Given right triangle ABC= with altitude BD drawn to hypotenuse AC. If AD=3 and, AC=27, what is the length of AB?

Answer:

Let two consecutive multiples of 3 be x and (x+3)

A/q,

x * (x+3) = 648

➡ x² + 3x = 648

➡ x² + 3x -648 = 0

➡ x² + 27x - 24x -648 = 0

➡ x ( x + 27 ) -24 ( x +27)

➡ ( x - 24) ( x + 27)

➡ x = 24 and x = -27

so, we take x = 24.

Required multiples of 3

➡ x = 24

➡ x +3 = 24+3 = 27.

Answer:

The three consecutive multiples are 210, 216, 222

Step-by-step explanation:

3 consecutive multiples of 6 be : 6n , 6n + 6 , 6n + 12

Given sum of these 3 numbers is = 648

That is ,

            6n + 6n + 6 + 6n + 12 = 648

           18 n + 18 = 648

            18n = 648 - 18

             18 n = 630

                n = 35

Therefore the three consecutive multiples are :

6 x 35 , 6 x 35 + 6,  6 x 35 + 12

210 , 210 + 6 , 210 + 12

 210 , 216, 222

Answer:

[tex]A=1099.56cm^{2}[/tex]

Step-by-step explanation:

Formula to ind surface area of cylinder:

[tex]A=2\pi \frac{d}{2} h+2\pi (\frac{d}{2} )^{2}[/tex]

[tex]A=2\pi \frac{10}{2} (30)+2\pi (\frac{10}{2} )^{2}[/tex]

[tex]A=1099.557443cm^{2}[/tex]

Therefore, area will be:

[tex]A=1099.56cm^{2}[/tex]

hope this helps :)

Answer:

Step-by-step explanation:

The solution is 4 laps

The number of laps ran by Levi is given by the equation w = 4 laps

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of laps ran by Levi be represented as w

Now , the equation will be

The total length of a lap = 400 m

The total length ran by Levi = 1600 m

So ,

The number of laps w ran by Levi = total length ran by Levi / total length of a lap

Substituting the values in the equation , we get

The number of laps ran by Levi w = 1600 / 400

On simplifying the equation , we get

The number of laps ran by Levi w = 4 laps

Therefore , the value of w is 4 laps

Hence , the number of laps is 4 laps

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Answer:

[tex]6\sqrt{6}[/tex]

Step-by-step explanation:

[tex]\sqrt{216}[/tex]

factorise 216

[tex]\sqrt{2*2*2*3*3*3}[/tex]

since it is square root (meaning it has index to) pair up the number

[tex]2*3\sqrt{2*3[/tex]

[tex]6\sqrt{6}[/tex]

Answer:

1:26

Step-by-step explanation:

You can divide both sides by 2.

Answer:

= X(5x+3)-4(5x+3)

= 5x²+ 3x- 20x-12

= 5x²-17x-12

Answer:

5x(squared)-17x-20

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let L be the given line, then, with a slope of -8

L :  y = -8x + b

where b is to be determined from the included point A(-10,0).

Substitute point A in L to get

0 = -8 (-10) + b

solve to get

b = -80

therefore

L : y = -8x -80

Now substitute B(-9,z) in L

z = -8(-9) - 80 = -8

Answer:

20/56 or 5/14

Step-by-step explanation:

Prob of red = 5/8

Second red prob = 4/7

multiply those = 20/56

simplify if needed = 5/14

Answer:

1

Step-by-step explanation:

2÷2=1

Answer:

1. a. miles or feet

b. inches

c. ounces

d. gallons

2. a.  1:36

b. 1/1

c. 63,360

Step-by-step explanation:

Answer:

slope is 3/7

Step-by-step explanation:

use the formula y2 - y1 / x2 - x1

Answer:

x = 0

Step-by-step explanation:

The axis of the symmetry has the same x coordinate of the vertex

V (x) = -b/2a

in both equations b is equal to 0 and a 0/a number different from 0 gives always 0 as a result

Answer:

x < 1

Step-by-step explanation:

2(x-7)<-12

Divide by 2

2(x-7)/2<-12/2

x-7 < -6

Add 7 to each side

x-7+7 < -6+7

x < 1

Answer:

The large square covers more

Step-by-step explanation:

Given

See attachment for squares

Required

Which covers more plane

The large square has the highest dimension and by extension, it has the highest area.

This means that, less large squares will be needed to cover more areas compared to other sizes of the squares.

Take for instance, the following analysis;

Large square

Dimension: 3 by 3;

[tex]Area=3*3 = 9[/tex]

Medium Square

Dimension: 2 by 2

[tex]Area = 2 * 2 = 4[/tex]

Small square

Dimension: 1 by 1

[tex]Area = 1 * 1 = 1[/tex]

The square with the largest area covers more of the plane.

Hence, the large square covers more of the plane

Answer:

333,333 Three hundred and thirty-three thousand , three hundred and thirty-three

Step-by-step explanation:

4000000/12

Answer:

(x+2)(x+6)

Step-by-step explanation:

that is the answer because math

=>x^2+8x+12

=>x^2+6x+2x+12

=>x(x+6)+2(x+6)

=>(x+6)(x+2)

Hope it helps you

Answer:

58

Step-by-step explanation:

Area = Area of entire recangle - area of cut out

a = (10 * 7) - (6 * 2)

a = 70 - 12

a = 58

Answer:

Step-by-step explanation:

You could start by using pemdas which start with parentheses so since 3+4 is in parentheses add those first and you'll get 7 then solve the remaining 4-2 in the bracket so 4-2 is 2. Since there is no plus sign you multiply 7 by 2 then multiply by three so 7x2 is 14 then 14x3 is 42 so your answer Is 42

Answer:

175

Step-by-step explanation:

7(2x-3y)

Let x = 8 and y = -3

7(2*8-3 (-3))

Inside parentheses first

7(16+9)

Add inside the parentheses

7(25)

Multiply

175

Answer:

10 minutes

Step-by-step explanation:

Mario can eat e21 hot dog in 6 minutes

Let 35 hot dog  eats in x minutes :

[tex]\frac{35}{x} =\frac{21}{6} \\x=\frac{35(6)}{21} \\x=10 min[/tex]

Therefore, mario would eat 35 dogs in 10 min.

Answer:

119 or 118.726577

Step-by-step explanation:

We should use the Pythagorean Theorem to solve this problem.

a^2+ b^2=c^2

64^2+100^2=c^2

4096+10000=14096

c^2=14096

c=\sqrt{14096}14096

And the root of 14096 is 118.726577.

So the Answer is About 119 meters, or 118.726577

hope this helps!

Answer:

n = 17

Step-by-step explanation:

For a quadratic equation to have equal roots b²-4ac should be equal to zero in the quadratic equation ax²+bx+c=0.

Equation : 3x² - 12 x + ( n - 5) = 0

a = 3, b = -12, c = ( n - 5)

b² - 4ac = 0

(-12)² - (4 x 3 x (n - 5)) = 0

144 - 12( n - 5 ) = 0

12( n - 5 ) = 144

n - 5 = 12

n = 17

Check if it's true :

3x² - 12 x + ( 17 - 5) = 0

3x² - 12 x + 12 = 0

3(x² - 4x + 4) = 0

(x² - 4x + 4) = 0

(x - 2)(x - 2) = 0

x = 2 , 2

Equal roots .

Lets Solve

[tex] \\ \rm \longmapsto \: {x}^{2} - 8x - 7 = 0 \\ \\ \rm \longmapsto \: {x}^{2} - 8 {}^{}x = 7 \\ \\ \rm \longmapsto \: 4( {x}^{2} - 8x) = 4 \times 7 \\ \\ \rm \longmapsto \: {4x}^{2} - 32x = 28 \\ \\ \rm \longmapsto \: {(2x)}^{2} - 2 \times 2x \times 8 = 28 \\ \\ \rm \longmapsto \: (2x) {}^{2} - 2 \times 2x \times 8 + {8}^{2} = 28 + {8}^{2} \\ \\ \rm \longmapsto \: {(2x - 8)}^{2} = 64 + 28 \\ \\ \rm \longmapsto \: {(2x - 8)}^{2} = 92 \\ \\ \rm \longmapsto \: 2x - 8 = \underline{ + }9.3 \\ \\ \rm \longmapsto \:2x = 8 + 9.3 \: or \: 8 - 9.3 \\ \\ \rm \longmapsto \:2x = 17.3 \:or \: - 1.3 \\ \\ \rm \longmapsto \:2x = 17.3 \\ \\ \rm \longmapsto \:x = \frac{17.3}{2} \\ \\ \rm \longmapsto x = \:8.6[/tex]

Answer:

Step-by-step explanation:

[tex]\frac{2*10^{14}}{8*10^{9}}=\frac{1}{4}*10^{14-9}=\frac{1}{4}*10^{5}\\\\\\\frac{a^{m}}{a^{n}}=a^{m-n}\\\\[/tex]

In exponent division , if bases are same, then find the difference of the exponents

Step-by-step explanation:

everything can be found in the picture