22. Look at the given triangles.
4x + 2
7x+7
X+3
2x-5
x+7
5x-4
a. Write an expression in simplest form for the perimeter of each triangle.
b. Write another expression in simplest form that shows the difference between the perimeter
of the larger triangle and the perimeter of the smaller triangle.
c. Find the perimeter for each triangle when x = 3

Answer:

bru its was in my head now its gone

Step-by-step explanation:

Answer: 15,048

Step-by-step explanation:

Answer:

The slope is 2 and the y intercept is (0, -4)

Step-by-step explanation:

Put the line in slope intercept form, y = mx + b, where m is the slope and b is the y intercept.

4x - 2y = 8

Subtract 4x from both sides

4x - 2y = 8

-2y = -4x + 8

Divide each side by -2

y = 2x - 4

So, the equation in slope intercept form is y = 2x - 4.

The slope is 2 and the y intercept is (0, -4)

The quadratic function is A(x) = 2(405 + 36x – x²). Then the maximum potential area of this year's resized garden will be 1458.

The condition for the maximum will be

f(x)'' < 0

The condition for the minimum will be

f(x)'' > 0

Every summer, Richard plants a garden on a rectangular plot of land.

Last summer, Richard's garden measured 45 feet in length and 18 feet in width.

This summer, Richard decides to resize his garden by decreasing the length of the garden, and increasing the width of the garden by two times the length reduction.

The area of this year's garden, A(x), can be modeled by a quadratic function, where x is the number of feet that the length is reduced.

Length = (45 – x)

Width = (18 + 2x)

Then the maximum potential area of this year's resized garden will be

A(x) = (45 – x)(18 + 2x)

A(x) = 810 + 72x – 2x²

A(x) = 2(405 + 36x – x²)

For maximum potential, A'(x) = 0

    A'(x) = 0

36 - 2x = 0

       2x = 36

         x = 18

Then the maximum potential area will be

A(x) = 2(405 + 36 × 18 – 18²)

A(x) = 1458

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Answer:

thanks for the points have a nice day

Step-by-step explanation:

(Steve's distance from the tip of the monument I'm assuming?)

ans: about 893.92 ft (√798,025)

a²+b²=c²

a=700

b=555

There are 2 tablespoons in 1 fluid ounce. This conversion is often used in cooking and baking recipes, where ingredients are measured in ounces or tablespoons.

Fluid ounces and tablespoons are both units of volume used to measure liquids in cooking and baking recipes. One fluid ounce is equal to 29.5735 milliliters or approximately 2 tablespoons, which is equivalent to 6 teaspoons. Therefore, there are 2 tablespoons in 1 fluid ounce.

This conversion is important to know when following recipes that call for ingredients in fluid ounces or tablespoons. It allows for accurate measurement of ingredients, which is crucial for successful cooking and baking. Other common units of volume used in the kitchen include teaspoons, cups, and quarts, among others.

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It is most important to have a random sample in inferential statistics, particularly in making statistical inferences about a population based on the sample data.

Random sampling is a critical component of inferential statistics because it helps to ensure that the sample is representative of the population. When a sample is randomly selected, each member of the population has an equal chance of being included in the sample, which reduces the risk of bias in the results. Without a random sample, the results of statistical analyses may not be accurate or generalizable to the population, and the conclusions drawn from the data may be flawed or misleading.

Therefore, random sampling is crucial in making valid statistical inferences about a population.

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The vertical stress increment at your location, 13 feet below grade and 9 feet off center of the concentrated load, due to the structural load is approximately 3,282 lb/ft². This information helps in understanding the stress distribution and its impact on the soil and nearby structures.

To calculate the vertical stress increment at your location due to the structural load, we need to consider the weight of the soil, the weight of the water table, and the weight of the concentrated load.

The total vertical stress at your location can be calculated as follows:

p_total = p_soil + p_water + p_load

1. Vertical Stress from Soil:

The vertical stress from the soil is given by the equation:

p_soil = γ_soil * z

Where:

- γ_soil is the unit weight of the soil (128 lb/ft³)

- z is the depth below grade (13 ft)

Substituting the given values:

p_soil = 128 lb/ft³ * 13 ft = 1,664 lb/ft²

2. Vertical Stress from Water:

The vertical stress from the water table can be calculated as follows:

p_water = γ_water * z_water

Where:

- γ_water is the unit weight of water (62.4 lb/ft³)

- z_water is the depth to the water table (6 ft)

Substituting the given values:

p_water = 62.4 lb/ft³ * 6 ft = 374.4 lb/ft²

3. Vertical Stress from Concentrated Load:

The vertical stress from the concentrated load can be calculated as follows:

p_load = P / A

Where:

- P is the concentrated load (460 tons)

- A is the area over which the load is distributed (considering a circular area with a radius of 9 ft)

Converting the concentrated load to pounds:

P = 460 tons * 2,000 lb/ton = 920,000 lb

Calculating the area of the circular load:

A = π * r²

A = 3.14 * (9 ft)² = 254.34 ft²

Substituting the values:

p_load = 920,000 lb / 254.34 ft² ≈ 3,618.39 lb/ft²

Therefore, the vertical stress increment at your location due to the structural load is approximately:

p = p_total - p_soil - p_water

p = 3,618.39 lb/ft² - 1,664 lb/ft² - 374.4 lb/ft²

p ≈ 3,282 lb/ft²

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Step-by-step explanation:

let eqn be y = mx + b.

m = (-2 - 8)/(1 - 3) = 5

sub (3, 8):

8 = 5(3) + b

b = -7

therefore equation of the line is y = 5x - 7

Topic: coordinate geometry

If you like to venture further, feel free to check out my insta (learntionary). I'll be constantly posting math tips and notes! Thanks!

Answer:y = 5x - 7

Step-by-step explanation: /

Answer: on the 14th year

Step-by-step explanation:

Answer:

I don't know that one sorry

the third-degree polynomial function with real coefficients, having the zeros 6 + i, 6 - i, and 7, is:

f(x) = (x² - 12x + 37)(x - 7)

To form a third-degree polynomial function with real coefficients such that the complex number 6 + i and the real number 7 are zeros, we can use the fact that complex zeros come in conjugate pairs.

Given that 6 + i is a zero, its conjugate 6 - i will also be a zero. Thus, the zeros of the polynomial are 6 + i, 6 - i, and 7.

To find the polynomial function, we start by forming the factors corresponding to each zero:

(x - (6 + i))   --> This corresponds to the zero 6 + i

(x - (6 - i))   --> This corresponds to the zero 6 - i

(x - 7)        --> This corresponds to the zero 7

To simplify the factors, we multiply them out:

(x - (6 + i))(x - (6 - i))(x - 7)

= ((x - 6) - i)((x - 6) + i)(x - 7)

= ((x - 6)² - i²)(x - 7)

= ((x - 6)² + 1)(x - 7)

Expanding the squared term:

= (x² - 12x + 36 + 1)(x - 7)

= (x² - 12x + 37)(x - 7)

Therefore, the third-degree polynomial function with real coefficients, having the zeros 6 + i, 6 - i, and 7, is:

f(x) = (x² - 12x + 37)(x - 7)

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The missing measurement of this right triangle is x=2√14

False. The derivative of the function f(x) = 5sin(x) + cos(x) is not equal to -5cos(x) - sin(x). The correct derivative of f(x) can be obtained by applying the rules of differentiation.

To find the derivative, we differentiate each term separately. The derivative of 5sin(x) is obtained using the chain rule, which states that the derivative of sin(u) is cos(u) multiplied by the derivative of u. In this case, u = x, so the derivative of 5sin(x) is 5cos(x).

Similarly, the derivative of cos(x) is obtained as -sin(x) using the chain rule.

Therefore, the derivative of f(x) = 5sin(x) + cos(x) is:

f'(x) = 5cos(x) - sin(x).

This result shows that the derivative of f(x) is not equal to -5cos(x) - sin(x).

In summary, the statement that f'(x) = -5cos(x) - sin(x) is false. The correct derivative of f(x) = 5sin(x) + cos(x) is f'(x) = 5cos(x) - sin(x).

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Answer: 1<x<3

Step-by-step explanation:

There are 3  rules in one that are needed for this problem

1st:  you can never get a 0 at the bottom of a denominator so x \(\neq\) 1

\(\sqrt{x-1}=0\\ x-1=0\\x=1\) would make a value of 0 on the bottom of a denominator which is not allowed.

2nd:  you can never get a - under the square root so x cannot be less than 1

3rd.  you can never get a log that is equal to 0 or less than 0 so x

3-x=0

-x=-3

x=3

so x cannot =3 or be greater than 3

the values that x CAN be are  1<x<3

To prove that a cycle graph Cn has exactly n labeled spanning trees, we can use the principle of inclusion-exclusion. First, consider a tree T that is composed of the n edges of Cn. This tree has n edges and is therefore an n-edge tree. In order for it to be a labeled spanning tree, every vertex must be labeled with a distinct label. Since Cn has n vertices, there are n! ways to label the vertices, giving us n! labeled spanning trees.

Now, we can use inclusion-exclusion to determine the number of labeled spanning trees that are a subset of T. For each vertex vi in T, we can choose any label from the set of n labels. For each of these labels, we can choose any edge from the n edges in T. The total number of labeled spanning trees that are a subset of T is therefore: n2 × n!

Now, we can subtract the number of labeled spanning trees that are a subset of T from the total number of labeled spanning trees to get the number of labeled spanning trees that are not a subset of T. The number of labeled spanning trees that are not a subset of T is: n! - n2 × n! = n! - n2! Therefore, the total number of labeled spanning trees of Cn is n!.

This proves that a cycle graph Cn has exactly n labeled spanning trees.

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Answer:

Honestly i dont even know

Step-by-step explanation:

Answer:

x= 17

HJ= 27

JK= 153

HK= 180

Step-by-step explanation:

If HJ=x+10

JK=9x

KH=14x−58

a) The diagram of sketch of the segments described above is attached to this answer.

b) KH = HJ + JK

14x - 58 = (x + 10) + 9x

14x - 58 = x + 10 + 9x

c)

14x - 58 = x + 10 + 9x

14x - 58 = 10x + 10

Collect like terms

14x - 10x = 10 + 58

4x = 68

Divide both sides by 4

4x/4 = 68/4

x = 17

d)

x= 17

HJ= x + 10

= 17 + 10

= 27

Hence, HJ = 27

JK= 9x

= 9 × 17

= 153

Hence, JK = 153

HK=14x −58

HK = 14 × 17 - 58

= 238 - 58

= 180

Hence, HK = 180

John's study aims to determine if exercise frequency has an effect on pulse rate. Statistical analysis can be used to verify the alternate hypothesis.

John wants to determine whether the frequency of exercise affects pulse rate. To investigate this, he randomly selects individuals at a local gym who agree to participate in his research. John divides the 55 individuals who agree into three exercise frequency categories: high, moderate, and low.

Following their exercise, he calculates their pulse rates. Is there a difference in pulse rates among those who exercise frequently, moderately, and infrequently?The null hypothesis for this research question would be that there is no relationship between the frequency of exercise and pulse rate. The alternate hypothesis would be that there is a correlation between frequency of exercise and pulse rate. Statistical tools like ANOVA or T-test can be used to test the hypothesis.

In conclusion, John's study aims to determine if exercise frequency has an effect on pulse rate. Statistical analysis can be used to verify the alternate hypothesis.

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Answer:

x=2

AB=8

BC=8

AC=16

Step-by-step explanation:

7x-6=12-2x

7x+2x=12+6

9x=18

x=2

AB=7x-6=7(2)-6=14-6=8

BC=12-2x-12-2(2)=12-4=9

AC=8+8=16

Answer:

The tube are similar in shape.

The height of the small tub is 5  cm.

The volume of the small tube is 150  cm3.

The volume of the large tub is 500  cm3.

Work out the height of the large tub.

Give your answer correct to 3  significant figures.

Step-by-step explanation: Hope this help(:

The length of side a is determined as 13.92 by applying sine rule of triangle.

The length of side a is calculated by applying the following formulas shown below;

Apply sine rule as follows;

a / sin (83) = 13 / sin (68)

Simplify the expression as follows;

multiply both sides of the equation by " sin (83)".

a = ( sin (83) / sin (68) ) x 13

a = 13.92

Thus, the value of side length a is determined as 13.92 by applying sine rule as shown above.

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Answer:

The independent variable is the variable that is manipulated or changed during an experiment. In this case, the independent variable is represented by the x-values of the given points.

So, the answer would be option A: {-2, 3, 1, 5}

Step-by-step explanation:

brainliest Plsssss

To ensure the best test results, Anita should be provided with the following information before her spirometry:

1. Instructions for taking the test: Anita should be thoroughly explained about how the spirometry test works and what steps she needs to follow. This includes taking a deep breath and blowing as hard as she can into the spirometer mouthpiece. It is important to emphasize that she needs to repeat this procedure a few times and take deep breaths between each exhale.

2. Emphasize the importance of taking medication as prescribed: Anita should be reminded of the importance of taking her medications as prescribed, including on the day of the test. It is crucial for her to bring her medications to the test appointment.

3. Avoid certain foods and drinks: Anita should be informed to avoid consuming certain substances before the spirometry test, such as caffeine, alcohol, and heavy meals. These can potentially affect the accuracy of the test results.

4. Arrive early for the test: Anita should be advised to arrive early for the test to allow herself sufficient time to relax and calm down before the procedure. This can help ensure more accurate results.

The rationale behind providing these instructions and information is that spirometry is a lung function test that measures the amount and speed of air being breathed in and out. By following the instructions and guidelines, Anita can achieve optimal results, aiding in the diagnosis and assessment of lung conditions.

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None of the options A, B, C, or D are the necessary step to verify InB + 2 = -2t as a solution to dB/dt = -2B.

what is differential equations?

Differential equations are mathematical equations that describe the relationship between an unknown function and its derivatives (or differentials).

To verify that InB + 2 = -2t is a solution to dB/dt = -2B, we can substitute InB + 2 for B in the differential equation and check if it satisfies the equation.

So, let's first differentiate InB + 2 with respect to t:

d/dt (InB + 2) = 1/B * dB/dt

Using the given differential equation, we can substitute dB/dt with -2B:

d/dt (InB + 2) = 1/B * (-2B)

Simplifying this expression, we get:

d/dt (InB + 2) = -2

Now, substituting InB + 2 for B in the original differential equation, we get:

dB/dt = -2(InB + 2)

We can differentiate this expression with respect to B to get:

d/dB (dB/dt) = d/dB (-2(InB + 2))

d²B/dt² = -2/B

Since we have already established that d/dt (InB + 2) = -2, we can differentiate this expression with respect to t to get:

d²B/dt² = d/dt (-2) = 0

Therefore, d²B/dt² = -2/B if and only if d/dt (InB + 2) = -2.

Now, let's check if the given solution satisfies this condition. Substituting InB + 2 = -2t in d/dt (InB + 2), we get:

d/dt (InB + 2) = d/dt (In(-2t) + 2) = -2/t

Since -2/t is not equal to -2, the given solution does not satisfy the differential equation dB/dt = -2B, and hence, we cannot verify it as a solution.

Therefore, none of the options A, B, C, or D are the necessary step to verify InB + 2 = -2t as a solution to dB/dt = -2B.

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Answer:

Two expressions for the area are;

i) x/3 + 2·y + 6

ii) (1/3) × (x + 6·y + 18)

Step-by-step explanation:

The given dimension of the rectangle are;

The height of the rectangle, h = 1/3

The width of the smallest rectangle, w₁ = x

The width of the med sized rectangle, w₂ = 6·y

The width the large rectangle, w₃ = 18

The area, 'A', of the entire rectangular figure, the big rectangle, can be expressed as follows;

A = A₁ + A₂ + A₃

Where;

A₁ = The area of the smallest rectangle

A₂ = The area of the mid sized rectangle

A₃ = The area of the large rectangle

∴ A = (1/3) × x + (1/3) × 6·y + (1/3) × 18 = x/3 + 2·y + 6

The area of the big rectangle. 'A', can also be found as follows;

A = (1/3) × (x + 6·y + 18)

Therefore, two expressions for the area of the big rectangle are;

x/3 + 2·y + 6 and (1/3) × (x + 6·y + 18).

Answer: The price of the apartment lies in the range of $1300 to $1800

Step-by-step explanation: Because Carlos doesn't exactly know how much  he'll make at his new job but he knows the range will be between 3000$ and 4000$ we will use inequality to solve this problem.

Let the rent on the new apartment = r

let monthly pay of Carlos = x

Given, apartment related fees = 200$

Given he is willing to use half of his monthly pay for rent and apartment related fees combined.

∴rent + apartment related fees = Monthly pay / 2

⇒\(r + 200 = \frac{x}{2}\)

⇒\(x=2*(r+200)\)

⇒\(x=2r+400\)                                                (1)

Given Carlos' monthly pay is in the range of $3000 to $4000

∴\(3000\leq x\leq 4000\)

⇒\(3000\leq (2r+400)\leq 4000\)                             (from equation (1))

⇒\(3000-400\leq 2r+400-400\leq 4000-400\)     (subtracting 400)

⇒\(2600\leq 2r\leq 3600\)

⇒\(\frac{2600}{2}\leq \frac{2r}{2}\leq \frac{3600}{2}\)                                           (dividing by 2)

⇒\(1300\leq r\leq 1800\)                                           (2)

ANS: The apartment lies in the price range of $1300 to $1800 as given by equation (2)

here is a problem solved using inequality

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