tan x= 3÷5 nearest tenth​

Answer:

its A (4,4)

Step-by-step explanation:

The solution of the system y = x² - 6x + 12 and y = 2x - 4 is (4, 4).

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

Given, y = x² - 6x + 12 and y = 2x - 4.

∴ The solution set of this system is,

x² - 6x + 12 = 2x - 4.

x² - 8x + 16 = 0.

x² - 4x - 4x + 16 = 0.

x(x - 4) - 4(x - 4) = 0.

(x - 4)(x - 4) = 0.

x - 4 = 0 Or x - 4 = 0.

x = 4 Or x = 4.

learn more about quadratic function here :

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Number of ways can the runners finish first, second, and third is 1,17,600 .

Step-by-step explanation:

Permutation is the act of arranging the members of a set into a sequence or order, or, if the set is already ordered, rearranging (reordering) its elements—a process called permuting. For example, written as tuples, there are six permutations of the set {1,2,3}, namely: (1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,1,2), and (3,2,1). Formula of Permutation is : [tex]P(n,r) = \frac{n!}{(n-r)!}[/tex] where n is the number of things to choose from,  and we choose r of them,  no repetitions,  order matters. Here , n = 50 , r= 3

⇒ [tex]P(n,r) = \frac{n!}{(n-r)!}[/tex]

⇒ [tex]P(50,3) = \frac{50!}{(50-3)!} = \frac{50(49)(48)47!}{47!}[/tex]

⇒ [tex]P(50,3) = 50(49)(48)[/tex]

⇒ [tex]P(50,3) = 1,17,600[/tex]

∴ Number of ways can the runners finish first, second, and third is 1,17,600 .

Answer:

10/11

Step-by-step explanation:

You can find this answer by dividing the top and bottom numbers by 2.

Final answer:

Equivalent fractions of 20/22 can be found by simplifying it to 10/11 or by scaling it up, such as 40/44 or 60/66, by multiplying the numerator and denominator by the same whole number.

Explanation:

To find fractions equivalent to 20/22, you can simplify or scale the fraction up by multiplying both the numerator and the denominator by the same nonzero whole number. An equivalent fraction is one that represents the same value when both the top number (numerator) and the bottom number (denominator) are multiplied or divided by the same value.

Simplifying 20/22 means finding the greatest common divisor of 20 and 22, which is 2. So, dividing both by 2, we get 10/11. To scale up, you can multiply both the numerator and the denominator by any nonzero whole number, such as 2, to get 40/44, or 3 to get 60/66, and so on. Each of these fractions represents the same part of a whole as 20/22.

[tex]Tan^2x= \frac{C -A}{(B-C)}[/tex]

Step-by-step explanation:

Here we have  , Acos²theta + Bsin²theta = C or , [tex]Acos^2theta + Bsin^2theta = C[/tex]

Let theta = x , So  [tex]Acos^2x + Bsin^2x = C[/tex] . Let's solve it further

⇒  [tex]Acos^2x + Bsin^2x = C[/tex]

⇒  [tex]\frac{Acos^2x}{cos^2x} + \frac{Bsin^2x}{cos^2x} = \frac{C}{cos^2x}[/tex]

⇒  [tex]A + B(\frac{sin^2x}{cos^2x}) = C\frac{1}{cos^2x}[/tex]            { [tex]\frac{sin^2x}{cos^2x} = Tan^2x , \frac{1}{cos^2x} = sec^2x[/tex]  }

⇒  [tex]A + B(Tan^2x) = C(sec^2x)[/tex]     {  [tex]sec^2x=1+Tan^2x[/tex]  }

⇒  [tex]A + B(Tan^2x) = C( 1+Tan^2x )[/tex]

⇒  [tex]A + B(Tan^2x) = C+C(Tan^2x )[/tex]

⇒  [tex]B(Tan^2x)-C(Tan^2x ) = C -A[/tex]

⇒  [tex](B-C)(Tan^2x)= C -A[/tex]

⇒  [tex]Tan^2x= \frac{C -A}{(B-C)}[/tex]

Therefore ,  [tex]Tan^2x= \frac{C -A}{(B-C)}[/tex] .

Answer:

part a) 13 scoops

part b) 3 scoops

Step-by-step explanation:

1) so we know that the volume of the sink is 660pi in^3

we have to divide this with the volume of each cup to find out the number of scoops it takes to get all the water out.

since we are dividing, I don't like leaving answers in terms of pi so

660*pi= 2073.45115137

formula for volume of cylinder(diameter) [tex]pi(\frac{d}{2} )^2 h[/tex]

pi*(5/2)^2*h=157.079632679

so

2073.45115137/157.079632679= 13.2 - for cup 1

for cup 2:

pi*(10/2)^2*8= 628.318530718

so

2073.45115137/628.318530718= 3.3- for cup 2

Hope this helps!

Answer:

x = 9   y = 27

Step-by-step explanation:

Since the two polygons are similar, we know that they are proportionate to each other. If we divide the values of corresponding sides:

16 ÷ 12 = 1 ¹/₃

32 ÷ 24 = 1 ¹/₃

We now know that the figure on the left is 1 ¹/₃ times the figure on the right. With this information, we can figure out the measurements of the two sides and then find the values of x and y.

6 · 1 ¹/₃ = 8

21 · 1 ¹/₃ = 28

Now that we know the values of each side, we can plug our equations in to find the values of x and y.

x - 1 = 8

x = 9

y + 1 = 28

y = 27

~Hope this helps!~

Answer:

[tex]y=\frac{1}{2} x+2.5[/tex]

Step-by-step explanation:

I graphed the equation on the graph below.

If this answer is correct, please make me Brainliest!

Answer:

11x-36

for your answers

Answer:

x= -12

or

x=3

Step-by-step explanation:

in order to factorise the equation x² + 9x - 36

it will be expressed like this to make it a complete equation by subtracting 36 from both sides

x² + 9x - 36=0

the next step is to look for two numbers that when multiplied will give us -36 and when added together it will give us 9.

the numbers would be -3 and 12

so we have

x²-3x + 12x -36 =0

x(x-3) + 12(x-3) = 0

(x+12)(x-3)=0

we have,

x + 12 =0

x = -12

or

x-3 =0

x= 3

Therefore, the factors for x are  -12 or 3.

Final answer:

To calculate the number of calories from fat in a serving of refried beans, multiply the grams of fat by the calories per gram of fat. In this case, there are 9 calories from fat in a serving of refried beans.

Explanation:

In order to determine the number of calories from fat in a serving of refried beans, we need to know the total amount of fat per serving. The question states that there is 1 gram of fat in a serving. It also mentions that each serving is 110 calories. To calculate the number of calories from fat, we can use the formula:

Calories from fat = Fat (in grams) × Calories per gram of fat

Plugging in the values: Calories from fat = 1 gram × 9 Calories/gram of fat = 9 Calories

Therefore, there are 9 calories from fat in a serving of refried beans.

Final answer:

In a serving of refried beans that contains 1 gram of fat, there are 9 calories from fat.

Explanation:

The question asks how many calories are from fat in a serving of refried beans. To answer this, we need to know the amount of fat and the calories in the serving. The question provides that there is 1 gram of fat in the serving and that the serving is 110 calories. Therefore, 1 gram of fat in the serving would contribute 9 calories (since fat contains 9 calories per gram). So, the number of calories from fat in the serving of refried beans is 9 calories.

To calculate the number of calories from fat in a serving of refried beans, we need to use the fact that fat provides 9 calories per gram. With 1 gram of fat in a serving of refried beans, we do the following calculation:

Multiply the amount of fat in grams by the number of calories that fat provides per gram: 1g × 9 calories/g = 9 calories.

Therefore, 9 calories of the total 110 calories in a serving of refried beans come from fat.

Answer:

15/10,000

Step-by-step explanation:

0.005 = 5/1000

0.3 = 3/10

5/1000 * 3/10 = 15/10,000

Answer:  15/10,000

The absolute error is 2 feet and percent error is 18.18%

Step-by-step explanation:

Given,

Estimated length = 13 feet

Actual length = 11 feet

Absolute error = Estimated length - Actual length

Absolute error = 11 - 13 = -2 feet

Absolute error = 2 feet

Percent error = [tex]\frac{Absolute\ error}{Exact\ value}*100[/tex]

Percent error = [tex]\frac{2}{11}*100[/tex]

Percent error = [tex]\frac{200}{11}=18.18 \%[/tex]

The absolute error is 2 feet and percent error is 18.18%

The absolute error is 2 feet and the percent error is approximately 18.2%

The absolute error in Deon's estimate can be found by subtracting the actual value from the estimated value and taking the absolute value. So that's |13 - 11| which equals 2 feet.

The percent error can be found by dividing the absolute error by the actual value and then multiplying by 100 to convert it into a percentage. That's (2 / 11) * 100 which equals approximately 18.2%. If we round to the nearest tenth, we get 18.2%.

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Answer:

W = 77

L = 98

Step-by-step explanation:

Question a:

Area of a rectangular field = 7392

Length L = 96

Width w = ?

Area of a rectangle = L x W

7392 = 96 x W

Divide both sides by 96

7392/96 = 96/96 x w

77 = w

W = 77

Question b:

Perimeter of a rectangular painting = 372

Width = 88

Length = ?

Perimeter of a rectangle =

2(L + w)

372 = 2(L + 88)

Distribute 2 into (L + 88)

We have

372 = 2 x L + 2 x 88

372 = 2L + 176

Subtract 176 from both sides

372 - 176 = 2L + 176 - 176

196 = 2L

Divide both sides by 2

196/2 = 2L/2

98 = L

L = 98

Answer:

4

Step-by-step explanation:

Rate of change = Slope (if Sidelength = x, and perimeter= y)

(1,4) and (2,8) are point (if it was a line)

Use the slope formula...

(8-4)/(2-1)=

4/1=

4

Answer:5

Step-by-step explanation:

Answer:

102

Step-by-step explanation:

To find the range of a set of data, you have to put all of the values in order from smallest to largest. Then you subtract the smallest and largest value to find your answer.

199 - 97 = 102

Answer:

%75

Step-by-step explanation:

30/40 is equal to 0.75

0.75 is also %75

Answer:  %75

Answer:

12 - 4

Step-by-step explanation:

Solution:

Given that,

A type of bacteria has a very high exponential growth rate of 80% every hour

There are 10 bacteria

The increasing function is given as:

[tex]y = a(1+r)^t[/tex]

Where,

y is future value

a is initial value

r is growth rate

t is time period

From given,

a = 10

[tex]r = 80 \5 = \frac{80}{100} = 0.8[/tex]

Determine how many will be in 5 hours

Substitute t = 5

[tex]y = 10(1 + 0.8)^5\\\\y = 10(1.8)^5\\\\y = 10 \times 18.89568\\\\y \approx 188.96[/tex]

y = 189

Thus, there are 189 bacteria in 5 hours

Determine how many will be in 1 day ?

1 day = 24 hours

Substitute t = 24

[tex]y = 10(1 + 0.8)^{24}\\\\y = 10(1.8)^{24}\\\\y = 10 \times 1338258.84\\\\y = 13382588.45\\\\y \approx 13382588[/tex]

Thus, there are 13382588 bacteria in 1 day

Determine how many will be in 1 week

1 week = 168

Substitute t = 168

[tex]y = 10(1 + 0.8)^{168}\\\\y = 10(1.8)^{168}[/tex]

Thus there are [tex]10(1.8)^{168}[/tex] bacteria in 1 week

Answer:

4

Step-by-step explanation:

Sin(30) = LJ/8sqrt(3)

Sin 30 = ½

LJ = 4sqrt(2)

LM = JM = x

x² + x² = (4sqrt(2))²

2x² = 32

x² = 16

x = 4

Answer:

106 gal

Step-by-step explanation:

step 1

Find the area of the path

we know that

The area of the path is given by the formula

[tex]A=\pi r_2^{2} -\pi r_1^{2}[/tex]

[tex]A=\pi [r_2^{2} -r_1^{2}][/tex]

where

r_2 is the radius of the pool plus the width of the path

r_1 is the radius of the pool

we have

[tex]r_1=22/2=11\ yd[/tex] ---> the radius is half the diameter

[tex]r_2=11+6=17\ yd[/tex]

substitute

[tex]A=\pi [17^{2}-11^{2}][/tex]

[tex]A=168\pi\ yd^2[/tex]

assume

[tex]\pi =3.14[/tex]

[tex]A=168(3.14)=527.52\ yd^2[/tex]

step 2

Find the gallons of coating needed

Divide the area of the path by 5

so

[tex]527.52/5=105.5\ gal[/tex]

Round up

therefore

106 gal

To calculate how many gallons of coating are needed, we find the area of the path by subtracting the area of the pool from the total area covered. This equals to 527.52 yd². As each gallon of coating covers 5 yd², we need 105.504 gallons. However, since the paint is sold in whole gallons, we round it up to 106 gallons.

To determine how many gallons of coating are needed, we first need to calculate the area of the ring-shaped path around the pool.

The pool is a circle with a diameter of 22 yd, so its radius is 11 yd. The path is around this pool and has a width of 6 yd. Therefore, the outer radius of the path is 11yd (radius of pool) + 6yd (width of path)=17 yd. The area of a circle is given by the formula πr² where r is the radius and π is a constant, approximately equal to 3.14.

So, the area of the outer circle is 3.14 × (17 yd)² = 907.46 square yards, and the area of the inner circle (pool) is 3.14× (11 yd)² = 379.94 square yards. The area of the path is the difference of those two areas, 907.46 yd² - 379.94 yd² = 527.52 yd².

Since one gallon of the coating can cover 5 sq yd, the number of gallons required is the total area divided by the area that one gallon can cover, which is 527.52 yd² / 5 yd²/gallon = 105.504 gallons. Since paint comes in whole gallons, you'll need to round up to the next whole number, which is 106 gallons.

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Answer:

[tex]y=\frac{3}{4}-1[/tex]  and   [tex]y=-\frac{4}{3}+9[/tex]

Step-by-step explanation:

step 1

Find the equation of the blue line

take the points

(0,-1) and (8,5) from the graph

Find the slope

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute

[tex]m=\frac{5+1}{8-0}[/tex]

[tex]m=\frac{6}{8}[/tex]

simplify

[tex]m=\frac{3}{4}[/tex]

Find the equation of the line in slope intercept form

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

we have

[tex]m=\frac{3}{4}[/tex]

[tex]b=-1[/tex] ---> see the graph

substitute the given values

[tex]y=\frac{3}{4}-1[/tex]

step 2

Find the equation of the black line

take the points

(0,9) and (3,5) from the graph

Find the slope

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute

[tex]m=\frac{5-9}{3-0}[/tex]

[tex]m=-\frac{4}{3}[/tex]

Find the equation of the line in slope intercept form

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

we have

[tex]m=-\frac{4}{3}[/tex]

[tex]b=9[/tex] ---> see the graph

substitute the given values

[tex]y=-\frac{4}{3}+9[/tex]

therefore

The system of equations is

[tex]y=\frac{3}{4}-1[/tex]  and   [tex]y=-\frac{4}{3}+9[/tex]

The equations of the blue and black lines are y = 3/4x - 1 and y = -4/3x + 9, respectively, based on their respective slopes and given points.

To find the equations of the blue and black lines, we start by determining their slopes using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on each line.

For the blue line:

Points: (0, -1) and (8, 5)

m = (5 - (-1)) / (8 - 0) = 6/8 = 3/4

Now, using the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept, we substitute the slope m = 3/4 and the given point (0, -1):

y = 3/4x - 1

For the black line:

Points: (0, 9) and (3, 5)

m = (5 - 9) / (3 - 0) = -4/3

Substituting the slope m = -4/3 and the given point (0, 9) into the slope-intercept form, we get:

y = -4/3x + 9

Therefore, the system of equations representing the blue and black lines is:

y = 3/4x - 1

y = -4/3x + 9

The question probable may be:

Write  system of equations could be used to solve for the point of intersection of the lines on the graph?

Final answer:

Linda and Ralph will owe approximately $9,905.52 in prorated property taxes for the year, after calculating the daily property tax rate and multiplying it by the number of days they will own the home in the current tax year.

Explanation:

Linda and Ralph need to determine their prorated expenses for the property taxes that have already been paid by the seller. To calculate this, we first need to determine the daily property tax rate, and then calculate how much they owe from the closing date, April 27, until the end of the year, December 31.

Calculating the Daily Property Tax Rate

The seller paid $14,578.15 for the full year. There are 365 days in a year, so the daily property tax rate is:

Daily rate = Total annual taxes / Number of days in the year

Daily rate = $14,578.15 / 365

Daily rate ≈ $39.94

Calculating Prorated Property Tax from Closing Date

Linda and Ralph will own the property starting on April 27, and there are 248 days remaining in the year from April 27 to December 31 (inclusive). Therefore, the prorated amount they owe for property taxes is:

Prorated taxes = Daily rate * Number of days from closing to end of year

Prorated taxes = $39.94 * 248

Prorated taxes ≈ $9,905.52

Linda and Ralph will owe approximately $9,905.52 in prorated property taxes for the year.

The unit rate is 17 chairs per table.

Step-by-step explanation:

Given,

Total number of chairs at 6 tables = 102 chairs

Number of tables = 6

Unit rate in terms of tables = [tex]\frac{Total\ chairs}{Number\ of\ tables}[/tex]

Unit rate in terms of tables= [tex]\frac{102}{6}[/tex]

Unit rate in terms of tables = 17

The unit rate is 17 chairs per table.

"The correct unit rate is 17 chairs per table.

To find the unit rate, we need to divide the total number of chairs by the number of tables. The question states there are 102 chairs and 6 tables. The unit rate is the number of chairs per table, which can be calculated as follows:

Unit rate = Total number of chairs / Number of tables

Unit rate = 102 chairs / 6 tables

Now, we divide 102 by 6 to find the unit rate:

Unit rate = 102 / 6

Unit rate = 17

Therefore, the unit rate is 17 chairs per table. This means that at each table, there are 17 chairs."

Answer:

A. Archie and Harris take turns picking yellow- or purple-colored chips from a dish.

C. Lily draws a marble from a bag filled with red and blue marbles, places her selection in a separate bag, and draws from the original bag of marbles again.

Step-by-step explanation:

Two events will be dependent if the first event influences the probability of the second event. If the first event takes something and doesn't put it back, that means the second event can't pull the same roll and the total pool of items changed.

A. Beth and Corrie take turns picking a card at random and recording each outcome. They replace the selected card at the bottom of the pile after each turn.

This option put replace the card, so it is independent

B. Archie and Harris take turns picking yellow- or purple-colored chips from a dish.

No replacement, the event should be dependent.

C. Jared pulls out a sock from the laundry basket containing white and black socks, puts it back, and then draws another sock at random.

This option  put back the pulls, so it is independent

D. Lily draws a marble from a bag filled with red and blue marbles, places her selection in a separate bag, and draws from the original bag of marbles again.

No replacement for the marble taken, each draws probability should depend on the earlier draw result.

Answer:

Part 1) [tex]y=3\ units[/tex]

Part 2) The length of the hypotenuse is 6 units

Step-by-step explanation:

Part 1) we know that

In the right triangle of the figure

[tex]sin(60^o)=\frac{y}{2\sqrt{3}}[/tex] ----> by SOH (opposite side divided by the hypotenuse)

solve for y

[tex]y=sin(60^o)2\sqrt{3}[/tex]

Remember that

[tex]sin(60^o)=\frac{\sqrt{3}}{2}[/tex]

substitute

[tex]y=(\frac{\sqrt{3}}{2})2\sqrt{3}[/tex]

[tex]y=3\ units[/tex]

Part 2)

Let

h ----> the length of the hypotenuse

we know that

In the right triangle of the figure

[tex]sin(45^o)=\frac{3\sqrt{2}}{h}[/tex] ----> by SOH (opposite side divided by the hypotenuse)

[tex]h=\frac{3\sqrt{2}}{sin(45^o)}[/tex]

Remember that

[tex]sin(45^o)=\frac{\sqrt{2}}{2}[/tex]

substitute

[tex]h=3\sqrt{2}:\frac{\sqrt{2}}{2}[/tex]

[tex]h=6\ units[/tex]

Work Shown:

i = P*r*t

157.50 = 2250*r*7 ... plug in given values

157.50 = 2250*7*r

157.50 = 15750r

15750r = 157.50

r = 157.50/15750 ... divide both sides by 15750

r = 0.01

The interest rate is 1%

To go from 0.01 to 1%, you move the decimal point 2 spots to the right.

Alternatively, you would multiply by 100.

Answer:7%

Step-by-step explanation:

Final answer:

The probability that Ichiro has Art on Friday, given that he has already had Library on Monday and the subjects are assigned randomly, is 1/6 or approximately 16.67%.

Explanation:

The subject of this question is Probability. Ichiro has Library on Monday, and since he cannot have the same special subject more than once in a week, there are six subjects left to schedule from Tuesday to Friday. The special subjects are considered to be assigned randomly.

To determine the probability that Ichiro has Art on Friday, we need to consider there are four days left in the school week (Tuesday to Friday) after Monday. Since the subjects are assigned randomly, each of the remaining subjects has an equal chance of being assigned to any day. By the time we get to Friday, there will be only one subject left unassigned, which has a 1 out of 6 chance of being Art, as the remaining subjects are randomly assigned to the days preceding.

The probability that Ichiro has Art on Friday is therefore 1/6, or approximately 16.67%

Addition property of equality

Division property of equality

Solution:

Given inequality is:

3x - 2 > 4

[tex]\mathrm{Add\:}2\mathrm{\:to\:both\:sides}[/tex]

Here, Addition property of equality is used

When the same amount is added to both sides of an inequality, then the inequality is still true

3x - 2 + 2 > 4 + 2

3x > 6

[tex]\mathrm{Divide\:both\:sides\:by\:}3[/tex]

Here, Division property of equality is used

When we divide both sides of an equation by the same nonzero number, the sides remain equal.

[tex]\frac{3x}{3}>\frac{6}{3}\\\\x > 2[/tex]

Thus the property used in each step of solving the inequality is found

Answer:

B) X || Z

Step-by-step explanation:

Hope it helps you in your learning process.

Answer:

Step-by-step explanation:

An obtuse triangle must contain an obtuse angle and two acute angles. An equilateral triangle must be 60 degrees in every corner, and thus there are 2+ acute angles. An isosceles triangle can have two angles that are 30 degrees (thus two acute), and a 120 degree angle