x²-6xy+11y²=3a²
x²-2xy-3y²=5a²​

Step-by-step explanation:

Given is the 30°x60°x90° right triangle.

The ratio of its sides is:

Find the missing sides using the ratio above:

Answer:

[tex]\sf x = 4\sqrt{6}[/tex]   and   [tex]\sf y = 6\sqrt{2}[/tex]

step-by-step explanation:

given:

using tan rule:

[tex]\sf tan(x)= \dfrac{opposite}{adjacent}[/tex]

[tex]\sf tan(60)= \dfrac{y}{2\sqrt{6} }[/tex]

[tex]\sf tan(60)*{2\sqrt{6}= y[/tex]

[tex]\sf y = 6\sqrt{2}[/tex]

using cosine rule:

[tex]\sf cos(x)= \dfrac{adjacent}{hypotensue}[/tex]

[tex]\sf cos(60)= \dfrac{2\sqrt{6} }{x}[/tex]

[tex]\sf x= \dfrac{2\sqrt{6} }{cos(60)}[/tex]

[tex]\sf x = 4\sqrt{6}[/tex]

Answer: 0.2916666665

Step-by-step explanation:

Answer:

[tex]\frac{7}{24}[/tex]

Step-by-step explanation:

By the Pythagorean Theorem, we know

[tex]\cos^2a=1-\sin^2a[/tex].

With this, we can find [tex]\cos a[/tex] by plugging in what we know for [tex]\sin a[/tex]:

[tex]\cos^2a=1-(\frac{4}{5})^2\\~~~~~~~~=1-\frac{16}{25}\\~~~~~~~~=\frac{9}{25}[/tex].

Taking the square root, we get

[tex]\cos a=\frac{3}{5}[/tex] .

Note: there seems to be a problem with the question? It doesn't specify what range [tex]a[/tex] lies in, so we don't know whether [tex]\cos a[/tex] is positive or negative. In this case, I assumed it was positive.

From this, we can find [tex]\tan a[/tex]:

[tex]\tan a=\frac{\sin a}{\cos a}\\~~~~~~~=\dfrac{\frac{4}{5}}{\frac{3}{5}},[/tex]

so [tex]\tan a=\frac{4}{3}[/tex].

Using the [tex]\tan[/tex] difference formula, we know

[tex]\tan (a-b)=\dfrac{\tan a -\tan b}{1+\tan a\tan b}[/tex] .

Plugging in the values we know for [tex]\tan a[/tex] and [tex]\tan b[/tex], we get

[tex]\tan(a-b)=\dfrac{\frac{4}{3}-\frac{3}{4}}{1+\frac{4}{3}\cdot\frac{3}{4}}\\~~~~~~~~~~~~~~=\dfrac{\frac{7}{12}}{1+1}\\~~~~~~~~~~~~~~=\boxed{\frac{7}{24}}~.[/tex]

Answer:

70.02ft≈70ft

Step-by-step explanation:

Here,

∠ABC=35°

BC=100ft

AC=?

Now,

[tex]tanB=\frac{AC}{BC} \\\\[/tex][tex]tanB=\frac{AC}{BC} \\\\tan35=\frac{AC}{100ft} \\\\0.7002=\frac{AC}{100ft} \\\\100ft*0.7002=AC\\\\AC=70.02ft[/tex]

Because tan=p/b

[tex]\\ \rm\rightarrowtail cot35=\dfrac{Base}{Perpendicular}[/tex]

[tex]\\ \rm\rightarrowtail cot35=\dfrac{BC}{AC}[/tex]

[tex]\\ \rm\rightarrowtail cot35=\dfrac{100}{AC}[/tex]

[tex]\\ \rm\rightarrowtail AC=\dfrac{100}{1.43}[/tex]

[tex]\\ \rm\rightarrowtail AC=69.93ft[/tex]

Answer: 152

Step-by-step explanation:

Let the number = x.

Therefore, x*25% = 38

25% as a decimal is 0.25.

So, 0.25x = 38

We can divide both sides by 0.25:

x = 152

Answer:

4) 14.5

6) 11.4

Step-by-step explanation:

4) Area = 20 * 21/2 = 29 * x/2

so x = 20 * 21/29 = 14.5

6) Area = 22.4 * 13.2/2 = 26 * x/2

so x = 22.4 * 13.2/26 = 11.4

Answer:

A) t = 0.25 s

B) h = 25 m

Step-by-step explanation:

Given equation:  [tex]h(t) = -16t^2 + vt + s[/tex]

where:

A)  To find the value of t when h is at its maximum, differentiate the equation with respect to t:

[tex]\implies h'(t)=-32t+v[/tex]

Substitute given value of v:

[tex]\implies h'(t)=-32t+8[/tex]

Set to zero and solve for t:

[tex]\implies -32t+8=0[/tex]

[tex]\implies t=0.25 \textsf{s}[/tex]

B)  Substitute the found value for t into the equation and solve for h:

[tex]\implies h(0.25) = -16(0.25)^2 + 8(0.25) + 24[/tex]

[tex]\implies h(0.25) = -1 + 2 + 24[/tex]

[tex]\implies h(0.25) =25 \textsf{ m}[/tex]

[tex]\\ \rm\Rrightarrow \sqrt{36x^{21}y^{64}}=6y^8x^{10.5}[/tex]

[tex]\\ \rm\Rrightarrow \sqrt[15]{7^{10}a^{25}b^{-35}}=7^{2/3}a^5b^{-7}{3}[/tex]

[tex]\\ \rm\Rrightarrow \sqrt[3]{648(3m-2n)^{64}}=648^{1/3}(3m-2n)^4[/tex]

[tex]\\ \rm\Rrightarrow \sqrt[4]{(a^2-2a+1)^{29}(a^2-1)^7}=(a^2-a+1)^{29/4}(a^2-1)^{7/4}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{3a^2b}{\sqrt[3]{18a^{21}b^{17}}}=\dfrac{3a^2b}{18^{1/3}a^7b^{17/3}}=\dfrac{3a^{-5}b^{-14/3}}{18^{1/3}}=\dfrac{3}{18^{1/3}a^5b^{14/3}}[/tex]

Answer:

the $4000 WILL EARN 4 TIMES THE AMOUNT OF INTEREST.

Step-by-step explanation:

If both investments have same interest they will grow in the same proportion that the initial amount have.

Answer:

The dragonfly is 4.5 feet per second faster.

Step-by-step explanation:

48 boards

Step-by-step explanation:

length of a board = 5½ in = 11/2

Total length should be covered = 22 ft = 264 in (1ft = 12in)

total boards needed = 264 ÷11/2

= 264 × 2/11

= 24 ×2

= 48 boards

please please please please please please

Answer:

155 cm2

Step-by-step explanation:

Answer:

153.86 cm² and 43.96

Step-by-step explanation:

The formula to find the area of a circle is A = πr²
A = 3.14(7)²
A = 3.14(49)
A = 153.86
To find the circumference, use the formula C = π2r
C = 3.14*2*7
C = 43.96
The area of the circle is 153.86 cm² and the circumference of the circle is 43.96.
Hope this helps :)

Answer:

the amount of a $3,000.00 annuity due at 12 percent compounded semiannually for 3 years. A. $334,321.00 B. $43,068.93 C. $22,180.50 D. $41,814.50

The amount of the annuity due in 23 years with 8% of interest compounded semiannually is $62053.35.

Compound interest is the interest on a loan or deposit calculated based on the initial principal and the accumulated interest from the previous period.

Scupper Molly invested $1,800 semiannually for 23 years at 8% interest compounded semiannually.

Then the amount of the annuity due will be

[tex]\rm A = 1800 (1 + 0.08)^{2\times 23}\\\\A = 1800 (1.08)^{46}\\\\A = 1800 \times 34.474\\\\A = 62053.35[/tex]

More about the compound interest link is given below.

https://brainly.com/question/25857212

Answer:

37°

Step-by-step explanation:

1. Label the sides: the hypotenuse (the longest, slanted side) is 5 and the adjacent is 4. This means that we are using cosine (CAH)

2. Write out the equation: cosine or cos (?) = adjacent ÷ hypotenuse

3. Substitute in the values: cos (?) = 4 ÷ 5

4. Simplify: cos (?) = 0.8

5.  Type this into a calculator to find ?:  [tex]cos^{-1}(0.8)[/tex]

? = 36.86989... ≈ 37°

Hope this helps!

There are no pictures provided.

( Talking about the models )

Answer:

i think it might be c

Step-by-step explanation:

tell me if its wrong or not and brain list please

Answer:

9 more mornings Jessica can drink orange juice

Step-by-step explanation:

1 4/5 = 1/5x

9/5  = 1/5 (divided below)

1/5       1/5

9/5  divided 1/5 = x

x = 9/5 x 5/1 = 45/5

45/5 divide by 5 = 9/1

long division and you get 9

hope this helps!

Answer:

The answer is 9

Step-by-step explanation:

Answer:

390 pennies that susan is holding

Answer:

3/4x-280=x/2

-3/4x-280=x/2 find the common factor for 3/4x-280/1 which is 4 3/4x-280/1 3xby

Answer:

$10.88

Step-by-step explanation:

To find the selling price, we first have to find the markup price by multiplying 8 by 36 and then dividing the product by 100.

Now, we add the markup price the cost of the book.

Therefore, the selling price is $10.88.

Hopefully, I have read the problems right. The small writing is slightly blurry.

[1] Both 1 and 2 are equal to 70°

    Angle 1 and Angle 2 will be equal to each other because they are vertical angles.

    A straight line is 180°, so 180° - 110° = 70°

[2] Both 3 and 4 are equal to 99°

    Again, Angle 3 and Angle 4 will be equal to each other because they are vertical angles.

    We can solve for the other two angles by putting them equal to each other since they are also vertical angles.

3x - 15° = 2x + 17°

3x = 2x + 32°

x = 32°

-

2x + 17°

2(32)° + 17°

64° + 17°

81°

    Also again, a straight line is 180°. 180° - 81° = 99°

[3] This one has too many subparts for Brainly.

    As a hint, you will use the same methods above. Find vertical angles and use the degree of a straight line.

Answer:

30

Step-by-step explanation:

solution

= (75*100)/250

= (7500)/250

= 7500/250

=30

Answer:

32,667

30,000+2,000+600+60+7

Answer:

a = ± [tex]\sqrt{\frac{4}{25} }[/tex]

Step-by-step explanation:

[tex]a^{2} =\frac{4}{25}[/tex]

[tex]\sqrt{a^{2} } =\sqrt{\frac{4}{25} } \\|a|=\sqrt{\frac{4}{25} \\[/tex]

a = ± [tex]\sqrt{\frac{4}{25} }[/tex]

Answer:

its b

Step-by-step explanation:

The measure of angle QPS in circle C is 112°

A circle is the locus of a point such that its distance from a fixed point known as the circle center is always constant. The sum of angles in a circle is 360 degrees.

From the circle:

PQ is parallel to SR, hence: ∠PQR + ∠QRS = 180°

∠PQR + 68 = 180

∠PQR = 112°

Also, PS =  QR (from the endpoint of  the diameter), hence:

∠QPS = ∠PQR = 112°

The measure of angle QPS in circle C is 112°

Find out more on circle at: https://brainly.com/question/24375372