What is the sum of the first 5 prime numbers

The length of the bd in the given triangle is 12 cm. This is obtained by applying the Pythagoras theorem.

The Pythagoras theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse. I.e., [tex]a^2+b^2=c^2[/tex].

The triangle is perpendicularly divided into two halves looking like right-angled triangles.

The side lengths for the given triangle are bc=13 cm and ac=10 cm

The line segment bd divides the triangle into two right-angled triangles symmetrically.

So, the base ac of the given triangle is divided at the mid-point d.

Thus,

ac = ad + dc

here, d is the mid point, ad = dc

So, ad=dc=5 cm

Now, the triangle forms a right-angled triangle with sides bd, dc, and bc. Where bc is the hypotenuse.

To find the length of bd, applying the Pythagoras theorem

[tex](bc)^2=(bd)^2+(dc)^2[/tex]

⇒ [tex](13)^2 = (bd)^2 + (5)^2[/tex]

⇒ [tex]169 = (bd)^2 +25[/tex]

⇒ [tex](bd)^2 = 169 - 25[/tex]

⇒ [tex](bd)^2 = 144[/tex]

∴ bd = 12 cm

Therefore, the length of the bd is 12 cm.

Learn more about Pythagoras's theorem here:

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Answer:

1.31950791

Step-by-step explanation:

I don't actually know if this is correct

Answer:

Thursday

Step-by-step explanation:

Since the forecast being  completely accurate would be 0, you would have to choose the closest number to 0, and if you look -2 or Thursday is the closest number the 0,

[tex]y = - 2(x - 2)(x - 10)[/tex]

[tex]0 = - 2(x - 2)(x - 10)[/tex]

[tex]x - 2 = 0 \\ x = 2[/tex]

[tex]x - 10 = 0 \\ x = 10[/tex]

Answer:

The zero's are x=2 and x=10

Step-by-step explanation:

y = -2(x-2) (x-10)

We want to find the zero's so we set y=0

0 = -2(x-2) (x-10)

Using the zero product property

x-2 = 0   and x-10 =0

x-2+2 =0+2     x-10+10 =0+10

x =2      x=10

The zero's are x=2 and x=10

Interest (I) = Principal (P) X Rate (R) X Time (T)

They tend to use 'Exact Interest' in which Interest calculated using a 365-day year. Time that counts exact number of days in the month that the borrower has the loan

Hope this helps :)

Answer:

Interest (I) = Principal (P) X Rate (R) X Time (T)

Hope this helps you:)

5INGH

Step-by-step explanation:

Answer:

[tex]10.3\ mi[/tex]

Step-by-step explanation:

we know that

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

we have

[tex]A(10,8)\\B(1,3)[/tex]

substitute the values

[tex]d=\sqrt{(3-8)^{2}+(1-10)^{2}}[/tex]

[tex]d=\sqrt{(-5)^{2}+(-9)^{2}}[/tex]

[tex]d=\sqrt{25+81}[/tex]

[tex]d=\sqrt{106}[/tex]

[tex]d=10.3\ mi[/tex]

Answer:

3/8

Step-by-step explanation:

1/2 of a yard is 4/8 of a yard, so you can subtract 7-4 to get 3/8 of a yard.

Answer:

Step-by-step explanation:

[tex]-6n-5=31\qquad\text{First step: add 5 to both sides}\\\\-6n-5+5=31+5\\\\-6n=36\qquad\text\qquad\text{Second step: divide both sides by (-6)}\\\\-6n:(-6)=36:(-6)\\\\n=-6[/tex]

Answer:

12

Step-by-step explanation:

Treat the less than or equal too sign as you would a normal equal sign.

Add 27 to -15 so that x is less than or equal to 12

Answer:

2,038,711

Step-by-step explanation:

For a continuously compounding rate r, the growth is modeled by ...

P = P0·e^(rt)

where P0 is the initial population, r is the annual growth rate (compounded continuously) and t is the number of years.

Putting your values into this formula, you have

P = 750000·e^(0.04·25) ≈ 2,038,711

Using the formula for continuous compound growth, the population of the district in 2025 is projected to be approximately 1,226,030.

The question is asking about the future population of a district based on continuous compound growth. In this case, the compound interest formula, which includes the principle amount, the rate of growth (interest), and time. The formula often looks as follows: A = P * e^(rt), where A is the amount in the future, P is the principle amount (initial population), r is the rate of growth (interest), and t is the time.

In your case, the calculation would be: A = 750,000 * e^(0.04 * 25). Here, 'e' represents Euler's number (approximately equal to 2.71828), 0.04 is the growth rate, and 25 is the time (years from 2000 to 2025).

Using this formula, we can calculate that the population of the district in 2025 will be approximately 1,226,030 people, assuming a steady growth rate of 4% annually.

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ANSWER

[tex] {i}^{31} = - i[/tex]

EXPLANATION

We want to evaluate

[tex] {i}^{31} [/tex]

Use indices to rewrite the expression as:

[tex] = {i}^{30} \times i[/tex]

We know that

[tex] {i}^{2} = - 1[/tex]

So we rewrite the expression to obtain;

[tex] = ({ {i}^{2}) }^{15} \times i[/tex]

This gives us;

[tex]= {( - 1) }^{15} \times i[/tex]

This simplifies to

[tex] = - 1 \times i[/tex]

[tex] = - i[/tex]

Answer:

The answer is c, 24 units.

The Pythagorean Theorem says for a right triangle with legs a,b and hypotenuse c,

[tex]c^2 = a^2+b^2[/tex]

Solving for each in turn,

[tex] c= \sqrt{a^2+b^2}[/tex]

[tex]a^2=c^2 - b^2[/tex]

[tex]a = \sqrt{c^2-b^2}[/tex]

[tex]b = \sqrt{c^2-a^2}[/tex]

Looking at our choices, we select the third and fourth.

The pythagorean theorem states that, in every right triangle, the following formula holds:

[tex]a^2+b^2=c^2[/tex]

where a and b are the legs, and c is the hypotenuse.

We can deduce the following expressions for a,b and c:

[tex]a = \sqrt{c^2-b^2},\quad b=\sqrt{c^2-a^2},\quad c=\sqrt{a^2+b^2}[/tex]

Answer: You multiply 1.5 each time.

Step-by-step explanation:

72*1.5=108

108*1.5=162

162*1.5=243

And so on and so forth....  Hope it helped!

243 = 3x3x3x3x3

162 = 3x3x3x3x2

108 = 3x3x3x2x2

72 = 3x3x2x2x2

The next two numbers in the sequence would be

48 = 3x2x2x2x2

32 = 2x2x2x2x2

The answers are:

[tex]f(x)=\frac{5x+3}{2}[/tex]

[tex]f(x)=2x-8[/tex]

[tex]f(x)=7x-2[/tex]

[tex]f(x)=\frac{1}{x+2}[/tex]

To find the inverse function of a function, we need to replace the variable (x for this case) for the function itself (f(x)), where we see "x" we must rewrite with "y" or "f(x) and then, isolate "y" or "f(x).  If we have the inverse function and we want to find the function, we need to reverse the process.

Let's find each function of the given inverse functions in order to match each one with its inverse.

First inverse function,

[tex]f^{-1}(x)=\frac{2x-3}{5}[/tex]

Replacing "x" with "f(x)" and "f-1(x)" with "x" we have:

[tex]x=\frac{2f(x)-3}{5}\\\\5x=2f(x)-3\\\\5x+3=2f(x)\\\\f(x)=\frac{5x+3}{2}[/tex]

Therefore, the function that matches with the first inverse function is:

[tex]f(x)=\frac{5x+3}{2}[/tex]

Second inverse function,

[tex]f^{-1}(x)=\frac{x+8}{2}[/tex]

Replacing "x" with "f(x)" and "f-1(x)" with "x" we have:

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

Hence, the function that matches with the second inverse function is:

[tex]f(x)=2x-8[/tex]

Third inverse function,

[tex]f^{-1}(x)=\frac{x+2}{7}[/tex]

Replacing "x" with "f(x)" and "f-1(x)" with "x" we have:

[tex]x=\frac{f(x)+2}{7}\\\\7x=f(x)+2\\\\7x-2=f(x)\\\\f(x)=7x-2[/tex]

So, the function that matches with the third inverse function is:

[tex]f(x)=7x-2[/tex]

Fourth inverse function,

[tex]f^{-1}(x)=\frac{1-2x}{x}[/tex]

Replacing "x" with "f(x)" and "f-1(x)" with "x" we have:

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

So, the function that matches with the fourth inverse function is:

[tex]f(x)=\frac{1}{x+2}[/tex]

Have a nice day!

Answer:

[tex]S=45m+15[/tex]

Step-by-step explanation:

we have

E------>the number of sit-ups

m---->  the time in minutes

S----> the number of sit-ups after drinking the sports drink

[tex]E=15m+5[/tex] ----> equation A

[tex]S=3E[/tex] ----> equation B

substitute the equation A in the equation B

[tex]S=3(15m+5)[/tex]

[tex]S=45m+15[/tex]

Answer: Its the Second one!

Step-by-step explanation: Ur welcome <3

Answer:6.2 and 6.5

Step-by-step explanation:

First, make a plotline from least to greatest and organize your list of numbers from least to Greatest.

Next, go through your list of organized numbers and add a dot to that number on the plotline. Repeat until done with list of numbers.

Then, go through your plotline and find the number(s) with the most dots and you have your mode.

Definition of mode: The number which appears most often in a set of numbers.

Answer provided in the image attached.

12) D'(3, 1) E'(1, -2) F'(5, 0)

13) Vertex E

14) D'(3, 1)

15) D'(1, 3) E'(3, 0) F'(-1, -2)

16) D'(-11, 11) E'(13, 8) F'(-9, 6)

P'(-9, 10) Q'(-7, 12) R'(-5, 10)

17) Translate 4 units down; (x, y) ---- (x, y - 4)

18) P'(-1, 2) Q'(-3, 4) R'(-5, 2)

19) P'(-2, 1) Q'(-4, 3) R'(-2, 5)

20) P'(-1, -2) Q'(-3, -4) R'(-5, -2); Rotated 180° about the origin

21) P'(3, 6) Q'(9, 12) R'(15, 6)

22) A'(-9, 0) B'(0, 12) C'(9, 0) D'(0, -12)

23) Image (yes, the answer is actually Image)

24) (x, y) → (1.5x, 1.5y)

This took me 45 mins to do, lol.

You're welcome? :) <3

The data set is

20

32, 34, 36

40, 42, 44, 48

55

65

We can see that each value only shows up one time. Therefore there is no mode. To have a mode, we need to have a value show up more than once, and it must be the most frequent value. For example, the set {1,2,3,3,4} has a mode of 3 since it shows up twice, the most of any value in that set. However we don't have that occur for the data set your teacher gave you.

Answer:

no mode i just got it right

Step-by-step explanation:

Answer:

-3/b

Step-by-step explanation:

The reciprocal of -b/3 is -3/b

[tex](2x + 1)(3x + 4) \\ = 2x(3x + 4) + 1(3x + 4) \\ = 6 {x}^{2} + 8x + 3x + 4 \\ = 6 {x }^{2} + 11x + 4[/tex]

Answer:

The correct answer is,

| -8|

| 4 |

Step-by-step explanation:

It is given two matrices,

1)Let Matrix A =   5  -2

                          -6    2

2) Matrix B =       -1

                          -1

Matrix A is 2 x 2 matrix and matrix B is 2 x 1 matrix

To find the product of two matrices

A x B =    5  -2       x      -1     =   -10+2      =   -8

             -6    2              -1             6 -2            4

Therefore the correct answer is

| -8|

| 4 |

[tex]\bf \stackrel{\textit{range is always the set of y-coordinates}}{f=\{(2,\stackrel{\downarrow }{3}),(5,\stackrel{\downarrow }{7}),(3,\stackrel{\downarrow }{3}),(5,\stackrel{\downarrow }{4}),(9,\stackrel{\downarrow }{1})\}}\qquad \qquad \{3,7,3,4,1\}\implies \{3,7,4,1\}[/tex]

Answer:

{3, 7, 3, 4, 1}

Step-by-step explanation:

Answer:

Step-by-step explanation: I hope that helps you.

Answer:

126.2 meters

Step-by-step explanation:

A trapezoid's area is found using the formula A = 1/2 (a+b)h where a and b are the two bases. Substitute A = 12,052.1, a = 82.4 and b=108.6. Then solve for h.

A = 0.5(a+b)h

12,052.1 = 0.5(82.4 + 108.6)*h

12,052.1 = 0.5(191)h

12,052.1 = 95.5h

126.2 = h

Answer:

12+x/8

Step-by-step explanation:

Answer:

17

Step-by-step explanation:

i hope it helps if not 17 then it is ..................... 12+x/8

Answer:

d = b/c.

Step-by-step explanation:

Just divide both sides by c:

b = cd

b / c = cd/ c

b/c = d.

Answer:

[tex] d = \frac { b } { c } [/tex]

Step-by-step explanation:

We are given the following equation and we are to solve it for d:

[tex] b = c d [/tex]

Since we are asked to solve this equation for d and it contains all variables, it means that we need to make the variable 'd' the subject of the equation by keeping all other variables at the other side of the equation.

[tex] b = c d [/tex]

[tex]d=\frac{b}{c}[/tex]

The decimal equivalent of 3/7 rounded to the nearest hundreds is 0.428

Answer: 0.43 cause hundredths place is the 3 and its rounded

Step-by-step explanation:

Answer:

y = 2.4

Step-by-step explanation:

first distribute into the parenthesis' -

2(y-3) = 1.2 -y

2y - 6 = 1.2 - y

+y                +y

3y -6 = 1.2

   +6     +6

3y = 7.2

/3      /3

y = 2.4

hope this helps!!

Answer:  y=2.4

Step-by-step explanation:

The work is below Hopefully this helps:)

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