A certain triangle has a 30° angle in a 60° angle. Which must be a true statement about the triangle

Answer:

x= 8, x= -8

Step-by-step explanation: 8 and -8

The hourly growth rate is 2%

An exponential growth is in the form:

y = abˣ;

where y, x are variables, a is the initial value of y and b > 1

Let y represent the number of bacteria after x hours.

There was initially 2200 bacteria, hence a = 2200. The equation becomes:

[tex]y=2200(b)^x\\\\\\After\ 1.5\ hours,y=2300:\\\\\\2300=2200(b)^{1.5}\\\\\\b^{1.5}=1.045\\\\1.5lnb=ln(1.045)\\\\ln(b)=0.0296\\\\b=1.02[/tex]

Therefore the hourly growth rate is 1.02 - 1 = 0.02 = 2%

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Answer: Sammi's work:

107d=1,773.4

1773.4 divided by 107 = 16.2

Step-by-step explanation:

The value of d for the given expression will be d = 16.2.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.

Given that the expression is  107d = 1,733.4. The value of d will be calculated as:-

107d=1,773.4

To calculate the value of d the number 1773.4 is divided by 107.

107d=1,773.4

d = 1,773.4 / 107

d = 16.2

Hence, the value of d will be 16.2.

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Answer:

=-80-5√5

this is the answer

hope this helps

Answer:

4.38

Step-by-step explanation:

Answer:

Its 4.38

Step-by-step explanation:

Its because 4.377¨s hundredth place is the 7 near the 7 so rounding a digit with a number of 5 or greater would lead to changing the hunderedth place into a bigger number.

Step-by-step explanation:

By 30°-60°-90° triangle theorem:

[tex]15 = \frac{1}{2} \times c.. (side\:opposite \: to \:30°)\\ c = 15 \times 2 \\ \\ \huge \red{ \boxed{c = 30 \: m}} \\ \\ b = \frac{ \sqrt{3} }{2} \times c.. (side\:opposite \: to \:60°) \\ \\ b = \frac{ \sqrt{3} }{2} \times 30 \\ \\ \huge \purple{ \boxed{b = 15 \sqrt{3} \: m}}[/tex]

Answer:

x = 3y

Step-by-step explanation:

In this question, we are asked to model an equation that clearly mimics what we have in the question using certain type of variables.

Now initially, we are told that we have 2 bunnies having 6 babies. what does this tell us?

Looking at this, we can see that the number of babies is exactly 3 times the number of bunnies. More like saying 3 times the number of bunnies equal the number of babies.

so leveraging in this finding and applying the variable, we can say each of the 2 bunnies has 3 babies per month.

Mathematically, this is same as x bunnies = 3y babies per month

Answer:

1 4/5 = peanuts

1 1/5 = raisins

3/5 = chocolate chips

Step-by-step explanation:

3 ÷ 1 1/4 = 2 2/5

2 2/5 × 3/4 = 1 4/5

2 2/5 × 1/2 = 1 1/5

2 2/5 × 1/4 = 3/5

To keep proportions with 3 cups of granola, Darcia would need 1 ½ cups of peanuts, 1 ¼ cups of raisins, and 3/5 cup of chocolate chips in her snack mix.

Darcia has increased her granola measurement to 3 cups, which is 2.4 times more than the original 1 ¼ cups used in the snack mix recipe (since 3 ÷ 1.25 equals 2.4). To keep the other ingredients proportional to the new quantity, we need to multiply their original amounts by the same factor of 2.4

Therefore, if she used 3 cups of granola, she would use 1 ½ cups of peanuts, 1 ¼ cups of raisins, and 3/5 cup of chocolate chips to maintain the proportions in her snack mix.

Answer:

Any dimensions can make a triangle, however

this does not make a right angled triangle.

Step-by-step explanation:

Determine the length of the hypotenuse of a right angle triangle with side lengths 5ft and 9ft by using the formula:

[tex]a^2+b^2=c^2\\[/tex]

[tex]\sqrt{a^2+b^2} = c[/tex]

[tex]c=10.29[/tex]

This is not equal to 14ft.

Answer: No, those measurements cannot make a triangle

Why not? Because of the fact that the first two sides (5 and 9) add to 5+9 = 14, which is exactly as long as the third side. I recommend you using a ruler to measure out 5 inches, 9 inches and 14 inches. Mark all three as separate segments on a piece of paper. Then cut out those segments to form strips of paper with the given lengths. Then try to form a triangle. You'll find that it is impossible since the smaller segments combine perfectly to get the longest segment. Instead of a triangle, you'll only have a line segment forming.

As a rule, when you add any two sides of a triangle, they must add to something larger than the third side. The rule more formally is

For any triangle with sides a,b,c, the following three inequalities must hold true

Answer:

option b and c are true ...

Answer:

The answer to your question is the letter A.    (4, -8)   and  (1, -5)

Step-by-step explanation:

Data

                x + y = -4              Equation l

                y = x² - 6x             Equation ll

Process

1.- Substitute equation ll in equation l

              x + x² - 6x = -4

2.- Solve the quadratic equation

                  x² - 5x + 4 = 0

Factor        (x - 4)(x - 1) = 0

-Solve for x

                   x₁ - 4 = 0         x₂ - 1 = 0

                   x₁ = 4               x ₂ = 1

3.- Substitute x₁ and x₂ in equation l

         4 + y₁ = -4                     1 + y₂ = -4

              y₁ = -4 - 4                      y₂ = -4 - 1

              y₁ = -8                           y₂ = -5

4.- Solutions

             (4, -8)   and  (1, -5)

Answer:

(10, -20) because y=_5x + 30x=10 and there are only 2 answers with 10 in the beginning so also 20 is greater than 40.

Step-by-step explanation:

B

Answer:

Step-by-step explanation:

Answer:

0.0487 = 4.87%

Step-by-step explanation:

The probability of one mail being returned is 1.5% = 0.015, so the probability of the mail not being returned is 1 - 0.015 = 0.985. If we want 0 mails returned from a total of 200 mails, we have 0 mails returned (probabilitity of 0.015) and 200 mails not returned (probability of 0.985), then the final probability is calculated as follows:

Probability = (0.985)^200 * (0.015)^0 = 0.0487 = 4.87%

To find the probability that none of the 200 mailings will be returned because of incorrect or incomplete addresses, we can calculate the probability of an individual mailing not being returned and multiply it by itself 200 times.

To find the probability that none of the 200 mailings will be returned, we need to calculate the probability that each individual mailing is not returned. Given that 1.5% of mailings are returned, the probability of an individual mailing not being returned is 1 - 0.015 = 0.985. We can then find the probability that none of the mailings are returned by multiplying this probability by itself 200 times.

P(no mailings returned) = (0.985)200

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Answer: The actual distance is 142 miles.  

Step-by-step explanation:

First, you multiply the 3.375 inches by 42 miles since you are trying to scale. It equals 141.75. If you round it to the nearest mile, it equals 142 miles.

Answer:

4 boxes

48/12 = 4

Step-by-step explanation:

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Answer:

4 boxes

Step-by-step explanation:

This problem is fairly simple all you need to do is divide 48 by 12 and you should get 4. If that is too hard than you can see what 12 multiplyes by to get 48.

Hope that Helped :)

[tex]y=4-x^2\\x-y=2 \\ \\ y = 4 - {x}^{2} \\ x = 2 + y \\ \\ y = 4 - {(2 + y)}^{2} \\ {y}^{2} + 5y = 0 \\ y(y + 5) = 0 \\ y = 0 \\ y = - 5[/tex]

[tex]x = 2 + 0 = 2[/tex]

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

Final answer:

To calculate Payne's annual contribution, multiply the annual premium by 20% and subtract that amount from the annual premium.

Explanation:

To calculate Payne's annual contribution, we need to determine 20% of the total cost of the health insurance premium and then subtract that amount from the annual premium.

Step 1: Find 20% of $6,486. Multiply $6,486 by 0.2 to get $1,297.20.

Step 2: Subtract the 20% contribution from the annual premium. $6,486 - $1,297.20 = $5,188.80.

Payne's annual contribution is $5,188.80.

Answer:

45%

Step-by-step explanation:

Diego's time is 20 and a whole is 100% so multiply 9 by 5 because 20 x 5 is 100 9x5=45. This means Noah's time is 45% of Diego's time

Answer:

45% or 45 percent

Step-by-step explanation:

Yes oof

Answer:

253.5

Step-by-step explanation:

basically i had the same question so yeah! and im a pro at math

Answer:

Yup, It's 253.5 :)

Step-by-step explanation:

I checked it. It was right ^^

Answer:

18 feet

Step-by-step explanation:

After each bounce, the ball reaches only a percentage of the maximum height it reached before.

The first height is 36 feet, after the first bounce, it will be 36*r, where r is the ratio of the height the ball can still reach by the previous maximum height.

In the second bounce, the height is 36*r^2

In the third bounce, the height is 36*r^3

In the fourth bounce, the height is 36*r^4, and this value is 2.25 ft, so:

36*r^4 = 2.25

r^4 = 2.25/36

r^4 =  0.0625

r = 0.5

So, after the first bounce, the height is:

36*r = 36*0.5 = 18 feet

The height should be 18 feet.

Given that,

Based on the above information, the calculation is as follows:

The first height is 36 feet.

Now after the first bounce, it will be 36r

Here r is the ratio of the height

In the second bounce, the height is [tex]36\times r^2[/tex]

In the third bounce, the height is [tex]36\times r^3[/tex]

In the fourth bounce, the height is [tex]36\times r^4[/tex], and this value is 2.25 ft, so:

Now

[tex]36\times r^4 = 2.25\\\\r^4 = 2.25\div 36\\\\r^4 = 0.0625[/tex]

r = 0.5

Now  

So, after the first bounce, the height is:

= 36r

= 36(0.5)

= 18 feet

Therefore we can conclude that The height should be 18 feet.

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Answer:

(6, - 5)

Step-by-step explanation:

The equation of circle in centre radius form is:

[tex](x - h)^{2} + (y - k)^{2} = {r}^{2} \\ plugging \: h = 3 \: \: k = - 9 \: and \: r = 5 \\ (x - 3)^{2} + \{y - ( - 9) \}^{2} = {5}^{2} \\ (x - 3)^{2} + (y + 9)^{2} = 25 \\ let \: us \: plug \: x = 6 \: and \: y = - 5 \: in \: lhs \\ lhs = (6 - 3) ^{2} + ( - 5 + 9) ^{2} \\ = (3) ^{2} + ( 4) ^{2} \\ = 9 + 16 \\ = 25 \\ = rhs \\ hence \: (6, \: \: - 5) \: is \: on \: the \: circle.[/tex]

Answer:

Answer is option b) (6,-5)

Step-by-step explanation:

[tex]given \: that \: \\ centr e\: of \: circle \: is(3, - 9) \\ and \: radius \: is \: 5 \\ when \: \: we \: calculate \: the \: distance \: between \: (3, - 9) \: and \: (6, - 5) \\ distance \: = \sqrt{ {(x1 - x2)}^{2} + {(y1 - y2)}^{2} } \\ here \: x1 = 3 \: \: y1 = - 9 \\ x2 = 6 \: \: \: \: y2 = - 5 \\ on \: substituting \: the \: values \\ = \sqrt{(3 - 6) + {( - 9 + 5)}^{2} }^{2 } \\ = \sqrt{ { - 3}^{2} + { - 4}^{2} } \\ = \\ = \sqrt{9 + 16} \\ = \sqrt{25} \\ = 5[/tex]

(6 -5) is a point on the circle.

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Answer:

The value of ∠LPM is 60°

Step-by-step explanation:

It is given that a straight line is 180° and line LN is a straight line. So in order to find angle LM, you have to substract angle MN from 180° :

∠LPN = 180°

∠MPN = 120°

∠LPM + ∠MPN = 180°

∠LPM = 180° - ∠MPN

= 180° - 120°

= 60°

Answer:

60°

Step-by-step explanation:

LPN is a diameter (straight line passing through the centre)

X + 120 = 180

X = 60°

The formula to calculate the expected population of Luttrell in t years, with a 10% annual growth rate, is P = 130,457 × (1 + 0.10)^t.

To determine the total expected population, P, of Luttrell in t years, given an annual growth rate of 10%, you would use the formula for exponential growth: P = P0 × (1 + r)t, where P0 is the initial population, r is the growth rate (expressed as a decimal), and t is the number of years after the initial time. In this case, since the population in 2012 (which is our initial time) is 130,457, and the growth rate is 10% or 0.10, the equation becomes P = 130,457 × (1 + 0.10)t. This equation will calculate the expected population after t years.

Final answer:

The equation to determine the total expected population of Luttrell in t years is P = [tex]130,457 × (1 + 0.10)^t,[/tex] where P is the population and t represents the number of years after 2012.

Explanation:

To determine the total expected population, P, of Luttrell in t years, given that it is expected to grow by 10% each year, you can use an exponential growth formula. The formula incorporating this percentage growth rate and starting population in 2012 is:

P = 130,457 × (1 + 0.10)^t

Here, 130,457 is the initial population in the year 2012, 1 + 0.10 represents the growth factor (where 0.10 is the 10% growth converted to a decimal), and t is the number of years after 2012.

For example, to find the population after 1 year (t = 1), you would calculate:

P =[tex]130,457 × (1 + 0.10)^1 = 130,457 × 1.10 = 143,502.7,[/tex] which you would round to the nearest whole person.

Answer:

4

Step-by-step explanation:

13497/1250

12500 + 997/1250

12500 + 0.7976

12500.7976

Answer:

4 places of decimals.

Step-by-step explanation:

13497.1250 = 10.7976.

Answer:

if I'm correct it's 22 don't quote me on it

Answer:

Surface area = 942.688

Answer:

$50,000 per year

($1,000 per week)

Answer:

8.2 ft

.Step-by-step explanation:

Sketch this situation.  Label the 55° angle.  The adjacent side is the distance from the stake to the bottom center of the tree.  The opposite side is the distance from the ground to the connection point of the wire on the tree.  The wire length represents the hypotenuse of this triangle.  We want to find the length of the side opposite the 55° angle.  Thus, we write

sin 55° = (opposite side)/(hypotenuse), or

(hypotenuse)(sin 55°) = (10 ft)(0.819) = 8.2 ft

Using trigonometry and the sine function, we can calculate the height of the tree as 10 ft * sin(55), which equals approximately 8.19 ft.

This problem can be solved using trigonometry, specifically the sine function. In a right triangle, the sine of an angle is defined as the length of the opposite side divided by the length of the hypotenuse. In this case, the tree forms the opposite side of our triangle, the support wire forms the hypotenuse and the angle of elevation is 55 degrees.

To express this mathematically, we can write: sin(55) = height / 10 ft. Solving this equation for height gives us: height = 10 ft * sin(55). Using a calculator, we find that sin(55) is approximately 0.81915, so the height is around 8.19 ft. Therefore, the connection point of the wire to the tree is at approximately 8.19 ft high.

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Answer:

x^2+x-20

Step-by-step explanation:

x = 4

x - 4 = 0

x = -5

x + 5 = -5

(x + 5)(x - 4)

x^2+x-20

The quadratic function with zeros 4 and -5 is f(x) = x² + x - 20.

To write a quadratic function f(x) whose zeros are 4 and -5, we can use the fact that the zeros of a quadratic function correspond to the values of x that make the function equal to zero.

A quadratic function can be represented in the form:

f(x) = a(x - r1)(x - r2)

where r1 and r2 are the zeros of the function.

Given zeros are 4 and -5. Substituting these into the formula, we get:

f(x) = a(x - 4)(x + 5)

Expanding this, we obtain:

f(x) = a(x² + x - 20)

To simplify, we can choose a value for a, usually 1 for simplicity:

f(x) = x² + x - 20

This is the quadratic function with zeros at 4 and -5.

Answer:

$80 + $60h =C

Step-by-step explanation:

$80 is the amount charged to come out

$60 times h (h is the number of hours)

add them together for total cost

The equation C = 80 + 60h describes Chris's total cost.

Independent variable: Hours of work, represented by h.

Dependent variable: Total cost, represented by C.

Equation: C = 80 + 60h

Y-intercept: $80, as it is the initial charge when no hours are worked.

Slope: $60 per hour, indicating the rate at which the cost increases per hour of work.

Answer:

60

Step-by-step explanation:

You first have to do the parenthesis

(5-7)= 5-7= -2

Then just multiply -30 by -2

Since negative x negative = positive, the answer will be positive.

(-2)(-30)= -2 x -30= 60

60