If abc is an equilateral triangle bc must be 2cm true or false?

The Pythagorean theorem is the idea that the sum of the two legs which are both squared is equal to the hypotenuse's length squared.

     *look at the image I attached for a better explanation

By looking at the picture, we are missing the leg's length, and by using the Pythagorean theorem, we get the equation

    [tex]?^2+5^2 = 13^2\\?^2 + 25 = 169\\?^2 = 144\\? = 12[/tex]

Thus the missing side length is 12 cm

Hope that helps!

Answer:

[tex]\huge\boxed{\bf\:62}[/tex]

Step-by-step explanation:

[tex](9*7) + 7 - 8 = ?[/tex]

We can solve this by using the PEMDAS concept where,

So, to solve this, we need to solve the numbers in the parentheses by doing the requested operation (here it is, mutiplucation).

[tex](9*7) + 7 - 8\\= (63) + 7 - 8[/tex]

Now, by looking at the PEMDAS rule, we can see that the next step is addition (as, we don't have to divide in this question).

[tex](63) + 7 - 8\\= 63 + 7 - 8\\= 70 - 8[/tex]

Now, subtract 8 from 70 .

[tex]70 - 8\\= \boxed{\bf\:62}[/tex]

[tex]\rule{150pt}{2pt}[/tex]

Answer/Step-by-step explanation:

the fibonacci sequence is {1, 1, 2, 3, 5, 8, 13, 21, 34…} and in the visual for the Golden Ratio, if you look those are the those are the numbers that basically equals the golden ration, 1.618.

Step-by-step explanation:

1) Angles opposite congruent sides in a triangle are congruent, so angle H is congruent to angle D.

2) For the same reason as the first problem, angle D is congruent to angle NSD.

3) Since sides opposite congruent angles in a triangle are congruent, segment AH is congruent to segment AS.

4) For the same reason as the third question, segment SA is congruent to segment SN.

[tex]\left[3+(-7)\times 2\right] - \left[10 \div(-5)\right]\\\\=(3-14) +\left(10\times \dfrac 15\right)\\\\=-11+2\\\\=-9[/tex]

Answer:

15 outfits

Step-by-step explanation:

Given

Probability : No. of outfits

P.S. Sorry I couldn't create the probability table.

[tex]6 - \sqrt{5} \times \frac{6 + \sqrt{5} }{6 + \sqrt{5} } [/tex]

[tex] \frac{(6 - \sqrt[]{5})(6 + \sqrt{5} ) }{6 + \sqrt{5} } = \frac{36 - 5}{6 + \sqrt{5} } = \frac{31}{6 + \sqrt{5} } [/tex]

Answer:

p(3,2)=====P'(-2,3)....

Answer:

1) what is the number of male part time students between the ages 15 - 19 years?

2) do students work more than 4 hours a day?

Answer:

6/11

Each time you spin the pointer there is a 3/8 for each of the two spins. That means there is a 6/11 chance of the pointer landing on blue for both times the pointer is spun.

Step-by-step explanation:

Each spin there are 8 possible sections the spinner can land on. The circle has 3 blue sections. The question asks what is the probability of the spinner landing on blue for BOTH spins. This means that you would have to show the denominator as 16. Each time you spin the pointer there is a 3/8 chance it will touch blue. When you spin it two times there is a 6/16 probability that the spinner will land on blue for each of the times the pointer is spun.

Have a great rest of your day
#TheWizzer

Answer:

[tex] 55 < A < \frac{149}{2} [/tex]

Step-by-step explanation:

Given:

Function g(x) = 2x²-x-1, [2,5],

N = 6 rectangles

To find:

Two approximation (Left endpoint and Right endpoint of the area) of the area.

Solution:

Using Right endpoint approximation,

[tex]\Delta x = \frac{b - a}{N} \\ \Delta x = \frac{5 - 2}{6} \\ \Delta x = \frac{3}{6} = \frac{1}{2}[/tex]

Now,

[tex]\displaystyle\sf \: R_n = \Delta x \: \sum_{i=1}^N f(a + i \Delta x)[/tex]

Where i = 1,2,3,4......

Substituting value of N, ∆x and a in above equation,

[tex]\displaystyle\sf \: R_n = \Delta x \: \sum_{i=1}^N f(a + i \Delta x) \\ \displaystyle\sf \: R_n = \frac{1}{2} \: \sum_{i=1}^6 f(2 + i \cdot \frac{1}{2} ) \\ \displaystyle\sf \: R_n = \frac{1}{2} \: \sum_{i=1}^6 f(2 + \frac{i}{2} ) \\ \displaystyle\sf \: R_n = \frac{1}{2} \: \sum_{i=1}^6 f( \frac{4 + i}{2} ) [/tex]

[tex]\displaystyle\sf \: R_n = \frac{1}{2} \bigg( f( \frac {5}{2}) + f( 3) +f( \frac {7}{2}) + f( 4) + f( \frac {9}{2}) + f( 5) \bigg) [/tex]

Substituting the corresponding values of x in given function 2x²-x-1

[tex]\displaystyle\sf \: R_n = \frac{1}{2} \bigg(2 \times { (\frac{5}{2} )}^{2} - \frac{5}{2} - 1 ....... +2 \times { ({5} )}^{2} - {5}- 1 \bigg) [/tex]

After solving each function,

[tex]\displaystyle\sf \: R_n = \frac{1}{2} \bigg(9 + 14 +20 + 27 + 35 + 44\bigg) \\ \displaystyle\sf \: R_n \: = \frac{149}{2} [/tex]

Similarly for left endpoint approximation,

[tex]\displaystyle\sf \: L_n = \Delta x \: \sum_{i=0}^{N - 1} f(a + i \Delta x)[/tex]

Where i = 0,1,2,3......

Substituting value of N, ∆x and a in above equation,

[tex]\displaystyle\sf \: L_n = \Delta x \: \sum_{i=0}^{N } f(a + i \Delta x) \\ \displaystyle\sf \: L_n = \frac{1}{2} \: \sum_{i=0}^{N } f(2 + i \frac{1}{2} ) \\\displaystyle\sf \: L_n = \frac{1}{2} \: \sum_{i=0}^6 f( \frac{4 + i}{2} ) [/tex]

[tex]\displaystyle\sf \: L_n = \frac{1}{2} \bigg(f( 2) + f( \frac {5}{2}) + f( 3) +f( \frac {7}{2}) + f( 4) + f( \frac {9}{2}) + \bigg) [/tex]

Substituting the corresponding values of x in given function 2x²-x-1

[tex]\displaystyle\sf \: L_n = \frac{1}{2} \bigg(5+ 9 + 14 +20 + 27 + 35 \bigg) \\ \displaystyle\sf \: L_n \: = \frac{110}{2} = 55 \\ [/tex]

Right approximation 149/2

Left approximation 55

Hence the Area is bounded in,

[tex] 55 < A < \frac{149}{2} [/tex]

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Answer:

Step-by-step explanation:

c) To find slope, choose any two points.

(2,16)  & (4 , 31)

[tex]\boxed{slope= \dfrac{y_2-y_1}{x_2-x_1}}[/tex]

         [tex]\sf =\dfrac{31-16}{4-2}\\\\=\dfrac{15}{2}=7.5[/tex]

The slope is 7.5, which means that Kobby's puppy gained 7.5 pounds a month for the first 6 months.

a) Equation of line in slope -intercept form: y  = mx +b

[tex]y =\dfrac{15}{2}x+b[/tex]

Now, substitute the point (2 ,16) in the above equaiton and find the y-intercept b.

[tex]\sf 16 =\dfrac{15}{2}*2+b\\\\16=15+b\\\\16-15=b[/tex]

b = 1

Equation of the line:

[tex]y=\dfrac{15}{2}x+1[/tex]

b)  y-intercept = 1

The y-intercept is 1, which means that Kobby'spuppy weighed 1 pound at birth

Using the z-distribution, as we have the standard deviation for the population, it is found that the 90% confidence interval for the mean cholesterol levels of his patients is (5.59, 6.73).

The confidence interval is:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

In this problem, we have a 90% confidence level, hence[tex]\alpha = 0.90[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.

Researching on the internet, the other parameters are given by:

[tex]\overline{x} = 6.16, \sigma = 1.3, n = 14[/tex]

Hence:

[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 6.16 - 1.645\frac{1.3}{\sqrt{14}} = 5.59[/tex]

[tex]\overline{x} + z\frac{\sigma}{\sqrt{n}} = 6.16 + 1.645\frac{1.3}{\sqrt{14}} = 6.73[/tex]

The 90% confidence interval for the mean cholesterol levels of his patients is (5.59, 6.73).

More can be learned about the z-distribution at https://brainly.com/question/25890103

Answer:

(5, -43)

Step-by-step explanation:

The value of the x-coordinate of the vertex of a function in standard form is given by -b/2a.  The value of a is the coefficient of the x^2 term.  The value of b is the coefficient of the x term.  In this problem, a = 2 and b = -20.  When you evaluate -b/2a you would replace the b with -20 and replace the a with 2 so you get -(-20)/2(2) so the value of x is 5.  Determine the value of y by evaluating f(5) = 2(5)^2 - 20(5) +7.

Answer:

(2,10)

Step-by-step explanation:

Whenever you want to find the point that is closest, it will always be perpendicular to the line

This is because the perpendicular line is the shortest distance to a point (it will make 90 degrees with the line)

So

In order to find the slope of the perpendicular line, you take the slop and you do the negative reciprocal of it.

In this case:

the slope is 5

So:

the negative reciprocal is -1/5

Now we know the slope of the line that will be made by point P to intersect with y=5x

Then, you use the equation:

y=mx+b

and plug in the numbers that you know which is the y coordinate, x coordinate, and slope to find the y-intercept:

0 = -1/5(52) + b

b = 52/5

Finally, set the equations equal to each other to find the point that the perpendicular line intersects y=5x

5x = -1/5x + 52/5

x = 2

then to find the y coordinate you plug the x back into the equation:

y = 5(2)

y = 10

So the answer is (2,10)

Answer:

Step-by-step explanation:

Take one side length

Scale factor (A to B)

[tex]\\ \rm\rightarrowtail \dfrac{16}{12)=\dfrac{4}{3}[/tex]

Scale factor (B to A)=1/4/3=3/4

#4

Scale factor (A to B)

Scale factor (B to A)

We will see that the expected value for X given that the first number is a 6, is:

E[X|A] = 9.5

We know that X represents the sum of both values. The first value is already 6, so we have that fixed:

X = 6 + p

Now, remember that all the numbers in the dice have the same probability of rolling up, then the expected value of p is:

E(p) = (1 + 2 + 3 + 4 + 5 + 6)*(1/6) = 3.5

Then the expected value of X, given the event A.

E[X|A] = 6 + p = 6 + 3.5 = 9.5

So the expected value for X is 9.5

If you want to learn more about expected values, you can read:

https://brainly.com/question/15858152

Answer:

D.

41.17 because it is possible answer to the question

The areas of the two parallelograms are 105 square inches and 20.997 square yards, respectively.

A parallelogram is a quadrilateral with two pairs of parallel sides with equal length and two pairs of angles of equal measure. The area of the parallelogram (A), in square yards or square inches, equals the product of its base length (b), in yards, and its height (h), in yards.

The area of each parallelogram is determined afterwards:

A = (10.5 in) · (10 in)

A = 105 in²

A = (9 yd) · (2.333 yd)

A = 20.997 yd²

The areas of the two parallelograms are 105 square inches and 20.997 square yards, respectively. [tex]\blacksquare[/tex]

To learn more on parallelograms, we kindly invite to check this verified question: https://brainly.com/question/1563728

Answer:

Monday

Step-by-step explanation:

If day before yesterday was Saturday, so today is Monday.

Answer:

700

Step-by-step explanation:

2016 - 2007 = 9

27,700 - 21,400 = 6300

6300 / 9 = 700.

Using a system of equations, it is found that Anne gets 5x - 10 pens.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, we consider that John gets x pens.

Lucy gets 2 pens less than john, hence:

L = x - 2.

Anne gets 5 times many pens as lucy, hence:

A = 5L = 5(x - 2) = 5x - 10.

More can be learned about a system of equations at https://brainly.com/question/24342899

Divide price by size of each and compare the u it price:

2.99/32 = 0.0934 per ounce

1.59/18 = 0.0883 per ounce

The 18 ounce do $1.59 has a lower cost per ounce so is the better buy

Answer:

㏒₆ (18) - ㏒₆ (6) = ㏒₆ (3)Here subtraction of logarithm given. So we have to use the property of logarithm of quotient.The property says that㏒ₐ (M) - ㏒ₐ (N) = ㏒ₐ (M/N)So for subtraction we have to divide them. That is logarithm of difference becomes the quotient.So we can write,㏒₆ (18) - ㏒₆ (6) = ㏒₆ (18/6) If we divide 18 by 6 we will get 3.So, ㏒₆ (18) - ㏒₆ (6) = ㏒₆ (3)

Step-by-step explanation:

Answer:Quotient Property

Step-by-step explanation:The property used to rewrite the expression is the quotient rule of logarithms, which states that log_b(x/y) = log_b(x) - log_b(y).