Tell whether the following two triangles can be proven congruent through SAS.

A.Yes, the two triangles are congruent because they’re both right triangles.
B.Yes, the two triangles are congruent because two sides and their included angle are congruent in both triangles.
C.No, the two triangles can only be proven congruent through SSS.
D.No, the two triangles can only be proven congruent through AAA.

Answer: 13/7 or as a decimal 1.857142857

How did i get the answer:

Step 1: Simplify both sides of the equation.

so 1/2 of 10 is 5, 1/2 of 16 is 8

-3/5 of 15 is -9 and -3/5 of -35 is POSITIVE 21

all together should look like 5x+8+−13=−9x+21

(now we have to combine like terms)

8+ -13= -5

5x -5 = -9x+21

Step 2: Add 9x to both sides

5x + 9x= 14x

14x -5 = 21

Step 3: Add 5 to both sides.

21+5= 26

14x=26

Step 4: Divide both sides by 14.

26/14= 1.85714286 or 13/7

Answer:

180

Step-by-step explanation:

Given the cost (in dollars) of buying x pounds of a party product is given by the function

C(x) = 10x + 300.

Suppose, for budgetary reasons; you can't spend more than $2100 on this product. You can spend less, but you have to buy at least 50 pounds.

To get the domain of the function, substitute C(x) =2100 and find x

2100 = 10x + 300

10x = 2100 - 300

10x = 1800

x = 1800/10

x = 180

Hence the domain of the function is 180

Answer:

What do you need help with

Step-by-step explanation:

Answer:

9:2

Step-by-step explanation:

im struggling with the same one

Answer:

the answer is 8

Step-by-step explanation:

Total amount Ted wishes to spend this month is $5000.

Mahogany costs $450 per block, and he has already bought 7 blocks of spruce at $200 each.

So, money spent on spruce =  dollars

Money left after buying spruce =  dollars

Now as $450 will be spent on buying 1 block of mahogany.

So, $3600 will be spent

and then your answer will be 8

Answer:

1) Isosceles

2) Acute

3) Right angled

4( Obtuse

5) Equilateral

Answer:

b=2

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

[tex] \frac{4 + 4i}{5 + 4i} [/tex]

[tex] \frac{4 + 4i}{5 + 4i} \times \frac{5 - 4i}{5-4i} [/tex]

[tex] \frac{(4 + 4i)(5 - 4i)}{(5 + 4i)(5 - 4i)} [/tex]

[tex] \frac{20-16i+20i-16i^2}{(5) {}^{2} - (4i) {}^{2} } [/tex]

(combining like terms)

[tex] \frac{20+(-16i+20i)-(-16)}{25-(-16)} [/tex]

[tex] \frac{(20+16)+4i}{25+16} [/tex]

[tex] \frac{36+4i}{41} [/tex]

distributing the denominator

[tex] \frac{36}{41} + \frac{4}{41}i [/tex]

That is, option B.

Answer:

Volume - 582.8848178 cm cubed

Step-by-step explanation:

Volume - to fine the volume start with the cone...

The formula is 1/3 pi r^2h

so for this problem it would be

1/3 * 3.14 * 26.01 * 11.2

so your answer would be...

305.061213 cm cubed

Your next step is to find the volume of the dome. to do that the formula is (4/3 pi r^3)/2

so for this problem it would be

(4/3 * 3.14 * 132.651)/2

so your answer would be...

277.8236048 cm cubed

Finally you add together those 2 volumes and get 582.8848178 cm cubed as your final answer.

Answer:

Total no. of students =175

percent of students athletes who attend a preseason meeting =84

No. of students who attend the meeting

= 84% of 175

=147

Answer:

Range = -1 ≤ y ≤ 2

Step-by-step explanation:

The function's range is the y-values the function can have as its output. -1 is the minimum y-value and 2 is the maximum y-value.

Step-by-step explanation:

[tex]\dfrac{dy}{dx} = \dfrac{2x}{y(x^2 + 1)}[/tex]

Rearranging the terms, we get

[tex]ydy = \dfrac{2xdx}{x^2 + 1}[/tex]

We then integrate the expression above to get

[tex]\displaystyle \int ydy = \int \dfrac{2xdx}{x^2 + 1}[/tex]

[tex]\displaystyle \frac{1}{2}y^2 = \ln |x^2 +1| + k[/tex]

or

[tex]y = \sqrt{2\ln |x^2 + 1|} + k[/tex]

where I is the constant of integration.

Hello,

Answer A

[tex]dom (B(n)) =\{0,1,2,3\} =\{ z\ in \ \mathbb{Z} \ |\ 0 \leq z \leq 4\}[/tex]

f(0) = 56

f(2) = 42

f(-2) = 70

f(x+1) = 7|x-7|

f(x²+2) = 7|x²-6|

Answered by GAUTHMATH

Answer:

1849  

Step-by-step explanation:

Margin of error, E=0.03

Confidence level=0.99

z=2.58

No prior estimate of p is given, so consider p=0.5

Sample size required ,n=2.58^2*0.5*(1-0.5)/0.03^2

n=1849  

Answer:

a) false

b) true

c) true

d) true

e) false

Step-by-step explanation:

In a statement of the type:

p ∧ q

where ∧ means "and"

The statement is true only if both p and q are true

the statement is false if p, q, or both, are false.

and in the case of:

p ∨ q

where ∨ means "or"

The statement is true if at least one of p or q (or both) are true.

The statement is false if both are false.

Now that we know that, let's solve the problem:

a) "5 is an odd number and 3 is a negative number."

Here we have:

p = 5 is an odd number

We know that this is true

q = 3 is a negative number

This is false.

then the complete statement is false.

b) "5 is an odd number or 3 is a negative number."

here we have:

p = 5 is an odd number.

this is true

q = 3 is a negative number

because in this case we have an "or", with only p being true, the whole statement is true.

c) "8 is an odd number or 4 is not an odd number."

p = 8 is an odd number  (this is false)

q = 4 is not an odd number  (this is true, 4 is a even number)

Again, we have an "or", so we need only one true proposition, then the statement is true.

d) "6 is an even number and 7 is odd or negative."

p = 6 is an even number  (true)

q = 7 is odd or negative  (notice that we have an or, and 7 is odd is true, so this proposition is true)

Then both propositions are true, then the statement is true.

e) "It is not true that either 7 is an odd number or 8 is an even number (or both)."

This is most complex, this will be true if at least one of the propositions is false.

but:

7 is an odd number is true

8 is an even number is true.

Then both statements are true, which means that the statement is false.

9514 1404 393

Answer:

  y = -4/7x +58/7

Step-by-step explanation:

The slope of the given line segment is ...

  m = (y2 -y1)/(x2 -x1)

  m = (17 -3)/(1 -(-7)) = 14/8 = 7/4

Then the slope of the perpendicular line is ...

  -1/m = -4/7 . . . . . slope of the perpendicular bisector.

__

The midpoint of the given line segment is ...

  M = 1/2(x1 +x2, y1 +y2)

  M = (1/2)(-7 +1, 3 +17) = 1/2(-6, 20) = (-3, 10)

__

The y-intercept of the bisector can be found from ...

  b = y -mx

  b = 10 -(-4/7)(-3) = 10 -12/7 = 58/7

Then the slope-intercept form equation for the perpendicular bisector is ...

  y = mx +b

  y = -4/7x +58/7

Answer:

.0421

about 4.21%

Step-by-step explanation:

[tex]\frac{{8\choose3}}{{21\choose3}}=\frac{56}{1330}=.042105263[/tex]

Answer:

[tex]b_0 = 16.471[/tex]

Step-by-step explanation:

Given

[tex]\begin{array}{ccccc}x & {15} & {12} & {10} & {7} \ \\ y & {5} & {7} & {9} & {11} \ \end{array}[/tex]

Required

The least square estimate [tex]b_0[/tex]

Calculate the mean of x

[tex]\bar x = \frac{\sum x}{n}[/tex]

[tex]\bar x = \frac{15+12+10+7}{4} =\frac{44}{4} = 11[/tex]

Calculate the mean of y

[tex]\bar y = \frac{\sum y}{n}[/tex]

[tex]\bar y = \frac{5+7+9+11}{4} =\frac{32}{4} = 8[/tex]

Calculate [tex]\sum(x - \bar x) * (y - \bar y)[/tex]

[tex]\sum(x - \bar x) = (15 - 11) * (5 - 8)+ (12 - 11) * (7 - 8) + (10 - 11) * (9 - 8)+ (7 - 11) * (11 - 8)[/tex]

[tex]\sum(x - \bar x) = -26[/tex]

Calculate [tex]\sum(x - \bar x)^2[/tex]

[tex]\sum(x - \bar x)^2 = (15 - 11)^2 + (12 - 11)^2 + (10 - 11)^2 + (7 - 11)^2[/tex]

[tex]\sum(x - \bar x)^2 = 34[/tex]

So:

[tex]b = \frac{\sum(x - \bar x) * (y - \bar y)}{\sum(x - \bar x)^2}[/tex]

[tex]b = \frac{-26}{34}[/tex]

[tex]b_0 = y - bx[/tex]

[tex]b_0 = 5 - \frac{-26}{34}*15[/tex]

[tex]b_0 = 5 + \frac{26*15}{34}[/tex]

[tex]b_0 = 5 + \frac{390}{34}[/tex]

Take LCM

[tex]b_0 = \frac{34*5+ 390}{34}[/tex]

[tex]b_0 = \frac{560}{34}[/tex]

[tex]b_0 = 16.471[/tex]

Answer:

32 miles per hour

Step-by-step explanation:

x+85+75=192 x+160=192 x=192-160 x=32..

Answer:

- 3.027

Step-by-step explanation:

First price = 10000 ; second price = 700

Number of tickets sold = 11000

Ticket cost = $4

Probability that a ticket wins grand price = 1 / 11000

Probability that a ticket wins second price = 1 / 11000

X ____ 10000 _____ 700

P(x) ___ 1 / 11000 ___ 1/11000

Expected winning for a ticket buyer :

E(X) = Σx*p(x)

E(X) = (1/11000 * 10000) + (1/11000 * 700) - ticket cost

E(X) = 0.9090909 + 0.0636363 - 4

E(X) = - 3.0272728

E(X) = - 3.027

Answer:

The numerical values of the circumference and area of the circle are equal.

Answer:

8. 36

Step-by-step explanation:

8.

The diameter of the square is x=[tex]\sqrt{6^{2} +6^{2} }\\[/tex] = [tex]\sqrt{72}[/tex] = 6 [tex]\sqrt{2}[/tex]

The diameter of the square is the diameter of the circle, therefore the radius of the circle is r = 6 [tex]\sqrt{2}[/tex]/2 = 3[tex]\sqrt{2}[/tex]

The area of the shaded region, which is a circle is A= π[tex]r^{2}[/tex] =  π[tex](3\sqrt{2} )^{2}[/tex] = 36π

Answer:

The standard deviation is of 8.586.

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they have a genetic mutation, or they do not. The probability of a person having the mutation is independent of any other person, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

About 9% of the population has a particular genetic mutation.

This means that [tex]p = 0.09[/tex]

900 people are randomly selected.

This means that [tex]n = 900[/tex]

Find the standard deviation for the number of people with the genetic mutation in such groups of 900.

[tex]\sqrt{V(X)} = \sqrt{900*0.09*0.91} = 8.586[/tex]

The standard deviation is of 8.586.

Let f(x) be the sum of the geometric series,

[tex]f(x)=\displaystyle\frac1{1-x} = \sum_{n=0}^\infty x^n[/tex]

for |x| < 1. Then taking the derivative gives the desired sum,

[tex]f'(x)=\displaystyle\boxed{\dfrac1{(1-x)^2}} = \sum_{n=0}^\infty nx^{n-1} = \sum_{n=1}^\infty nx^{n-1}[/tex]

Answer:2x + 50 > 68

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

because is you skip count on two you will count on to 68 so that is why the answer is 7.