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Answer: x =2
Step-by-step explanation: Since the two triangles have to shared sides then all sides must be equal so 9x-12=3x. -6x=-12 and x =2
Answer:
9x=12
so
x=12/9 = 4/3
and
A dry cleaner charges $2.95 to clean a shirt and a different price to clean a pair of pants. Tiwon paid $29.05 to clean 4 shirts and 5 pairs of pants. Which of these number sentences represents the cost to clean a pair of pants? Need help with this !!
Answer:
We can set up an equation using the information provided. Let x be the cost to clean a pair of pants.
The cost to clean 4 shirts is 4*2.95 = $11.80
The cost to clean 5 pants is 5x
The total cost is $11.80 + 5x = $29.05
So, we can represent the cost to clean a pair of pants as:
x = $29.05 - $11.80 / 5
This number sentence shows the cost to clean a pair of pants is x = $4.81
Determine the distance between the points (-2,3) and (5,-3):
The distance between the given 2 points (-2, 3) and (5, -3) is 9.21 units.
What is the distance?The length of the line segment bridging two points on a plane is known as the distance between the points. d=((x2 - x1)2 + (y2 - y1)2) is a common formula to calculate the distance between two points.
This equation can be used to calculate the separation between any two locations on an x-y plane or coordinate plane.
So, we have the points:
(-2, 3) and (5, -3)
Distance formula: d=((x2 - x1)² + (y2 - y1)²)
Insert values and calculate as follows:
d=((5 - (-2))² + (-3 - 3)²)
d=((7)²+(-6)²)
d=√85
d=9.21
Therefore, the distance between the given 2 points (-2, 3) and (5, -3) is 9.21 units.
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What are the answers to these
Step-by-step explanation:
Let’s use the equation: 3|2x-1|-8=-14
3(|2x−1|)−8=−14
Step 1: Add 8 to both sides.
3(|2x−1|)−8+8=−14+83(|2x−1|)=−6
Step 2: Divide both sides by 3.3. (|2x−1|)3=−63|2x−1|=−2
Step 3: Solve Absolute Value. |2x−1|=−2
No solutions. (Absolute value cannot be less than 0.)
HELPPPPPPPPPPPPPPP!!!!!
f(1) = -1
Step-by-step explanation:Quadratic equations form the shape of a parabola, which looks like a U-shape.
Graph
To find f(1) we need to find the y-value when x = 1. To do this, we can just look at the graph. Find where on the graph x = 1, then look for where the graph intersects this value. This graph has an x value of 1 when y = -1. We can see this at the coordinate point (1,-1). Thus, f(1) = -1.
Equation
We can also solve this using the equation of the function. This function is represented by f(x) = x² - 2. Now, to find f(1), plug 1 in for x.
f(1) = 1² - 2f(1) = -1This also shows that f(1) = -1.
1/2(x-5)=9 what is the value of x
Answer:
23
Step-by-step explanation:
1/2-2.5=9
1/2x=9+2.5
x=11.5/0.5
x=23
Find the area of each triangle. Round intermediate values to the nearest tenth. Use the rounded
values to calculate the next value. Round your final answer to the nearest tenth.
The area of the given triangle is 45 square units.
What is the area of a triangle?The area of a triangle is defined as the total space occupied by the three sides of a triangle in a 2-dimensional plane. The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h.
In the given triangle, measure of the side base is 10 units and height is 9 units.
Here, area of a triangle = 1/2 ×10×9
= 45 square units
Therefore, the area of a triangle is 45 square units.
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In June, Lupita saved $115 for retirement. In July, she saved $165. To the nearest percent, what was the increase in Lupita's retirement savings from June to July?
To the nearest percentage point, Lupita's retirement funds increased by 44% from June to July.
What is a percentage?A percentage is a term used in mathematics to describe a value or ratio that may be expressed as a fraction of 100. If we need to calculate a percentage of a number, we should first divide it by 100 before multiplying it by the remainder. Consequently, the percentage refers to a portion per hundred.
Given that Lupita had $115 in her bank account at the beginning of June
The amount Lupita had set aside climbed to $165 in July.
We are expected to calculate the percentage growth in money.
% increase
[tex]= {(165 - 115) / 115 } × 100 = 43.48%. ≈ 44%[/tex]
To the nearest percentage point, Lupita's retirement funds increased by 44% from June to July.
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solve the given differential equation by undetermined coefficients. y'' + 2y = −18x2e2x
The general solution to the differential equation y'' + 2y = −18x^2e^(2x) by undetermined coefficients is y = (-9x^2)e^(2x).
The given differential equation is y'' + 2y = −18x^2e^(2x)
To solve this equation by undetermined coefficients, we first find the characteristic equation of the homogeneous equation, which is r^2 + 2 = 0.
The solutions to this equation are r = i and r = -i. Therefore the general solution to the homogeneous equation is yh(x) = c1 cos(x) + c2 sin(x)
Now, we use the method of undetermined coefficients to guess the form of the particular solution. Since the non-homogeneous term is −18x^2e^(2x), we guess that the particular solution is of the form
yp = (Ax^3 + Bx^2)e^(2x) + Cx^2e^(2x).
Substituting this into the differential equation, we get
y'' + 2y = (6Ax + 2B)e^(2x) + 2Cxe^(2x) = −18x^2e^(2x)
Equating the coefficients of the like terms, we get:
6A = 0, 2B = −18, and 2C = 0
Solving for A, B and C, we get A = 0, B = −9 and C = 0
Therefore, the general solution to the differential equation y'' + 2y = −18x^2e^(2x) by undetermined coefficients is y = (Ax^3 + Bx^2)e^(2x) + Cx^2e^(2x) = (-9x^2)e^(2x)
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An arithmetic sequence is defined by fn = 7 + 8(n – 1). What is the value of f1
Answer:
f(11) = 87
Step-by-step explanation:
substitute n = 11 into f(n) , that is
f(11) = 7 + 8(11 - 1) = 7 + 8(10) = 7 + 80 = 87
I NEED HELP ASAP
8th grade Pre-algebra
Pre-algebra is a primary branch of algebra designed to prepare students for a standard high school algebraic course
In eighth grade, what is Pre-Algebra?Real number system, linear connections, functions, linear equations, systems of equations, geometric concepts such as transformations, Pythagorean Theorem and angle relationships, and scatter plots are all studied.You will learn about and investigate subjects such as integers, order of operations, algebraic expressions, one and two-step equations, proportions, percents, probability, geometry, and linear equations in Pre-Algebra.
Pre-algebra classes are intended to prepare pupils for a typical algebraic curriculum in high school. Integers, fractions, square roots, step equations, linear equations, and decimals are introduced to students. They will also learn how to use variables to solve basic problems.
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Colah Company purchased $2,000,000 of Jackson, Inc., 6% bonds at par on July 1, 2021, with interest paid semi-annually. Colah determined that it should account for the bonds as an available-for-sale investment. At December 31, 2021, the Jackson bonds had a fair value of $2,300,000. Colah sold the Jackson bonds on July 1, 2022 for $1,800,000.
Required:
1. Prepare Colah’s journal entries for the following transactions:
The purchase of the Jackson bonds on July 1.
Interest revenue for the last half of 2021.
Any year-end 2021 adjusting entries.
Interest revenue for the first half of 2022.
Any entries necessary upon sale of the Jackson bonds on July 1, 2022, including updating the fair-value adjustment, recording any reclassification adjustment, and recording the sale.
2. Complete the following table to show the effect of the Jackson bonds on Colah’s net income, other comprehensive income, and comprehensive income for 2021, 2022, and cumulatively over 2021 and 2022.
If Colah Company purchased $2,000,000 of Jackson, Inc., 6% bonds at par on July 1, 2021. The journal entries for the purchase of the Jackson bonds on July 1 is: Debit Available-for-sale securities $2,000,000
Credit Cash $2,000,000.
What is journal entry?Journal entry is used by companies to record their day to day business transaction.
July 1 2021
Debit Available-for-sale securities $2,000,000
Credit Cash $2,000,000
December 31 2021
Debit Cash $60,000
Credit Interest income $60,000
(6% ×$2,000,000 / 2)
December 31 2021
Debit Available-for-sale securities $300,000
Unrealized Gain - Other comprehensive income $300,000
($2,000,000 - $2,300,000)
June 30 2022
Debit Cash $60,000
Credit Interest income $60,000
(6% ×$2,000,000 / 2)
The entry necessary upon sale of the Jackson bonds on July 1, 2022 is:
July 1 2022
Debit Available-for-sale securities $2,300,000
Unrealized Gain-Other comprehensive income account $300,000
Credit Cash $1,800,000
Credit Realized Loss on the sale of Available-for-sale securities $200,000
[$1,800,000 - $2,000,000= $200,000 (Realized Loss)]
2. Table to show the effect of the Jackson bonds on Colah’s net income,
2021 2022 Total
Net Income $60 ,000 ($140,000) ($80,000)
( 60,000 - $200,000= -$140,000)
OCI $300,000 $300,000
Comprehensive Income $360,000 ($140,000) $220,000
Therefore the journal entries for the purchase of the Jackson bonds on July 1 is: Debit Available-for-sale securities $2,000,000
Credit Cash $2,000,000.
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Write a quadratic equation with solutions -3 and 4/7.
1. a. Provide two independent events that you know the probability of.
b. Explain how you know these events are independent.
c. Find the probability that they both occur.
2. a. Provide two dependent events.
b. Explain how you know these events are dependent.
c. Explain why these dependent events might require a different method for calculating the probability of both events occurring.
Example of dependent events and independent events and their probabilities are as given below.
How to provide two independent events with known probability?1. a. Two independent events that I know the probability of are:
Rolling a fair die and getting a 4 (probability of 1/6)
Flipping a fair coin and getting heads (probability of 1/2)
b. I know these events are independent because the outcome of one event does not affect the outcome of the other event. The outcome of rolling a die does not affect the outcome of flipping a coin, and vice versa.
c. The probability of both events occurring is (1/6) × (1/2) = 1/12
2a. Two dependent events:
i. Drawing a red card from a deck of cards and then drawing another card (without replacement)
ii. Drawing a red ace and then drawing another red card (without replacement)
b. I know these events are dependent because the outcome of the first event affects the outcome of the second event. The probability of the second event depends on the outcome of the first event.
c. These dependent events might require a different method for calculating the probability of both events occurring, such as conditional probability.
The probability of both events occurring would be P(A and B) = P(A) × P(B|A)
where P(A) is the probability of the first event and P(B|A) is the probability of the second event given that the first event has occurred.
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A teacher gave her students two tests. If 45% of the students passed both tests and 60% passed the first test. What is the probability that a student who passed the first test also passed the second?
Answer: We can use the concept of conditional probability to find the probability that a student who passed the first test also passed the second. Conditional probability is the probability of an event occurring given that another event has already occurred.
The probability that a student who passed the first test also passed the second is the probability of both events occurring (passing both tests) divided by the probability of the first event occurring (passing the first test).
We can use the information provided to calculate this probability:
Probability of passing both tests = 0.45 (45%)
Probability of passing the first test = 0.60 (60%)
Probability of passing both tests given that the student passed the first test = (Probability of passing both tests) / (Probability of passing the first test) = 0.45 / 0.60 = 0.75
So the probability that a student who passed the first test also passed the second is 0.75 or 75%.
It means, if we know that a student passed the first test, there's a 75% chance that the student also passed the second test.
Step-by-step explanation:
What is Lateral surface area?
Answer:
The lateral surface of an object is all of the sides of the object, excluding its base and top (when they exist). The lateral surface area is the area of the lateral surface. This is to be distinguished from the total surface area, which is the lateral surface area together with the areas of the base and top.
Can someone help I will give all stars!!! Please help! I’ll help you aswell
Answer:
D) y = 5/3x - 7
A) 5/3
Step-by-step explanation:
5x - 3y = 21 Subtract 5x from both sides
5x - 5x - 3y = -5x + 21
-3y = -5x + 21 Divide all the way through by -3
[tex]\frac{-3y}{-3}[/tex] = [tex]\frac{-5}{-3}[/tex] x + [tex]\frac{21}{-3}[/tex]
y = [tex]\frac{5}{3}[/tex] x = 7
The slope is the number before the x 5/3
Prove that the bisectors of two supplementary angles are perpendicular to each other.
the bisectors of two supplementary angles are perpendicular to each other is proved along with the given diagram.
What is an angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.
Here, we have,
from the given diagram we get,
∠BOP=x & ∠AOP=180-x
and, ∠NOP=x/2 & ∠MOP=(90-x/2)
Now,
∠MON=∠MOP+∠NOP
=90-x/2 + x/2
=90
Hence, it is proved that the bisectors of two supplementary angles are perpendicular to each other.
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Mr. Coupe and his friend have 2,798
paddle balls to split among 40 hoppers.
How many will be in each hopper?
MULTIPLICATION
Estimate:
Solve:
DIVISION
Answer:
To find out how many paddle balls will be in each hopper, you can divide the total number of paddle balls by the number of hoppers.
paddle balls ÷ hoppers = paddle balls per hopper
2798 ÷ 40 = 69.95
So there will be approximately 69.95 paddle balls in each hopper. Since it's not possible to put 0.95 of a paddleball in a hopper, you can round it to the nearest whole number. This means each hopper will have 70 paddleballs.
Step-by-step explanation:
Find the perimeter of the triangle 4 square root 16
Answer:
I beleive 4
Step-by-step explanation:
let me know if im wrong
(4-347-12)-(8+7-27)
PLEASE HELPPPP
Answer:
=4-347-12-8-7+27
=-343
*Mark me brainliest -_- *_*
Answer: (4-347-12)-(8+7-27)= -343
Which point on the number line represents the difference 2.6 - 1.2?
The answer is 1.4
What is the number line?In elementary mathematics, a number line is a picture of a graduated straight line that serves as visual representation of the real numbers. Every point of a number line is assumed to correspond to a real number, and every real number to a point.
Given here:
2.6-1.2=1.4
Hence, The answer is 1.4
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Show the relationship between the number of miles and the number of hours in the ratio 24 to 2
The ratio of miles to hours is 24 to 2, which can be written as 24:2 or 12:1.
What is the ratio?
A ratio is a mathematical comparison of two or more quantities. It is used to show the relationship between the sizes of different quantities or amounts. It is typically expressed as a ratio of two numbers, such as 24:2, with a colon separating the numbers.
The ratio of miles to hours is 24 to 2. This can also be written as 24:2 or 12:1. It means that for every 24 miles, 2 hours are required to travel that distance.
Hence, The ratio of miles to hours is 24 to 2, which can be written as 24:2 or 12:1.
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Aunt Sue used 1/6 teaspoon of vanilla to make 2/12 containers of pudding. How much vanilla is in one container of pudding?
The amount of vanilla in one container of pudding is given as follows:
One teaspoon.
How to obtain the amount of vanilla?The amount of vanilla in one container of pudding is found applying the proportions in the context of the problem, via a rule of three.
The rule of three is defined as follows:
1/6 teaspoon - 2/12 containers.
x teaspoon - 1 container.
The first line can be simplified as follows:
1/6 teaspoon - 1/6 containers.
(as 2/12 = 1/6).
Hence there is one teaspoon of vanilla in one container of pudding.
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A shopkeeper buys 1800 eggs st $1.20 per dozen. 5% of the eggs are rotten. Find the selling price of each egg if he wants to earn 33% profit on the cost price
$0.14 is the selling price of each egg.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that shopkeeper buys 1800 eggs $1.20 per dozen.
1 dozen = 12 eggs
So 1.20 ÷ 12 = $0.1 cost of one egg
Total cost (C) 1800×0.1 = $180
1800×0.95 = 1710 eggs to be sold
Profit % = 100×(SP - C)/C
33 = 100×(SP - 180/180
SP = $239.4
239.4 ÷ 1710 = $0.14 is the selling price of each egg.
Hence, $0.14 is the selling price of each egg.
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A diamond speculator used the line with equation
y = 5000x250 to estimate the price of diamond
rings.
5) What would the speculator predict fot he price of the
0.29-carat diamond ring?
6) What would the speculator predict fot he price of the
0.21 -carat diamond ring?
A speculator estimates that the price of the 0.29 carat diamond ring will be y = 1200 by y = 5000x - 250.
what is equation ?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to express the connection between two phrases on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
given
y = 5000x - 250
y = 5000 * 0.29 - 250
y = 1200
A speculator estimates that the price of the 0.29 carat diamond ring will be y = 1200 by y = 5000x - 250.
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A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation.
Using this equation, find the maximum height reached by the rocket, to the nearest tenth of a foot.
У = -16x^2 + 246x + 100
The rocket reaches a maximum height of 1045.6 feet.
How to find the maximum height of a parabola by quadratic formula
The height of the rocket under free fall is described by a parabola and parabolas are explained by second order polynomials, whose form are:
y = a · x² + b · x + c
Where:
a, b, c - Real coefficients.x - Time, in seconds.y - Height, in feet.The maximum height can be found by means of discriminant of the quadratic formula associated with following variant:
a · x² + b · x + (c - y) = 0
Discriminant
b² - 4 · a · (c - y) = 0
b² = 4 · a · (c - y)
b² / (4 · a) = c - y
y = c - b² / (4 · a)
If we know that a = - 16, b = 246 and c = 100, then the maximum height reached by the rocket is:
y = 100 - 246² / [4 · (- 16)]
y = 1045.563 ft
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What is 249 rounded to the nearest 10?
Answer: 250
Step-by-step explanation:
249 is closer to 250 than 240
Answer:
Step-by-step explanation:
249 is rounded to closest to 250
Which linear system could the graph represent?
Responses
A 4x + 4y = 4
x + y = 14x + 4y = 4 x + y = 1
B 2x − y = 4
x + 2y = −32x − y = 4 x + 2y = −3
C −x + y = 2
x + 2y = 2−x + y = 2 x + 2y = 2
D x + y = 2
2x + 2y = 8x + y = 2 2x + 2y = 8
Question 2
The system represented by the graph has how many solutions?
Responses
A 1
B 2
C 0
D infinitely many
The linear system could the graph represent is, x + y = 2 & 2x + 2y = 8
So, Option D is correct.
What is the equation of line?The equation of a straight line is a relationship between x and y coordinates, The equation of a straight line for given two points is y-y₁ = y₂-y₁/x₂-x₁(x-x₁)
Given that,
The graph of linear system
first line intersects the x & y axes at (2,0) & (0,2) respectively
Similarly, second line intersects the x & y axes at (4,0) & (0,4) respectively
By using two point form of the line we can write equation for both the lines,
x + y = 2 _____ (1)
x + y = 4 _____ (2)
by multiplying 2 in equation (2)
2x + 2y = 8
Hence, The linear system is x + y = 2 & 2x + 2y = 8
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In a random sample of 8 customers, what is the probability that exactly 4 of them will use the Self-Checkout?
In the box below, give your answer correct to 3 significant figures. If you are correct, you will receive a CORRECT message here.
The binomial probability that exactly 4 out of 8 customers will use the Self-Checkout is 0.008.
What is binomial probability?Binomial probability is the probability based on the binomial distribution.
The binomial distribution is used in statistics to summarize the likelihood that a value will take one of two independent values (for example, success or failure) under a given set of parameters or assumptions.
The binomial distribution formula is:
Pₓ = {ⁿ \ ₓ} pˣ qⁿ ⁻ ˣ
P = binomial probability
x = number of times for a specific outcome within n trials
{ⁿ \ ₓ} = number of combinations
p = probability of success on a single trial
q = probability of failure on a single trial
n = number of trials
Random sample, n = 8
Specific outcome within n trials = 4
pˣ = 0.5⁴
= 0.0625
qⁿ = (1 - 0.5)⁸ ⁻ ⁴
= 0.5⁴
= 0.0625
Pₓ = {ⁿ \ ₓ} pˣ qⁿ ⁻ ˣ
= 8/4 x 0.0625 x 0.0625
= 2 x 0.0625 x 0.0625
= 0.0078125
= 0.008
Thus, the probability of precisely 4 customers using the Self-Checkout is 0.008.
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