The equation that can be used to find the length of the remaining side is z² = 14² - 9²
How to determine the length of sideUsing the Pythagorean theorem that states that the square of the hypotenuse side is equal or equivalent to the sum of square of the other two sides.
This is represented as;
x² = y² + z²
Given that the parameters are enumerated as;
x is the hypotenuse sidey is the opposite sidez is the adjacent sideNow, substitute the values
14² = 9² + z²
collect like terms
z² = 14² - 9²
Hence, the equation is z² = 14² - 9²
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The length of the remaining side can be calculated using 14² = x² + 9² is 10.7 units
What is an equation?An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.
Pythagoras theorem is used to show the relationship between the sides of a right angled triangle. It is given as:
hypotenuse² = adjacent² + opposite²
Let x represent the missing side.
The hypotenuse of a right triangle has a length of 14 units and a side that is 9 units long. Hence:
14² = x² + 9²
x² = 14² - 9²
x² = 115
x = 10.7 units
The length of the remaining side is 10.7 units
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After an 8% price increase the new price was $450. What was the original price?
Answer:
$416.67
Step-by-step explanation:
8% = 0.08
adding 8% to something means you add 0.08 of it
original = 100% = 1
original + 8% increase = 1 + 0.08 = 1.08
1.08 of original price = new price = 450
1.08 * original price = 450
450/1.08 = original price = $416.67
Courtney can run a 1/4 mile in 2 minutes. At this rate, how many minutes will it take Courtney to
run 1.25 miles?
Answer:
10 minutes
Step-by-step explanation:
1/4 in 2 minutes
1 1/4 = 1/4 x 5
2 x 5 = 10
(That's REALLY good honestly)
5 Heena and Sudha share Profit & Loss equally. Their capitals were Rs.1,20,000 and Rs. 80,000 respectively. There was also a balance of Rs. 60,000 in General reserve and revaluation gain amounted to
Rs. 15,000. They admit friend Teena with 1/5 share. Teena brings Rs.90,000 as capital. Calculate the
amount of goodwill of the firm.
a) Rs.85,000
b) Rs.1,00,000
c) Rs.20,000
d) None of the above
On solving the provided question, we can say that by unitary method, Total capital of the firm = Rs. 85,000
What is unitary method ?The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.
Heena and Sudha share profits and losses equally.
If the capital of Teena is 1/5 of the total capital which is equal to Rs. [tex]90,000[/tex] 1/5 of Total capital = Rs. [tex]90,000[/tex]
Total capital = Rs. 90,000 × 5 = 4,50,000, capital of all partners = Rs. [tex]1,20,000 + Rs. 80,000 + Rs. 90,000 + 60,000 + Rs. 15,000[/tex]
Total capital of all partners = Rs. [tex]3,65,000[/tex]
Total capital of the firm = Rs. [tex]85,000[/tex]
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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.
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A function is given.
g(x) = 1 −
3
4
x; x = −4, x = 3
(a) Determine the net change between the given values of the variable.
(b) Determine the average rate of change between the given values of the variable.
On solving the provided question, we can say that the function is
and f(-2) = -13 and f(0) = 3
What is function?The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.
the function is
= 3 - 4(4)
= 3 - 16
=-13
= 3 - 4(0)
= 3 - 0
= 3
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Sarah, James, and Matthew are on a team in a game show. In the game, Sarah always earns $5$ points, Matthew always earns $-2$ points, and James always earns $3$ points. To calculate their team's score, they multiply the first person's score by the second person's score, then subtract the third person's score. If they can choose the order in which they play the game, what is the maximum possible score that their team can earn?
Answer:
17
Step-by-step explanation:
5 x 3 = 15
15 - (-2) = 17
Sarah goes first, James goes second, and Matthew goes third.
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]
Find the value of b if the graph of y = 0.3x + b goes through the point.
N(5,d)
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.
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
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]
RECORDING SNEET
Naper is buying fabric to make pillows. At the store, 3 yards of
annel fabric costs $12.60, and 5 feet of fleece fabric costs $8.75.
know the units need to be the same to compare the prices.
suy the length of the flannel fabric to feet.
From unit prices gotten, the price of one feet of annel fabric is cheaper than the price of one feet of fleece fabric.
How to find unit prices?A unit price is defined as the price for one item or measurement, such as a pound, a kilogram, or a pint. This can be used to compare the same type of goods sold in varying weights and amounts.
The parameters are;
3 yards of annel fabric costs $12.60
5 feet of fleece fabric costs $8.75.
From conversion units;
1 yard = 3 feet
Thus;
3 yards = 3 * 3 = 9 ft
Thus;
Unit price of Annel fabric = 12.6/9 = $1.4 per ft
Unit price of fleece fabric = 8.75/5 = $1.75 per ft
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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;
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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.
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Answer:
The correct answer is 143.86 gallons
Step-by-step explanation:
its (3,-2) i did the test
Examine the right triangle below, solve for x, round to two decimal places if
necessary.
C
Answer:
Step-by-step explanation:
sinX = 18/32
sinX = 0.5625
X = 34.23
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.
Troy has an album that holds 400 compact discs. Each page of the album holds 4 compact discs. If 66% of the album is empty, how many pages are filled with compact discs?
pages are filled with compact discs.
Troy has an album that holds 400 compact discs, and each page holds 4 compact discs. If 66% of the album is empty, that means that 34% of the album is filled with compact discs. Since each page holds 4 compact discs, that means that 34% of 400 compact discs is 136 compact discs. Since each page holds 4 compact discs, that means that 136 compact discs is 34 pages. Therefore, 34 pages are filled with compact discs.
Answer:
34 pages are full
Step-by-step explanation:
Help me, please!!!!!!!!!
Answer: D, 3x+12
Step-by-step explanation: Distributing a number means that you have to multiply the number by all of the numbers inside the parentheses. 3*x is 3x, and 3*4 is 12. 3x+12 is 3x+12.
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
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The profit a company makes decreases exponentially at a rate of 0.9% per year. In 2014, the profit was $9500. Calculate the profit in 2019.
Answer: $9080.13
Step-by-step explanation:
use the equation y=b(x)^t, where b is the original profit, x is the percent remaining after one year, and t is the amount of years.
SUBSTITUTE:
y=9500(0.991)^5
Use calculator, and y=9080.126 in 2019. Round off to $9080.13
hope this helps!
MM
The frequency diagram shows the heights of students in a class.
a) How many students were over 145 cm?
b) How many students had a height
between 125 cm and 140 cm?
c) How many students were in the class?
a.) The number of students that are over 145cm = 13
b.) The number of students with the height between 125 cm and 140 cm = 21 students.
C.) The number of students that were in class = 37
What is a frequency table?A frequency table is defined as a statistical tool that is used to organize the data given so that it makes it more meaningful and easier to understand.
To calculate the number of students that are over 145cm = 8+4+1 = 13 students.
To calculate the number of students that had a height
between 125 cm and 140 cm = 2+5+6+8 = 21 students.
To calculate the number of students that were in class= 3+2+5+6+8+8+4+1 = 37 students.
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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
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.
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.
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Answer:
15%
Step-by-step explanation:
flip edge
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.
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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.
Need helpppp with this problem!! thanks!
Answer:
20
Step-by-step explanation:
[tex]\sqrt[3]{64xy^{3}}[/tex] = [tex]\sqrt[3]{64}[/tex] × [tex]\sqrt[3]{x}[/tex] × [tex]\sqrt[3]{y^{3}}[/tex]
a = coefficient
= [tex]\sqrt[3]{64}[/tex]
∴a = 4
[tex]x^{b}[/tex] = [tex]x^{-2}[/tex]×[tex]\sqrt[3]{x}[/tex]
= [tex]x^{-2}[/tex]×[tex]x^{\frac{1}{3}}[/tex]
= [tex]x^{-2+\frac{1}{3}}[/tex]
= [tex]x^{\frac{-6}{3} + \frac{1}{3}}[/tex]
= [tex]x^{\frac{-6+1}{3}}[/tex]
[tex]x^{b}[/tex] = [tex]x^{-\frac{5}{3}}[/tex]
∴b = [tex]-\frac{5}{3}[/tex]
[tex]y^{c}[/tex] = [tex]y^{-4}[/tex]×[tex]\sqrt[3]{y^{3}}[/tex]
= [tex]y^{-4}[/tex]× [tex](y^{3})^{\frac{1}{3}}[/tex]
= [tex]y^{-4}[/tex] × [tex]y[/tex]
= [tex]y^{-4 + 1}[/tex]
[tex]y^{c}[/tex] = [tex]y^{-3}[/tex]
∴c = [tex]-3[/tex]
∴Product of a, b and c = [tex](4)[/tex]×[tex](-\frac{5}{3})[/tex]×[tex](-3)[/tex]
= 20
Solving right triangle
Answer:
[tex]BC= 2.23[/tex]
Step-by-step explanation:
We can solve this problem using the trigonometric identity of [tex]sin[/tex].
We know:
[tex]sin(\theta) = \frac{opposite}{hypotenuse}\\\\sin(50 \textdegree) = \frac{?}{3}\\[/tex]
If we solve for [tex]?[/tex] we get:
[tex]3sin(50 \textdegree) \approx 2.23[/tex]
Isaac Newton sat under an apple tree to drink some tea and think. While he was thinking, an apple fell off a branch of the tree. The equation v=(19.8d)12
can be used to find the velocity, in meters per second, of the apple after dropping a distance , in meters. If the apple was connected to a branch 9 meters above the ground, what was the velocity of the apple, to the nearest hundredth, when it hit the ground?
The velocity of the apple, to the nearest hundredth, when it hit the ground is equal to 13.35 meters per seconds.
What is a function?In Mathematics, a function is a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables.
How to determine the velocity of the apple?From the information provided about an apple that fell off a branch of the tree, a function that models the velocity of the apple include the following:
Velocity = (19.8d)^{1/2}
Where:
d represents the distance in meters.
Velocity = (19.8 × 9)^{1/2}
Velocity = (178.2)^{1/2}
Velocity = 13.35 meters per seconds.
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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.
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