How many solutions does the system have?
x+y=3
5x + 5y = 15
Choose 1 answer:
A. Exactly one solution
B. No solutions
С. Infinitely many solutions

They’re the same.

Give them common denominators by looking at their least common multiples. 6 and 21 are the denominators and they have to be the same to compare. Their least common multiple is 42.

So 1 4/6 will turn into 1 28/42. I know this because their least common multiple is 42. So I multiplied the 6 by 7 to get 42 as the denominator and you must also multiply the numerator by 6.

1 14/21 will need to be multiplied by 2 to get a denominator of 42. It will turn into 1 28/42. Both simplify down to 1 2/3.

Answer:

The are the same.

Step-by-step explanation:

Because both begin with a 1, ignore that for now.

You have 4/6 and 14/21. Do your best to reduce each. Think about a number that can go into each.

Start with 4/6. They are both even numbers, so 2. 4/2 =  2 and 6/2 = 3

so 4/6 can be reduced to 2/3.

14/21 is trickier, one is odd and the other is even, so no even number will work. 3 can't go in to 14, or 5, but 7 can, and cool! 7 can go in to 21 as well!

14/7 = 2   21/7 = 3    so 14/21 can be reduced to 2/3!

You can also use a common denominator, but you need a calculator for this problem. To solve that way you would take 4/6 and multiply by 21/21 and you would multiply 14/21 by 6/6, this way you'll end up with 126 on the bottom, and you'll see you get 84 on the top.

[tex]\frac{4}{6} * \frac{21}{21} = \frac{84}{124}[/tex]

[tex]\frac{14}{21} * \frac{6}{6} = \frac{84}{124}[/tex]

This is much harder without a calculator. Always try and reduce first, because if you end up having to find a common denominator, it will be smaller and more manageable.

Answer:

Use the distance formula to determine the distance between two points.

Exact Form:

4 √ 10

The distance between points (-8, 5) and (4, 9) is 4√10.

A coordinate plane is a plane in which a set of two number lines are represented, horizontal line is called x-axis and vertical line is called y-axis.

The given points are,

P(-8, 5) and Q(4, 9)

To find the distance between points P(-8, 5) and Q(4, 9),

Use formula,

The distance between two points A(x₁, y₁) and B(x₂, y₂)

Distance[tex]AB =\sqrt{(x_2-x_1)^2+ (y_2-y_1)^2}[/tex]

Distance between P(-8, 5) and Q(4, 9),

[tex]PQ = \sqrt{(4+8)^2 + (9-5)^2}\\\\PQ = \sqrt{12^2+4^2}\\\\ PQ = \sqrt{144 + 16}\\\\PQ = \sqrt 160\\\\PQ = 4\sqrt10\\[/tex]

The distance between points P(-8, 5) and Q(4, 9) is 4√10.

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Answer:

6.25 hours

Step-by-step explanation:

pages per hour

pages/hour

90/2.5 = 36

36 pages per hour

225 / 36 = 6.25 hours

Answer:

6.25 hours

Step-by-step explanation:

2 and half hours = 2.5 hours

Proportions:

90 pages  ⇔  2.5 hours

225 pages  ⇔  E hours

E = 225*2.5/90

E = 6.25 hours

6.25 hours = 6 and 1 quarter hours

Answer:

8[tex]x^{3}[/tex] + 9[tex]x^{2}[/tex] + 5x -3

Step-by-step explanation:

Answer:

55 packages

Step-by-step explanation:

33×5 = 165

165÷3 = 55

Answer:

x=-9

3x+1=5x+19

    -1        -1  

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

3x=5x+18

-5x -5x

----------

-2x=18

x=-9

Answer:

Answers in the pics

Step-by-step explanation:

If you have any questions about the way I solved it, don't hesitate to ask ÷)

Answer:

x = -15

Step-by-step explanation:

3x–7x=60

Combine like terms

-4x = 60

Divide by -4

-4x/-4 = 60/-4

x = -15

Answer:  x=-15

Step-by-step explanation:

3x -7x =60  

-4x = 60

x= -15  

Step-by-step explanation:

Use the function to find the coordinates of the endpoints.  Find the slope between those points, then use point-slope form to write the equation.  If you wish, you can simplify to slope-intercept form.

For example, #66:

f(2) = -4(2) + 1 = -7

f(5) = -4(5) + 1 = -19

So the endpoints of the secant line are (2, -7) and (5, -19).  The slope between those lines is:

m = (-19 − (-7)) / (5 − 2)

m = -12 / 3

m = -4

The equation of the line in point-slope form is:

y − (-7) = -4 (x − 2)

y + 7 = -4 (x − 2)

Simplifying:

y + 7 = -4x + 8

y = -4x + 1

f(x) is a line, so unsurprisingly, the secant line connecting two points on that line has the same equation.

Let's try #68:

g(2) = (-1)² + 1 = 2

g(5) = (2)² + 1 = 5

So the endpoints of the secant line are (-1, 2) and (2, 5).  The slope between those lines is:

m = (5 − 2) / (2 − (-1))

m = 3 / 3

m = 1

The equation of the line in point-slope form is:

y − 2 = 1 (x − (-1))

y − 2 = x + 1

Simplifying:

y = x + 3

Answer:

Ok, let's define the notation:

A is the number of 2-point field goals that your team scored.

B is the number of 3-point field goals that your team scored:

We know that:

" your team scored three times as many 2-point field goals than it did 3-point field goals,"

This can be written as:

A = 3*B

" And scored a total of 90 points."

A*2 + B*3 = 90

Then we have a system of two equations and two variables:

A = 3*B

A*2 + B*3 = 90

Now we can replace the first equation into the second one and get:

(3*B)*2 + B*3 = 90

B*6 + B*3 = 90

B*9 = 90

B = 90/9 = 10

And we know that:

A = 3*B

A = 3*10 = 30

Then your team scored 30 2-point field goals and 10 3-point field goals (a total of 40 if you combine them)

Answer:

74

Step-by-step explanation:

answer: 74

explanation: hope it helped

Answer:

186

Step-by-step explanation:

10×9+32×3

90+96

=186

HOPE THIS HELP YOU

Answer: Hi!

First we will substitute the variables and then solve the equation.

The equation will look like this after we substitute:

10(9) + 32(3)

We will multiply:

(90) + (96)

We will add:

186

This equation is equal to 186.

Hope this helps!

Answer:

n + 32

Step-by-step explanation:

More than indicates you are adding. 32 more than n is shown by the expression n + 32.

The algebraic expression for 32 more than a number n is 32 + n where n is the real number.

It is defined as the combination of constants and variables with mathematical operators.

It is given that:

32 more than a number n

Here n is the real number.

As we know,

The linear expression can be defined as the relation between two variables, if we plot the graph of the linear expression we will get a straight line.

If in the linear expression, one variable is present, then the expression is known as the linear expression in one variable.

The expression can be written mathematically,

32 more than a number n = 32 + n

Thus, the algebraic expression for 32 more than a number n is 32 + n where n is the real number.

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Step-by-step explanation:

Hey, there!!

Let's simply work with it,

60° + 2x° + (2x+12)° = 180° { being a linear pair}.

or, 72° + 4x = 180°

4x = 180° - 70°

[tex]x = \frac{108}{4} [/tex]

Therefore, the value of x is 27°.

Now,

2x° = (2×27)°= 54°

(2x+12)° = 2×27°+12°= 66°.

(x+2)= 27+ 2= 29°

Now, The left angle is 27°.

Therefore, The answer is option A.

Hope it helps...

Answer:

1,11,110

Step-by-step explanation:

Answer:

Cylinder Volume = PI * radius^2 * height

Radius = Square Root [Volume / (PI * height)]

Radius = Square Root [ 134 / (3.14 * 7.1)]

Radius = 2.45103

Radius = 2.45

Step-by-step explanation:

B

Because you multiply the denominator by four and see if its close enough than multiply ot by .05

Answer: it will be 1/6

Step-by-step explanation:

The word in the problem that indicates that a negative sign should be used is "descend".

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

We know that he stops for water breaks four times, and between each water break, he descends 15 meters.

The written equation is:

4 x (-15)m = -60m

The negative sign is used because the hiker is descending, so its height is decreasing. The word in the problem that indicates that a negative sign should be used is "descend"

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Answer:

X=8-3

X=5

Step-by-step explanation:

X is equal to 5

8-3

The symbol change always when we move digit from the equalent sign

Hey there! I'm happy to help!

We want to get c all by itself on one side of the equation. Usually variables go on the left side, so let's flip the equation around.

c/9=-8

If we multiply c/9 by 9, the 9 will cancel out because if you divide by 9 and then multiply by 9 it just equals 1. We can do this to isolate the c, but whatever you do to one side of the equation, you have to do to the other. So, we multiply both sides by 9.

c/9×9=-8×9

c=-72

Have a wonderful day! :D

Answer:

c = -72

Step-by-step explanation:

I hope this helps!

Answer:

-3q - 10

Step-by-step explanation:

-5q - 2 + 2q - 8

-5q + 2q - 2 - 8

-3q - 10

Answer:

[tex]y = \frac{x}{36}[/tex]

Step-by-step explanation:

Given

Length of string = x inches

Required

Determine the length in yards

Represent the equivalent length with y

Such that

[tex]y = x\ inches[/tex]

Divide x by 36 to get equivalent in yards

[tex]y = \frac{1}{36} * x[/tex]

[tex]y = \frac{x}{36}[/tex]

Hence, the equivalent in yards is [tex]\frac{x}{36}[/tex]

The expression should be [tex]x \div 36[/tex]

Here we need to divide x by 36 so that the equivalent in yards could come

[tex]=\frac{1}{36} \times x\\\\ = \frac{x}{36} [/tex]

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Answer:

6

Step-by-step explanation:

Let the two integers be a and b.

The difference of them is 26. Thus:

[tex]a-b=26[/tex]

One of them (let's use a) is 2 more than 5 times the other. Thus:

[tex]a=2+5b[/tex]

Substitute:

[tex]a-b=26\\(2+5b)-b=26[/tex]

Combine like terms:

[tex]4b+2=26[/tex]

Subtract 2 from both sides:

[tex]4b=24[/tex]

Divide by 4:

[tex]b=6[/tex]

And the second number is:

[tex]a-b=26\\a-6=26[/tex]

Add 6 to both sides:

[tex]a=32[/tex]

So, our two numbers are 32 and 6

And the smaller integer is 6.

And we're done :)

Answer:

The smaller intrger is:

6

Step-by-step explanation:

a = 5b + 2

a - b = 26

then:

(5b+2) - b = 26

4b = 26 - 2

4b = 24

b  = 24/4

b = 6

a = 5b + 2

a = 5*6 + 2

a = 30 + 2

a = 32

Check:

32-6 = 16

32 = 5*6 + 2

32 = 30 + 2

6<32

the smaller integer is:

6

Answer: A & C & D

Step-by-step explanation:

The Angles which are in linear pairs are,

∠SRT and ∠TRV,

∠VRW and ∠WRS,

∠VRU and ∠URS.

When two lines meet at a single point, they form a linear pair of angles. After the intersection of the two lines, the angles are said to be linear if they are adjacent to one another. A linear pair's angles always add up to 180 degrees. Additional angles are another name for these angles. The angles with a common vertex are called the adjacent angles.

Given the figure and finding linear pair of angles,

The property of linear pair of angles says that the sum of two angles is 180⁰.

A: ∠SRT + ∠TRV = 180⁰

pair is linear

B:  ∠SRT + ∠TRU > 180⁰

pair is nonlinear

C: ∠VRW + ∠WRS  = 180⁰

pair is linear

D: ∠VRW + ∠URS = 180⁰

par is linear

E: ∠URW + ∠WRS < 180⁰

pair is nonlinear

Hence the linear pairs are (∠SRT and ∠TRV), (∠VRW and ∠WRS), and (∠VRW and ∠URS).

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Answer:

2x-7

Step-by-step explanation:

Answer:

2x-7

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

You would first add c to the side that k is on and then divide k+c by 4 because it is 4x which means they are being multiplied together so you have to divide to get them apart.

Answer:

Step-by-step explanation:

[tex]4x- c = k[/tex]

Move -c to the right side and change its sign

[tex]4x = k+c\\[/tex]

Divide both sides of the equation by 4

[tex]\frac{4x }{4} = \frac{k+c}{4}\\ \\x = \frac{k+c }{4}[/tex]