The value of the expression 16-^3/4 is___
8
1/8
-6
6
1/40
1/64

Answer:

The constant of proportionality in the equation y=5/9x​ is k=5/9.

Step-by-step explanation:

Equation for direct proportional function is  

y = kx, where k is a constant of proportionality

so for   y=5/9 x

k=5/9.

Answer:

f(x) × g(x)= x^4 - x^3 - 28x^2 + 16x + 192

Step-by-step explanation:

We have the function f(x) = x^2 − x − 12  and g(x) = x^2 − 16 and we need to find the multiplication of both functions.

f(x) × g(x) = ( x^2 − x − 12)(x^2 − 16) = x^4 - 16x^2 -x^3 + 16x -12x^2 + 192

Simplifying:

f(x) × g(x)= x^4 - x^3 - 28x^2 + 16x + 192

Answer: [tex]f(x)*g(x)=x^4-x^3-28x^2+16x+192[/tex]

Step-by-step explanation:

Given the function f(x) and g(x):

[tex]f(x)=x^2 - x -12\\\\g(x)= x^2 - 16[/tex]

We need to multiply them. To do this we need to remember the Product of power property, which states:

[tex](a^m)(a^n)=a^{(m+n)}[/tex]

And the multiplication of signs:

[tex](+)(+)=+\\(+)(-)=-\\(-)(-)=+[/tex]

Then:

[tex]f(x)*g(x)=(x^2 - x -12)(x^2 - 16)\\\\f(x)*g(x)=x^4-16x^2-x^3+16x-12x^2+192[/tex]

Adding like terms, we get:

[tex]f(x)*g(x)=x^4-x^3-28x^2+16x+192[/tex]

Answer:

(5, - 4)

Step-by-step explanation:

Given a quadratic in standard form : ax² + bx + c : a ≠ 0

Then the x- coordinate of the vertex is

[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]

x² - 10x + 21 ← is in standard form

with a = 1, b = - 10, so

[tex]x_{vertex}[/tex] = - [tex]\frac{-10}{2}[/tex] = 5

Substitute x = 5 into the quadratic for the corresponding value of y

y = 5² - 10(5) + 21 = 25 - 50 + 21 = - 4

vertex = (5, - 4)

Answer:

Equation of this line is y = 1

Step-by-step explanation:

We have to write an equation of a line passing through (0,1) and slope 0.

Standard equation of a line in slope form is y = mx + c

Where m = slope and c = y intercept.

Since m = 0

so y = c is the equation.

This line passes through (0,1)

so equation will be Y = 1

Equation of this line is y = 1

Answer:

Attached below

Step-by-step explanation:

Given f(x) =1/x    and g(x) = x-2   then;

f.g (x) = f (g(x) )

         =f(x-2)

        =1/x⇒⇒⇒1/x-2

    f.g(x)    =  

[tex]\frac{1}{x-2}[/tex]

Answer:

Choice A) a² - 9a - 11.

Step-by-step explanation:

Separate the terms by the power of the variable, [tex]a[/tex].

Terms with power 2 on [tex]a[/tex]:

Terms with power 1 on [tex]a[/tex]:

Terms with power 0 on [tex]a[/tex], which are also known as constant terms:

Apply the distributive property of multiplication in reverse. In other words, factor out terms with the same power and add the coefficients.

Terms with power 2 on [tex]a[/tex]:

[tex]6a^{2} + (-5a^{2}) = (6 + (-5))a^{2} = a^{2}[/tex].

Terms with power 1 on [tex]a[/tex]:

[tex]-17 a + 8a = ((-17) + 8)a = -9a[/tex].

Constant terms:

[tex](-9) + (-2) = -11[/tex].

Add the sum of the individual terms to find the sum of the two polynomials:

[tex]a^{2} + (- 9a) +(- 11) = a^{2}-9a -11[/tex].

Use the midpoint formula

(x1 + x2/2, y1 + y2/2)

Input the corresponding numbers

(-12 +5/2, 3 + -10/2)

(-7/2,-7/2)

So, the midpoint of the line segment is (-7/2,-7/2)

The midpoint of the line segment is (-3.5, -3.5)

To find the midpoint of a line segment, we can use the midpoint formula. The formula is:

Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

Using the coordinates (-12, 3) and (5, -10), we can substitute the values into the formula:

Midpoint = ((-12 + 5) / 2, (3 + -10) / 2)

After simplifying, the midpoint is (-3.5, -3.5).

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use the substitution method

f(x)= 5x+40

f(-5)= 5(-5)+40

f(-5)= -25+40

f(-5)= 15

Answer is f(-5)= 15

Answer:

r(5)=3.05 t(5)=15

Step-by-step explanation:

x=5

r(5)=(1.25)^5

r(5)=3.05

t(5)=3(5)

t(5)=15

Use the distance formula to find the distance between each vertices:

Distance formula: √((x2-x1)^2 + (y2-y1)^2)

(-1,4) (2,7) = 4.24

(-1,4) (1,5) = 2.24

(2,7) (1,5) = 2.24

Perimeter = 4.24 + 2.24 + 2.24 = 8.72

Answer:

7.40 units

Step-by-step explanation:

Answer:

A:33,22,55

Step-by-step explanation:

Answer:

12.25 miles

Step-by-step explanation:

We can write a proportion to solve.  Miles over time in minutes

1 hour = 60 minutes

1 hours 10 minutes = 60+10 = 70 minutes

3.5 miles         x miles

---------------   = --------------

20 minutes         70 minutes

Using cross products

3.5 *70 = 20x

245 = 20x

Divide each side by 20

245/20 = 20x/20

12.25 =x

Jimmy can go 12.25 miles

Check the picture below.

Answer:

-1,-2

Step-by-step explanation:

If you are doing this for FLVS and this helped make me the brainlist

Answer: 21

Step-by-step explanation:

x is a tangent line, 56-7 is a secant line.  The length is equal to the outside segment times the entire segment. Notice that the length of the outside of the segment is equal to the entire segment for the tangent line.

[tex]x^2=7(56+7)\\\\x^2=7(63)\\\\x=\sqrt{7(63)}\\\\x=\sqrt{7(7\cdot 9)}\\\\x=7\cdot 3\\\\\large\boxed{x=21}[/tex]

Answer:The last experimental design is the best of the options: 'Compare the average number of

tomatoes that are produced by 10 tomato plants that are grown in clay soil to

the average number of tomatoes that are produced by 10 tomato plants that are

grown in sandy soil''.

The first two experimental designs measure the growth of

tomato plants, which is not necessarily related to the yield of tomatoes. The

third experimental design compares the tomato yield of the two

soils with only one plant grown in each soil. Obviously, the result obtained

from this experiment would be statistically weak. The last experimental design

compares tomato yield and also uses a larger number of plants in each soil

type, so the results obtained would be of slightly greater statistical

significance.

Step-by-step explanation:

The mean absolute deviation is M = 2.2

The mean value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values.

Mean = Sum of Values / Number of Values

Given data ,

Let the total number of plants be n

Now , the value of n = 10

And , the number of tomatoes on each plant is given by set A

Now , the value of set A = { 5 , 5 , 5 , 6 , 9 , 10 , 10 , 10 , 10 , 10 }

So , the total number of tomatoes = 5 + 5 + 5 + 6 + 9 + 10 + 10 + 10 + 10 + 10

The total number of tomatoes = 80 tomatoes

Now , the mean number of tomatoes = 80 / 10 = 8

And , the mean deviation is M

where M = 1/10 [ ( 8 - 5 ) + ( 8 - 5 ) + ( 8 - 5 ) + ( 8 - 6 ) + | ( 8 - 9 ) | + 5( 10 - 8 )

M = ( 1/10 ) [ 3 + 3 + 3 + 2 + 1 + 5 ( 2 ) ]

M = ( 1/10 ) [ 22 ]

M = 2.2

Therefore , the value of M is 2.2

Hence , the mean deviation is 2.2

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Answer:

[tex] ({ {x}^{m} )}^{3} = ( { {x}^{13} )}^{5} \times ( { {x}^{ - 8} )}^{ - 5} [/tex]

[tex] {x}^{3m} = {x}^{65} {x}^{40} [/tex]

[tex] {x}^{3m} = {x}^{105} [/tex]

[tex]3m = 105[/tex]

[tex]m = 35[/tex]

Answer:

m = 12f

Or

m/12 = f

Step-by-step explanation:

The conversion from inches to feet involves a constant factor of variation which is 12. Inches is a smaller unit while feet are obtained by dividing the inches with 12.

As we know,

1 foot = 12 inches

Given in the question:

m = measurement in inches

and

f= measurement in feet

Hence the equation will be:

m = 12f

Or

m/12 = f ..

C. to show the populations of major cities in 1500

Answer:

C. to show the populations of major cities in 1500

Step-by-step explanation:

correct on edge

Equations would you use the zero product property on is (x-5)(x-10)=0

The zero product property states that if a⋅b=0 then either a or b equal zero.

To get the positive value we have consider those factor which have negative in their expression.

As, by the property if we equate both of them equal to zero one by one then we get the desired value.

(x-5)(x-10)= 0

if x-5=0

x=5

and if, x-10=0

x=10

Hence, equations would you use the zero product property on is (x-5)(x-10).

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Answer:

If two pyramid have the same height , for volume to be the same the base area of the pyramids should be equal

Step-by-step explanation:

Volume of a pyramid is given by;

[tex]V=l*w*h /3[/tex]

where l is length of base, w is width of base, and h is height of base

If two pyramid have the same height , for volume to be the same the base area of the pyramids should be equal

The base area= l×w

For example if we have two pyramids A and B with the following properties;

A= height= x , length=l₁ and width = w₁

B= height=x, length=l₂ and width = w₂

Then the volume of the two pyramid will be the same if;

l₁*w₁=l₂*w₂

Thus

V₁= (l₁*w₁*x )/3  = (l₂*w₂*x)/3

For two pyramids with the same height to have the same volume, they must have bases with equal areas.

The volume [tex]\( V \)[/tex] of a pyramid can be calculated using the formula:

[tex]\[ V = \frac{1}{3} \times \text{base area} \times \text{height} \][/tex]

Given that the height [tex]\( h \)[/tex] is the same for both pyramids, the volume formula simplifies to:

[tex]\[ V = \frac{h}{3} \times \text{base area} \][/tex]

For the volumes [tex]\( V_1 \)[/tex] and [tex]\( V_2 \)[/tex] of the two pyramids to be equal, the following equation must hold:

[tex]\[ \frac{h}{3} \times \text{base area}_1 = \frac{h}{3} \times \text{base area}_2 \][/tex]

Since the height [tex]\( h \)[/tex] is constant for both pyramids, it can be cancelled out from both sides of the equation:

[tex]\[ \text{base area}_1 = \text{base area}_2 \][/tex]

Therefore, the bases of the two pyramids must have equal areas to ensure that they have the same volume, given that they have the same height.

Answer:

[tex]\large\boxed{x\approx-4.19\ \vee\ x\approx1.19}[/tex]

Step-by-step explanation:

[tex]x^2+3x-5=0\qquad\text{add 5 to both sides}\\\\x^2+3x=5\\\\x^2+2(x)(1.5)=5\qquad\text{add}\ 1.5^2=2.25\ \text{to both sides}\\\\x^2+2(x)(1.5)+1.5^2=5+2.25\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(x+1.5)^2=7.25\Rightarrow x+1.5=\pm\sqrt{7.25}\\\\x+1.5\approx\pm2.69\\\\x+1.5\approx-2.69\ \vee\ x+1.5\approx2.69\qquad\text{subtract 1.5 from both sides}\\\\x\approx-4.19\ \vee\ x\approx1.19[/tex]

Answer:

13170

Step-by-step explanation:

We could just use heron's formula

S=(a+b+c)/2=(155+175+260)/2=295

area=sqrt(S(S-a)(S-b)(S-c))

area=sqrt(295(140)(120)(35))

area=sqrt(173460000)

area=13170 is closest whole number

you could check my work for little errors before you enter anything in if you want :p

Answer:

13170 units^2 to the nearest whole number.

Step-by-step explanation:

Use Heron's formula:

Area = √s(s-a)(s-b)(s-c)

s = the semi-perimeter

= (155 + 175 + 260) / 2

= 590/2 =  295.

Area = √ [295(295-155)(295-175(295-260)]

= √ 173460000

= 13170.42 units^2.

Answer:

C' = (-6, -5)

Step-by-step explanation:

We are given that a triangle ABC is reflected over the line y = x.

Given the points of the vertices of the triangle ABC to be (-6, -1) (-2, -1) and (-5, -6) respectively, we are to determine the coordinates of C'.

When reflected over the line y = x, the x and y coordinates exchange their place.

(x, y) ---> (y, x)

Therefore, if C = (-5,-6) then C' = (-6, -5).

Answer:

[tex]\boxed{(-6,-5)}}[/tex]

Step-by-step explanation:

When you reflect a point (x, y) across the line y = x, the coordinates get interchanged. Thus,

(a,b) ⟶ (b,a)

Here are the coordinates of your triangle before and after the reflection.

[tex]\begin{array}{rcl}\textbf{Before} & & \textbf{After}\\A(-6,-1) & \longrightarrow \, & A'(-1,-6)\\B(-2,-1) & \longrightarrow \, & B'(-1,-2)\\C(-5,-6) & \longrightarrow \, & C'(-6,-5)\\\end{array}[/tex]

The diagram below shows ∆ABC with its reflection ∆A'B'C'.

[tex]\text{The coordinates of C' have become } \boxed{\mathbf{(-6,-5)}}[/tex]

Answer:

Step-by-step explanation:

All marbles here are identical. Also, the question isn't concerned about the order in which the marbles are drawn. Thus, all calculations here shall be combinations rather than permutations.

How many ways to choose three out of six identical red marbles without replacement?

[tex]\displaystyle _6C_3 = c(6, 3) = {6\choose 3} = 20[/tex].

Note that these three expressions are equivalent. They all represent the number of ways to choose 3 out of 6 identical items without replacement.

How many ways to choose three out of all the 6 + 10 + 6 = 22 marbles?

[tex]\displaystyle _{22} C_{3} = 1540[/tex].

The probability of choosing three red marbles out of these 22 marbles will be:

[tex]\displaystyle \frac{\text{Number of ways for choosing three out of six red marbles}}{\text{Number of ways to choose three out of 22 marbles}} = \frac{20}{1540} = \frac{1}{77}[/tex].

How many ways to choose two out of six identical red marbles without replacement?

[tex]\displaystyle _6 C_2 = 15[/tex].

How many ways to choose one out of 10 + 6 = 16 non-red marbles?

[tex]_{16} C_1=16 [/tex].

Choosing two red marbles does not influence the number of ways of choosing a non-red marble. Both event happen and are independent of each other. Apply the product rule to find the number of ways of choosing two red marbles and one non-red marble out of the pile of 22.

[tex]_6 C_2 \cdot _{16} C_1= 240[/tex].

Probability:

[tex]\displaystyle \frac{240}{1540} = \frac{12}{77}[/tex].

Double check that the order doesn't matter here.

None of the marbles are red. In other words, all three marbles are chosen out of a pile of 10 + 6 = 16 white and blue marbles. Number of ways to do so:

[tex]_{16} C_{3} = 560[/tex].

Probability:

[tex]\displaystyle \frac{560}{1540}= \frac{4}{11}[/tex].

Answer:

A) 1/77; B) 12/77; C) 4/11

Step-by-step explanation:

A) There are a total of 22 marbles.  6 of them are red.

On the first draw, the probability of getting a red marble is 6/22.

On the second draw, there's one less red marble and one less marble total, so the probability of getting another red marble is 5/21.

Similarly, on the third draw, the probability of getting a red marble is 4/20.

So the probability that all three draws are red marbles is:

P = (6/22) (5/21) (4/20)

P = 1/77

Another way this can be calculated is with combinations:

P = (ways to choose 3 red marbles from 6) / (ways to choose 3 marbles from 22)

P = ₆C₃ / ₂₂C₃

P = 20 / 1540

P = 1/77

B) The same logic can be repeated here.  Using the first method, if the first two selection are red:

P = (6/22) (5/21) (16/20) = 4/77

If the first and third are red:

P = (6/22) (16/21) (5/20) = 4/77

If the last two are red:

P = (16/22) (6/21) (5/20) = 4/77

So the total probability is:

P = 4/77 + 4/77 + 4/77

P = 12/77

Using the second method:

P = (ways to choose 2 red from 6) × (ways to choose 1 non-red from 16) / (ways to choose 3 from 22)

P = ₆C₂ ₁₆C₁ / ₂₂C₃

P = 15 × 16 / 1540

P = 12/77

C)

Same logic:

P = (16/22) (15/21) (14/20)

P = 4/11

Or:

P = ₁₆C₃ / ₂₂C₃

P = 560 / 1540

P = 4/11

Answer:

x+3x+5=101 (Option C).

Step-by-step explanation:

This question requires to be solved using the supposition method.

Let Aylen's savings be $x. Therefore, Rich's savings would be $(3x+5). This is because it is mentioned that Rich has $5 more than 3 times the amount of money Aylen has. The sum of the savings is $101. Therefore the sum of the savings of Aylen and Rich is given by:

x + 3x + 5 = 101. Thus, Option C is the correct answer.

Solve the equation for x gives x = $24. This is Aylen's share. To calculate Rich's share, simply put x=24 in 3x+5. Thus, Rich's share will be $77.

In short, Rich's share = $77, Alan's share = $24, and this has been calculated using the equation x+3x+5=101 (Option C)!!!

Answer:

C x+3x+5=101

Step-by-step explanation:

For this case we give as data the following equation:

[tex]4x + 12 = 48[/tex]

Where "x" represents the cost of a ticket.

By clearing the value of "x" of the equation we can know the cost of a ticket.

If we subtract 12 from both sides of the equation, we have:

[tex]4x = 48-12\\4x = 36[/tex]

If we divide between 4 on both sides of the equation:

[tex]x = \frac {36} {4}\\x = 9[/tex]

Therefore, the cost of a ticket is $ 9.00

Answer:

Option C

Answer:

40

Step-by-step explanation:

5√64 = 5 x 8 = 40

Answer:

√5

==

 8

or

Sqrt5

  over

  8

Step-by-step explanation:

Answer:

Could you repost your question with a picture of the arc?

Answer: AD = 5

because AB equals 10, logically we assume AD equals 5, hopefully this helps you.

Answer:

AD=5

Step-by-step explanation:

We are given that

[tex]\angle 1=\angle 2[/tex]

AB=10, AC=6 BC=6

We have to find the value of AD.

Let AD=x

BD=AB-AD

BD=10-x

By angle bisector theorem

[tex]\frac{AC}{AD}=\frac{BC}{BD}[/tex]

Substitute the values then we get

[tex]\frac{6}{x}=\frac{6}{10-x}[/tex]

[tex]\frac{10-x}{x}=\frac{6}{6}[/tex]

[tex]\frac{10-x}{x}=1[/tex]

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

[tex]x+x=10[/tex]

[tex]2x=10[/tex]

[tex]x=\frac{10}{2}=5[/tex]

Hence, the value of AD=5 units

Answer:

lcm = 4

Step-by-step explanation:

20 = 2 × 2 × 5 ← product of prime factors

12 = 2 × 2 × 3 ← product of prime factors

The lowest common multiple (lcm) = 2 × 2 × 5 × 3 = 60

Answer:

60

Step-by-step explanation:

First, break down each of the numbers into their prime factors.

20 = 2² x 5

12 = 2² x 3

To find the LCM, underline each of the prime numbers. If there is a repeated prime number, underline the one with the largest possible value. For example, if there is 3² and 3³, underline the second one. In this case, the values are the same, so just underline one.

20 = 2² x 5

12 = 2² x 3

Next, multiply all the underlined numbers.

LCM (20, 12) = 2² x 5 x 3 = 60