how to arrange four 3's to produce 33?​

If both triangles are similar then ratio of sides will be same.

[tex]\\ \sf\longmapsto \dfrac{12}{14}=\dfrac{y}{21}[/tex]

[tex]\\ \sf\longmapsto 12(21)=14y[/tex]

[tex]\\ \sf\longmapsto 14y=252[/tex]

[tex]\\ \sf\longmapsto y=\dfrac{252}{14}[/tex]

[tex]\\ \sf\longmapsto y=18[/tex]

Answer:

y = 18

Step-by-step explanation:

Since the triangles are similar, the corresponding sides are in proportion, that is

[tex]\frac{BC}{EF}[/tex] = [tex]\frac{AC}{DF}[/tex] , substitute values

[tex]\frac{y}{12}[/tex] = [tex]\frac{21}{14}[/tex] ( cross- multiply )

14y = 252 ( divide both sides by 14 )

y = 18

Segment addition postulate states that given points X, and Z, on a line, a point Y, can be located between X, and Z, ony if we have;

XZ = XY + YZ

The length of the segment BD is 36  cm

The reason the above value is correct is as follows:

Known:

The ratio in which the points A, B, C, and D divide the line segment = 4:3:1

The length of segment AD = 72 cm

Required:

The length of BD

Method:

Calculate the length of BC and CD and add their values to get BD

Solution:

Let the ratios be given unit proportions of the segment AD such that we have;

AB = 4 units

BC = 3 units

CD = 1 unit

By segment addition postulate, we have;

AD = AB + BC + CD

∴ AD = 4 units + 3 units + 1 unit = 8 units = 72 cm

∴ 1 unit = 72 cm/8 = 9 cm

1 unit = 9 cm

BD = BC + CD by segment addition postulate

BC = 3 units = 3 × 1 unit

∴ BC = 3 × 9 cm = 27 cm

BC = 27 cm

CD = 1 unit

∴ CD = 9 cm

∴ BD = 27 cm + 9 cm = 36 cm

The length of segment BD = 36 cm

Learn more about segment addition postulate here:

https://brainly.com/question/17015321

Answer:

x^5/y^7

Step-by-step explanation:

x^8 y^2 / x^3 y^9

We know that a^b/ a^c = a^(b-c)

Simplify the x terms

x^8 / x^3 = x^(8-3) = x^5

Simplify the y terms

y^2 / y^9 = y^(2-9) = y^-7

We know a^-b = 1/a^b

y^-7 = 1/y^7

Put the terms back together

x^5/y^7

Answer:

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

[tex]\left(\frac{\left(6\cdot \:\:\:sin\left(30\right)\right)}{sin\left(90\right)}\right)^2+x^2=36[/tex]

Step-by-step explanation:

a school has 2500 pupils. when 52 boys and 1/9 of the girls are absent, the number of the boys present is equal to the number of girls. how many pupils does the school have ?

Let the number of boys be x

Data :

Total pupils = 2500

Absent no. of boys and girls = 52 and 1/9

Now,

Remaining no of pupils = 2500 - 52 ➝ 2448

Hence, the no. of girls absent = 1/9 of 2448 ➝ 272

Therefore,

Total no. of pupils absent = 52 + 272 ➝ 324

No. of pupils present = 2500 - 324 ➝ 2176

Henceforth, 2176 pupils are present

Answer:

13.9

Step-by-step explanation:

For the 41° angle, x is the opposite leg, and 16 is the adjacent leg. The trig ratio that relates the opposite leg and the adjacent leg is the tangent.

tan A = opp/adj

tan 41° = x/16

x = 16 * tan 41°

x = 13.9085...

Answer: 13.9

Answer:

[tex]\displaystyle \displaystyle \cos A = \frac{a^2-b^2}{a^2 + b^2}\text{ and } \sin A = \frac{2ab}{a^2 + b^2}[/tex]

Step-by-step explanation:

We are given that:

[tex]\displaystyle \tan A = \frac{2ab}{a^2 - b^2}[/tex]

And we want to find the value of cos(A) and sin(A).

Recall that tangent is the ratio of the opposite side to the adjacent side.

Therefore, the opposite side measures 2ab, and the adjacent side measures a² - b².

Using the Pythagorean Theorem, solve for the hypotenuse:

[tex]\displaystyle \begin{aligned} c^2 &= a^2 + b^2 \\ \\ c&= \sqrt{(2ab)^2 + (a^2-b^2)} \\ \\ &= \sqrt{(4a^2b^2)+(a^4-2a^2b^2+b^4)} \\ \\ &= \sqrt{a^4 + 2a^2b^2 + b^4 } \\ \\ &= \sqrt{(a^2 +b^2)^2} \\ \\ &= a^2 + b^2\end{aligned}[/tex]

Thus, our hypotenuse is given by a² + b².

Cosine is the ratio between the adjacent side and the hypotenuse. Thus:

[tex]\displaystyle \cos A = \frac{a^2-b^2}{a^2 + b^2}[/tex]

And sine is the ratio between the opposite side and the hypotenuse. Thus:

[tex]\displaystyle \sin A = \frac{2ab}{a^2 + b^2}[/tex]

In conclusion:

[tex]\displaystyle \displaystyle \cos A = \frac{a^2-b^2}{a^2 + b^2}\text{ and } \sin A = \frac{2ab}{a^2 + b^2}[/tex]

Answer:

Step-by-step explanation:

[tex]sec^2A-tan^2A=1\\sec^2A=1+tan^2A=1+\frac{4a^2b^2}{(a^2-b^2)^2} =\frac{(a^2-b^2)^2+4a^2b^2}{(a^2-b^2)^2} =\frac{(a^2+b^2)^2}{(a^2-b^2)^2} \\cos^2A=\frac{(a^2-b^2)^2}{(a^2+b^2)^2} \\cos A=\frac{a^2-b^2}{a^2+b^2} \\sin A=\sqrt{1-cos^2A} =\sqrt{1-(\frac{a^2-b^2}{a^2+b^2} )^2} =\sqrt{\frac{(a^2+b^2)^2-(a^2-b^2)^2}{(a^2+b^2)^2} } =\sqrt{\frac{4a^2b^2}{(a^2+b^2)^2} }=\frac{2ab}{a^2+b^2}[/tex]

Answer:

5m

Step-by-step explanation:

5^(k-1)+5^(k-1)=m

Going to combine like terms on left:

2×5^(k-1)=m

Law of exponents applied:

2×5^k×5^(-1)=m

Reciprocal:

2×5^k×1/5=m

Multiply 5 on both sides to obtain the requested:

2×5^k=5m

Answer:

I think E

Step-by-step explanation:

You know the shortest building is 25 m.

to find the rest, use trigo so Tan(20)=opposite/adjacent.

Adjacent is 50. Do the math and add the answer with 25.

Answer:

The answer would be E. 43.2

According to TOA, The opposite side is tan(20) x adjacent side( 50m)

the answer is 18.2( to 1 dp). Add the height of the second building together with 18.2 and you will get ur answer. HOpe this helps:)

Answer:

see explanation

Step-by-step explanation:

Using x and y to represent the 2 numbers with x > y , then

x + y = 15 → (1)

x - y = 11 → (2)

Adding the 2 equations term by term to eliminate y

2x = 26 ( divide both sides by 2 )

x = 13

Substitute x = 13 into (1)

13 + y = 15 ( subtract 13 from both sides )

y = 2

The 2 numbers are 13 and 2

Answer:

- 2 x y^2+3 x^2 y -xy

-120

Step-by-step explanation:

xy – 2xy + 3x^2 y — 4x y^2 + 2xy^2

Combine like terms

xy – 2xy + 3x^2 y — 4x y^2 + 2xy^2

- x y+3 x^2 y - 2 x y^2

Let x = 4 y = -2

-(4)(-2) +3(4)^2 (-2) -2(4)(-2)^2

Exponents first

-(4)(-2) +3(16) (-2) -2(4)(4)

Multiply

+8 -96-32

Add and subtract

-120

Answer:

-4

Step-by-step explanation:

a = 3

b = -4

c = -2

2a + 3b - c

= 2(3) + 3(-4) - (-2)

= 6 + (-12) + 2

= -4

Answer:

200.96

Step-by-step explanation:

Volume of cone=(1/3)*pi*r^2*h

Volume=(1/3)*pi*16*12=64*3.14=200.96

Answer:

Klog earned $135.45 altogether.

Step-by-step explanation:

Hours

Monday - Friday : 5 days / 3.5 hours

Saturday : 1 day / 4 hours

3.5 · 5 + 4

= 17.5 + 4

= 21.5

Money

$6.30 per hours / 21.5 hours

6.30 · 21.5

= $135.45

Answer:

[tex]6(4c + 6d + 3})[/tex]

Step-by-step explanation:

Given

[tex]{24c + 36d + 18}[/tex]

Required

Apply distributive property

We have:

[tex]{24c + 36d + 18}[/tex]

Factor out 6 (to apply distributive property)

[tex]{24c + 36d + 18} = 6(4c + 6d + 3})[/tex]

Hence, the equivalent is:

[tex]6(4c + 6d + 3})[/tex]

Answer:

sorry

Step-by-step explanation:

polynomial is not given

question is incomplete

Answer:

x = 35

Step-by-step explanation:

Let x be the one of the other angles

X is also the third angle since we know they are equal

The sum of the angles of a triangle is 180

110+x+x = 180

110 +2x= 180

2x = 180-110

2x= 70

Divide by 2

2x/2 = 70/2

x = 35

Answer:

[tex]x = 35 \degree[/tex]

Step-by-step explanation:

Let the unknown angle be x

Unknown Angles are equal to each other so,

[tex]x + x + 110 = 180[/tex]

sum of the interior angles in a triangle is 180°

[tex]2x + 110 = 180 \\ 2x = 180 - 110 \\ 2x = 70 \\ \frac{2x}{2} = \frac{70}{2} \\ x = 35 \degree[/tex]

Part (a)

This is the empty set

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

Explanation:

It doesn't matter what set A is composed of. Intersecting any set with the empty set Ø will always result in the empty set.

This is because we're asking the question: "What does some set A and the empty set have in common?". The answer of course being "nothing" because there's nothing in Ø. Not even the value zero is in this set.

We can write Ø as { } which is a set of curly braces with nothing inside it.

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

Part (b)

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

Explanation:

When you union the universal set with any other set, you'll get the universal set.

The rule is [tex]A \cup B = B[/tex] where I've made B the universal set to avoid confusion of the letter U and the union symbol [tex]\cup[/tex] which looks nearly identical.

Why does this rule work? Well if an item is in set [tex]\overline{A}[/tex], then it's automatically in set U (everything is in set U; it's the universe). So we're not adding anything to the universe when applying a union involving this largest set.

It's like saying

we can see that [tex]\overline{A} \cup U[/tex] will basically form the set of every item, aka the universal set.

Answer:

2=124  124/2

4=248 248/4

5=310 310/5

8=496 496/8

Step-by-step explanation:

40 + 22 = 62

62 x 2 = 124

62 x 4 = 248

62 x 5 = 310

62 x 8 = 496

i think

Answer:

[tex]P(x \ge 5) = 0.60[/tex]

Step-by-step explanation:

Given

[tex]S = \{5, 2, 7, 2, 3, 4, 10, 6,4,6,3, 6, 6, 4, 8,5,7,7,1,5\}[/tex]

[tex]n(S) = 20[/tex]

Required

[tex]P(x \ge 5)[/tex]

First, we count the number of trials that are at least 5

[tex]x = \{5, 7, 10, 6,6, 6, 6, 8,5,7,7,5\}[/tex]

So, we have:

[tex]n(x \ge 5) = 12[/tex]

So, we have:

[tex]P(x \ge 5) = \frac{n(x \ge 5)}{n(S)}[/tex]

This gives

[tex]P(x \ge 5) = \frac{12}{20}[/tex]

[tex]P(x \ge 5) = 0.60[/tex]

Answer:

(2x+3y)^2

= (2x)^2 + 2(2x)(3y) + (3y)^2

= 4x^2 + 12xy + 9y^2

Answer:

4x^2 12xy +9y^2

Step-by-step explanation:

(2x+3y)^2

(2x+3y)(2x+3y)

FOIL

4x^2 + 6xy+6xy + 9y^2

4x^2 12xy +9y^2

The statistical question is; "What are the ages of the students in this class?

A statistical question is always aimed at data collection which can subsequently used for analysis and decision making. Statistical questions are asked in the course of research.

Among the two questions, the statistical question is; "What are the ages of the students in this class?

Learn more about statistics:https://brainly.com/question/8058700

#SPJ1

Answer:

Equation of line is y = -8x + 21

Step-by-step explanation:

Slope, m = -8

General equation of line:

[tex]{ \boxed{ \bf{y = mx + c}}}[/tex]

At point (2, 5), y = 5 and x = 2:

[tex]{ \tt{5 = ( - 8 \times 2) + c}} \\ { \tt{c = 21}}[/tex]

Therefore:

[tex]{ \sf{y = - 8x + 21}}[/tex]

[tex]{ \underline{ \blue{ \sf{christ \:† \: alone }}}}[/tex]

Answer:

8 cm

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

So first let's write the information we got

Angle BAC = 90 degrees

Midpoint of BC = M

AC = 6cm

Am= 5cm

Also I found MC = BM, since it has a line that represents both lines are same

so to find it we have to Pythagoras theorem (A^2 + B^2 = C^2), well it is question we have the 'A value and C Value', also we need to find the value of B to find the length of MC and BM

A = 5

C = 6

so therefore to find B^2, we have to do the reverse, we don't add but subtract

C^2 - A^2 = B^2

___________________________________________________________

Moving on to Calculation

6^2 - 5^2 = B^2

36 - 25 = B^2

B^2 = 9

B = √9

B = 3

MC and BM Length =  3 cm

____________________________

Now, we know the length we again need to use Pythagoras theorem to solve this.

Since we know

A = 5

B = 3

So..

A^2 + B^2 = C^2

5^2 + 3^2 = C^2

25 - 9 = C^2

C^2 = 16

C = √16

C = 4

Answer:

0.9

Step-by-step explanation:

100,000 in 90,000

Answer:

y = 3/5×x + 1

Step-by-step explanation:

Slope intercept form y= mx + b

since slope = 3/5 => y= [tex]\frac{3}{5}[/tex]x + b

Plug point (-5,-2) to the equation -2 = [tex]\frac{3}{5}[/tex] x (-5) + b

=> b=1

Answer:

B. Never

Step-by-step explanation:

When a number is irrational, it means that it cannot be written as a fraction.

I hope this helps!

pls ❤ and mark brainliest pls!

Answer:

c) when it is improper fraction