If the sum of the legs of a right triangle is 49cm and the hypotenuse is 41cm find the length of the two legs... without using guess or check.

Please show work

Answer:

Let

Tinky's age=x

Laa's age=x+2

According to the question

[tex]\qquad\quad {:}\longmapsto\sf 5 (x+x+2)-1=x (x+2)[/tex]

[tex]\qquad\quad {:}\longmapsto\sf 5(2x+2)-1=x^2+2x [/tex]

[tex]\qquad\quad {:}\longmapsto\sf 10x+5-1=x^2+2x [/tex]

[tex]\qquad\quad {:}\longmapsto\sf 10x+4=x^2+2x [/tex]

[tex]\qquad\quad {:}\longmapsto\sf 10x-2x+4=x^2 [/tex]

[tex]\qquad\quad {:}\longmapsto\sf x^2=8x+4 [/tex]

[tex]\qquad\quad {:}\longmapsto\sf x^2-8x-4=0 [/tex]

Answer:

558.7805

Step-by-step explanation:

Answer:

a)

[tex]\displaystyle x=-\frac{1}{2}p\pm\sqrt{\frac{1}{4}p^2-4}[/tex]

b) p is in the interval (-4,4)

Step-by-step explanation:

Quadratic Equation

It's given the following quadratic equation:

[tex]x^2+px+4=0[/tex]

a)

It's required to complete squares and find the roots. This can be done by recalling the polynomial identity:

[tex]a^2+2ab+b^2=(a+b)^2[/tex]

We already have the first term squared, and we need to find the second term. Rewriting the equation:

[tex]\displaystyle x^2+2(\frac{1}{2}px)+4=0[/tex]

The second term of the binomial is 1/2p, thus completing the squares with [tex]b^2[/tex]:

[tex]\displaystyle x^2+2(\frac{1}{2}px)+\left(\frac{1}{2}p\right)^2+4-\left(\frac{1}{2}p\right)^2=0[/tex]

Factoring:

[tex]\displaystyle \left(x+\frac{1}{2}p\right)^2+4-\frac{1}{4}p^2=0[/tex]

Moving the independent term to the right side:

[tex]\displaystyle \left(x+\frac{1}{2}p\right)^2=\frac{1}{4}p^2-4[/tex]

Taking the square root:

[tex]\displaystyle x+\frac{1}{2}p=\pm\sqrt{\frac{1}{4}p^2-4}[/tex]

Solving for x:

[tex]\displaystyle x=-\frac{1}{2}p\pm\sqrt{\frac{1}{4}p^2-4}[/tex]

b) If the equation won't have real roots, then the radicand should be negative:

[tex]\displaystyle \frac{1}{4}p^2-4<0[/tex]

Factoring:

[tex]\displaystyle \left(\frac{1}{2}p-2\right)\left(\frac{1}{2}p+2\right)<0[/tex]

The zeros of the left-side polynomial are:

[tex]\displaystyle \frac{1}{2}p-2=0[/tex]

[tex]\displaystyle \frac{1}{2}p=2[/tex]

p = 4

[tex]\displaystyle \frac{1}{2}p+2=0[/tex]

[tex]\displaystyle \frac{1}{2}p=-2[/tex]

p = -4

The inequality:

[tex]\displaystyle \left(\frac{1}{2}p-2\right)\left(\frac{1}{2}p+2\right)<0[/tex]

Is satisfied for values of p in the interval (-4,4)

Answer:

$850

Step-by-step explanation:

35 x 20 = 700 + 150 = $850 or 850

$20 per person and 35 people = $700 + the $150 fee = $850

Answer:

[tex]x_1=3+2\sqrt{6}[/tex]

[tex]x_2=3-2\sqrt{6}[/tex]

Step-by-step explanation

[tex]\rule{100mm}{0.5mm}[/tex]

                           [tex]x^2-6x=15[/tex]

[tex]x^2-6x+\left(\dfrac{6}{2}\right)^2-\left(\dfrac{6}{2}\right)^2=15[/tex]

                   [tex]x^2-6x+3^2=15+3^2[/tex]

                     [tex]x^2-6x+9=15+9[/tex]

                          [tex](x-3)^2=24[/tex]

                       [tex]\sqrt{(x-3)^2} =\sqrt{24}[/tex]

                              [tex]x-3=\pm2\sqrt{6}[/tex]

                                  [tex]\red{\boxed{x_1=3+2\sqrt{6}}}[/tex]

                                  [tex]\red{\boxed{x_2=3-2\sqrt{6}}}[/tex]                                

[tex]\rule {100mm}{0.5mm}[/tex]

Answer:

camilla needs 4 scoops of flow because 3 is related to 15 bc "5x3=15" and that gives us to only need 1 more cup to get 20 cookies

Answer:

C.) y=-2/3+4

Step-by-step explanation:

You can look at the y-intercept to find the equation really quickly!

For example, the line crosses the y-axis at the value of 4, therefore, the y-intercept is 4.

The only option with a y-intercept of 4 is C

Answer:

55 + 14[tex]\sqrt{6}[/tex]

Step-by-step explanation:

Given

(7 + [tex]\sqrt{6}[/tex] )² = (7 + [tex]\sqrt{6}[/tex] )(7 + [tex]\sqrt{6}[/tex] )

Each term in the second factor is multiplied by each term in the first factor, that is

7(7 + [tex]\sqrt{6}[/tex] ) + [tex]\sqrt{6}[/tex] (7 + [tex]\sqrt{6}[/tex] ) ← distribute both parenthesis

= 49 + 7[tex]\sqrt{6}[/tex] + 7[tex]\sqrt{6}[/tex] + 6 ← collect like terms

= 55 + 14[tex]\sqrt{6}[/tex]

b +cV 6 ÷12a

Step-by-step explanation:

let meknow 8i I am wrong

Answer:

Add up all the sides.

Step-by-step explanation:

Add up all the sides.

Add up all the sides of the triangle that is the perimeter.

Hope this helps plz hit the crown :D

Answer: 15.44 m

Step-by-step explanation:

We can think this as two triangle rectangles.

In both cases, the adjacent cathetus is 120m.

When the angle is 32°, the opposite cathetus will be the height of the cliff.

When the angle is 37°, the opposite cathetus will be the heigth of the cliff plus the height of the flagpole.

Then we need to compute both of them and calculate the difference.

We can use the trigonometric relation:

Tan(θ) = (opposite cathetus)/(adjacent cathetus)

in this case we have:

Tan(32°) = (height of the cliff)/(120m)

Tan(32°)*120m = height of the cliff = 74.98m

Now we can use the other angle to compute:

Tan(37°) = (heigth of the cliff + heigth of the flagpole)/120m

Tan(37°)*120m = heigth of the cliff + heigth of the flagpole = 90.42m

Then the height of the flagpole will be:

H = 90.42m - 74.98m = 15.44 m

Answer:

um in languages or different angles

Step-by-step explanation:

Answer:

16. C

17. B

sorry if i got it wrong

Answer:

THE ANSWER

A

B

Step-by-step explanation:

MARK BRAINLIEST

Answer:

2/-5

Step-by-step explanation:

(-2) - (-4) = 2

(-6) - (-1) = -5

Answer:

-2/5

Step-by-step explanation:

you have to do y2-y1 over x2-x1

then you plot in your points :

y2=-2

y1=-4

x1=-1

x2=-6

after you do that you need to subtract them and that's how you will get your  answer.

Final Answer: [tex](x + 7)(x + 8)[/tex]

Steps/Reasons/Explanation:

Question/Given: Factor the polynomials [tex]x^{2} + 15x + 56[/tex]

Step 1: Ask: Which two numbers add up to [tex]15[/tex] and multiply to [tex]56[/tex]?

[tex]7[/tex] and [tex]8[/tex]

Step 2: Rewrite the expression using Step 1.

[tex](x + 7)(x + 8)[/tex]

~I hope I helped you :)~

wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink  wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink wink

Given:

[tex]d(t)=80t[/tex]

[tex]C(d)=0.09d[/tex]

To find:

The value of [tex]C(d(10))[/tex].

Solution:

We have,

[tex]C(d(10))=C(80(10))[/tex]           [tex][\because d(t)=80t][/tex]

[tex]C(d(10))=C(800)[/tex]

Now,

[tex]C(d(10))=0.09(800)[/tex]           [tex][\because C(d)=0.09d][/tex]

[tex]C(d(10))=72[/tex]

Therefore, the value of [tex]C(d(10))[/tex] is 72.

Answer:

-3

Step-by-step explanation:

pls mark as brainliest

Answer:

16)

Bobby - 70

Hannah - 90 (Wins the round)

Carlos - 80

17)

Bobby - 7  (Wins the round)

Hannah - 3

Carlos - 5

Step-by-step explanation:

First we can make the variable n into each of the values they chose for the equations. Let's start with 16.

The equation is - (3+7) X (10 - n ÷2)

Now let's input the numbers 6 , 2, and 4 one at a time to figure out the answer.

USE PEMDAS!!!

16)

Bobby -

1. (3+7) X (10 - 6 ÷2)

2. 10 X (10 - 6 ÷ 2)

3. 10 X 7

4.  Answer for Bobby - 70

Hannah -

1.  (3+7) X (10 - 2 ÷2)

2. 10 X (10- 2 ÷2)

3. 10 X 9

4. Answer for Hannah - 90 (Wins the round)

Carlos -

1. (3+7) X (10 - 4 ÷2)

2. 10 X (10 - 4 ÷ 2)

3. 10 X 8

4. Answer for Carlos - 80

17)

Bobby -

1. (2 X 6 + 2) ÷ 2

2. (12 + 2) ÷ 2

3. 14 ÷ 2

4. Answer for Bobby - 7 (Wins the round)

Hannah -

1.  (2 X 2 + 2) ÷ 2

2. (4+2) ÷ 2

3. 6 ÷ 2

4. Answer for Hannah - 3

Carlos -

1. (2 X 4 + 2) ÷ 2

2. (8+2) ÷ 2

3. 10 ÷ 2

4. Answer for Carlos - 5

Hope this Helps!!! :)

Let me know if I should change anything or if the answer was perfect!!!

Answer:

12 because 12/15 =.8 so does 8/10

Answer:

w=12

Step-by-step explanation:

8/10 is equal to 4/5. 4/5 is equal to 12/15. Therefore, W represents 12.

Brainliest are always appreciated :)

Answer:

565.5 in²

Step-by-step explanation:

Lateral area of a cone is represented by,

Lateral surface area = πrl

Here 'r' = Radius of the circular base

l = lateral height of the cone

By this formula,

Lateral area = π(12)(15)

                    = 565.49

                    ≈ 565.5 square inch

Therefore, 565.5 in² is the answer.

Step-by-step explanation:

your answer is 60

hope it helps :)

try this...............

Answer: No. The two frames does not have the same ratio of white shells to orange shells.

Step-by-step explanation:

Ryan glued 9 white shells and 15 orange shells to the border of his frame. This will give us a fraction of:

9/15 = 3/5

The ratio is 3:5

Russell glued 8 white shells and 10 orange shells to the border of his frame. This will give us a fraction of:

= 8/10 = 4/5

The ratio will be 4:5.

Therefore, the two frames does not have the same ratio of white shells to orange shells.

Answer:

1e+14

Step-by-step explanation:

Answer:

[tex]\displaystyle \frac{14}{3}\sqrt{5}[/tex]

Step-by-step explanation:

Simplify:

[tex]\displaystyle \sqrt{80} + \sqrt{2\frac{2}{9}}[/tex]

We must express the mixed fraction into an improper fraction:

[tex]2\frac{2}{9}=2+\frac{2}{9}=\frac{20}{9}[/tex]

[tex]\displaystyle \sqrt{80} + \sqrt{2\frac{2}{9}}=\displaystyle \sqrt{80} + \sqrt{\frac{20}{9}}[/tex]

Since 80 = 16*5 and 20=4*5

[tex]\displaystyle \sqrt{80} + \sqrt{2\frac{2}{9}}=\displaystyle \sqrt{16*5} + \sqrt{\frac{4*5}{9}}[/tex]

[tex]\displaystyle \sqrt{80} + \sqrt{2\frac{2}{9}}=\displaystyle 4\sqrt{5} + \frac{2}{3}\sqrt{5}[/tex]

Adding the fractions:

[tex]\displaystyle \sqrt{80} + \sqrt{2\frac{2}{9}}=\displaystyle (4 + \frac{2}{3})\sqrt{5}[/tex]

[tex]\mathbf{\displaystyle \sqrt{80} + \sqrt{2\frac{2}{9}}=\displaystyle \frac{14}{3}\sqrt{5}}[/tex]

Answer:

1.2

Step-by-step explanation:

X×5=0.75

X=(6, 5)

x=1.2

Answer:

no

Step-by-step explanation:

5+x=8+0.75x

x=12

Answer:

5x -  North American Butterflies.

3x - South American Butterflies.

5x = 30 (Divide By 5).

x = 6.

3x = 18.

3x - South American Butterflies.

2x - European Butterflies.

2x = 2 * 6 = 12

There Are 12 European Butterflies And 18 South American Butterflies.

Step-by-step explanation:

Answer:

48

Step-by-step explanation:

2 + 2 is 4, 1 - 4 is -3, 3 - 4 is -1 and +4 is 4 if you multiply these together, you will get 48.

Answer:

a) The exponential growth function

P(t) = 5,690,000(1.0287)^t

b) 6,742,868.7374 million

c) 12.04 years

d) 2439.0243902

Step-by-step explanation:

In​ 2012, the population of a city was 5.69 million. The exponential growth rate was 2.87​% per year. ​

The formula for exponential growth is given as:

P(t) = Po( 1 + r) ^t

Where P = Population size after time t

Po = Initial population size

r = Growth rate in percentage

t= time in years

a) Find the exponential growth function.

P(t) = Population size after time t

Po = Initial population size = 5.69 million

r = Growth rate in percentage = 2.87% = 0.0287

t= time in years

The Exponential growth function

P(t) = 5,690,000(1 + 0.0287)^t

P(t) = 5,690,000(1.0287)^t

​b) Estimate the population of the city in 2018. ​

From 2012 to 2018 = 6 years

t = 6 years

Hence,

P(t) = Po( 1 + r) ^t

P(t) = 5,690,000(1 + 0.0287)^6

P(t) = 5,690,000(1.0287)^6

P(t) = 6,742,868.7374 million

c) When will the population of the city be ​8 million?

P(t) = 8,000,000

P(t) = Po( 1 + r) ^t

P(t) = 5,690,000(1 + 0.0287)^t

8,000,000 = 5,690,000(1 + 0.0287)^t

8,000,000 = 5,690,000(1.0287)^t

Divide both sides by 5,690,000

8,000,00/5,690,000 = 5,690,000(1.0287)^t/5,690,000

= 1.4059753954 = 1.0287^t

Take logarithm of both sides

log 1.4059753954 = log 1.0287^t

Log 1.4059753954 =t Log 1.0287

t = Log 1.4059753954/Log 1.0287

t = 12.041740264

t = 12.04 years

​d) Find the doubling time.

The formula is given as 70/Growth rate

= 70/0.0287

= 2439.0243902

Answer:

3/5

Step-by-step explanation:

ir would be 6/10 but simplified it would be 3/5