When subtracted -2a+7b=-5 from the other equation so the b-terms become opposites, we get 2a -7b = 5 as the result.
What is equation?In mathematics, an equation is an expression or a statement made up of two algebraic expressions with the same value that are separated by the equal sign. It is a mathematically quantified version of an otherwise expressed statement. Equations can take many different forms. Equations are used to compare two expressions.
To Subtract -2a+7b=-5 from the other equation so the b-terms become opposites, we need to make +7b to -7b
This is only possible when the other term has 14,
Lets solve
2a + 7b = - 5
- 4a + 14b = -10
-2a -7b = 5
Thus, when subtracted -2a+7b=-5 from the other equation so the b-terms become opposites, we get 2a -7b = 5 as the result.
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Stefan sells Jin a bicycle for $146 and a helmet for $19. The total cost for Jin is 150% of what Stefan spent originally to buy the bike and helmet. How much did Stefan spend originally? How much money did he make by selling the bicycle and helmet to Jin?
Stefan spend price $110 and made price $60 by selling bicycle and helmet to Jin.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100.
Here, given that,
Selling price of bicycle = $146
Selling price of helmet = $19
Total = 146+19= $165
Let,
x represents the original cost Stefan to buy the bike and helmet.
150% of x = $165
1.5x=$165
Dividing both sides by 1.5
we get ,
x=$110
Stefan bought bicycle and helmet for $110.
Profit made by Stefan = Selling price - buying price
Profit made by Stefan = 165-110= 55
Hence, Stefan spend price $110 and, made $55 by selling bicycle and helmet to Jin.
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Under his cell phone plan, Gabriel pays a flat cost of $52.50 per month and $5 per gigabyte. He wants to keep his bill under $75 per month. Write and solve an inequality which can be used to determine 9, the number of gigabytes Gabriel can use while staying within his budget.
The number $m$ is a three-digit positive integer and is the product of the three distinct prime factors $x$, $y$ and $10x y$, where $x$ and $y$ are each less than 10. What is the largest possible value of $m$
largest possible value of $m$ is x=5, y =3, 10*5+3=53: 3 x 5 x 53 =795
What is prime factors ?A prime factor is a natural number, other than 1, whose only factors are 1 and itself. The first few prime numbers are actually 2, 3, 5, 7, 11, and so on.The simplest algorithm to find the prime factors of a number is to keep on dividing the original number by prime factors until we get the remainder equal to 1. For example, prime factorizing the number 30 we get, 30/2 = 15, 15/3 = 5, 5/5 = 1. Since we received the remainder, it cannot be further factorizedPrime factorisation is a method to find the prime factors of a given number, say a composite number. These factors are nothing but the prime numbers. A prime number is a number which has only two factors, i.e. 1 and the number itself.For example, 2 is a prime number which has two factors, 2 × 1. Whereas a composite number has more than two factors present in it. For example, 4 has three factors such as 1 × 2 ×To learn more about prime factors refers to:
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A carpenter needs to be sure that a frame he has built is rectangular. He knows that the opposite sides of his frame are congruent. Which additional fact would be sufficient to prove that the frame is a rectangle?
A)
If two adjacent angles are supplementary, then the frame must be rectangular.
cross out
B)
If the adjacent sides are also congruent, then the frame must be rectangular.
cross out
C)
If opposite angles are congruent, then the frame must be rectangular.
cross out
D)
If one angle is a right angle, then the frame must be rectangular
The answer is D) If one angle is a right angle, then the frame must be rectangular,
What is angle?An angle is a measure of the amount of rotation between two lines or planes. It is measured in degrees or radians. Angles are formed by the intersection of two lines, called the sides of the angle, and a point, called the vertex of the angle. There are different types of angles such as acute angle, right angle, obtuse angle, and straight angle.
What is rectangle?A rectangle is a four-sided polygon with four right angles. It has opposite sides that are parallel and congruent, and the opposite angles are also congruent. A rectangle can be defined by its length and width or by the coordinates of its vertices. Rectangles are a special case of parallelograms, which have opposite sides parallel but not necessarily congruent. The special properties of rectangles make them a popular shape in design and construction, such as in building and engineering.
A rectangle is defined as a four-sided polygon with four right angles. Opposite sides of a rectangle are congruent, but adjacent sides may or may not be congruent. Therefore, A and B are not sufficient to prove that the frame is a rectangle. Also, two adjacent angles being supplementary does not guarantee that the frame is a rectangle. The only way to be sure that the frame is a rectangle is if it has one right angle, this is the only way to ensure that all angles are right angles. Therefore, D) is the correct answer.
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How do you match a logarithmic function with its graph?
Matching a logarithmic function with its graph can be done by understanding the key characteristics of logarithmic functions and how they are represented on a graph.
A logarithmic function is of the form y = log base b (x), where b is the base of the logarithm (usually 10 or e).
The graph of a logarithmic function is a reflection of the exponential function of the same base b, across the line y=x.
Here are some key characteristics of logarithmic functions and their corresponding graphs:
1) Asymptote: The graph of a logarithmic function has a vertical asymptote at x=0, since the logarithm of a non-positive number is undefined.
2) Domain: The domain of a logarithmic function is x>0, since the logarithm of a negative number is undefined.
3)Range: The range of a logarithmic function is all real numbers
4) Increasing or decreasing: A logarithmic function is increasing over its domain
5) Shape: The graph of a logarithmic function is concave down.
6) x-intercept: The x-intercept of the graph is (1,0), since the logarithm of 1 is always 0.
By keeping these characteristics in mind, you can match a logarithmic function with its graph by observing the shape, asymptote, domain and range of the graph.
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PLEASE HELP I WILL GIVE FIVE STARS AND BRAINLIEST Transformation and plot image.
Answer: You need to drew , this arrow , to each point K,L,M,N,
Drawing must be parallel to , this arrow, AND , exactly the same length, as the arrow .
step 2. when you drew it , then at the end are your new points, K",L",M",N".
Ok?
step 3.
Then you just read the coordinates. of new points .
I would gladly drew it , but I do not knew how to put picture in this , jet .
Step-by-step explanation:
What kind of triangle has 25 90 65?
25-90-65 is a right-angle triangle because one of the angles is 90°.
A right-angle triangle or orthogonal triangle is a triangle in which one angle is a right angle (that is, a 90-degree angle), and two sides are perpendicular. The relationship between the sides and angles of the right triangle is the basis for trigonometry.
The hypotenuse is the facing side to the right angle. Legs are the adjoining sides to the right angle.
Properties of right angle triangle:
The right angle is the largest angle in a right-angle triangle.The hypotenuse, the opposite of the right angle, is the longest side.There are no obtuse angles in a right-angle triangle.Read more about right-angle triangles:
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help please and thank you
The equation that represents the situation is
2p + 194.99 = 284.97
Option B is the correct answer.
The price of each game is $44.99.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Game system price = $194.99
Total price = $284.97
194.99 + 2 games = $284.97
Games = p
Now,
The price of each game.
194.99 + 2p = 284.97
2p = 284.97 - 194.99
2p = 89.98
p = 44.99
Thus,
The equation is 194.99 + 2p = 284.97.
The price of each game is $44.99.
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Karime walks 3/4 of a mile each day for 5 days. The number of miles karime walks altogether is between which two whole numbers? Lacey chose A that is 0and1 as the correct answer how did she get that answer?
On solving the provided question, we can say that - by fraction we karime walks = 3/4 so, 3/4 X 5 = 15/4
what is fraction?Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.
karime walks = 3/4
for = 5 days
so, 3/4 X 5 = 15/4
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BRAINLIEST FOR THIS QUESTION
A shop sells orange juice in the following ways: 500 ml bottle for £1.40 2 litre carton for £2.50 each or 2 cartons for £4.50 3 litre carton for £3.50 What's the cheapest way of buying exactly 7 litres with no extra? Find the amount of each type of bottle or carton you need and the total cost of buying 7 litres.
The cheapest way of buying exactly 7 litres with no extra is buying 500 ml bottle for £1.40
The amount of buying 7 litres of orange juice at the cheapest buy is £2.52
What is the cheapest buy?500 ml bottle for £1.40
Convert ml to liters:
500 ml = 0.5 liters
Unit rate = 0.5/1.40
= £0.36 per liter
2 litre carton for £2.50
Unit rate = 2/2.50
= £0.8 per liter
2 cartons for £4.50
Unit rate = 2/4.50
= $0.44 per carton
3 litre carton for £3.50
Unit rate = 3 / 3.50
= £0.86 per liter
The cheapest buy per liter of the orange juice is buying 500 ml bottle for £1.40.
Therefore, the cost of 7 liters at the cheapest buy
= £0.36 per liter × 7
= £2.52
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6. Subtract and simplify. 1/6m- (-5/8m + 1/3)
Answer:
19/24m-1/3
Step-by-step explanation:
Emily is using glass to make a display case in the shape of a triangular prism the net of the display shown exactly how much glass is needed to make a display case
The net of the display consists of one rectangle and two right triangles. 168 ft² is needed to make a display case. Hence option D is the correct option.
What is surface area?
The size of a patch on a surface is determined by its area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
The surface area of the triangular prism is the display area of the glass.
The surface area of a triangular prism consists of one rectangle and two right triangles.
The length of the rectangle is (10ft + 6 ft + 8ft) = 24ft.
The width of the rectangle is 5 ft.
The area of a rectangle is the product of length and width.
The area of the rectangle is 24ft × 5ft = 120 square ft
The length of the base of the triangle is 8 ft and the height is 6ft
The area of the triangle is 1/2 × base × height = 1/2 × 8 × 6 = 24 square ft
The display area is 120 square ft + 2 ×24 square ft = 120 + 48 = 168 ft².
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In a sale, the normal price of a car has been reduced by 30%. The new price is £6300, what was the normal price
The normal price of the car is given as follows:
£9000.
How to obtain the normal price of the car?The normal price of the car is obtained applying the proportions in the context of this problem.
In a sale, the normal price of a car has been reduced by 30%. The new price is £6300, meaning that 70% of the price x is equivalent to 6300.
Thus the equation used to obtain the value of x is given as follows:
0.7x = 6300
x = 6300/0.7
x = £9000.
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Tran is making fasnachts (deep-fried German doughnuts) to sell the
Tuesday before Ash Wednesday, her bakery's biggest fasnacht day of
the calendar year. She has 8 pounds of butter and her recipe calls for
1/4 cup of butter per 2 dozen
fasnachts. If 1 pound of butter is 2 cups,
then how many individual fasnacht doughnuts will Tran be able to
make?
Answer:
1,536
Step-by-step explanation:
1 pound equals 2 cups, so 8 pounds will be 16 cups.
[tex]\frac{16}{\frac{1}{4} }[/tex] = 16 x 4 = 64
She can make 64 2 dozen fasnachts. There are 24 fasnachts in 2 dozen.
64 x 24 = 1536 individual fasnachts doughnuts.
Identify the independent variable and the dependent variable. A pool store owner wants to determine the effect of algaecide brands on the treatment of pool water with algae. He contacts customers who have purchased the brands of algaecide and asks their opinion of the algaecide.
The independent variable is the brand of algaecide. The dependent variable is the treatment of pool water with algae.
What is the independent and dependent variable?
In mathematical modeling, statistical modeling, and experimental sciences, there are dependent and independent variables. Dependent variables get their name because, during an experiment, their values are investigated under the presumption or requirement that they are dependent on the values of other variables due to some law or rule.
Here, we have
Given
A pool store owner wants to determine the effect of algaecide brands on the treatment of pool water with algae. He contacts customers who have purchased the brands of algaecide and asks their opinion of the algaecide.
We have to determine the independent variable and the dependent variable.
We concluded that the independent variable is the brand of algaecide and the dependent variable is the treatment of pool water with algae.
Hence, the independent variable is the brand of algaecide and the dependent variable is the treatment of pool water with algae.
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Annie round $280. 05$ to the nearet hundred. Bobby round $280. 05$ to the nearet ten. Ciro round $280. 05$ to the nearet integer. Denie round $280. 05$ to the nearet tenth. What i the um of Annie' anwer, Bobby' anwer, Ciro' anwer, and Denie' anwer?
The sum of Annie's, Bobby's, Ciro's, and Denise's answers is $ 1140.1.
What is rounding off the numbers?A number is simplified when it is rounded off, preserving its value while moving it closer to the next number. It is done for whole numbers as well as decimals at various places of hundreds, tens, tenths, etc.
If the number following the decimal is between 0 and 4, a number may be rounded off to its lowest value. If the number after it is between 5 and 9, the number will be rounded off to a greater value.
Annie rounds $ 280.05 to the nearest hundred
$ 280.05 will be equal to $ 300
Bobby rounds $ 280.05 to the nearest ten
$ 280.05 will be equal to = $ 280
Ciro rounds $ 280.05 to the nearest integer
$ 280.05 will be equal to = $ 280
Denise rounds $ 280.05 to the nearest tenth
$ 280.05 will be equal to = $ 280.1
Then, the sum of Annie's answer, Bobby's answer, Ciro's answer, and Denise's answer = $ 300 + $ 280 + $ 280 + $ 280.1 = $ 1140.1
Therefore,
The sum of Annie's, Bobby's, Ciro's, and Denise's answers is $ 1140.1.
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pleaseeeeeee someone help me asappp i need help so bad.
The slope of the linear equation that passes through the points (-6, -2) and (3, -2) is 0.
How to find the slope with the two known points?We can write a linear equation using the sope-intercept form as:
y = m*x + b
Where m is the slope and b is the y-intercept.
For any linear equation, if we know that the line passes through two known points (x₁, y₁) and (x₂, y₂), then the slope is given by:
m = (y₂ - y₁)/(x₂ - x₁).
In this case we know that the line passes through the points (-6, -2) and (3, -2).
Then the slope will be:
m = (-2 + 2)/(3 + 6) = 0
m = 0
The slope is zero, meaning that this is an horizontal line.
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What should be added to XXYY to obtain 2x² 3xy?
(a) x² + 2xy - y² must be added to x² + xy + y² to get 2x² + 3xy. (b) 5a + b -6 must be subtracted from 2a + 8b + 10 to get -3a + 7b + 16.
a)
Here we are given the expression x² + xy + y²
Now we need to add something so that this expression becomes x² + 3xy
Let the expression to be added be p.
Hence we get
x² + xy + y² + p = 2x² + 3xy
or, p = 2x² + 3xy - (x² + xy + y²)
or, p = 2x² + 3xy - x² - xy - y²
or, p = x² + 2xy - y²
Hence, x² + 2xy - y² must be added.
b)
Here we are given the expression 2a + 8b + 10
We need to subtract another expression to get -3a + 7b + 16
Let the expression be t. Hence we get
2a + 8b + 10 - t = -3a + 7b + 16
or, t = 2a + 8b + 10 - (-3a + 7b + 16)
or, t = 2a + 8b + 10 + 3a - 7b - 16
or, t = 5a + b - 6
Hence 5a + b - 6 must be subtracted,
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Correct Question
(a) What should be added to x² + xy + y² to obtain 2x² + 3xy?
(b) What should be subtracted from 2a + 8b + 10 to get -3a + 7b + 16?
Which is greater, 1 2cup or 1 3cup? How much greater *fractions*
Answer:
Step-by-step explanation:
A half of a cup is greater than 1/3 of a cup. This is because if you convert the fractions to the nearest common denominator (6) you can see that 1/2 = 3/6 and 1/3 = 2/6, so 1/2 of a cup is greater.
I hoped this helped!!
Question 2
In 2007 the US Census Bureau reported that 71.3% of American families owned their
homes. The city council is debating on whether to offer tax breaks to first time
homebuyers, but they only want to do so if there is strong evidence that the rate of
home ownership has increased since 2007 since it will cost the city money to do so.
a) What are the null and alternative hypothesis?
b) Describe a Type I error in context along with the consequence.
c) Describe a Type Il error in context along with the consequence.
d) Which is a more serious error in this context? Justify your answer
e) For each type of error, tell who would be harmed.
(These are questions to answer, not answer choices.)
The answer to all the questions is explained below with justifications.
What is hypothesis testing?In statistics, the process of hypothesis testing involves putting an analyst's presumption about a population parameter to the test. The type of data used and the purpose of the study will determine the methodology the analyst uses.
a) The null hypothesis[tex](H_o)[/tex] is that 71.3% or more of American families owned their homes.
The alternative hypothesis[tex](H_1)[/tex]is less than 71.3% of American families owned their homes.
b) The type I error is the null hypothesis is true but we assumed it to be false that is 71.3% or more of American families owned their homes but the council did not provide tax breaks.
The type II error is the null hypothesis is false and we assumed it to be true
that is less than 71.3% of American families owned their homes and the council provides tax breaks.
c) The consequences of the type II error would be the council will provide tax breaks to more people and it would cost them a large amount of money.
d) Type II error is more serious in this context as the council has to lay off a large amount as compared to individual homeowners who already can afford to buy a house.
e) For type I error house owners will be harmed and for type II error counsel will be harmed.
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Find the slope (2,2) and (6,8)
Therefore the slope of the line joining the points (2,2) and (6,8) is equal to 2/3.
What is meant by slope?
A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).
The formula for finding the slope of a line is [tex]m= \frac{X2-X1}{Y2-Y1}[/tex].
Where (X1, Y1) and (X2, Y2) are the points on the line.
The given points are (2,2) and (6,8).
Therefore slope is
[tex]m=\frac{6-2}{8-2} \\m=\frac{4}{6} \\m=\frac{2}{3}[/tex].
The slope is 2/3.
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6.36 CAR COLORS Choose a new car or light truck at random and note its color. Here are the probabilities of the most popular colors for vehicles made in North America in 2000:5 Color: Silver White Black Dark green Dark blue Medium red Probability: 0.176 0.172 0.113 0.089 0.088 0.067 (a) What is the probability that the vehicle you choose has any color other than the six listed
The probability that the vehicle you choose has any color other than the six listed is 0.295.
In the given question, the probabilities of the most popular colors for vehicles made in North America in 2000 is given as:
Color: Silver White Black Dark green Dark blue Medium red
Probability: 0.176 0.172 0.113 0.089 0.088 0.067
We have to find the probability that the vehicle you choose has any color other than the six listed.
P(the probability that the vehicle you choose has any color other than the six listed) = 1 - (the sum of the vehicle that are listed)
P(the probability that the vehicle you choose has any color other than the six listed) = 1 - (0.176 + 0.172 + 0.113 + 0.089 + 0.088 + 0.067)
P(the probability that the vehicle you choose has any color other than the six listed) = 1 - 0.705
P(the probability that the vehicle you choose has any color other than the six listed) = 0.295
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Mila cuts a sphere with a 13-inch radius in half. Whats the area of the cross section of the sphere in square inches in terms of pi
The area of the cross-section of the sphere in square inches in terms of pi will be 169π inch^2.
The area of a two-dimensional shape created when a three-dimensional object, like a cylinder, is cut perpendicular to a predetermined axis at a point is known as the cross-sectional area.
An area is projected onto the plane when a plane slices through a solid object. The axis of symmetry is then perpendicular to that plane. The cross-sectional area refers to its projection.
The cross-section of a sphere is a circle. Hence the area of the cross-section is the area of a circle with a radius of 13, which is given by π*r^2
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Which expression is equivalent to 2x² 4 3x² 2x 7?
Given Expression is equivalent to 5x^2 - 2x + 3 With the Same Variable and exponent we have added or subtracted their constant value.
First, try to learn what is an expression.
Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4x+ 15, for instance, the terms 4x and 15 are separated from the variable x by the arithmetic sign +.
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
The following components make into a mathematical expression:
Constant, Variables, Terms, Operators.
Given expression is (2x^2-4) - (-3x^2+2x-7)
let's Multiply - sign inside the bracket.
2x^2 - 4 + 3x^2 - 2x + 7
With the Same Variable and exponent and their constant value, we can perform mathematical operations like addition, multiplication, and subtraction.
2x^2 + 3x^2 = 5x^2
5x^2 - 2x + 3.
Given Question is incomplete complete question here.
Which expression is equivalent to
[tex](2x^2-4)-(-3x^2+2x-7)[/tex]
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Analyze and Persevere
Javi is building
a birdhouse. Each of the four walls of the
birdhouse needs to be 5.5 inches long.
Javi has a piece of board that is 24.5 inches
long. Is the board long enough to be
cut into the four walls of the birdhouse?
Estimate using compatible numbers.
Consequently, the solution of the given problem of perimeter comes out to be 24.5 inches will be adequate to build the bird house, which needs 24 inches.
Define perimeter.The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges.
Here,
As stated, Hodi is making a birdhouse.
Four walls make up a birdhouse.
There must be 5.5 inches on each wall.
Board = 24.5 inches for Hodi.
Using comparable numbers, we must now estimate.
6 in. is a suitable size for 5.5 in.
The entire amount of wood needed to construct the bird home will be determined first.
The amount of board needed is equal to the number of walls in the house times the length of each wall.
Required total board: 4 x 6 = 24 inches for a wall count multiplied by the length of each wall.
It takes 24 inches of board in total.
His board is 24.5 inches long.
Consequently, the solution of the given problem of perimeter comes out to be 24.5 inches will be adequate to build the bird house, which needs 24 inches.
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How many zeros are at the end of the product $25 \times 240$?
Answer: There are three 0s
240 x 25 = 6000 and there are three 0s in 6000
For the initial 90 miles of a flight, the pilot heads 8° off course in order to avoid a storm. The pilot then changes direction to head toward the destination for the remainder of the flight, making a 157° angle to the first flight course. Determine the total distance of the flight
A. 48.4
B. 135.9
C. 138.4
D. 228.4
In the above scenario, note that the total distance of the flight is given as: 48.4 miles (approximately). This is solved using the law of Sines to find x.
What is the law of Sines?The connection between the sides and angles of non-right (oblique) triangles is defined by the Law of Sines. Simply put, it asserts that the ratio of the length of a triangle's side to the sine of the angle opposite that side is the same for all triangle sides and angles.
Thus, with regard to the problem modeled in the attached triangle, because two angles are given, the missing angle is 180° − (157° + 8°) or 15°. Use the Law of Sines to find x.
Using the law of ins we can state that:
Sin 8°/x = sin 15°/90
90 (Sin 8°) /x = Sin 15°
90 Sin 8° = x Sin 15°
90 Sin 8° / Sin 15° = x
90 (0.13917310096)/ 0.2588190451 = x
Thus,
x = 48.3951213156
x [tex]\approx[/tex] 48.4
Thus, the distance of the flight is approximately 48.4 miles.
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What coins would I need to make 77 cents fewest possible
Answer:
Step-by-step explanation: Two quarters, 50 pennies: N = 52 (N+1 = 53) One quarter, 75 pennies: N = 76 (N+1 = 77) 100 pennies, N = 100 (N+1 = 101) 6 nickels, 70 pennies: N = 76 (N+1 = 77)
Answer:
2 quarters, 2 dime's, 1 Nickel, 2 penny's
Step-by-step explanation:
Well u well need to quarters because 2 quarters are $25 cent then u well need 2 dimes because when your counting dime's that 10 20 30 40 50 so to dime's and 1 Nickel that makes $75 cents so u need 2 penny's and that makes 77
What is ideal or real solution?
Answer:
An Ideal solution follows the Raoult's law strictly
A Real solution shows deviation from the Raoult's law.
Step-by-step explanation:
−4 1 + 2/3 × 3/5 ÷(−2/5 )
the answer to −41 + 2/3 × 3/5 ÷(−2/5 ) is -42