(4x²y³ + 2xy² - 2y) - (-7x²y³ + 6xy² - 2y)

[tex]\huge\bold{To\:find:}[/tex]

✎ The length of the hypotenuse.

[tex]\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}[/tex]

[tex]\sf\purple{The\:length\:of\:the\:hypotenuse \:"c"\:is\:5.10\:km.}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

Using Pythagoras theorem, we have

[tex]( {perpendicular})^{2} + ( {base})^{2} = ( {hypotenuse})^{2} \\ ⇢ ( {5 \: km})^{2} + ( {1 \: km})^{2} = ( {c})^{2} \\ ⇢ 25 \: {km}^{2} + 1 \: {km}^{2} = {c}^{2} \\ ⇢ 26 \: {km}^{2} = {c}^{2} \\ ⇢  \sqrt{26 \: {km}^{2} } = c \\ ⇢5.0990 \: km = c \\ ⇢5.10 \: km = c[/tex]

[tex]\sf\blue{Therefore,\:the\:length\:of\:the\:hypotenuse\:is\:5.10\:km.}[/tex]

[tex]\huge\bold{To\:verify :}[/tex]

[tex]( {5 \: km})^{2} + ( {1 \: km})^{2} = ( {5.10 \: km})^{2} \\ ⇝25 \: {km}^{2} + 1 \: {km}^{2} = 26 \: {km}^{2} \\ ⇝26 \: {km}^{2} = 26\: {km}^{2} \\ ⇝L.H.S.=R. H. S[/tex]

Hence verified.

[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]

Answer:

exact: 48pi cm^2

approximate: 150.8 cm^2

Step-by-step explanation:

SA = 2 * (pi)r^2 + 2(pi)rh

SA = 2 * pi * (3 cm)^2 + 2(pi) * 3 cm * 5 cm

SA = pi(18 cm^2 + 30 cm^2)

SA = 48pi cm^2

SA = 150.8 cm^2

Answer:

10.50

Step-by-step explanation:

Answer:

4 x 8.50

100

= 0.34

8.50 - 0.34 = 8.16

Step-by-step explanation:

a percentage is always over 100 so i 4 percent of 8.50 which gave me 0.34

Dont forget we are only focused on on the increase so we gotta subtract to make it normal from the original number which gives u 8.16...

Note dont forget it said an hour so multipy it by 1 hour since it said one hour which stills gives u the same answer

Answer: It's C f"(x)= 15x^2+235 Hope that helps!

Step-by-step explanation:  

Find the Greatest Common Factor (GCF).

GCF = 5

2. Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)

5(15x^2/5+235/5)

3. Simplify each term in parentheses and that would give you 5(3x^2+47) and that's why I think it C but i'm not so sure but if you get it right can you please make me Brainliest bye and I hope you get it right!

Answer:

B is most credible

Hope this helped.

Answer:

x = 5

Step-by-step explanation:

Given

2x + 7 = 17 ( subtract 7 from both sides )

2x = 10 ( divide both sides by 2 )

x = 5

Answer:

84

Step-by-step explanation:

0.5 · 7 · 24

0.5 · 168

84

Answer:

84

Step-by-step explanation:

Step 1: Convert number to a fraction

[tex]24=\frac{24}{1}[/tex]

[tex]\frac{1}{2}\times \frac{24}{1}\times \:7[/tex]

Step 2: Factor the number

[tex]\:24=2\times \:12[/tex]

[tex]\frac{2\times \:12}{2}\times \:7[/tex]

Step 3: Cancel the common factor

[tex]2[/tex]

Step 4: Multiply the remaining numbers

[tex]12\times \:7\\\\= 84[/tex]

Therefore, [tex]\frac{1}{2}\times 7\times 24\:=\:84[/tex]

Answer:

60 : 32

Step-by-step explanation:

Let x = Their present ages

Ritu : Nitu = 15x : 8x

After 10 years, their ages will be in the ratio 5:3

In 10 years

15x + 10 : 8x + 10 = 5 : 3

15x + 10 / 8x + 10 = 5/3

Cross product

15x + 10 * 3 = 8x + 10 * 5

45x + 30 = 40x + 50

45x - 40x = 50 - 30

5x = 20

x = 20/5

x = 4

Ritu : Nitu = 15x : 8x

Ritu : Nitu = 15 * 4 : 8 * 4

= 60 : 32

Ritu : Nitu = 60 : 32

=========================================

Explanation:

Since AB is smaller than AD, this must mean the angle ACB is smaller than angle ACD. Note how these angles are opposite the sides mentioned.

So 2x-10 < 48

At the same time, 2x-10 is also larger than 0.

Overall, we can say 0 < 2x-10 < 48

---------

Let's solve for x

0 < 2x-10 < 48

0+10 < 2x < 48+10 ...... add 10 to all sides

10 < 2x < 58

10/2 < x < 58/2 ..... divide all sides by 2

5 < x < 29

Answer:

Step-by-step explanation:

This is quite a doozy, so try and follow along. If you don't know your circle stuff well, it will be more difficult for you to understand how all this comes together.

First, we were given that angle CBD = 55. That means that angle CED is also 55 since they are both inscribed angles and they both intercept the same arc, arc CD. Angle BFC is congruent to angle 5 because they are vertical and vertical angles are congruent, so that means that triangle BFC is congruent to triangle EFD because of Angle-Angle-Side. Now that we got that out of the way, let's move on. We will come back to that in a bit.

Angle 1 intercepts arc BE and since angle 1 is an inscribed angle, it is half the measure of its intercepted arc. Therefore,

∠1 = 25° ; angle BCE also equals 25 degrees since they are both inscribed and they both intercept the same arc (again, arc BE).

If angle BCE is 25, and angle CBD is 55, then angle F, by the Triangle Angle Sum Theorem, must equal 180 - 25 - 55 = 100. And if Angle F = 100, then

∠5 = 100° . Angles 4 and 5 are supplementary, therefore,

∠4 = 80°

Since angle CBD was given as 55 and is an inscribed angle for arc CD, then arc CD is twice the measure of its inscribed angle and arc CD is 110 degrees. Angle 6, then, is one-half the difference of arc CD and arc BE so

∠6 = 30°

Angles 2 and 3 are congruent since they are both inscribed and they both intercept the same arc (arc DE); and since triangles BFC and EFD are congruent, by CPCTC, sides BF and EF are congruent...which means by the IsoscelesTriangle Theorem, angle 2 and angle BEC are congruent. 180 - 80 = 100 and divide that in half to get that

∠2 ≅ ∠3 = 50°

Lastly, angle 7 is half the measure of its intercepted arc (arc BE, given as 50), therefore,

∠7 = 25°

Answer:

[tex]\displaystyle \cos(A + B) =\frac{969}{1769}[/tex]

Step-by-step explanation:

We are given that:

[tex]\displaystyle \cos A=\frac{20}{29}\text{ and } \tan B=\frac{11}{60}[/tex]

Where A and B are positive acute angles.

And we want to find cos(A + B).

Recall that cosine is the ratio of the adjacent side to the hypotenuse. Using this information, find the opposite side with respect to Angle A:

[tex]o=\sqrt{29^2-20^2}=21[/tex]

Tangent is the ratio of the opposite side to the adjacent side. Find the hypotenuse with respect to Angle B:

[tex]h=\sqrt{11^2+60^2}=61[/tex]

In summary:

With respect to Angle A, the adjacent side is 20, opposite is 21, and the hypotenuse is 29.

With respect to Angle B, the adjacent side is 60, the opposite is 11, and the hypotenuse is 61.

We can rewrite our expression as:

[tex]\displaystyle \cos(A+B)=\cos A\cos B-\sin A\sin B[/tex]

Using the above information, substitute in the appropriate values. Note that since A and B are positive acute angles, all trigonometric values will be positive. Hence:

[tex]\displaystyle \cos(A + B)=\left(\frac{20}{29}\right)\left(\frac{60}{61}\right)-\left(\frac{21}{29}\right)\left(\frac{11}{61}\right)[/tex]

Simplify:

[tex]\displaystyle \cos(A + B) =\frac{1200-231}{1769}=\frac{969}{1769}[/tex]

Step-by-step explanation:

1/4+3/10+5/21

105+42+100/420

=247/420

=0.588

[tex]\huge{ \mathcal{  \underline{ Answer} \:  \:  ✓ }}[/tex]

[tex]\longrightarrow \dfrac{247}{420} [/tex]

or

[tex]\longrightarrow0.588[/tex]

_____________________________

[tex]\mathrm{ ☠ \: TeeNForeveR \:☠ }[/tex]

Answer:

$496800

Step-by-step explanation:

You need to find 3.5% of 480,000 and then add it to 480000:

You convert 3.5% to 0.035 (divided by 100).

Now you multiply 0.035 * $480,000 = $16800 (this is the amount of money to add to the value of the house)

Total value of the house: $480,000 + $16,800 = $496800

Answer:

the answer 240

Step-by-step explanation:

times 24 and 10 to get 240 m

Answer:

The answer is 5.5 because half of 11 is 5.5 and diameter is half of circumference.

Answer:

5.5

Step-by-step explanation:

diameter=11

radius = diameter÷2

r=11÷2

radius=5.5

Answer:

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

13x is 13

x is 1

6x is 1 times 6 is 6

Answer:

13x+2=15

13x=15-2

x=13/13

x=1

6x=6*1

=6

Step-by-step explanation:

Answer:

D.

Step-by-step explanation: they can be different widths

Answer:

B: 42°, 48°

Step-by-step explanation:

I took the test.

The pair of angles have congruent values for the sin x° and the cos y° is 42; 48.

Angles that are of the same measurement are called congruent.

Suppose that two angles ∠A and ∠B are of the same measure,

then

[tex]m\angle A = m\angle B[/tex]

is the notation to say that they are of the same measurement, where the small m shows that its the measurement of the angles they're preceding.

We write the congruency between them as;

[tex]\angle A \cong \angle B[/tex]

Congruent angles can be defined as a type of angle that is known to have all sides in equal measure.

sin x  = cos (90-x)

therefore,  sin 42 = cos(90-42)

                             = cos 48

Hence, option B) 42°, 48° is correct

Learn more about congruent angles ;

brainly.com/question/2938476

#SPJ2

Answer:

A. [tex]2\frac{2}{3}[/tex]

Step-by-step explanation:

[tex]-2\frac{1}{3} -(-5)[/tex]

[tex]-2\frac{1}{3} +5[/tex]

V = ( 4/3 ) × π × r^3

V = ( 4/3 ) × π × ( 6/2 )^3

V = ( 4/3 ) × π × ( 3 )^3

V = ( 4/3 ) × 3 × 9 × π

V = 4 × 9 × π

V = 36 π m^3

Thus the correct answer is option D .

Answer:

I believe it would be B. SAS

Step-by-step explanation:

You have two sides and one angle that are congruent in both

Answer:

the third one ig

Step-by-step explanation:

Answer:

1.368

Step-by-step explanation: 1.14x1.2=1.368

=======================================================

Explanation:

15% of 15 = 0.15*15 = 2.25

The cost has increased by $2.25 which means the cost per kilogram is now 15+2.25 = 17.25 dollars

------------

As a slight shortcut, we can multiply the old cost (15) by the multiplier 1.15 to get the same result:

1.15*15 = 17.25

This method allows us to chain together many percentage increases, and it also allows us to include percentage decreases as well. Note how 1.15 is basically the result of 100% + 15% = 1.00+0.15 = 1.15