which linear function shows a direct variation

Step-by-step explanation:

(+4)+(-7)

=4-7

=-3

Hope it will help you..

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]

Count how many multiples of 8, 12, or 18 there are in the range {1, 2, 3, …, 300}:

⌊300/8⌋ = 37

⌊300/12⌋ = 25

⌊300/18⌋ = 16

(where ⌊n⌋ denotes the floor of n, i.e. the largest integer that is smaller than n; for instance, 300/8 = 37.5, so ⌊300/8⌋ = ⌊37.5⌋ = 37)

Take pairwise LCMs, as well as the LCM of all three numbers:

LCM(8, 12) = LCM(2³, 2²×3) = 2³×3 = 24

LCM(8, 18) = LCM(2³, 2×3²) = 2³×3² = 72

LCM(12, 18) = LCM(2²×3, 2×3²) = 2²×3² = 36

LCM(8, 12, 18) = LCM(2³, 2²×3, 2×3²) = 2³×3² = 72

Count how many multiples there are of each of these LCMs that are less than 300:

⌊300/24⌋ = 12

⌊300/72⌋ = 4

⌊300/36⌋ = 8

Then, using the inclusion/exclusion principle, the number of numbers less than 300 that are exactly divisible by 8, 12, or 18 is

{multiples of 8} + {multiples of 12} + {multiples of 18}

- {multiples of 24} - {multiples of 72} - {multiples of 36}

+ {multiples of 72}

= 37 + 25 + 16 - 12 - 4 - 8 + 4 = 58

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:

B

Step-by-step explanation:

8 yards = 3 * 8 = 24 ft^2

1 mile = 5280

3*3 = 9 square feet

9 square feet holds 9 people.

1 square foot holds 1 person

8*3 * 5280 people could stand in an area of 8 yards * 1 mile

Though it's not quite correct, the answer is B

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:

Option C, 93.6 mi³

Step-by-step explanation:

Volume of the triangular prism,

base area × height

= (8×3.9/2)×6

= 93.6 mi³

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:

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

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:

(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

Answer:

m = negative StartFraction 10 over 4 EndFraction

m = negative five-halves

Step-by-step explanation:

Given equation :

Which equations are equivalent to Three-fourths + m = negative StartFraction 7 over 4 EndFraction

3/4 + m = - 7/4

Subtracting 3/4 from both sides

3/4 + m - 3/4 = - 7/4 - 3/4

m = - 10/4

m = - 5/2

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:

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:

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:

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:

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

[tex]\\ \sf\longmapsto (-42)+15+(-63)[/tex]

[tex]\\ \sf\longmapsto -42+15+(-63)[/tex]

[tex]\\ \sf\longmapsto -27+(-63)[/tex]

[tex]\\ \sf\longmapsto -27-63[/tex]

[tex]\\ \sf\longmapsto -90[/tex]

Answer:

42 + 15 + (-63) = -90

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

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: See explanation

Step-by-step explanation:

Since Smart Dot Company costs $12 per month plus $0.50 for each hour of Internet used, the equation to represent the cost of using the internet with them will be:

C = 12 + 0.5t

Since Communication Plus costs $2.50 for every hour of Internet used, the equation to represent the cost of using the internet with them will be:

C = 2.5t

Answer:

sorry

Step-by-step explanation:

polynomial is not given

question is incomplete

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:

so the division of a number and -9 or

x/-9+10=11 or

(x/-9)+10=11

subtract 10 from both sides

x/-9=1

multiply both sides by -9

x=-9

Step-by-step explanation:

its on the picture.........

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:

C. y = -f(x) - 3

Step-by-step explanation:

The given (parent) function is f(x) = √x

The given graph shows a real curve that starts from y = -3, when x = 0 and the y-value increases in magnitude in the negative direction as the x-values increases positively from left to right, by the same amount that the parent function increases from left to right

Therefore;

The graph is real, therefore, the value of x in √x is x ≥ 0, and y ≠ f(-x) + D

Where, D, is the vertical shift

The graph starts at x = 0, y = -3, compared to the parent function, the vertical shift, D = -3

The y-value of the given curve increases in the opposite direction (negatively) as the y-value of the parent function increases in magnitude in the positive direction

Therefore, the equation of the given curve comprises of the reflection of the parent function or -f(x)

The graph shows the reflection of the parent function, across the x-axis, and we have, reflection of the parent function, f(x) which is -f(x)

Therefore, the equation that describes the graphed function is y = -f(x) - 3