In the triangle below which of the following is equivalent to the tangent of 52 degrees?

Answer:

The rate of cases is [tex]\frac{40}{19}[/tex] per hour

Step-by-step explanation:

we are given

Total number of cases =5

total time is

[tex]=2\frac{3}{8}[/tex] hour

we can simplify it

total time is

[tex]=\frac{2\times 8+3}{8}[/tex] hour

[tex]=\frac{19}{8}[/tex] hour

we can use formula

rate of cases = ( total number of cases)/( total time)

now, we can plug values

Rate of cases is

[tex]=\frac{5}{\frac{19}{8} }[/tex]

[tex]=\frac{40}{19}[/tex]

Answer: -Jerry hears  [tex]2\frac{2}{19}[/tex] per hour.

Step-by-step explanation:

Since time is given in mixed fraction [tex]2\frac{3}{8}[/tex] , thus first convert it into improper fraction

Time=[tex]\frac{19}{8}[/tex] hours

The total number of cases Jerry hears in  =5 cases

⇒The number of cases Jerry hears in 1 hour

[tex]=\frac{5}{\frac{19}{8}}\\\\=\frac{5\times8}{19}\\\\=\frac{40}{19}=2\frac{2}{19}[/tex] cases per hour.

Thus, Jerry hears [tex]2\frac{2}{19}[/tex] cases per hour .

Answer:

-2

Step-by-step explanation:

Answer:

h = 1

Step-by-step explanation:

If in a function, you replace x with x - h, you translate the function horizontally h units. The black function is f(x) = |x|. The blue function is the black function translated 1 unit to the right. That means h is 1.

Black function: f(x) = |x|

Blue function: f(x) = |x - 1|

h = 1

Answer:

The first three, (2, 8), (3, 9) and (4, 10).

Step-by-step explanation:

The unit rate, or rate of change, is another term for the slope.

The formula for slope is

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex].

The slope in the table would be given by

m = (22-11)/(10-5) = 11/5 = 2.2.

For the slope of the line that goes through (2, 8) and (0, 0), we have

m = (8-0)/(2-0) = 8/2 = 4.  This is greater than 2.2.

For the slope of the line that goes through (3, 9) and (0, 0), we have

m = (9-0)/(3-0) = 9/3 = 3.  This is greater than 2.2.

For the slope of the line that goes through (4, 10) and (0, 0), we have

m = (10-0)/(4-0)/ = 10/4 = 2.5.  This is greater than 2.2.

For the slope of the line that goes through (5, 8) and (0, 0), we have

m = (8-0)/(5-0) = 8/5 = 1.6.  This is not greater than 2.2.

For the slope of the line that goes through (6, 7) and (0, 0), we have

m = (7-0)/(6-0) = 7/6 = 1.16.  this is not greater than 2.2.

For the slope of the line that goes through (7, 6) and (0, 0), we have

m = (6-0)/(7-0) = 6/7 = 0.86.  This is not greater than 2.2.

[tex]Domain:\ x\geq0\ \wedge\ y\in\mathbb{R}[/tex]

[tex]\sqrt{8x^7y^8}=\sqrt8\cdot\sqrt{x^7}\cdot\sqrt{y^8}=\sqrt{4\cdot2}\cdot\sqrt{x^6\cdot x}\cdot\sqrt{y^{4\cdot2}}\\\\=\sqrt4\cdot\sqrt2\cdot\sqrt{x^6}\cdot\sqrt{x}\cdot\sqrt{(y^4)^2}=2\sqrt2\cdot\sqrt{x^{3\cdot2}}\cdot\sqrt{x}\cdot y^4\\\\=2y^4\sqrt2\cdot\sqrt{(x^3)^2}\cdot\sqrt{x}=2y^4\sqrt{2x}\cdot x^3\\\\=\boxed{2x^3y^4\sqrt{2x}}[/tex]

[tex]Used:\\\\\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\\sqrt{a^2}=a\ for\ a\geq0[/tex]

Answer:

c is correct

Step-by-step explanation:

edge 2020

Answer:

because 3x6=18 so it will be the same problem

Step-by-step explanation:

Let's go:

6x + 7 + 12x - 3 = 112

18x + 4 = 112

18x = 112 - 4

18x = 108

x = 6

mADB = 6.6 + 7 = 43°

I hope I helped you.

Answer:

43°

Step-by-step explanation:

Since we know that ∠ADC, which is the sum of ∠ADB and ∠BDC, is 112, we can solve for x:

112 = 6x + 7 + 12x - 3

112 = 18x +4

112 - 4 = 18x → 108 = 18x

108/18 = x → 6 = x.

Now, we can substitute 6 for x in the equation for ∠ADB to get the answer:

6(6) + 7 ⇒ 36 + 7 ⇒ 43°.

Hope this helps! Have a nice day!

Answer:

-5

Step-by-step explanation:

The integers are ..., -4, -3, -2, -1, 0, 1, 2, 3, 4, ... -- all the whole numbers and their opposites (the positive whole numbers, the negative whole numbers, and zero). Fractions and decimals are not integers. All whole numbers are integers (and all natural numbers are integers), but not all integers are whole numbers or natural numbers. For example, -5 is an integer but not a whole number or a natural number.

An example of an integer that is not a whole number is -1, as whole numbers are non-negative and -1 is negative.

The set of integers includes all the positive whole numbers, zero, and their opposites, which are the negative whole numbers. Whole numbers are defined as non-negative integers (0, 1, 2, 3, ...). Therefore, any negative integer like -1, -2, -3, and so forth, while being an integer, is not considered a whole number.

[tex]8x^2+7x-1=0\ \wedge\ 24x^2+53x-7=0\\\\\text{The equation:}\\\\24x^2+53x-7=8x^2+7x-1\qquad\text{subtract}\ 8x^2\ \text{and}\ 7x\ \text{from both sides}\\\\16x^2+46x-7=-1\qquad\text{add 1 to both sides}\\\\16x^2+46x-6=0\qquad\text{divide both sides by 2}\\\\8x^2+23x-3=0\\\\8x^2+24x-x-3=0\\\\8x(x+3)-1(x+3)=0\\\\(x+3)(8x-1)=0\iff x+3=0\ \vee\ 8x-1=0\\\\x+3=0\qquad\text{subtract 3 from both sides}\\\boxed{x=-3}\\\\8x-1=0\qquad\text{add 1 to both sides}\\8x=1\qquad\text{divide both sides by 8}\\\boxed{x=\dfrac{1}{8}}[/tex]

The values for x in the given equations, 8x^2 + 7x - 1 = 0 and 24x^2 + 53x - 7 = 0 are x = 1/4, x = -1/2, x = 1/8, and x = -7/6 respectively when the quadratic formula is applied.

To find the value of x for each equation, you will need to use the quadratic formula (x = [-b ± sqrt(b^2 - 4ac)] / (2a)). The quadratic formula is used in algebra to solve quadratic equations (polynomials of degree 2). The formula provides solutions for the variable x in terms of the coefficients of the equation, denoted as a, b, and c.

For the first equation, 8x^2 + 7x - 1 = 0, a = 8, b = 7, and c = -1. Plugging these values into the quadratic formula, the solutions come out to be x = 1/4 or x = -1/2.

Similarly, for the second equation, 24x^2 + 53x - 7 = 0, a = 24, b = 53, and c = -7. The solutions for x in this case come out to be x = 1/8 or x = -7/6.

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Answer:

Option C : ASA

Step-by-step explanation:

Side WS Lies between ∠W and ∠S

Side NT lies between ∠N and ∠T

Hence the theorem which supports the congruency  of the two triangles

is ASA

Angle - Side - Angle

Answer:

No, every relation is not a function.  

Step-by-step explanation:

Every function is a relation because there are two points (x,y) somehow related to each other.

But every relation is not a function

The given ordered pairs are the function

Since, we are getting different value of y for ecah x.

The condition for function is we should get different value of y for each x.

Answer:

104 = B

Step-by-step explanation:

A quick way to do this is to use this formula

Since this is an estimate, you are only guided to whether your answer is correct or not. Here's the actual formula

Answer:

The x intercept = -9

The y intercept = -12

Step-by-step explanation:

To find the x intercept, set y = 0 and solve for x

-4x - 3y = 36

-4x -0 = 36

Divide by -4

-4x/-4 = 36/-4

x = -9

The x intercept = -9

To find the y intercept, set x = 0 and solve for y

-4x - 3y = 36

0 -3y = 36

Divide by -3

-3y/-3 = 36/-3

x = -12

The y intercept = -12

Answer:

x = -9

y = -12

Step-by-step explanation: Substitute 0 for x & y to get your points.

-4x - 3y = 36

-4(0) - 3y = 36

0 - 3y = 36

-3y = 36

-3y    -3y

y = -12

-4x - 3y = 36

-4x - 3(0) = 36

-4x - 0 = 36

-4x = 36

-4       -4

x = -9

Hope this helps you!!! :)

Answer5,90,000

Step-by-step explanation:

780,000 subtract 190,000 = 590,000

after every 6 years

i'm not sure if its correct. please let me know

Answer:

[tex] y = 300(0.78)^x [/tex]

Step-by-step explanation:

x is the number of years. y is the population after x years.

Each year, the population decreases by 22%, since 100% - 22% = 78%, and 78% = 0.78, each year, the population is 0.78 of the previous year's population.

year zero: y = 300

year 1: y = 300 * 0.78 = 300 * (0.78)^1

year 2: y = (300 * 0.78) * 0.78 = 300 * (0.78)^2

year 3: y = ((300 * 0.78) * 0.78) * 0.78 = 300 * (0.78)^3

year x: y = 300(0.78)^x

Answer:-47

Step-by-step explanation:

1# 11+4=15

2# 15+4=19

3# 19+4=23

4# 23+4=27

5# 27+4=31

6# 31+4=35

7# 35+4=39

8# 39+4=43

9# 43+4=47

REMEBER its negative not positive.

Answer:

≈ 376.99 pulgadas

Step-by-step explanation:

El volumen de un cono con una altura de 10 pulgadas y un radio de 6 pulgadas es de aproximadamente 376.99 pulgadas en cubos.

La fórmula para el volumen de un cono es π (r ^ 2) (h / 3). Puedes sustituir r con 6 yh con 10 para obtener El volumen de un cono con una altura de 10 pulgadas y un radio de 6 pulgadas es de aproximadamente 376.99 pulgadas en cubos.

La fórmula para el volumen de un cono es π (r ^ 2) (h / 3). Puedes sustituir r con 6 yh con 10 para obtener  aproximadamente 376.99

The midpoint between the numbers 6 and -15 on a number line is -4.5. The distance between 6 and -15 on the number line is 21.

The midpoint on a number line between two points is found by adding the two points together and then dividing by 2. So, for points 6 and -15, the midpoint would be (6-15)/2 = -9/2 = -4.5. This means the midpoint between 6 and -15 on the number line is -4.5.

The distance between two points on a number line is found by subtracting the smaller number from the larger number and taking the absolute value. So, the distance between 6 and -15 is |6 - (-15)| = |-9| = 21. Therefore, the distance between 6 and -15 on the number line is 21.

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Answer:

8x + 10y = $830

Step-by-step explanation:

8x + 10y = total revenue

if the total revenue is 830 then you can equate the above formula to 830 to give

8x + 10y = $830

Answer:

The required equation is [tex]8x+10y = 830[/tex].

Step-by-step explanation:

Consider the provided information.

As it is given that variable x represents the number of cars that paid to park and variable y represents the number of trucks that paid to park.

The cost of parking a car is $8 per day, the expression to represent the cost of parking x cars per day is 8x.

The cost of parking a truck $10 per day, the expression to represent the cost of parking y trucks per day is 10y.

The total revenue for the day was $830.

Thus, the equation represent the number of cars and trucks that paid to park that day is:

[tex]8x+10y = 830[/tex]

Hence, the required equation is [tex]8x+10y = 830[/tex].

Answer:

There are only two choices, a black or white duck, so a coin is the best choice. To represent a set of possible outcomes, toss the coin three times. Repeat the experiment multiple times. To find the probability, divide the observed desired outcomes by the total number of trial

Step-by-step explanation:

Answer:

7/20

Step-by-step explanation:

I came across the question

Answer:

2

Step-by-step explanation:

3/2 + (-k) + (-2) =

= 3/2 + [-(-5/2)] - 2

= 3/2 + 5/2 - 2

= 8/2 - 2

= 4 - 2

= 2

Answer:

12 Meters Per Second

Step-by-step explanation:

Average Speed = Distance divided by time

Average Speed = 120 Meters / 10 Seconds

Average Speed = 12 Meters Per Second

if  sprinter can run 120 meters in 10 seconds then 12 meters per second is the average speed.

Speed is defined as the rate of change of position of an object in any direction

Given that A sprinter can run 120 meters in 10 seconds.

Average Speed = Distance divided by time

Speed = Distance/ Time

The distance is 120 meters and times is 10 seconds.

Speed=120/10

=12 meters per second

Hence, if  sprinter can run 120 meters in 10 seconds then 12 meters per second is the average speed.

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Answer:

50√3 or  86.6

Step-by-step explanation:

Divide the hexagon into six equilateral triangles as in Figure 1 below.

Then draw a line from the midpoint of one side to the midpoint of the opposite side.

The height (h) of each triangle will be 5.

To find the area of the whole triangle, we first need to find the length of the base (see Figure 2).

If the base length (b) is 2s, we have the relation

5/s = tan60°

5/s = √3      Multiply each side by s

5 = s√3        Divide each side by √3

s = 5/√3       Rationalize

s = (5√3)/3

b = 2s

b = (10√3)/3

The area (A) of the triangle is

A = ½bh

A = ½ × (10√3)/3 × 5

A = (25√3)/3

There are six equilateral triangles in the hexagon, so

Total area = 6A

Total area = 6 × (25√3)/3

Total area = 50√3

Total area ≈ 86.6  

Answer:

The sides are as follows: [tex]x=18,\,\,\,y=9\sqrt{3}[/tex]

Step-by-step explanation:

Starting with the side y, we can use the tan to solve for y:

[tex]\tan 30^\circ = \frac{9}{y}\implies y = \frac{9}{\tan 30^\circ}={9}\sqrt{3}[/tex]

The side x can be determined using sin:

[tex]\sin 30^\circ = \frac{9}{x}\implies x = \frac{9}{\sin 30^\circ}= 18[/tex]

So, the sides as as follows: [tex]x=18,\,\,\,y=9\sqrt{3}[/tex]

(you can also verify this result is correct using the Pythagorean theorem)

Answer:

x=18

y=[tex]\sqrt 18[/tex]

Step-by-step explanation:

[tex]\sec x=\dfrac{1}{\cos x}\to \sec60^o=\dfrac{1}{\cos60^o}\\\\\text{Use the table of values of a trigonometric functions}\\\\\cos30^o=\dfrac{\sqrt3}{2}\\\\\sin\dfrac{\pi}{4}=\dfrac{\sqrt2}{2}\\\\\cos60^o=\dfrac{1}{2}\to\sec60^o=\dfrac{1}{\frac{1}{2}}=2\\\\\text{Substitute:}\\\\\cos30^o\sin\dfrac{\pi}{4}+\dfrac{\sec60^o}{3}=\dfrac{\sqrt3}{2}\cdot\dfrac{\sqrt2}{2}+\dfrac{2}{3}=\dfrac{\sqrt6}{4}+\dfrac{2}{3}\\\\=\dfrac{3\sqrt6}{3\cdot4}+\dfrac{4\cdot2}{4\cdot3}=\dfrac{3\sqrt6}{12}+\dfrac{8}{12}\\\\=\boxed{\dfrac{8+3\sqrt6}{12}}[/tex]

Answer:

Step-by-step explanation:

Let x be the number of buses and y be the number of vans.

We know that there are 5 more buses than vans, therefore, we can set up:

[tex]x=y+5[/tex]

Since a bus transports 55 people and a van transports 12 people, therefore, we can set up:

[tex]55x+12y = 409\\[/tex]

Now lets solve the above two equations together by substitution

[tex]55(y+5)+12y = 409\\\\55y+275+12y=409\\\\67y+275=409\\\\67y=409-275\\\\67y=134\\\\y=2,x=2+5=7[/tex]

Total number of students and teachers who rode to the zoo in buses[tex]=55*7=385[/tex]

Total number of students and teachers who rode to the zoo in vans[tex]=12*2=24[/tex]

Hey there!

Simple interest is based on only the original deposit of money, which in this case is $500.

To find 5.6% of 500, we can multiply it by the decimal that represents that part of a whole: 0.056.

[tex]500 \times 0.056 = 28[/tex]

The question asks for how much money is in the account after 8 1/2 years. This means we multiply the interest for 1 year (28) by 8 1/2.

[tex]28 \times 8.5 = 238[/tex]

Lastly, we add the interest to the original deposit.

[tex]500 + 238 = 738[/tex]

The answer is $738.

Hope this helps!

Answer:

y = 225

Step-by-step explanation:

since y and x are directly proportional the equation relating them is

y = kx ← k is the constant of proportionality

to find k use the given condition y = 288 when x = 32

k = [tex]\frac{y}{x}[/tex] = [tex]\frac{288}{32}[/tex] = 9

y = 9x ← is the equation of proportionality

when x = 25, then

y = 9 × 25 = 225

7. (x-7)(x-7)

8. (3x-5y)(3x-5y)

9. (x-15)(x+3)

10.(7m+6n)(7m+6n)

11. (2x+1)(2x+1)

12. (7x+2)(7x+2)

13. (p-18)(p+4)

Notice how 7,8,10,11, and 12 are all perfect squares. A good way to tell if a trinomial can be factored into a perfect square is if the square root of the coefficient of your variable multiplied by the square root of the constant (number with no variable) multiplied by 2 equals the middle term's coefficient.

For example, take 4x^2+16x+16. Taking the square root of 4 gives us 2. Taking the square root of 16 gives us 4. So, 2*2*4=16, which is our middle term, thus proving that this trinomial is indeed a perfect square.

Answer:

A) 2 * Length + 2 * Width = 276

B) L = 5W  then multiplying equation B) by -2 we get

-2L +10W = 0 then we add this to A)

A) 2L + 2W = 276 and get

12W = 276

Width = 23

Length = 115

Step-by-step explanation: