hi can you help me?​

Answer:

B

Step-by-step explanation:

Using Pythagoras' identity in right triangle ABC

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

AB² + AC² = BC² , substitute values

5² + AC² = 13²

25 + AC² = 169 ( subtract 25 from both sides )

AC² = 144 ( take the square root of both sides )

AC = [tex]\sqrt{144}[/tex] = 12

Since the triangles are congruent then corresponding sides are congruent, then

DE = AC = 12 inches → B

Answer:

Total surface area of the prism = 920 cm²

Step-by-step explanation:

Given prism has 2 similar triangular surfaces and 3 rectangular surfaces of different dimensions.

Area of one triangular side = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]

Area of 2 similar sides = Base × Height

                                     = 8 × 15

                                     = 120 cm²

Area of rectangular side with dimensions 17cm × 20cm

Area of the side = 17 × 20 = 340 cm²

Area of the second rectangular side with dimensions 8cm × 20cm

Area of the side = 8 × 20 = 160 cm²

Area of third rectangular side with dimensions 20cm × 15cm

Area of the side = 20 × 15 = 300 cm²

Total surface area of the given triangular prism = 120 + 340 + 160 + 300

                                                                               = 920 cm²

Answer:

6/20 as a decimal is 0.3 i hope i helped you

Given:

The two points on a coordinate plane are C(-5,-1) and D(0,3).

To find:

The distance between C and D.

Solution:

Distance formula:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Using the distance formula, the distance between C(-5,-1) and D(0,3) is

[tex]CD=\sqrt{(0-(-5))^2+(3-(-1))^2}[/tex]

[tex]CD=\sqrt{(0+5)^2+(3+1)^2}[/tex]

[tex]CD=\sqrt{(5)^2+(4)^2}[/tex]

[tex]CD=\sqrt{25+16}[/tex]

On further simplification, we get

[tex]CD=\sqrt{41}[/tex]

[tex]CD=6.40312424[/tex]

[tex]CD\approx 6.40[/tex]

Therefore, the distance between C and D is 6.40 units.

Answer:

The median is 2

Step-by-step explanation:

The middle number of the data set(highlighted dots) is 2.

Hope this helps!

:)

Answer:

Step-by-step explanation:

Answer:3b+10

Explanation:Distribution:5(b+2)-2b

5b+10b-2b

Combine like terms:5b+10b-2b

=3b+10

Answer:

3b+10

Step-by-step explanation:

Answer:

$1856.47

Step-by-step explanation:

500 x 1.3^5=1856.465

Answer:

The numbers which have definite value is known as constant. The numbers which don't have a definite value is known as variables.

Answer:

What?

Step-by-step explanation:

Answer:

- 1

Step-by-step explanation:

[tex]\frac{1}{\cot ^2\left(x\right)}-\frac{1}{\cos ^2\left(x\right)}\\\\\mathrm{Use\:the\:basic\:trigonometric\:identity}:\quad \frac{1}{\cos \left(x\right)}=\sec \left(x\right),\\\frac{1}{\cot ^2\left(x\right)}-\sec ^2\left(x\right)\\\\\mathrm{Use\:the\:basic\:trigonometric\:identity}:\quad \frac{1}{\cot \left(x\right)}=\tan \left(x\right),\\\tan ^2\left(x\right)-\sec ^2\left(x\right)\\\\=> \frac{\sin ^2\left(x\right)}{\cos ^2\left(x\right)}-\frac{1}{\cos ^2\left(x\right)}\\[/tex]

[tex]=> \frac{\sin ^2\left(x\right)-1}{\cos ^2\left(x\right)}\\\\=> -\frac{\cos ^2\left(x\right)}{\cos ^2\left(x\right)}\\=> - 1[/tex]

Hope  that  helps!

By using trigonometric identities,  [tex]\frac{1}{cot^{2}(x) } -\frac{1}{cos^{2}(x) }[/tex] = -1

"Trigonometric identities are equations that relate to different trigonometric functions and are true for any value of the variable that is there in the domain."

Given expression

[tex]\frac{1}{cot^{2}(x) } -\frac{1}{cos^{2}(x) }[/tex]

We know the trigonometric identity

[tex]{cot^{2}(x) } =( \frac{sinx}{cosx})^{2}[/tex]

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

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

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

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

We know the trigonometric identity

[tex]sin^{2}(x) +cos^{2}(x) = 1[/tex]

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

= -1

Hence, [tex]\frac{1}{cot^{2}(x) } -\frac{1}{cos^{2}(x) }[/tex] = -1

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Answer:

negative

1

4,6

Step-by-step explanation:

Answer:

A&C

Step-by-step explanation:

Answer:

180-165= 15

(They tried to throw you off with the second line)

Answer is 15 degrees

Answer:

=177

Step-by-step explanation:

The sum of the digits in the expansion (10³⁶ + 26/18) will be 18.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ (10³⁶ + 26/18)

The sum of the digits in the expansion is given as,

⇒ 1 + 0 + 2 + 6 + 1 + 8

⇒ 18

The sum of the digits in the expansion (10³⁶ + 26/18) will be 18.

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Answer:

0.08

Step-by-step explanation:

Answer:

0.8=x

Step-by-step explanation:

4x+8=7.2+5x

Subtract 4x from both sides of the equation. This eliminates 4x from one side of the equation and leaves the other side with just 1x or x.

Subtract 7.2 from both sides of the equation to isolate x.

So this concludes that 0.8=x

To check your answer, substitute 0.8 into x.

Answer:

Step-by-step explanation:

wow, this is kinda complicated math for HS..  :?   we have to know what type of series this is, and that means knowing all the different kinds.. unless maybe in the instructions it tells you you are working with arithmetic series? It is one of those so we can use those formulas... other series can have much more complex formulas..  series comes up in Calc II in college.. but .. unless you're going to be an engineer you probably don't need it..  soooooo anyway..

we can use  Sn = n/2(2a1 + d(n-1) )

where d is the difference of a2 -a1 ( this will be the same for all terms)

since we're given Sn = 209 set the problem to 209 and solve for n  :/

sounds hard huh.. :?  let's see

209 = n/2( 2(4) + 3(n-1))

209 = n/2(8 + 3n-3)

209 = n/2(5+3n)

2*209 = n(5+3n)

418 = 3[tex]n^{2}[/tex] + 5n

0 = 3[tex]n^{2}[/tex] + 5n-418    ( use quadratic formula to find n )

( -5 ± [tex]\sqrt{5^{2}-4*3*(-418) }[/tex]  ) / 2(3)

( -5 ±[tex]\sqrt{25+5016}[/tex] ) / 6

( -5 ±[tex]\sqrt{5041}[/tex] ) / 6

( -5 ± 71 ) / 6  ( they were nice to us and make it work out perfectly :)  )

positive route =  71-5 /6 = 66/6 =11

negative route = 71-(-5) /6  = 71+5/6 = 76/6 = 12[tex]\frac{2}{3}[/tex]

since 12[tex]\frac{2}{3}[/tex]  isn't going to really work for us... let's try 11

an= a1 + d(n-1)

an = 4 + 3(11-1)

an = 4 + 30

an = 34

now let's see if we can get 209 for our 11 terms of the series

Sn = 11/2(2(4) + 3(11-1))

Sn = 11/2(8 + 30)

Sn = 418 /2

Sn = 209  yay.. we got it.. it's the 11th term.. and thank you  quadratic formula.  You get a Christmas present this year  :P

n = 11

The number of the terms of the sequence will be equal to 11.

The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression.

Given series is  4+7+10+.....  and the sum of the terms of the series is 209.

The summation of the n terms of the series is written by the formula below,

Sn = n / 2 [( 2a+(n-1)d]

Substitute the values in the equation above,

209 = n / 2 [(2 x 4 + ( n -1)3]

418 = n(5+3n)

3n² + 5n - 418 = 0

The above quadratic equation will give two values of n. The values of n are,

n = 11

n = -12.55

The terms can not be equal to a negative number.

Therefore, the number of the terms of the sequence will be equal to 11.

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Answer:

y = 3x - 14

Step-by-step explanation:

y - y₁ = m(x - x₁)

⇒ y - 1 = 3(x - 5)

⇒ y - 1 = 3x - 15

⇒ y = 3x - 14

Answer:

The operation is commutative

Step-by-step explanation:

Operations

The * operation is defined on the set of real numbers R by

[tex]a * b=a^3+b^3-3ab[/tex]

For the operation to be commutative a*b should be equal to b*a.

Computing b*a:

[tex]b * a=b^3+a^3-3ba[/tex]

Rearranging:

[tex]b * a=a^3+b^3-3ab[/tex]

It's apparent that a*b=b*a, thus the operation is commutative

Answer:

The answer is 51 degrees

Step-by-step explanation:

i like to convert the fraction first and then round up

Step-by-step explanation:

y=-2x²-25x+10

=x²+25/2x-5

Answer:

= 0.2 pound per day

Step-by-step explanation:

This is a fraction equal to

1 pound ÷ 5 days

We want a unit rate where

1 is in the denominator,

so we divide top and bottom by 5

1 pound ÷ 5

5 days ÷ 5

=  

0.2 pound

1 day

=  

0.2 pound

day

= 0.2 pound per day

Answer:

every other term is negative, so it would be -64

Step-by-step explanation:

hope it helps!

Answer:

I dont know

Step-by-step explanation:

Answer:

2/3

Step-by-step explanation:

You first multiply 4x1/3 which equals 4/3. Now you do -2/3+4/3=2/3. Hope this helps!

Answer:

2/3

Step-by-step explanation:

[tex]\frac{-2}{3}+4*\frac{1}{3}=\frac{-2}{3}+\frac{4}{3}\\\\=\frac{(-2) + 4}{3}\\\\\\= \frac{2}{3}[/tex]

Answer:

Step-by-step explanation:

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Answer:

x = [tex]\frac{b-7}{a-2}[/tex]

Step-by-step explanation:

Given

ax + 7 = 2x + b ( subtract 2x from both sides )

ax - 2x + 7 = b ( subtract 7 from both sides )

ax - 2x = b - 7 ← factor out x from each term on the left side

x(a - 2) = b - 7 ← divide both sides by (a - 2)

x = [tex]\frac{b-7}{a-2}[/tex]

Answer:

1/3, 2/6, 3/9, 4/12..are equivalent fractions. Equivalent fraction of a given fraction is got by multiplying or dividing its numerator and denominator by the same whole number. For example, if we multiply the numerator and denominator of 2/3 by 4 we get.

Step-by-step explanation:

The equivalent fractions of  the given fraction [tex]\dfrac{2}{6}[/tex] are [tex]\dfrac{4}{12} ,\dfrac{6}{18} ,\dfrac{8}{24}[/tex] .

The fractions which have the same value but can  have different numerators or denominators when either multiplying , dividing or converting it into the lowest form is called equivalent fractions

The upper part of a fraction or part of a whole is called numerator and the lower part of a fraction or the whole is called denominator.

Equivalent fraction can be obtained by multiplying  numerator and denominator with the same number .

Example : equivalent fraction of  [tex]\dfrac{5}{8}[/tex] is

[tex]\dfrac{5}{8} = \dfrac{5 \times 1 }{8 \times 1} =\dfrac{5\times2}{8\times2} ........=\dfrac{5}{8}[/tex]

According to the data provided in the problem

[tex]\dfrac{2}{6} = \dfrac{2 \times 1 }{6 \times 1} =\dfrac{2\times2}{6\times2} ........=\dfrac{2}{6}[/tex]

Thus the equivalent fractions of [tex]\dfrac{2}{6}[/tex] are  [tex]\dfrac{4}{12} ,\dfrac{6}{18} ,\dfrac{8}{24}[/tex]

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