evaluate 1 + (-2/3) - (-m) where m= 9/2

Answers

Answer 1

The value is evaluated to 5 1/4

What is a fraction?

A fraction can be described as the part of a whole value, variable or element.

The different types of fractions are;

Mixed fractionsProper fractionsSimple fractionsComplex fractionsImproper fractions

From the information given, we have that;

1 + (-2/3) - (-m)

If the value of m = 9/2, let's substitute the value, we have;

1 - 2/8 - ( 9/2)

expand the bracket

1 - 2/8 + 9/2

Find the LCM

8 - 2 +  36 /8

42/8

5 1/4

Hence, the value is 5 1/4

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Related Questions

What are the three credit reporting agencies you would possibly need to contact to report an error on your credit report?

Answers

Answer:

Experian, Equifax, and/or Transunion

Step-by-step explanation:

None

this is the question ​

Answers

Answer:

25

Step-by-step explanation:

[tex]0<5x-35<90 \\ \\ 0<x-7<18 \\ \\ 7<x<25[/tex]

Helppppppppppppppppppp

Answers

lol they used art how do u not know this

a sqaure of area 36cm is
cut rectangles

Answers

Answer: dimensions of the two rectangles are 6x4 and 6x2

Okay im learning algebra right now and this question hit my head here, its asked which expression was equivalent to this 2v+6v+3c. here are the answer 2v + 9c / 8v + 3c / 11vc / 11+ v+ c

Answers

Answer:

8v+3c

Step-by-step explanation:

Given 2v+6v+3c

1) Add all like terms

-Since both 2 and 6 have "v" and the two together

2) 8v+3c

Answer: 8v+3c

Hope this helps :)

What is an equation of the line that passes through the points (-5, -6) and (5, 6)?

Answers

Answer:

y = [tex]\frac{6}{5}[/tex] x

Step-by-step explanation:

the equation of a line in slope- intercept form is

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

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 5, - 6 ) and (x₂, y₂ ) = (5, 6 )

m = [tex]\frac{6-(-6)}{5-(-5)}[/tex] = [tex]\frac{6+6}{5+5}[/tex] = [tex]\frac{12}{10}[/tex] = [tex]\frac{6}{5}[/tex] , then

y = [tex]\frac{6}{5}[/tex] x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation.

using (5, 6 ) , then

6 = 6 + c ⇒ c = 6 - 6 = 0

y = [tex]\frac{6}{5}[/tex] x ← equation of line

Dilbert has p pennies, n nickels, d dimes, and q quarter with a total value of $1. 8. If the numbers p, n, d, and q are distinct and positive, and the greatest common divisor of each pair of these numbers is 1, which is the least possible value of p+n+d+q?

Answers

The least possible value of p+n+d+q would be 6 + 3 + 3 + 3 = 15. So, the least possible value of p+n+d+q is 15.

To solve this problem, we need to use the concept of prime factorization. First, we need to find the least common multiple of the four numbers, p, n, d, and q. To do this, we can factor each of the numbers into their prime factors:

[tex]p = 2^a * 3^b * 5^c * 7^d \\n = 2^e * 3^f * 5^g * 7^h\\d = 2^i * 3^j * 5^k * 7^l\\q = 2^m * 3^n * 5^o * 7^p[/tex]

The least common multiple (LCM) of p, n, d, and q is the product of the highest power of each prime factor that appears in any of the numbers. For example, the LCM would be 2^i * 3^j * 5^k * 7^l, because that is the highest power of each prime factor that appears in any of the numbers.

Now that we have the LCM of the four numbers, we need to find out how much money that is worth. Since we know that the total value is $1.08, we can divide both sides by the LCM to find out how much each factor is worth:

[tex]1.08/2^i * 3^j * 5^k * 7^l = x[/tex]

x = 0.01102

So, each factor of the LCM is worth 0.01102. Now, we just need to add up the total number of factors that appear in p, n, d, and q. The least possible value of p+n+d+q would be the sum of the number of powers of each prime factor in p, n, d, and q. For example, if[tex]p = 2^2 * 3^3 * 5^1 * 7^0, n = 2^1 * 3^2 * 5^0 * 7^2, d = 2^0 * 3^1 * 5^2 * 7^1,[/tex] and [tex]q = 2^2 * 3^0 * 5^2 * 7^1.[/tex]

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Find the perimeter and area of these shapes

Answers

Answer:

Just add each one and you will get the answer

Step-by-step explanation:

For example 7+9+18+24 = 58

Which statements are true? Check all that apply.
Negative 2.5 = negative 2 and one-half
–1.5 > –0.5
–0.5 < 0
–2.5 < –2
1 and one-half greater-than 1.5

Answers

The statements that are true include;

Negative 2.5 = negative 2 and one-half–0.5 < 0–2.5 < –2

What is an inequality?

An inequality can be described as a relation with a non-equal comparison between two elements, values, variables, numbers or other algebraic expressions.

Inequalities are mostly used to compare two numbers on the number line on the basis of their size.

It is important to note that the positive values are greater than the negatives .

Also, zero(0) is greater than the negative numbers from the left side of the number line.

Hence,  -1. 5 is less than -0. 5, -0. 5 is less than 0, -2. 5 is less than -2

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The coordinates A(0,8),and C(-4,-6) are dilated by a scale factor of 1/2;what is the new coordinate pair for A’?

Answers

The new coordinate pair of A' is (0,4) when dilated by a scale factor of 1/2

Given,

The coordinates A(0,8),and C(-4,-6) are dilated by a scale factor of 1/2

let the scale factor be k.

What are coordinates?

coordinates can be defined as the pair of numbers which are used to determine the position of a given point.

k = 1/2

and coordinates A(0,8) and C(-4,-6)

the rule of dilation

If a point (x,y) dilated for the scale factor of 'k', we do get image as (kx,ky)

Using this concept, we know scale factor is  , we could get image as

A' (0*1/2 , 8*1/2)

A' ( 0 , 4)

And for C(-4,-6)

C'(-4*1/2 , -6*1/2)

C' (-2,-3)

Hence, The new coordinate pair of A' is (0,4) when dilated by a scale factor of 1/2 .

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Let F be a differentiable function such that f(-1)= -6 and f'(x)=4x-1. What is the approximation for f(-1.2) found by using the line tangent to the graph of f at x= -1?

Answers

The tangent line approximation for f(-1.2) is defined as follows:

f(-1.2) = -5.

How to obtain the equation of the tangent line?

The point-slope format for the equation of the tangent line is given as follows:

y - y* = m(x - x*).

In which the parameters are given as follows:

(x*, y*) are the coordinates of the point.m is the slope of the linear function, representing the numeric value of the derivative at point (x*, y*).

The derivative for this problem is given as follows:

f'(x) = 4x - 1.

f(-1)= -6, hence the coordinates of the point are given as follows:

x* = -1, y* = -6.

Hence the slope is given as follows:

m = f'(-1).

m = 4(-1) - 1

m = -5.

Thus the tangent line is defined as follows:

y + 6 = -5(x + 1).

y = -5(x + 1) - 6.

At x = -1.2, the approximation is calculated as follows:

y = -5(-1.2 + 1) - 6

y = -5.

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Please someone help me

Answers

The linear function that models the amount left is a = 84 - 16d where 16 is the slope of the equation. At the fourth day, there isn't enough money left for the shirt.

What is Linear Function

A linear function is a type of mathematical function in which the output is directly proportional to the input. A linear function can be expressed by a linear equation of the form y = mx + b, where m is the slope and b is the y-intercept.

To solve this problem, we have to write a linear function that shows how much is spent in d number of days.

a)

The linear function is

a = 84 - 16d

a = Total amount left

d = number of days.

b)

The cost of the shirt is $38, at the end of the fourth day, we would have

a = 84 - 16(4)

a = 84 - 64

a = 20

The money left isn't enough

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Convert the masses from grams to the indicated derived units. 0.379 g = _____ mg 787 g = _______Mg74.3 g = ______kg

Answers

These conversions can be carried out for any amount of mass given in grams.

0.379 g = 379 mg

787 g = 0.787 Mg

74.3 g = 0.0743 kg

1. To convert 0.379 g to mg, multiply 0.379 by 1000. 0.379 x 1000 = 379 mg.

2. To convert 787 g to Mg, divide 787 by 1000. 787 / 1000 = 0.787 Mg.

3. To convert 74.3 g to kg, divide 74.3 by 1000. 74.3 / 1000 = 0.0743 kg.

The 0.379 g was converted to 379 mg, 787 g was converted to 0.787 Mg, and 74.3 g was converted to 0.0743 kg.

The conversion of 0.379 g to mg is done by multiplying 0.379 by 1000. The result is 379 mg. To convert 787 g to Mg, divide 787 by 1000. The result is 0.787 Mg. To convert 74.3 g to kg, divide 74.3 by 1000. The answer is 0.0743 kg. In summary, 0.379 g was converted to 379 mg, 787 g was converted to 0.787 Mg, and 74.3 g was converted to 0.0743 kg. This demonstrates how to convert mass from grams to different derived units. These conversions can be carried out for any amount of mass given in grams.

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can someone please help me with this question pleaseeeeeeeeeee

Answers

There is no solution for the given system of inequalities there is no point that satisfies both inequalities.

The following system of inequalities is given as:

a.

y ≥ x + 1

y ≤ -x - 2

b.

y ≥ x + 1

y ≥ - x - 2

The system of the given inequalities represents a region in the x-y plane that is the solution set for the inequalities. To find the solution set, we can graph the inequalities on the same coordinate plane and find the region where they overlap.

The inequality y ≥ x + 1 represents the line y = x + 1 and all the points above it. Similarly, y ≤ -x - 2 represents the line y = -x - 2 and all the points below it.

When we graph these two lines on the same coordinate plane, we find that the lines intersect at the point (-1.5,-0.5) which means that the common region of the two lines(the region where they overlap) is the empty set. This means that there is no point that satisfies both inequalities and therefore there is no solution for the given system of inequalities.

Similarly, therefore there is no solution for the system of inequalities y ≥ x + 1 ; y ≥ - x - 2.

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Suppose that the function f is defined, for all real numbers, as follows.
[tex]f(x)\left \{ {{x-3 IF x \leq -2} \atop {4x+5IFx\ \textgreater \ -2}} \right.[/tex]
Graph the function f. Then determine whether or not the function is continuous.

Answers

Answer:

See attached graph

Graph is not continuous

Step-by-step explanation:

The function is not continuous as you can see from the break in the graph

It is discontinuous at x = -2

Answer:

See attachment for graph.

The function is not continuous.

Step-by-step explanation:

Piecewise functions have multiple pieces of curves/lines where each piece corresponds to its definition over an interval.

Given piecewise function:

[tex]f(x)=\begin{cases} x-3 \;\;\;\;\: \text{if}\;\;\;x \leq -2\\4x+5 \;\;\; \text{if}\;\; \;x > -2 \end{cases}[/tex]

Therefore, the function has two definitions:

f(x) = x - 3  when x is less than or equal to -2.f(x) = 4x + 5  when x is greater than -2.

When graphing piecewise functions:

Use an open circle where the value of x is not included in the interval.Use a closed circle where the value of x is included in the interval.Use an arrow to show that the function continues indefinitely.

First piece of the function

Substitute x = -2 into the first function:

[tex]\implies f(-2)=-2-3=-5[/tex]

As the interval for the first equation is x ≤ -2, it includes the value of x = -2.  Therefore, place a closed circle at point (-2, -5).

To help graph the line, find another point on the line by inputting another value of x that is less than -2 into the same function:

[tex]\implies f(-5)=-5-3=-8[/tex]

Plot point (-5, -8) and draw a straight line from the closed circle at (-2, -5) through (-5, -8).  Add an arrow at the other endpoint to show it continues indefinitely as x → -∞.

Second piece of the function

Substitute x = -2 into the second function:

[tex]\implies f(-2)=4(-2)+5=-3[/tex]

As the interval for the second equation is x > -2, it does not include the value of x = -2.  Therefore, place an open circle at point (-2, -3).

To help graph the line, find another point on the line by inputting another value of x that is more than -2 into the same function:

[tex]\implies f(1)=4(1)+5=9[/tex]

Plot point (1, 9) and draw a straight line from the open circle at (-2, -3) through (1, 9).  Add an arrow at the other endpoint to show it continues indefinitely as x → ∞.

See attachment for the graph.

[tex]\boxed{\begin{minipage}{8cm}\underline{Determining if a function is continuous at $x=a$}\\\\Condition 1: $f(a)$ exists\\\\Condition 2: $\displaystyle \lim_{x \to a}f(x)$ exists at $x=a$\\\\Condition 3: $\displaystyle \lim_{x \to a}f(x)=f(a)$\\\end{minipage}}[/tex]

If all three conditions are satisfied, the function is continuous at x = a.

If any one of the conditions is not satisfied, the function is not continuous at x = a.

To determine whether or not the given piecewise function is continuous, find if the function is continuous at x = -2.

Condition 1

Does f(-2) exist?  Yes → f(-2) = -5

Condition 2

[tex]\textsf{Does}\;\;\displaystyle \lim_{x \to -2} f(x)\;\; \sf exist\;at\;\;x=-2?[/tex]

To the left of  x =- 2, f(x) = x - 3

To the right of  x = -2 , f(x) = 4x + 5

Evaluate the left and right limits as x approaches -2:

[tex]\displaystyle \lim_{x \to -2^-}f(x)=\lim_{x \to -2^-} -2-3=-5[/tex]

[tex]\displaystyle \lim_{x \to -2^+}f(x)=\lim_{x \to -2^+} 4(-2)+5=-3[/tex]

[tex]\textsf{As}\;\;\displaystyle \lim_{x \to -2^-} f(x) \neq \lim_{x \to -2^+} f(x), \;\; \lim_{x \to -2} f(x)\;\; \textsf{does not exist}.[/tex]

As condition 2 fails, there is no need to proceed to condition 3.

Therefore, the function is not continuous.

Find the surface area and volume of the composite figure.

The surface area of the composite figure is __________ yd2.

The volume of the composite figure is ____________ yd3.

Answers

The surface area of the composite figure is 217.28yd²

The volume of the composite figure is 141.12yd³

What are composite figure?

A composite figure can be defines as a shape created with two or more basic shapes.

The composite figure consist of a triangular prism and cuboid

The surface area of the cuboid =2(lh+lb+bh)

= 2 ( 4.8×2.8 + 8× 2.8 + 4.8×8)

= 2( 13.44+22.40+38.4)

= 2(74.24)

= 148.48yd²

The surface area of the prism = 2B+ph

Base area = 1/2 × 3×8 = 12

The perimeter = 3+8+5 = 16

SA = 2×12+ 16×2.8

SA = 24+44.8

SA = 68.8yd²

the surface area of the composite figure = 148.48+68.8 = 217.28yd²

The volume of the cuboid = 4.8× 2.8 × 8 = 107.52yd³

Volume of the prism = base area × height = 12×2.8 = 33.6yd³

Therefore the volume of composite figure= 107.52+33.6 = 141.12 yd³

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How do you know if HL is congruent?

Answers

To determine if two triangles are congruent, the following conditions must be met:

All corresponding pairs of vertical angles are equal.All corresponding pairs of alternate interior angles are equal.All corresponding pairs of alternate exterior angles are equal.All corresponding pairs of consecutive interior angles are supplementary.

Determining Congruence of Triangle HL

To determine if triangle HL is congruent, you must first compare the lengths of each side. If the lengths of each side are equal, then the triangles are similar. Next, you must compare the angles of each triangle. If the angles of each triangle are equal, then the triangles are congruent. Finally, you must compare the pairs of vertical angles, alternate interior angles, alternate exterior angles, and consecutive interior angles. If all of these pairs are equal or supplementary, then the triangles are congruent. If all three conditions are met, then it can be concluded that triangle HL is congruent.

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A thermometer shows the temperature in degrees celsius (°c) and degrees fahrenheit (°f). one day, it shows 58°f and 14°c. the next day, it shows 38°f and 3°c. determine if there is a proportional relationship between the temperature in degrees celsius and the temperature in degrees fahrenheit. yes, there is a proportional relationship because degrees celsius and degrees fahrenheit are the same measurement. no, there is not a proportional relationship because degrees celsius and degrees fahrenheit are not the same measurement. yes, there is a proportional relationship because 58 over 14 equals 38 over 3. no, there is not a proportional relationship because 58 over 14 does not equal 38 over 3.

Answers

Answer:

  (d)  no, there is not a proportional relationship because 58 over 14 does not equal 38 over 3.

Step-by-step explanation:

You want to know if there is a proportional relationship between °C and °F, given the relation (°F, °C) = (58, 14) or (38, 3).

Proportional relation

The relationship is proportional if the ratio of input and output is the same in all cases. Here, we see that ...

  58/14 ≠ 38/3 . . . . . . . the relationship is not proportional

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Find the 50th derivative of y = cos 2x.

Answers

The 50th derivative of y=cos2x is [tex]& y^{50}(x)=-2^{50} \cos (2 x)[/tex].

Consider y=cos 2x

Derivative: The rate of change of a function with respect to a variable. Derivatives are fundamental to the solution of problems in calculus and differential equations.

Finding the nth derivative means to take a few derivatives (1st, 2nd, 3rd…) and look for a pattern. If one exists, then you have a formula for the nth derivative. To find the nth derivative, find the first few derivatives to identify the pattern.  Apply the usual rules of differentiation to a function, then find each successive derivative to arrive at the nth.

The first derivative is

[tex]$$\begin{aligned}& y^{\prime}=-2 \sin 2 x \\& =-2\left[\cos \left(2 x+\frac{\pi}{2}\right)\right]\end{aligned}$$[/tex]

The second derivative is

[tex]$$y^{\prime \prime}=-2^2\left[\cos \left(2 x+2 \cdot \frac{\pi}{2}\right)\right]$$[/tex]

Similarly, we get the [tex]n^{th}[/tex] derivative

[tex]$$y^n(x)=-\left[2^n \cos \left(2 x+n \frac{\pi}{2}\right)\right]$$[/tex]

When n=50

[tex]$$\begin{aligned}& y^{50}(x)=-\left[2^{50} \cos \left(2 x+50 \cdot \frac{\pi}{2}\right)\right] \\& y^{50}(x)=-2^{50} \cos (2 x)\end{aligned}$$[/tex]

Therefore, the [tex]50^{th}[/tex] derivative of y = cos 2x is [tex]& y^{50}(x)=-2^{50} \cos (2 x)[/tex].

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What is the answer for 5x10?

Answers

Answer:

50

Step-by-step explanation:

10 x 5 = 50

What is fraction give 5 examples?

Answers

A fraction is a numerical expression that represents a part of a whole using two numbers separated by a fraction bar .Fractions can be used to describe how much of a quantity is being referred to. Examples of fractions include 1/2, 3/4, 5/8, 7/10, and 11/12.

1. 1/2 (one half)

2. 3/4 (three fourths)

3. 5/8 (five eighths)

4. 7/10 (seven tenths)

5. 11/12 (eleven twelfths)

Fractions are numerical expressions used to represent parts of a whole. To express a fraction, two numbers are separated by a fraction bar. The top number (numerator) represents the number of parts taken from the whole, and the bottom number (denominator) represents the total number of parts in the whole. For example, if a pizza is divided into four equal slices, each slice can be described as being "1/4" of the pizza. Other examples of fractions include 3/4, 5/8, 7/10, and 11/12. Fractions can help to quickly and accurately describe how much of a quantity is being referred to.

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A fraction is a mathematical phrase that uses two integers and a fraction bar to indicate a portion of a whole. The fractions 5/7, 9/11, 23/53, 35/37, and 43/51 are a few examples.

Parts of a whole can be represented numerically using fractions. Two numbers are separated by a fraction bar to represent a fraction. The total number of pieces in the whole is represented by the bottom number (denominator), while the number at the top (numerator) indicates how many parts were picked from the whole. As an illustration, if a pizza is cut into four equal pieces, each piece might be referred to as "1/4" of the pizza. The fractions 9/11, 23/53, 35/37, and 43/51 are other examples. Fractions make it easier to express a quantity's size succinctly and precisely.

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read the image attatched.

Answers

The amount of water needed for 90 mL concentrate is 225 mL

How to determine the amount of water needed

From the question, we have the following parameters that can be used in our computation:

2 parts concentrate to 5 parts of water

The above parameter can be expressed using the following ratio expression

Ratio = Concentrate : Water

Substitute the known values in the above equation, so, we have the following representation

Concentrate : Water = 2 : 5

From the question, we have

Concentrate = 90 ml

Substitute the known values in the above equation, so, we have the following representation

90 : Water = 2 : 5

Multiply the second ratio by 45

This gives

90 : Water = 90 : 225

By comparison, we have

Water = 225

Hence, the amount of water  is 225 mL

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Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator.
0.30 m to 0.48 m

Answers

Answer:

[tex]\frac{5}{8}[/tex]

Step-by-step explanation:

[tex]\frac{.30}{.48}[/tex] x [tex]\frac{100}{100}[/tex] = [tex]\frac{30}{48}[/tex] ÷ [tex]\frac{6}{6}[/tex] = [tex]\frac{5}{8}[/tex]

Ryosuke is picking up his friend from work. The odometer reads 74,568 when he picks his friend up, and it reads 74,592 when he drops his friend off at his house. Ryosuke's car gets 28 miles per gallon and the price of one gallon of gas is $\$4.05$. What was the cost of the gas that was used for Ryosuke to drive his friend back home from work

Answers

Ryosuke drove his friend 24 miles, which used 1.14 gallons of gas. The total cost of the gas was $4.64, calculated by multiplying 1.14 gallons by the price of one gallon which was $4.05.

1. Calculate the number of miles driven: Subtract the odometer reading when Ryosuke picked his friend up (74,568) from the odometer reading when he dropped his friend off (74,592). This gives us the total number of miles driven (24).

2. Calculate the number of gallons used: Divide the total number of miles driven (24) by the car's gas mileage (28). This gives us the number of gallons used (1.14).

3. Calculate the cost of the gas: Multiply the number of gallons used (1.14) by the price of one gallon of gas ($4.05). This gives us the cost of the gas used ($4.64).

28 miles

= [tex]$\frac{74,592-74,568}{28}$[/tex]

= 1.14 gallons

Cost of gas

= 1.14 gallons x[tex]$\$4.05$[/tex]

= [tex]$\$4.64$[/tex]

1. 74,592 - 74,568 = 24

2. 24 / 28 = 1.14

3. 1.14 x $4.05 = $4.64

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Find the product in simplest form 2/5 x 3/7 in fraction

Answers

Answer: It would be 6/35

The product would be 6/35

Write 0.00064 in standard form

Answers

Answer:

6.4 x10^ -4

Step-by-step explanation:

the number has to berween 1 and 9 ao multiply by 10000 and because you went from a small number to a bigger number ,it is a negative power

all real numbers greater than or equal to -5

Answers

[-5, 3) is the interval of all real numbers greater that or equal to -5 but less than 3

What is Number system?

A number system is defined as a system of writing to express numbers.

We need to write all real numbers greater that or equal to -5 but less than 3

[-5, 3)

-5 is included in the interval because it is greater than or equal to.

But the 3 is not included in the interval because it is strictly less than

Hence, [-5, 3) is the interval of all real numbers greater that or equal to -5 but less than 3

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What is the area of the parallelogram shown below? 10cm, 9cm, 5cm. A=? Cm2

Answers

Answer: 45cm^2

Step-by-step explanation:

The area of the parallelogram is the base x the height.

So in this question, you multiply 5 (which is the base) by 9, (which is the height).

Answer:

A = 45 cm²

Step-by-step explanation:

the area (A) of a parallelogram is calculated as

A = bh ( b is the base and h the perpendicular height )

here b = 5 and h = 9 , then

A = 5 × 9 = 45 cm²

in the Venn diagram 60 farms only grow potatoes or sugar beets 4/5 of these 60 farms grow potatoes the number of farms that grow potatoes are 3 times the number that grow sugar beets complete the Venn diagram

Answers

Complete the Venn diagram using Potatoes only = 48, sugar beets only = 12, the intersection of P and S = 6 and the box outside the P and S = 34

How to complete the Venn diagram?

Given: ξ = 100 farms

60 farms only grow potatoes or sugar beets.

4/5 of these 60 farms grow only potatoes.

The number of farms that grow potatoes are 3 times the number that grow sugar beets

Potatoes only = 4/5 × 60 = 48

sugar beets only = 60 - 48 = 12

Let the intersection of P and S be x

Since P = 3S, we have:

48 + x  =  3 (12+x)

48 + x = 36 + 3x

12 = 2x

x = 6

Since we have 100 farms, we can write:

48 + 6 + 12 + y = 100  (y represents the box outside the circles of P and S)

66 + y = 100

y = 100 - 66

y = 34    

Complete the Venn diagram according

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Write the equation in slope-intercept form of the line that is parallel to the graph of each of equation and passes through the given point.

1. y = x – 4; (-2, 3)
2. y + 2x = 4; (-1, 2)

Answers

Answer: To write the equation of the line that is parallel to the graph of y = x – 4 and passes through the point (-2, 3), we can use the fact that parallel lines have the same slope.

The slope of y = x – 4 is 1, since the coefficient of x is 1.

So, we can write the equation of the line in the slope-intercept form y = mx + b, where m = 1 and b is the y-intercept. To find the y-intercept, we can substitute the point (-2, 3) into the equation:

y = 1x + b

3 = 1(-2) + b

3 = -2 + b

b = 5

so the equation of the line in slope-intercept form is y = 1x + 5

To write the equation of the line that is parallel to the graph of y + 2x = 4 and passes through the point (-1, 2), we can use the fact that parallel lines have the same slope.

The slope of the equation y + 2x = 4 is -1/2, since the coefficient of x is -1/2.

So, we can write the equation of the line in the slope-intercept form y = mx + b, where m = -1/2 and b is the y-intercept. To find the y-intercept, we can substitute the point (-1, 2) into the equation:

y = -1/2 x + b

2 = -1/2(-1) + b

2 = -1/2 + b

b = 5/2

so the equation of the line in slope-intercept form is y = -1/2x + 5/2

It's important to note that the slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. The y-intercept is the point where the line crosses the y-axis.

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