The linear equation that passes through the two given points is:
y = (5/8)*x + 19/8
How to write the linear equation?We want to find the equation of a line that passes through (1, 3) and (9, 8).
Remember that the slope of a line that passes through two points (x₁, y₁) and (x₂, y₂) is given by the equation:
slope = (y₂ - y₁)/(x₂ - x₁)
Here we know the two points (1, 3) and (9, 8).
Then the slope is:
slope = (8 - 3)/(9 - 1) = 5/8
We can write the line as:
y = (5/8)*x + b
To find the value of b,we can evaluate in one of the given points, for example, if we use (1, 3) then we will get:
3 = (5/8)*1 + b
3 = 5/8 + b
3 - 5/8 = b
24/8 - 5/8 = b
19/8 = b
The linear equation is:
y = (5/8)*x + 19/8
Learn more about linear equations at:
https://brainly.com/question/1884491
#SPJ1
When an accountant records_ on hand, they are noting a company's ____
A. human resources; total liquid assets
B. cash; total of amount dollars, money orders, checks, and other forms of
money
C. supplies; materials that need to be purchased soon
D. inventory; number of employees on payroll
Answer: Choice B
Explanation: The phrase "cash on hand" means the amount of money the company has. It could be literal cash as the phrase directly implies. Or it could be near equivalents to cash. A near equivalent is something you can convert to cash fairly easily, meaning a bank would readily accept it. The only drawback is that it's not actual cash so its not as liquid as cash itself. Also, you would need to take into account the delay time between deposit and when the bank balance is updated.
A soccer player has a large cylindrical water cooler that measures 3.5 feet in diameter and is 2 feet tall. If there are approximately 7.48 gallons of water in a cubic foot, how many gallons of water are in the water cooler when it is completely full? Use π = 3.14 and round to the nearest hundredth.
575.44 gallons
143.86 gallons
76.93 gallons
19.23 gallons
There are approximately 205.33 gallons of water in the water cooler when it is completely full.
What is the volume of the cylinder?
The volume of a cylinder is given by the formula:
V = πr^2h
where V is the volume, r is the radius, and h is the height of the cylinder.
The volume of the cylindrical water cooler is:
V = πr^2h
where r is the radius and h is the height. Substituting the given values:
V = 3.14 x (3.5/2)^2 x 2
= 27.44 cubic feet
To convert cubic feet to gallons, we can multiply by 7.48 gallons/cubic foot:
V = 27.44 x 7.48
= 205.32 gallons
Rounding to the nearest hundredth, the answer is:
205.32 ≈ 205.33 gallons
Hence, there are approximately 205.33 gallons of water in the water cooler when it is completely full.
To learn more about the volume of the cylinder, visit:
https://brainly.com/question/9554871
#SPJ1
Answer:
The correct answer is 143.86 gallons
Step-by-step explanation:
Given sin 0 = and angle Ø is in Quadrant I, what is the exact value of cos ✪ in simplest form? Simplify all radicals if needed.
Answer:
cosΘ = [tex]\frac{\sqrt{21} }{5}[/tex]
Step-by-step explanation:
using the identity
• sin²Θ + cos²Θ = 1 ⇒ cos²Θ = 1 - sin²Θ
given Θ is in quadrant 1 , then cosΘ > 0
sinΘ = [tex]\frac{2}{5}[/tex] , then
cos²Θ = 1 - ( [tex]\frac{2}{5}[/tex] )² = 1 - [tex]\frac{4}{25}[/tex] = [tex]\frac{25}{25}[/tex] - [tex]\frac{4}{25}[/tex] = [tex]\frac{21}{25}[/tex] , then
cosΘ = [tex]\sqrt{\frac{21}{25} }[/tex] = [tex]\frac{\sqrt{21} }{\sqrt{25} }[/tex] = [tex]\frac{\sqrt{21} }{5}[/tex]
What is the average rate of change? Problem in the picture
The average rate of change of the function f(x) over the interval (-1, 2) is; 3.
What is the difference quotient of the function over the given interval?As evident in the task content; the given function is as represented by the graph of f(x).
Hence, the average rate of change of the function over the given interval; (-1, 2) is;
= ( f (2) - f (-1) ) / (2 - (-1))
where; f (2) = 5 and f (-1) = -4.
Therefore, the average rate of change is;
= (5 - (-4)) / (2 - (-1))
= 9 / 3.
= 3.
Ultimately, the difference quotient of f (x) over the given interval is; 3.
Read more on difference quotient;
https://brainly.com/question/28490181
#SPJ1
Miss brown butt the following items to make a cake for her daughter's 13th birthday party quantity for flower is 5LB the unit costs $2.74 per LB the total cost is $6.54The next item is sugar free for the sugar is 2 1⁄2 LB the unit costs $1.70 per LB the total cost is $1.60 the other item is butter quantity for the butter is 2LBP The next item is sugar free for the sugar is 2 1⁄2 LB the unit costs $1.70 per LB the total cost is $1.60 the other item is butter quantity for the butter is 2LBP that you need to cost is $7.49 per lb the total cost is $4.49Miss brown also needed to buy some eggs exhaust sole 6 for $4.85 and she needs to buy 1⁄2 dozen eggs calculate the cost of eggs calculated her total bill for the 4 items there is a 5% discount if you spend $50 on how much more money will she need to spend to get the discounts which is the best deal spent $50 And get the 5% Discounts Or purchase the four tems ?explain your reasoning.
The total cost of the ingredient to make the cake and the comparison to the percentage discount to get the best deal indicates that we get;
The total cost of the ingredient for the cake is $37.78The best deal is to purchase the 4 items and minimize spendingWhat is a percentage?A percentage is the representation of a proportion of an item per 100 of a set of items.
Quantity of flour = 5 lb
Unit cost for the flour = $2.74 per lb
Quantity of sugar = 2 1/2 lb
Unit cost of the sugar = $1.70 per lb
Quantity of butter = 2 lb
Unit cost of the butter = $7.49 per lb
Quantity of eggs required = 1/2 dozen
Cost of six eggs = $4.85
Miss Brown's total bill for the four items, C, is therefore;
C = 5 × 2.74 + (2 1/2) × 1.7 + 2 × 7.49 + 4.85 = 37.78
Her total cost for the four items, C = $37.78The discount available for purchases of $50 or more = 5% discount on the purchase
The amount of more money she will have to spend to get the 5% discount is therefore;
$50 - $37.78 = $12.22
Miss Brown will have to spend $12.22 extra to get the 5% discount
The 5% discount indicates that spending $50, Miss Brown only has to pay $50 - $50 × 5% = $47.5
Therefore, in order to get the discount, the total amount spent on the purchase is increase by $47.5 - $37.78 = $9.72, and the amount saved from the discount is $2.5, therefore;
Miss Brown should purchase the four itemsLearn more on percentage discount here: https://brainly.com/question/26950456
#SPJ1
Based on previous sales, Ron predicted sales of 80 pen sets. He actually sold 100 pen sets. Find the error and absolute error for the pen sets. A 5-column table with 3 rows. Column 1 is labeled Item with entries folders, erasers, pen sets. Column 2 is labeled Approximate Value with entries 25, 220, 80. Column 3 is labeled Exact value with entries 30, 200, 100. Column 4 is labeled Error with entries negative 5, 20, a. Column 5 is labeled Absolute Error with entries 5, 20, b.
The error is 20 and absolute error for the pen sets is also 20. Absolute error is the difference between a quantity's observed or inferred value and its actual value.
What is a absolute error statement?Absolute error is the difference between such a quantity's observed or assumed value and its real value. Because it doesn't indicate the error's magnitude, the absolute inaccuracy is insufficient.
What are absolute and relative error?The difference between a quantity's measured value and its actual value is known as absolute error. The difference between the measurement's absolute error and the quantity's actual value is referred to as relative error.
To know more about absolute error visit;
https://brainly.com/question/11599357
#SPJ1
Answer:
15%
Step-by-step explanation:
flip edge
Help needed on this question:
How to determine this
Using product rule,
[tex]\frac{d}{dx}[/tex](u.v) = du/dx.v + dv/dx.u
where u = x-5
v = x+7
Using the rule,
d/dx = 1(3x + 7) + 3(x - 5)
d/dx = 3x +7 +3x - 15
d/dx = 6x - 8
Using the expanding, then differentiating,
d/dx = (x - 5)(3x + 7)
open bracket,
d/dx = 3x^2 + 7x - 15x - 35
Differentiating it,
d/dx = 6x + 7 - 15
d/dx = 6x - 8
Therefore, using different rule,it has been verified that both methods gave the same results.
Read more about Diffferentiation
https://brainly.com/question/19408236
#SPJ1
please help meee
here is the picture
Answer:
f(-2) = 46
f(-1) = 17
f(0) = 2
f(1) = 1
f(2) = 14
Step-by-step explanation:
F(-2) = 46
F(-1)= 17
F(0)= 2
F(1)= 1
F(2)= 14
What are the exact value of a and b?
Answer:
a = 5, b = 5√3
Step-by-step explanation:
Use sin law
sin A/a = sin C/c
sin 30/a = sin 90/10
sin 30/(sin90/10) = a
a = 5
sin B/b = sin C/c
sin 60/b = sin 90/10
sin 60/(sin90/10) = b
b = 5√3
Solve for x, will give brainliest
Answer:
2
Step-by-step explanation:
Line MN ≅ Line LK
Since Line MN ≅ Line LK, that means the diagonals must be congruent ∴ MK ≅ NL.
Now that we know MK ≅ NL, we can set them equal to each other.
MK = [tex]16[/tex]
NL = [tex]7x + 2[/tex]
[tex]16=7x+2\\14=7x\\2=x[/tex]
Therefore, 2 is your final answer.
If Lisa works part-time, she will make 35% less than she does now.
How much will her monthly net income be?
What will their new total net income be?
Answer:
Lisa: $3302Family: $11372Step-by-step explanation:
Given a family net income of $13150, Lisa's current annual gross of $76200, deductions of 20% of Lisa's gross salary, you want to know Lisa's monthly net income and the new family net income if Lisa makes 35% less by working part-time.
Lisa's incomeLisa's current annual income is $76200, and her annual net income is 80% of that, or $60960. On a monthly basis, her net income is ...
$60960/12 = $5080 . . . . . . Lisa's current net monthly income
If her income is reduced by 35%, the reduction is ...
0.35 × $5080 = $1778
Then Lisa's part-time monthly net income will be ...
$5080 -1778 = $3302 . . . . . Lisa's part-time monthly net income
Family incomeThe family net income will be reduced by the same amount:
$13150 -1778 = $11372 . . . . . new family monthly net income
__
Additional comment
It appears the total of budgeted items is $10343, so those items can be paid even if Lisa works part-time. The family's current surplus income of $2807 would be reduced to $1029, about a 63% reduction. That gives a lot less cushion to pay for off-budget expenses that may come up.
A crew of construction workers are disassembling the inside of a building and dropping things into dumpsters at the base of the building. The equation Va=(64d)122
is used to find the average velocity, or speed, in feet per second of an object that has fallen a distance of d feet. What is the average velocity, to the nearest hundredth, of a ceiling tile that fell 43 feet ?
The average velocity, to the nearest hundredth, of a ceiling tile that fell 43 feet is 344 feet per second
What is speed?Velocity is the pace and direction of an item's movement, whereas speed is the time rate at which an object is travelling along a route.
Given that the formula for the speed of a falling object is v= √64d,
where v is the speed of the object in feet per second and d is the distance the object has fallen, in feet.
And also given that d = 43 feet.
Substituting the value to the formula,
v = √64 (43)
v = 8 x 43
v = 344
Therefore, 344 feet per second is the velocity.
To learn more about the speed;
brainly.com/question/7359669
#SPJ1
what is the solution to | x | -2 <= -3
Find the value of b if the graph of y = 0.3x + b goes through the point.
N(5,d)
Solve the system by substitution.
y = 5x
y = 4x + 9
Answer:
x=9
Step-by-step explanation:
Since y=5x, you plug it into the other equation's y and it'd look like this 5x=4x+9. Then you subtract 4x on both sides and that would leave you with an x=9.
A scientific model is used to predict the average global high
temperature on earth by anaylizing the data from previous
years. In 1940, the temperature was 55° F However, the
temperature has grown to 59.5° F in 1990.
A) Find an equation in the form T = ax + b, where x is the
number of years since 1940 and T is the average gobal high
temperture on Earth.
Answer:
chapter 1
Step-by-step explanation:
Robert has a job transporting soft drinks by truck. His truck is filled with cans that weigh 16 ounces each
and bottles that weigh 54 ounces each. There is a combined total of 280 cans and bottles in his truck.
Let c be the number of cans in his truck. Write an expression for the combined total weight (in ounces)
of the cans and bottles in his truck.
O Total weight in ounces = 70c + 280
O Total weight in ounces = -54c + 15, 120
O Total weight in ounces = 38c + 280
O Total weight in ounces = -38c + 15, 120
The simplest form of the given expression will be 38c + 280.
What is polynomials?
Using variables and coefficients, polynomials are algebraic expressions. The term "indeterminates" is sometimes used to describe variables. The terms Poly and Nominal, which together signify "many" and "terms," make up the word polynomial. When exponents, constants, and variables are combined using mathematical operations like addition, subtraction, multiplication, and division, the result is a polynomial (No division operation by a variable). The expression is categorized as a monomial, binomial, or trinomial based on the number of terms it contains.
His truck is filled with cans that weigh 16 ounces each and bottles that weigh 54 ounces each. There is a combined total of 280 cans and bottles in his truck.
Let c be the number of cans in his truck. Write an expression for the combined total weight (in ounces) of the cans and bottles in his truck.
O Total weight in ounces = 38c + 280
Hence the simplest form of the given expression will be 38c + 280.
Learn more about polynomials, by the following link.
https://brainly.com/question/2833285
#SPJ1
Find the perimeter of the polygon. 14 ft, 15 ft, 7 ft
Answer:
the perimeter of the polygon is 36 feet.
Step-by-step explanation:
The perimeter of a polygon is the sum of the lengths of all its sides. In this case, you have three sides with lengths of 14 ft, 15 ft, and 7 ft. To find the perimeter, simply add these lengths together:
Perimeter = 14 ft + 15 ft + 7 ft
Perimeter = 36 ft
So the perimeter of the polygon is 36 feet.
Raul tried to evaluate an expression step by step. \qquad\begin{aligned} &3 -(-5) - 7\\\\ \\ =&3+5-7&\green{\text{Step } 1}\\\\ \\ =&3+2&\blue{\text{Step } 2}\\\\ \\ =&5&\purple{\text{Step } 3} \\\\ \end{aligned} = = = 3−(−5)−7 3+5−7 3+2 5 Step 1 Step 2 Step 3
Raul made a mistake in evaluating the expression 3 - (-5) - 7 in B) Step 2 by not following PEMDAS.
What is PEMDAS?PEMDAS means Parentheses, Exponents, Multiplication and Division, Addition and Subtraction from left to right.
PEMDAS refers to the correct order for evaluating mathematical expressions.
The expression 3 - (-5) - 7 should be evaluated as follows:
3 - (-5) - 7
= 3 + 5 - 7
= 8 - 7
= 1
Thus, if Raul did not make a mistake in Step 2, he would have valued the expression as 1.
Learn more about PEMDAS at https://brainly.com/question/345677
#SPJ1
Complete Question:Raul tried to evaluate an expression step by step.
3 - (-5) - 7
Step 1: 3 + 5 - 7
Step 2: 3 + 2
Step 3: 5
Find Raul's mistake.
Answer Options:A) Step 1
B) Step 2
C) Step 3
D) Raul did not make a mistake.
One cubic foot holds 7.48 gallons of water, and 1 gallon of water weighs 8.33 pounds. How much does 4.3 cubic feet ofwater weigh in pounds? In tons?
To find the weight of 4.3 cubic feet of water, we need to first find the number of gallons of water that 4.3 cubic feet holds and then multiply that by the weight of 1 gallon of water.
1 cubic foot holds 7.48 gallons of water, so 4.3 cubic feet holds 4.3 x 7.48 = 31.964 gallons.
1 gallon of water weighs 8.33 pounds, so 31.964 gallons of water weigh 31.964 x 8.33 = 265.9012 pounds.
Therefore, 4.3 cubic feet of water weigh 265.9012 pounds.
To find the weight in tons, we need to divide the weight in pounds by 2000:
265.9012 pounds ÷ 2000 = 0.13295 tons
So 4.3 cubic feet of water weigh 0.13295 tons.
Answer:
0.13314 tons.
Step-by-step explanation:
We can start the calculation by first converting the cubic feet of water to gallons and then converting the gallons to pounds.
Conversion from cubic feet to gallons:
4.3 cubic feet = 4.3 cubic feet * 7.48 gallons/cubic foot = 32.084 gallons
Conversion from gallons to pounds:
32.084 gallons = 32.084 gallons * 8.33 pounds/gallon = 266.279 pounds
Conversion from pounds to tons:
266.279 pounds = 266.279 pounds / 2000 pounds/ton = 0.13314 tons
So, 4.3 cubic feet of water weigh 266.279 pounds or 0.13314 tons.
inverse function of f(x)= \frac{5}{x} +4
The inverse of the function is f⁻¹ ( x ) = 5 / ( x - 4 )
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
f ( x ) = ( 5/x ) + 4 be equation (1)
On simplifying the equation , we get
y = ( 5/x ) + 4
Now , replacing x with y , we get
x = ( 5/y ) + 4
On solving for y , we get
5/y = x - 4
y = ( 5 / x - 4 )
Now , the inverse of the function is f⁻¹ ( x ) = 5 / ( x - 4 )
Hence , the equation is f⁻¹ ( x ) = 5 / ( x - 4 )
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ1
please help me i’ll give you brainlist
Answer:
its c
Step-by-step explanation:
si en una division el dividendo es 872 el cociente es 62 y el residuo es 4 cual es el divisor
The divisor in the situation given is 14.
What is division algorithm?We can write the division algorithm as -
dividend = (divisor × quotient) + remainder
Given is that in a division the dividend is 872 the quotient is 62 and the remainder is 4
We can write -
dividend = (divisor × quotient) + remainder
872 = (d x 62) + 4
62d = 868
d = 868/62
d = 14
Therefore, the divisor in the situation given is 14.
To solve more questions on division, visit the link below
https://brainly.com/question/26809668
#SPJ9
{Question in english -
if in a division the dividend is 872 the quotient is 62 and the remainder is 4 what is the divisor}
5x + 3y = 28
y=-1/5x+2
Answer:
x = 5, y = 1
Step-by-step explanation:
For x :
Substitute y into the equation : 5x + 3 ( -1/5x + 2 ) = 28
Simplify : 22/5x + 6 = 28
Isolate x : x = 5
For y :
Substitute x for 5 : y = -1/5 * 5 + 2
Solve: y = 1
Help with these questions pls?
Answer:
£76
Step-by-step explanation:
[tex]28+16(1.5/0.5)=28+16(3)=28+48=76[/tex]
In a fruit cocktail, for every 20 ml of orange juice you need 45 ml of apple juice and 100 ml of coconut milk. What is the ratio of apple juice to coconut milk to orange juice expressed in its simplest form?
In a cas e whereby a fruit cocktail, for every 20 ml of orange juice you need 45 ml of apple juice and 100 ml of coconut milk the ratio of apple juice to coconut milk to orange juice expressed in its simplest form is 9: 20 : 4
How can the the ratio of apple juice to coconut milkbe determined?The concept that will be used here is ratio.
The amount of orange juice can be expressed as 20mL
The amount of apple juice can be expressed as 45mL
The amount of coconut milk can be expressed as 100 mL
Then the ratio of the three can be expressed as :
(apple: coconut: orange)
= 45: 100 : 20
We can divide through by 5, then we have
9: 20 : 4
Learn more about ratio at:
https://brainly.com/question/2328454
#SPJ1
can you please please please help me w this question!!! 40 points!!
A washer and a dryer cost $993 combined. The washer costs $43 more than the dryer. What is the cost of the dryer?
Answer:425
Step-by-step explanation:
993-43=950
950/2=425
Answer:
$475
Step-by-step explanation:
Let's call the cost of the dryer x. That means the cost of the washer is x + $43. The combined cost of the two is $993, so we can write the equation:
x + (x + $43) = $993
Expanding the right side:
2x + $43 = $993
Subtracting $43 from both sides:
2x = $950
Dividing both sides by 2:
x = $475
So the cost of the dryer is $475.
The following table shows the approximate population increases of a small town
Year (x) 0,1,2,3
Population (y) 88,000, 90,640, 93,359, 96,160
Write an equation that models that growth
[tex]b = \bar y - m\bar x[/tex]An equation that models that population growth of the small town is y = 2,453.75x + 88,499.37 .
What is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
The given table is:
Year (x) 0, 1, 2, 3
Population (y) 88,000, 90,640, 93,359, 96,160
We can use the least squares method to estimate the slope and y-intercept.
The formula for the slope (m) is:
[tex]m = \dfrac{\sum(x - \bar x)(y - \bar y)}{ \sum(x - \bar x)^2}[/tex]
The formula for the y-intercept (b) is:
[tex]b = \bar y -m \bar x[/tex]
Using the data from the table, we can calculate the mean of x and y:
[tex]\bar x[/tex] = (0 + 1 + 2 + 3) / 4
= 1.5
[tex]\bar y[/tex] = (88,000 + 90,640 + 93,359 + 96,160) / 4
= 92,180
Next, we can calculate the slope (m) and y-intercept (b):
m = (0 - 1.5)(88,000 - 92,180) + (1 - 1.5)(90,640 - 92,180) + (2 - 1.5)(93,359 - 92,180) + (3 - 1.5)(96,160 - 92,180)² / (0 - 1.5) + (1 - 1.5)² + (2 - 1.5)² + (3 - 1.5)²
= (-2.25)(-4,180) + (-0.5)(-1,540) + (0.5)(1,179) + (2.25)(4,980) / 2.25² + 0.5²+ 0.5² + 2.25²
= 2,453.75
b = 92,180 - (2,453.75 x 1.5)
= 92,180 - 3,680.63
= 88,499.37
So, the equation that models the growth of the population is:
y = 2,453.75x + 88,499.37
To know more about Equation check:
https://brainly.com/question/1529522
#SPJ1
Find the length of WB
Answer:
WB = 16 in---------------------------
According to picture we observe:
W is midpoint of AT and B is the midpoint of TE.The segment connecting the midpoints is the midsegment.
As per property of the midsegment, it is parallel to opposite side and is half of its measure.
It tells us that WB is parallel to AE and:
WB = AE/2 WB = 32/2WB = 16 in