Solve the following system algebraically. Show all of your work. (5 points)

y = x + 3
3x + y = 19

Answer:

[tex]6x^{2} +x-12[/tex]

Step-by-step explanation:

All you need to do is multiply equation B by 2 and multiply equation A by 3, then put an addition sign between them and combine like terms after you've distributed what you needed for each one.

Answer:

Yes, Samuel dart does land on the dart board

Step-by-step explanation:

The given parameters are;

The height from the floor to the bulls eye = 5 feet 8 inches

The size of the standard board = 18 inches diameter

The distance of the bulls eye from the wall to the left = 11 feet

The distance the dart Samuel throws land from the left wall = 11.5 feet

The distance above the ground, the dart Samuel throws land = 5.5 feet

Whereby Samuel throws the dart directly at the dartboard, we have;

The location of the bulls eye = (11, 5.67)

The equation of the circle representing the dart board = (x - 11)² + (y - 5.67)² = 0.75² = 0.5625

The unit of the radius is in feet

The position of Samuel's dart is represented by the coordinate, (11.5, 5.5)

Plugging in the coordinates of the position of Samuel's dart into the equation of the circle of the dart board gives;

(11.5 - 11)² + (5.5 - 5.67)² = 0.2789 ≈ 0.528²

Therefore, given that the square of the distance of the position of Samuel's dart is less than the square of the radius of the dart board, we have;

Yes, Samuel dart does land on the dart board.

From the parameters given to find out if Samuel's dart landed on the dartboard, we can say that;

Samuel's dart does not land on the dartboard.

We are given;

Height from the floor to the bulls eye = 5 ft 8 in = 5.67 ft

Diameter of the standard dartboard = 18 in = 1.5 ft

Thus, radius; r = 1.5/2 = 0.75 ft

Distance of the bulls eye from the wall to the left = 11 ft

Distance of dart thrown by Samuel from the left wall = 11.5 ft

Height of dart thrown by Samuel above the ground = 5.5 ft

We know that general equation of a circle is;

(x - a)² + (y - b)² = r²

Since Height from the floor to the bulls eye is 5.67ft,then a = 5.67 ft

And also since Distance of the bulls eye from the wall to the left = 11 ft, then b = 11 ft

Thus;

(x - 11)² + (y - 5.67)² = 0.75²

(x - 11)² + (y - 5.67)² = 0.5625

Now, since he throws a dart at the dartboard that lands at a point 11.5 feet from the left wall and 5.5 feet above the floor. Thus;

r² = (11.5 - 11)² + (5.5 - 5.67)²

r² = 0.2789

r² of 0.2789 gotten here is lesser than 0.5625 gotten earlier, we can conclude that Samuel's dart does not land on the dart board.

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Answer:

x=14

Step-by-step explanation:

3x-15=27 (add 15 to both sides)

3x=42 (divide both sides by three)

x=14

The required number is -4.

A linear equation only has one or two variables. No variables in a linear equation is raised to power greater than 1 or used as denominator of a fraction.

Now it is given that, 15 is subtracted from three times a certain number,

the result is 27.

Now let x be the number.

Three times the number = 3x

Therefore, 15 is subtracted from three times a certain number = 15 - 3x

Therefore, the equation for 15 is subtracted from three times a certain number, the result is 27 is,

15 - 3x = 27

Subtracting 15 both the side we get,

15 - 3x - 15 = 27 - 15

⇒ -3x = 12

or, x = -12/3

⇒ x = -4

which is the required number.

Thus, the required number is -4.

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Answer:

56/210---> 8/30---> 4/15

Step-by-step explanation:

Answer:

D. SAS

Step-by-step explanation:

Given: ΔABC

Bisecting <ABC to create point D implies that BD is a common side to  ΔABD and ΔCBD.

Also,

m<ABD = m<CBD (angle bisector)

BA = BC (given property of the isosceles triangle)

Therefore,

ΔABD ≅ ΔCBD (Side Angle Side)

The reason for statement 5 in this proof is that ΔABD ≅ ΔCBD by SAS (Side-Angle-Side) relations of the congruent triangles.

Answer:

Option D is correct trust me

Step-by-step explanation:

Given :

An alloy is a mixture of metals. Suppose that a certain alloy is made by mixing 50 g of an alloy containing 12% copper with 78 g of an alloy containing 92% copper.

To Find :

How many grams of copper are in the resulting mixture what percentage of the resulting mixture is copper.

Solution :

Mass of copper in 50 gm alloy = [tex]50\times 0.12 = 6\ gram[/tex].

Mass of copper in 78 gm alloy = [tex]78\times 0.98 = 76.44\ gram[/tex].

Total mass of copper, ( 6 + 76.44 ) gm = 82.44 gram.

Percentage of copper in resulting mixture :

[tex]\%=\dfrac{82.44}{50+78}\\\\\%=64.4\ \%[/tex]

Hence, this is the required solution.

Answer:

It would be 2x-y=3.

Answer:

The largest area she can enclose for her garden with this fencing is [tex]56 ft^2[/tex]

Step-by-step explanation:

Suppose the rectangular space Mrs. Greene wants to plant has dimensions x feet and y feet.

Since each section of fencing is 1-foot long, both x and y must be integer numbers.

The perimeter of the rectangular space is calculated as:

P = 2x + 2y

And we know she uses all 30 sections of fencing, thus:

2x + 2y = 30, where x, y are integers and positive.

Simplifying by 2:

x + y = 15

Solve for x:

x = 15 - y

This equation doesn't have infinitely many solutions, since both numbers must be integers and positive. Suppose we start by setting y=1, then x=14. That is a possible arrangement for the garden.

Another valid option is for y=2, x=13

Continuing with these patterns, we find the maximum value for y is 7, x=8, because if we set y=8, x=7, this is the same condition as y=7, x=8.

Thus, from y=1 to y=7, there are 8 possible combinations for the arrangement of the garden.

The area of a rectangle is

[tex]A=x\cdot y[/tex]

Testing some possible arrangements:

y=1, x=14

[tex]A=1\cdot 14= 14 ft^2[/tex]

y=2, x=13

[tex]A=2\cdot 13= 26 ft^2[/tex]

y=3, x=12

[tex]A=3\cdot 12= 36 ft^2[/tex]

We can notice the combination y=7, x=8 has an area of:

[tex]A=7\cdot 8= 56 ft^2[/tex]

This is the largest possible area of all combinations, thus:

The largest area she can enclose for her garden with this fencing is [tex]56 ft^2[/tex]

Step-by-step explanation:

there were 50 boxes of gum

each box had 36 packs of gum

in each pack were 15 pieces of gum

so total pieces of gum:

for one box of gum total pieces= 15*36= 540 pieces

for 50 boxes= 540*50= 27000 pieces of gum in total

number sentence:

15*36=540

540*50= 27000

bonus question:

27 gums in 1 day

27000 gums in x days

27000/27= 1000 days

Answer:

540 pieces x 50

27000/27=1000 days

Answer:

16r - 250 = 768

Step-by-step explanation:

First, create a term that represents his revenue:

Since he charges students $16 per hour, the amount of money he makes from this can be represented by 16r.

Then, subtract the advertising cost of $250 from this.

Set it equal to 768, because that is how much the gaming system costs.

16r - 250 = 768 will be the equation

Answer:

20 gigabytes

Step-by-step explanation:

Let n represent the amount of gigabytes used.

First make an equation for each senario, Brynlee's would be 60+2.50n and Raylin's would be 45+3.25n.

Set them to equal each other, 60+2.50n=45+3.25n.

Then isolate for n.

60-45=3.25n-2.50n

15=0.75n

Divide both sides by 0.75 to get 20

Answer:

5 ^15

Step-by-step explanation:

(5 ^3)^5 =5 ^(3×5)=5 ^15

The rule used is (a^b)^c = a^(b*c)

If you raise some exponential expression to another exponent, then you multiply the exponents. You keep the base the same.

In this case, a = 5, b = 3, c = 5.

Using a calculator,

5^15 = 30,517,578,125

But it's likely your teacher will want you to keep the answer in exponential form since it's easier to work with.

Step-by-step explanation:

Hey there!

It's obvious that 4 and 4/1 are exactly same.

Reason: something divided by 1 is always a a number same in a numerator.

Example;

1. 7/1 = 7

2. 5/1 = 5

Hope it helps..

Answer:

20, 22, and 24

Step-by-step explanation:

hope this helps. can I also have brainliest please :)

Answer:

BRAINLIEST PLZZ

Step-by-step explanation:

The other 2 numbers are (x + 2) and (x + 4)

Their sum is 66:

x + (x + 2) + (x + 4) = 66

x + x + 2 + x + 4 = 66

3x + 6 = 66

3x = 60

x = 20

2nd number = x + 2 = 20 + 2 = 22

3rd number = x + 4 = 20 + 4 = 24

Answer: The numbers are 20, 22 and 24

Answer:

1. 371 × d = 52

2. n - 320 = 139

3. 317 = k + 110

4. 374 + k = 305

5. 398 = d + 6

Step-by-step explanation:

1. 371 × d = 52

d = 52/371

d = 0.14016172506

2. n - 320 = 139

n = 139 + 320

n= 459

3. 317 = k + 110

k = 317 - 110

k = 207

4. 374 + k = 305

k = 305 - 374

k = -69

5. 398 = d + 6

d = 398 - 6

d = 392

Answer:

Step-by-step explanation:

Given that 8 rolls cost $4.80

let us compute how much 1 roll will cost (that is the unit cost of a roll)

so  8 rolls cost $4.80

     1 roll will cost x

x= 4.8/8

x=$0.6

so the paper tower cost $0.6 per roll (this is the rate)

therefore 6 rolls will cost

=6*0.6

=$3.6

A,B,C

Step-by-step explanation:

Answer:

A, B and C

Step-by-step explanation:

Answer: x=49

x-17=32

Subtract 17 from both sides.

x=32+17

x=49

Answer:

The slope of the line that passes through the points M(-3, 5) and N(1, 8) in decimal form is 0.75

Step-by-step explanation:

The given points are M(-3, 5) and N(1, 8)

The formula for finding the slope, m, given the coordinates of two points on the line is given as follows;

[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Where, (x₁, y₁) = (-3, 5), and (x₂, y₂) = (1, 8), we have;

[tex]Slope, \, m =\dfrac{8-5}{1-(-3)} = \dfrac{3}{4} = 0.75[/tex]

The slope, m = 0.75

The slope of the line that passes through the points M(-3, 5) and N(1, 8) in decimal form = 0.75.

Answer:

A

Step-by-step explanation:

There is no way to tell a pattern.

Answer:

0.15

Step-by-step explanation:

6 divided by 24 equals 0.25

12 divided by 30 equals 0.4

0.4 minus 0.25 is 0.15

$0.15 more per ounce does her conditioner cost than her shampoo.

Given that, the shampoo Eva likes to use costs $6 for a 24-ounce bottle.

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

The conditioner she likes to use costs $12 for a 30-ounce bottle.

Cost of shampoo per ounce =Total cost/Number of ounce

= 6/24

= $0.25 per ounce

Cost of conditioner per ounce =Total cost/Number of ounce

= 12/30

= $0.4 per ounce

Difference =0.4-0.25

= $0.15

Therefore, $0.15 more per ounce does her conditioner cost than her shampoo.

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Answer:

$31.90

Step-by-step explanation:

Hope it helps :)

Have a good day/night

Brainliest pls?

Answer:

V /(lw) = h

Step-by-step explanation:

V = lwh

Divide each side by lw

V/ ( lw) = lwh/(lw)

V /(lw) = h

V /(lw) = h

V = lwh

Divide each side by lw

V/ ( lw) = lwh/(lw)

V /(lw) = h

Answer:

8.950 kg

Step-by-step explanation:

Lemme know if incorrect

Answer:

3 million dollars

Step-by-step explanation:

i just did this and got it right

Answer:

2

Step-by-step explanation:

63/9 = 7 and -5 + 7 is the same thing as 7-5 so it's 2

Answer:

2

Step-by-step explanation:

I hope this helps!

Answer:

78

Step-by-step explanation: