What is 4 5 as an equivalent fraction?.

Answer:

y = 7x + 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + b ( m is the slope and b the y- intercept )

here m = 7 , then

y = 7x + b ← is the partial equation

to find b substitute (1, 8 ) into the partial equation

8 = 7(1) + b = 7 + b ( subtract 7 from both sides )

1 = b

y = 7x + 1 ← equation of line

The domain of a function is the complete set of possible values of the independent variable, i.e., x-coordinates.

Let y = f(x) be a function with independent variable x and dependent variable y. If a function f provides a way to successfully produce a single value y using values of x for that purpose, then the chosen x-value is said to belong to the domain of f . When finding your domain, keep the following in mind:

In general, you determine the domain of a function by finding the values of the independent variable (usually, x) that we can use. Consider function y = sinx as an example , As we know the range of sinx is lie between −1 and 1. The domain of y = sin x is "all values of x", since there are no restrictions on the values for x. All those values of x for which the fi sinx value in [-1,1] interval are belongs to domain set. Graph of functions also help to find out domain and range set.

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Answer:

d) x[tex]\geq 4[/tex]

Step-by-step explanation:

Answer:

option d is correct ok hope it helps

The solution to the system of inequalities given by x + y > −2 and −x + y < 1 is the ordered pair that lies under the conditions x > -3/2 and y > -1/2. One of which is (1, 0).

An inequality is a statement about the relative size or order of two values. It's a statement that one value is greater than, less than, greater than or equal to, less than or equal to, or not equal to another value. It's represented using mathematical symbols such as <, >, ≤, ≥, ≠.

To find the solution to a system of inequalities, rewrite any of the two inequalities as y in terms of x.

x + y > -2 can be rewritten as y > -x - 2

Substitute the value of y into the other inequality.

-x + y < 1 will become -x + (-x - 2) < 1

Solve for the value of x.

-x + (-x - 2) < 1

-2x -2 < 1

-2x < 1 + 2

-2x < 3

2x > -3

x > -3/2

Plug in the value of x into the equation of y and solve for y.

y > -x - 2

y > -(-3/2) - 2

y > -1/2

So, the solution of the system of inequalities will be the region where both of these conditions, x > -3/2 and y > -1/2, are true, which is the area where the graph of y > -x - 2 and y < x + 1 overlap.

One ordered pair (1 , 0) is a solution to the system of inequalities x + y > -2 and -x + y < 1.

We can check it by plugging in the ordered pair into the inequalities.

x + y > -2 becomes 1 + 0 > -2 which is true

-x + y < 1 becomes -1 + 0 < 1 which is true

So (1,0) satisfies both inequalities.

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Answer:

6 12 18 24

Step-by-step explanation:

i think you mean finding a multiple of 6 in between 1 and 25. how it will work is times 6 until you get out of the 25 range 1x 6 = 6 2x6 = 12 3x6 = 18 and 4x6 = 24 5x 6 = 30 which is not between 1 and 25. pick any of these four to  answer with

The 4 inverse operations in math are addition, multiplication, square root and cube root.

The term inverse in math is referred to as the opposite of another operation and for example, the inverse of the number 2 is written as 1/2.

Here we need to identify the four inverse operations in math.

Here we also need to know that a function or operation which reverses the order or operation of another function or operation

According to the definition of the term inverse, the type of inverse operation in math is defined as follows:

=> addition and subtraction,

=> multiplication and division,

=> squares and square roots only for positive numbers,

=> cubes and cube roots.

And basically these inverse operations are used in solving algebraic equations

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Answer:

51.1 (degrees)

Step-by-step explanation:

Use the tangent function to solve for the angle x since we have the opposite and adjacent sides of the angle x:

[tex]tan(x)=\frac{9.3}{7.5} \\x=tan^{-1}(\frac{9.3}{7.5}) \\x=51.11550356[/tex]

Rounding gives:

[tex]x=51.1[/tex]

The x intercept of f(x) is same as x intercept of g(x) and the statements the y intercept of f(x) is same as y intercept of g(x) are true.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The function  f (x) = x² -7x

when we translate the graph f(x) to g(x) it can be seen that g(x) is a translation of f(x) by left and upwards.

So the statements the x intercept of f(x) is same as x intercept of g(x) and the statements the y intercept of f(x) is same as y intercept of g(x)

Hence, the x intercept of f(x) is same as x intercept of g(x) and the statements the y intercept of f(x) is same as y intercept of g(x) are true.

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There are 7 images are formed by the plane mirror if the angle is 45°.

The term angle in math is known as a combination of two rays with a common endpoint.

Here we have given that we need to find the number of image are formed by a plane mirror if the angle is 45.

As we all know that when the object is asymmetrically placed between the mirrors, then the number of images formed will be calculated by using the overall degree value that is 360 degree.

The general form to calculate the number of images is formed is calculated as

=> (360/n) -1    

As we all know that the value of n in the given question is 45.

Then the value is calculated as,

=> (360 / 45) - 1

=> 8 - 1 = 7

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The graph of an inverse proportion is a curved graph.

When two variables are related in a way where their product is always constant, that relationship is called an inverse proportion. Y = k/x or xy = k, where k is a constant, are two ways to express it mathematically. Hyperbolas which are curved graphs are formed with inverse proportions. Collecting all points in the plane where the gap between two fixed points and a fixed point is constant is known as a hyperbola.

With the foci on the y-axis and the x-axis serving as the hyperbola's centre, the graph of the equation y = k/x is a hyperbola. The y-axis serves as the hyperbola's centre of gravity, with the x-axis serving as its foci, on the graph of the equation xy = k.

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The inequality that can be used to determine x, the maximum number of outfits Luis can purchase while staying within his budget is x ≤ 4

How is inequity resolved?

Luis has $420 to spend at a bicycle shop on new accessories and clothing.

He spends $209.67 on a brand-new bicycle.

He spends $6.04 apiece on two bicycle reflectors and $25.77 on a pair of cycling gloves.

He intends to use all or part of the remaining funds to purchase new riding clothing at $37.16 apiece.

Therefore,

x is the maximum amount of clothes Luis can buy on a tight budget.

In order to illustrate the scenario, the inequality that may be employed is as follows:

209.67 + 6.04(2) + 25.77 + 37.16x ≤ 420

235.44 + 12.08 + 37.16x ≤ 420

247.52 +  37.16x ≤ 420

37.16x ≤ 420 - 247.52

37.16x ≤ 172.48

divide both sides by 37.16

x ≤ 4.64155005382

x ≤ 4

Therefore, the inequality that can be used to determine x, the maximum number of outfits Luis can purchase while staying within his budget is x ≤ 4

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Answer:

I hope this is helpful. I had to crop it slightly to insert it.

Answer:  See the graph image attached

Step-by-step explanation:

x   y

0  -3

1   -4

When you divide a fraction by a negative number, it doesn't matter what happens to the denominator because the entire result, or quotient, is the reverse of whatever the original fraction was.

In mathematics, a denominator is the lowest number in a fraction that indicates how many equal parts are divided into a whole.

It is a fraction's divisor. In this case, the denominator is 4, thus there are four components overall.

The top number in a fraction is referred to as the numerator, while the bottom number is referred to as the denominator.

4/5, for instance, is a fraction.

What happens to the denominator of a fraction when you divide it by a negative number is unimportant because the entire result, or quotient, is the opposite of whatever the original fraction was.

Therefore, when you divide a fraction by a negative number, it doesn't matter what happens to the denominator because the entire result, or quotient, is the reverse of whatever the original fraction was.

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Quadratic equation x² + 6 · x - 27 = 0 contains roots x₁ = - 9 and x₂ = 3.

In this question we find the case of a quadratic equation of the form x² + b · x + c = 0, whose roots are x₁ = - 9 and x₂ = 3, respectively. A value of x is a roots when x² + b · x + c = 0. Then, we proceed to find the values of the two coefficients.

First, write the resulting system of linear equations:

- 9 · b + c = - 81

3 · b + c = - 9

Second, use numerical methods to find the values of the coefficients:

(b, c) = (6, - 27)

Third, write the resulting quadratic equation:

x² + 6 · x - 27 = 0

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Answer:

Step-by-step explanation:

Plot 213, −56, and −312 on the number line.

Answer: 370 cubic centimeters

Step-by-step explanation:

They're just boxes stack on top of another. Find volume of both box and add together.

Use the cuboid formula to find volume of each box:

[tex]Volume = length *width * height[/tex]

Bottom box volume: [tex]10cm*5cm*5cm=250^3cm[/tex]

Top box volume: [tex]8cm*5cm*3cm=120^3cm[/tex]

Total volume = [tex]250^3cm+120^3cm=370^3cm[/tex]

The value of k is 7

Consider the given equations are:

2x+3y=7

(k−1)x+(k+2)y=3k

The general equations

[tex]a_{1} x+b_{1} y =c_{1}[/tex]

[tex]a_{2} x+b_{2} y =c_{2}[/tex]

substituting the values,

[tex]a_{1} = 2, b_{1} y=3,c_{1}=7[/tex]

[tex]a_{2}=(k-1) ,b_{2} =( k+2), c_{2}= 3k[/tex]

An equation can have infinitely many solutions when it should assure some conditions. The system of an equation has infinitely numerous solutions when the lines are coincident, and they have the same y-intercept.

We know, the condition of infinite solutions

[tex]\frac{a_{1} }{a_{2} } = \frac{b_{1} }{b_{2} } = \frac{c_{1} }{c_{2} }[/tex]

Therefore,

[tex]\frac{2}{k-1} = \frac{3}{k+2} =\frac{7}{3k}[/tex]

⇒[tex]\frac{2}{k-1} =\frac{3}{k-2}[/tex]

⇒ 2k -4 = 3k-3

⇒ k = 7

Hence, the value of k is 7.

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The complete question is:

Find the value of k, infinitely many solutions

2x+3y=7,(k−1)x+(k+2)y=3k

Conditions for the parallel lines are as follow :

a. Lines should not intersect each other.

b. Slope of the given lines should be equal.

c. Parallel lines represent equations has no solution.

As given in the questions ,

Conditions for the parallel lines are given by :

a. If the two given lines are parallel to each other then they should not intersect each other.

Distance between the lines remains same.

b. Slope of the two parallel lines should be equal.

y = m₁ x + c

y = m₂ x + c

Here slope represented by m.

⇒m₁ = m₂

c. If two given equation has no solution then the given lines are parallel lines.

2x = 4x + 5

x = 2x + 3

Here m₁ = m₂ = 2

Therefore, the condition of the parallel lines are:

a. Lines should not intersect each other.

b. Slope of the given lines should be equal.

c. Parallel lines represent equations has no solution.

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This would then result in the answer of t = 5/4.

Emma's first mistake was when she set up the equation. She started with:

−

3

5

=

4

5

t

−

3

5

This equation does not make sense mathematically, as it cannot be solved. The equation should have been set up as:

3

5

=

4

5

t

By setting up the equation correctly, Emma could have proceeded to solve the equation. To solve the equation, she would have needed to subtract 3/5 from both sides of the equation, resulting in

3

5

−

3

5

=

4

5

t

−

3

5

This would then result in the answer of t = 5/4.

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Answer:

calculating

Step-by-step explanation:

The angle 180  is not an acute angle.

We know that an angle is the figure, in which two rays meet at a common point (vertex).

The types of angles (based on their magnitude) are:

Acute Angle (angle measuring greater than 0° and less than 90°)

Obtuse Angle, (an angle which is less that 180° and greater than 90°)

and Right Angle (an angle that measures 90°)

There are some types of angle based on their rotation:    

Straight Angle, (an angle measuring 180 degrees)

Reflex Angle, (an angle which is greater than 180 degrees but less than 360 degrees )

and Full Rotation (an angle measuring 360 degrees)

From the definition of acute angle,

acute angle measures greater than 0° and less than 90°

So, 180 degrees can not be an acute angle.

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Answer:

√50 must lie between 7 and 8

Step-by-step explanation:

To some extent you have to know the squares of integers

7² = 49

8² = 64

So √50 must lie between 7 and 8

The formula is a fact or a rule written with mathematical symbols. It usually connects two or more quantities with an equal sign.

In arithmetic, a chain is an enumerated series of gadgets in which repetitions are allowed and order matters. Like a hard and fast, it consists of contributors (additionally referred to as elements, or terms). The quantity of elements (possibly endless) is called the duration of the series.

Unlike a fixed, the same factors can appear a couple of times at distinct positions in a chain, and unlike a fixed, the order does be counted. formally, a chain can be described as a function from herbal numbers (the positions of elements inside the collection) to the factors at each position. The belief of a sequence may be generalized to a listed family, defined as a character from an arbitrary index set.

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Answer:

15:17

Step-by-step explanation:

We know

Fifteen of the 32 students in the class own a dog, so the ratio of students who have a dog to students who do not is

15:17

The two numbers are  x = 13/2 and y = 11/2.

Let's call the two numbers x and y. We are given that:

x + y = 12 (the sum of the two numbers is 12)

x - y = 1 (the difference between the two numbers is 1)

We can use these two equations to solve for x and y.

From the first equation, we can add y to both sides to get:

x = 12 - y

Now we can substitute this into the second equation:

(12 - y) - y = 1

12 - 2y = 1

12 = 1 + 2y

2y = 11

y = 11/2

Now that we know the value of y, we can substitute it back into x = 12 - y to find the value of x:

x = 12 - (11/2)

x = 12 - 11/2

x = (24 - 11)/2

x = 13/2

So the two numbers are x = 13/2 and y = 11/2.

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Answer:

x=7 because scince it got dilated by 7

In 90 degrees turn there are 1/4 (one fourth) of the full turn.

A degree is the name given to the mathematical unit of measurement for an angle. A protractor is a device used to determine the degree of an angle. Angles can be measured at different angles with different degrees, such as 30°, 45°, 60°, and so on. A complete circle rotates at 360°.

A right angle is defined as an angle in geometry and trigonometry that is exactly 90 degrees, or pi /2 radians, or one-quarter turn. The adjacent angles are right angles if a ray is positioned so that its terminus is on a line and they are equal.

A right angle is one that is 90 degrees. A 90-degree angle exists when the angle formed by the horizontal and vertical lines is exactly equal to 90 degrees.

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A rotation of 270° counterclockwise will map the blade formed by ΔFEG onto the blade formed by ΔHGI

The measure of the amount a figure is rotated about the center of rotation is called the angle of rotation. The angle of rotation is usually measured in degrees. We specify the degree measure and direction of a rotation.

90° clockwise rotation: (x,y) becomes (y,-x)

90° counterclockwise rotation: (x,y) becomes (-y,x)

180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)

270° clockwise rotation: (x,y) becomes (-y,x)

270° counterclockwise rotation: (x,y) becomes (y,-x)

Given data ,

Let the first triangle be represented as ΔFEG

Let the second triangle be represented as ΔHGI

Now , for both the triangles to be similar , the mapping of the rotation of the blade should be rotated once in the clockwise or three times in the counterclockwise direction

So , for a rotation of 90° clockwise rotation: (x,y) becomes (y,-x)

So , for a rotation of 270° counterclockwise rotation: (x,y) becomes (y,-x)

The ΔFEG of the blade will map itself onto the ΔHGI of the blade after a rotation of 270° counterclockwise rotation

Hence , the rotation is 270° counterclockwise rotation

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Write down the set of numbers for which you want to find the GCF.

Starting from 1, check if each number in the set is divisible by it. If all the numbers are divisible by it, mark it as a common factor.

Repeat step 2, incrementing the number by 1, until you reach the smallest number in the set.

The largest common factor that you marked in step 2 is the GCF.

This method is based on the idea of checking each number starting from 1 till the smallest number in the set and checking if it is divisible by all numbers in the set. It's a simple method that can be applied to find GCF of any set of numbers.

It's worth noting that this method may not be the most efficient way to find GCF of set of numbers, as it involves checking each number starting from 1 till the smallest number in the set. In cases where the numbers are large, more efficient methods like prime factorization and Euclidean algorithm are preferred.

The ratio of comparision of the cup is given as 4:2

A mathematical comparison of two or more values or quantities is called a ratio. It can be used to compare the relative sizes or amounts of various items since it expresses the relationship between the values in terms of a proportion or a fraction.

let the number of cups of strawberries required be x. and the number of cups of whipped cream required be y

given that x=4 and y=2

so the ration of comparision is given by:

x:y

=>4:2

so 2:1

so the ratio of comparision is given as 4:2

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