Find the equation of a line whose x intercept is 5 and y intercept is 2.​

Answer:

Step-by-step explanation:

Given the expression 1/6.43 +2/3.56 +1/8.51, If 'a' is a number, the reciprocal of such number is 1/a. According to the question, the reciprocal of 6.43, 3.56 and 8.51 are  1/6.43 and 1/3.56 and 1/8.51 respectively.

1/6.43 = 0.1555

2/3.56 = 2 * 1/3.56

= 2 * 0.2809

= 0.5618

1/8.51 = 0.1175

Taking the sum of the reciprocals;

1/6.43 +2/3.56 +1/8.51 = 0.1555 + 0.5618 + 0.1175

1/6.43 +2/3.56 +1/8.51 = 0.8348

Hence, the sum of 1/6.43, 2/3.56 and 1/8.51 is 0.8348

so first day and so on

7, 10, 13,....

as you can see it's an arithmetic progression

so sum for nth term= n/2 { 2a + (n-1) d}

it's the sum of the 7th term

so

7/2 { 7 ×2 + ( 7-1) 3}

7/2 × 32

7× 16

112 fishes

Answer:

I think the answer is 25

Step-by-step explanation:

Answer:

Examine the system of equations.

–2x + 3y = 6

–4x + 6y = 12

Answer the questions to determine the number of solutions to the system of equations.

What is the slope of the first line?  

✔ 2/3

What is the slope of the second line?  

✔ 2/3

What is the y-intercept of the first line?  

✔ 2

What is the y-intercept of the second line?  

✔ 2

How many solutions does the system have?  

✔ infinitely many

The equations are a multiple of the other, therefore, by the multiplicative

property of equality, the equations are equivalent.

Response:

The given system of equations are;

-2·x + 3·y = 6

-4·x + 6·y = 12

Required:

The slope of the first line.

Solution:

The slope of the first line is given by the coefficient of x when the equation is expressed in the form; y = m·x + c.

Therefore, from -2·x + 3·y = 6, we have;

3·y = 2·x + 6

[tex]y = \dfrac{2}{3} \cdot x + \dfrac{6}{3} = \dfrac{2}{3} \cdot x + 2[/tex]

[tex]y =\dfrac{2}{3} \cdot x + 2[/tex]

[tex]\underline{The \ slope \ of \ the \ first \ equation \ is \ \dfrac{2}{3}}[/tex]

Required:

The slope of the second line;

Solution:

The equation of the second line, -4·x + 6·y = 12, can be expressed in the form;

[tex]y =\dfrac{4}{6} \cdot x + \dfrac{12}{6} = \dfrac{2}{3} \cdot x + 2[/tex]

[tex]y = \mathbf{\dfrac{2}{3} \cdot x + 2}[/tex]

[tex]\underline{The \ slope \ of \ the \ second \ equation \ is \ therefore \ \dfrac{2}{3}}[/tex]

Given that the equation have the same slope and the same y-intercept, the equations are equations of the same line, therefore;

Learn more about the solutions of a system of equations here:

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Answer:

C - LA = 2πrh

Step-by-step explanation:

Lateral surface area of right cylinder = 2 * π * radius * height

Answer:

[tex]\boxed{-4.1x-11y}[/tex]

Step-by-step explanation:

[tex](-12.7y-3.1x) + 5.9y-(4.2y + x)[/tex]

Expand brackets.

[tex]-12.7y-3.1x+ 5.9y-4.2y - x[/tex]

Combining like terms.

[tex]- x-3.1x-12.7y+ 5.9y-4.2y[/tex]

[tex]-4.1x-11y[/tex]

Answer:

[tex] \boxed{\red{ - 11y - 4.1x}}[/tex]

Step-by-step explanation:

[tex] (- 12.7y - 3.1x) + 5.9y - (4.2y + x) \\ - 12.7y - 3.1x + 5.9y - 4.2y - x \\ - 12.7y + 5.9y - 4.2y- 3.1x - x \\ = - 11y - 4.1x[/tex]

Answer:

[tex]V = \frac{1}{3} (\pi \cdot 10^2 \cdot 16) \\\\V = \frac{1}{3} (1600 \pi ) \\\\V = 1675.52 \: m^3[/tex]

The maximum amount of sand that can be stored in this structure is 1675.52 m³.

Step-by-step explanation:

The volume of a conical-shaped structure is given by

[tex]V = \frac{1}{3} (\pi \cdot r^2 \cdot h)[/tex]

Where r is the radius and h is the height of the structure.

We are given that

radius = 10m

height = 16m

Substituting the above values into the formula, we get

[tex]V = \frac{1}{3} (\pi \cdot 10^2 \cdot 16) \\\\V = \frac{1}{3} (1600 \pi ) \\\\V = 1675.52 \: m^3[/tex]

Therefore, the maximum amount of sand th can be stored in this structure is 1675.52 m³.

Answer:

11 /13 = t

Step-by-step explanation:

5/13  = t -6/13

Add 6/13 to each side

5/13 + 6/13  = t -6/13+ 6/13

11 /13 = t

Answer:

[tex]t=\frac{11}{13}[/tex]

Step-by-step explanation:

[tex]\frac{5}{13} = t -\frac{6}{13}[/tex]

Add [tex]\frac{6}{13}[/tex] to both sides.

[tex]\frac{5}{13} + \frac{6}{13} = t -\frac{6}{13} + \frac{6}{13}[/tex]

[tex]\frac{11}{13} =t[/tex]

Answer:

a) -900 L/min

b) 63000 L

c)  -900t +63000

 d) 7200 L

Step-by-step explanation:

a) You are given two points on the curve of volume vs. time:

(t, V) = (20, 45000) and (70, 0)

The rate of change of volume

= ΔV/Δt = (0 -45000)/(70 -20) = -45000/50 = -900 liters per minute

b) In the first 20 minutes, the change in volume was

(20 min)(-900 L/min) = -18000 L

So, the initial volume was

initial volume - 18000 = 45000

initial volume = 63,000 liters

c) Since we have the slope and the intercept, we can write the equation in slope-intercept form as

 V= -900t +63000.

d) now putting the number in the equation and do the arithmetic.

When t=62, the amount remaining is

= -900(62) +63000 = -55800 +63000 = 7200

Thus, 7200 L remain after 62 minutes.

Answer:

3√6

Step-by-step explanation:

tan60=opp/adj

opp(d)=tan60*3√2=√3*3√2=3√6

Answer:

Y= 2/3x +(5/3)

Step-by-step explanation:

First, have to get Y alone on one side 3y=2x+5

Second, have to get read of the 3 with the Y so divide each side by three.

Answer: Zak - Resp after 24 months = $4,344.00

              Zak - Technology Fund after 24 months = $1,102.98

              Zak's Technology Fund has enough money to buy a laptop.

              Zak's Savings (Resp) will last less than 6 months

Step-by-step explanation for Zak:

January - June 2019

$15/hr x 20 hr x 4 wks x 6 months = $7200 Gross Income

Taxable Income is $7200 - $1080 = $6120    (Annual Income $12,240)

→ $7,200 - ($1080 + $360 + $144 + $0 + $129.60) = $5,486.40 Net Income

Tech Fund (5%): $5486.40(0.05) = $274.32

Food Expense (30%): $5486.40(0.3) = $1,645.92

Clothing Expense (30%): $5486.40(0.3) = $1,645.92

Entertainment Expense (25%): $5486.40(0.25) = $1,371.60

Miscellaneous Expense (10%): $5486.40(0.1) = $548.64      

                                               Other Expenses: $5,212.08

July - December 2019 (excluding August)

$16/hr x 20 hr x 4 wks x 5 months = $6400 Gross Income

Taxable Income is $6400 - $960 = $5440    (Annual Income $11,560)

→ $6,400 - ($960 + $320 + $128 + $0 + $75.20) = $4,916.80 Net Income

Tech Fund (5%): $4916.80(0.05) = $245.84

Food Expense (30%): $4916.80(0.3) = $1,475.04

Clothing Expense (30%): $4916.80(0.3) = $1,475.04

Entertainment Expense (25%): $4916.80(0.25) = $1,229.20

Miscellaneous Expense (10%): $4916.80(0.1) = $491.68      

                                              Other Expenses: $4,670.96

January - June 2020

$17/hr x 20 hr x 4 wks x 6 months = $8160 Gross Income

Taxable Income is $8160 - $1224 = $6936    (Annual Income $13,872)

→ $8,160 - ($1224 + $408 + $163.20 + $0 + $194.88) = $6,169.92 Net Income

Tech Fund (5%): $6169.92(0.05) = $308.50

Food Expense (30%): $6169.92(0.3) = $1,850.98

Clothing Expense (30%): $6169.92(0.3) = $1,850.98

Entertainment Expense (25%): $6169.92(0.25) = $1,542.48

Miscellaneous Expense (10%): $6169.92(0.1) = $616.98      

                                               Other Expenses: $5,861.42

July - December 2020 (excluding August)

$18/hr x 20 hr x 4 wks x 5 months = $7200 Gross Income

Taxable Income is $7200 - $1080 = $6120    (Annual Income $13,056)

→ $7,200 - ($1080 + $360 + $144 + $0 + $129.60) = $5,486.40 Net Income

Tech Fund (5%): $4916.80(0.05) = $274.32

Food Expense (30%): $5486.40(0.3) = $1,645.92

Clothing Expense (30%): $5486.40(0.3) = $1,645.92

Entertainment Expense (25%): $5486.40(0.25) = $1,371.60

Miscellaneous Expense (10%): $5486.40(0.1) = $548.64      

                                              Other Expenses: $5,212.08

[tex]\boxed{\begin{array}{l|r|r|r|r||r}\underline{ZAK}&\underline{Jan-Jun'19}&\underline{Jul-Dec'19}&\underline{Jan-Jun'20}&\underline{Jul-Dec'20}&\underline{Totals\quad }\\Gross&\$7200.00&\$6400.00&\$8160.00&\$7200.00&\$28960.00\\Resp&\$1080.00&\$960.00&\$1224.00&\$1080.00&\$4344.00\\Net&\$5486.40&\$4916.80&\$6169.92&\$5486.40&\$22059.52\\Other&\$5212.08&\$4670.96&\$5861.42&\$5212.08&\$20956.54\\Tech&\$274.32&\$245.84&\$308.50&\$274.32&\$1102.98\end{array}}[/tex]

Answer:

x = -3 , x = 1

Step-by-step explanation:

Hello,

you need to draw the graph of the two functions and then find the intersection points.

please see below

So the solution is the two points A and B

(-3,9) and (1,1)

Hope this helps

Answer:

6 is the best estimate.

Step-by-step explanation:

(90/7) / (1 & 3/4) == (90/7) / (7/4) == (90/7) * (4/7) == 360/49 > 7.

Choose 6 as your best approximation.

Answer:

AC = EF

Step-by-step explanation:

ABC = DEF

You would need to know that AC = EF

In the first place, using deduction we know that we dont need another angle. We also know that BC does not equal DF by looking at the angles on the triangles.

The solution is : ∠C ≅ ∠F is congruent to show that ΔABC ≅ ΔDEF, else would need to be congruent to show that AABC= ADEF by the AAS theorem.

The angle-angle-side theorem, or AAS, tells us that if two angles and a non-included side of one triangle are congruent to two angles and a non-included side of another triangle, then the triangles are congruent.

here, we have,

to find congruency in a triangle:

ΔABC ≅ ΔDEF

Therefore,

AAS congruence rule or theorem states that if two angles of a triangle with a non-included side are equal to the corresponding angles and non-included side of the other triangle, they are considered to be congruent.

Therefore,

∠C ≅ ∠F

Hence, The solution is : ∠C ≅ ∠F is congruent to show that ΔABC ≅ ΔDEF, else would need to be congruent to show that AABC= ADEF by the AAS theorem.

learn more on AAS here:

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Answer:

37.8 m

Step-by-step explanation:

The computation of the distance is shown below:

In triangle ADE

[tex]AD^2 = AE^2 + DE^2 \\\\ AD^2 = 5^2 + 3^2 \\\\ AD^2 = 34[/tex]

AD = 5.8

Now the distance walked after completing his edging is

Distance = AD + AB + BC + CD

= 5.8 + 12 + 5 + 15

= 37.8 m

We simply added these four sides so that the correct distance could arrive

Hence, the distance walked after completing his edging is 37.7

Answer:

1. [tex]27^{\frac{2}{3} } =9[/tex]

2. [tex]\sqrt{36^{3} } =216[/tex]

3. [tex](-243)^{\frac{3}{5} } =-27[/tex]

4. [tex]40^{\frac{2}{3}}=4\sqrt[3]{25} =4325[/tex]

5. Step 4: [tex](\frac{343}{27}) ^{-1} =\frac{27}{343}[/tex]

6. [tex]D. -72cd^{7}[/tex]

Step-by-step explanation:

Use the following properties:

[tex]a^{\frac{x}{y} } =\sqrt[x]{a^{y} }[/tex]

[tex]\sqrt[n]{ab} =\sqrt[n]{a} \sqrt[n]{b}[/tex]

[tex]a^{-n} =\frac{1}{a^{n} }[/tex]

[tex](xy)^{z} =x^{z} y^{z} \\\\[/tex]

[tex](x^{y}) ^{z} =x^{yz}[/tex]

[tex]x^{y} x^{z} =x^{y+z}[/tex]

So:

1. [tex]27^{\frac{2}{3} } =\sqrt[3]{27^{2}} =\sqrt[3]{729} }=9[/tex]

2. [tex]\sqrt{36^{3} } =\sqrt{36*36*36} =\sqrt{36} \sqrt{36} \sqrt{36} =6*6*6=216[/tex]

3. [tex](-243)^{\frac{3}{5} } =\sqrt[5]{-243^{3} } =\sqrt[5]{-14348907} =-27[/tex]

4. [tex]40^{\frac{2}{3}}=\sqrt[3]{40^{2} } =\sqrt[3]{2^{6} 5^{2} } =\sqrt[3]{2^{6} } \sqrt[3]{5^{2} } =2^{\frac{6}{3} } 5^{\frac{2}{3} } =4 *5^{\frac{2}{3} } =4\sqrt[3]{5^{2} } =4\sqrt[3]{25}=4325[/tex]

5. [tex](\frac{343}{27}) ^{-1} =\frac{1}{\frac{343}{27} } =\frac{27}{343}[/tex]

6.

[tex](-8c^{9} d^{-3} )^{\frac{1}{3} } *(6c^{-1}d^{4})^{2} =\sqrt[3]{-8} c^{3} d^{-1} 36c^{-2} d^{8} \\\\-2c^{3} d^{-1} 36c^{-2} d^{8}=-72cd^{7}[/tex]

Answer:

y = -3

Step-by-step explanation:

y + 3 = 7(2 - 2)

y + 3 = 0

Subtract 3 from both sides

y + 3 - 3 = 0 - 3

y = -3

Answer:

  7x - y = 17

Step-by-step explanation:

Maybe you want the standard form of the point-slope equation ...

  y +3 = 7(x -2)

__

  y + 3 = 7x -14 . . . . . eliminate parentheses

  17 = 7x -y . . . . . . . . add 14-y

  7x - y = 17

Answer:

Option B is the correct option.

Step-by-step explanation:

[tex] {(4 - 2)}^{3} - 3 \times 4[/tex]

Subtract the numbers

[tex] = {(2)}^{3 } - 3 \times 4[/tex]

Multiply the numbers

[tex] = {(2)}^{3} - 12[/tex]

Evaluate the power

[tex] = 8 - 12[/tex]

Calculate the difference

[tex] = - 4[/tex]

Hope this helps..

Best regards!!

Answer:

[tex]\boxed{-4}[/tex]

Step-by-step explanation:

[tex](4-2)^3-3 \times 4[/tex]

Brackets or parenthesis are to be evaluated first. Subtract the numbers in the brackets.

[tex](2)^3-3 \times 4[/tex]

Evaluate the power or exponent.

[tex]8-3 \times 4[/tex]

Multiply the numbers.

[tex]8-12[/tex]

Finally, subtract the numbers.

[tex]=-4[/tex]

Answer:

A. 3

Step-by-step explanation:

ΔDEC is bigger than ΔABC by 5. For the hypotenuse, 25 is 5 times bigger than 5.

So, side DE on ΔDEC has to be 5 times bigger than side AB on ΔABC.

If side AB equals 3, side DE equals 18 - 3, which is 15.

15 is five times bigger than 3, so the answer is A. 3.

Hope that helps.

Answer:

1/3

Step-by-step explanation:

There are three elements that are intersecting: 5, 14, 22

Probability of choosing an item is 1/3

Answer:

3x^2 + 3/2 x -9

Step-by-step explanation:

f(x) = x/2 -3

g(x) =3x^2 +x -6

(f+g) (x) =  x/2 -3 + 3x^2 +x -6

   Combine like terms

            = 3x^2 + x/2 +x -3-6

              = 3x^2 + 3/2 x -9

Answer:

Hey there!

Marked down by 20 percent is equal to 80 percent of the original value.

4.5(0.8)=3.6

9 percent sales tax

3.6(1.09)=3.92

Hope this helps :)

Answer:

$3.92

Step-by-step explanation:

I took the test

Answer:

-7/6

Step-by-step explanation:

If a = 1/2 and b = -3/7, then your given:

1/2 divided by -3/7=

-7/2*3=

-7/6

Sorry if its a bit unclears

Answer:

[tex]\frac{7}{-6}[/tex]

Step-by-step explanation:

To do this you are basically dividing the fractions so when you set up the equation it will look like this [tex]\frac{1}{2}/\frac{-3}{7}[/tex] now that we have this we will take the reciprocal of -3/7 which is 7/-3 and than multiply the 2 fractions we we get 7/-6

Answer:  3.2 yd

Step-by-step explanation:

Notice that TWV is a right triangle.  

Segment TU is not needed to answer this question.

∠V = 32°, opposite side (TW) is unknown, hypotenuse (TV) = 6

[tex]\sin \theta=\dfrac{opposite}{hypotenuse}\\\\\\\sin 32=\dfrac{\overline{TW}}{6}\\\\\\6\sin 32=\overline{TW}\\\\\\\large\boxed{3.2=\overline{TW}}[/tex]

Answer:

second one

Step-by-step explanation:

Answer:

x = 6 and x = 11.

Step-by-step explanation:

sqrt(x - 2) + 8 = x

sqrt(x - 2) = x - 8

(sqrt(x - 2))^2 = (x - 8)^2

x - 2 = x^2 - 16x + 64

x^2 - 16x + 64 = x - 2

x^2 - 17x + 66 = 0

We can use the discriminant to find whether there are solutions to the equation.

b^2 - 4ac; where a = 1, b = -17, and c = 66.

(-17)^2 - 4 * 1 * 66

= 289 - 264

= 25

Since the discriminant is positive, we know there are two valid solutions to the equation.

x^2 - 17x + 66 = 0

(x - 6)(x - 11) = 0

The solutions are when x - 6 = 0 and x - 11 = 0.

x - 6 = 0

x = 6

x - 11 = 0

x = 11

Hope this helps!

Answer:

x=11 solution

x=6 extraneous

Step-by-step explanation:

sqrt( x-2) + 8 = x

Subtract x from each side

sqrt(x-2) = x-8

Square each side

(sqrt(x-2))^2 = (x-8) ^2

x-2 = x^2 -8x-8x+64

x-2  = x^2 -16x+64

Subtract ( x-2) from each side

0 = x^2 -17x +66

Factor

0 = (x-6) ( x-11)

Using the zero product property

x=6  x=11

Checking the solutions

x=6

sqrt( 6-2) + 8 = 6

sqrt(4) +8 = 6

2 +8 = 6

False  not a solution

x=11

sqrt( 11-2) + 8 = 11

sqrt(9) +8 =11

3 +8 = 11

solution

Answer: x = -12

Step-by-step explanation:

-1/2x=6

Divide by -1/2

x = -12

Hope it helps <3

x^2+y^2-12x+6y+36=0

Top Point: (6,0)

Left Point: (3,-3)

Right Point: (9,-3)

Bottom Point: (6,-6)

Answer:

[tex] x^2 +y^2 -12x +6y +36 =0[/tex]

And we can complete the squares like this:

[tex] (x^2 -12x +6^2) + (y^2 +6y +3^2) = -36 +6^2 +3^2[/tex]

And we got:

[tex] (x-6)^2 + (y+3)^2 = 9[/tex]

And we have a circle with radius r =3 and the vertex would be;

[tex] V= (6,-3) [/tex]

The graph is on the figure attached.

Step-by-step explanation:

For this case we have the following expression:

[tex] x^2 +y^2 -12x +6y +36 =0[/tex]

And we can complete the squares like this:

[tex] (x^2 -12x +6^2) + (y^2 +6y +3^2) = -36 +6^2 +3^2[/tex]

And we got:

[tex] (x-6)^2 + (y+3)^2 = 9[/tex]

And we have a circle with radius r =3 and the vertex would be;

[tex] V= (6,-3) [/tex]

The graph is on the figure attached.

By the factor theorem,

[tex]3x^2+5x+7=3(x-u)(x-v)\implies\begin{cases}uv=\frac73\\u+v=-\frac53\end{cases}[/tex]

Now,

[tex](u+v)^2=u^2+2uv+v^2=\left(-\dfrac53\right)^2=\dfrac{25}9[/tex]

[tex]\implies u^2+v^2=\dfrac{25}9-\dfrac{14}3=-\dfrac{17}9[/tex]

So we have

[tex]\dfrac uv+\dfrac vu=\dfrac{u^2+v^2}{uv}=\dfrac{-\frac{17}9}{\frac73}=\boxed{-\dfrac{17}{21}}[/tex]

The value of [tex]\frac{u}{v} +\frac{v}{u}[/tex] is [tex]\frac{-17}{21}[/tex].

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is[tex]ax^{2} +bx+c=0[/tex], where a and b are the coefficients, x is the variable, and c is the constant term.

If [tex]ax^{2} +bx+c = 0[/tex] be the quadratic equation then

Sum of the roots = [tex]\frac{-b}{a}[/tex]

And,

Product of the roots = [tex]\frac{c}{a}[/tex]

According to the given question.

We have a quadratic equation [tex]3x^{2} +5x+7=0..(i)[/tex]

On comparing the above quadratic equation with standard equation or general equation [tex]ax^{2} +bx+c = 0[/tex].

We get

[tex]a = 3\\b = 5\\and\\c = 7[/tex]

Also, u and v are the solutions of the quadratic equation.

⇒ u and v are the roots of the given quadratic equation.

Since, we know that the sum of the roots of the quadratic equation is [tex]-\frac{b}{a}[/tex].

And product of the roots of the quadratic equation is [tex]\frac{c}{a}[/tex].

Therefore,

[tex]u +v = \frac{-5}{3}[/tex] ...(ii) (sum of the roots)

[tex]uv=\frac{7}{3}[/tex]   ....(iii)       (product of the roots)

Now,

[tex]\frac{u}{v} +\frac{v}{u} = \frac{u^{2} +v^{2} }{uv} = \frac{(u+v)^{2}-2uv }{uv}[/tex]                    ([tex](a+b)^{2} =a^{2} +b^{2} +2ab[/tex])

Therefore,

[tex]\frac{u}{v} +\frac{v}{u} =\frac{(\frac{-5}{3} )^{2}-2(\frac{7}{3} ) }{\frac{7}{3} }[/tex]         (from (i) and (ii))

⇒ [tex]\frac{u}{v} +\frac{v}{u} =\frac{\frac{25}{9}-\frac{14}{3} }{\frac{7}{3} }[/tex]

⇒ [tex]\frac{u}{v} +\frac{v}{u} = \frac{\frac{25-42}{9} }{\frac{7}{3} }[/tex]

⇒ [tex]\frac{u}{v} +\frac{v}{u} = \frac{\frac{-17}{9} }{\frac{7}{3} }[/tex]

⇒ [tex]\frac{u}{v} +\frac{v}{u} =\frac{-17}{21}[/tex]

Therefore, the value of [tex]\frac{u}{v} +\frac{v}{u}[/tex] is [tex]\frac{-17}{21}[/tex].

Find out more information about sum and product of the roots of the quadratic equation here:

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Answer:

Step-by-step explanation:

Question:

7^1/5

The number given has an exponent of a fraction: fraction exponent = 1/5

Since the top is one, the number 7 stays the same. = 7^1 = 7

The bottom is a 5. This means it is to the fifth root.

Answer = D

Hope this helped,

Kavitha

Answer: If 36/7 is one of the options, choose that one.

If the question involves an exponent, you should use the "caret" which is ^ found above the 6 on a keyboard. [Shift + 6]. That helps avoid confusion.

Step-by-step explanation: 7 is equal to 35/5 because 7×5=35

Add 1/5 and you end up with 36/5. A Common rational number.

7^(1/5) = the 5th root of 7. A very small irrational number!