take a look at the following figure if angle B measures 78°, and is the measure of BDC?


a. 204 degree

b. 156 degree

c. 39 degree

d. 78 degree

Answer:

2750

Step-by-step explanation:

5500 ÷ 2 (multiplying by 50% is the same as dividing by 2)= 2750

50% of 5500 commuters is calculated as 2750. Hence, 2750 commuters carpool to work.

To find the number of commuters who carpool, we'll use a very basic principle in mathematics: percentage calculation. The problem states that 50% of the 5500 commuters carpool to work. To find the number of commuters carpooling, we multiply the total number of commuters by the percentage of those who carpool. In mathematical terms, it looks like this:(50/100) * 5500 = 2750. Therefore, 2750 commuters carpool to work.

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The number of mice in the field after 1 year is 221 mice.

Given data:

If the population of mice in the field grows exponentially, we can use the exponential growth formula to determine the future population.

The exponential growth formula is given by:

P(t) = P₀ * e^(kt)

Where:

P(t) is the population at time t,

P₀ is the initial population,

e is Euler's number (approximately 2.71828), and

k is the growth rate.

So, the initial population (P₀) is 3 mice, and after five months, the population (P(t)) is 18 mice.

18 = 3 * e^(5k)

Dividing both sides by 3, we get:

6 = e^(5k)

To solve for k, we can take the natural logarithm (ln) of both sides:

ln(6) = 5k

k = ln(6) / 5 ≈ 0.35835

So, the growth rate is k = 0.3583

Now that we have the growth rate, determine the population after 1 year (12 months).
Substituting the values into the formula:

P(12) = 3 * e^(0.35835 * 12)

Calculating this expression, we find:

P(12) ≈ 3 * e^(4.3) ≈ 3 * 73.699 ≈ 221.09

Hence, it is expected that there will be approximately 221 mice in the field after 1 year if the population grows exponentially.

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Final Answer:

After 1 year, the field is expected to have approximately 221 mice.

Explanation:

To solve this exponential growth problem, we'll use the exponential growth formula:
[tex]\[ P(t) = P_0 \times e^{rt} \][/tex]
where:
- [tex]\( P(t) \)[/tex] is the population at time t,
- [tex]\( P_0 \)[/tex] is the initial population size,
- r is the growth rate,
- e is Euler's number (approximately 2.71828),
- t is the time in consistent units.
We need to find the growth rate r using the information that we have (the initial population [tex]\( P_0 \)[/tex] is 3, and after 5 months,[tex]\( P(5) \)[/tex] is 18). Then, we'll calculate the population after 1 year (12 months).
Let's apply the given values to the formula at t = 5 months:
[tex]\[ 18 = 3 \times e^{5r} \][/tex]
Now we need to solve for r. We start by dividing both sides of the equation by 3:
[tex]\[ 6 = e^{5r} \][/tex]
Next, we take the natural logarithm (ln) of both sides to solve for r. The natural logarithm of [tex]\( e^{5r} \)[/tex] is equal to 5r:
[tex]\[ \ln(6) = 5r \][/tex]
Now we divide by 5:
[tex]\[ \frac{\ln(6)}{5} = r \][/tex]
We can use a calculator to find r. The natural logarithm of 6 is approximately 1.79176, so:
[tex]\[ r = \frac{1.79176}{5} \\\\\[ r \approx 0.358352 \][/tex]

Now that we have the monthly growth rate r, we can use it to find the population after 12 months. Plugging r, [tex]\( P_0 \)[/tex], and t = 12  months into the exponential growth formula, we get:
[tex]\[ P(12) = 3 \times e^{0.358352 \times 12} \][/tex]
Using a calculator, we compute the value of [tex]\( e^{0.358352 \times 12} \)[/tex], which is approximately [tex]\( e^{4.300224} \)[/tex].
[tex]\[ P(12) = 3 \times e^{4.300224} \][/tex]
Using a calculator to find [tex]\( e^{4.300224} \)[/tex], we get a value of approximately 73.699.
[tex]\[ P(12) = 3 \times 73.699 \\\\\[ P(12) \approx 221.097 \][/tex]
Since we can't have a fraction of a mouse, we would round to the nearest whole number.

Thus, after 1 year, the field is expected to have approximately 221 mice.

Answer:

A line parallel to this line will have slope 4/5.

Step-by-step explanation:

2 parallel lines will have the same slope.

y = mx + c is the general form of the slope-intercept formula of a line, the slope is given by m.

y = 4/5 x - 3

-we see by comparing the 2 equations that the slope of this line (m) is 4/5.

Final answer:

The slope of a line parallel to the one given by the equation y = 4/5x - 3 is 4/5. This maintains the definition that parallel lines have identical slopes.

Explanation:

The slope of a line that is parallel to the line represented by the equation y = 4/5x - 3 is 4/5. This is because parallel lines have the same slope. In the context of algebra and straight lines, the slope of a line is a measure of its steepness, commonly identified as 'm' in the slope-intercept form y = mx + b, where 'b' is the y-intercept. Each of the provided figures and examples illustrate that the slope of a straight line remains constant regardless of other changes.

Looking specifically at the equation y = 4/5x - 3, this is in slope-intercept form where the coefficient of 'x' is the slope, which is 4/5. Therefore, any parallel line would have the same slope of 4/5.

Answer:

x = 50.9

Step-by-step explanation:

35.6 = √(15.3²) + √(x²)

35.6 = 15.3 + x

x = 35.6 + 15.3

x = 50.9

Answer:

D

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

y - 3 = 4(x - 10) ← is in point- slope form

with slope m = 4

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{4}[/tex]

The perpendicular line passes through (- 3, 7), hence

y - 7 = - [tex]\frac{1}{4}[/tex](x - (- 3)), that is

y - 7 = - [tex]\frac{1}{4}[/tex](x + 3) → D

Answer:

C. 10,4

Step-by-step explanation:

Using the Law of Cosines [Solving for Angle Measures → cos<A = -a² + b² + c²\2bc, cos<B = a² - b² + c²\2ac, cos<C = a² + b² - c²\2ab; Solving for Sides → a² = b² + c² - 2bc cos<A, b² = c² + a² - 2ac cos<B, c² = b² + a² - 2ab cos<C], set up your triangle with your angles and sides OPPOSITE from each other.

Suggestion: make Side b 12 and Side a 6, leaving you with Side c to find. According to the problem and how you set up your triangle, <C can be 60°. This is how you should set it up:

c² = 36 + 144 - 144 cos 60°; 108 = c²

The reason being is because 6² is 36, 12² is 144, 2ab → 2[12][6] is 144, and cos 60° is ½. Putting this altogether will give you 108 = c². Obviously, the final step is to take the square root of 108, which rounded to the nearest tenth, is 10,4.

If you are ever in need of assistance, do not hesitate to let me know by subscribing to my channel [USERNAME: MATHEMATICS WIZARD], and as always, I am joyous to assist anyone at any time.

**Whenever you are solving for an angle using the Law of Cosines, towards your final answer, use the cos⁻¹ function to cancel the cos to isolate your angle measure.

Final answer:

Using the law of cosines with the given sides 6 cm and 12 cm and included angle of 60 degrees, the length of the third side is approximately 10.4 cm, corresponding with answer choice C.

Explanation:

To calculate the length of the third side of a triangle when two sides and the included angle are known, we can use the law of cosines. The law of cosines states that c² = a² + b² - 2abcos(C), where a and b are the lengths of the sides, C is the included angle, and c is the length of the third side opposite to angle C.

In this question, we have been given two sides of lengths 6 cm and 12 cm with an included angle of 60 degrees. Plugging these values into the law of cosines formula, we get c² = 6² + 12² - [tex]2\(\cdot\)6\(\cdot\)12\(\cos(60^\circ)\)[/tex].

Since [tex]\(\cos(60^\circ)\)[/tex] equals 0.5, the calculation simplifies to c² = 36 + 144 - 72 = 108. Taking the square root of both sides, we find that c ≈ 10.4 cm, which aligns with answer choice C.

Answer:

Definition of Point by Gray:

    A point is a location in a region.

→A point is smallest and simplest representation of any location or any thing or an object in two, three, or n-dimensional plane.

This can be explained in following way.

For a large enclosed room , Lighting a small bulb will represent a point.Similarly , stars in the sky appear as a point with respect to earth.Sun in the Universe can be  called as a point.

Answer:

A

Step-by-step explanation:

The statement uses the terms location and region that are defined based on an understanding of a point.

Brainliest Please

Have a nice day *smiley face emoji

1,2

1,3

1,4

1,5

2,1

2,3

2,4

2,5

3,1

3,2

3,4

3,5

4,1

4,2

4,3

4,5

5,1

5,2

5,3

5,4

20 looks like the number.

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The absolute value of  I-32I = 32

For given question,

We need to find the absolute value of -32

We know that, for any number 'a',

the absolute value of a is |a| = a (positive value)

|-32| = 32

Therefore,  the absolute value of  I-32I = 32

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Answer:

Difference = 2.25°

Step-by-step explanation:

Here we are given that at depth the Temperature T is inversely proportional to the depth x.

[tex]T[/tex] ∝ [tex]\frac{1}{x}[/tex]

[tex]T= 4500 \times \frac{1}{x}[/tex]

Where 4500 is constant

Now we have to find the difference in the temperature at 1200 mts and 3750 mts

1. x=1200

[tex]T= 4500 \times \frac{1}{x}[/tex]

[tex]T= 4500 \times \frac{1}{1200}[/tex]

[tex]T= 3.75[/tex]

2. x=3750

[tex]T= 4500 \times \frac{1}{x}[/tex]

[tex]T= 4500 \times \frac{1}{3750}[/tex]

[tex]T=1.2[/tex]

Hence Difference is

T = 3.75 -1.20

= 2.25

Therefore The difference of the temperature at 1200 mts and 3750 mts is T=2.25°

[tex]3x^2 - x+ 7 =0\\\Delta=(-1)^2-4\cdot3\cdot7=1-84=-83\\x\in\emptyset[/tex]

no real solutions

Answer:

$70

Step-by-step explanation:

10.50/ 3 = 3.5

3.5 times 20 =70

The answer is D!!!

y=6x^2-24x+16

Answer:

Option 4 - [tex]y=6x^2-24x+16[/tex]

Step-by-step explanation:

Given : The vertex form of the equation of a parabola is [tex]y=6(x-2)^2-8[/tex]

To find : What is the standard form of the equation?

Solution :

The vertex form of the equation of a parabola is [tex]y=6(x-2)^2-8[/tex]

We solve the equation to get standard form,

[tex]y=6(x^2-2^2-2(x)(2))-8[/tex]

[tex]y=6(x^2+4-4x)-8[/tex]

[tex]y=6x^2+24-24x-8[/tex]

[tex]y=6x^2-24x+16[/tex]

The standard form of the equation is [tex]y=6x^2-24x+16[/tex]

Therefore, Option 4 is correct.

Answer:

Option a) Hyperbola

Step-by-step explanation:

Answer:

The function is defined along the x-axis. Yes the equations y = 0 is a function

Step-by-step explanation:

It means that  y  is  0  in all values of  x

The graph y = 0 would be a horizontal line that overlaps the x-axis. This would be a function because the y-value (zero) never has the same x-value.  This means that it would pass the vertical line test since the graph would only pass through it once.

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

This is an acute triangle

Step-by-step explanation:

Pythagoras theorem is used to determine if a triangle is right, acute or obtuse

If the sum of squares of two shorter lengths is greater than the square of third side then the triangle is an acute triangle.

If the sum of squares of two shorter lengths is less than the square of third side then the triangle is an obtuse triangle.

If the sum of squares of two shorter lengths is equal the square of third side then the triangle is a right triangle.

so,

[tex](40)^2 = (37)^2 + (24)^2\\1600 = 1369+576\\1600<1945[/tex]

As 1600<1945, the given triangle is an acute triangle ..

Denise has conducted an observational study to learn about different influences that affect which colleges students choose to attend. Denise surveyed 400 students at her new college and found that 80% of the students chose their college based on a friend who also attends that college.

What conclusion can Denise make from her study?

A. There may be a link between knowing current students and choosing a college, and she can draw a cause-and-effect conclusion from an observational study.

B. There may be a link between knowing current students and choosing a college, but she cannot draw a cause-and-effect conclusion from an observational study.

C. Knowing a current student enrolled at a college causes incoming students to choose that college, but she cannot draw a cause-and-effect conclusion from an observational study.

D. Knowing a current student enrolled at a college causes incoming students to choose that college, and she can draw a cause-and-effect conclusion from an observational study.

The conclusion that Denise can make from her observational study is B. There may be a link between knowing current students and choosing a college.

An observational study is a study that observes individuals and measures variables of interest but doesn't influence the responses.

In this case, Denise has conducted an observational study to learn about different influences that affect which colleges students choose to attend.

Here, the conclusion that Denise can make from her study is that there may be a link between knowing current students and choosing a college even though she cannot draw a cause-and-effect conclusion from the study.

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To find the possible combinations of pens and notebooks Amanda can purchase, we need to consider her budget and the cost of each pen and notebook. The correct graph representing these combinations is Graph B.

To find the possible combinations of pens and notebooks that Amanda can purchase, we need to consider her budget and the cost of each pen and notebook.

Each pen costs $2 and each notebook costs $3.

Let's assume Amanda buys x number of pens and y number of notebooks.

So, the total cost of pens would be 2x and the total cost of notebooks would be 3y.

Given that Amanda has $30 to spend, we can set up the equation: 2x + 3y = 30.

To graph this equation, we can plot different points that satisfy this equation.

The graph that represents the possible combinations of pens and notebooks Amanda can purchase would be a line passing through points where the x-coordinate represents the number of pens and the y-coordinate represents the number of notebooks.

Answer: The correct graph is Graph B.

Amanda allocates $30 for pens and notebooks. Each pen costs $2, and each notebook is $3. The inequality 2P + 3N ≤ 30 is solved algebraically (P ≤ 15, N ≤ 10) and graphically, considering whole numbers for precision.

Amanda is limited to spending $30 on pens and notebooks. With each pen costing $2 and each notebook priced at $3, the total cost equation is C = 2P + 3N. The corresponding inequality is 2P + 3N ≤ 30.

Algebraically, solving for P and N involves finding values when N = 0 and when P = 0.

When N = 0:

2P ≤ 30

P ≤ 15

When P = 0:

3N ≤ 30

N ≤ 10

So, the solution is P ≤ 15 and N ≤ 10.

For a graphical representation:

Draw a coordinate plane.

Plot the points (15, 0) and (0, 10).

Shade the region below and to the left of the line formed by connecting these points.

The question probable may be:

Amanda only has $30 to buy pens and notebooks. Each pen costs $2. Each notebook costs $3.  write inequality showing the relationship and solve them also solve them graphically.

Answer:

X=1

Step-by-step explanation:

1. You subtract 6x with 9x so it should equal 2=3x-1

2.You add 1 to the 2 so it should be 3=3x

3.You divide 3 on both sides so it should be 3/3=3x/3

4.After you divide you finally get the answer 1=x or x=1

6x + 2 = 9x - 1

6x - 9x = - 1 - 2

-3x = -3

x = -3/-3

x = 1

Prove:

Let x = 1

6x + 2 = 9x - 1

6(1) + 2 = 9(1) - 1

6 + 2 = 9 - 1

8 = 8

It checks to be true.

The answer is x = 1.

Answer:

74mm

Step-by-step explanation:

296 divided by 4 sides is 74 mm each side

Answer:

X = 21

Step-by-step explanation:

X- 12 = 9

Add 12 to each side

X- 12+12 = 9+12

X = 21

Answer:

1/3

Step-by-step explanation:

Multiplicative inverse means we want to end up with 1

3 * what = 1

Divide each side by 3

3* what /3 = 1/3

what = 1/3

The multiplicative inverse of 3 is 1/3

Answer:

1/3

Step-by-step explanation:

The mult. inverse of 3 is 1/3.

Answer:

W (-1, 4) ---> W' (-4, -1)

X (-1, 2)  ---> X' (-2, -1)

Y (2, 2)  ---> Y' (-2, 2)

Z (2, 4)  ---> Z' (-4, 2)

Step-by-step explanation:

We have with a rectangular figure WXYZ and we are to find the coordinates of its vertices W'X'Y'Z' after the transformation of 90° rotation.

We know that, the rule for 90° rotation of a point (x, y) gives (-y, x).

So,

W (-1, 4) ---> W' (-4, -1)

X (-1, 2)  ---> X' (-2, -1)

Y (2, 2)  ---> Y' (-2, 2)

Z (2, 4)  ---> Z' (-4, 2)

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]y+2=\frac{1}{5}(x-1)[/tex]  

This is the equation of the line into point slope form

The point is (1,-2) and the slope  is m=1/5

we know that

To correctly identify the graph find out the x and y intercepts of the graph

Find the y-intercept

The y-intercept is the value of y when the value of x is equal to zero

For x=0

[tex]y+2=\frac{1}{5}(0-1)[/tex]

[tex]y=-\frac{1}{5}-2[/tex]

[tex]y=-\frac{11}{5}=-2.2[/tex]

The y-intercept is the point (0,-2.2)

Find the x-intercept

The x-intercept is the value of x when the value of y is equal to zero

For y=0

[tex]0+2=\frac{1}{5}(x-1)[/tex]

[tex]10=x-1[/tex]

[tex]x=11[/tex]

The x-intercept is the point (11,0)

To graph the line plot the intercepts and join the points

see the attached figure

Answer:

12

Step-by-step explanation:

You want the costs to be the same so set them equal.

180+10t=25t

Subtract 10t on both sides:

180. =15t

Divide both sides by 15:

180/15. =t

12. =t

So t=12 would give us the costs being the same.

Answer:

Step-by-step explanation:

The given functions are

[tex]C(t)=180+10t\\C(t)=25t[/tex]

To answer the question, we just need to solve this system. We are gonna replace the second function into the first one,

[tex]C(t)=C(t)\\180+10t=25t\\15t=180\\t=\frac{180}{15}=12[/tex]

Therefore, after 12 months, the service contracts will cost the same.

M= 1488

This is how many number of minutes Justin has used his phone in a month.

I solved this by first subtracting 24 from 113.28, which is 89.28.

Next I knew multiplication would have to be involved.

I had to figure out 0.06 times what equals 89.28.

Well that would be 1488.

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Based on the given monthly fee and per-minute charge for Justin's phone, if the minimum monthly charge is $113.28, this indicates that he has used his phone for at least 1488 minutes in that month.

To solve this question, we can start by setting up an inequality because we want to find the possible numbers of minutes Justin can use his phone. Given that Justin pays a monthly fee of $24 and $0.06 per minute of use, the total charge (T) in a month is given by the equation:

T = 24 + 0.06m

It is stated that the least he has been charged in a month is $113.28. To find the possible number of minutes, we need to solve this inequality for m:

113.28 <= 24 + 0.06m

If we subtract $24 from each side, it becomes:

89.28 <= 0.06m

Then by dividing each side by 0.06, we get:

m >= 1488

So, Justin has used his phone for at least 1488 minutes in a month.

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The divisor is 4.033 because it divides 198,200. Rounded to the nearest whole number, it is 4 because 0 is less than 5, so the next highest (whole) place is unchanged.

For this case we have a division where:

If we want to round the divisor to the nearest whole number we have:

4.033 is equivalent to 4, because:

3 is less than 5, then we have 4.03

3 is less than 5, so we have 4.0 equivalent to 4.

Answer:

The divisor remains as 4, rounded to the nearest whole number.

[tex]\bf \begin{cases} f(x)=&x^2+3\\\\ g(x)=&\cfrac{x+2}{x}\\\\ (f\circ g)(x)=&f(~~g(x)~~) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ g(2)=\cfrac{(2)+2}{(2)}\implies g(2)=\cfrac{4}{2}\implies g(2)=\boxed{2} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{x=2}{f(~~g(2)~~)}=\left( \boxed{2} \right)^2+3\implies f(~~g(2)~~)=4+3\implies \stackrel{(f\circ g)(2)}{f(~~g(2)~~)}=7[/tex]

Answer:

40

Step-by-step explanation:

6*6/6*-2i/2i*6/2i*-2i

Answer:

40

Step-by-step explanation:

Answer:

A. (x - 10)(x - 4)

Step-by-step explanation:

The product is 0 if one of the factors is 0.

(4 - 10)(4 - 4)

= (4 - 10)*0

= 0

Answer:

A. (x - 10)(x - 4)

Step-by-step explanation:

Let x=4

O A. (4 - 10)(4 - 4) = -6 * 0 = 0

OB. (4 + 4)(4 - 10) = 8* -6 = -48

O C. (4 + 6)(4 - 2) = 10 * 2 = 20

OD. 4*4(4-6)=16*-2 = -32