Please help! THE QUESTION IS IN THE PIC!

Answer:

⇒[tex](Base)^2 + ( Perpendicular)^2 = (Hypotenuse)^2[/tex]  is the required relationship.

Step-by-step explanation:

Let us assume, the given right angled triangle is ΔPQR.

Here. PQ = Perpendicular of the triangle.

QR = Base of the triangle.

PR = Hypotenuse of the triangle.

Now, PYTHAGORAS THEOREM states:

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“

⇒[tex](Base)^2 + ( Perpendicular)^2 = (Hypotenuse)^2[/tex]

Hence in ΔPQR:  [tex](QR)^2 + ( PQ)^2 = (PR)^2[/tex]

And the above expression is the required relationship between the sides of a right triangle.

The sides of a right triangle have a specific relationship given by the Pythagorean Theorem, which states a² + b² = c², where a and b refer to the lengths of the sides and c refers to the length of the hypotenuse. Additionally, the sides have relationships to the angles of the triangle expressed through trigonometric functions.

The relationship between the sides of a right triangle is given by the Pythagorean Theorem which was demonstrated by the ancient Greek philosopher, Pythagoras. This theorem states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In mathematical terms, if the lengths of the sides are a, b, and c (where c represents the length of the hypotenuse), then the relationship can be represented as a² + b² = c².

Moreover, the sides of a right triangle also have specific relationships to the measures of the angles of the triangle, which are expressed through the trigonometric functions sine, cosine, and tangent. For example, for an angle in a right triangle, the sine is the length of the opposite side divided by the length of the hypotenuse, the cosine is the length of the adjacent side divided by the hypotenuse, and the tangent is the length of the opposite side divided by the adjacent side.

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Answer:

[tex]\large\boxed{s(x)\cdot t(x)=2x^3+11x^2+8x-16}[/tex]

Step-by-step explanation:

[tex]s(x)=2x^2+3x-4,\ t(x)=x+4\\\\s(x)\cdot t(x)\\\\\text{use the distributive property:}\ a(b+c)=ab+ac\\\\s(x)\cdot t(x)=(2x^2+3x-4)(x+4)\\\\=(2x^2+3x-4)(x)+(2x^2+3x-4)(4)\\\\=(2x^2)(x)+(3x)(x)+(-4)(x)+(2x^2)(4)+(3x)(4)+(-4)(4)\\\\=2x^3+3x^2-4x+8x^2+12x-16\\\\\text{combine like terms}\\\\=2x^3+(3x^2+8x^2)+(-4x+12x)-16\\\\=2x^3+11x^2+8x-16[/tex]

Final answer:

The product of the functions [tex]s(x) = 2x^2 + 3x - 4[/tex] and t(x) = x + 4 is obtained by multiplying each term of s(x) with each term of t(x), resulting in [tex]2x^3 + 11x^2 + 8x - 16[/tex].

Explanation:

To find the product of s(x) and t(x), given  [tex]s(x) = 2x^2 + 3x - 4[/tex], and t(x) = x + 4, we use the distributive property to multiply each term in s(x) by each term in t(x). The steps are as follows:

Adding up all these products:

[tex]2x^3 + (8x^2 + 3x^2) + (12x - 4x) - 16[/tex]

Simplifying:

[tex]2x^3 + 11x^2 + 8x - 16[/tex]

Thus, the product s(x) · t(x) is  [tex]2x^3 + 11x^2 + 8x - 16[/tex]

Answer:

[tex]A=10^0[/tex]

Step-by-step explanation:

Number 2.247 has 2 in ones place, 2 in tenths place, 4 in hundredths place and 7 in thousandths place.

This means you can rewrite this number as

[tex]2.247=2\times 1+2\times 0.1+4\times 0.01+7\times 0.001\\ \\2.247=2\times 10^0+2\times \dfrac{1}{10^1}+4\times \dfrac{1}{10^2}+7\times \dfrac{1}{10^3}[/tex]

So,

[tex]A=10^0\\ \\B=\dfrac{1}{10^1}\\ \\C=\dfrac{1}{10^2}\\ \\D=\dfrac{1}{10^3}[/tex]

Answer:

x=8

Step-by-step explanation:

You divide both sides by 4 to get x alone.

Answer:

x = 8

Step-by-step explanation:

Answer:

Sample size n = 96.04

Explanation:

Given the interval is 5.6 hours to 6.4 hours

Let x be the midpoint, then x = (5.6+6.4)/2 = 6

Let E be the radius, then E = (6.4-5.6)/2 = 0.8/2 = 0.4

σ = 2 hours; as standard deviation is given and α = 0.05

Therefore, the sample size is:

[tex]n=\left(\frac{1.96 * 2}{0.4}\right)^{2}=96.04[/tex]

The student's question pertains to a 95% confidence interval estimate of the mean time required for caffeine to leave the body after consumption, which was found to be 5.6 to 6.4 hours in adults. This suggests that if the study were conducted multiple times, the mean time for caffeine to leave the body would lie within this range in 95% of those studies. The influence of variances in individual's metabolism, body mass, and general health can impact the range of the confidence interval.

The subject of this discussion revolves around statistics and more specifically around the concept of confidence intervals. In the provided context, researchers conducted a study to estimate the mean time it takes for an adult body to process and remove caffeine. They found, with a 95% confidence interval, that this time lies between 5.6 hours and 6.4 hours.

This means that if the researchers were to conduct this study multiple times, in 95% of those studies, the mean (average) time for caffeine to leave the body would lie within that given range (5.6 to 6.4 hours). This is a common method in statistics and is used as a way to give an estimate about where the actual (population) value might lie in the context of sampling error.

However, it's important to note that variance in the sample population can impact the confidence interval. Individual differences such as metabolism rate, body mass, and overall health can influence how quickly a person processes caffeine, which may result in a wider confidence interval.

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He sold 32 small watermelons and 17 large watermelons.

Step-by-step explanation:

Let,

Small watermelons = x

Large watermelons = y

Cost of one small watermelon = $7

Cost of one large watermelon = $10

According to given statement;

x = y+15   Eqn 1

7x+10y=394   Eqn 2

Putting value of x from Eqn 1 in Eqn 2

[tex]7(y+15)+10y=394\\7y+105+10y=394\\17y=394-105\\17y=289\\[/tex]

Dividing both sides by 17

[tex]\frac{17y}{17}=\frac{289}{17}\\y=17[/tex]

Putting y=17 in Eqn 1

[tex]x=17+15\\x=32[/tex]

He sold 32 small watermelons and 17 large watermelons.

Keywords: linear equations, substitution method

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Answer:

$12159 per year.

Step-by-step explanation:

If I invest $x each year at the simple interest of 7.5%, then the first $x will grow for 35 years, the second $x will grow for 34 years and so on.

So, the total amount that will grow after 35 years by investing $x at the start of each year at the rate of 7.5% simple interest will be given by

[tex]x( 1 + \frac{35 \times 7.5}{100}) + x( 1 + \frac{34 \times 7.5}{100}) + x( 1 + \frac{33 \times 7.5}{100}) + ......... + x( 1 + \frac{1 \times 7.5}{100})[/tex]

= [tex]35x + \frac{x \times 7.5}{100} [35 + 34 + 33 + ......... + 1][/tex]

= [tex]35x + \frac{x \times 7.5}{100} [\frac{1}{2} (35) (35 + 1)][/tex]

{Since sum of n natural numbers is given by [tex]\frac{1}{2} (n)(n + 1)[/tex]}

= 35x + 47.25x

= 82.25x

Now, given that the final amount will be i million dollars = $1000000

So, 82.25x = 1000000

⇒ x = $12,158. 05 ≈ $12159

Therefore. I have to invest $12159 per year. (Answer)

To convert 2 meters to inches, you multiply by the conversion factor of approximately 39.37, resulting in 78.7 inches when rounded to the nearest tenth.

The measurement 2 meters is equivalent to

78.7 inches.

To convert meters to inches, we know that 1 meter is approximately 39.37 inches. Therefore, 2 meters would be equal to 2 x 39.37 = 78.74 inches. Rounding to the nearest tenth, this equals 78.7 inches.

Answer:

4.924 units.

Step-by-step explanation:

See the attached diagram.

If P is the midpoint of AB and Q is the midpoint of AC, then PQ is parallel to BC and the length of PQ will be half of BC.

Now, the coordinates of B are (1,1) and that of C is (10,-3).

Therefore the length of BC is [tex]\sqrt{(10 - 1)^{2} + (- 3 - 1)^{2}} = 9.848[/tex] units (Approximate)

Therefore, the length of PQ = 0.5 × 9.848 = 4.924 units. (Answer)

We know that the distance between two given points ([tex]x_{1},y_{1}[/tex]), and ([tex]x_{2},y_{2}[/tex]) is given by the formula

[tex]\sqrt{(x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2}}[/tex]

Answer: The answer is 32

Answer:

32

Step-by-step explanation:

25%=0.25

8/0.25=32

Answer:

27 cats.

Step-by-step explanation:

The fraction of cats = 9 / (9 + 13) and dogs = 13 / ( 9 + 130

= 9/22 and 13/22

So the number of cats = (9/22) * 66

= 9 *3

= 27.

=

Answer:

Lin needs 12.53 square feet of fabric

Step-by-step explanation:

we know that

The area of the window covering is equal to the area of the square plus the area of semicircle

step 1

Find the area of the square

The area of the square is equal to

[tex]A_1=b^{2}[/tex]

where

b is the length side of the square

we have

[tex]b=3\ ft[/tex]

substitute

[tex]A_1=3^{2}=9\ ft^2[/tex]

step 2

Find the area of semicircle

The area of semicircle is equal to

[tex]A_2=\frac{1}{2}\pi r^{2}[/tex]

The length side of the square is equal to the diameter of semicircle

so

[tex]r=3/2=1.5\ ft[/tex] ----> the radius is half the diameter

assume

[tex]\pi =3.14[/tex]

substitute

[tex]A_2=\frac{1}{2}(3.14)(1.5)^{2}[/tex]

[tex]A_2=3.53\ ft^2[/tex]

Adds the areas

[tex]A=A_1+A_2[/tex]

[tex]A=9+3.53=12.53\ ft^2[/tex]

therefore

Lin needs 12.53 square feet of fabric

Final answer:

Lin needs approximately 12.54 square feet of fabric for a window covering with a half-circle on top of a square, both with a side length of 3 feet. Calculating the areas of the square and the half-circle and summing them gives the total fabric required.

Explanation:

To calculate the amount of fabric Lin needs for the window covering with a half-circle on top of a square with a side length of 3 feet, we need to find the area of both the square and the half-circle and add them together. The area of the square is straightforward - since all sides are equal, the area is side × side, which is 3 feet × 3 feet = 9 square feet. For the half-circle, we first need to calculate the area of a full circle using the formula πr² (where π is pi, approximately 3.14159, and r is the radius of the circle). The diameter of the circle is the same as the side length of the square, which is 3 feet, making the radius 1.5 feet.

So, the area of a full circle is π × (1.5 feet)² = π × (2.25 square feet).

To find the area of the half-circle, we simply divide this by 2, resulting in π × 2.25 square feet / 2 = 3.53429174 square feet. Adding the area of the square and the half-circle gives us the total fabric needed: 9 square feet + 3.53429174 square feet = 12.53429174 square feet.

Therefore, Lin needs approximately 12.54 square feet of fabric for her window covering.

Answer:

Step-by-step explanation:

Answer:

Total bill=$51.75

Step-by-step explanation:

Step 1: Determine the cost of her meal

Cost of meal=$45

Step 2: Calculate the amount of the tip

Tip amount=15% of the cost of meal

where;

cost of meal=$45

replacing;

Tip amount=(15/100)×45=6.75

The tip amount=$6.75

Step 3: Total bill

The total bill can be expressed as;

Total bill=tip amount+subtotal

where;

tip amount=$6.75

cost of meal=$45

replacing;

Total bill=(45+6.75)=51.75

Total bill=$51.75

D. g(x) = f(x) +9 is the right answer

Step-by-step explanation:

The shifting of graphs is mathematically denoted by adding or subtracting a number from the output or input.

When the graph is shifted up, a number is added to the functions's output

For example

For a function

f(x)

Shifting up is represented as g(x) = f(x)+b where b is a number

So,

Given function is:

f(x) = x

Shifting the graph 9 units upwards we will get

g(x) = f(x) + 9

Hence,

D. g(x) = f(x) +9 is the right answer

Keywords: Functions, Graphs

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Answer: D. g(x) = f(x) +9 is the right answer

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

8 / (1/5)

When dividing fractions, the second fraction just flips upside down. Then you just multiply.

So it's now 8 * 5 = 40

Answer:

The final price is $ 22.68  And Proportional constant is 1.4  

Step-by-step explanation:

Given as :

The Original price = $ 16.20

The rate of increase = 40%

Let The final price = x

Now,

Final price after increase = initial price × ( 1 + [tex]\frac{\textrm Rate}{100}[/tex]

Or. Final price after increase = $ 16.20 × ( 1 + [tex]\frac{\textrm 40}{100}[/tex]

Or, Final price after increase = $ 16.20 × ( 1.4 )

∴ Final price after increase = $ 22.68

Now , Proportional constant = [tex]\frac{22.68}{16.20}[/tex]

I.e Proportional constant = 1.4

Hence The final price is $ 22.68  And Proportional constant is 1.4  Answer

Answer: 3.sas

4.sas

5.sas

6.asa

7.sas

8. not possible

9. hl

Step-by-step explanation:

Answer:

x^2/3

Step-by-step explanation:

(x^5/6)/(x^1/6)=x^(5/6-1/6)=x^4/6

simplify 4/6, you get 2/3.

Answer:a total of 45 students per bus

Step-by-step explanation: 450-5= 445

445/10= 44.5

a total of 45 students per bus

Answer:9 nickels and 19 dimes.

Step-by-step explanation:

Let [tex]n[/tex] be the number of nickels Kay has.

Let [tex]d[/tex] be the number of dimes Kay has.

Value of [tex]1[/tex] nickel is $[tex]0.05[/tex]

Value of [tex]n[/tex] nickels is $[tex]0.05n[/tex]

Value of [tex]1[/tex] dime is $[tex]0.1[/tex]

Value of [tex]d[/tex] nickels is $[tex]0.1dn[/tex]

Given that Kay has a total of [tex]28[/tex] coins.

So,[tex]n+d=28[/tex]                                                ...(i)

Given that Kay has a total value of $[tex]2.35[/tex]

So,[tex]0.05n+0.1d=2.35[/tex]                                 ...(ii)

Using (i) and (ii),

[tex]0.05n+0.1(28-n)=2.35\\0.05n+2.8-0.1n=2.35\\2.8-2.35=0.05n\\0.45=0.05n\\n=9[/tex]

[tex]d=28-n=28-9=19[/tex]

Answer:

300.407

Step-by-step explanation:

100*3=300

4*0.1=0.4

7*0.001=0.007

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

300+0.4+0.007

300.407

Answer:

.8

Step-by-step explanation:

because 24/30

The probability that a randomly selected house with 2 bathrooms

has 3.

We have given that,

The two-way table shows the number of houses on the market in the Castillos’ price range.

A 6-column table has 4 rows.

The first column has entries 1 bathroom, 2 bathrooms and 3 bathrooms, in total.

The second column is labeled 1 bedroom with entries 67, 0, 0, 67.

The third column is labeled 2 bedrooms with entries 21, 6, 18, 45.

We are only considering the houses that have 2 bathrooms.

 There are a total of 30 of these houses.

Out of these 30, 24 have 3 bedrooms.  

The probability of an event can only be between 0 and 1 and can also be written as a percentage.

This makes the probability 24/30, which is 0.8.

Therefore, the probability that a randomly selected house with 2 bathrooms has 3.

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Answer:

$52080

Step-by-step explanation:

46, 500 + (.12×46,500) =52080

Answer:

step 2 i believe

Step-by-step explanation:

hope this helps

Answer:

The answer is B

Step-by-step explanation:

Hope this helps :))

Answer:

False

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

Answer:

21, 24, 29

5

Step-by-step explanation:

The first term is when n = 1.

(1)² + 20 = 21

The second term is when n = 2.

(2)² + 20 = 24

The third term is when n = 3.

(3)² + 20 = 29

To find how many terms are less than 50, set n² + 20 equal to 50 and solve for n:

n² + 20 = 50

n² = 30

n ≈ 5.477

Rounding down, n = 5 is the last term that is less than 50.

Therefore, there are 5 terms in the sequence that are less than 50.

Answer:

a = 6 units

[tex]c= 6\sqrt{2}\ units[/tex]

Step-by-step explanation:

Given:

Let Labelled the diagram first

Δ ABC right angle at ∠ C = 90°

∠ B = 45 °

AB = c

BC = a

AC = 6

To Find:

a =?

c =?

Solution:

In Δ ABC

∠ A + ∠ B + ∠ C = 180°.....{Angle Sum Property of a Triangle}

∴ ∠ A + 45 + 90 = 180°

∴ ∠ A = 180 - 135

∴ ∠ A = 45°

Now ∠ A = ∠ B = 45°  in Δ ABC

∴ Δ ABC is an Isosceles Triangle.

∴ Two sides are equal of an  Isosceles Triangle.

∴ AC = BC = a = 6 units

Now for c we use Pythagoras theorem

[tex](\textrm{Hypotenuse})^{2} = (\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}[/tex]

Substituting the given values we get

c² = a² + 6²

c² = 6² + 6²

c² = 36 + 36

c² = 72

∴ c = ±√72

as c cannot be negative

∴ [tex]c = 6\sqrt{2}\ units\\[/tex]

a = 6 units

[tex]c= 6\sqrt{2}\ units[/tex]

Answer:

[tex]\frac{x}{-3} =6\\x=-18[/tex]

x= -18

Answer: X = -18

Step-by-step explanation: In this problem, notice that x is being divided by -3 so to get x by itself, we need to multiply both sides of the equation by -3.

Notice that on the left side, the -3 and -3 cancel each other out so we're just left with x.

On the right side, we have 6 × -3 which is -18 so X = -18.

Finally, we can check our answer by plugging a -18 back into the original equation.

So we have -18 ÷ -3 = 6, which is a true statement which means that our answer is correct.

Image provided.

Answer:

Choice C)

x^2 - 2x + 4 - 12/(x+2)

[tex]x^2 - 2x + 4 - \frac{12}{x+2}[/tex]

====================================================

Explanation:

To see how I got that answer, I have provided two attached images below. One of them shows the polynomial long division. The other shows synthetic division. Both are valid options to get to the same answer.

For each method, I used 1x^3 + 0x^2 + 0x - 4 in place of x^3 - 4 so that the proper terms could align.