r + 3 = 3 ( r - 5 )​

Answer:

Bottom Left, Top right, bottom right

Step-by-step explanation:

5. = 5/10 or 5/100

.75 = 75/100

Answer:

5/10×75/100

50/100×75/100

75/100×5/10

Step-by-step explanation:

Option- 3 is correct that is both a and b are true.

a. The statement is true that is cosx = \(1 - \frac{sinx}{cscx+cotx}\)

b. The statement is true that is sinx = \(1 - \frac{cosx}{secx+tanx}\)

Given that,

a. We have to prove the statement is true or false.

Statement: cosx = \(1 - \frac{sinx}{cscx+cotx}\)

Now, Take the right hand side

= \(1 - \frac{sinx}{cscx+cotx}\)

= \(1 - \frac{sinx}{\frac{1}{sinx} +\frac{cosx}{sinx} }\)

By using LCM

= \(1 - \frac{sinx}{\frac{1+cosx}{sinx} }\)

= \(1 - \frac{sinx\times sinx}{1+cosx} }\)

= \(1 - \frac{sin^2x}{1+cosx} }\)

= \(\frac{1+cosx - sin^2x}{1+cosx} }\)

We know from trigonometric identities 1 - sin²x = cos²x

= \(\frac{cos^2x+cosx }{1+cosx} }\)

= \(\frac{cosx(1+cosx )}{1+cosx} }\)

= cosx

LHS = RHS

Therefore, The statement is true

b. We have to prove the statement is true or false.

Statement: sinx = \(1 - \frac{cosx}{secx+tanx}\)

Now, Take the right hand side

= \(1 - \frac{cosx}{secx+tanx}\)

= \(1 - \frac{cosx}{\frac{1}{cosx} +\frac{sinx}{cosx} }\)

By using LCM

= \(1 - \frac{cosx}{\frac{1+sinx}{cosx} }\)

= \(1 - \frac{cosx\times cosx}{1+sinx} }\)

= \(1 - \frac{cos^2x}{1+sinx} }\)

= \(\frac{1+sinx - cos^2x}{1+sinx} }\)

We know from trigonometric identities 1 - cos²x = sin²x

= \(\frac{sin^2x+sinx }{1+sinx} }\)

= \(\frac{cosx(1+sinx )}{1+sinx} }\)

= sinx

LHS = RHS

Therefore, The statement is true

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\(\\ \rm\hookrightarrow \dfrac{7-1}{7-1}\times \dfrac{7-4}{7-10}=-1\)

\(\\ \rm\hookrightarrow \dfrac{6}{6}\times \dfrac{3}{-3}=-1\)

\(\\ \rm\hookrightarrow 1(-1)=-1\)

Hence they are vertices of right angled triangle

C is the right angle

Answer:

Determine the slopes (gradients) of each line.

If the slopes of two of the lines are negative reciprocals (if their product is -1), the lines are perpendicular (the vertex is 90°).

Using slope formula: \(m=\dfrac{y_2-y_1}{x_2-x_1}\)

Slope of AC:

A = (1, 1) = \((x_1,y_1)\)

C = (7, 7) = \((x_2,y_2)\)

\(m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{7-1}{7-1}=1\)

Slope of AB:

A = (1, 1) = \((x_1,y_1)\)

B = (10, 4) = \((x_2,y_2)\)

\(m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{4-1}{10-1}=\dfrac13\)

Slope of BC:

B = (10, 4) = \((x_1,y_1)\)

C = (7, 7) = \((x_2,y_2)\)

\(m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{7-4}{7-10}=-1\)

Therefore, as AC and BC are negative reciprocals of each other (1 x -1 = -1), m∠C = 90° which proves that the triangle is a right triangle.

Answer:

Not in the right time

Step-by-step explanation:

ana is the root of before and chronous=krounus, being the Greek word for time.

The most likely meaning of the word anachronous is not in the right time. Option C is correct.

Given that,
To determine the most likely meaning of the word anachronous.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
anachronous means at the time a nonrelevant exception event happens to keep the former experience aside. Which is related to not in the right time.

Thus, the most likely meaning of the word anachronous is not in the right time. Option C is correct.

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The conditions for normality have been met for the sampling distribution of the difference in sample means of two populations of coins (pennies and quarters) where a random sample of 25 pennies was selected, and the mean age of the sample was 32 years, and a random sample of 35 quarters was taken, and the mean age of the sample was 19 years.

For each of the samples, the sample size is sufficiently large (n1 = 25, and n2 = 35), and we have no information about the population distribution. We can use the Central Limit Theorem to conclude that the sampling distribution of the difference in sample means is approximately normal.

Population standard deviation is known or the sample size is sufficiently large: We do not know the population standard deviation of the two populations. Therefore, we must ensure that the sample size of each group is large enough to justify using the Central Limit Theorem.

Both the sample sizes (25 and 35) are greater than 30. Therefore, the sample size is sufficiently large, and we can use the Central Limit Theorem to assume that the sampling distribution of the difference in sample means is approximately normal.

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The unit rate for three dollars for 2 1/2 hours of work will be $1.2 using the concept of unitary method.

The unitary method is a technique that involves determining the value of a single unit and then calculating the value of the requisite number of units based on that value. The term unitary refers to a single or unique entity. As a result, the goal of this approach is to determine values in reference to a single unit. The unitary technique is a method for determining the value of any necessary quantity by first obtaining the value of the unit (one) quantity.

Here,

$3 for 2.5 hours of work,

1 hour will cost $x,

3/2.5=x/1

2.5x=3

x=$1.2

Using the unitary technique, the unit rate for three dollars for two and a half hours of labour will be $1.2.

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The expression that can be used to calculate the rate per second at which the machine launches the balls is a) Fraction 12 over 2.

To calculate the rate per second at which the machine launches the balls is:

First, we need to know the meaning of rate is: it is the amount of something per unit of time. In this case, we want to find the rate at which the machine launches the balls per second.

The fraction 12 over 2 represents the number of balls launched by the machine in 12 seconds. If we want to find the rate per second, we need to divide this number by the number of seconds.

12/ 2 = 6, so the machine launches 6 balls in 1 second.

Therefore, the rate per second at which the machine launches the balls is 6.

So, the expression that can be used to calculate the rate per second at which the machine launches the balls is Fraction 12 over 2, which simplifies to 6.

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Answer:

The ratio of girls to total students is 12:30, which can be simplified to 2:5.

Step-by-step explanation:

You can express the ratio in different ways by using the same numbers, for example, you could say that for every 2 girls, there are 5 total students, or that for every 5 total students, 2 of them are girls.

Answer:

mean

Step-by-step explanation:

Answer:

○D. 21,34 branches would be there on the next two level of that tree.

To check which point satisfies the inequality 2x + y > 10, we substitute each value of x and y in the equation.

A. 2(2) + 3 > 10

    7 > 10

  This is incorrect. So the point does not satisfy the expression.

B. 2(3) + 2 > 10

    8 > 10

    This is also incorrect.

C. 2(4) + 3 >10

     11 > 10

     This is correct since 11 is greater than 10. So point (4,3) satisfies the inequality.

D. 2(3) + 4 > 10

    10 > 10

 This is also incorrect.

What is inequality?

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At the end of 251 days, George will pay Carol approximately $14,428.82, rounded to the nearest cent, for the loan of $13,070 at an interest rate of 17%.

The amount George will pay Carol at the end of 251 days, we can use the formula for simple interest:

Interest = Principal × Rate × Time

Given that the principal (loan amount) is $13,070, the interest rate is 17%, and the time is 251 days, we can calculate the interest:

Interest = 13070 × 0.17 × (251/360)

Next, we add the interest to the principal to find the total amount George will pay:

Total Amount = Principal + Interest

Finally, rounding the total amount to the nearest cent, we can determine that George will pay approximately $14,428.82 to Carol at the end of 251 days.

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The solution to this equation is x = 1, as 2log3x = 1 implies that log3x = 1/2, and then log3(x2 - 2) = 1/2.

The equation log3x log3(x2 2) = 1 2log3x can be simplified to log3x2 - log32 = 1 2log3x. This equation can be further simplified by combining like terms on both sides, resulting in log3x2 - 2log3x = log32. We can now take the logarithm of both sides, resulting in x2 - 2x = 2. This equation can be rearranged to x2 - 2x - 2 = 0, and then solved using the quadratic formula. The solutions of this equation are x = 1 and x = 2. However, since log3x must be positive, the only valid solution to the equation is x = 1. This implies that 2log3x = 1, and then log3(x2 - 2) = 1/2. Therefore, the solution to the equation log3x log3(x2 2) = 1 2log3x is x = 1.

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The number of volunteers needed for each case is given as follows:

a. 0.4 miles: 5.

b. 2/7 miles: 7.

c. 0.125 miles: 16.

d. 6/45 miles: 15.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using the unit rates of the context of the problem along with basic arithmetic operations, especially multiplication and division.

In this problem, a two mile section will be cleaned, hence the number of volunteers needed is calculated as follows:

n = 2/s.

In which s is the section cleaned by each volunteer.

In item a, the section is of 0.4 miles, hence the number of volunteers is given as follows:

n = 2/0.4 = 5 volunteers.

In item b, the section is of 2/7 miles, hence the number of volunteers is given as follows:

n = 2/(2/7) = 2 x 7/2 = 7 volunteers.

In item c, the section is of 0.125 miles, hence the number of volunteers is given as follows:

n = 2/0.125 = 2/(1/8) = 2 x 8 = 16 volunteers.

In item d, the section is of 6/45 miles, hence the number of volunteers is given as follows:

n = 2/(6/45) = 2 x 45/6 = 90/6 = 15 volunteers.

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Answer:

sin^2α

Step-by-step explanation:

I will just  pose  x instead  of alpha  here to make things simpler

\(\tan ^2\left(x\right)\left(2\cos ^2\left(x\right)+\sin ^2\left(x\right)-1\right)\\\\\)

we know that sin^2x = 1 -  cos^2x so...

\(=\left(-1+1-\cos ^2\left(x\right)+2\cos ^2\left(x\right)\right)\tan ^2\left(x\right)\)

\(=\cos ^2\left(x\right)\tan ^2\left(x\right)\)

we can rewrite using trigonometric identities (tan = sin/cos)...

\(=\left(\frac{\sin \left(x\right)}{\cos \left(x\right)}\right)^2\cos ^2\left(x\right)\\= \sin ^2\left(x\right)\)

Answer:

A

\(2y {}^{4} \div x {}^{4} \)

Step-by-step explanation:

Divide 14 by 7 it will be 2.

Now divide the variables.

X variable will give you X{}^{-4} and y{}^{4}.

So bring X variable in the denominator to make it positive.

So your answer will be option A.

Answer:

A

Step-by-step explanation:

It was right for me

Answer:

x=5

y=5

Step-by-step explanation:

6(5)=30-3(5)=15

2(5)=10+2(5)=20

so the points where they meet is 5,5

Answer:

a = 16 - b - c

Step-by-step explanation:

8 = (a + b + c) ÷ 2

×2 on both sides to cancel out ÷

16 = a + b + c

- b - c to cancel out +

a = 16 + b + c

Answer:

200

Step-by-step explanation:

6.6/3.3 = 2

10^-2 / 10^-4 = 10^2

10^2 = 100

2 x 100 = 200

The correct answer is:

x + 12 ≤ 5 − y ≤ 2(x − 3)

Explanation:

From the given inequalities:

x + 12 ≤ 5 − y ... (1)

5 − y ≤ 2(x − 3) ... (2)

We can see that 5 - y is common in both inequalities. We can isolate this term by subtracting 5 from both sides of (1) and (2):

x + 7 ≤ -y ... (3)

-y ≤ 2(x - 8) ... (4)

Multiplying (3) by -1, we get:

y - 7 ≥ x ... (5)

Substituting this value of x in (4), we get:

y - 7 ≤ -2(7 - y)

y - 7 ≤ -14 + 2y

y ≤ 7

Substituting this value of y in (5), we get:

0 ≤ x + 7 ≤ 14

Subtracting 7 from all sides, we get:

-7 ≤ x ≤ 7

Therefore, the statement x + 12 ≤ 5 − y ≤ 2(x − 3) is not true, but the statement -7 ≤ x ≤ 7 is true.

Answer:

A rhombus and a square since a square is also a rhombus.

The diameter of the ball is approximately 16.67 meters.

To find the diameter of the ball, we can use the relationship between the distance traveled and the number of revolutions.

The circumference of a circle is given by the formula C = πd, where C is the circumference and d is the diameter.

Given that the ball rolls a distance of 3.5 meters and makes 15.0 revolutions, we can calculate the circumference of the path it travels:

C = 3.5 m * 15.0 = 52.5 m

Since each revolution covers the circumference of the ball, we have C = πd. Plugging in the known value for C, we can solve for the diameter (d):

52.5 m = πd

Dividing both sides of the equation by π, we get:

d = 52.5 m / π

Using a calculator, we can evaluate this expression:

d ≈ 16.67 meters

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Answer:

No they don’t have enough money

Step-by-step explanation:

No:

54+20=74=that’s not enough

211+189=400

Thats enough but they’re are two of them so it would only be enough for one of them

I HOPE THIS IS WHAT YOU’RE LOOKING FOR AND IF NOT THEN I’M SO SO SORRY

Answer:

The measure of ∠A = 107.5°

Step-by-step explanation:

Given that

ABCD is a kite such that

AB = BC and AD = DC

Join A and C

Since AB = BC

→ ∠BAC = ∠BCA

Since , the angles opposite to equal sides are equal.

Let ∠BAC = ∠BCA = x°

and

Since AD = DC

→ ∠CAD = ∠ACD

Since , the angles opposite to equal sides are equal.

Let ∠CAD = ∠ACD = y°

Now

In ∆ ADC ,

∠ADC + ∠CAD + ∠ACD = 180°

Since , the sum of the all angles in a triangle is 180°

⇛ 30° + y°+ y° = 180°

⇛ 30°+2y° = 180°

⇛ 2y° = 180°-30°

⇛ 2y° = 150°

⇛ y° = 150°/2

⇛ y° = 75°

Therefore, ∠CAD = ∠ACD = 75°

and

In ∆ ABC,

∠ ABC + ∠BAC + ∠BCA = 180°

Since , the sum of the all angles in a triangle is 180°

⇛ 115° + x° + x° = 180°

⇛ 115°+2x° = 180°

⇛ 2x° = 180°-115°

⇛ 2x° = 65°

⇛ x° = 65°/2

⇛ x° = 32.5°

Therefore, ∠BAC = ∠BCA = 32.5°

Now, ∠ A = ∠BAC + ∠CAD

⇛ ∠A = 32.5° + 75°

⇛ ∠A = 107.5°

Therefore, ∠A = 107.5°

Answer:-

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ABCD is a kite with AD=AB A= 116° B=2x° D=(5x-147)° Find the size of the smallest angle of the kite.

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The probability that the first tile is less than 15 and the second tile is even or greater than 25 is 0.448.

The probability is found as follows:

Favorable outcomes:

The first tile is less than 15: There are 14 tiles numbered from 1 to 14 in the first box that satisfy this condition.

The second tile is even or greater than 25: In the second box, there are 10 even tiles and 6 tiles greater than 25.

Total outcomes:

Total number of outcomes = 25 * 20 or 500

Therefore, the probability will be:

Probability = (14 * 16) / 500

Probability = 224 / 500

Probability = 0.448

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Complete question:

Tiles numbered 1 through 25 are placed in a box. Tiles numbered 11 through 30 are placed in a second box. The first tile is randomly drawn from the first box. The second tile is randomly drawn from the second box. Find the probability that the first tile is less than 15 and the other tile is even or greater than 25.

In order to calculate the time it will take for Andrew to settle the loan, we can use the formula for compound interest. So, it will take Andrew approximately 5.22 years to settle the loan.

The formula is given as A = P(1 + r/n)^(nt), Where: A = the final amount, P = the principal (initial amount borrowed), R = the annual interest rate, N = the number of times the interest is compounded in a year, T = the time in years.

We know that Andrew borrowed R200 000 from a bank at an annual interest rate of 5.25% compounded quarterly and that he will make repayments of R6 000 at the end of every 3 months.

Since the first repayment will be made 3 months from now, we can consider that the initial loan repayment is made at time t = 0. This means that we need to calculate the value of t when the total amount repaid is equal to the initial amount borrowed.

Using the formula for compound interest: A = P(1 + r/n)^(nt), We can calculate the quarterly interest rate:r = (5.25/100)/4 = 0.013125We also know that the quarterly repayment amount is R6 000, so the amount borrowed minus the first repayment is the present value of the loan: P = R200 000 - R6 000 = R194 000

We can now substitute these values into the formula and solve for t: R194 000(1 + 0.013125/4)^(4t) = R200 000(1 + 0.013125/4)^(4t-1) + R6 000(1 + 0.013125/4)^(4t-2) + R6 000(1 + 0.013125/4)^(4t-3) + R6 000(1 + 0.013125/4)^(4t)

Rearranging the terms gives us: R194 000(1 + 0.013125/4)^(4t) - R6 000(1 + 0.013125/4)^(4t-1) - R6 000(1 + 0.013125/4)^(4t-2) - R6 000(1 + 0.013125/4)^(4t-3) - R200 000(1 + 0.013125/4)^(4t) = 0

Using trial and error, we can solve this equation to find that t = 5.22 years (rounded to 2 decimal places). Therefore, it will take Andrew approximately 5.22 years to settle the loan.

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none of these

Step-by-step explanation:

ans : 514 496+18 = 514

well, we know is an EQUIlateral triangle, so all 3 sides are equal,  so hmmm we can just get the distance between those two vertices and triple it for its perimeter.

\(~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-8}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{7})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[3 - (-8)]^2 + [7 - (-5)]^2}\implies d=\sqrt{(3+8)^2 + (7+5)^2} \\\\\\ d=\sqrt{265}\implies \stackrel{triple~that}{3\sqrt{265}} ~~ \approx ~~ 48.84\)