Use horizontal strips to find the area of the region enclosed by y = 1.752 and x = a First find the y coordinates of the two points where y = 1.752 meets 2 = 3.5 - y². lower coordinate y = c = and up

Answer:

The roots you found should be \((3x-4)(x+1)=0\), which shows that \(x = \frac{4}{3} \\ x=-1\)

Step-by-step explanation:

You likely messed up when trying to one or both of the roots back into the equation.

The Fundamental Pythagorean Identity in trigonomety sin²(x)+cos²(x)=1

Using  the Pythagorean Identity: \(\frac{1-2cos^2x}{sinxcosx}=tanx-cotx\) ,

Hence prove.

Trigonometry formulas can be used to address many different kinds of issues. These issues could involve Pythagorean identities, product identities, trigonometric ratios (sin, cos, tan, sec, cosec, and cot), etc. Many formulas, such as those involving co-function identities (shifting angles), sum and difference identities, double angle identities, half-angle identities, etc., as well as the sign of ratios in various quadrants,

We know that the Pythagorean theorem,

sin²(x)+cos²(x)=1

We have

1-2cos²x = sin²(x)+cos²(x) -2cos²x

1-2cos²x = sin²(x)-cos²(x)

\(\frac{1-2cos^2x}{sinxcosx}=tanx-cotx\)

To prove this take the right-hand sides

\(\frac{sin^2x}{sinxcosx}-\frac{cos^2x}{sinxcosx}\\\\=\frac{sinx}{cosx}-\frac{cosx}{sinx}\\\\= tanx-cotx\)

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The number of miles covered every afternoon Mount Pine Bike Race using a system of equation 5(7 + m) = 70 is 15 miles.

System of equation:

The term 'System of equation' refers a comprises two or more equations and seeks common solutions to the equations.

Given,

Matt has been training for the Mount Pine Bike Race. The first week he trained, he rode 5 days and took the same two routes each day: 6 miles to work in the morning and a longer route home in the afternoon.

Here we need to find the system of equation when he had ridden a total of 70 miles.

Let us consider the number of miles per afternoon as m.

Here we know that,

Number of days he rode = 5

Number of miles per morning rode = 6 miles

Total miles covered per week = 70 miles

Therefore, the system of equation for the given situation is defined as

Number of days(miles per morning + miles per evening) = Total miles

Apply the values on the equation, then  we get,

=>5(8 + m) = 115

Expand the equation,

=> 40 + 5m = 115

=>5m = 115 - 40

=>5m = 75

m = 75 / 5

Therefore, the m = 15 miles

So, the Number of miles covered per afternoon is 15 miles.

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The factors of the quadratic expression x² - 4x - 21 is (x - 7)(x + 3), making the first option the right choice.

A quadratic expression is of the form ax² + bx + c, which can be factorized using the mid-term factorization method, where b is shown as the sum or difference of two such numbers, whose product is equal to the product of a and c.

In the question, we are asked to factorize the quadratic expression, x² - 4x - 21.

In the given expression, a = 1, b = -4, and c = -21.

Thus, ac = -21.

The numbers having a product 21 are:

1*21 = 21,

3*7 = 21.

Since, 3 - 7 = -4 (That is b), we break b into 3 and -7.

Thus, the expression can now be shown as:

x² - 4x - 21

= x² + (3 - 7)x - 21

= x² + 3x - 7x - 21

= x(x + 3) - 7(x + 3) {By taking common}

= (x - 7)(x + 3) {By taking common}.

Thus, the factors of the quadratic expression x² - 4x - 21 is (x - 7)(x + 3), making the first option the right choice.

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Jane has (2/3)d dollars left after buying one beanie boo.

Let's call the cost of one beanie boo "x".

Then, if Jane wants to buy 3 beanie boos, she would spend 3x.

However, she only bought one beanie boo, so she spent x. We know that she spent all of her money, which is "d", so we can set up the equation:

3x = d (the cost of 3 beanie boos is equal to the amount of money Jane has)

To find out how much money Jane has left after buying one beanie boo, we need to subtract the cost of one beanie boo (x) from the total amount of money she has (d). We can solve for x by dividing both sides of the equation by 3:

3x/3 = d/3

x = d/3

Now we can substitute this value of x into our original equation:

3x = d

3(d/3) = d

d = d

So we can see that the amount of money Jane has is "d", and since she only spent "x" to buy one beanie boo, she has "d - x" left:

d - x = d - (d/3)

d - x = (2/3)d

Therefore, Jane has (2/3)d dollars left after buying one beanie boo.

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Answer: 8575/2

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

It looks like the graph is passing through (5,20)

so on y, from 0 to 20 is 20

on x, from 0 to 5 is 5

so slope = rise/run = 20/5 = 4

Step 1

Vertices in shapes are the points where two or more line segments or edges meet (like a corner). The singular of vertices is vertex.]

A)

The edge is the side of a polygon or a line segment where two faces of a solid figure meet.

B)

A prism is a 3-dimensional shape with two identical shapes facing each other. These identical shapes are called “bases”. The bases can be a triangle, square, rectangle or any other polygon. Other faces of a prism are parallelograms or rectangles.

C)

Answer:21

Step-by-step explanation:

.07 x 300

Answer: 21

Step-by-step explanation: For these questions try to find shortcuts instead of solving the traditional way. We know that 300 is three times greater than 100. We know that 7% of 100 is seven. To find 7% of 300 we just multiply that seven by 3 and get 21.

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Answer:

25 x 0.01

Step-by-step explanation:

here you go . ..........................................

Answer:

a

Step-by-step explanation:

Bc i just did on edge

The pair of equations below is a result of constructing the altitude, h, in Triangle ABC is A; sin C = h/a and sin A = h/c.

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

We know:

\(\sin(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of Hypotenuse}}\)

So from the attached figure;

sin C = h/a

sin A = h/c

These expressions have an h term in common. We can combine them if we can find forms of the expressions in terms;

h = a (sin C)

h = c (sin A)

Thus, option A is correct pair.

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Answer:

x = 16

y = 105°

Step-by-step explanation:

Given:

∆ABC ~ ∆XYZ

a = 24

Required:

Value of x and y

Solution:

Since ∆ABC ~ ∆XYZ, therefore:

<A ≅ <X

<B ≅ <Y

<C ≅ <Z

Also, the ratio of their Corresponding sides will be the same. That is,

\( \frac{21}{14} = \frac{15}{10} = \frac{24}{x} \)

Find the value of x using,

\( \frac{15}{10} = \frac{24}{x} \)

Cross multiply

\( 15*x = 24*10 \)

\( 15x = 240 \)

Divide both sides by 15

\( x = \frac{240}{15} \)

\( x = 16 \)

y = 180° - 75°(linear pair/angles on a straight line theorem)

y = 105°

for ever 12 elephants there is 11 lions

so it would be 12:11

Answer:

42

Step-by-step explanation:

758 divided by 18 is 42.1 I just rounded down to 42

Answer:

42 pieces

Step-by-step explanation:

758/18 = 42.1 repeating

42 is the maximum amount of pieces

Answer:

1) x = 12

2) x = 2

Step-by-step explanation:

Because each figure is a parallelogram, we know that the opposite sides are congruent. Now, we set 12 equal to 2x - 12 to solve. For number one, x = 12. For number two, we set 5x + 1 equal to -1 + 6x to solve. This equals 2.

Answer:

  11

Step-by-step explanation:

If each letter represents a digit, and digits are possibly repeated, you want to know the number of possible values of HELPS such that FLU+SHOT=HELPS.

The addition of two single decimal digits must necessarily result in a sum with a value from 0 to 18. That is, the carry from the sum can only be 0 or 1.

If two decimal numbers are added, the carry from one column to another cannot ever by 2, as the maximum sum of any column of digits is 19, when the carry from the previous column is considered.

These facts tell us that H=1, S=9, E=0, and the sum F+H ≥ 10.

Already we know that H=1, so F+H ≥ 10 means F=9.

For F+H = 10, the carry from L+O must be 0. The value of L will be 0, so P=O may be any of 10 values, 0–9. HELPS will be 10009–10099.

For F+H = 11, the carry from L+O must be 1. The value of L will be 1, and we require L+O = 10. That is, O=9. HELPS will be 10109.

HELPS can be any of 11 possible values: from 10009 to 10099, and 10109.

If the p-value of a hypothesis test is 0.016, it means that the probability of observing the data or more extreme data assuming the null hypothesis (i.e., the conveyor works properly) is 0.016. So, we reject the null hypothesis.

This p-value is relatively small and falls below the conventional significance level of 0.05. Therefore, we can reject the null hypothesis that the conveyor works properly and conclude that the conveyor is not sorting packages correctly.

However, we cannot determine the cause of the problem with the conveyor from this hypothesis test alone. Further investigation is necessary to identify the root cause of the issue and determine the appropriate corrective actions.

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Using the Fundamental Counting Theorem, it is found that there are 60 possible 3-course meals.

Given,

In the question:

A restaurant offers a choice of 4 salads, 5 main courses, and 3 desserts.

To find the how many possible 3-course meals are there?

Now, According to the question:

Let's know:

What is the Fundamental Counting Theorem?

It is a theorem that states that if there are n things, each with  ways to be done, each thing independent of the other, the number of ways they can be done is:

\(N=n_1\) × \(n_2\) × \(n_3\)... ×\(n_n\)

In this problem, considering the number of salads, main courses and desserts, we have that:

\(n_1=4 , n_2=5,n_3=3\)

The total number of options is given by:

N = 4 × 5 × 3

N = 60

Hence, Using the Fundamental Counting Theorem, it is found that there are 60 possible 3-course meals.

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A probability distribution model is a guide you use to fit a random variable in order to generalize its behavior.

A probability distribution is a list of all of the possible outcomes of a random variable, along with its corresponding probability values.

A probability distribution links each outcome of a random variable or process with its probability of occurrence.

A probability distribution model is a guide you use to fit a random variable in order to generalize its behavior.

These models have a mathematical background, and can be very picky. For them to work properly, the random variable you are trying to fit in must meet different assumptions so that the outcomes of the model have the correct probabilities, and also so that you can test and validate the model against real data from the random variable.

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Trent will need a total of 100 star stickers to line both the top and bottom edges of his 0.75-meter-long poster, with each sticker being 15 millimeters wide.

To find out how many star stickers Trent needs for his poster, you should first convert the length of the poster and the width of the stickers to the same unit, either meters or millimeters.

Step 1: Convert the length of the poster to millimeters (1 meter = 1000 millimeters)
0.75 meters * 1000 = 750 millimeters

Step 2: Divide the length of the poster by the width of a star sticker
750 millimeters / 15 millimeters = 50 stickers

Step 3: Since there are two edges (top and bottom) of the poster, multiply the number of stickers needed for one edge by 2
50 stickers * 2 = 100 stickers


Trent needs 100 star stickers for his poster. First, convert the length of the poster to millimeters, which is 750 millimeters. Then divide this length by the width of a star sticker, 15 millimeters, which results in 50 stickers. Since there are two edges, multiply by 2 to get 100 stickers in total.


Trent will need a total of 100 star stickers to line both the top and bottom edges of his 0.75-meter-long poster, with each sticker being 15 millimeters wide.

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The difference in the rate of change between Function A and function B is -2.

The difference in the rate of change between function A and function B, we first need to identify the rate of change for each function. The rate of change, also known as the slope, represents how much the dependent variable (y) changes for every unit increase in the independent variable (x).

Let's assume function A is represented by the equation y = 2x + 3, and function B is represented by the equation y = 4x - 1.

For function A: y = 2x + 3, the coefficient of x is 2, indicating that for every unit increase in x, y increases by 2. Therefore, the rate of change for function A is 2.

For function B: y = 4x - 1, the coefficient of x is 4, indicating that for every unit increase in x, y increases by 4. Therefore, the rate of change for function B is 4.

Now, to find the difference in the rate of change between function A and function B, we subtract the rate of change of function B from the rate of change of function A:

Difference in rate of change = Rate of change of function A - Rate of change of function B

                          = 2 - 4

                          = -2

The difference in the rate of change between function A and function B is -2. This means that for every unit increase in x, function B increases at a rate that is 2 units greater than function A. It indicates that function B has a steeper slope and a faster rate of change compared to function A.

In summary, the difference in the rate of change between function A and function B is -2.

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Inequality stating that there are 8000 sq. m. of land available: Let B be the number of units of house B and C be the number of units of house C.

Therefore,B+C ≤ 8000/200 [Reason: House C requires 200 sq. m. of land]⇒B+C ≤ 40b. Inequality that the engineer has at most 6400 man-hour available for construction:

160B + 256C ≤ 6400c

Inequality stating that the engineer has at least 12 million pesos to spend for materials:

600B + 800C ≤ 12000d

. Let us write down a table to calculate the cost, income and profit as follows:Units of house BLabor Hours per unit of house BUnits of house CLabor Hours per unit of house CTotal Labor HoursMaterial Cost per unit of house BMaterial Cost per unit of house CTotal Material CostIncome per unit of house BIncome per unit of house C

Total IncomeTotal ProfitBC=8000/200-B160CB+256C600000800000+256C12,000,0003,500,0004,000,0003,500,000B+C ≤ 40 160B + 256C ≤ 6400 600B + 800C ≤ 12000 Units of house B requires 160 man-hour and a unit of house C requires 256 man-hour.

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Answer:

Here's the modified code using a for loop to add up the even integers from 2 to 10:

sum = 0

for evenNum in range(2, 11, 2):

   sum += evenNum

print(sum)

In the original code, there were repetitive lines incrementing the sum variable by different even numbers. To make the code more efficient and concise, we can use a for loop with the range function. The range(2, 11, 2) generates a sequence of even numbers from 2 to 10 with a step of 2. Inside the loop, each even number is added to the sum variable using the += operator. Finally, we print the value of sum, which will be the sum of all the even numbers. This approach eliminates the repetitive lines and achieves the desired result with just two lines of code.

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Answer:

  (a)  (-1, -5)

Step-by-step explanation:

An ordered pair is a solution to an equation when using those x and y values makes the equation true. Here, the equation tells you the y-value is 4 less than the x-value. Of the choices offered, that is only true for ...

  (x, y) = (-1, -5)

Answer: x=y=z=88

Step-by-step explanation:

All sides of a rhombus are congruent.

Answer:

11/30

Step-by-step explanation:

The quadratic equation 2a^2 = -6 + 8a has two solutions: a = 3 and a = 1.

To solve the quadratic equation 2a^2 = -6 + 8a, we need to rearrange it into standard quadratic form, which is ax^2 + bx + c = 0, where a, b, and c are coefficients.

Step 1: Move all the terms to one side of the equation to set it equal to zero:

2a^2 - 8a + 6 = 0

Step 2: The equation is now in standard quadratic form, so we can apply the quadratic formula to find the solutions for 'a':

a = (-b ± √(b^2 - 4ac))/(2a)

Comparing with our equation, we have:

a = (-(-8) ± √((-8)^2 - 4(2)(6)))/(2(2))

Simplifying further:

a = (8 ± √(64 - 48))/(4)

a = (8 ± √16)/(4)

a = (8 ± 4)/(4)

Now, we can calculate the two possible solutions:

a1 = (8 + 4)/(4) = 12/4 = 3

a2 = (8 - 4)/(4) = 4/4 = 1

Therefore, the quadratic equation 2a^2 = -6 + 8a has two solutions: a = 3 and a = 1.

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Answer: Yes, 59 is a prime number

Step-by-step explanation: 59 is a prime number, it has only two factors, such as one and the number itself. Hence, the factors of 59 are 1 and 59.

Yes, 59 is a prime number.

What is a prime number?

Any natural number greater than 1 that is not the sum of two smaller natural numbers is referred to as a prime number. A composite number is a natural number greater than one that is not prime.

In other terms, prime numbers are positive integers greater than one that only has the number itself and 1 as factors. 2, 3, 5, 7, 11, 13, and other prime numbers are just a few examples. Never forget that 1 is neither a prime number nor a composite. Apart from 1, the other numbers can all be categorised as prime and composite numbers. Except for 2, which is the smallest prime number and the only even prime number, all prime numbers are odd.

The number in question, which is 59,  has only two factors: 1 and 59.

Therefore 59 is a prime number.

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Answer:

\(6x + 42\)

Step-by-step explanation:

Apply the distributive property:

\(6x + 6 \times 7\)

Multiply 6 by 7

\(6x + 42\)