Huilan is 11 years younger than Thomas. The sum of their ages is 31. What is Thomas's age?
years old

Answer:

Based on the information given, we know that angles 3 and 4 are supplementary (they add up to 180 degrees) and angles 2 and 4 are vertical angles (they are congruent). Therefore, we can write:

m∠4 + m∠3 = 180 (since angles 3 and 4 are supplementary)

m∠4 = m∠2 (since angles 2 and 4 are vertical angles)

Substituting m∠4 = m∠2 into the first equation, we get:

m∠2 + m∠3 = 180

Now we can solve for m∠2 and m∠3:

m∠3 = 43 (given)

m∠2 = 180 - m∠3 = 180 - 43 = 137

Since angles 1 and 2 are also supplementary, we can find m∠1 by subtracting m∠2 from 180:

m∠1 = 180 - m∠2 = 180 - 137 = 43

Therefore, m∠1 = 43 degrees and m∠2 = 137 degrees.

Increasing 2400 by 5% gives us 2520

we can increase the value by using the formula:

\(initial value+ percentage increase *initial value\) = increased percentage

in the aforementioned question we have

initial value = 2400

percentage increase = 5%

thus we can find out the increased percentage by:

2400 + 2400 X (5/100)

=2400 + 120

=2520

the value by which 2400 is increased is 120

to arrive at the increased value which is 2520

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Question 6

\(\left(\frac{-7-2}{2}, \frac{-10-3}{2} \right)=(-4.5, -6.5)\)

Question 7

\(\left(\frac{-4+8}{2}, \frac{-3+2}{2} \right)=(2, -0.5)\)

Therefore , the solution of the given problem of function comes out to be g(x) is given by g(x) = (x-4)² + 6

The study of numbers, their variations, mathematics and the regional tissue, structures, and both their actual and imagined locations, is known as mathematics. A function is a mathematical representation of the relationship between a set of inputs, each of which has an associated output. A function is a group of inputs that, when combined, result in a single, recognized output for each input. Each function is given a city, town, or scope, which is frequently referred to as a realm.

Here,

Given the graph of the original function f(x), whose vertex is at (0, 0), and indeed the graph of the translating function g(x), whose vertex is at (0, 0), (5, 2).

Be aware that the translated function's vertex is 2 units higher and 5 units to the right of the f graph's graph (x).

The function f(x) is then translated 5 units toward the right и 2 units up to arrive at g(x).

Recall that provided a function, f(x), is characterized as a parabola with a vertex at (h, k).

=> f(x) = (x-h)² + k

The outcome of translating a unit to the right with b unit up is

=>f'(x) = (x-h-a)² + k + b

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There were 8 slices in the whole pizza.

An equation means the formula that expresses the equality of two expressions by connecting them with the equals sign =.  Let us assume the number of slices in the whole pizza is "x".

Since Jim ate two slices which is 25% of the pizza, we will set up the equation:

2 = 0.25x

To solve for "x":

2 / 0.25 = x

x = 8.

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The coordinates of point E are found as (1/3, 8/3).

The given coordinates of the point are-

D(-2,-5) = (x₁, y₁)

F(5,3) = (x₂, y₂)

The section formula for point is given as;

E(x, y) =>

x =(mx₂ + nx₁)/(m + n)

y = (my₂ + ny₁)/(m + n)

The ratio is given as;  DF: FE = 4:2

Thus, m = 4 and n = 2

Put the given values and find the coordinates of point E

x =(mx₂ + nx₁)/(m + n)

x = (4×5 + 2×(-2))/(4 + 2)

x = 16/6

x = 8/3

y = (my₂ + ny₁)/(m + n)

y = (4×3 + 2×(-5))/(4 + 2)

y = 2/6

y = 1/3

Thus, the coordinates of the point E are (8/3, 1/3).

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The correct question is-

Point Flies on segment DE. The coordinates of point D are (-2,-5). The coordinates of point F are (5,3). If DF: FE= 4:2, what are the

coordinates of point E?

(3,5)

O (9,2)

0 (2)

O (1/3, 8/3)

Answer:(8.5,7)

Step-by-step

The value of f(-0.01) is approximately 0.99005.

To evaluate f(-0.01), we substitute -0.01 into the function f(x) = (1+x)^(1/x). Thus, we have f(-0.01) = (1+(-0.01))^(1/(-0.01)).

Using a calculator, we simplify this expression to f(-0.01) = 0.99005. Therefore, the value of f(-0.01) rounded to five decimal places is approximately 0.99005.

The function f(x) = (1+x)^(1/x) represents an exponential function with a variable exponent. In this case, we are evaluating the function at x = -0.01.

By substituting this value into the function and performing the necessary calculations, we find that f(-0.01) is approximately 0.99005. This means that when x is equal to -0.01, the function value is approximately 0.99005.

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The volume of the container is approximately 12.9516 cubic meters when rounded to the nearest hundredth.

To find the volume of the container, we need to multiply its length, width, and height. Let's convert the given measurements to meters to ensure consistent units.

The length of the container is 2.76 meters.

The width of the container is 23.5 decimeters, which is equal to 2.35 meters (since 1 decimeter = 0.1 meters).

The height of the container is 196 centimeters, which is equal to 1.96 meters (since 1 meter = 100 centimeters).

Now we can calculate the volume of the container:

Volume = Length × Width × Height

Volume = 2.76 meters × 2.35 meters × 1.96 meters

Volume ≈ 12.9516 cubic meters (rounded to four decimal places)

Therefore, the volume of the container is approximately 12.9516 cubic meters when rounded to the nearest hundredth.

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Answer:

5(8-m)

5 x 8 = 40

5 x m = 5m

40-5m

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

An arithmetic sequence has a common difference d between consecutive terms.

Sequence a

30 - 10 = 20

90 - 30 = 60

270 - 90 = 180

This sequence is not arithmetic

Sequence b

200 - 100 = 100

300 - 200 = 100

400 - 300 = 100

This sequence is arithmetic but is finite, that is last term is 400

Sequence c

300 - 150 = 150

450 - 300 = 150

600 - 450 = 150

This sequence is arithmetic and infinite, indicated by ........ within set

Sequence d

2 - 1 = 1

4 - 2 = 2

8 - 4 = 4

This sequence is not arithmetic

Thus the infinite arithmetic sequence is sequence c

Answer:

$45,900

Step-by-step explanation:

Answer:

$73.04

Step-by-step explanation:

362.41-289.37=73.04

Answer:

The expression that represents how much more Elena spent is $3.2 + p

Step-by-step explanation:

Hey there!

\( \rightarrow \sf{ r = \sqrt{3 \frac{v}{\pi \ h} }} \: \rm{or} \: \sf{v = \frac{1}{3} \pi \: {r}^{2} \times h}\)

\( \rightarrow \sf{923.16 = \frac{1}{3} (3.14) {r}^{2} \times h}\)

\( \rightarrow \sf{\: 1.046667 {hr}^{2} =923.16}\)

\( \rightarrow \sf{ \frac{1.046667 {hr}^{2} }{1.046667} = \frac{923.16}{1.046667} }\)

\( \rightarrow \: \sf{ {r}^{2} = \frac{923.16}{1.046667h}}\)

\( \rightarrow \: \sf{ r = \sqrt{ \frac{923.16}{1.046667h}}}\)

A and B are mutually exclusive events

The correct answer is yes

What are mutually exclusive events?

Two events are mutually exclusive in statistics and probability theory if they cannot happen simultaneously. A coin toss is the most basic illustration of two events that cannot coexist. The result of tossing a coin can be either heads or tails, but neither outcome can happen at the same time.

We are given that Amanda has 5 office assistants.

Events A is the event that at least 4 of them are men. this means that there is at most 1 female assistant

Events B is the event that at least 4 of them are women. this means that there is at most 1 male assistant.

Now one of the conditions is possible but both at the same time is not possible

Hence the both events are mutually exclusive.

The correct answer is yes

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Answer:

c<190

Step-by-step explanation:

Step 1: Subtract 670 from both sides.

7c+670−670<2000−670

7c<1330

Step 2: Divide both sides by 7.

7c  7 <

1330

7

anyways thjis would be the answer c<190

Answer:

Step-by-step explanation:

I believe its either c

So just look at each expression carefully 2 books per student their are 6,7 tables full of students so those will be mutiplied by 2 sooner or later and the rest you can figure it out very easily

The probability that more than 2 students will attend is 0.9179.

Part (a) List the values that X may take on.

X may take on the values 0, 1, 2, 3, ..., 13.

Part (b) Give the distribution of X.

The distribution of X can be represented as follows: X-0:0, 1:0.23, 2:0.23, 3:0.23, 4:0.23, 5:0.23, 6:0.23, 7:0.23, 8:0.23, 9:0.23, 10:0.23, 11:0.23, 12:0.23, 13:0.23

Part (c) How many of the 13 students do we expect to attend the festivities? (Round your answer to the nearest whole number.)

We can expect 3 students to attend the festivities.

Part (d) Find the probability that at most 3 students will attend. (Round your answer to four decimal places.)

The probability that at most 3 students will attend is 0.6923.

Part (e) Find the probability that more than 2 students will attend. (Round your answer to four decimal places.)

The probability that more than 2 students will attend is 0.9179.

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Answer:

The answer is 23

Step-by-step explanation:

8 · 2=16+7=23

Answer:

23

Step-by-step explanation:

1. Calculate the action in () 8*2 =16

2. Sum 7 + 16 = 23

Answer:

6/35

Step-by-step explanation:

2/5x3/7

Multiply Numerators and Denominators

= 6/35

You can't further simplify so the answer is 6/35.

Answer:

6/35

Step-by-step explanation:

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The component form of AB with initial point A(8, -2) and terminal point B(-2, -2) is (-10, 0).

To find the component form of vector AB with initial point A(8, -2) and terminal point B(-2, -2), we need to subtract the coordinates of point A from the coordinates of point B.

Let's calculate the components:

The x-component of AB is obtained by subtracting the x-coordinate of point A from the x-coordinate of point B:

x-component = x-coordinate of B - x-coordinate of A

= -2 - 8

= -10

The y-component of AB is obtained by subtracting the y-coordinate of point A from the y-coordinate of point B:

y-component = y-coordinate of B - y-coordinate of A

= -2 - (-2)

= -2 + 2

= 0

In vector notation, we can represent vector AB as AB = (-10, 0), where the x-component represents the horizontal displacement and the y-component represents the vertical displacement from point A to point B.

Geometrically, the vector AB can be visualized as the directed line segment from point A to point B, with a horizontal displacement of -10 units and no vertical displacement (0 units). The negative sign indicates that the direction of AB is from right to left along the x-axis.

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Answer:

-6

Step-by-step explanation:

27 - 1.5x ≤ 36

54 - 3x ≤ 72

54 - 72 ≤3x

-18 ≤ 3x

-6 ≤ x

x ≥ -6          Hope this helped and sorry if its wrong

It has no solution. There's the graph just in case

Answer:

No solution.

Step-by-step explanation:

First, we must convert the first equation (-6x+3y = 12) into y=mx+b form so we can graph it.

There are two ways to convert the first equation to y=mx +b. By substitution or by elimination. For this, I will do substitution.

Solving by substitution means you replace one of the variables so all the terms are equal and can be solved.

Thankfully, we know that y is equal to 2x +1, so in place of y, we can replace it with 2x + 1.

\(-6x+3(2x+1)=12\)

Now, lets merge and solve for X!

\(-6x+3(2x+1)=12\\-6x+6x+3=12\\3=12\\\)

Hmm...that alone means that there actually isn't a solution since 3 and 12 does not equal each other.

There is no solution to this system of linear equations.

The solution is Option A.

The coordinate of the triangle after the translation is given by A' ( 0 , -3 ) with 4 units right and 4 units down

A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.

Given data ,

Let the coordinate of the triangle be represented as A

Now , the coordinate A = A ( -4 , 1 )

Now , the coordinate of the triangle after translation is A' ( 0 , -3 )

when there is a translation of the coordinate A by 4 units to the right , we get

A to 4 units right = A ( -4 + 4 , 1 )

The new coordinate of A = A ( 0 ,  1 )

Now , A to 4 units down , we get

The coordinate of A' = A' ( 0 , 1 - 4 )

The coordinate of A' = A' ( 0 , -3 )

Hence , the translated coordinate is A' ( 0 , -3 )

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Angle ∠EBD is congruent to angle ∠DBA. Option D is the true statement.

An angle bisector is the line segment that bisects the angle into two equal halves.

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

Here,

Ray BE is a bisector of angle CBA,

∠CBE = ∠EBA = 60°

∠EBD = ∠EBA - ∠DBA

∠EBD = 60 - 30 = 30

So,

∠EBD = ∠DBA [DB becomes angle bisector of angle EBA]

Thus, ∠EBD is congruent with ∠DBA is the only correct answer among the option.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

Which of the following statements is true if ray BE is a bisector of angle CBA?

A. Ray BD is a bisector of angle CBA.

B. ∠EBD is congruent to ∠CBE.

C. Ray BE is a bisector of angle ABE.

D. ∠EBD is congruent to ∠DBA.

Answer:

what do you mean by land ?

The intensity of sound is proportional to the square of its amplitude.

Thus, if I9 and I8 are the intensities of sounds at 9 decibels and 8 decibels respectively, then:

I9/I8 = (10^(9/10))/(10^(8/10))

I9/I8 = 10^(0.1)

I9/I8 = 1.2589

Therefore, the relative intensity of 9 decibels is approximately 1.26 times higher than that of 8 decibels.

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x = 3/5 * 1 + 2/5 * 11 = 3/5 + 22/5 = 25/5 = 5

y = 3/5 * 1 + 2/5 * 6 = 3/5 + 12/5 = 15/5 = 3

So the point 2/5 of the way between (1, 1) and (11, 6) is (5, 3).

Answer:

5/3

Step-by-step explanation:

ust took test