Select the correct number from each drop-down menu to complete the equation. ​ 7 8 − ( − 2 + 3 4 ) = 8 7 ​ −( − 2+ 4 3 ​ )= ( + ) + 7 8 + 8 7 ​

Step-by-step explanation:

1.

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

(6 -8) = m(1 -(-2))

-2 = 3m

m = -2/3

2.

slope = ∆y/∆x

slope = (8 -6)/(-2 -1)

slope = 2/-3

Now to find the full expression let's substitute the values of x and y using the slope:

6 = 1×2/-3 + b

6 = 2/-3 +b

b = 6 - 2/-3

b = 16/3

So the expression is:

y = 2x/-3 + 16/3

Answer: 38 degrees

Step-by-step explanation:

HZJ and FZG are congruent angles so then that means that they are the same 38 degrees.

The equation of the osculating plane is 24x + 12√10(y-π) - 3z - 6π√10 = 0.

Given curve,  x=5sin(3t), y=t, z=5cos(3t); (0, π,-5).

To find the normal plane equation, the unit normal vector of the curve at the point must first be found. The unit tangent and unit binormal vectors are both derived from the unit tangent vector.

To calculate the tangent vector, the following steps are taken:

Equation of the curve is given as,

x=5sin(3t),

y=t,

z=5cos(3t).

Differentiating above equation with respect to t, we get;

dx/dt = 15 cos(3t)

dy/dt = 1

dz/dt = -15 sin(3t)

The unit tangent vector T is given by,

T = 1/√(dx/dt² + dy/dt² + dz/dt²) (dx/dt i + dy/dt j + dz/dt k)

Substituting the given values, we get

T = (3√10/10) i + (1/√10) j - (3/√10) k

Since we have to find the normal vector, we will differentiate the unit tangent vector,T, to get the unit normal vector N.

Let's differentiate T to obtain N:

dn/dt = 1/√(dx/dt² + dy/dt² + dz/dt²) [d²x/dt² i + d²y/dt² j + d²z/dt² k] + {(-1/2)(2t)(2t')/√(dx/dt² + dy/dt² + dz/dt²)³} [dx/dt i + dy/dt j + dz/dt k]

On substituting, we get,

N = (-9/√10) i + (3√10/10) j + (9/√10) k

Therefore, the normal plane equation is given by,(-9/√10)(x) + (3√10/10)(y-π) + (9/√10)(z+5) = 0.

To find the osculating plane equation, the coordinates of the point of tangency (P) and the principal normal vector, N, are required.

The equation of the osculating plane is then written as follows:

xT + yN = c,

where c is a constant value that is calculated by substituting the coordinates of P into the equation.Let us calculate the value of P and N,

To find the value of P, we substitute t=π in the given curve,

Thus,

x(π) = 5sin(3π) = 0,y(π) = π,z(π) = 5cos(3π) = -5

Therefore, the point of tangency P is (0, π, -5).

From the above derivation, we know that the unit normal vector N is(-9/√10) i + (3√10/10) j + (9/√10) k

Therefore, the unit principal normal vector is given by,

B = T x N= [(3√10/10) i + (1/√10) j - (3/√10) k] x [- (9/√10) i + (3√10/10) j + (9/√10) k]

= [(3√10/10) (9/√10) + (3/√10) (3/√10)] i + [(9/√10) (1/√10) - (3√10/10) (- 3/√10)] j + [(1/√10) (- 3/√10) - (3√10/10) (3√10/10)] k

= (24/√10) i + (12√10/10) j - (3/√10) k

The osculating plane equation is given by,

xT + yB = c

Now substituting x=0, y=π and z=-5 in above equation, we get

c = π(12√10/10) = (6π√10/5)

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Answer:

mk lets dk this. also remember don't get stressed over stuff like this! you got it!

Step-by-step explanation:

1) 5

2) 3

3) 6

4) 5

5) 9

6) 8

7) 3

because there were so many I didn't include the work but if you need work for one of them I can give you!

1. x = 5

2. y = 3

3. x = 6

4. y = 5

5. y = 9

6. w = 8

7. x = 3

The series Σ(9n + 1) is a divergent series.

To determine the convergence or divergence of the series Σ(9n + 1), we can use the Integral Test or compare it to a p-series. Let's use the Integral Test to analyze the series.

The Integral Test states that if f(x) is positive, continuous, and decreasing on the interval [1, ∞), and if a(n) = f(n), then the series Σa(n) converges if and only if the improper integral ∫f(x)dx from 1 to ∞ converges.

In this case, a(n) = 9n + 1. To check the convergence, we can evaluate the integral ∫(9x + 1)dx from 1 to ∞.

∫(9x + 1)dx = (9/2)x^2 + x + C

Now, we need to evaluate the integral from 1 to ∞:

∫(9x + 1)dx evaluated from 1 to ∞ = lim as b approaches ∞ [(9/2)b^2 + b + C] - [(9/2) + 1 + C]

Taking the limit, we have:

lim as b approaches ∞ [(9/2)b^2 + b + C] - [(9/2) + 1 + C] = ∞

Since the improper integral diverges, the series Σ(9n + 1) also diverges. Therefore, the series is not convergent.

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An equivalent expression to the given expression 36x³ – 64xy² is 4x(3x + 4y)(3x - 4y) respectively.

An expression, also known as a mathematical expression, is a finite collection of symbols that are correctly formed in accordance with context-dependent requirements.

A statement, at least two variables or integers, and one or more arithmetic operations make up a mathematical expression.

This mathematical procedure makes it possible to multiply, divide, add, or subtract quantities.

So, the equivalent expression would be:

We have the expression as follows: 36x³ – 64xy²

Now, calculate as follows:

= 36x³ – 64xy²

= 4x(9x² - 16y²)

= 4x(3x + 4y)(3x - 4y)

Therefore, an equivalent expression to the given expression 36x³ – 64xy² is 4x(3x + 4y)(3x - 4y) respectively.

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Correct question:

Write an expression that is equivalent to the expression 36x³ – 64xy².

Answer

Sorry but you didn’t put a table but at least I can answer this a table can be shown by following the same rule by adding, subtracting, multiplication or division. yeah thats right

Step-by-step explanation:

cant not solve unless u explain

Answer:

97

Step-by-step explanation:

< LMN = 33

The sum of the interior angles equal 180

180 - 92 - 55 = 33

<QM (can't read the last letter 50

180 - 45 - 85 = 50

<LMQ This is a straight angle and straight angles are 180

180 - 33 -50 = 97

The answer is ,  the Taylor series (centered at c=0) for the function f(x) = e^(4x) is given by:

\($$\large f(x) = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n$$\)

The Taylor series expansion is a way to represent a function as an infinite sum of terms that depend on the function's derivatives.

The Taylor series of a function f(x) centered at c is given by the formula:

\(\large f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(c)}{n!}(x-c)^n\)

Using the definition of Taylor series to find the Taylor series (centered at c=0) for the function f(x) = e^(4x), we have:

\(\large e^{4x} = \sum_{n=0}^{\infty} \frac{e^{4(0)}}{n!}(x-0)^n\)

\(\large e^{4x} = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n\)

Therefore, the Taylor series (centered at c=0) for the function f(x) = e^(4x) is given by:

\($$\large f(x) = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n$$\)

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The Taylor series for f(x) = e^(4x) centered at c = 0 is:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

To find the Taylor series for the function f(x) = e^(4x) centered at c = 0, we can use the definition of the Taylor series. The general formula for the Taylor series expansion of a function f(x) centered at c is given by:

f(x) = f(c) + f'(c)(x - c) + f''(c)(x - c)^2/2! + f'''(c)(x - c)^3/3! + ...

First, let's find the derivatives of f(x) = e^(4x):

f'(x) = d/dx(e^(4x)) = 4e^(4x)

f''(x) = d^2/dx^2(e^(4x)) = 16e^(4x)

f'''(x) = d^3/dx^3(e^(4x)) = 64e^(4x)

Now, let's evaluate these derivatives at x = c = 0:

f(0) = e^(4*0) = e^0 = 1

f'(0) = 4e^(4*0) = 4e^0 = 4

f''(0) = 16e^(4*0) = 16e^0 = 16

f'''(0) = 64e^(4*0) = 64e^0 = 64

Now we can write the Taylor series expansion:

f(x) = f(0) + f'(0)(x - 0) + f''(0)(x - 0)^2/2! + f'''(0)(x - 0)^3/3! + ...

Substituting the values we found:

f(x) = 1 + 4x + 16x^2/2! + 64x^3/3! + ...

Simplifying the terms:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

Therefore, the Taylor series for f(x) = e^(4x) centered at c = 0 is:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

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a) True, b) False, c) False, d) True, e) False, f) False, g) True

a) The statement is true. The symbol "∅" represents the empty set, which does not contain any elements. Since 0 is not an element of the empty set, the statement "0 ∈ ∅" is false.

b) The statement is false. The symbol "{0}" represents a set containing the element 0. The empty set, represented by "∅", does not contain any elements. Therefore, the empty set is not an element of the set {0}.

c) The statement is false. The symbol "{0}" represents a set containing the element 0. However, the empty set, represented by "∅", does not contain any elements. Therefore, the set {0} is not a subset of the empty set.

d) The statement is true. The empty set, represented by "∅", does not contain any elements. Every set is a subset of the empty set, including the set {0}.

e) The statement is false. The symbol "{0}" represents a set containing the element 0. In this case, {0} is not an element of itself. Therefore, the statement "{0}∈{0}" is false.

f) The statement is false. The symbol "{0}" represents a set containing the element 0. In this case, {0} is not a proper subset of itself. Therefore, the statement "{0}⊂{0}" is false.

g) The statement is true. The symbol "{∅}" represents a set containing the empty set. In this case, {∅} is a subset of itself because it contains the element ∅. Therefore, the statement "{∅} ⊆ {∅}" is true.

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Answer:

8648.6

Step-by-step explanation:

This is because the cost is $8300, so to add interest, you would multiply it by 1 plus the percent of interest, so 8300*1.042 would be 8648.6:)

Salma can therefore rent the vehicle for a maximum of 5 days and go 275 miles. When A rental car company charges $22. 50 per day to rent a car and $0. 10 for every mile driven. Salma wants to rent a car, knowing that: she plans to drive 275 miles. She has at most $140 to spend.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign (≠)" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

Given

Although your question is incomplete, you might be referring to the following in its entirety: Renting a car from a rental car agency costs $22.50 per day plus $0.10 every mile driven. Salma wants to rent a car because she knows she will go 275 kilometres. She can only spend up to $140. The number of days Salma can rent the car for while staying within her budget can be calculated by writing and solving an inequality.

The formula that solves this issue is:

Let x represent how many days Salma can afford to rent the automobile for.

Inequality

22.5x + 0.10(275) ≤ 140

22.5x + 2.75 ≤ 140

22.5x ≤ 140 - 2.75

22.5x ≤ 137.25

x ≤ 5

automobile rental on a daily basis get x <= 5

Salma can therefore rent the vehicle for a maximum of 5 days and go 275 miles.

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Using the Mean and median formulae ,

The difference between the mean and median score of the students' scores on this quiz is 3.

Mean : The mean is the number which we get by dividing the sum of a set of values by the number of values in the set.

Median: the median is the middle number in a set of values when those values are arranged in either ascending or descending order.

let us consider there are a total 100 students.

and X denotes the marks obtained by students.

We have given that,

10% of student scored 70 points i.e.,

P(X=70) = 10% of 100 = 10

35% of students scored 80 points i.e., number of students whose obtained 80 points

= 35% of 100 = 35

30% of students scored 90 points , number of students whose obtained 90 points

= 30% of 100 = 30

remained ( 25%) of students scored 100 points

= 100 - 10 - 35 - 30 = 25

total marks obtained by students

= 80+70+90+100

= 340

Mean of score of students'scores on the quiz

= (70×10+ 80×35 + 90×30 + 100×25)/100 = 87

when we arranged the in ascending students in order , the 50th and 51th student lies in middle and marks obtained by both (50th and 51th) is 90 points .

So, Median score of the students' scores on this quiz = 90

Now, we shall calculate the difference between mean and median of score of the students' scores on this quiz which is equal to( 90 -87)

= 3

Hence, difference between the mean and median score of the students' scores on this quiz = 3

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Answer:

  134 square feet

Step-by-step explanation:

You want to know the area of the composite shape shown in the figure.

The figure can be divided by two horizontal lines into two trapezoids and a parallelogram. (See the first attachment.) The area formulas for these are ...

  A = 1/2(b1 +b2)h . . . . . trapezoid with bases b1, b2

  A = bh . . . . . . . . . . . parallelogram with base b

Each of the horizontal sections in the figure is 4 feet high.

The top trapezoid has an area of ...

  A = 1/2(5 +11)(4) = 32 . . . . square feet

The middle parallelogram has an area of ...

  A = (11)(4) = 44 . . . . square feet

The bottom trapezoid has an area of ...

  A= 1/2(16 +13)(4) = 58 . . . . square feet

The total area is ...

  (32 +44 +58) ft² = 134 ft²

Desiree needs to cover 134 square feet.

__

Additional comment

The 5' diagonal measures are not used in the computation. They can help you see that all of the right triangles in the figure are 3-4-5 right triangles. (The hexagonal shape is not a regular hexagon.)

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Total number of permutations of abcde in which the first character is a, b, or c and the last character is c, d, or e is 48 permutations.

Case 1 : First letter is "a", last letter is any of {c, d, e}. Hence there are 3!  ways of arranging the remaining three letters

3! * 3 = 18 combinations.

Case 2 : First letter is "b", last letter is any of {c, d, e}. Hence there are 3!  ways of arranging the remaining three letters

3! * 3 = 18 combinations.

Case 3 : First letter is "c", last letter is any of {d, e}. Hence there are 3! ways of arranging the remaining two letters

3! * 2 = 12 combinations.

Hence, total number of combinations = 18 +18 + 12 = 48 permutations.

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Jacquelyn added the numbers 249 and 3922 to obtain a sum of 4171.

To determine which equation represents the sum of the two numbers that Jacquelyn added, we need to find the equation that results in a sum of 4171.

Let's evaluate each equation:

1. 248 + 3922 = 4170

2. 249 + 3922 = 4171

3. 259 + 3922 = 4181

Out of the three equations, only the second equation, 249 + 3922, results in a sum of 4171. Therefore, the correct equation is:

249 + 3922 = 4171

Thus, Jacquelyn added the numbers 249 and 3922 to obtain a sum of 4171.

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Answer:

They are all acute triangles or iscoles triangles

Step-by-step explanation:

y intercept: 80, it means that peyton sells 0 dollars worth of computer on a day, she just makes a base pay amount that day.

A mathematical declaration that two mathematical expressions are equal is the definition of an equation in algebra in its most basic form. An equation where the components 3x + 5 and 14 are separated by the equal sign, such as 3x + 5 = 14, is an illustration of this.

In the equation ,

y=mx+b, m is the slob and b is the y intercept

For, P = 0. 025x+80p=0. 025x+80

The y intercept is 80.

it means that peyton sells 0 dollars worth of computer on a day, she just makes a base pay amount that day.

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Answer:

Depth of the submarine = 668.09 feet

Step-by-step explanation:

From the figure attached,

In triangle ABC,

Distance between a navy cruiser and a nuclear submarine = 2500 feet

Angle between the water level and the submarine = 15.5°

By applying sine rule in the given triangle,

sin(∠BAC)° = \(\frac{BC}{AC}\)

sin(15.5°) = \(\frac{BC}{2500}\)

BC = 2500[sin(15.5)]

BC = 668.09 feet

Therefore, submarine is 668.09 feet deep in the sea.

Answer:

D. x^2-x-9-12/x-2

Step-by-step explanation:

We can use synthetic division to divide (x^3 - 3x^2 - 7x + 6) by (x - 2). First, we set up the division as follows:

    2 |   1   -3   -7    6

       |______2___-2__-18

       | 1   -1   -9  -12

The numbers on the bottom row of the synthetic division table represent the coefficients of the quotient polynomial. Therefore, the quotient is x^2 - x - 9, and the remainder is -12.

So, we have:

(x^3 - 3x^2 - 7x + 6) / (x - 2) = x^2 - x - 9 + (-12 / x - 2)

Therefore, the correct option is D: x^2 - x - 9 - 12/(x - 2).

Answer:

b. 84.612cm

c. 314.15cm

d. 5cm

Step-by-step explanation:

b. solve for both triangles and height of rectangle using Sin

c. pi(r)h  3.1415(10)(10)

d. 3*3-2*2=5

Answer:

24 sq. in

Step-by-step explanation:

your formula is A=h(b/2)

h=8

b=2

A=?

A=8(6/2)

A=8(3)

A=24

Psychologists theorize that the mean time on the test for non-schizophrenics (1) will be less than the mean time for schizophrenics (2).

We have two groups: schizophrenics and non-schizophrenics. The time spent on the psychological test is used as a measure of cognitive function.

Let's denote the mean time for schizophrenics as μ2 and the mean time for non-schizophrenics as μ1.

According to the psychologist's theory, they expect μ1 < μ2, meaning that the mean time for non-schizophrenics will be less than the mean time for schizophrenics.

This hypothesis can be tested using statistical analysis such as a t-test or a hypothesis test comparing the means of two independent groups.

Based on the psychologist's theory, they anticipate that the mean time on the psychological test for non-schizophrenics will be lower than the mean time for schizophrenics. Statistical analysis can be conducted to test this hypothesis and determine if there is evidence to support the theory.

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Answer: 625

Step-by-step explanation:

Let x be the total number of readers have newspaper.

Given: 8% of x = 50  

Since 8% = 0.08  [we divide percent by 100yo convert it in decimal ]

So, 0.08x =50

\(\Rightarrow\ x=\dfrac{50}{0.08}=\dfrac{5000}{8}\)

\(\Rightarrow\ x= 625\)

Hence,  the total number of readers have newspaper = 625

Find the direct proportion:

28/7 = 4

When F is known divide it by the proportion to get a:

A = 40/4

A = 10

Answer:

To regroup means to rearrange groups in place value to carry out an operation.

Answer:$

$3.97

Step-by-step explanation:

Answer:

$3.48+9¢=$3.57

Step-by-step explanation:

i added 48 cents to 9 cents

Answer:

Step-by-step explanation:

√2+√2= 2√2=√8

-2√18+2√2= -2√9*2 +2√2= -6√2+2√2=-4√2=-√32