer:
Parallel: m = -3/5
Perpendicular: m = 5/3
Step-by-step explanation:
First let's find the slope of the line.
To do so, we must make [tex]y[/tex] the subject of the line's equation. The slope would then be the coefficient of [tex]x[/tex].
[tex]3x + 5y = -1 \text{ // -3x} \\3x + 5y - 3x = -3x - 1\\\to 5y = -3x - 1 \text{ // :5}\\\\\frac{5y}5 = \frac{-3x - 1}5\\\\y = -\frac35x - \frac15[/tex]
Therefore, the slope of the line is [tex]m = -\frac35[/tex].
Parallel lines have similar slopes, therefore a line parallel to the line 3x + 5y = -1 would have a slope of -3/5.
If a line is perpendicular to our line, then its slope would be the negative invert of our line's slope. Therefore, its slope would be [tex]m = -\left(-\frac35\right)^{-1} \to -\left(-\frac53\right) \to \frac53[/tex]
You have a set of consecutive integers from (−5) to 5, inclusive. You multiply any three of the integers. What is the least positive integer you can get as the product?
The least positive integer we can get as the product is 2.
What is the least positive integer you can get?Here we have the following set of numbers:
{-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}
And we want to take the product between 3 of them and find the least positive integer that we can get as the product.
So it makes sence to choose the smallest absolute value numbers (not zero) such that one is positive and two are negative (we want two negative ones so the signs cancell eachother)
Then we will get:
1*(-1)*(-2) = 2
That is the least positive integer we can get as the product.
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You want to build a sand castle on the seashore that will last two days. What two things should you consider?
Answer: sand and water
Sand : The first and most important thing you need to know about sand is that you can't do a thing with it unless it's wet. Here's why: when you add water to grains of sand, the liquid forms "bridges" that connect the granules to one another. This is why damp sand sticks together, so you can shape and carve it.
Water : Use lots of water. Dry sand in its natural state is lazy stuff. It wants to lie down and spread out into all sorts of nooks and crannies. The good news is that as long as you keep gravity working for you, there is really no way to add too much water. Which brings us to our second rule.2 Let it drain. If you've ever tried to make the base of a sandcastle by filling a plastic bucket with wet sand and then trying to unmould it, you've seen how important this rule is. With no place for the excess water to drain off, the sand makes a sucking, sticking, vacuum seal with the plastic and it becomes difficult, if not impossible, to remove the bucket.This is why successful sand sculptors do not use plastic buckets or other closed moulds but build their shapes by stacking handfuls of wet sand or by tamping it down in a topless and bottomless form.
Answer:
Placement and shape/size
Step-by-step explanation:
Placement: if the castle is to stay up for two days, you need to take into consideration the tide, and how far up on the seashore it will get. You need to know for a fact the ocean will not touch it, because if it does, chances are it will dig away at the foundation, making it topple over. You also need to make it in a place That little to no people will be there, so that they will not knock it over.
Shape/size: again, if it is to stay up for two days, you need to also consider the other weather than may occur. You need a good foundation that will not topple over. You need it tall enough that if some sand blows away, it will not matter. If it rains, you should have enough sand there that it would stay, and/or have something covering it, protecting it.
How do you find the highest total surplus?
when the price is equal to the market equilibrium price, total surplus is maximized.
What is surplus?
Making the most of society's well-being is a desired goal for an economic system. Do free markets perform that? Buyers must profit from their purchases, and sellers must profit from their sales, in order to provide an answer. Consumer surplus is the difference between the price consumers are willing to pay and the price they actually pay for a commodity or service. When individuals buy something, they typically pay less than they would have otherwise. Similar to producers, sellers might command a higher price for a good than it costs them to make it; this is known as producer surplus because it occurs when the cost of production is less than the price at which the good is sold.
Consumer Surplus = Willingness to Pay Price − Market Price
Producer Surplus = Market Selling Price − Economic Cost
Total Surplus = Consumer Surplus + Producer Surplus
Only the most effective producers will be able to produce a product for less than the market price in highly competitive markets. Therefore, only those vendors will create a good.
Therefore, when the price is equal to the market equilibrium price, total surplus is maximized.
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Graph the equation then find the solution
By graphing the system of equations, we can see that the solution is (4, -2)
How to solve the system of equations?Here we want to solve the system of equations:
y = (-3/2)*x + 4
y = (1/2)*x - 4
To solve this graphically, we just need to graph both equations on the same coordinate axis and find the point where the lines intersect.
The graph can be seen on the image at the end.
We can see that the solution is (4, -2)
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A cheetah can run 103 feet per second. A zebra can run x
feet per second. Use the Distributive Property to write and simplify an expression for how much farther the cheetah can run in 10 seconds.
expression: 10
(
)
simplified expression:
A cheetah can run 103 feet per second. A zebra can run x
feet per second. Use the Distributive Property to write and simplify an expression for how much farther the cheetah can run in 10 seconds.
expression: 10
(
)
simplified expression:
The expression of the distance between cheetah and zebra is (1030 – 10 x).
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
The rate of cheetah Rc is given in the question, as follows:
Rc = 103 / sec
The rate of zebra Rz is given in the question, as follows:
Rz = x / sec
We have to determine the distance between the two are 10 seconds, that is:
distance = (103 – x) 10
Apply the Distributive Property in the above expression and we get
distance = 1030 – 10 x
Thus, the required expression is (1030 – 10 x).
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Including a 6% sales tax, a new bike costs $514.1. Find the cost of the bike before
tax.
the cost of the bike before tax
514.1/106%=$485