Solve the system of equations by substitution.
6 = −4x + y −5x − y = 21
Answer:


Solve the system by the elimination method.
2x + y = 20 6x – 5y = 12
Answer:

Let's label them 1-6, for convenience.

1. 1 solution (a positive # of ys equaling a positive constant)

2. Infinitely many solutions (You get 0=0 if you completely simplify)

3. No solution (take out the 3z's; 2.5 doesn't equal 3.2)

4. Infinitely many solutions (take out the 3/4 x; 1.1+2 = 3.1)

5. No solution (take out the 4.5r; 0 doesn't equal 3.2)

6. 1 solution (x = 3 1/2)

Answer:

1) [tex]\frac{1}{2}y+\frac{32}{10}y=20[/tex] One solution

2)[tex]\frac{15}{2}+2z-\frac{1}{4}=4z+\frac{29}{4}-2z[/tex] Infinite Number of Solutions

3) [tex]3z+2.5=3.2+3z[/tex] No solution.

4) [tex]1.1+\frac{3}{4}x+2=3.1+\frac{3}{4}x[/tex] Infinitely Many Solutions

5) [tex]4.5r=3.2+4.5r[/tex] No solution

6) [tex]2x+4=3x+\frac{1}{2}[/tex] One solution

Step-by-step explanation:

Equations may have exactly one solution, uncountable solutions or even no possible solution when the solution is a contradiction and this solution is never true.

1) [tex]\frac{1}{2}y+\frac{32}{10}y=20[/tex] One solution Let's prove it by solving it:

[tex]\frac{1}{2}y+\frac{32}{10}y=20\Rightarrow \frac{37}{10}y=20\Rightarrow 10*\frac{37}{10}y=20*10\\37y=200\Rightarrow \frac{37}{37}y=\frac{200}{37}\Rightarrow y=\frac{200}{37}\Rightarrow S=\left \{ \frac{200}{37} \right \}[/tex]

2)[tex]\frac{15}{2}+2z-\frac{1}{4}=4z+\frac{29}{4}-2z[/tex] Infinite Number of Solutions because infinitely many solutions satisfies for z.

[tex]\frac{15}{2}+2z-\frac{1}{4}=4z+\frac{29}{4}-2z\\\frac{29}{4}+2z=\frac{29}{4}+2z[/tex]

3) [tex]3z+2.5=3.2+3z[/tex] No solution. There's no way to add 2.5 to 3z and have the same amount as adding 3.2 to 3z. This is contradiction. This is a false equality.

4) [tex]1.1+\frac{3}{4}x+2=3.1+\frac{3}{4}x[/tex] Infinitely many solutions. This equation has infinitely many solutions since the left side is equal to the right side, any value plugged in x may result in many solutions.

5) [tex]4.5r=3.2+4.5r[/tex] No solution Similarly, again. There's no way of adding 3.2 to 4.5r being equal to 4.5r. Another contradiction. This is a false equality.

6) [tex]2x+4=3x+\frac{1}{2}[/tex] One solution

[tex]2x+4=3x+\frac{1}{2}\\2x+4-2x=3x+\frac{1}{2}-2x\\4=x+\frac{1}{2}\\4-\frac{1}{2}=x\Rightarrow x=\frac{7}{2}\Rightarrow S=\left \{ \frac{7}{2} \right \}[/tex]

Since we can see on the left side different expressions than on the right side. All that is left is doing the test, by solving it.

Answer:

Well 3/5 is .60 and 2/4 is .50 so in these regards she grew .10 more inches then her

Step-by-step explanation:

Answer:

1/10 of an inch taller

Step-by-step explanation:

3/5 2/4

12/20   10/20

2/20= 1/10

[tex]Use:\\\\a(b-c)=ab-ac\\\\a^n\cdot a^m=a^{n+m}[/tex]

[tex]10c^4(9-8c^2)=(10c^4)(9)-(10c^4)(8c^2)=90c^4-80c^{4+2}\\\\=\boxed{90c^4-80c^6}[/tex]

Answer:

a) AC = [tex]\sqrt{13}[/tex]

b) Area = [tex]\frac{\sqrt 3}{4}[/tex] × [tex]a^{2}[/tex]

Step-by-step explanation:

a) From question,

                      AC = BC, CD⊥AB

Now in ΔCAD and ΔCBD

AC=BC, ∠A = ∠B and AD=BD (because in isosceles triangle perpendicular bisects the side).

then, from SAS potulates

                     ΔCAD≅ΔCBD

So,

    AD = [tex]\frac{AB}{2}[/tex] = [tex]\frac{4}{2}[/tex] = 2 in

From Pythagorean theorem in ΔADC

[tex]AC^{2}[/tex] = [tex]AD^{2}[/tex] + [tex]CD^{2}[/tex]

[tex]AC^{2}[/tex] = [tex]2^{2}[/tex] + [tex]3^{2}[/tex]

[tex]AC^{2}[/tex] = 4 + 9 = 13

AC = [tex]\sqrt{13}[/tex]

b) In given ΔABC,

               AB = BC = AC = a,  means ΔABC is a equilateral triangle.

So, area of equilateral triangle is

                              Area = [tex]\frac{\sqrt 3}{4}[/tex] ×  [tex]side^{2}[/tex]

                                side = a

then,

       Area = [tex]\frac{\sqrt 3}{4}[/tex] × [tex]a^{2}[/tex]              

Answer:

a) √7

Step-by-step explanation:

Answer:

a. ∠D'A'B'

Step-by-step explanation:

From the graph it is clear that the transformation doesn't affect the size and shape of the figure ABCD.

Only the coordinates of the points are changed with the length of each side remaining the same.

Hence the corresponding angle values will also remain unaltered.

∴ ∠DAB = ∠D'A'B'

18/5 is 3.6. You must always round down because you would be using more buttons if you did. So round down 3.6 to get 3.

Answer:

Step-by-step explanation:

y= -3x+1

you use inverse operations, and since you want the y alone, you subtract 3x on both sides, giving you y= -3x+1

Answer:

1/6 is the probability of it being a green plastic marble.

Step-by-step explanation:

Note that there are 18 marbles in all (12 + 6 = 18).

Half of the green marbles (6) are made of plastic: 6/2 = 3

From the information above, we see that 3 green marbles are made of plastic. There are 18 marbles in all.

Divide, and simiplify.

(3/18)/(3/3) = 1/6

1/6 is the probability of it being a green plastic marble.

~

Answer:

[tex](2.2,-1.35)[/tex]

Step-by-step explanation:

we have

[tex]y=-\frac{7}{4}x+\frac{5}{2}[/tex] ------> equation A

[tex]y=\frac{3}{4}x-3[/tex] ------> equation B

Remember that

The solution of the system of equation is the intersection point both graphs

Using a graphing tool

see the attached figure

The intersection point is [tex](2.2,-1.35)[/tex]

Final answer:

To find the approximate solution to the system of linear equations, set the equations equal to each other, combine like terms, simplify, solve for x, substitute the value of x back into either equation to find y, and simplify further. The approximate solution is x = 3/2 and y = -1/8.

Explanation:

Given the system of linear equations:

y = -7/4 x + 5/2

y = 3/4 x - 3

Set the two equations equal to each other:

-7/4 x + 5/2 = 3/4 x - 3

Combine like terms:

2x + 5 - 14 = 6 - 12

Simplify:

2x - 9 = -6

Add 9 to both sides:

2x = 3

Divide both sides by 2:

x = 3/2

Substitute the value of x back into either equation to find the value of y:

y = -7/4 * (3/2) + 5/2

Simplify:

y = -21/8 + 20/8

Add the fractions:

y = -1/8

Therefore, the approximate solution to the system of linear equations is x = 3/2 and y = -1/8.

You can add two square roots of the numbers if the numbers are the same:

[tex]\sqrt{a}+\sqrt{a}=2\sqrt{a}\\\\n\sqrt{a}+m\sqrt{a}=(n+m)\sqrt{a}\\\\\sqrt{a}+\sqrt{b}=\sqrt{a}+\sqrt{b}[/tex]

Final answer:

To find the sum of square roots, you can add the square roots together if the numbers underneath are the same. If the numbers are different, you cannot simplify them further.

Explanation:

To find the sum of a square root, you need to add the square roots together. However, the numbers under the square roots must be the same. For example, if you have √2 + √2, you can add them to get 2√2. But if you have √2 + √3, you cannot simplify it any further.

Another way to find the sum of square roots is to simplify them using the multiplication property. For example, if you have √2 + 2√2, you can combine them as (1+2)√2 = 3√2.

It is important to note that you can only add square roots with the same number underneath. If the numbers are different, you cannot simplify them further.

Answer:

[tex]4\sqrt{5}\ un.[/tex]

Step-by-step explanation:

The picture shows rectangular prism with rectangular base and heigth h. The dimenssions of base rectangle are l and w.

The diagonal of reactangle with known length l and width w can be calculated using the Pythagorean theorem:

[tex]d^2=l^2+w^2,\\ \\d^2=8^2+4^2,\\ \\d^2=64+16,\\ \\d^2=80,\\ \\d=4\sqrt{5}\ un.[/tex]  

Answer:

Neither

Step-by-step explanation:

It's neither. The terms do not differ (which means you add the same number to each term) by any constant amount.  (Arithmetic)

The terms do not have a common number that you multiply the present term to get the next term. (Geometric)

So this one is neither.

Answer:

144

Step-by-step explanation:

You just multiply 12x12

Each "x" represents one tree that produced that amount of sap in gallons.

To find the total amount of sap produced, add all of the amount of sap produced from each tree

3 trees produced 1/4 gallons of sap

2 trees produced 3/8 gallons of sap

4 trees produced 5/8 gallons of sap

1 tree produced 1 gallon of sap

You can do this:

[tex]\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{3}{8}+\frac{3}{8} +\frac{5}{8}+\frac{5}{8}+\frac{5}{8}+\frac{5}{8}+1[/tex]

[tex]=\frac{3}{4}+\frac{6}{8}+\frac{20}{8}+1[/tex]      

[tex]\frac{3}{4}+\frac{26}{8}+1[/tex] Make all the denominators the same

[tex]\frac{6}{8}+\frac{26}{8}+\frac{8}{8}=\frac{40}{8}=5[/tex]

5 gallons

Or you could have done:

[tex](\frac{1}{4} *3)+(\frac{3}{8}*2)+(\frac{5}{8}*4)+(1*1)[/tex]

[tex]=\frac{3}{4}+\frac{6}{8}+\frac{20}{8}+1[/tex]      

[tex]\frac{3}{4}+\frac{26}{8}+1[/tex] Make all the denominators the same

[tex]\frac{6}{8}+\frac{26}{8}+\frac{8}{8}=\frac{40}{8}=5[/tex]

5 gallons

Answer:

5 gallons

Step-by-step explanation:

because if u add all togather u get 6/8+26/8+8/8+40/8= It would be 5 Gallons

Answer:

3 1/2

Step-by-step explanation:

You have to do 7 divided by 2 or 1/2 x 7

Answer:

Well it normally be 3.5

Step-by-step explanation:

You take seven and divide it by 2 (ps) if you are talking about your answer needing to be a whole answer just round up

Answer:

x > -3

Step-by-step explanation:

- 4x - 10 < 2

     + 10 < + 10

- 4x < 12

-4      -4

x > -3

I think the sign flips because the negative sign is w/the X.... If it doesn't, sorry 4 being wrong...

The solution to the inequality -4x - 10 ≤ 2 obtained by isolating the variable x is x ≥ -3. This includes all real numbers x that are greater than or equal to -3.

Let's solve the inequality -4x - 10 ≤ 2 step-by-step.

Therefore, the solution to -4x - 10 ≤ 2 is x ≥ -3. This means that for any real number x that is greater than or equal to -3, the inequality -4x - 10 ≤ 2 is true.

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Winston drove 89 miles in the morning and 159 miles in the afternoon.

Let's assume that Winston drove x miles in the morning. Since he drove 70 fewer miles in the morning than he did in the afternoon, he drove (x + 70) miles in the afternoon.

According to the question, he can drive a total of 248 miles in a day. So, we can write the equation: x + (x + 70) = 248

Simplifying the equation, we get: 2x + 70 = 248

Subtracting 70 from both sides, we have: 2x = 178

Finally, dividing both sides by 2, we find: x = 89

Therefore, Winston drove 89 miles in the morning and (x + 70) = 89 + 70 = 159 miles in the afternoon.

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It's a linear function. We need only two points to the plotting of the graph.

[tex]3x+2y=12\qquad\text{subtract 3x from both sides}\\\\2y=-3x+12\qquad\text{divide both sides by 2}\\\\y=-\dfrac{3}{2}x+6\\\\for\ x=0\to y=-\dfrac{3}{2}(0)+6=0+6=6\to(0,\ 6)\\\\for\ x=4\to y=-\dfrac{3}{2}(4)+6=-6+6=0\to(4,\ 0)[/tex]

Answer:

k = 60

Step-by-step explanation:

2k + 11 = 131

2k = 131 - 11

2k = 120

k = 60

I hope I helped you.

It takes 4 ounces of blue paint and 3 ounces of red paint to make Patrick's favorite shade of purple.

Multiply the numbers by 2. This will not affect the proportion. Thus, the new statement will be true respect to the original one.

It takes 8 ounces of blue paint and 6 ounces of red paint to make Patrick's favorite shade of purple. That's answer choice B.

Multiply the original numbers by 5. Again, this will not affect the proportion, meaning that the statement will remain true.

It takes 20 ounces of blue paint and 15 ounces of red paint to make Patrick's favorite shade of purple. This is answer choice D.

Thus, the answers are answer choices B and D.

Answer:7 pints is more than 4 quartz

Step-by-step explanation:

One pint is the equivalent to 0.5 quartz.

Answer: 1. D) Exponents     2. A) Addition and subtraction from left to right

Step-by-step explanation: PEMDAS will help you to understand! Remember, first, its parentheses, then exponents (Answer for Question 1), then multiply and divide from left to right, then add and subtract from left to right (Answer for Question 2).

Hope this helped!

Plz mark brainliest!

length = area/width

l = 105/7 = 8

The length of the rectangle is 15.

Answer:

F = 2

Step-by-step explanation: If you want to know which one is a solution, you have to substitute the numbers in for F.

F = 7:

3 > f

3 > 7

This is false because 3 is NOT greater than 7, it is less than 7.

F = 9:

3 > f

3 > 9

This is false because 3 is NOT greater than 9, it is less than 9.

F = 2:

3 > f

3 > 2

This is TRUE because 3 IS greater than 2.

Hope this help you!!! :)

Answer:

x=2

y=-5

Step-by-step explanation:

-3(4y+22)-y=-1

-12y-66-y=-1

-13y-66=-1

-13y=65

y=-5

x=4(-5)+22

x=-20+22

x=2

Answer:

y = 5

x = 2

Step-by-step explanation:

So we know what x is already.

x = 4y + 22

Now we plug that in to the first equation.

-3 ( 4y + 22) - y = -1

Distribute the -3.

-12y - 66 - y = -1

Combined like terms:

-13y - 66 = -1

-13y = 65

Divide -13 on both sides:

y = -5

Now plug your y into the second equation:

x = 4(-5) + 22

x = -20 + 22

Simplify:

x = 2

Check your answer:

-6 - (-5) = -1

2 = -20 + 22

Answer:

35 because if you multiply youll get hat you need

i hope its correct

Step-by-step explanation:

Answer:

100%

Step-by-step explanation:

Use the equation:

100=(72-36)÷36×100

Answer:

D) 140

Step-by-step explanation:

The equation for direct variation is y= kx

If we know x and y we can solve for k

35 = k*2

Divide each side by 2

35/2 =k

Now the equation for direct variation is

y= 35/2 x

Given x=8 we can substitute in

y = 35/2 * 8

y = 140

Answer: D) 140

(both x and y are multiplied by 4)