The equation for the graph is y = 20x + 50, where the rate of change is 20 and the initial value is 50.
What is a linear equation?When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."
There are both one-variable and two-variable linear equations.
Given graph shows the relationship between the number of cubic yards of mulch ordered and the total cost of the mulch delivered,
x-axis shows the cubic yards and y-axis shows cost,
A. to find the constant rate of change,
from graph, we find that x₁ = 0 and x₂ = 5
y₁ = 50 and y₂ = 150
constant rate of change = (y₂ - y₁)/(x₂ - x₁)
rate of change = (150 - 50)/(5 - 0)
rate of change = 100/5 = 20
the constant rate represents the slope of the line,
for equation of line y = mx + c
here m = slope of the line or constant rate of change.
2. to find the initial value,
the initial value represents the y-intercept or the value of constant for equation y = mx + c,
where c is the initial value
we have m = 20 x = 0 and y = 50
50 = 20(0) + c
c = 50
the equation for the graph is y = 20x + 50
Hence the rate of change is 20 and the initial value is 50.
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Please help!!!!! Find the perimeter of the figure. Round to the nearest hundredth if needed
The perimeter of the figure is 48 meters
How to determine the perimeter of the figureFrom the question, we have the following parameters that can be used in our computation:
Shape = rectangle
length = 10 meters
width = 14 meters
The perimeter of the figure is then calculated as
Perimeter = 2 * (length + width)
Substitute the known values in the above equation, so, we have the following representation
Perimeter = 2 * (10 + 14)
Evaluate
Perimeter = 48
Hence, the perimeter is 48 meters
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1
Jenny is arranging rows of chairs for the student play.
There are 7 chairs in the first row.
Each row behind the first row has two more chairs than the previous row.
Complete the explicit definition for this sequence. Your answer must be fully simplified.
Explicit Definition of an Arithmetic Sequence
an = a₁ + (n-1) d
an
=
In the first row there are 7 chairs, and common difference is 2 implies that, the sequence in increasing order.
What is arithmetic sequence ?An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence.
Given that,
The definition of the arithmetic sequence is given by,
an = a₁ + (n-1) d (1)
Also, in first row, there are 7 chairs.
And after that row two more chairs are behind the first row.
Implies that, a₁ = 7 and d = 2.
Substitute this value in equation (1),
aₙ = 7 + (n - 1) 2
aₙ = 7 + 2n - 2
an = 5 + 2n
For the value of n the number of chairs can be found.
Hence, the arithmetic sequence is in increasing order.
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When the dimensions of a particular rectangle are expressed in feet, the ratio of the numerical value of the perimeter to the numerical value of the area is $\frac{3}{4}$. What is this ratio if the dimensions are expressed in inches instead of feet
The ratio if the dimensions are expressed in inches instead of feet is 1/16.
Ratio is defined as the relationship between two quantities. It can be expressed as a to b, a : b, or a / b.
Meanwhile, proportion is defined as the equality between two ratios.
a / b = c / d
If the ratio of the numerical value of the perimeter to the numerical value of the area, expressed in feet, is 3/4, then converting each component to inches will give its ratio, expressed in inches.
perimeter / area
= 3 feet / 4 feet²
= 3 feet(12 inches / 1 foot) / 4 feet²(12 inches / 1 foot)(12 inches / 1 foot)
= 36 inches / 576 inches²
Simplifying the ratio by dividing both by 36.
36 / 576 = 1 / 16
Hence, the ratio will become 1/16.
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For j(x) = 5^x − 3, find j of the quantity x plus h end quantity minus j of x all over h period
For j(x) = 5^x − 3, find j(x+h) - j(x)/h
If j(x) = 5^(x - 3), using laws of exponents to solve the given expression [j(x + h) - j(x)]/h gives; [j(x + h) - j(x)]/h = [(5^(x - 3))(5^(h) - 1)]/h
How to utilize laws of exponents?We are given the function as;
j(x) = 5^(x - 3)
Now, we want to solve the expression;
[j(x + h) - j(x)]/h
This gives us;
j(x + h) = 5^(x - 3 + h)
Thus, our expression is now;
[j(x + h) - j(x)]/h = [5^(x - 3 + h) - 5^(x - 3)]/h
Now, according to laws of exponents, we know that;
y³ × y² = y³ ⁺ ²
Thus;
5^(x - 3 + h) = 5^(x - 3) × 5^h
Therefore;
[5^(x - 3 + h) - 5^(x - 3)]/h = [(5^(x - 3))(5^(h) - 1)]/h
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Write the equation the line through the point b) (1,3) with slope = -4
Answer:
Below
Step-by-step explanation:
Here is the point-slope form of this line to start:
y-3 = -4 ( x-1) which can be re-arranged to
y = -4x +7 which is y = mx + b form ( slope -intercept from)
or
4x + y = 7 sometimes called 'standard form'
PLEASE HELP
question 3
Determine the solution to the inequality.
The solution to the inequality expression 1/4|x + 1| ≥ 4 is (b) x ≤ -17 or x ≥ 15
How to determine the solution to the inequality.From the question, we have the following parameters that can be used in our computation:
1/4|x + 1| ≥ 4
Multiply through the inequality by 4
So, we have the following representation
|x + 1| ≥ 16
Remove the absolute bracket
-16 ≥ x + 1 ≥ 16
Subtract 1 from all sides
-17 ≥ x ≥ 15
So, we have
x ≤ -17 or x ≥ 15
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0.0319 as a fraction
On the spinner below, what is P(odd)?
A circle is divided equally into eight sections.· One of the sections is labeled with a 1.
· One of the sections is labeled with a 2.
· Two of the sections are labeled with a 3.
· One of the sections is labeled with a 4.
· Two of the sections are labeled with a 5.
· One of the sections is labeled with a 6.
· The pointer originating from the middle of the circle is pointing at one of the sections labeled with a 3.
A. start fraction 5 over 8 end fraction
B. The fraction is 5 over 3.
C. one-half
Answer:
Isha Chawla the viewer's attention to detail and the game name is the viewer's of the viewer's the viewer's of math and science and time of year for you are interested please contact me homework for the same to the viewer's attention to the seller if
It's spaghetti night at Emily's house! She has 8 ounces of freshly grated cheese to sprinkle evenly over 5 bowls of spaghetti. How much cheese will be in each bowl?
Answer:
1.6 oz
Step-by-step explanation:
8 oz to spread into 5 bowls = 8/5
8/5=1.6
Answer:1.6
Step-by-step explanation: First your going to divide 8/5 but do it like this-8.0 divided by 5= 1.6 so that gonna be your answer. Hope it was helping you.
26. Which of the following is an equation for the line that is perpendicular to the line y = 2x - 9
and passes through the point (-4,5)?
A. y = 2x+7
B. y = -1/2x+3
C. y = 2x+5
D. y = -14x-9
Answer:
y = -1/2x+3
Step-by-step explanation:
We have y = 2x-9
This is in slope intercept form
y = mx+b where m is the slope
The slope is 2
We want a line that is perpendicular
Perpendicular lines have slopes that are negative reciprocals
The slope is -1/2
The equation of the new line is
y = -1/2x+b
Substituting the point into the equation
5 = -1/2(-4)+b
5 = 2+b
5 -2=b
3=b
y = -1/2x+3
Answer:
y = -1/2x + 3
Step-by-step explanation:
We know that if two lines are perpendicular to each other the multiplication of the slopes of those 2 lines equals -1.
m₁ × m₂ = -1
Given that, the slope of one line is 2 (m₁). Now, let us find the slope of the other line (m₂) using the above formula.
2 × m₂ = -1
2m₂ = -1
Divide both sides by 2.
m₂ = -1/2
And now let us find the value of the y-intercept ( c in the formula y = mx + c) using the given coordinate.
( -4 , 5 )⇒ ( x , y ).
Let us find it now.
y = mx + c
5 = -1/2x × -4 + c
5 = 2 + c
5 - 2 = c
3 = c
And now let us write the equation for the new line.
y = m x + c
y = -1/2x + 3
Solve the equation for all values of x.
|4x +9|-6 = x
Answer: x = 4
Step-by-step explanation: (4x+9)−6.
Subtract 6 from 9 to get 3.
d/dx (4x+3)
The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^n
is nax^n-1.
4x^1-1
Subtract 1 from 1.
4x^0
For any term t, t×1=t and 1t=t.
x = 4
someone please. i need help w this,
Answer:
y = [tex]\frac{-8}{3}[/tex] x + [tex]\frac{8}{3}[/tex]
Step-by-step explanation:
The slope is the change in y over the change in x.
[tex]\frac{0-8}{1 - -2}[/tex] = [tex]\frac{-8}{1+2}[/tex] = [tex]\frac{-8}{3}[/tex]
The slope (m) is [tex]\frac{-8}{3}[/tex]
Use the slope and one of the points to find the y intercept
I will use the point (1,0)
x = 1
y = 0
m = [tex]\frac{-8}{3}[/tex]
y = mx + b Substitute in what you know and solve for b
0 = [tex]\frac{-8}{3}[/tex](1) + b
0 = [tex]\frac{-8}{3}[/tex] + b Add [tex]\frac{8}{3}[/tex] to both sides
[tex]\frac{8}{3}[/tex] = b
The y-intercept (b) is [tex]\frac{8}{3}[/tex]
y = mx + b
y = [tex]\frac{-8}{3}[/tex] x + [tex]\frac{8}{3}[/tex]
A solid is in the form of cone mounted on a hemisphere in such a way that the centre of the base of the cone just coincide with the centre of the base of the cone is 1 upon 2 hour where r is the radius of the hemisphere prove that the total surface area of the solid is pie upon 4 (11 r 2 l) r ?
When proved, the total surface area of the solid is π/4 r(11r - 2l)
What is the total surface area of the solid?
The Solid comprise a cone mounted on top of a hemisphere. The total surface area of the object is given as follows
Total surface area = Total surface area of cone -total surface area of the hemisphere.
This implies that TSA = 1/2πr(1/2r +l) -3πr²
πr/2(r+2l)/2 -3πr²
This implies that the expression will be (πr² +2πrl)/4 - 3πr²
⇒(πr² +2πrl - 12πr²)/4
Conclusively, the expression finally gives π/4 r (11r - 2l)
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What's the principal sum?
The principal sum refers to the amount payable in one sum in the case of accidental death and, in some cases, accidental dismemberment.
The amount paid in the case of accident or medical insurance in the event that the insured person dies, loses a limb, or loses sight is known to be as principal sum. It means that the principal sum amount is the maximum amount paid to the insured person for all injuries resulting from the accident.
Thus, the principal sum is the amount insured to be paid by the company to the beneficiary in the case of the insured individual's accidental death as well as in the loss of limb or sight.
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How many 4 digit even numbers can be formed using the digits 2 3 5 17 9?
There are 125 four-digit even numbers that can be formed using the digits 2, 3, 5, 17, and 9.
To calculate the number of 4-digit even numbers that can be formed with the given digits, we can use the formula n^r, where n is the number of digits and r is the number of digits in the number. In this case, n = 5 and r = 4, so we can calculate 5^4 = 625.
Since we are looking for even numbers, we must eliminate any numbers that end in an odd digit. This means that we must eliminate the numbers with the digits 3 and 5 as the last digit. Therefore, 625 - (3*25) - (5*25) = 625 - 75 - 125 = 425.
Now we must eliminate any numbers that do not begin with an even digit. This means that we must eliminate the numbers with the digits 3 and 9 as the first digit. Therefore, 425 - (3*25) - (9*25) = 425 - 75 - 225 = 125. Therefore, there are 125 four-digit even numbers that can be formed with the given digits.
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SOMEONE PLEASEEEE HELP MEE ASAP 20 POINTTSS
Answer:
x intercept is 7.5
y intercept is -3
Step-by-step explanation:
let me know if you need more help
x/3 +x/5=8 solve in equation
Answer:
x=15
Step-by-step explanation:
x/3+x/5=8
Both multipling 15: 15(x/3+x/5)=15*8
5x+3x=120
8x=120
x=15
A conical water tank with vertex down has a radius of 12 feet at the top and is 26 feet high. If water flows into the tank at a rate of 20 ft3/minft3/min, how fast is the depth of the water increasing when the water is 17 feet deep?
The depth of the water is increasing at _____________ ft/min
The depth of the water is increasing at 0.167 ft/min.
In this problem, we are given the radius of the conical tank (12 feet), the height of the tank (26 feet) and the rate at which water is flowing into the tank (20 ft3/min). To calculate the rate of the water's increase in depth, we need to first calculate the volume of the tank.
The volume of a conical tank can be calculated using the formula V = 13r2h, where r is the radius and h is the height. Using this formula, we can calculate the volume of the tank to be 13(12)2(26) = 7584 ft3.
Next, we need to calculate the rate at which the depth of the water is increasing. This can be done by dividing the rate at which water is flowing into the tank (20 ft3/min) by the volume of the tank (7584 ft3). This gives us a rate of 0.0026 ft3/min. To get the rate at which the depth is increasing, we need to divide this number by the area of the tank's base (113 ft2). This gives us a rate of 0.167 ft.
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Will mark Brainiest
How can you find the unit price for 1 can of diet soda if a case of 24 costs 5.99
I’m too lazy to solve it
Will mark brainiest
Answer:
Original: 0.24958333333... | Rounded Up: 0.25
Step-by-step explanation:
unit price = total price divided by quantity
5.99 divided by 24 = 0.24958333333...
We can round this to 0.25
The medal to achieve at the Summer Olympics in London in 2012 is not composed solely of it is an alloy of gold, silver and bronze of cylindrical shape it had a diameter of 8.5 cm and a thickness of 7 mm Here are the percentages of the volume of a gold medal which occupied the alloy:
(92.5% silver, 6.69% copper and 0.81% gold
Here is the table giving the densities and the prices per g of each alloy
Density/Price
g/cm3 €/g
Gold. 19.3. 42.55
money. 10.5. 0.74
copper. 8.9. 0.0075
1) Proves that there was only 6g of gold in this "gold medal"
2) gives the total cost of the lethal contained in this medal.
The composition of the 8.5 cm diameter, 7 mm thick medal metal alloy, which is composed of gold silver and bronze are as follows;
1) The mass of the gold in the alloy is 0.81% × 39.72 cm³ × 19.3 g/cm³ ≈ 6 g
2) The total cost of the medal is about €540.95
What is an alloy?An alloy is made by combining two or more different metals to produce a metal of desired qualities such as strength, durability or to prevent corrosion.
1) The percentage of silver by volume = 92.5%
Percentage of copper = 6.69%
Percentage of gold = 0.81%
Volume of the medal = π × (8.5 cm)²/4 × 7 mm ≈ 39.72 cm³
Volume of the gold ≈ 0.81% × 39.72 cm³ ≈ 0.32 cm³
Mass = Density × Volume
Mass of the gold ≈ 19.3 g/cm³ × 0.32 cm³ ≈ 6 grams
The mass of gold in a medal containing 0.81% of gold is about 6 g2) The mass of the silver in the medal is found as follows;
Mass = 92.5% × 39.72 cm³ × 10.5 g/cm³ ≈ 385.78 g
Mass of the copper is found as follows;
Mass = 6.69% × 39.72 cm³ ×8.9 g/cm³ ≈ 23.65 g
The total cost of the medal is therefore;
Total cost ≈ 6 × 42.55 + 385.78 × 0.74 + 23.65 × 0.0075 ≈ 540.95
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Find the mean of a distribution if it's median and mode are 45 and 13 respectively
The mean of the distribution is 61.
What is Mean?The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.
Given, the median and mode of a dataset are 45 and 13 respectively
They have given that the median of the distribution is 45
They have given that the mode of distribution is 13
To find the mean of the distribution, let's consider
The relationship between the mean, mode, and the median is given by
Mode = 3 Median - 2 Mean
Mean = (3* 45 - 13)/2
Mean = 122/2
Mean = 61
Therefore, the mean of a distribution if its median and mode are 45 and 13 respectively is 61.
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Violet was given a box of assorted chocolates for her birthday. Each night, Violet treated herself to some chocolates. Violet ate 4 chocolates each night and there were originally 24 chocolates in the box. Write an equation for C,C, in terms of t,t, representing the number of chocolates remaining in the box tt days after Violet's birthday.
The equation for C, in terms of t, representing the number of chocolates remaining in the box t days after Violet's birthday is C = 24 - 4t
How to write an equation?Number of chocolate violet eats each night = 4
Number of chocolate originally in the box = 24
Number of chocolate remaining = C
Number of days after violet birthday = t
Number of chocolate remaining = Number of chocolate originally in the box - (Number of chocolate violet eats each night × Number of days after violet birthday)
C = 24 - (4 × t)
C = 24 - 4t
In conclusion, the equation which represents violet's remaining chocolate after her birthday is C = 24 - 4t
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What does an HL triangle look like?
An HL triangle is a type of triangle with two sides of equal length and one side that is longer than the other two sides. The triangle has an acute angle between the two equal sides, and an obtuse angle between the longest side and one of the equal sides.
Understanding the HL TriangleAn HL triangle can be described as an isosceles triangle with one side longer than the other two. The sides that are of equal length form an acute angle, while the longest side forms an obtuse angle with one of the equal sides. The longest side of the HL triangle is typically referred to as the hypotenuse, while the two equal sides are referred to as the legs. The hypotenuse is always the longest side, and the two legs are always of equal length.
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Pete traveled 1,380 miles in two days. The first day, he traveled 1.5 times as far as he did the second day. How many miles did he drive on
He drove 828 miles on the first day.
An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question.
Let x = distance Pete traveled on the second day
If on the first day, he traveled 1.5 times as far as he did the second day, then
distance Pete traveled on the first day = 1.5x
If Pete traveled 1,380 miles in two days, the the sum of the distance he traveled in two days is equal to 1380.
x + 1.5x = 1380
Simplify the equation and solve for the value of x.
x + 1.5x = 1380
2.5x = 1380
x = 552
distance Pete traveled on the second day = 552 miles
distance Pete traveled on the first day = 1.5(552) = 828miles
Therefore, he drove 828 miles on the first day.
The problem seems incomplete. The question must be
"Pete traveled 1,380 miles in two days. The first day, he traveled 1.5 times as far as he did the second day. How many miles did he drive on the first day?"
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What is the value of the expression ƒ2+ 5 if ƒ = 3?
Answer:
f2 + 5 when f = 3 is 11.
Step-by-step explanation:
So let's start by replacing f with 3:
3(2) + 5 =
When we have a variable right next to another number, we multiply. Some examples of this are 2x or 5y or 10000t, or even 0.001j.
Therefore, we multiply the 3 and 2 together, which gets us 6:
6 + 5 =
And 6 plus 5 equals 11
6 + 5 = 11, final answer.
if we set c=19!, then express 21!-20! in terms of c
[tex]\begin{array}{ll|ll} 21!\implies &21\cdot 20\cdot 19\cdot 18\cdot 17.....\\&\\ &21\cdot 20\cdot 19! \end{array} \begin{array}{llll} 20!\implies &20\cdot 19\cdot 18\cdot 17\cdot 16\cdot 15.....\\\\ & 20\cdot 19! \end{array} \\\\[-0.35em] ~\dotfill\\\\ (21\cdot 20\cdot 19!)-(20\cdot 19!)\implies (21\cdot 20\cdot c)-(20\cdot c) \\\\\\ 420c-20c\implies \text{\LARGE 400c}[/tex]
you deposit $4000 in an account earning 4% interest compounded quarterly. How much will you have in the account in 10 years
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &10 \end{cases} \\\\\\ A = 4000\left(1+\frac{0.04}{4}\right)^{4\cdot 10}\implies A=4000(1.01)^{40} \implies A \approx 5955.45[/tex]
Answer:
$5955.45
Step-by-step explanation:
We can use the formula to find the sum of the money, when we calculate the amount of money according to compound interest.
Before we getting ready to solve the sum, we have to keep these points in our mind.
Interest will calculate quarterly. So, we have to divide the interest by 4.I year has 4 quarters. So, number of years should me multiply by 4.Formula to find the sum of money after compound interest is:
[tex]\sf S = X ( 1 + r )^n[/tex]
Here,
S = Sum of money
X = Amount of money deposited
r = Interest rate
n = Time ( in years )
Let us solve it now.
[tex]\sf S = X ( 1 + r )^n\\\\\sf S = 4000 ( 1 + \frac{4}{100}*\frac{1}{4} )^4^0\\\\\sf S = 4000 ( 1 + \frac{4}{400} )^4^0\\\\\sf S = 4000 ( 1 + 0.01 )^4^0\\\\\sf S = 4000 ( 1.01 )^4^0\\\\\sf S = 5955.45[/tex]
Please help me asap, I suck at math fr fr
Answer:
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
C : is the hypotenuse
A and B are two sides
[tex] {6}^{2} + \: {x}^{2} = {15}^{2} \\ {15}^{2} - {6}^{2} = 189 \\ \sqrt{189} = 3 \sqrt{21} [/tex]
PLEASE HELP WILL GIVE BRANLIEST!!
Answer:
B. x <= -17 or x >= 15
Step-by-step explanation:
To solve this inequality, we need to split the absolute value expression into two separate cases, one for each possible sign of the expression within the absolute value bars.
For the case where the expression within the absolute value bars is positive, we can remove the absolute value bars and solve the resulting inequality as follows:
1/4(x+1) >= 4
(x+1) >= 16
x >= 15
For the case where the expression within the absolute value bars is negative, we can again remove the absolute value bars and solve the resulting inequality as follows:
-1/4(x+1) >= 4
-(x+1) >= 16
x <= -17
Combining these two cases, we get that the solution to the inequality is:
x <= -17 or x >= 15
So, the correct answer is B.
Please I need it asap
Answer:
lol.
Step-by-step explanation:
Refer to the image attached. Please rate, and let me know if you have any questions. Thanks!