AB = 6cm, AC = 12cm
Calculate the length of CD.
Give your answer to 3 significant figures.

Answer:

3 [tex]\frac{3}{4}[/tex] inches

Answer: I'm pretty sure it's 3 5/8, it's the S that's blocking the view but it gotta be 3 5/8.

Step-by-step explanation: PLS MAKE ME BRAINLIST

28 miles upstream requires 28/7 = 4 hours.

28 miles downstream requires 28/21 = 4/3 hours, or 1 hour and 20 minutes.

Apply the distance formula:

d = rt

where

d is distance

r is rate or speed

t is time

21 = t*(r+7)  = rt+ 7t

7 = t *(r-7)   = rt - 7t

            28 = 2rt

             14 = rt

             21 = rt + 7t

             21 = 14 + 7t

               7 = 7t

                 t=1

              21 = (r+7)*1 = r+7

                r = 14

The speed of the boat is 14 mph. With the current (downstream), the speed is 14+7 = 21 mph, so 21 miles are traveled in 1 hour. Against the current (upstream), the speed is 14-7 = 7 mph, which means 7 miles are traveled in the same 1-hour time frame.

28 miles downstream requires 28/21 = 4/3 hours, or 1 hour and 20 minutes.

28 miles upstream requires 28/7 = 4 hours.

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The diameter of the circle is 11.8 units

The circle equation is given as:

(x - 2)^2 + (y + 6)^2 = 35

A circle equation is represented as:

(x - a)^2 + (y - b)^2 = r^2

Where

Diameter = 2r

By comparing both equations, we have

r^2 = 35

Take the square root of both sides

r = 5.9

Multiply by 2

2r = 11.8

Hence, the diameter of the circle is 11.8 units

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Answer:

Exact form: 7/143

Decimal form: /0.048951

Answer:

[tex]x=\frac{7}{143}[/tex]

Step-by-step explanation:

Simplify the right side of the equation. [tex]3x+21=432x[/tex]. Subtract 21 from both sides of the equation. [tex]3x=432x-21[/tex]. Subtract 432x from both sides of the equation, [tex]-429x=-21[/tex]. The negative signs cancel out to get [tex]429x=21[/tex]. Divide both sides but 429 to get [tex]x=\frac{21}{429}[/tex].  Reduce to get [tex]x=\frac{7}{143}[/tex].

The time taken in years for money invested to accumulate to $1500 is 18.45 years

Simple interest = Total savings - principal

= 1500 - 1000

= $500

Simple interest = principal × rate × time

500 = 1000 × 0.0271 × t

500 = 27.1 × t

500 = 27.1t

t = 18.4501845018450

Approximately,

t = 18.45 years

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Answer:

-3

Step-by-step explanation:

[tex]f\left( x\right) =\sqrt{3x} \ \ \text{and} \ \ g\left( x\right) =x+3[/tex]

it’s clear that :

f is defined if and only if  x ≥ 0

Therefore ,

fºg is defined if and only if x + 3 ≥ 0

x + 3 ≥ 0

⇔ x ≥ -3

Then ,the smallest number that is in the domain of fºg is -3

None of the equation of the line is parallel because there slope are not equal.

Parallel line have the same slope.

Therefore, using slope intercept equation,

y = mx + b

where

Hence,

y = −5x − 5 , slope = -5

x + 12y = −4; y = -1 / 3 - 1 / 12 x, slope = 1 / 12

y = −2x + 4: slope = -2

y + 8 = -15x + 135; y  = -15x + 127, slope  = -15

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Notice that

[tex]7^{2014} - 7^{2012} = 7^{2012} \bigg(7^2 - 1\bigg) = 7^{2012} \times 48 = 2^4 \times 3 \times 7^{2012}[/tex]

[tex]12=2^2\times3[/tex], so

[tex]\dfrac{7^{2014}-7^{2012}}{12} = 2^2 \times 7^{2012}[/tex]

Then taking the positive square root gives

[tex]\sqrt{\dfrac{7^{2014}-7^{2012}}{12}} = \sqrt{2^2 \times 7^{2012}} = 2\times7^{1006}[/tex]

so [tex]\boxed{a=2}[/tex] and [tex]\boxed{b=1006}[/tex].

Someone may think this graph is misleading because it does not start from the origin

As a general rule, graphs are to begin from the origin

The origin of a graph is

(x, y) = (0, 0)

From the given graph, the origin is

(x, y) = (0, 60)

This means that someone may think this graph is misleading because it does not start from the origin

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Answer:

[tex] \sf{b. \frac{x}{2} <3}[/tex]

step by step explanation:

We will try one by one.

A. x + 5 < 3

Step 1. Subtitution Value of x

= 4 + 5 < 3

Step 2. Add by 4 with 5

= 9 < 5

A is wrong because 9 is bigger then 5

B. x/2 < 3

= 4/2 < 3

= 2 < 3

is true because 2 is smaller than 3

C. 9x > 36

9(4) > 36

36 > 36

is wrong, should 36 = 36

D. 18 < 8

is wrong because 18 is bigger than 8

Considering the situation described, the null hypothesis is given as follows:

[tex]H_0: \mu = 64,000[/tex].

At the null hypothesis, it is tested if the mean is the same as in the Census, of $64,000, hence:

[tex]H_0: \mu = 64,000[/tex].

At the alternative hypothesis, it is tested if the mean is different from the Census, hence:

[tex]H_1: \mu \neq 64,000[/tex].

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Answer:

[tex]3(2x + 5)(3x - 1)[/tex]

Step-by-step explanation:

Hello!

We can first factor out the greatest common factor between the coefficients: 3.

Now, let's work with what we have inside the brackets.

Standard form of a quadratic: [tex]ax^2 + bx+ c = 0[/tex]

Given our equation: [tex]6x^2 + 13x - 5[/tex]

We need to find two numbers that add up to b (13) and multiply to ac (-30).

The two numbers are 15 and -2. Expand 13x to 15x and -2x and factor by grouping.

Now, we simply add the other factor, 3, to the final factored form.

Factored Solution: [tex]3(2x + 5)(3x - 1)[/tex]

The sum of the arithmetic series is 325

The given parameters are

a1 = 45

an = 85

n = 5

The formula for the sum of arithmetic series is:

[tex]S_n = \frac n2 * (a_1 + a_n)[/tex]

Substitute the values of a1, an and n in the above equation

[tex]S_5 = \frac 52 * (45 + 85)[/tex]

Add 45 and 85

[tex]S_5 = \frac 52 * 130[/tex]

Divide 130 by 2

[tex]S_5 = 5 * 65[/tex]

Multiply

[tex]S_5 = 325[/tex]

Hence, the sum of the arithmetic series is 325

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The x and y intercepts of the given equation of the line are 8 and 6 respectively for the given line 3x+4y=24. They are shown in the graph at X and Y respectively.

The standard equation of a line is ax + by + c = 0.

Then, its x-intercept is calculated by -c/a, and the y-intercept is calculated by -c/b.

In the graph, the x-intercept is obtained at y=0 and the y-intercept is obtained at x=0.

It is given that,

The equation of the given line is 3x + 4y = 24

Rewriting the given equation into the general form,

3x + 4y - 24 =0

On comparing with ax + by + c = 0,

a = 3, b = 4 and c = -24

So,

The x-intercept of the line (-c/a) = -(-24)/3 = 8 and

The y-intercept of the line (-c/b) = -(-24)/4 = 6

Therefore, the required x and y intercepts are 8 and 6 respectively.

(The graph showing the intercepts of the given line is shown below)

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Answer:

monopoly, order 1

Step-by-step explanation:

because the x has just power of one that is why is monopoly and in order 1

The  NPV of this investment if the discount rate is 10 percent is: 1.58%.

Year Cash flow  PVIF 10%  Present value

0         ($11.86)     1.000           ($11.86)

1           1.90          0.909           $1.73

2          1.90          0.826           $1.57

3          1.90           0.751           $1.43

4          1.90           0.683          $1.30

5          1.90           0.621           $1.18

6          1.90           0.564          $1.07

7          1.90            0.513          $0.98

8          1.90           0.467          $0.89

9          1.90           0.424          $0.81

10         6.45          0.386         $2.49

NPV                                          $1.58

1.9+5.25-2×35%=6.45

Hence, the NPV is $1.58.

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Answer:

31 units

Step-by-step explanation:

If a quadrilateral has a pair of sides that is both parallel and congruent, then the quadrilateral is a parallelogram.

Sides AD and BC are given as parallel.

If they are also congruent, then quadrilateral ABCD is a parallelogram.

3x + 7 = 5x - 9

-2x = -16

x = 8

AD = 3x + 7

AD = 3(8) + 7

AD = 31

Answer: 31 units

The simplified expression of [tex]\frac{x^{3}-8x^{2}}{x^2-64}[/tex] is [tex]\frac{x^2}{x + 8}[/tex]

The expression is given as:

[tex]\frac{x^{3}-8x^{2}}{x^2-64}[/tex]

Factor the numerator

[tex]\frac{x^{2}(x-8)}{x^2-64}[/tex]

Express the denominator as a difference of two squares

[tex]\frac{x^{2}(x-8)}{(x-8)(x + 8)}[/tex]

Cancel out the common factor

[tex]\frac{x^2}{x + 8}[/tex]

Hence, the simplified expression of [tex]\frac{x^{3}-8x^{2}}{x^2-64}[/tex] is [tex]\frac{x^2}{x + 8}[/tex]

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The set of all months that contains less than 31 days is; {February, April, June, September, November}.

It follows from the task content that the set whose elements are to be determined is characterized by containing less than 31 days.

On this note, it follows that the elements of the set are; February (28/29 days), April (30 days), September (30 days), June (30 days) and November (30 days).

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Answer:

4/91

Step-by-step explanation:

There are a total of 15 marbles.  In the first selection there are 15 marbles and 6 are blue.  That would be 6/15.

Since we are not replacing marbles, we now have 14 marbles and we want to select one of the 5 white marbles.  That would be 5/14.

Lastly we now only have 13 marbles and of those we want to select one of the 4 red ones.  That would be 4/13.

Now we take these 3 fractions and multiply them together.

6/15(5/14)(4/13).  I am going to try to make this a little easier and see if I can find any factors that any top number shares with any bottom number.

I see 5 on the top shares a common factor with 15 on the bottom.  I will divide these numbers by 3, so now I have

6/3(1/14)(4/14).  I think that I can do better than that.  I see that 6 on the top and 3 on the bottom share a common factor of 3.  I will divide both of these numbers by 3.  Which will give me:

2/1(1/14)(4/13) I see a 4 on top and a 14 on the bottom.  Those are both divisible by 2 so, I will divided them both by 2 and that leaves me with

2/1(1/7)(2/13)  That is a lot easier, now I will just multiple the top numbers and multiply the bottom numbers to get

4/91

Answer:

1.138789 is equivalent to 8 to the second power to the -4 power.

Hope this helps :)

The value of x from the given expression is -2

The formula for calculating the slope of a line is expressed as:

Slope = y2-y1/x2-x1

Given the following parameters

m = 1

(x1, y1) = (0, 2)

(x2, y2) = (x, 0)

Substitute

1 = x-0/0-2

1 = x/-2

x = -2

Hence the value of x from the given expression is -2

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Answer:

278,861,394

Step-by-step explanation:

put in the calculator e but then just square the numbers add it and there is your answer

The equation, in point-slope from, of the line that is perpendicular to the given line and passes through the point (-4,-3) is  y + 3 = 1/4(x + 4)

The complete question is added as an attachment

The points on the line are given as:

(-1, 1) and (0, -3)

Start by calculating the slope of the line using

m = (y2 - y1)/(x2 - x1)

The slope of the perpendicular line is

m2 = -(x2 - x1)/(y2 - y1)

So, we have:

m2 = -(0 + 1)/(-3 - 1)

This gives:

m2 = 1/4

The equation of the line is then calculated as

y - y1 = m(x - x1)

This gives

y + 3 = 1/4(x + 4)

Hence, the equation, in point-slope from, of the line that is perpendicular to the given line and passes through the point (-4,-3) is  y + 3 = 1/4(x + 4)

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based on the number of mice that took part in the experiment, the total number of mice that had at least one effect is 20 mice.

15 mice had at least 1 tumor while 4 mice had both a tumor and respiratory failure.

the number of mice with just a tumor is:

= 15 - 4

= 11 mice

the number of mice with respiratory failure alone is:

= 9 - 4

= 5 mice

the mice that had at least one symptom is:

= 11 + 5 + 4 mice with both

= 20 mice

question is:

what are the number of mice with at least one effect?

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Answer: [tex]m\angle BAM=30^{\circ}[/tex]

Step-by-step explanation:

[tex]AD=x\sqrt{3}[/tex] (Pythagorean theorem)

[tex]m\angle ACD=60^{\circ}[/tex] (30-60-90 triangle)

[tex]m\angle MCA=30^{\circ}[/tex] (angle subtraction)

[tex]m\angle MAC=30^{\circ}[/tex] (base angles theorem)

[tex]m\angle CAD=30^{\circ}[/tex] (30-60-90 triangle)

[tex]m\angle BAM=30^{\circ}[/tex] (angle subtraction)

A is the set of integers greater than -14 and less than -5. B={h, i, s, x, z}. The cardinalities of A and B are, n(A) = 8 and n(B) = 5.

-12 ∈ A, s ∈ B, and m ∉ B are True statements. Since, -21 does not belong to A, 21 ∈ A is a False statement.

Cardinalities of A and B

It is given that,

A = {n : -14 < n < -5, n ∈ Z}  ............ (1)

B = {h, i, s, x, z} ......... (2)

Thus, from (1),

A = {-13, -12, -11, -10, -9, -8, -7, -6} ........... (3)

Cardinalities of A and B are the number of members in the set A and B, respectively. Therefore,

n(A) = 8

n(B) =5

Reason Behind True or False

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The graph is shown in the attached image.

The solution of x is x = 0, x =2 and x = -5

The equation is given as:

2x^3+6x^2-20x=0​

Factor out x

x(2x^2+6x-20)=0​

Split the equation

x = 0 or 2x^2+6x - 20=0​

Solve for x in 2x^2+6x - 20=0​

Expand the equation

2x^2 + 10x - 4x - 20 = 0

Factorize the equation

(2x - 4)(x +5) = 0

Split the equation

2x - 4 = 0 and x + 5 = 0

Solve for x

x =2 and x = -5

Hence, the solution of x is x = 0, x =2 and x = -5

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The value of J ∩ F =  ∅

The value of J ∪ F = {c, e, f, g, k, j}

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Sets J and F are defined as follows;

J = {c, e, f}

F = {g, k, j}

Now,

Since, Sets J and F are defined as follows;

J = {c, e, f}

F = {g, k, j}

Hence, The value of J ∩ F =  {c, e, f} ∩ {g, k, j}

                                         = ∅

The value of J ∪ F = {c, e, f} ∪ {g, k, j}

                            = {c, e, f, g, k, j}

Thus, The value of J ∩ F =  ∅

The value of J ∪ F = {c, e, f, g, k, j}

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