How many angles and sides are there in a Heptagon?ANGLES:SIDES:

Explanation:

The equation is given below as

Step 1:

Collect similar terms, we will have

Hence,

The simplified form of the equation will be

The function given in the graph stretches from negative to positive infinity.

Hence the domain of the function is given by:

Answer: 6 hours

Explanation:

We have that "Ruth studied 2 hours less than twice as many hours as Jackie". I will call the hours that Ruth studied "R" and the hours that Jackie studied "J". The first equation is as follows:

The hours that Ruth studied as 2 less than twice as many as Jackie. This will be referred to as equation 1.

Now, we are told that "Together, their study time was 10 hours" so we have the following equation:

This will be our equation 2.

The next step is to substitute equation 1 into equation 2:

And we solve for J.

Combining like terms:

We add +2 on both sides of the equation to cancel the -2 on the left side:

And we divide both sides by 3:

Jackie studied for 4 hours.

Since we are asked for Ruth, we substitute J=4 into the equation 1:

Ruth studied for 6 hours.

When a plane intersects both bases of a cylinder, passing through the center of each base of the cylinder, the cross section formed is a rectangle.

We know that

• Ethan burns 650 calories per hour.

If he runs 5 hours we just have to multiply this time with the given rate.

From the question, we can derive the following:

Micheal earns 2x³ + 3x

His wife earns 3x² + 6

If x represents the number of days they work, in a month, we are asked to find the total earnings in a month.

So we will have:

(2x³ + 3x) + (3x² + 6)

Adding up the two earnings:

2x³ + 3x² + 3x + 6

So, (2x³ + 3x² + 3x + 6) is the total earnings in a month.

So the correct answer is the second option wich is (2x³ + 3x² + 3x + 6).

Let

x -----> the missing number

we know that

80%=80/100=0.80

so

0.80x=20

solve the linear equation for x

Divide by 0.80 both sides

x=20/0.80

x=25

the answer is 25

if the number of shoppers increases by 20% daily and 671 shoppers had visited over 4 days then let the num ber of shoppers on the first day be x

The numebr of shopperes the next day will be

= x(100 + 20)%

= 1.2x

teh number of shoppers the day after

= 1.2x(100 + 20)%

= 1.44x

the next day, the number

= 1.44x (100 + 20)%

= 1.728x

Given that the total number of people that have shopped after 4 days is 671 then

x + 1.2x + 1.44x + 1.728x = 671

5.368x = 671

x = 671/5.368

= 125

if the number of shoppers increases by 20% daily and 671 shoppers had visited over 4 days then let the num ber of shoppers on the first day be x

The numebr of shopperes the next day will be

= x(100 + 20)%

= 1.2x

teh number of shoppers the day after

= 1.2x(100 + 20)%

= 1.44x

the next day, the number

= 1.44x (100 + 20)%

= 1.728x

Given that the total number of people that have shopped after 4 days is 671 then

x + 1.2x + 1.44x + 1.728x = 671

5.368x = 671

x = 671/5.368

= 125

So, our answer is 9!

We can solve this using the next property:

If a

Replace f (x) = - 2x- 5 ​, then:

-21 < f (x) < 0

-21 < -2x-5 < 0

Solve -21 < -2x-5 and -2x-5 < 0

Therefore:

-21 < -2x-5

Add both sides 5

-21+5 < -2x-5 +5

-16 < -2x

(-1)-16 < (-1)(-2x)

16>2x

x<16/2

x<8

and

-2x-5 < 0

Add both sides 5

-2x-5 +5 < 0+5

-2x<5

(-1)-2x < (-1)5

2x > -5

x > -5/2

Hence, the resulting interval is:

-5/2 < x < 8

Answer:

B. SAS
:)

Step-by-step explanation:

Solution:

Given that;

For B∩C, i.e . common elements between bot sets

Then, A∪(B∪C), i.e. all the elements in A and B∩C

Hence, A∪(B∪C) is

Answer:

No

Step-by-step explanation:

3 × [tex]\frac{2}{5}[/tex] = [tex]\frac{6}{5}[/tex] = 1 [tex]\frac{1}{5}[/tex] cups required to triple her recipe

she only has 1 cup

so does not have enough to triple her recipe

Answer:

No

Step-by-step explanation:

If she triples it that means you need to triple the 2/5 so she would neew 6/5 of flour which is 1/5 more than what she has.

Answer:  expect to lose 679.07 dollars

==========================================================

Explanation:

Assuming each free throw is independent of any other, the probability of making the next free throw is 359/449

The probability of making 3 in a row is (359/449)^3 = 0.511145 approximately which represents the probability of earning the $39

That must mean 1-0.511145 = 0.488855 is the approximate probability of losing $43

Let's make a table of outcomes and their associated probabilities.

X = amount of money the player earns (the person shooting the free throws)

[tex]\begin{array}{|c|c|} \cline{1-2}\text{X} & \text{P(X)}\\\cline{1-2}39 & 0.511145\\\cline{1-2}-43 & 0.488855\\\cline{1-2}\end{array}[/tex]

Then from here we'll multiply each X and P(X) value for each separate row.

Example: 39*0.511145 = 19.934655

Let's form a third column of these products

[tex]\begin{array}{|c|c|c|} \cline{1-3}\text{X} & \text{P(X)} & \text{X}*\text{P(X)}\\\cline{1-3}39 & 0.511145 & 19.934655\\\cline{1-3}-43 & 0.488855 & -21.020765\\\cline{1-3}\end{array}[/tex]

Add up everything in the X*P(X) column and you should get roughly -1.08611 which rounds to -1.09

The player expects, on average, to lose about $1.09 each time they play this game. Playing 623 times means they should expect to lose 623*1.09 = 679.07 dollars

Of course, given the nature of this random process, it's not a guarantee they will lose this amount. This is just the average of many attempts.

A number which is 5 more than 8009998 is 8010003

In this question we need to find a number which is 5 more than 8009998.

Let x be a number which is 5 more than 8009998.

We get the required number by adding 5 to 8009998.

so, we write it down as:

x = 8009998 + 5

x = 8010003

Therefore, a number which is 5 more than 8009998 is 8010003

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45/152 is fraction of the students are freshmen.

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction is a portion of a whole and is used to represent how many pieces of a particular size there are while speaking in ordinary English, for example, one-half, eight-fifths, and three-quarters. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. There is a proportion there in numerator or denominator of a complicated fraction. There are three main categories of fractions in mathematics. Proper fractions, incorrect fractions, and mixed fractions are these three types. The expressions with a numerator and a denominator are called fractions.

Total students = 152

Freshman = 45

Fraction = 45/152

This is the simplest form .

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2 . 0 5 0

0 . 0 0 4

---------------------------------

8 2 0 0

+ 0 0 0 0

0 0 0 0

0 0 0 0

------------------------------

0 . 0 0 8 2 0 0 =

-----------------------------

We have the following

Let's find a, b and c in order to solve the problem

a.

a = 10,000

b.

b=1.0E-16

c.

c=1.0E19

Thus, the value of log [ a^2c/sqrt(c) ] is :

replace:

simplify:

Therefore, the answer is 35

Given:

David had $350. After shopping, he was left with $235.

Required:

If c represents the amount he spent, write an equation to represent this situation. Then use the equation to find the amount of money David spent.

Explanation:

We know c is the amount spent

So,

Available amount = Total amount - spent amount

235 = 350 - c

c= 350 - 235

c = 115

Answer:

Hence, David spent $115.

Convert 7 liters into gallons

We have the measurement conversion 1 liter= 1.0567 quarts

and the gallons = 4 quarts

So, 7 liters = 7 * 1.0567 quarts = 7.3969 quarts

We will convert from the quarts to gallons as follows:

1 gallons = 4 quarts

x gallons = 7.3969 quarts

so, the value of x will be:

Round to two decimals

so, the answer will be 1.85 gallons

ok

The sum of the internal angles in a triangle equals 180°

R + B = T = 180

Substitution

19 + 56 + T = 180

T = 180 - 19 - 56

T = 105°

Result:

T = 105°

In order to find the greatest common factor (GCF) of the terms, first let's factor the numeric values in their prime factors:

The common factor between these three numbers is the product of the common prime factors, that is, 2 * 2 = 4.

Now, to find the common factor of the variables, we choose for each variable the one with the smaller exponent:

Therefore the common factor is -4(m^5)n.

(we can put the negative signal as well, since all terms are negative).

Equation for a rational function is 10(x2 + 7x + 12) / (x2 + 11x + 30) = 0.

What is Rational Function?

Any function that can be expressed mathematically as a rational fraction—an algebraic fraction in which both the numerator and the denominator are polynomials—is referred to as a rational function. The polynomials' coefficients don't have to be rational numbers; they can be found in any field K.

So this will be a rational function with the vertical asymptotes given by the denominators:

(x + 5) and (x + 6).

The x-intercepts will be provided by the numerator,

which will be:

a(x + 3)(x + 4)

The letter an is a constant.

Given that (0,4) is the y intercept, we have:

4 = a(0+3)(0+4) / (0+5)(0+6)

4= 12a / 30

12a = 120

now,

a = 120/12,

a = 10,

and a = 1.

Now,

a(x+3)(x+4) / (x+5)(x+6) = 0

10 (x^2 + 7x + 12) / (x^2 + 11x + 30) = 0

Hence, We have the following equation for a rational function:

10 (x2 + 7x + 12) / (x2 + 11x + 30) = 0.

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The distributive property of multiplication states the following:

So, for the given expression, we have:

Absolute Minimum: an absolute minimum point is a point where the function obtains its least possible value.

The given function :

In the graph of the f(x) , the least value of x of the given curve is : (-0.939)

and the f(x) at x = (-0.939) is -10.065

The absolute minimum value is (x,y) = (-0.939, -10.065)

To round off in the nearest hundredth : (x, y) = (-0.94, -10.07)

Answer : (x, y) = (-0.94, -10.07)

Answer

D. (-3, 0) and (3, -4)

Explanation

Let the coordinate of the points be A(-9, 4) and B(9, -8).

We shall look for the gradient m of line using

m = (y₂ - y₁)/(x₂ - x₁)

Substitute for x₁ = -9, y₁ = 4, x₂ = 9 and y₂ = -8

m = (-8 - 4)/(9 - -9) = -12/18 = -2/3

From option A - D given, only C and D would have the same gradient of -2/3 as line AB

To know the correct option, we shall look for the equation of the line AB, that is,

(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)

(y - 4)/(x - -9) = (-8 - 4)/(9 - -9)

(y -4)/(x + 9) = -12/18

(y - 4)/(x + 9) = -2/3 -----------*

Between option C and D, only D satisfies the equation *

That is, using (-3, 0), we have (0 - 4)/(-3 + 9) = -4/6 = -2/3

Also, using (3, -4), we have (-4 - 4)/(3 + 9) = -8/12 = -2/3

The company estimates a residual value of $1,500 and a six-year service life.

It is given that,

Cost of truck delivery = $ 23100

Salvage value = $ 1500

Useful life = 6 years

Depreciation expenses by using the straight-line method are calculated as,

Substituting the value in the formula,

Thu

Answers:

Part A.

C. AD = AE

Part B.

BC = 26

Explanation:

Part A.

If DE is a midsegment of triangle ABC, D is a point that divides AB into two equal segments, so option A. 1/2 AB = AD is true.

Additionally, if DE is a midsegment of triangle ABC, its length is equal to half the length of the side that the segment doesn't cross. So:

Therefore, option B is also true.

Triangle ABC is scalene, it means that all their sides have different length, it means that AD is not equal to AE and option C is not true.

Finally, segments AE and EC form AB, so:

AC = AE + EC

AC - AE = AE + EC - AE

AC - AE = EC

So, option D is also true.

Therefore, the answer for part A is C. AD = AE

Part B.

We know that 2DE = BC, so replacing the expression for each segment, we get:

Solving for x:

Now, with the value of x, we get that BC is equal to:

BC = 5x - 4

BC = 5(6) - 4

BC = 30 - 4

BC = 26

So, the answer for part B is 26.

Solution

Step 1:

Write the two given points:

p(4,2) and q(8,12)

Step 2

Find the distance between the two points:

Answer