A Bunch of Systems
Solve each system of equations without graphing and show your reasoning. Then, check
your solutions.

2x + 3y = 7
-2x + 4y = 14

Manny's total bill is $1699.75 when the dog spent 4 days in veterinary hospital.

According to the question,

We have the following information:

Manny's dog spent 4 days in a veterinary hospital. Manny paid $1585 for the surgery, $16.25 a day for board, and $49.75 for medicine.

Now, for 4 days, we will first find the bill for boarding using multiplication.

Bill for 4 days of boarding = 16.25*4

Bill for 4 days of boarding = $65

Now, in order to find the total bill of 4 days, we will add all the given bills.

Total bill = 1585+65+49.75

Total bill = $1699.75

Hence, Manny's total bill is $1699.75 when the dog spent 4 days in veterinary hospital.

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Fraction of the area of the circle is the area of the shaded region is 5/18.

From the figure:

The shaded region has angle = 100

In the circle the total angle is 360.

Fraction = 100/360

= 50/180

= 25/90

= 5/18

Therefore fraction of the area of the circle is the area of the shaded region is 5/18.

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Regarding the data from the table, it is found that:

a) The percentage of students who failed, given that they completed the review, is of 15.38%.

b) The percentage of students who failed, given that they did not complete the review, is of 42.86%.

c) There is an inverse association between failing the exam and completing the exam review.

A percentage is calculated applying proportions, as it is a fraction of a total amount, obtained as the division of the number of desired outcomes by the number of total outcomes and multiplied by 100%.

For item a, the outcomes are given as follows:

Hence the percentage is:

p = 10/65 x 100% = 15.38%.

For item b, the outcomes are given as follows:

Hence the percentage is:

p = 15/35 x 100% = 42.86%.

Regarding the association between failing the exam and completing the exam review, it is an inverse association, as the percentage of those who failed completing the review is way less than the percentage of those who failed without completing the review.

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If the person who had forgot to pay had paid, the shopkeeper would have earned a 20% profit.

It is given that 5 customers bought 10, 15, 20, 25, and 30 toffees from a shop.

Therefore, the total number of toffees bought is

10 + 15 + 20 + 25 + 30 toffees

= 100 toffees.

Let the cost of one toffee be $x.

Hence the cost of 100 toffees is $100x

It is said that we need to consider the customer who had forgotten to pay has actually paid.

Therefore,

the shopkeeper has received money for 100 toffees.

Now, he makes a 20% profit on each toffee

Therefore the selling price of each toffee is-

20% of x  +  x

= 0.2x + x

= $1.2x

Hence for 100 toffees, he receives

$120x

Therefore, the profit made on those toffees is

$120x - $100x

$20x

Therefore profit percentage

= Profit/Cost Price  X  100

= 20x/100x  X 100

= 20%

Hence, he would have made a 20% profit.

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Answer:

f>1/2

Step-by-step explanation:

 8 + 10ƒ > 14 – 2ƒ.

-8                   +2f

12f > 6

/12      /12

f>1/2

The ratio of the perimeters is 8:3 and the ratio of the area of the shaded to the non-shaded is 64 : 9 .

We know that when two figures are similar then the ratio of all the corresponding sides of the two figures are the same.

1) Given the ratio of the sides of shaded : non-shaded = 8 : 3

Therefore the perimeter of the shaded figure : perimeter of non shaded rectangle= 8 : 3

Again ratio of areas =  ratio of the square of corresponding sides.

Area of shaded : area of non -shaded = 8² : 3² = 64 : 9

2) ratio of perimeter of shaded to non shaded trapezium

ratio = 6 : 10 = 3: 5

ratio of areas = 3² : 5² = 9 : 25

3) From the property of similarity of triangle :

8/10 = 3/ x

or, x = 30/8 = 3.75

4) From the property of similarity:

x/7=12/5

or, x = 16.8

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The milligrams of the vitamin in the​ drink are 80 mg,

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

We have been given that A new health drink has 160​% of the recommended daily allowance​ (RDA) for a certain vitamin. The RDA for this vitamin is 50 mg.

Therefore, we can say that 50 = 100%,

Now; 60% of 50

0.60 x 50 = 30

Then we have to add;

30 + 50 = 80 mg

Hence, The milligrams of the vitamin in the​ drink are 80 mg,

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The coefficients of the expression are 6, 1.

The constant of the expression is 9.

The error Jake might have made is that: D. Jake did not include the coefficient 1.

In Mathematics, a coefficient simply refers to a constant quantity or numerical value (number or numeral) that is typically placed before the variable in an algebraic expression.

Based on the algebraic expression provided, we can reasonably infer and logically deduce that there are two (2) coefficients and these include 6 as the coefficient of b and 1 as the coefficient of y.

This ultimately implies that, the error Jake made was not including the coefficient 1 for y.

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Complete Question:

On a math test a student, Jake, has to identify all the coefficients and constants of the expression 9 + 6b + y. Jake says that 6 is a coefficient and 9 is a constant. Identify all the coefficients and constants of the expression. What error might Jake have made?

The coefficient(s) of the expression is/are __

Use a comma to separate answers as needed.)

The constant(s) of the expression is/are __

(Use a comma to separate answers as needed.)

What error might Jake have made?

A. Jake said 9 is a coefficient. It is actually a constant.

OB. Jake said 6 is a constant. It is actually a coefficient.

OC. Jake did not include the constant 1.

OD. Jake did not include the coefficient 1.

If Pedro made a quilt for his cousin's doll. The quilt had a 7 × 7 array of different color square patches. If each patch is 3 1/2 in long, then the area of the whole quilt is 600.25 in²

Square is a regular quadrilateral, which has all the four sides of equal length and all four angles are also equal.

Pedro made a quilt for his cousin's doll.

This shows that there are seven rows and there are seven columns.

So, the total quilt is

7 × 7 = 49 squares patches

We are told that each of this square patches are 3½ in long

Then, since it is a square patch, it's area is

A = S² = 3½ × 3½ = 12¼ in²

So, each square patch has an area of 12¼in²,

Then, for 49 square patches

The total area of 49 Square patches is

A = 49 × 12¼ = 600.25 in²

Hence, the area of the whole quilt is 600.25 in²

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Answer:

When a shape is transformed by rigid transformation, the sides lengths and angles remain unchanged.

Rigid transformation justifies the SAS congruence theorem by keeping the side lengths and angle, after transformation.

Assume two sides of a triangle are:

And the angle between the two sides is:

When the triangle is transformed by a rigid transformation (such as translation, rotation or reflection), the corresponding side lengths and angle would be:

Notice that the sides and angles do not change.

Hence, rigid transformation justifies the SAS congruence theorem by keeping the side lengths and angle, after transformation.

Step-by-step explanation:

The correct statement about the given negative numbers is none of these

Negative numbers

A number whose value is always less than zero and it has a minus (-) sign before it is known as negative number.

Given,

Four numbers are listed.

-√50,- 36/5, - 7.05, - 2.3n

Here we need to find the correct statement that describes given numbers.

In order to find the correct statement we have to convert all the number into the same decimal form.

So, first number is written as,

-√50 = -7.07

Then the decimal form of the second number is

-36/5 = -7.2

The value is

=> -2.3n here we have to place any value for n but we have take the value of 1, then we get

=> -2.3(1) = -2.3

So, this one is rapidly decreasing based on the value of n.

Now, we have the decimal equivalent for all the four numbers.

Then we looking into the given statements we have identified that the statement none of these

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On solving the 3 variable equation you will get the answer x=6, y=1, and z=2. It is solved by elimination method.

What is elimination method?

The elimination method involves removing a variable from a system of linear equations by employing addition or subtraction along with multiplication or division of the variable coefficients.

Now, consider the first two equations.
-3x + 3y +2z = -11
3x + 5y - 5z = 13

Multiply the upper eqation with 5 and lower eqation with 2 to make coefficient of z equal.

-15x + 15y + 10z = -55
6x + 10y - 10z = 26

Add these two equations to eliminate z.

-9x + 25y = -29                   ... (1)

Now, consider second and third eqation from the the eqation given in the question.
3x + 5y - 5z = 13
5x - 6y - z = 22

Multiply the upper equation with 5 to make coefficient of z equal in both the equations.

3x + 5y - 5z = 13
25x - 30y - 5z = 110

Now, subtract the lower equation from the upper equation.
3x + 5y - 5z = 13
-25x + 30y + 5z = -110

To get the following equation:
-22x + 35y = -97                   ... (2)

Now, consider equation (1) and (2).
-9x + 25y = -29
-22x + 35y = -97

Multiply the upper equation with 35 and lower equation with 25.

-315x + 875y = -1015
-550x + 875y = -2425

Now, subtract these two equations to get the following equation:

235x = 1410
x = 6

Substitute the value of x in equation (1).

-9x + 25y = -29
-9 (6) + 25y = -29
25y = 25
y = 1

Now, substitute the value of x and y in following eqation:

-3x + 3y + 2z = -11
-3(6) + 3(1) + 2z = -11
-15 + 2z = -11
2z = 4
z =2

Hence, on solving the 3 variables equation, you will get the answer x=6, y=1, and z=2.

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The number of signatures that Sadie and Cora have is 40 signatures.

Sadie has 10 and she is collecting signatures at an average rate of 3 per day. This will be:

10 + 3d

Cora has 20 and is averaging 2 signatures every day. This will be:

= 20 + 2d

The equation will be:

10 + 3d = 20 + 2d

Collect like terms

3d - 2d = 20 - 10

d = 10

Therefore, the number of signature will be:

= 10 + 3d

= 10 + 3(10)

= 10 + 30

= 40

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The width of George Washington's face would be f = 40

The question tells us to find the width of Washington’s face, using the variable f. The equation that we are to use in order to find this is given as 4f - 100 = 60

The next thing would be for us to take the like terms of the equation

4f - 100 = 60

4f = 60 + 100

The sign next to 100 changed to positive because it went over the equal to sign

4f = 160

divide through by 4

f = 160 / 4

f = 40

Hence the width of the face of George Washington is given as 40 ft

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Answer:

-5

Step-by-step explanation:

5x+y=-4
-5x      -5x
y=-5x-4

slope intercept form = y=mx+b, where m=slope

and a line parallel to this line would have the same slope right

so i assume the answer to be -5

The examples of unit rates include miles per hour, blinks per second, calories per serving, and steps per day.

A unit rate is the price for one unit of something. This is written as a ratio with a denominator of one. For instance, if you ran 70 yards in 10 seconds, you averaged 7 yards per second. Both ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but only the latter is a unit rate.

The denominator of a unit rate is always 1. To find the unit rate, divide the denominator by the numerator so that the denominator equals 1.

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The paths that will stay outside or on the boundary of the square-2≤ x≤2, -2≤y ≤2 at each step will be 1698

We'll make advantage of the complementary counting idea. If you enter the square, you must exit by the boundaries and by the designated points because otherwise, you would touch another point in one of the sets of points in the connection (Call it S). Since y=x is symmetric, we simply need to take into account (1,-1), (1,0), and (1,1). We can only investigate one scenario and multiply it by two since (1,1) can cross the barrier in two different ways. We may just multiply (1,0) by two and (1,-1) by two. Therefore, we count the routes from (-4,4) to each of these sites and multiply that number by the total number of routes from the starting position.

[tex](\left {{16} \atop {8}} \right.) -2[(\left {{8} \atop {3}} \right.) (\left {{7} \atop {2}} \right.) +(\left {{9} \atop {4}} \right.) (\left {{6} \atop {2}} \right.) +(\left {{10} \atop {5}} \right.) (\left {{5} \atop {2}} \right.)] =1698[/tex]

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Your question is incomplete, but most probably, the full question was:

A 16-step path is to go from (-4,-4) to (4,4) with each step increasing either the x-coordinate or the y-coordinate by 1. How many such paths stay outside or on the boundary of the square -2≤ x≤2, -2≤y ≤2 at each step?

A.92

B.144

C.1568

D.1698

E.12800

The slope by the given point is m = -1.

What is slope?

Slope is a value that describes the steepness and direction of a line. In variable format, it is commonly represented by the letter m. The slope of a line is also called its gradient or rate of change. The slope formula is the vertical change in y divided by the horizontal change in x, sometimes called rise over run.

The formula to find the slope = (y2-y1)/(x2-x1)

here the points are (5,-4) and (-15,16)

m = 16+4/-15-5

m = 20/-20

m = -1

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Step-by-step explanation:

The y intercept is the y value when x=0,

So plug in x=0,

[tex]5(0) - 2y = 20[/tex]

[tex] - 2y = 20[/tex]

[tex]y = - 10[/tex]

Answer:

y+6=9(x+4)

Step-by-step explanation:

point slope form is y-y1=m(X-x1)

y1 is -6

x1 is -4

And the slope or m is 9 so we can fill it in

y-(-6)=9(x-(-4))

y+6=9(x+4)

we can fill the equation out to see if it’s true

-6+6=9(-4+4)

0=9(0)

0=0

It is true

Hopes this helps please mark brainliest

There is currently $62.65 billion in the fund.

Given that;

If the FDIC must use 7.6% of its $67.8 billion insurance reserve to pay for several bankrupt banks,

To get how much money is left in the fund, we need to;

The total insurance fund = $67.8 billion

To cover several failed banks = 7.6% = 0.076

Therefore, the money left = $67.8 * 0.076

                                           = $5.15

So, the final amount left in the fund = $67.8 - $5.15

                                                           = $62.65

Hence, the money left in the fund is $62.65 billion.

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The probability to take 5 classes is 0.1, while the probability to take at least one class is 0.6, the probability to take 2 or 3 classes is 0.23 and the expectation of the distribution is 1.37.

1.

We know that in a probability distribution,  the sum of all the probabilities is always equal to 1.

Let the probability of X = 5 be a

Hence,

0.4 + 0.25 + 0.15 + 0.08 + 0.02 + a = 1

or, 0.9 + a = 1

or, a = 1 - 0.9

or, a = 0.1

Hence the probability to take 5 classes is 0.1.

2.

We need to find P(X ≥ 1)

= 1 - P(X = 0)

we already know from the table that P(X = 0) is 0.4

Hence, P(X ≥ 1)

= 1 - 0.4

= 0.6

Hence, the probability to take at least one class is 0.6

3.

The probability to take 2 or 3 classes in a semester = P( X = 2)  +  P(X = 3)

= 0.15  +  0.08

= 0.23

4.

We know that the expectation of any distribution

= ∑xp(x)

where,

x is the random variable

p(x) is the probability of the random variable

Therefore,

E(X) = 0 X 0.4  +  1 X 0.25  +  2 X 0.15  +  3 X 0.08  +  4 X 0.02  +  5 X 0.1

= 0  +  0.25  +  0.30+  0.24  +  0.08  +  0.50

= 1.37

Therefore the expectation of the given distribution is 1.37

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Answer:

y=-4x+2/3.,......,....................,-

Claribel needs to pay $875 for 17 months to gym, $25 for one time membership fee and $50 for 17 months.

A set or group of equations that you solve all at once is referred to as a "system" of equations. A linear equation can be represented as Ax + By +C = 0, Where A, B are coefficient and C is the constant. Linear equations (those that graph as straight lines) are easier to understand than non-linear ones.

To find the amount for Claribel, we have to find the monthly fee and one time membership fee for the gym.

Let x be one time membership fee for the gym and y be the monthly fees, so the system of equations will be,

x + 6y = 325

x + 9y = 475

Now, subtracting the above equations, we get

3y = 150

y = 50

Now, putting the value of y in first equation, we get

x + 6(50) = 325

x+300 = 325

x = 25

Now, finding the amount for Claribel,

One time membership fee + 17(Monthly Fee) = Total Amount

Putting the values,

Total Amount = 25 + 17(50)

= 25 + 850

=$ 875

Therefore, Claribel needs to pay $875 for 17 months to gym.

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For the given expression, the values are a = 3, b = 3, c = 5 and d=2

What are prime number?

What is prime factorization?

The prime factorization of 600 is given by

600 = 2 * 2 * 2 * 3 * 5 * 5

       = 2³ * 3 * 5²

Compare this to the given expression.

Hence, the values are a = 3, b = 3, c = 5 and d=2

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Step-by-step explanation:

counting numbers means whole numbers.

these divisible rules mean numbers that are divisible by 4 and by 3 and by 5.

4 = 2×2

so, everything that is divisible by 4 is also divisible by 2.

6 = 2×3

everything that is divisible by 2 and by 3 is also divisible by 6. therefore everything that is divisible by 4 and by 3 is also divisible by 6.

5 is a prime number on its own.

so, we are looking for all numbers that are divisible by

3×4×5 = 60

the smallest common multiple of 2, 3, 4, 5 and 6.

formally we get this by the combination of the longest chains of the prime factors :

2 = 2

3 = 3

4 = 2×2

5 = 5

6 = 2×3

the longest chain of 2 is 2×2.

the longest chain of 3 is 3.

the longest chain of 5 is 5.

so, 2×2×3×5 = 60

therefore, our solution is all numbers divisible by 60.

that means all multiples of 60 between 200 and 500.

what is the lowest number for that ?

3×60 = 180 too low

4×60 = 240 ok

what is the highest number ?

8×60 = 480 ok

9×60 = 540 too high

so, we only have

4×60 = 240

5×60 = 300

6×60 = 360

7×60 = 420

8×60 = 480

we have 5 numbers between 200 and 500 that are divisible by all of 2, 3, 4, 5 and 6.

The equation that represents the relationship between h and c is given by h = c + 29.

It is given to us that -

The local coffee shop sells 29 more hot coffee items than iced coffee items

Let h represent the number of hot coffee items sold

Let c represent the number of iced coffee items sold

We have to write an equation that represents the relationship between h and c.

According to the given information, the local coffee shop sells 29 more hot coffee items than iced coffee items

=> h = c + 29

The equation that represents the relationship between h and c is given by h = c + 29.

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Answer:

32 cm²

Step-by-step explanation: