QUESTION 7 7.1 The fifth term of an arithmetic sequence is zero and the thirteenth term is equal to 16. Determine: the common difference
​

Answer:

Total area = 141,

the trapezoid = 117, the triangle=24

The value of AB is,

⇒ AB = 5.9

(rounded to nearest tenth)

We have to given that,

A right triangle ABC is shown.

Now, By trigonometry formula,

we get;

⇒ cos 33° = Base / Hypotenuse

Substitute all the values, we get;

⇒ cos 33° = AB / 7

⇒ 0.84 = AB / 7

⇒ AB = 0.84 × 7

⇒ AB = 5.88

⇒ AB = 5.9

(rounded to nearest tenth)

Thus, We get;

AB = 5.9

(rounded to nearest tenth)

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Answer: \(x=0, -\frac{3}{2}\)

Step-by-step explanation:

\(4x^2 +6x=0\\\\2x(2x+3)=0\\\\2x=0, 2x+3=0\\\\x=0, -\frac{3}{2}\)

The total amount the man had = 52,200 rupees. Out of this, he gave 21,750 rupees to his son, 13,050 rupees to his daughter, and 17,400 rupees to his wife , the total amount given away by the man = 21,750 + 13,050 + 17,400 = 52,200 rupees.

A man gave 5/12 of his money to his son, 3/7 of the remainder to his daughter, and the remaining to his wife. If his wife gets Rs. 8,700, what is the total amount?

The given problem can be solved using the concept of ratios and fractions. Let us solve the problem step-by-step.Assume the man had x rupees with him.The man gave 5/12 of his money to his son.

The remaining amount left with the man = x - 5x/12= (12x/12) - (5x/12) = (7x/12)The man gave 3/7 of the remainder to his daughter.'

Amount left with the man after giving it to his son = (7x/12)The amount given to the daughter = (3/7) x (7x/12)= (3x/4)The remaining amount left with the man = (7x/12) - (3x/4)= (7x/12) - (9x/12) = - (2x/12) = - (x/6) (As the man has given more money than what he had with him).

Therefore, the daughter's amount is (3x/4) and the remaining amount left with the man is (x/6).The man gave all the remaining amount to his wife.

Therefore, the amount given to the wife is (x/6) = 8700Let us find the value of x.x/6 = 8700 x = 6 x 8700 = 52,200

Therefore, the man had 52,200 rupees with him.He gave 5/12 of his money to his son. Therefore, the amount given to his son is (5/12) x 52,200 = 21,750 rupees.

The remaining amount left with the man = (7/12) x 52,200 = 30,450 rupees.He gave 3/7 of the remainder to his daughter. Therefore, the amount given to his daughter is (3/7) x 30,450 = 13,050 rupees.

The amount left with the man = (4/7) x 30,450 = 17,400 rupees.The man gave 17,400 rupees to his wife.
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Note that the angle labeled ∠PQR is given as 70°

First, note that the Lengths of tangents drawn from external points to a circle are equal in length. This means that:

Length of PT = Lenght of TR

This makes Δ TPR and Isosceles Triangle.

This also makes ∠P = ∠R..............................1

Thus:

∠P + ∠R + ∠T = 180°

Given expression 1 above,

we can say:

x + x + 38° = 180°

Thatis 2x = 180 - 40

2x = 140°

x = 140/2

x = 70°

Note that Line TP is parallel to Line QR and Line PQ is a transversal line. Thus, ∠P and ∠Q are co-interior angles. This means that:

∠P + ∠Q = 180°

Recall that:

70 + 40 + ∠Q = 180°
∠Q = 180 -70 -40

∠Q = 70°

Thus: ∠ PQR = 70°

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Full Question:

See attached image.

Answer: \(5\sqrt 5\)

Step-by-step explanation:

Sol \(\sqrt 125\) = \(\sqrt{25.5}\)

= \(\sqrt{25}\)  x  \(\sqrt{5}\)

\(5 \sqrt{5}\)

The following elements were included in the response: labeling x-axis as age, labeling y-axis as texting speed, plotting points according to age and texting speed, and identifying a relationship between texting speed and age.

In the response, the following elements were included:

1. Labeling the x-axis as the input variable, age: This is important to indicate the independent variable being plotted.

2. Labeling the y-axis as the output variable, texting speed: This is crucial to indicate the dependent variable being represented.

3  Plotting the points according to age and texting speed: This involves placing the ordered pairs (age, texting speed) on the coordinate plane, with age values on the x-axis and texting speed values on the y-axis.

4. Identifying a relationship between the change in texting speed as age increases: By analyzing the plotted points and examining the pattern or trend, one can determine if there is a relationship between age and texting speed. For example, if the texting speed generally increases as age increases or if there is a linear or nonlinear relationship between the two variables.

Including all of these elements allows for a comprehensive analysis of the relationship between age and texting speed, providing a visual representation and enabling the identification of any patterns or trends.

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Answer:

∠ W = 53°

Step-by-step explanation:

the measure of the secant- secant angle W is half the difference of the measures of the intercepted arcs , that is

∠ W = \(\frac{1}{2}\) (YC - GT) = \(\frac{1}{2}\) (160 - 54)° = \(\frac{1}{2}\) × 106° = 53°

Answer:

I don't understand the question.  

Step-by-step explanation:

I don't know how to explore the slope intercept line equation.  

However, 'b' is the y axis intercept (the point where is crosses the y axis and 'm' is the slope of the line.  The 'm' and the 'b' can be positive or negative numbers.  

A positive 'm' is a line that goes 'up' (the y value increases from the left to right) and a negative 'm' is a line that goes 'down' (the y value decreases from left to right).

Answer:

vjfkkfjjkuuoooo99999

Step-by-step explanation:

Create a right triangle with the hypotenuse = 2400in (same as 200ft) and angle from horizontal =15 degrees

you can create the equation to find the opposite line (y-value)

2400sin(15) =

621 in

To maximize the volume, of the rectangular prism, the carton should have dimensions of approximately 10.74 inches (length), 10.74 inches (width), and 5.37 inches (height).

Assuming the height of the rectangular prism is h inches.

According to the given information, the length and width of the prism will be twice the height, which means the length is 2h inches and the width is also 2h inches.

The total surface area of the rectangular prism is given by the formula:

Surface Area = 2lw + 2lh + 2wh

Substituting the values, we have:

576 = 2(2h)(2h) + 2(2h)(h) + 2(2h)(h)

576 = 8h² + 4h² + 4h²

576 = 16h² + 4h²

576 = 20²

h² = 576/20

h² = 28.8

h = √28.8

h = 5.37

The height of the prism is approximately 5.37 inches.

The length and width will be twice the height, so the length is approximately 2 * 5.37 = 10.74 inches, and the width is also approximately 2 * 5.37 = 10.74 inches.

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Answer:

\(y = \frac{x}{4} \)

Step-by-step explanation:

we find the slope which also represented as m by the formula

\( m = \frac{(y2 - y1)}{(x2 - x1)} \)

where from point (-4, -2) the x1 is -4 and the y1 is -2 and also from point (6, 3) the x2 is 6 and the y2 is 3.

so we substitute

\( \frac{(3 - ( - 2))}{(6 - ( - 4))} = \frac{(3 + 2)}{(6 + 4)} = \frac{5}{10} = \frac{1}{2} \)

\(m = \frac{1}{2} \)

after we have the slope, we calculate the equation of the line by using the formula

\((y - y1) = m(x - x1)\)

but for now, we only have y1, m and x1 so can substitute

\((y - ( - 2)) = \frac{1}{2} (x - ( - 4))\)

we have to get rid of the fraction 1/2 so we multiply it through by the denominator 2

\(2(y + 2) = 2 \times \frac{1}{2}(x + 4) \)

we get

\(2(y + 2) = 1 \times (x + 4)\)

so now we expand the brackets

\(2y + 4 = x + 4\)

we make y stand alone by grouping liked terms.

\(2y = x + 4 - 4\)

we get

\(y = \frac{x}{4} \)

The spinner illustrates a fair probability because it has equal sections and the value of P(Not T)= 5/6

The sample space of the spinner is:

S = {P,Q,R,S,T,U}

Using the sample space, the probability of T is:

P(T)  = 1/6

Using the complement probability formula, the probability of not T is:

P(Not T)= 1 - P(T)

So, we have:

P(Not T)= 1 - 1/6

Evaluate

P(Not T)= 5/6

Hence, the value of P(Not T)= 5/6

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Answer:1/6

Step-by-step explanation:

P is 1 out of 6 probability's so the answer is 1/6 (i dont know the Not T probability)

Since all three points satisfy the equation 2x + 2y = 24 when their coordinates are substituted, we can conclude that the points (4,8), (2,10), and (5,7) indeed lie on the line represented by the equation 2x + 2y = 24.

To determine if the points (4,8), (2,10), and (5,7) lie on the line 2x + 2y = 24, we can substitute the x and y values of each point into the equation and check if the equation holds true.

For the point (4,8):

2(4) + 2(8) = 8 + 16 = 24, which satisfies the equation.

For the point (2,10):

2(2) + 2(10) = 4 + 20 = 24, which also satisfies the equation.

For the point (5,7):

2(5) + 2(7) = 10 + 14 = 24, which satisfies the equation as well.

Since all three points satisfy the equation 2x + 2y = 24 when their coordinates are substituted, we can conclude that the points (4,8), (2,10), and (5,7) indeed lie on the line represented by the equation 2x + 2y = 24.

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Answer:

C

Step-by-step explanation:

All sides make a cube

Answer:

D

Step-by-step explanation:

Answer:

$2,500 or 25%

Step-by-step explanation:

Let's use the same example:

Cost of Equipment = $10,000

Useful Life = 4 years

Depreciation Rate = (Annual Depreciation / Cost of Equipment) * 100

Annual Depreciation = Cost of Equipment / Useful Life

Annual Depreciation = $10,000 / 4 years

Annual Depreciation = $2,500

Depreciation Rate = ($2,500 / $10,000) * 100

Depreciation Rate = 0.25 * 100

Depreciation Rate = 25%

Answer:

13.48 - 8.263 = 5.217

Answer:5.217

Step-by-step explanation: caculate it

x | - 8 | - 4 | 2 | 1 | 1/2 | - 1/4 | 0

------------------------------------------------------

y | - 16/3 | - 8/3 | 4/3 | 2/3 | 1/3 | -1/6 | 0

K = 2/3

The value of cos(45°) is √2/2. The correct answer choice is D. √2.

In the given diagram, the angle labeled as 45° is part of a right triangle. To find the value of cos(45°), we need to determine the ratio of the adjacent side to the hypotenuse.

Since the angle is 45°, we can assume that the triangle is an isosceles right triangle, meaning the two legs are congruent. Let's assume the length of one leg is x. Then, by the Pythagorean theorem, the length of the hypotenuse would be x√2.

Now, using the definition of cosine, which is adjacent/hypotenuse, we can substitute the values:

cos(45°) = x/(x√2) = 1/√2

Simplifying further, we rationalize the denominator:

cos(45°) = 1/√2 * √2/√2 = √2/2

Therefore, the value of cos(45°) is √2/2.

The correct answer choice is D. √2.

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Out of the 400 surveyed students, 327 were either seniors or commuters.

To find the number of students who were either seniors or commuters out of the 400 surveyed students, we need to add the number of seniors and the number of commuters while avoiding double-counting those who fall into both categories.

According to the information given:

There were 262 seniors.

There were 215 commuters.

150 of the seniors were also commuters.

To avoid double-counting, we need to subtract the number of seniors who were also commuters from the total count of seniors and commuters.

Seniors or commuters = Total seniors + Total commuters - Seniors who are also commuters

= 262 + 215 - 150

= 327

Therefore, out of the 400 surveyed students, 327 were either seniors or commuters.

It's important to note that in this calculation, we accounted for the overlap between seniors and commuters (150 students who were both seniors and commuters) to avoid counting them twice.

This ensures an accurate count of the students who fall into either category.

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Answer:

The answer is down below

Step-by-step explanation:

v-u=◇velocity

\( = 9 - 5\)

◇velocity =4ms‐¹

acceleration =◇velocity/time

\(a = \frac{4}{5} \)

\(a = 0.8m {s}^{ - 2} \)

Change in velocity:

\( \sf \:final \: velocity - initial \: velocity = change \: in \: velocity\)

\( \therefore \tt \delta \: v = 9 - 5 \\ \tt = 4m {s}^{ - 1} \)

To find acceleration:

\( \rm \: a = \frac{ \triangle \: v}{\triangle \: t} \)

\( \rm \: a = \frac{ 4}{5 - 0} = \frac{4}{5} = 0.8m {s}^{ - 1} \)

The size he should bring more of is small and is denoted as option C.

This is a term which refers to the number of goods sold within a given period of time.

Given that, a vendor is thinking about changing the number of sweatshirts he brings to an event.

To make sure he doesn't run out, he plans to bring more of the size most likely to be sold.

we need to determine that which size should he bring more of,

So, here according to the table,

Small size has the smallest remaining which is 9 when the difference between the number sold and number put up for sale is calculated.

This is therefore why bringing more of small size will ensure he doesn't run out of stock in the next event as more people prefer it.

Hence, the size he should bring more of is small and is denoted as option C.

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According to the question, therefore, the maximum number of grams of fat he should consume will be 76.3 grams.

Directly divide 687 by 9 as both are fat content. Therefore, by dividing them, we get to know about how grams of fat can be consumed.

✍️ By Benjemin

Answer:

"hack you" lol answer is 22in

Step-by-step explanation:

the base of the pyramid is 100in^2

so the rest of the surface area is 440

formula for a triangle area is A=1/2bh

1 of the triangles is 110 440/4

110=1/2*10*h

110=5*h

h=22

The equivalent expression for the given expression is 28p + 14q + 21r.

An expression that gives the same value as the original expression when the same value of a variable is substituted is said to be an equivalent expression.

An equivalent expression is simplified to the original expression by using the distributive property.

The distributive property is

a(b + c) = ab + ac

The given expression is 7(4p + 2q + 3r)

Applying the distributive property,

7(4p + 2q + 3r) = 7(4p) + 7(2q) + 7(3r)

⇒ 28p + 14q + 21r

Thus, the equivalent expression for the given expression is 28p + 14q + 21r.

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7(4p+2q+3r)=7(4p+2q+3r)

Apply distributive law

So

This is the required expression

Answer:

The answer is 6!!!

Step-by-step explanation:

Answer:

Step-by-step explanation:

Now, in order for it to be a proportion, both the number and the denominator must turn to the other number by the same method. I'll clarify when we do the steps.

So, the first one is 4/10 and 10/25

The first thing that you would do is divide 10 by 4, and then 25/10

When you do that, it turns out that they both equal 2.5. This means that both the number and denominator go to the new number with the same method, multiplying by 2.5

So, the answer would be A

Answer:

A. A reflection over the line x = 6

Step-by-step explanation:

You can see in the picture if you follow the line every edge has the same

Number x=6

The expression (X - Y) 5 ÷ 8 - 1 ÷ 4 (X + Y) is equivalent to

(20X² - 20Y² - 1) / (4X + 4Y)

We have,

We can simplify the given expression as follows:

(X - Y) 5 ÷ 8 - 1 ÷ 4 (X + Y)

= (5X - 5Y) ÷ 8 - 1 ÷ (4X + 4Y)

[distributing the factors]

= (5X - 5Y) /8 - 1/(4X + 4Y)

[finding a common denominator]

= ((5X - 5Y)(4X + 4Y) - 1)/(4X + 4Y)

= (20X² + 20XY - 20XY - 20Y² - 1) / (4X + 4Y)

= (20X² - 20Y² - 1) / (4X + 4Y)

Therefore,

The expression (X - Y) 5 ÷ 8 - 1 ÷ 4 (X + Y) is equivalent to

(20X² - 20Y² - 1) / (4X + 4Y)

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