Without attempting to solve, how many solutions does this system of equations have? y=2x+1 −3y=6x+6 1. One Solution 2. No Solution 3. An infinite number of solutions 4. Cannot be determined without solving

Answer:

y=13  , x=36

Step-by-step explanation:

The diagonal of parallelogram bisect at a point where the sides across the intersection are equal

DH=HF

x+3=3y

x=3y-3   first equation

HE=GH

2x-5=5y+2 ⇒ 2x-5y=7 second equation

solve by substitution: x=3y-3

2x-5y=7

2(3y-3)-5y=7

6y-6-5y=7

y=7+6

y=13

x=3y-3

x=3(13)-3

x=36

Answer:

( 2x +3) (x+1)

Step-by-step explanation:

2x^2 + 5x + 3

2 factors to 2 and 1

3 factors to 3 and 1

We need to get 5x in the middle

( 2x +3) (x+1)

Answer:

Glass A

Step-by-step explanation:

Volume = п r ² h

п = 3.14  aprox.

r = radius = diameter/2

h = tall

volume = 3.14 * (84/2)² * 175

volume = 3.14 * 42² * 175

volume = 3.14 * 1764 * 175

volume = 969318mm³

volume = 3.14 * (96/2)² * 125

volume = 3.14* 48² * 125

volume = 3.14 * 2304 * 125

volume = 904320mm³

Answer:

969318 > 904320

then:

Glass A holds more liquid

Answer:

2.64 km

Step-by-step explanation:

24*110=2640 meters

2640/1000=2.64 km

Answer:

Step-by-step explanation:

Let the number of files he had be x

He gave 3/5 of the files

That's

3/5x

After that he still had 14 files left which means when we subtract 14 from the original files we should get 3/5 of the original files

So we subtract 14 from the original number of files

That's

x - 14

We equate the two statements

that's

[tex] \frac{3}{5} x = x - 14[/tex]

Multiply through by 5

[tex]5 \times \frac{3}{5} x = 5x - 70[/tex]

We have

3x = 5x - 70

3x - 5x = 70

-2x = - 70

Divide both sides by -2

We have the final answer as

Therefore he had 35 files at first

Hope this helps you

Answer:

35 files

Step-by-step explanation:

gave=3/5

left=2/5 = 14f

had= 5/5

2/5=14

5/5

5×14÷2 = 35

Answer:

x = 2

Step-by-step explanation:

Probability that the marble comes to rest in the shaded region is equal to the ratio of the shaded area to the total area.

Probability 'P' = [tex]\frac{A'}{A}[/tex]

Area of the shaded region (A')= (x + 1)(x + 2)

Total area of the figure (A) = (2x + 1)(3x + 2)

P = [tex]\frac{(x+1)(x+2)}{(2x+1)(3x+2)}=\frac{3}{10}[/tex]

10(x + 1)(x + 2) = 3(2x + 1)(3x + 2)

10(x² + 3x + 2) = 3(6x² + 7x + 2)

10x² + 30x + 20 = 18x² + 21x + 6

(18x² - 10x²) + (21x - 30x) + (6 - 20) = 0

8x² - 9x - 14 = 0

x = [tex]\frac{9\pm\sqrt{(-9)^2-4(8)(-14)} }{2(8)}[/tex]

x = [tex]\frac{9\pm \sqrt{81+448}}{16}[/tex]

x = [tex]\frac{9\pm 23}{16}[/tex]

x = -[tex]\frac{7}{8}, 2[/tex]

Therefore, positive value of x = 2 will be the answer.

Step-by-step explanation:

You can solve a system of three equations by multiplying each equation by a number that allows you to add or suvtract the same equation together by eliminating the x or y variable

Answer:

To use elimination to solve a system of three equations with three variables, follow this procedure:

Write all the equations in standard form cleared of decimals or fractions.

Choose a variable to eliminate; then choose any two of the three equations and eliminate the chosen variable.

Select a different set of two equations and eliminate the same variable as in Step 2.

Solve the two equations from steps 2 and 3 for the two variables they contain.

Substitute the answers from Step 4 into any equation involving the remaining variable.

Check the solution with all three original equations.

Step-by-step explanation:

Answer:

D) 972

Step-by-step explanation:

2160*9/20 = 19440/20

= 972

Answer: 20%

Step-by-step explanation: $20-$16=$4. 4/20=1/5 or 20%.

Answer: Melody's percent error was 20%

Step-by-step explanation:

20-16=4

4/20=1/5

Answer:

Step-by-step explanation:

[tex]3x+4\geq13\\\\3x\geq9\\\\x\geq3\\\\A=\big<3\,,\ \infty)[/tex]                         [tex]\frac12x+3\leq4\\\\\frac12x\leq1\\\\x\leq2\\\\B=(-\infty\,,\ 2\big>[/tex]

[tex]A\cup B\not=\varnothing\quad for\ all\ x\in(-\infty\,, 2\big>\cup\big<3\,,\ \infty)[/tex]

so:

     [tex]A\cup B=\varnothing\quad for\ x\in(\,2\,,\ 3\,)[/tex]

Answer:hi, the answer would be (a) or 2<x<3 hope this helps :)

Step-by-step explanation: i just took the test got em all correct

Answer:

The answer is C.

Step-by-step explanation:

First, you want to isolate the variable you are look for, 'l'. First subtract [pi]L from both sides. Then subtract S from both sides.

-[pi]L+S=[pi]r(superscript)2 ->

-[pi]L=[pi]r(superscript)2-S

Now, since you have your variable 'l', you want to remove the [pi] away from your variable. To do this, multiply by negative 1 divided by pi, or -1/[pi].

L=S-r(superscript)2.

Therefore, the answer is C.

Answer:

C

Step-by-step explanation:

[tex]s = \pi .l \: + \pi. {r}^{2} [/tex]

Make the term including 'l' stand alone.

[tex]s - \pi. {r }^{2} = \pi.l[/tex]

Now make L stand alone by dividing through by pi.

[tex] \frac{s - \pi. {r}^{2} }{\pi} = l[/tex]

This is the same as

[tex] \frac{s}{\pi} - {r}^{2} = l[/tex]

Answer:

  6

Step-by-step explanation:

The angle bisector divides the other segments proportionally. There are many ways the proportion can be written. One is ...

  XN/NY = XA/AY

  XN = NY×XA/AY = 4 × 18/12

  XN = 6

Answer:

(x+3)(x-2)

Step-by-step explanation:

We can immediately see that there are roots at x = -3, and x = 2.

Because the website gives us that this in the form of (x + _) (x - _), our anwser is (x+3)(x-2)

oops I just saw your comment. Too late i guess...

Answer:

f(x)=1(x+3)(x-2)

Step-by-step explanation:

Answer:

x = 5, y = 8, z = -3

Step-by-step explanation:

Opposite sides of a parallelogram are congruent so to find x:

x + 7 = 3x - 3

-2x = -10

x = 5

To find y:

y + 2 = 2y - 6

-y = -8

y = 8

Therefore, z = x - y = 5 - 8 = -3.

Answer:

9

Step-by-step explanation:

Consider the polygon to consist of 2 rectangles, rectangle X (The bigger rectangular) and Y(the smaller rectangle), as shown in the diagram attached below.

To find DE + EF, let's find each lengths as follows:

DE = BC - FA

DE = 9 - 5 = 4

EF = AB - DC

EF = 8 - DC (we don't know DC)

Let's find out DC by considering the area of the entire polygon to derive an equation that will enable us to find DC.

Area of a rectangle = L*B

Therefore:

Area of the polygon = Area of rectangle X + Area of rectangle Y

Area of Polygon = (AB*FA) + (DE*DC)

52 = (8*5) + (4*DC)

52 = 40 + (4*DC)

Subtract 40 from both sides

52 - 40 = 4*DC

12 = 4*DC

Divide both sides by 4 to make DC the subject.

12/4 = DC

3 = DC

DC = 3

Thus,

DE + EF = (BC - FA) + (AB - DC)

= (9 - 5) + (8 - 3)

= 4 + 5

= 9

Answer:

-0.65

Step-by-step explanation:

Step 1: Write out fraction

-13/20

Step 2: Evaluate fraction

-13/20 = -0.65

Answer: [tex]\dfrac{1}{5}+\dfrac{1}{2}=\dfrac{7}{10}[/tex]

Step-by-step explanation:

A or B = A+B

Given: In a fish tank, [tex]\dfrac15[/tex] of the fish are guppies and [tex]\dfrac{1}{12}[/tex] of the fish are goldfish.

Then,  the fraction of the fish that are guppies or goldfish in the tank=[tex]\dfrac{1}{5}+\dfrac{1}{2}=\dfrac{2+5}{5\times2}[/tex]

[tex]\dfrac{7}{10}[/tex]

Hence, the equation most closely estimates the fraction of the fish that are guppies or goldfish in the tank:

[tex]\dfrac{1}{5}+\dfrac{1}{2}=\dfrac{7}{10}[/tex]

Answer:

Step-by-step explanation:

-0.25z= -1.25

Convert the decimals to improper fractions

That's

So we have

Multiply through by 4

We have

- z = - 5

Divide both sides by - 1

the final answer is

Hope this helps you

Answer:

Step-by-step explanation:

[tex] \mathsf{ - 0.25z = - 1.25}[/tex]

Divide both sides of the equation by -0.25

[tex] \mathsf{ \frac{ - 0.25z}{ - 0.25} = \frac{ - 1.25}{ - 0.25} }[/tex]

Calculate

[tex] \mathsf{z = 5}[/tex]

Hope I helped !

Best regards!

Answer:

Domain = x - values

Range = y - values

Step-by-step explanation:

main points I'll use as examples for the rest on graph are: (-3,4) (1,2) and (1,6)

Domain: simple numbers here are {-3,1} dont repeat the same x value twice!

Range: {2,4,6}

Make sure values are in numerical order.

Find the rest by these three points! (Which are on graph)

Hope this helps, have a good day :)

Answer:

try 2

Step-by-step explanation:

because it an X-value and it on the graph

Answer:well the answer is 2 hours 16 minutes.

Step-by-step explanation:

To find your plane's rate of speed, you calculate the distance ... amount of time in the air (2 hours and 16 minutes) to.

Answer:

-16128

Step-by-step explanation:

This expression can be calculated by algebraic means, whose process is described below:

1) [tex](-28)^{3}+(12)^{3}+(16)^{3}[/tex] Given.

2) [tex](-12-16)^{3} + (12)^{3}+(16)^{3}[/tex] Definition of addition.

3) [tex](-12)^{3} + 3\cdot (-12)^{2}\cdot (-16)+3\cdot (-12)\cdot (-16)^{2}+(-16)^{3}+(12)^{3}+(16)^{3}[/tex] Cubic perfect binomial.

4) [tex](12)^{3}+[(-1)\cdot (12)]^{3}+(16)^{3} + [(-1)\cdot (16)]^{3}+3 \cdot (-12)^{2}\cdot (-16) + 3\cdot (-12)\cdot (-16)^{2}[/tex] Commutative property/[tex](-x)\cdot y = -x\cdot y[/tex]

5) [tex](12)^{3} + (-1)^{3}\cdot (12)^{3} + 16^{3} +(-1)^{3}\cdot (16)^{3} + (-3)\cdot [(-12)^{2}\cdot (16) +(-16)^{2}\cdot (12)][/tex] Distributive property/[tex](-x)\cdot y = -x\cdot y[/tex]/[tex]x^{n}\cdot y^{n} = (x\cdot y)^{n}[/tex]

6) [tex](12)^{3} + [-(12)^{3}]+(16)^{3} + [-(16)^{3}]+ (-3)\cdot [(-12)^{2}\cdot (16)+(-16)^{2}\cdot (12)][/tex] [tex](-x)\cdot y = -x\cdot y[/tex]

7) [tex](-3)\cdot [(-12)^{2}\cdot (16) + (-16)^{2}\cdot (12)][/tex] Existence of the additive inverse/Modulative property for addition.

8) [tex](-3) \cdot [(12)^{2}\cdot (16)+(16^{2})\cdot (12)][/tex] [tex]x^{n}\cdot y^{n} = (x\cdot y)^{n}[/tex]/[tex](-x)\cdot (-y) = x\cdot y[/tex]

9) [tex](-3)\cdot (12)\cdot (16)\cdot (12+16)[/tex] Distributive property.

10) [tex]-16128[/tex]     [tex](-x)\cdot y = -x\cdot y[/tex]/Definition of sum/Definition of multiplication/Result

Answer

[tex] \boxed{10p}[/tex]

Step by step explanation

[tex] \mathsf{ - 4p + (- 6p)}[/tex]

When there is a ( + ) in front of an expression in parentheses, the expression remains the same

[tex] \mathsf{ - 4p - 6p}[/tex]

Collect like terms

[tex] \mathsf{ - 10p}[/tex]

Hope I helped!

Best regards!

Answer:

30 i think because he has done numbers from 1 -30, which are all integers except for decimals...

Answer:

Hey there!

12^2+5^2=c^2

144+25=c^2

c=13

Let me know if this helps :)

Answer:

[tex]\Large \boxed{\mathrm{D) \ 13}}[/tex]

Step-by-step explanation:

[tex]\sf We \ can \ apply \ Pythagorean \ theorem.[/tex]

[tex]c=\sqrt{a^2 +b^2 }[/tex]

[tex]\sf Plug \ in \ the \ values.[/tex]

[tex]c=\sqrt{5^2 +12^2 }[/tex]

[tex]\sf Evaluate.[/tex]

[tex]c=\sqrt{25+144}[/tex]

[tex]c=\sqrt{169}[/tex]

[tex]c=13[/tex]

Answer:

- 24 - 70i

Step-by-step explanation:

Given

([tex]\sqrt{5}[/tex] - 7i)²

= ([tex]\sqrt{5}[/tex] - 7i)([tex]\sqrt{5}[/tex] - 7i)

= 5 - 7[tex]\sqrt{5}[/tex] i - 7[tex]\sqrt{5}[/tex] i + 49i² ( note that i² = - 1 )

= 5 - 14[tex]\sqrt{5}[/tex] i - 49

= - 44 - 14[tex]\sqrt{5}[/tex] i

Answer:

Step-by-step explanation:

(a - b)² = a² - 2ab + b²

[tex][\sqrt{5} - 7i]^{2}= (\sqrt{5})^{2} - 2*\sqrt{5}*7i + (7i)^{2}\\\\\\= 5 - 14i\sqrt{5}+7^{2}*i^{2}]]= 5 -14i\sqrt{5} +49 * -1\\\\= 5 -14i\sqrt{5} - 49\\\\= -44 - 14i\sqrt{5}[/tex]

Let f(x) = y

y = log3(x+1) - 1

Plug x in y and y in x

x = log3(y+1) - 1

x + 1 = log3(y+1)

3^(x+1) - 1 = y

[tex]y = 3^{x+1}[/tex] - 1

This is the inverse function.

Hope it helps! xxxx

Answer:

y = [tex]3^{(x+1)}[/tex] -1

Step-by-step explanation:

x = [tex]log_{3}[/tex](y + 1) - 1

x + 1 = log₃(y + 1)

[tex]3^{(x+1)}[/tex] = y + 1

[tex]3^{(x+1)}[/tex] -1 = y

Answer:

30.51 meters

Step-by-step explanation:

Given that:

The distance from the point to the base of the tower = 42 m, the angle of elevation = 36°.

According to sine rule if a,b,c are the sides of a triangle and its respective opposite angles are A, B, C. Therefore:

[tex]\frac{a}{sin(A)} =\frac{b}{sin(B)}=\frac{c}{sin(C)}[/tex]

Let the height of the tower be a and the angle opposite the height be A = angle of elevation = 36°

Also let the  distance from the point to the base of the tower be b = 42 m, and the angle opposite the base of the tower be B

To find B, since the angle between the height of the tower and the base is 90°, we use:

B + 36° + 90° = 180° (sum of angles in a triangle)

B + 126 = 180

B = 180 - 126

B = 54°

Therefore using sine rule:

[tex]\frac{a}{sin(A)} =\frac{b}{sin(B)}\\\\\frac{a}{sin(36)}=\frac{42}{sin(54)}\\\\ a=\frac{42*sin(36)}{sin(54)}\\ \\a=30.51\ meters[/tex]

The height of the tower is 30.51 meters

Answer:

a(1):30%

(2):2135.34

(3):15000

Step-by-step explanation:

a(1):the total is 18750 and 5625 was not taxed therefore 5625 of 18750 was not taxed so get the amount expressed as a percentage by multiplying by 100

{5625/18750}×100

(2):so get the tax from the taxable amount and the taxable amount is 13125 and the tax is 22% of it so (22/100)×13125=2887.5

she takes home the amount remaining after taxation so 18750-2887.5(tax)(don't subtract 5625)=15862.5

she receives the above amount in 52 equal amounts so divide 15862.5/52 to get one amount =305.048 (meaning that per week she receives one of the 52 equal amounts I guess)

(3):so the original salary before moving to A was 100% but after moving it increases by 25 so the salary is 125% =18750(don't deduct tax I guess) so it will be (100/125)×18750

Answer:

Step-by-step explanation:

If the sides exist in a ratio to one another, then when you multiply some number x by both the length and the width, they still remain as a ratio. The length will be 3x and the width will be 1x. The perimeter formula is

P = 2L + 2W and since our perimeter is 72 and we have both the length and the width, we can fill in the formula and solve for x:

72 = 2(3x) + 2(1x) and

72 = 6x + 2x and

72 = 8x so

9 = x.

If x = 9, then 1x = 9 and 3x = 27. Let's check the perimeter against those side lengths.

P = 2(3x) + 2(1x) and

P = 2(27) + 2(9) and

P = 54 + 18 so

P = 72

and you're done! (The bold numbers above are the width and length, respectively.)

Answer:

140°

Step-by-step explanation:

[tex] \because m\widehat{BG} = 360\degree - m\widehat{GCB} \\

\therefore m\widehat{BG} = 360\degree - 300\degree \\

\therefore m\widehat{BG} = 60\degree \\

\because m\widehat{BGD} = m\widehat{BG}

+m\widehat{GD}\\

\therefore m\widehat{BGD} = 80\degree+60\degree\\

\therefore m\widehat{BGD} = 140\degree\\

\because m\angle BAD = m\widehat{BGD} \\

\huge\purple {\boxed {\therefore m\angle BAD =140\degree}} [/tex]