AABC-ADEC. 1 and 2 have the same measure. Find DC and
DE. (Hint: Let DC = x and AC=x+4, Use the figure shown to the right.)
DC is unit(s) long.
(Round to the nearest tenth as needed.)
D
4
A
14
E
B

Answer:

-90

Step-by-step explanation:

Answer: the first third fourth and last one

Step-by-step explanation:

Answer:

Step-by-step explanation:

The correct answer is true. If you know that the relationship between quantities is proportional, you can use proportions to find missing quantities.

Answer:

5+n(-4)

Step-by-step explanation:

this is the equation if that helps??

Answer:

5*N-4 five times a number n minus four

Answer:

d. Definite integral can be used to calculate area under a curve in a given interval

General Formulas and Concepts:

Calculus

Integration

Area of a Region Formula:                                                                                    \(\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx\)

Step-by-step explanation:

We know that by definition, an integral is an antiderivative.

Also by definition, an integral is also the area under the curve. This can be extended to area between 2 curves.

We have a formula specifically to find an area under a curve (region), as listed above.

∴ our answer is D.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Answer:

Can you show us the circle so we can solve the problem?

Step-by-step explanation:

Answer:

\(\displaystyle \large{y\prime = 2t \sin (2t) + 2t^2 \cos (2t)}\)

Step-by-step explanation:

We are given a function:

\(\displaystyle \large{y = t^2 \sin (2t)}\)

To differentiate a function, we are going to use the product rules since there are two functions which are t^2 and sin(2t) multiplying together.

From the product rules, \(\displaystyle \large{y = f(x)g(x) \to y\prime = f\prime (x) g(x)+f(x) g\prime (x)}\)

Therefore, \(\displaystyle \large{y = t^2 \sin (2t) \to y\prime = (t^2)\prime \sin (2t) + t^2 (\sin (2t))\prime}\)

Before we start differentiating, I’d like you to look at [sin(2t)]’. A function like this, you cannot just directly derive and answer. You need to use chain rules.

We know that, \(\displaystyle \large{y = \sin (x) \to y\prime = \cos (x)}\) but what if the “x” is another function? Like sin(3x), sin(x^2) as examples. The insides are another function, can be expressed as fog(x) or gof(x) is composite function.

Basically, chain rule is a rule or formula for composite function and it’s the most common and useful as well as being always used in differentiation.

Chain Rules

\(\displaystyle \large{\frac{dy}{dx} = \frac{dy}{du} \frac{du}{dx}}\)

where u is another function in a bracket. From the formula above, it can be also written as:

\(\displaystyle \large{[f(g(x))]\prime = f(g(x))\prime \cdot g(x)\prime\)

To simply say, you differentiate the whole function first then multiply with the chain or inner derived function.

So from the function, we obtain:

\(\displaystyle \large{y\prime = 2t \sin (2t) + t^2 \cos (2t) \cdot (2t)\prime}\\ \displaystyle \large{y\prime = 2t \sin (2t) + t^2 \cos (2t) \cdot 2}\\ \displaystyle \large{y\prime = 2t \sin (2t) + 2t^2 \cos (2t)}\)

The factored form would be:

\(\displaystyle \large{y\prime = 2t ( \sin (2t) + t \cos (2t))}\)

From above, for polynomial function, to differentiate, you can do by using the power rules.

Power Rules

\(\displaystyle \large{y = ax^n \to y\prime = nax^{n-1}}\)

Answer: d.12

Step-by-step explanation:

we can pretty much split the middle part into two trapezoids. Check the picture below.

so we really have one trapezoid and one square, each twice, so simply let's get the area of the trapezoid and sum it up with the area of the square, twice, and that's the area of the shape.

\(\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h=height\\ a,b=\stackrel{\textit{parallel sides}}{bases}\\[-0.5em] \hrulefill\\ h=5\\ a=3\\ b=7 \end{cases}\implies A=\cfrac{5(3+7)}{2}\implies A=25 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{sum of areas}}{[25+(3\cdot 3)]}\cdot \stackrel{twice}{2}\implies [34]2\implies \underset{in^2}{68}\)

Hello!

area

= 2*25 + (20 - 2)*(25-8)

= 50cm² + 306cm²

= 356cm²

Answer:

1st one is b.  2nd one is A

Step-by-step explanation:

i did the quiz

\(x^2-8x+10=x^2-8x+16-6=(x-4)^2-6\)

Answer:

what are c and d?

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

john earns more than don

The correct graph of the inequality -0.4x - 2 < - 1.2 is option 2.

Equation containing a relational operator and a linear expression is known as a linear inequality. In a coordinate plane or space, regions that satisfy a linear inequality are defined. A linear inequality defines a half-plane in two dimensions, which, depending on the inequality, can be either above or below a line. A linear inequality defines a half-space in three dimensions, which, depending on the inequality, is either above or below a plane. The goal of optimization problems is to determine the maximum or minimum value of a linear function under a set of constraints, which are typically represented by linear inequalities.

The given inequality is -0.4x - 2 < - 1.2.

-0.4x - 2 < - 1.2

Adding 2 on both sides of the equation we have:

-0.4x < -1.2 + 2

-0.4x < 0.8

-x < 2

x > -2

Hence, the correct graph of the inequality is option 2.

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Answer is

2, 4, 6, 8

9514 1404 393

Answer:

  C. none of these

Step-by-step explanation:

The given information tells us ΔACD is isosceles, but gives no information about any lines that might conceivably be parallel.

To find the amount of wet food Luck mixed with the dry food, we can use the fact that he put 5/4 cups into each of the 4 bowls. Therefore, he used a total of 5/4 x 4 = 5 cups of wet food.

Thus, Luck mixed 3 cups of dry food and 5 cups of wet food to prepare the dog's meal.

Segments MS and QS are therefore congruent by the definition of bisector. Therefore, the correct answer option is: D. MS and QS.

In Mathematics and Geometry, a perpendicular bisector is a line, segment, or ray that bisects or divides a line segment exactly into two (2) equal halves and forms an angle that has a magnitude of 90 degrees at the point of intersection.

This ultimately implies that, a perpendicular bisector bisects a line segment exactly into two (2) equal halves, in order to form a right angle that has a magnitude of 90 degrees at the point of intersection.

Since line segment NS is a perpendicular bisector of isosceles triangle MNQ, we can logically deduce the following congruent relationships;

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Complete Question:

The proof that ΔMNS ≅ ΔQNS is shown. Given: ΔMNQ is isosceles with base MQ, and NR and MQ bisect each other at S. Prove: ΔMNS ≅ ΔQNS

We know that ΔMNQ is isosceles with base MQ. So, MN ≅ QN by the definition of isosceles triangle. The base angles of the isosceles triangle, ∠NMS and ∠NQS, are congruent by the isosceles triangle theorem. It is also given that NR and MQ bisect each other at S. Segments _____ are therefore congruent by the definition of bisector. Thus, ΔMNS ≅ ΔQNS by SAS.

NS and NS

NS and RS

MS and RS

MS and QS

Answer:

76.553 yards

Step-by-step explanation:

1m=1.094 yards

70×1.094=76.553yards

The percentage of students that have scored more than you is 1.39%

a) Probility that people scored more than Nancy = P(X>1390) = 1- P(X<1390).

Now z= (1390-950)/200

z= 2.2

P(Z<2.2) = 0.9861

So 1- P(X<1390) = 1 - P(Z<2.2) = 1 - 0.9861 = 0.0139

= 1.39 %

Let P1 be the % of people who score below 1100 and P2 be the % of people who scored below 1200

Then % of students between scores of 1100 and 1200 = P2 - P1

Z (X=1100) =0.75 and Z (X=1200) = 1.25

P1 = P(X<1100)= P (Z< 0.75) =0.7734

P2 = P(X<1200)= P (Z< 1.25) =0.8944

Then % of student between score of 1100 and 1200 = P2 - P1 = 0.8944 - 0.7734 = 0.121 = 12.10%

Middle 87.4 % score means that a total of 12.6 % of the population is excluded. That is 6.3% from both sides of the normal curve. So the minimum value for the middle 87.4% will the one which is just above 6.3% of the population i.e. it will have value x such that P(X<x)= .063.

z value (for P(X<x)= .063) = (-1.53)

But Z= (x-u)/ \sigma from here calculating x, x=644

The minimum value of the middle 87.4% score is 644

The maximum value for the middle 87.4 % of the scores will be the one that has 6.3% scores above it, i.e. it will have value x such that P(X>x)= .063.

P(X<x)= 1 -P(X>x)= 1 - 0.063 = 0.937.

Z value (for P(X<x)= 1.53

But Z= (x-u)/ \sigma from here calculating x, x=1256

The maximum value of the middle 87.4% score is 1256

Z value for (X=1432)= 2.41

P(Z<2.41) =0.9920

It means that 99.2 % of scores are less than 1432

So only 0.8% of scores are higher than 1432

but , 0.8% = 165

So 100% = 20625

20625 students took SAT

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Answer:

i wish i did know

Step-by-step explanation:

Answer:

$95.4

Step-by-step explanation:

6% in decimal form is 0.06

we need to find what 6% of 90 is to see how much sales tax there is on this item

0.06*90=5.4

the sales tax is 5.4

5.4 is 6% of 90 so we need to add 5.4 to 90

90+5.4=95.4

$95.4---total amount noah paid(normal price+ sales tax)

Given

To find

we know that

Inserting the value of radius

The class width used for the frequency distribution is 6.

The class midpoint for the class 23-29 is 26.

The class midpoint for the class 30-36 is 33.

The class midpoint for the class 37-43 is 40.

To find the class width of the frequency distribution, we need to determine the range of each age class. The range is the difference between the upper and lower boundaries of each class. Looking at the table, we can see that the class boundaries are as follows:

23-29

30-36

37-43

For the class 23-29, the lower boundary is 23 and the upper boundary is 29. To find the class width, we subtract the lower boundary from the upper boundary:

Class width = 29 - 23 = 6

So, the class width for the frequency distribution is 6.

To find the class midpoint for each class, we take the average of the lower and upper boundaries of each class.

For the class 23-29:

Class midpoint = (23 + 29) / 2 = 52 / 2 = 26

For the class 30-36:

Class midpoint = (30 + 36) / 2 = 66 / 2 = 33

For the class 37-43:

Class midpoint = (37 + 43) / 2 = 80 / 2 = 40

So, the class midpoint for the class 23-29 is 26, for the class 30-36 is 33, and for the class 37-43 is 40.

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Given statement solution is :- a) The area of one semi-circle at one end is  58.09 square feet.

b) The area of the garden is 274.42 square feet.

c) The area in square metres is approximately 58.09 square feet.

The area of the garden is approximately 274.42 square feet, and the area in square meters is approximately 25.49 square meters.

a) To find the area of one semi-circle at one end, we need to calculate the area of a complete circle and then divide it by 2. The formula for the area of a circle is A = πr², where A represents the area and r is the radius.

Since the diameter of the semi-circle is equal to the width of the rectangular portion, which is 8.6 feet, the radius will be half of that, which is 8.6 / 2 = 4.3 feet.

Now we can calculate the area of the semi-circle:

A = (π * 4.3²) / 2

A ≈ 58.09 square feet

b) To find the area of the garden, we need to sum the area of the rectangular portion with the areas of the two semi-circles.

Area of the rectangular portion = length * width

Area of the rectangular portion = 18.4 feet * 8.6 feet

Area of the rectangular portion ≈ 158.24 square feet

Area of the two semi-circles = 2 * (area of one semi-circle)

Area of the two semi-circles ≈ 2 * 58.09 square feet

Area of the two semi-circles ≈ 116.18 square feet

Total area of the garden = area of the rectangular portion + area of the two semi-circles

Total area of the garden ≈ 158.24 square feet + 116.18 square feet

Total area of the garden ≈ 274.42 square feet

c) To convert the area from square feet to square meters, we need to know the conversion factor. Since 1 foot is approximately 0.3048 meters, we can use this conversion factor to convert the area.

Area in square meters = Total area of the garden * (0.3048)²

Area in square meters ≈ 274.42 square feet * 0.3048²

Area in square meters ≈ 25.49 square meters

Therefore, the area of one semi-circle at one end is approximately 58.09 square feet. The area of the garden is approximately 274.42 square feet, and the area in square meters is approximately 25.49 square meters.

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Answer:

y-1= -1/3(x+3)

Step-by-step explanation:

y-y1=m(x-x1)

y-1=m(x+3)

the slope is rise over run

the slope is -1/3

Answer:

y - 1 = 3/2 (x + 3)

Step-by-step explanation:

To find the equation of a line parallel to the given line and passing through the point (-3, 1), we can use the point-slope form of a linear equation. The point-slope form is given by:

y - y₁ = m(x - x₁)

Where (x₁, y₁) is the given point and m is the slope of the line.

First, let's calculate the slope of the given line using the two points (-2, -4) and (2, 2):

slope = (y₂ - y₁) / (x₂ - x₁)

= (2 - (-4)) / (2 - (-2))

= 6 / 4

= 3/2

Since the line we want to find is parallel to the given line, it will have the same slope. Therefore, the slope (m) of the new line is also 3/2.

Now we can substitute the values into the point-slope form using the point (-3, 1):

y - 1 = (3/2)(x - (-3))

y - 1 = (3/2)(x + 3)

The equation in point-slope form of the line parallel to the given line and passing through the point (-3, 1) is:

y - 1 = 3/2 (x + 3)

Answer:

The answer is

Step-by-step explanation:

Usng the formula

\(A(n) = 3(2) ^{n - 1} \)

Where n is the number of terms

For the first term

\(A(1) = 3(2)^{1 - 1} \\ = 3(2) ^{0} \\ = 3(1) \\ \\ = 3\)

For the fourth term

\(A(4) = 3(2)^{4 - 1} \\ = 3 ({2})^{3} \\ = 3 \times 8 \\ \\ = 24\)

For the eighth term

\(A(8) = 3 ({2})^{8 - 1} \\ = 3 ({2})^{7} \\ = 3(128) \\ \\ = 384\)

Hope this helps you

Answer: –3; –24; –384

Step-by-step explanation: