Which equation represents the line that passes through (–6, 7) and (–3, 6)?

y = –x + 9
y = –x + 5
y = –3x – 11y
y = –3x + 25

Answer:

Positive real numbers

Step-by-step explanation:

The domain is all the possible values of x.  Here, x represents the time that the ball falls.

Natural numbers are integers greater than 0 (1, 2, 3, etc.).  However, the time doesn't have to be an integer (for example, x=1.5).

Positive integers are the same as natural numbers.

Positive rational numbers are numbers greater than 0 that can be written as a ratio of integers (1/1, 3/2, 2/1, etc.).  However, the time can also be irrational (for example, x=√2).

Positive real numbers are numbers greater than 0 and not imaginary (don't contain √-1).  This is the correct domain of the function.

The domain for the function ƒ(x) = 1,000 - 16x^2 is Positive Real Numbers.

The domain for the function ƒ(x) = 1,000 - 16x^2 is a set of Positive Real Numbers. This is because in real-world situations, such as the height of an object, negative time values do not make sense, and the function itself involves squaring x, which ensures that the result is positive. Therefore, the appropriate set of numbers as the domain for this function would be Positive Real Numbers.

Answer:

* The shorter side is 270 feet

* The longer side is 540 feet

* The greatest possible area is 145800 feet²

Step-by-step explanation:

* Lets explain how to solve the problem

- There are 1080 feet of fencing to fence a rectangular garden

- One side of the garden is bounded by a river so it doesn't need

 any fencing

- Consider that the width of the rectangular garden is x and its length

 is y and one of the two lengths is bounded by the river

- The length of the fence = 2 width + length

∵ The width = x and the length = y

∴ The length of the fence = 2x + y

- The length of the fence = 1080 feet

∴ 2x + y = 1080

- Lets find y in terms of x

∵ 2x + y = 1080 ⇒ subtract 2x from both sides

∴ y = 1080 - 2x ⇒ (1)

- The area of the garden = Length × width

∴ The area of the garden is A = xy

- To find the greatest area we will differentiate the area of the garden

  with respect to x and equate the differentiation by zero to find the

  value of x which makes the area greatest

∵ A = xy

- Use equation (1) to substitute y by x

∵ y = 1080 -2x

∴ A = x(1080 - 2x)

∴ A = 1080x - 2x²

# Remember

- If y = ax^n, then dy/dx = a(n) x^(n-1)

- If y = ax, then dy/dx = a (because x^0 = 1)

∵ A = 1080x - 2x²

∴ dA/dx = 1080 - 2(2)x

∴ dA/dx = 1080 - 4x

- To find x equate dA/dx by 0

∴ 1080 - 4x = 0 ⇒ add 4x to both sides

∴ 1080 = 4x ⇒ divide both sides by 4

∴ x = 270

- Substitute the value of x in equation (1) to find the value of y

∵ y = 1080 - 2x

∴ y = 1080 - 2(270) = 1080 - 540 = 540

∴ y = 540

* The shorter side is 270 feet

* The longer side is 540 feet

∵ The area of the garden is A = xy

∴ The greatest area is A = 270 × 540 = 145800 feet²

* The greatest possible area is 145800 feet²

To expand and simplify the expression 4(2x+3)+4(3x+2), distribute the 4 to both sets of parentheses and combine like terms to get 20x + 20.

To expand and simplify the expression 4(2x+3)+4(3x+2), we can use the distributive property of multiplication over addition. The distributive property states that for any numbers a, b, and c, a(b+c) = ab+ac.

First, we distribute the 4 to both terms inside the first set of parentheses: 4 * 2x + 4 * 3. This simplifies to 8x + 12. Then, we distribute the 4 to both terms inside the second set of parentheses: 4 * 3x + 4 * 2. This simplifies to 12x + 8.

Combining the like terms, the final simplified expression is: 8x + 12 + 12x + 8 = 20x + 20.

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Most likely infinite? Just a guess.

Answer:

Step-by-step explanation:

The question says nothing about repetition, so I'm assuming that 943449 is OK,

This can be solved this way

9 10 10 10 10 9

810,000

Answer:

4  3/8

Step-by-step explanation:

1 7/8 × 2 1/3

Change the numbers to improper fractions

1 7/8 = (8*1 +7) /8 = 15/8

2 1/3 = (3*2 +1)/3 = 7/3

15/8 * 7/3

Rearranging

15/3 * 7/8

5/1 * 7/8

35/8

Now we need to change this back to a mixed number

8 goes into 35   4 times with 3 left over

4 3/8

Answer:

35/8 or 4 3/8

Step-by-step explanation:

Change each fraction to improper

15/8 * 7/3

multiply

105/24

reduce

35/8

make it mixed if the answer wants it to be

4 3/8

Answer:

its simplest form is 4/5

Answer:

4(x - 5)(x + 3)

Step-by-step explanation:

Given

4x² - 8x - 60 ← factor out 4 from each term

= 4(x² - 2x - 15)

To factor the quadratic

Consider the factors of the constant term ( - 15) which sum to give the coefficient of the x- term ( - 2)

The factors are - 5 and + 3, since

- 5 × 3 = - 15 and - 5 + 3 = - 2, hence

x² - 2x - 15 = (x - 5)(x + 3) and

4x² - 8x - 60 = 4(x - 5)(x + 3)

Answer:

Step-by-step explanation:

Let CD = x

(x + 40)/2 = 31                  The midline is 1/2 the sum of the 2 bases. multiply by 2 on both sides.

x + 40 = 31 * 2

x + 40 = 62                       Subtract 40 from both sides.

x +40-40 = 62 - 40          Combine

x = 22

Check

(22 + 40)/2

62 / 2

31 = PQ

To find the missing length of a trapezoid with similar triangles inside, we use the ratio of the sides of the triangles, which is approximately 8.667 based on the provided lengths.

When determining the missing length of a trapezoid, we need to consider the properties of similar triangles or the geometric shape of a trapezoid itself. The given information suggests a scenario where similar triangles are within a trapezoid and leads to a proportional relationship between the sides of the triangles. If a trapezoid has triangles within it that share an angle, the lengths of the corresponding sides of those triangles will be proportional.

Based on the data provided, if the long sides of the triangles are in the ratio of 13.0 in to 1.5 in, which simplifies to an approximate factor of 8.667, the bottom sides of the triangles - which are the parallel sides of the trapezoid - will also be in the same ratio. By finding the length of the shorter bottom side, we can divide the length of the longer bottom side by 8.667 to get the missing length on the shorter side.

Answer:

I don't know what the following sentence is:

But D is the equation to represent the situation

and A is what turns out to be his current age.

(If you want more help, on this question please post the following sentence).

Step-by-step explanation:

Let x represent the current age.

15 years from now his age is 3 times his age 5 years ago means we have the equation:

x+15=3(x-5)

(I added x to 15 because we said 15 years in the future)

Let's solve this to see if makes any sense just for fun:

Distribute:

x+15=3x-15

Add 15 on both sides:

x+30=3x

Subtract x on both sides:

   30=2x

Divide both sides by 2:

   15=x

So this means his current age is 15.

5 years ago his age would have been 10.

15 years in the future his age will be 30.

Is 30 equal to 3 times 10? Yes, it is! The equation does make sense.

Answer:

D,

Step-by-step explanation:

x is the present age of William, 15 years from now is x+15, and that is equal to  3 times 3() the age he had 5 years ago (x-5)., the equation is  x+15=3(x-5)

Answer:

[tex]\large\boxed{a_n=2(-4)^{n-1}=\dfrac{(-4)^n}{2}}[/tex]

Step-by-step explanation:

The explicit equation of a geometric sequence:

[tex]a_n=a_1r^{n-1}[/tex]

The domain is the set of all Counting Numbers.

We have the first term of [tex]a_1=2[/tex] and the second term of [tex]a_2=-8[/tex].

Calculate the common ratio r:

[tex]r=\dfrac{a_{n-1}}{a_2}\to r=\dfrac{a_2}{a_1}[/tex]

Substitute:

[tex]r=\dfrac{-8}{2}=-4[/tex]

[tex]a_n=(2)(-4)^{n-1}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\a_n=(2\!\!\!\!\diagup^1)\left(\dfrac{(-4)^n}{4\!\!\!\!\diagup_2}\right)\\\\a_n=\dfrac{(-4)^n}{2}[/tex]

Answer:

Step-by-step explanation:

A geometric sequence has a common ratio. in this case the common ratio

r = -8/2 = -4.

The explicit formula is an = 2(-4)^(n-1).

Answer:

The factors are the binomials (x - 7)(x + 2)

Step-by-step explanation:

* Lets explain how to factor a trinomial

- The trinomial  ax² ± bx ± c has two factors (x ± h)(x ± k), where

# h + k = -b/a

# h × k = c/a

- The signs of the brackets depends on the sign of c at first then

  the sign of b

# If c is positive, then the two brackets have the same sign

# If b is positive , then the signs of the brackets are (+)

# If b is negative then the sign of the brackets are (-)

# If c is negative , then the brackets have different signs

* Lets solve the problem

∵ The trinomial is x² - 5x - 14

∴ a = 1 , b = -5 and c = -14

∵ c is negative

∴ The brackets have different signs

∴ (x - h) (x + k) are the factors of the trinomial

∵ h + k = -5/1

∴ h + k = -5 ⇒ (1)

∵ h × k = -14/1

∴ h × k = -14 ⇒ (2)

- From (1) , (2) we search about two numbers their product is 14 and

 their difference is 5 , they will be 7 and 2

∵ 7 × 2 = 14

∵ 7 - 2 = 5

- The sign of b is negative then we will put the greatest number in the

 bracket of (-)

∴ h = 7 and k = 2

∴ The brackets are (x - 7)(x + 2)

* The factors are the binomials (x - 7)(x + 2)

Answer:

False because on the left side of the equation you are adding 18 and 35 first and on the right you are multiplying 35 and 4 first. This will give you an unequal equation when solved.

Let's solve each side

(18+35)*4=212

but 18+(35*4)=158

Answer:

The correct answer option is C. [tex] g ( x ) = | x - 4 | + 6 [/tex].

Step-by-step explanation:

We know that the transformation which shifts a function along the horizontal x axis is given by [tex]f(x+a)[/tex], while its [tex]f(x-a)[/tex] which shifts the function to the right side.

Here we are to shift the function 4 units to the right and 6 units up.

Therefore, the function will be:

[tex] g ( x ) = | x - 4 | + 6 [/tex]

Answer: Option C

[tex]g (x) = | x-4 | +6[/tex]

Step-by-step explanation:

If we have a main function and perform a transformation of the form

[tex]g (x) = f (x + h)[/tex]

So:

If [tex]h> 0[/tex] the graph of the function g(x) will be equal to the graph of f(x) displaced h units to the left

If [tex]h <0[/tex] the graph of the function g(x) will be equal to the graph of f(x) displaced h units to the right

Also if the transformation is done

[tex]g (x) = f(x) + k[/tex]

So

If [tex]k> 0[/tex] the graph of the function g(x) will be equal to the graph of f(x) displaced k units up

If [tex]k <0[/tex] the graph of the function g(x) will be equal to the graph of f(x) displaced k units downwards.

In this case the main function is [tex]f(x) = | x |[/tex] and moves 4 units to the right and 6 units to the top, then the transformation is:

[tex]g (x) = f (x-4) +6[/tex]

[tex]g (x) = | x-4 | +6[/tex]

Answer:

First exercise: [tex]x=7[/tex]

Second exercise: [tex]x=2[/tex]

Step-by-step explanation:

Acording to the Intersecting Secants Theorem the products of the segments of two secants that intersect each other outside a circle, are equal.

Based on this, in order to solve the first exercise and the second exercise, we can write  the following expressions and solve for "x":

First exercise:

[tex](5)(5+x)=6(6+4)\\\\25+5x=60\\\\5x=60-25\\\\x=\frac{35}{5}\\\\x=7[/tex]

Second exercise:

[tex](4)(4+x)=3(3+5)\\\\16+4x=24\\\\4x=24-16\\\\x=\frac{8}{4}\\\\x=2[/tex]

Answer:

the line will pass through yellow and red

Answer:

1.B

first picture is x greater than or equal to 4

second picture is x less than or equal to 4

then x>4 is a open circle and a line to the  right

then x<4 to the left

Step-by-step explanation:

Answer:

a=11.8,b=12,c=8,A=68.7°, B=72°, C= 39.3°

Step-by-step explanation:

Given data:

b = 12

c= 8

a= ?

∠B= 72°

∠C= ?

∠A=?

To find the missing angle we will use law of sine:

a/sinA=b/sinB=c/sinC

Find m∠C.

b/sinB = c/sinC

Substitute the values:

12/sin72°=8/sinC

Apply cross multiplication.

12*sinC=sin72° * 8

sinC=0.951*8/12

sinC=7.608/12

sinC= 0.634

C= 39.3°

Now we know that the sum of angles = 180°

So,

m∠A+m∠B+m∠C=180°

m∠A+72°+39.3°=180°

m∠A=180°-72°-39.3°

m∠A= 68.7°

Now find the side a:

a/sinA=b/sinB

a/sin68.7°=12/sin72°

Apply cross multiplication:

a*sin72°=12*sin68.7°

a*0.951=12*0.931

a=0.931*12/0.951

a=11.172/0.951

a=11.75

a=11.8 ....

a chord intersected by a radius segment at a right-angle, gets bisected into two equal pieces, namely MO = NO and PZ = QZ.

[tex]\bf MO=NO\implies \stackrel{MO}{18}=NO\qquad \qquad NO=6x\implies \stackrel{NO}{18}=6x \\\\\\ \cfrac{18}{6}=x \implies 3=x \\\\[-0.35em] ~\dotfill\\\\ PZ=x+2\implies PZ=3+2\implies PZ=5=QZ \\\\[-0.35em] ~\dotfill\\\\ PQ=PZ+QZ\implies PQ=5+5\implies PQ=10[/tex]

Answer:

See explanation

Step-by-step explanation:

There 2 black shapes (one circle and one square) and 2 white shapes (1 circle and 1 square).

1. The ratio of the number of white shapes to the number of black shapes is 2:2=1:1.

2. The ratio of the number of white circls to the number of black squares is 1:1.

3. The ratio of the number of black circles to the number of black squaress is 1:1.

4. There are 4 shapes and 2 are circles (1 white and 1 black), so circles are [tex]\dfrac{2}{4}=\dfrac{1}{2}[/tex] of all shapes.

Answer:

x = 12

Step 1 helps solve the equation, for it helps isolate the x, which is what you are solving for.

Step-by-step explanation:

Isolate the variable x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS:

Step 1: Add 18 to both sides.

6x - 18 (+18) = 54 (+18)

6x = 54 + 18

6x = 72

Step 2: Divide 6 from both sides:

(6x)/6 = (72)/6

x = 72/6

x = 12

x = 12 is your answer.

~

Answer:

[tex]\huge \boxed{X=12}[/tex]

Step-by-step explanation:

Add by 18 from both sides of equation.

[tex]\displaystyle 6x-18+18=54+18[/tex]

Add numbers from left to right.

[tex]\displaystyle 54+18=72[/tex]

[tex]\displaystyle 6x=72[/tex]

Divide by 6 from both sides of equation.

[tex]\displaystyle \frac{6x}{6}=\frac{72}{6}[/tex]

Simplify, to find the answer.

[tex]\displaystyle 72\div6=12[/tex]

[tex]\huge \boxed{x=12}[/tex], which is our answer.

Answer:

A.) $56

Step-by-step explanation:

1.  Convert 7% into the numerical version by either

    A. Moving the decimal two spaces to the right, giving us .07

                                               or

    B. Making 7% into a fraction, 7/100

2. Now make an equation with the total amount of money (M) multiplied by the interest (P) inside of parenthesis. This will give us 7% of $800 in your case.

                                        (800 × .07) → 56

3.  Then, multiply by the number of years the interest has been accumulated.

                                              56 × 1

The official equation for this is: a = p(1 + r)^t

a = amount at end (initial amount + interest gained)

p = initial amount

r = rate (percent interest)

t = time in years

The correct option will be option A: Man will receive $56 interest in a year.

Simple Interest amount can be calculated by the product of principal amount, rate of interest, and time.

Simple Interest= S.I. =p*t*r/100

where p is the principal amount,

r is interest rate (in %)

t is the time (in year).

Here, given,

principal amount P = $800

rate of interest= r=7%

time=t=1 year

using the above formula,

Simple Interest S.I.= p*t*r/100= (800*1*7)/100= $56

Therefore man will receive $56 interest in a year.

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See the attached picture:

Answer:

Answer is option B. 1,111.84 ft²

Step-by-step explanation:

The given dimensions of the un shaded region or rectangle are 18 feet x 22 feet.

Now we have additional 7 feet at both ends to form the diameter of the semicircle, making it [tex]14+18=32[/tex] feet

Radius = [tex]\frac{32}{2}=16[/tex] feet

We have 2 semicircles, one at each end. If we combine it it forms a circle.

Area of the circle (2 semicircles) = [tex]\pi r^{2}[/tex]

= [tex]3.14\times(16)^{2}[/tex] = 803.84 square feet

Now we will find the area of the shaded rectangles above and below the non shaded one. The length is 22 feet and width is 7 feet.

So, area = [tex]22\times7=154[/tex] square feet

We have 2 similar rectangles. So, area of both = [tex]2\times154=308[/tex] square feet

So, total area of shaded region = [tex]803.84+308=1111.84[/tex] square feet.

Answer:

Step-by-step explanation:

[tex]5^{x-2}=625\\\\5^{x-2}=5^4\qquad(5^4=5\cdot5\cdot5\cdot5=625)\\\\5^{x-2}=5^4\Rightarrow x-2=4\qquad\text{add 2 to both sides}\\\\x-2+2=4+2\\\\x=6\\\\\text{check:}\\\\5^{6-2}=5^4=625\qquad\bold{CORRECT}[/tex]

[tex]\bf \textit{height or altitude of an equilateral triangle}\\\\ h=\cfrac{s\sqrt{3}}{2}~~ \begin{cases} s=\stackrel{length~of}{a~side}\\ \cline{1-1} s=8\sqrt{3} \end{cases}\implies h=\cfrac{8\sqrt{3}\cdot \sqrt{3}}{2}\implies h=\cfrac{8\sqrt{3^2}}{2} \\\\\\ h=4\cdot 3\implies h=12[/tex]

Answer:

After month 3.

Step-by-step explanation:

If you know that the crop will be completely infected after 6 months and the area infected doubles each month, you can work backwards. So picture the 6th month as 100%. Then, basically divide that percentage by 2 until you reach 1/8, or .125, or 12.5. So 100% (month 6) > 50% (month 5) > 25% (month 4) > 12.5% (month 3). So 12.5% is equal to 1/8 or .125, which is what you are trying to look for.

Hope this helps!

The non-food crop will be infected by one-eighth of the crop after 3 months.

The sum of n terms of a geometric sequence is given by the formula,

Sn = [a(1 - r^n)]/(1 - r)

Where r - a common ratio

a - first term

n - nth term

Sn - the sum of n terms

Given that,

The crop is infected by pests.

The area infected doubles after each month. So, it forms a geometric progression or sequence.

The entire crop is infected after six months.

So, n = 6, r = 2(double) and consider a = x

Then the area of the infected crop after 6 months is,

S(6) = [x(1 - 2^6)]/(1 - 2)

      = x(1 - 64)/(-1)

     = -x(-63)

     = 63x

So, after six months the area of the infected crop is about 63x

So, the one-eighth of the crop = 63x/8 = 7.875x

For one month the infected area = x (< one-eighth)

For two months it will be x + 2x = 3x (< one-eighth)

For three months it will be x + 2x + 4x = 7x ( < one-eighth)

For four months it will be x + 2x + 4x + 8x = 15x (> one-eighth)

So, the one-eighth of the crop will be infected after 3 months.

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Answer:

30 times

Step-by-step explanation:

Weight of adult blue whale = [tex]9 \times 10^{4}[/tex] kilogram

Weight of an elephant = [tex]3 \times 10^{3}[/tex] kilogram

In order to find how many times a quantity is as compared to the other quantity, we divide the two. So here we have to divide the weight of adult blue whale by the wight of elephant.

[tex]\frac{9 \times 10^{4}}{3 \times 10^{3}}\\= 30[/tex]

This means, adult blue whale is 30 times heavier than the elephant.

[tex](9x-4)-(3x+2)=9x-4-3x-2=6x-6[/tex]

Answer:

The correct answer is third option.  994

Step-by-step explanation:

Points to remember

Volume of cylinder = πr²h

Where 'r' is the radius and 'h' is the height of cylinder

From the given question we get the cylinder height and radius

The height h = 3 times the diameter of one ball

 = 3 * 7.5 = 22.5 cm

Radius = half of the diameter of a ball

 = 7.5/2 = 3.75 cm

To find the volume of cylinder

Volume of cylinder = πr²h

 = 3.14 * 3.75² * 22.5

 = 993.515 ≈ 994

The correct answer is third option.  994