The area of rectangle abcd is 28 cm a) what is the length of side ab in terms of x? length of ab = 4 cm x cm 6 cm x cm b) if the area of rectangle abcd is 28 cm?, we can show that x2 + ax = b where a and b are integer values. work out the values of a and b. a : (1) b= (1) total marks: 3

The sum of a number w is more than -12 becomes w > -12

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality.

We have been given that the sum of a number w is more than -12.

Now the sum of a number = w

It is more than -12 means the inequality form as;

w > -12

Therefore, the overall expression becomes w > -12

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Answer:

addition?

Step-by-step explanation:

The proof that show show how ΔTRS ≅ ΔQRP by SAS congruence theorem is explained below.

The SAS congruence theorem states that if two triangles have one pair of corresponding included angles that are congruent, and two pairs of corresponding sides that are also congruent, then both triangles are congruent to each other.

Using the SAS, the proof that shows both triangles are congruent is explained below.

Statements                        Reasons                                          

1. SR ≅ PR                          1. Given

2. SP bisects TQ               2. Given

3. TR ≅ QR                        3. Definition of bisection

4. ∠TRS ≅ ∠QRP              4. Vertical ∠s theorem

5. ΔTRS ≅ ΔQRP              5. SAS congruence theorem

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The probability that the sample mean would differ from the population mean by greater than 0.5 millimeters is 1

From the question, the given parameters about the distribution are

The standard deviation is the square root of variance

So, we have

Standard deviation = 6

The z-score is calculated using the following formula

z = (x - mean value)/standard deviation

Substitute the given parameters in the above equation

z = (0.5 - 127)/6

Evaluate

z = -21.08

The probability is then calculated as:

P(x > 0.5) = P(z > -21.08)

From the z table of probabilities, we have;

P(x < 0.5) = 1

Hence, the probability is 1.0

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Answer:

y = -x + 4

Step-by-step explanation:

The equation of a line follows the form y=mx+c, where x and y are the coordinates, c is the y-intercept (the value of x where the line crosses the y-axis), and m is the slope.

We are given two points/coordinates - (-3,7) and (1,3) - so we know the following is true for our equation:

7=-3m+c

3=m+c

Rearranging the second equation above, we get c=3-m. Sub this into the first one, and we get

7=-3m+3-m

4=-4m

m=-1

Knowing c=3-m, we can say c=3-(-1)=3+1=4

Having found values for m and c, we can now write our equation:

y = -x + 4

Hope this helps :)

Answer:

x = 9/5 y - 4/5

Step-by-step explanation:

Make x the subject:

9y - 5x =4

Subtract 9y from each side

9y-9y - 5x =-9y+4

-5x = -9y +4

Divide each side by -5

-5x/-5 = -9y/-5 + 4/-5

x = 9/5 y - 4/5

Answer:

x = (9/5)y - (4/5)

Step-by-step explanation:

Given equation,

→ 9y - 5x = 4

Solving for the required value of x,

→ 9y - 5x = 4

→ -5x = -9y + 4

→ x = (-9y + 4)/-5

→ [ x = (9/5)y - (4/5) ]

Hence, value of x = (9/5)y - (4/5).

The amount of pasta and sauce since he wants each bag to have the same amount is 16.

A factor simply means a number that can multiplied with another number which is also.a factor to get the original number.

In this case, Cesar has 32 boxes of pasta and 48 jars of sauce that he will be putting into bags for a food drive.

It should be noted that to get the number in each bag, it means that we have to find the highest common factor for both numbers. This will be:

Factors of 32 = 1, 2, 3, 4, 6, 8, 16 and 32

Factor of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.

Therefore, the answer is 16.

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The graph of the function  y=3 -1/2x is attached below.

Function:

Function refers the relationship between inputs where each input is related to exactly one output.

Given,

Here we have the function  y=3 -1/2x.

Now, we have to plot the graph of the function.

In order to plot the graph of the function, we have to take some sample values for x.

So, we will take the values of the x as -2, -1, 0, 1, 2.

Now, we have to apply the values on the given function then we get,

=> x = -2 => y = 3 - 1/2(-2) => y = 3 + 1 => y = 4

=> x = -1 => y = 3 - 1/2(-1) => y = 3 + 1/2 => y = 7/2 = 3.5

=> x = 0 => y = 3 - 1/2(0) => y = 3 - 0 => y = 3

=> x = 1 => y = 3 - 1/2(1) => y = 3 - 1/2 => y = 5/2 = 2.5

=> x = 2 => y = 3 - 1/2(2) => y = 3 - 1 => y = 2

When we enter these values into the table, then we get the table like the following.

By using the table we have to plot the graph and then we get the graph like the following.

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Answer:

5/11 > 4/9

Step-by-step explanation:

5/11 = 0.45454545....

4/9 = 0.44444444....

The spreadsheet that shows the distances between the cities, indicates that the distances between the cities are as follows;

a) From Hereford to Chester, the distance is 95 miles

b) Chester is the town that is 99 miles from Kendal

c) Ellen will have driven 201 miles if she drives from Kendal to Hereford through Chester

A spreadsheet application is used for the storage analysis, organization, and computation of data.

The interpretation of the distances in the chart which is in the form of a spreadsheet are;

The value in the cell corresponding to the distance from Kendal to Chester that is the cell which is on the same column as Kendal and on the same row as Chester is 99

Therefore, the distance from Kendal to Chester is 99 miles

The value in the cell that directly links Chester to Hereford that is the cell which is on the same column as Chester and on the same row as Hereford is 95

Therefore, the distance from Chester to Hereford is 95 miles

The value in the cell that connects Kendal to Hereford, that is the cell which is on the same column as Kendal and which is on the same row as Hereford is 201

Therefore the distance from Kendal to Hereford is 201 miles

a) The distance from Hereford to Chester is 95 miles

b) The town that is 99 miles from Kendal is Chester

c) The distance Ellen will have driven if she drives from Kendal to Hereford via Chester is 201 miles

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The value of x is 32.5°(degree) when isosceles triangle has a base angle of (4x-3)degrees and non base angle is 54 degrees.

We know that an isosceles triangles is composed of a vertex angle and two base angles. The base angles are congruent to each other. We also know that the sum of a triangle's angles is 180°(degrees).

According to given data,

⇒ 180 - {(4x-3)+54}= 0

⇒180 - 4x + 3 - 54 = 0

⇒130 = 4x

∴ x = 32.5°(degree).

That means that each base angle is 32.5°(degree).

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Taking into account the definition of a system of linear equations, the number of 2-pointers and 3-pointers Sarah made is 2 and 3 respectively.

A system of linear equations is a set of equations relating two or more unknown values, the goal of which is to determine those values so that the equations are true.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values ​​of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

You know:

The system of equations to be solved is

x + y= 10

2x+3y= 24

It is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, isolating the variable "x" from the first equation:

x= 10 - y

Replacing this expression in the second equation:

2×(10-y)+3y= 24

Solving:

2×10 -2y +3y= 24

20 -2y +3y= 24

-2y +3y= 24 - 20

y= 4

Remembering that x= 10 -y, you get:

x= 10 -4

x= 6

Finally, the number of 2-pointers Sarah made is 2 and the number of 3-pointers she made is 3.

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The value of prime numbers c in the equation is c = 2.

What is prime numbers?

Those greater than one are known as prime numbers. They simply have two variables, the number itself and factor 1.

We have given that a - b = c requires all of the integers to be positive prime numbers,

c can only have one outcome, which is 2.

                 [tex]e.g., 13 - 11 = 7 - 5 = 2.[/tex]

Hence in the given prime numbers c in the equation is c = 2.

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Answer:

The answer is gonna be B. Sorry if I’m late :((

Step-by-step explanation:

Answer: 25

Step-by-step explanation:

The area of the new garden is found to be (x-3)(y+2) square units where x and y are the original dimensions.

When calculating a rectangle's area, we multiply the length by the width of the rectangle.

The area of the floors and walls must be measured before applying carpet or tiles on the floor, painting the walls, or installing cabinets in a space.

Given: A rectangular garden has x and y dimensions. The garden's width is increased by 2 feet while its length is decreased by 3 feet.

New length = x-3

New width = y+2

Area of new garden is given as:

=(length)(width)

= (x-3)(y+2)

Therefore, the area of the new garden is found to be (x-3)(y+2) square units where x and y are the original dimensions.

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Answer:

See attached worksheet.

Step-by-step explanation:

The worksheet summarizes the steps for analyzing the data on the graph.  Note that a "line of best fit" was drawn to help illustrate the linear behavior of the data, and to better the question concerning hours of sunshine in another British town.  There are techniques for ensuring a line such as this fits the actual data as closely as possible.  These techniques draw a line that has the least overall deviation from the actual data.  For our purposes, a hand-drawn line appears to match the data reasonably well, so we are able to concule that the relationship is liner:  There is a proportional change in y for every set change in x.  That change is known as the slope.  The slope of this liner would represent the direct relationship between hours of sun and maximum temperature.

Answer: False

Step-by-step explanation:

Can not divide a number by 0.

Answer:

y=1/3x+6

Step-by-step explanation:

Use the formula "Y=mx+b"

Answer:

y= -1/3x - 6

Step-by-step explanation:

x+3y = -18

3y = -x -18

y= -1/3x - 6

The value of y is 24 when x is -2.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given,

There are direct variations

y= 24 when x=2

We need to find value of y when x =-2

This can be found by forming an equation.

Let the value of unknown y be a

2/24=-4/a

Apply cross multiplication

2a=24(-2)

2a=-48

We need to divide by 2 on both sides

a=-24

Hence the value of y is 24 when x is -2.

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The budget deficit is how much less the budget is to buy a thing, thus Bobbi has the budget deficit as $3.75 - $0.75 = $3.00 thus option (B) is correct.

To subtract in mathematics is to take something away from a group or a number of objects.

In other meaning, subtraction is a mathematical operation such that two values are going to subtract and give a resultant value.

As per the given,

Cost of bandana = $3.75

Budget = $0.75

Budget deficit = $3.75 -$0.75

⇒ $3.00

Hence, "The budget deficit is how much less the budget is to buy a thing, thus Bobbi has the budget deficit as $3.75 - $0.75 = $3.00".

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The given question is incorrect, the correct question follows;

Bobbi wants to buy a bandanna that costs $3.75, but she has only $0.75 in her budget. What is her budget deficit?

A. $0.20

B.$ 3.00

C. $5.00

D.$4.50

ans=y=8

[tex] \frac{change \: in \: y}{change \: in \: x?} [/tex]

8-8=0

-7--9=2

hence the gradient is 0÷2=0

gradient(0)=

[tex] \frac{y - 8}{x - - 9?} [/tex]

so..,0=y-8

hence the equation is y=8

The amount that Sascha will receive in annual interest based on the information is $63.40.

From the information, Sascha owns stock in Lewis Corp, and she bought a $1,000 corporate bond and the bond pays 6.34% annual interest.

In this case, it should be noted that the simple interest is calculated as:

Principal × Rate × Time

Principal = $1000

Time = 1 year

Rate = 6.34%

The interest will be:

= Principal × Rate × Time

= 1000 × 0.0634 × 1

= $63.40

The interest is $63.40.

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The number of sodas sold is 168

The number of hot dogs sold is 56

Total of sodas and hot dogs=224

Let the number of sodas sold be s, and the number of hot dogs sold be s

So we have the following:

s=3h.................i

s+h=224..........ii

we solve the two equation to find the value of s and h,

From equation ii, s=224-h, replacing this in equation i, we have:

224-h=3h

224=4h

h=56

Now, s=3*56

          =168

s=168

Number of sodas=168

Number of hot dog sold=56

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The complete question is given below;

A vender sold a combined total of 224 sodas and hot dogs. The number of sodas sold was three times the number of hot dogs sold. Find the number of sodas and the number of hot dogs sold.

do you mean 712 or 7.12?

If for 712 it is 1808.48

if for 7.12 it is 18.0848

Answer:

|x-7|=3

Step-by-step explanation:

x is 3 units away from 7

x-3=7

x-7=3

x+3=7

3=7-x

|x-7|=3

Magnitude of an earthquake releasing 3.4*10^14 joules of energy is M ≈ 6.754.

Given:

The magnitude, M, of an earthquake is represented by the equation M=2/3log(E/E0) where E is the amount of energy released by the earthquake in joules and E0=10^4.4 .

E = 3.4*10^14

M = 2/3*log(3.4*10^14 / 10^4.4)

= 2/3*log(13535643798.8)

= 2/3*10.1314

= 20.2628 / 3

M = 6.754

Therefore Magnitude of an earthquake releasing 3.4⋅1014 joules of energy is M ≈ 6.754.

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Answer:

C) 9 hours

Step-by-step explanation:

as per your picture the equation is

D(t) = 0.75×cos(pi/6 × t) + 1.5

the function cosine continuously "waves" from +1 to -1 and back.

the lowest value of this function for the first time after t>0 is when the cosine part reaches -1 the first time.

that is at 270° or 3pi/2.

so,

pi/6 × t = 3pi/2

1/6 × t = 3/2

t = 3×6/2 = 3×3 = 9

Answer:

Step-by-step explanation:

yes Saab do