(-5.12)-(-4.7)+(7.021

Answer:

If a = B and b = C, then

a = C

Answer:

13) The planes ABF and FHG are  perpendicular

14)  Segments Ab and CD are parallel.

Step-by-step explanation:

13)

Planes ABF and FHG are perpendicular (they intersect along side EF)

14)

In order to find out about the segments AB and CD, let's use the formula for the slope that joins any two points [tex](x_1,y_1)\,\,\&\,\,(x_2,y_2)[/tex] on the plane:

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

Therefore, given:

A = (-3, 2)

B = (1, 4)

C = (-3, -1)

D = (1, 1)

we have for segment AB the following slope:

[tex]slope_{AB}=\frac{4-2}{1+3} =\frac{2}{4} =\frac{1}{2}[/tex]

and for segment CD the following slope:

[tex]slope_{CD}=\frac{1+1}{1+3} =\frac{2}{4} =\frac{1}{2}[/tex]

Since they show the same slope, these two segments are parallel.

Answer:

  yes

Step-by-step explanation:

Every polynomial has "all real numbers" in its domain. 5 is a real number, so is in the domain of f(x).

Answer:

Step-by-step explanation:

Given , value of b = -4

To find : ( - b )²

plug the value of b

⇒[tex] \sf{( - {( - 4))}^{2} }[/tex]

we know that ,

[tex] \sf{( - ) \times ( - ) = ( + )}[/tex]

⇒[tex] \sf{ {4}^{2} }[/tex]

Evaluate the power

⇒[tex] \sf{16}[/tex]

Hope I helped!

Best regards!!

Answer:

8 feet

Step-by-step explanation:

Distance can be explained as the way to measure how far a thing or something is apart from each other numerically, it shows how close or far apart between two point

From the question, we are given two point

Point1= 12 feet

Point 2= 4 feet

Then Distance between the two point= 12feet-4feet

= 8feet

Hence the distance= 8 feet

Hey there! I'm happy to help!

QUESTION 100

Here, we are looking for the number of permutations. A permutation is the number of possible arrangements you can make from a given set of things (order matters). If you have 6 kids standing in alphabetical order in line, that is one permutation. If you do reverse alphabetical order, that is a different permutation.

We are asked to find the number of permutations using the given format:

[tex]_{n}P_{r}\\[/tex]

This is simply a representation of what we want to find. The P means we are looking for the number of permutations. The n is the total number of objects in the set (for example, if there were 26 kids we could choose from to make this 6 person line, n would be 26). The r is the number of things chosen from the set (in our line example, the r would be six because we are choosing 6 kids).

The formula for finding the number of permutations is [tex]\frac{n!}{(n-r)!}[/tex]. The ! is factorial, it means you multiply that number by every integer counting backwards towards 1. 6! is 6×5×4×3×2×1. There is an option to do this on your calculator, though.

Let's solve this problem.

[tex]_{5}P_{4}=\frac{5!}{(5-4)!}= \frac{120}{1} =120[/tex]

This means that there are 120 permutations.

QUESTION 101

Now we have a C. This is similar to permutations but with combinations order does not matter. With our line example, having the same six kids in alphabetical order is a different permutation than having it in backwards alphabetical order. With combinations, if you have those specific six kids, it is just one combination; the order does not matter.

The formula for combinations is [tex]\frac {n!}{r!(n-r)!}[/tex]. Let's plug in our numbers and solve for this.

[tex]_{8}C_{2}=\frac{8!}{2!(8-2)!} =\frac{8!}{2!(6!)}=\frac{40320}{1440} =28[/tex]

QUESTION 102

Quick note: 0! is equal to 1. I don't really know why but there's probably proof somewhere.

[tex]_{7}C_{0}=\frac{7!}{0!(7-0)!} =\frac{7!}{7!} =1[/tex]

And I believe you already have Question 103 figured out.

4!=4×3×2×1=24

Have a wonderful day! :D

Answer:

Step-by-step explanation:

Given the exponential growth formula expressed as [tex]P = Ae^{kt}[/tex] where P is the countrys population and t is the time.

Initially in 1991, at t= 0, P = 147 million

[tex]P = Ae^{kt}\\147 = Ae^{k(0)}\\147 = Ae^0\\147 = A(1)\\A = 147[/tex]

If by 1998 it was 153 million, this means that the population is 153 million 7 years later i.e when t = 7, P = 153. On substituting into the formula to get the constant 'k';

[tex]P = Ae^{kt}\\153 = 147e^{k(7)}\\153 = 147e^{7k}\\153/147 = e^{7k}\\e^{7k} = 1.041\\Taking \ ln \ of \ both \ sides\\lne^{7k} = ln 1.041\\7k = 0.04018\\k = 0.04018/7\\k = 0.00574[/tex]

To estimate the population in 2017, to number of years from 1991 to 2017 is 26 years. Hence we are to find the value of P given t = 27, A = 147 and k = 0.00574

[tex]P = Ae^{kt}\\P = 147e^{0.00574*26}\\P = 147e^0.14924\\P = 147*1.16095\\P = 170.659[/tex]

Hence the population in 2017 using exponential growth formula to the nearest million is 171 million.

Answer:

Hey there!

3 x 5/4 = 3 x 5 ÷ 4 = 5 x 3 ÷ 4

5 x 4/3 = 5 x 4 ÷ 3 = 4 x 5 ÷ 3

4 x 3/5 = 4 x 3 ÷ 5 = 4 x 3 ÷ 5

Hope this helps :)

Answer:

x = 80.4

Step-by-step explanation:

Step 1: Realize you have to use tangent to solve

[tex]tan()=\frac{o}{a}[/tex]

Step 2: Use tangent to solve

o = x

a = 300

[tex]tan()=\frac{o}{a} \\tan(15)=\frac{x}{300}\\x = 300tan(15)\\x = 80.4[/tex]

Therefore x is equal to 80.4 rounded to the nearest tenth

Answer:

Step-by-step explanation:

[tex]Opposite = x\\Adjacent = 300\\\alpha =15\\Using \: SOHCAHTOA\\\\Tan \alpha = \frac{Opposite}{Adjacent} \\\\Tan 15 =\frac{x}{300} \\\\2-\sqrt{3} = \frac{x}{300}\\\\ 2-\sqrt{3} \times 300=x\\\\80.384=x\\\\x = 80.4[/tex]

Answer:

C

Step-by-step explanation:

Given

f(x) = 3x - 40 and f(x) = 8 , then equate the right sides, that is

3x - 40 = 8 ( add 40 to both sides )

3x = 48 ( divide both sides by 3 )

x = 16 → C

Answer:

A,C, and D I believe.

Step-by-step explanation:

In 1 minute, bison runs 3520 feet

In 60 minutes, the bison would run

3520*60 feet

211200 feet per hour.

These are equivalent to;

40 miles per hour since 1 mile is equivalent to 5280 feet.

The bison is faster by 10 miles per hour

Answer:

144

Step-by-step explanation:

Using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]

Given

4[tex]\sqrt{2}[/tex] × 6[tex]\sqrt{18}[/tex]

= 4 × 6 × [tex]\sqrt{2}[/tex] × [tex]\sqrt{18}[/tex]

= 24 × [tex]\sqrt{36}[/tex]

= 24 × 6

= 144

Step-by-step explanation: the answers are a and d

Answer:

a d

Step-by-step explanation:

got it right

Answer:

sue = 18  

tony = 18

sue = 18 - x  

tony = 18 + x  

sue = 18 - x - 5  

tony = (18 + x) / 2  

sue = 13 - x  

tony = (18 + x) / 2

Step-by-step explanation:

You Simplify The Equation by using PEMDAS

P: Parentheses

E: Exponents

M: Multiplication

D: Division

A: Addition

S: Subtraction

Answer:

Your value expression is 10

Step-by-step explanation:

We know that [tex]1\frac{1}{2}=\frac{3}{2}=1.5[/tex]

The value experssion:

Giving: [tex]\frac{9.5-3(1\frac{1}{2}) }{0.5}[/tex]

Change [tex]1\frac{1}{2}[/tex] into a whole number:  [tex]\frac{9.5-3(1.5)}{0.5}[/tex]

Multiply 3 into 1.5: [tex]\frac{9.5-4.5}{0.5}[/tex]

Divide: [tex]\frac{5}{0.5}[/tex]

Your answer equals: 10

Answer:

x = 9

Step-by-step explanation:

Take the angle of LOJ (3x) and JOK (2x+12).

LOJ + JOK = LOK.

LOK = 57.

So, 3x + 2x + 12 = 57

3x + 2x = 5x

5x + 12 = 57

57 - 12 = 45

5x = 45

x= 9

Answer:

SU = 70

Step-by-step explanation:

First, we need to find the value of x. Since M is the midpoint of SU, that means that SM = MU, therefore:

x + 15 = 4x - 45

15 = 3x - 45

60 = 3x

x = 20

We know that SU = SM + MU = (x + 15) + (4x - 45) = 5x - 30 and that x = 20 so SU = 5x - 30 = 5 * 20 - 30 = 100 - 30 = 70.

The evaluation of the numeric expression is:

5(−6) = -30

A numeric expression is a mathematical statement that involves only numbers and one or more operation symbols.

Examples of operation symbols are addition, subtraction, multiplication and division. It can also be expressed in the radical symbol (the square root symbol) or the absolute value symbol.

We can evaluate 5(−6) as follow:

5(−6) = 5 * (-6)

        = -30

Learn more about numeric expression on:

https://brainly.com/question/4344214

#SPJ6  

Answer:

2(x-5)

Step-by-step explanation:

the number will be ''x''

difference between the number (x) and 5 =

                 x-5

twice the difference is =

            2(x-5)

Answer: a piecewise function is a function that is defined on a sequence of intervals.

Step-by-step explanation:

A piecewise function is a function that is "different" at different intervals.

The function may behave linearly between x = 0 and x = 10, and after that point, the function may be constant for a while, then change again.

This type of functions can be written as:

f(x) = g(x) if x1 ≤ x ≤ x2

f(x) = h(x) if x2 ≤ x ≤ x3

f(x) = k(x) if x3 ≤ x ≤ x4

and so on, where g(x), h(x) and k(x) are different functions, and those functions only act on the givenintervals: (x1, x2), (x2, x3) and (x3, x4)

Answer:

A

Step-by-step explanation:

We would like to find the value of x.

Since the triangle is isosceles, the drawn altitude bisects the base of length 8. This means that the big triangle is split into two congruent triangles with base 4 and height 5.

Notice that by definition, as well, the altitude of 5 is perpendicular to the base of length 8. So, we have two right triangles, each with legs of 4 and 5 and hypotenuse x.

We apply the Pythagorean Theorem, which states that for a right triangle with legs a and b and hypotenuse c:

a² + b² = c²

Here, we have:

4² + 5² = x²

16 + 25 = x²

41 = x²

x = √41

The answer is thus A.

~ an aesthetics lover

Answer:

length: 30 meters

width: 12 meters

Step-by-step explanation:

2(a+b) = 84

a = 2b + 6

a = length

b = width

then:

2((2b+6)+b) = 84

2b + 6 + b = 84/2

3b + 6 = 42

3b = 42 - 6

3b = 36

b = 36/3

b = 12

a = 2b + 6

a = 2*12 + 6

a = 24 + 6

a = 30

Check:

84 = 2(12+30)

84 = 2*42

Answer:

w = -1

Step-by-step explanation:

Answer:

[tex]\Huge \boxed{w=-1}[/tex]

Step-by-step explanation:

[tex]w-5-4= -8-6w+8w[/tex]

Combining like terms.

[tex]w-9= -8+2w[/tex]

Adding -w and 8 to both sides.

[tex]-9+8=2w-w[/tex]

[tex]-1=w[/tex]

Answer:

25

Step-by-step explanation:

97-72= 25

Hope this helped!

Answer:

25

Step-by-step explanation:

97-72= 25

Answer:79°

Step-by-step explanation:

Given the 124° angle, the other angle formed by that line and the top side of the square must be 56°, as they are supplementary angles (they must add up to 180°). This means that the angle formed by that same line and the bottom side of the square is also 56° since it is a corresponding angle and the top and bottom sides of a square are parallel. The angle that a diagonal of a square forms with the sides of a square is always 45°.

So now we have a triangle (in red in my diagram) with angles of 45°, 56°, and x°. The sum of the angles of a triangle must always equal 180°, so we solve for x:

56 + 45 + x = 180

x = 180 - 56 - 45 = 79

So angle x must be 79°.

Answer:

here is a formulae

cos2A= 2cos square a -1

Step-by-step explanation:

as given cos A= 1/2 (a+1/a)

by simplifying

cosA =a²+1/2a

now by following the formulae

cos2A = 2cos²A-1

=2(a²+1/2a)² -1

=2(a⁴+2a²+1/4a²)-1

=a⁴+2a²+1/2a² -1

=a⁴+2a²+1-2a²/2a²

=a⁴+1/2a²

=1/2 (a⁴+1/a²)

=1/2(a⁴/a²+1/a²)

=1/2(a²+1/a²)

{proved}

please mark me as a brainilist...plzzz

thank uuu

Answer:  see proof below

Step-by-step explanation:

Use the Double Angle Identity: cos 2A = 2cos²A - 1

Proof  LHS → RHS

Given:                                [tex]\cos A=\dfrac{1}{2}\bigg(a+\dfrac{1}{a}\bigg)[/tex]

LHS:                                   cos 2A

Double Angle Identity:      2(cos²A) - 1

                                     [tex]=2\bigg(\dfrac{1}{2}\bigg(a+\dfrac{1}{a}\bigg)^2\bigg)-1[/tex]

Simplify:                           [tex]2\bigg(\dfrac{1}{4}\bigg(a^2+2+\dfrac{1}{a^2}\bigg)\bigg)-1[/tex]

                                     [tex]=\dfrac{1}{2}\bigg(a^2+2+\dfrac{1}{a^2}\bigg)-1[/tex]

                                    [tex]=\dfrac{1}{2}a^2+1+\dfrac{1}{2a^2}-1[/tex]

                                    [tex]=\dfrac{1}{2}a^2+\dfrac{1}{2a^2}[/tex]

Factor:                         [tex]=\dfrac{1}{2}\bigg(a^2+\dfrac{1}{a^2}\bigg)[/tex]

[tex]\dfrac{1}{2}\bigg(a^2+\dfrac{1}{a^2}\bigg)=\dfrac{1}{2}\bigg(a^2+\dfrac{1}{a^2}\bigg)\quad \checkmark[/tex]

Answer:

Complement​t angle = 44°

Step-by-step explanation:

Given:

One angle = 46°

Find:

Complement​t angle

Computation:

In complement​ angle

∠A + ∠B = 90°

46° + ∠B = 90°

∠B = 90° - 46°

∠B = 44°

Complement​t angle = 44°

Answer:

1 + 1 · 7 + 1 · 72 + . . . 1 · 76

Step-by-step explanation:

bc

Answer:

1 + 1 · 7 + 1 · 72 + . . . 1 · 76

Step-by-step explanation:

Hope this helps!