∠A and \angle B∠B are vertical angles. If m\angle A=(3x-30)^{\circ}∠A=(3x−30)
∘
and m\angle B=(2x-9)^{\circ}∠B=(2x−9)
∘
, then find the value of x.

Answer:

[tex]\approx 2\ miles[/tex]

Step-by-step explanation:

Difference of 10 seconds between the lightning flash and its thunder clap.

Given that the speed of light is infinite.

So, lightning will be seen at the same time it happens.

10 seconds is the time taken by the sound to reach to the person.

Time taken = 10 seconds

Speed of sound = 1080 ft/sec

To find:

Distance from lightning flash in miles.

Solution:

First of all, let us a have a look at the formula:

[tex]Distance = Speed \times Time[/tex]

Putting the given values:

Distance = [tex]1080\times 10 = 108000\ feet[/tex]

5280 feet = 1 mile

1 feet = [tex]\frac{1}{5280}[/tex] miles

10800 feet = [tex]\frac{1}{5280}\times 10800 \approx 2\ miles[/tex]

Answer:

13.44 pounds

Step-by-step explanation:

3.2x4.2=13.44 or 13 and 11/25

13.44 pounds of newspapers were collected by Rudy.

Two or more expressions with an Equal sign is called as Equation.

Given that alya collected [tex]3\frac{1}{5}[/tex] pounds of newspaper for the recycling Drive

Rudy collected [tex]4\frac{1}{5}[/tex] times as much newspaper as a liar

We need to find how many pounds of newspaper did Rudy collect​.

Let us convert  [tex]3\frac{1}{5}[/tex] as improper fraction

[tex]3\frac{1}{5}[/tex]=16/5

[tex]4\frac{1}{5}[/tex] =21/5

As Rudy collected 4 1/5 times as much newspaper of alya

So multiply 16/5 with 21/5

16/5×21/5

3.2×4.2

13.44 pounds

Hence, 13.44 pounds of newspapers were collected by Rudy.

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Answer:

width = 6 ft

Step-by-step explanation:

let  A = 24 3/5 = (24*5 +3)/5 = 123/5 ft^2 the area

l = 4 1/10 = (4*10 + 1)/10 = 41/10 ft the length

w = the width, w>0

since the area = length*width we have:

l*w = A

(41/10)*w = 123/5

by solving we find:

w = 6 ft

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

Explanation:

r = amount of salad Reagan ate

v = amount of salad Olivia ate

"Olivia ate twice as much as Reagan", meaning

amount Olivia ate = 2*(amount Reagan ate)

v = 2*r

v = 2r

2r = v

Answer:

-17

Step-by-step explanation:

Ans. - 17

We just substitute the values of a, b and c and find the answer

Answer: 9(3+2)

Step-by-step explanation:

The GCF of 27 and 18 is 9  because the factors of 27 are, 1,3,9 and 27 and the the factors of 18 are, 1,2,3,9 and 18.

The greatest factor that they both share is 9.

And 9 times three is 27 and 9 times 2 is 18.

Answer:

[tex]k=5.2[/tex]

Step-by-step explanation:

So we have the equation:

[tex]9.3=k+4.1[/tex]

To solve for k, subtract 4.1 from both sides:

[tex](9.3)-4.1=(k+4.1)-4.1[/tex]

The right cancels. Simplify the left:

[tex]5.2=k\\k=5.2[/tex]

Thus, the value of k is 5.2

Answer:

[tex]\huge \boxed{k=5.2}[/tex]

Step-by-step explanation:

[tex]9.3=k+4.1[/tex]

Subtract 4.1 from both sides.

[tex]9.3-4.1=k+4.1-4.1[/tex]

[tex]5.2=k[/tex]

Answer:

7

Step-by-step explanation:

A line segment partitioned by a ratio of 3:4 can be thought of as having 7 congruent sections

According to the ratio in which it is partitioned, the line segment can be thought as having 7 congruent sections.

If it can be divided into a ratio of a:b, it can be partitioned into a + b congruent segments.

In this problem, it has a ratio of 3:4, hence, the line segment can be thought as having 7 congruent sections.

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This question is Incomplete because it lacks the appropriate diagram for the square pyramid. Please kindly find attached the required diagram

Answer:

45 square inches

Step-by-step explanation:

From the question, we are told that the foil covers the body of the trophy including the bottom, hence the formula we would be applying =

Total Surface Area of the Square pyramid = 2bs + b²

Where s = Height of the square pyramid

b = Edge length of the square pyramid

From the attached diagram, we can see that:

s = 6 inches

b = 3 inches

Total Surface Area of the Square pyramid = 2bs + b²

= 2 × 3 × 6 + 3²

= 36 + 9

= 45 square inches.

Therefore, the amount of gold foil it took to cover the trophy, including the bottom is 45 square inches

Answer:

1/2

Step-by-step explanation:

from one point to another it goes up 1 and over two. so rise over run, 1 over 2

Answer:

1/2 or .5

Step-by-step explanation:

to find slope of a line, you can count the rise, or fall, of a line over its left and right direction. the line rises one and to the right 2 between each point, which makes the slope 1/2. we know the slope is positive because the line moves upwards.

Answer:

A: Linear

B: Linear

C: Linear

Step-by-step explanation:

So we have three functions:

[tex]f(x)=3x+1\\f(x)=x-6x+5\\f(x)=4x-x+1[/tex]

To determine the type of graph for each function, simplify each of them and then we can determine whether it's linear or quadratic.

1)

We have:

[tex]f(x)=3x+1[/tex]

This has a degree of 1. Quadratics have a degree of 2. In other words, quadratics have a x^2 term. There isn't one here, so this is a linear equation.

2)

We have:

[tex]f(x)=x-6x+5[/tex]

Simplify:

[tex]f(x)=-5x+5[/tex]

Again, this is of degree 1. There is no x^2 term. Thus, this is also a linear equation.

3)

We have:

[tex]f(x)=4x-x+1[/tex]

Simplify:

[tex]f(x)=3x+1[/tex]

This has a degree of 1. There is no x^2 term. Thus, this is also a linear equation.

Answer:

Step-by-step explanation:

a- f(x)=3x+1 it is linear equation

b: f(x)=x-6x+5

f(x)=-5x+5  linear equation

c: f(x)=4x-x+1

f(x)=3x+1  (linear equation)

(if there is no exponent then the graph is linear)

Answer:

16

Step-by-step explanation:

Answer:

The answer 14

Step-by-step explanation:

Answer:

4.56miligrams-->0.00456 g

Step-by-step explanation:

4.56miligrams-->0.00456 g

You simply add 3 zeros before it because 1000 miligrams=1 gram, and there are 3 zeros in 1000.

Answer:

A

Step-by-step explanation:

Parallel lines have the same slope since the slope is like a measure of steepness and since parallel lines are of the same steepness, thus, are of the same slope. The correct option is C.

Parallel lines have the same slope since the slope is like a measure of steepness and since parallel lines are of the same steepness, thus, are of the same slope.

Since the given parallel line has equation y = 2x + 2, thus its slope is 2 and thus, the slope of the needed line is 2 too.

Of the four of the given options, the options that are true are A and C, but since option, A says If two lines are parallel, then they do not intersect; T. Therefore, in the given option the result is given first and then the condition.

Opposite of that option C says If two lines do not intersect, then they are parallel; T. Therefore, it states the condition and then the answer. Thus, it is the correct option.

Hence, the correct option is C.

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Answer:

(3,0)

Step-by-step explanation:

Co-ordinates of J =(4,3)

Co-ordinates of K = (2,-3)

Midpoint formula :

 = [tex]\frac{x_{1}+x_{2} }{2} , \frac{y_{1} +y_{2} }{2} \\ \frac{4+2}{2} ,\frac{3+(-3)}{2}\\\frac{6}{2},\frac{3-3}{2}\\3, 0[/tex]

Coordinates of the midpoint M (3,0)

The coordinates of the midpoint M is (3,0) and the distance between J(4,3) and K(2,-3) is 6.32 units.

The distance between two points of the xy-plane can be found using the distance formula. The distance formula is:

√[(x₂ - x₁)² + (y₂ - y₁)²].

Now given coordinates of two points are,

J(4,3) and K(2,-3)

Therefore we have,

x₁ = 4

y₁ = 3

x₂ = 2

y₂ = -3

To find the midpoint between J and K we have,

{[(x₁+x₂ )/2] , [(y₁+y₂ )/2]}

Put the values, we get

{[(4+2)/2] , [(3+(-3)/2]}

solving them,

{(6/2) ,(0/2)}

or,

(3,0)

which is the required midpoint M.

Now distance between J(4,3) and K(2,-3) = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(2 - 4)² + (-3 - 3)²]

= √[(- 2)² + (-6)²]

= √4 +36

= √40

= 6.32 units

Thus, the coordinates of the midpoint M is (3,0) and the distance between J(4,3) and K(2,-3) is 6.32 units.

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Answer:

[tex]n = 500e^{-4.1589x}[/tex]

Step-by-step explanation:

Using the exponential growth equation [tex]N(t) = N_0e^{-kt}[/tex] where;

N₀ is the initial population of the bacteria

N(t) is the population of the bacteria during time t

If a biologist puts an initial population of 500 bacteria into a growth plate, this means that N₀ = 500 at t = 0

[tex]N(t) = N_0e^{-kt}\\N(t) = 500e^{-k(0)}\\N(t) = 500e^0\\N(t) = 500[/tex]

If the population is expected to double every 4 hours, this means when t = 4, N₀  = 2(500) = 1000

[tex]N(t) = N_0e^{-kt}\\500 = 1000e^{-4k}\\\frac{500}{1000} = e^{-4k}\\0.5 = e^{-4k}\\ln(0.5) = lne^{-4k}\\ln(0.5) = -4k\\k = \frac{ln0.5}{-4} \\k = 0.1733[/tex]

The equation that will give the expected number of bacteria, n, after x days, can be gotten by substituting N(t) = n and t = x days = 24x hours

[tex]N(t) = N_0e^{-kt}\\n = N_0e^{-0.1733(24x)}\\n = 500e^{-4.1589x}[/tex]

Hence the equation that will give the expected number of bacteria, n, after x days is [tex]n = 500e^{-4.1589x}[/tex]

Step-by-step explanation:

Number of apples = A

Number of boxes = B

Amount of apples in each box

[tex] =\frac{A}{B}\\

=\frac{200}{5}\\

= 40[/tex]

Answer:

Step-by-step explanation:

[tex]-2x-14=7x+6\\\\\mathrm{Add\:}14\mathrm{\:to\:both\:sides}\\-2x-14+14=7x+6+14\\\\Simplify\\-2x=7x+20\\\\\mathrm{Subtract\:}7x\mathrm{\:from\:both\:sides}\\-2x-7x=7x+20-7x\\\\Simplify\\-9x=20\\\\\mathrm{Divide\:both\:sides\:by\:}-9\\\frac{-9x}{-9}=\frac{20}{-9}\\\\x=-\frac{20}{9}\\\left(\mathrm{Decimal}:\quad x=-2.22222\dots \right)\\x =-2.2[/tex]

Answer:

x = -2.2

Step-by-step explanation:

-2x - 14 = 7x + 6

-2x - 7x = 6 + 14

-9x = 20

x = 20/-9

x = -2.2222

x = -2.2   (nearest tenth)

  Check

-2*-2.2 - 14 = 7*-2.2 + 6

4.4 - 14 = -15.4 + 6 = -9.6

Answer:

Step-by-step explanation:

x  - total of population

35%x - women

1560 - men

35%x + 1560 = x

0.35x + 1560 = x

1560 = x - 0.35x

0.65x  =  1560

÷0.65     ÷0.65

x = 2400

Answer:

-15 meters

Step-by-step explanation:

If it goes up 50 meters from the ground, it will be 0+50 which is 50.

Then it says it drops 65 meters into an underground tunnel.  So at 50 meters, it dropped 65 meters.  That means you subtract this: 50-65, which equals -15 meters because 50 goes into 65 but there is still 15 left, so the 15 is negative.

The ground level is at 0.  And we just found out that the tunnel is at -15 meters.  To find out how many meters the tunnel is below the ground, just do 0-15, which is still -15 meters.   :)

Answer:

-8

Step-by-step explanation:

Answer:

a = -4

a= -8

Step-by-step explanation:

[tex]a^2+12a=-32\\\\\mathrm{Add\:}32\mathrm{\:to\:both\:sides}\\a^2+12a+32=-32+32\\\\Simplify\\a^2+12a+32=0\\\\Solve\:by\:factoring\\\mathrm{Factor\:}a^2+12a+32:\quad \left(a+4\right)\left(a+8\right)\\\\\mathrm{Solve\:}\:a+4=0:\quad a=-4\\\mathrm{Solve\:}\:a+8=0:\quad a=-8\\\\a=-4,\:a=-8[/tex]

Answer:

-10

Step-by-step explanation:

a - b = 7 - (-3) = 7 + 3 = 10

--> | a - b | = 10

--> - | a - b | = -10

Answer:

D: 54, 162, 486

Step-by-step explanation:

2, 6, 18 are all mulitplyed by 3 thus D: 54, 162, 486

Answer:

See below

Step-by-step explanation:

Q1. if a counting number is selected at random from a set of whole number less than or equal to 20 find the probability of getting:

Counting numbers are Natural numbers: [tex]\mathbb{N}[/tex]

Also, we have Whole numbers. Despite not having an official symbol, I usually denote the set as [tex]\mathbb{Z}_{\ge 0}[/tex]

Whole numbers less than or equal to 20: [tex]A\leq 20, A \subset \mathbb{Z}_{\ge 0} \\\implies A=\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20\}[/tex]

A. Prime numbers

From the set A, the prime numbers are 2, 3, 5, 7, 11, 13, 17, 19.

Once we have 21 numbers in total and 8 prime numbers, the probability is:

[tex]$P=\frac{8}{21} \approx 40\%$[/tex]

B. Composite numbers

From the set A, the composite numbers are 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20.

Once we have 21 numbers in total and 11 composite numbers, the probability is:

[tex]$P=\frac{11}{21} \approx 52\%$[/tex]

C. Divisible by three

From the set A, the numbers divisible by three are 3, 6, 9, 12, 15, 18.

Once we have 21 numbers in total and 6 numbers divisible by three, the probability is:

[tex]$P=\frac{6}{21} \approx 30\%$[/tex]

D. Square of 2

From the set A, the numbers square of 2 are 0, 1, 4, 9, 16.

[tex]\sqrt{0} =0[/tex]

[tex]\sqrt{1} =1[/tex]

[tex]\sqrt{4} =2[/tex]

[tex]\sqrt{9} =3[/tex]

[tex]\sqrt{16} =4[/tex]

Once we have 21 numbers in total and 5 numbers square of 2 , the probability is:

[tex]$P=\frac{5}{21} \approx 24\%$[/tex]

Q2. The opposite angle of acyclic quadrilaterals is in the ratio of 2:3. Find the degree measure of each opposite angle?

Once they're opposite, they add up to 180º

[tex]2x+3x=180 \implies 5x=180 \implies x=36[/tex]

The first angle is 72º

The second angle is 108º

Q3. what is the solution set of  9x-4<13x-7 (domain, x e z) ?

[tex]x \in \mathbb{Z}\\[/tex]

[tex]$x>\frac{3}{4} $[/tex]

[tex]$x\in \left(\frac{3}{4},\infty \right)$[/tex]

Q4. if three fourth of a number is one tenths, what is the number?

[tex]$\frac{3}{4} x =\frac{1}{10} \implies 3x=\frac{4}{10} \implies \boxed{x = \frac{2}{15}} $[/tex]

Q5. which one is the equation of the line passing through the origin and having a slope 4?

[tex]y=mx+b[/tex]

[tex]m: \text{slope}[/tex]

[tex]b: \text{y-intercept}[/tex]

B. Y= 4x

Answer:

4

Step-by-step explanation:

Answer:

[tex] \frac{3}{2} \: or \: 1.5 [/tex]

Step-by-step explanation:

[tex] \frac{12}{6 + 2} = \frac{12}{6 + 2} = \frac{12}{8} = \frac{6}{4} = \ \frac{3}{2} \: or \: 1.5[/tex]

Answer:

A.

Step-by-step explanation:

Step-by-step explanation:

i hope it helped you. thankyou

Answer:

15/19

Step-by-step explanation:

Nesta pergunta, queremos calcular a probabilidade de que uma bola retirada da urna não seja preta.

Existem três cores, uma vez que a bola removida não é preta, então é uma das outras duas cores.

Isso significa que a bola é branca ou vermelha. Observe que a probabilidade de a bola não ser preta é 1 menos a probabilidade de a bola ser preta Vamos descobrir a probabilidade de que a bola seja preta;

Matematicamente, isso seria;

número de bolas pretas / número total de bolas.

O número total de bolas é; 10 + 5 + 4 = 19 número de bolas pretas = 4

A probabilidade de a bola ser preta é de 4/19

Portanto, a probabilidade de que a bola não seja uma bola preta é

1 - 4/19 = 15/19