How do you multiply fractions in Grade 7?.

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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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:

To simplify a polynomial, we have to do two things:

1) combine like terms, and

2) rearrange the terms so that they're written in descending order of exponent.

In order to combine like terms, we must first determine which terms can be added to or subtracted from one another. The same variable (with the same exponent) is always associated with like expressions. For instance, adding one "x-squared" to two "x-squareds" results in three "x-squareds," but adding one "x-squared" to a "x" is impossible because the two words are unrelated.

An algebraic expression that displays the sum of monomials is called a polynomial. Since "mono" signifies "one" in the prefix, a monomial is a singular element or phrase. 'Poly' is a prefix that means'many. Thus, an expression that has numerous terms is said to be polynomial. The relationships between the terms may be sums or differences.

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Answer:4682.830393

Step-by-step explanation:

The width of the flag is 640 ft and the length is 1040 ft

To calculate this we can take the width of the flag can be represented as "w" and the length as "l".

From the information given, we know:

l = w + 400 (because the length is 400 ft greater than the width)

2 * (w + l) = 2080 (because the perimeter is 2,080 ft)

We can substitute the first equation into the second equation to get:

2 * (w + w + 400) = 2080

2w + 800 = 2080

2w = 1280

w = 640

Therefore, the width of the flag is 640 ft and the length is 1040 ft (since l = w + 400)

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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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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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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

Answer:

The grand pacer test stated that the percentage of the core would be 50%

SThe range of tep-by-step explanation:

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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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:

Sandra has 34 classmates.

Step-by-step explanation:

Answer:

The number of students in Sandra's class is 34.

Step-by-step explanation:

Step 1: Let x be the number of students in Sandra's class.

Step 2: We know that Sandra has at least 10 toffees left after giving some toffees away to her classmates. This means that:

x + 10 <= 44

Step 3: We can simplify the inequality in step 2 as:

x <= 44 - 10

x <= 34

Step 4: This means that the number of students in Sandra's class is 34 or fewer.

Step 5: The number of students in her class is the number of toffees Sandra gives away, so we can set up an equation:

x = 44 - 10

Step 6: Solving the equation in step 5 gives:

x = 34

Answer:

Domain is  [-1, 3]

Range is [1, 2]

================================

Explanation:

The domain is the set of allowed input values. It's the set of all possible x coordinates of the points shown.

The left-most point is when x = -1, while the right-most point is at x = 3.

We can say [tex]-1 \le \text{x} \le 3[/tex] meaning x is between -1 and 3, including both endpoints.

That compound inequality translates to the interval notation [-1, 3]

Square brackets are used to include the endpoints.

-----------------

The range handles the set of possible y outputs.

The lowest we can go on the graph is y = 1, and the highest is y = 2

Therefore we arrive at [tex]1 \le \text{y} \le 2[/tex] which translates to [1, 2]

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

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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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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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 range of a number collection in mathematics is the difference between its highest and lowest values.

By dividing the greatest number by the lowest value, the range is computed. The difference between a group of numbers' highest and lowest values is regarded as the range.

Subtract the distribution's lowest number from its greatest number to calculate it. The function's range is the resolution. f(x) is [0,∞] and its domain f(x)=|x-1| is R.

The space between the greatest and smallest data points in a set of numerical information is termed the range. The average of the greatest and smallest data points is intermediate.

The minimum value from the maximum value from the supplied set of observations must always be subtracted in order to establish the range. The range between the maximum and least frequencies is regarded as the range.

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The equation 2x + 3y = 16 has infinitely many solutions.

We know that a linear equation in two variables is of the form ax + by + c = 0, where a, b, c are non-zero real numbers.

Here we have been given a linear equation in two variables 2x + 3y = 16

We solve this equation for x,

Consider 2x + 3y = 16

2x + 3y - 3y = 16 - 3y            .........(subtract 3y from each side of equation)

2x/2 = (16 - 3y)/2                   .........(divide each side by 2)

x = (16 - 3y)/2

for any real value of y we can find value of x.

This means, an equation 2x + 3y = 16 has infintely many solutions.

For x = 0,

2(0) + 3y = 16

y = 16/3

y = 5.333

This means, the y-intercept of line 2x + 3y = 16 is (0, 5.333)

For y = 0 ,

2x + 3(0) = 16

x = 16/2

x = 8

This means, the x-intercept of line 2x + 3y = 16 is (8, 0)

The graph of 2x + 3y = 16 is shown below.

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The complete question is:

How many solutions does the equation 2x + 3y = 16 have?.

Answer:

x=7 because scince it got dilated by 7

Answer:

Step-by-step explanation:

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

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

So, the mass of a teaspoon of sugar in milligrams is 4200 milligrams.

A teaspoon of sugar has a mass of 4.2 grams. To convert this mass to milligrams, we can use the conversion factor of 1 gram = 1000 milligrams. This means that for every gram, there are 1000 milligrams. To convert a value in grams to milligrams, we simply multiply the value in grams by 1000.

So to convert the mass of 4.2 grams to milligrams, we can use the following calculation:

4.2 grams * 1000 milligrams/gram = 4200 milligrams

Therefore, the mass of a teaspoon of sugar in milligrams is 4200 milligrams. This is because 4.2 grams is equivalent to 4200 milligrams. The conversion factor of 1 gram = 1000 milligrams is used to convert the value of 4.2 grams to 4200 milligrams.

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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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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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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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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:

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

Step-by-step explanation:

Answer:

option d is correct ok hope it helps