Sandy has a garden in her backyard. The drawing shows
the dimensions of her garden. A bag of fertilizer covers 3
square feet

Here is the graph for the equation

Given function to be graphed is,

f(x) = (x - 2)(x - 6)

We will convert the equation of the function into the vertex form,

(x - 2)(x - 6) = x(x - 6) - 2(x - 6)

                  = x² - 6x - 2x + 12

                  = x² - 8x + 12

                  = x² - 2(4x) + 16 - 4

            f(x) = (x - 4)²- 4

By comparing this equation with the vertex form of the equation of a parabola,

g(x) = a(x - h)² + k

Here, (h, k) is the vertex of the parabola.

Therefore, vertex of the function 'f' will be (4, 4).

Now we will find the x-intercepts and y-intercept of the function.

For x-intercept, put f(x) = 0

0 = (x - 4)²- 4

(x - 4) = ±2

x = 4 ± 2

x = 2, 6

Therefore, x-intercepts of the function are (2, 0) and (6, 0).

For y-intercept, put x = 0

f(0) = (0 - 2)(0 - 6)

f(0) = 12

Therefore, y-intercept of the function is (0, 12).

By plotting these ordered pairs and joining them by a curve we can get the graph of the parabola.

Learn more how to graph a curve,

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Answer:

284.6 square yards

284.6 yd^2

Step-by-step explanation:

Base: 7 × 13 = 91

Rectangle Sides: 6.1 × 13 = 79.3 (x2 = 158.6)

Triangle Sides: 5 × 7 = 35 (÷2 ×2 = 35)

Add: 91 + 158.6 + 35 = 284.6

Answer: 1) 1 1/2, 2 1/4, and 4

Step-by-step explanation: 1) We know that the equation would be the cups of flour being multiplied by the batches. Like, 5 times 3/4 would equal 15/4 which would simplify to 3 3/4.

                 So, to find the first missing number, we do 2 x 3/4, which equals 6/4( 1 1/2).

                The next missing number would be 3, because we're going in order-- like 1, 2, 3, 4. So we do 3 x 3/4.

               We then don't have a number for batches this time. So we still do, 3/4 x 3 but this time we cross out both the 3 on the top and we're left with 4, our answer.

                The equation for this is 3/4 x b. (Did this help..?)

We have to divide the dimensions by 9 to get a similar rectangle that's area is only 2 in.^2

Solution:

Given that,

For a game, Tony has a rectangle drawn on a piece of paper that has an area of 18 in.^2

In order to have a similar rectangle that's area is only 2 in.^2

Thus, we need to find the scale factor

Let "c" be the scale factor

Let "x" be the area of original rectangle

Let "y" be the area of dilated rectangle

Therefore,

[tex]c = \frac{y}{x}\\\\c = \frac{2}{18}\\\\c = \frac{1}{9}[/tex]

Therefore, we have to divide the dimensions by 9 to get a similar rectangle that's area is only 2 in.^2

Answer:

Divide them by three.

Answer:

7.071 cm

Step-by-step explanation:

Final answer:

To find the length AG in the cuboid ABCDEFGH, use the three-dimensional Pythagorean theorem twice. First finding the diagonal AC (which is equal to 5 cm), and then using it to find AG. The length AG, to three significant figures, is approximately 7.07 cm.

Explanation:

The length AG of a cuboid ABCDEFGH can be found by using the Pythagorean theorem in three dimensions. This theorem is an extension of the traditional Pythagorean theorem used in two dimensions. For the given cuboid, we start by using the Pythagorean theorem on triangle ABC to find the diagonal AC. The formula for the Pythagorean theorem is:

c2 = a2 + b2

Where c is the diagonal and a and b are the sides of the right triangle:

AC2 = AB2 + BC2

Plugging in the given values, we have:

AC2 = 32 + 42 = 9 + 16 = 25

So, AC = 5 cm.

Now, to find AG, we use the diagonal AC and side CG in another application of the Pythagorean theorem for the right triangle ACG:

AG2 = AC2 + CG2

AG2 = 52 + 52 = 25 + 25 = 50

AG = √50 ≈ 7.071 approximately.

Therefore, the length AG, expressed to three significant figures, is approximately 7.07 cm.

Answer:

cube

Step-by-step explanation:

the four cubes in the middle make a square and the two other ones fill in the sides of the cube

The slope-intercept form is y = 2x-3.

Step-by-step explanation:

Given,

Comparing the given equation with general equation, it can be determined that :

m = 2 and c = 7 (y-intercept).

The given line passes through the point (3,3) which is equal to (x1,y1)

Therefore, x1=3 and y1=3.

Substitute m=2 and the values of (x1,y1) in the slope-intercept form,

The slope-intercept form is (y-y1) = m (x-x1)

(y-3) = 2(x-3)

y = 2x-6+3

y = 2x-3

Answer:

Slope=4.25

Step-by-step explanation:

Formula for slope is y2-y1/x2-x1

Y1=51,y2=17,x1=12,x2=4

Input this values into the above formula

17-51/4-12

Slope=-34/-8

Divide both numerator and denominator by -2

Slope=17/4

Slope=4.25

Answer:

an = a1 + d(n - 1)

a88 = 4 + (-5)(88 - 1)

a88 = 4 + (-5)(87)

a88 = 4 - 435

a88 = -431

So, the 88th term of the arithmetic sequence is -431.

The 88th term of the given arithmetic sequence is equal to -431.

Given the following data:

To calculate the 88th term of the given arithmetic sequence:

Mathematically, the nth term of an arithmetic sequence is given by the formula:

[tex]a_n = a_1 + d(n - 1)[/tex]   ...equation 1.

Where:

First of all, we would determine the common difference as follows:

[tex]d = a_2 - a_1\\\\d=-1-4[/tex]

d = -5

Substituting the values into eqn. 1, we have:

[tex]a_{88} = 4 + [-5](88 - 1)\\\\a_{88} = 4 -5(87)\\\\a_{88} = 4 -435\\\\a_{88} = -431[/tex]

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Answer:

Step-by-step explanation:

A supplementary angle is equal to 180 degrees. So subtract 96.7 degrees from 180. 180-96.7= 83.3 degrees

Your answer is 83.3 degrees.

Answer: 83.7 is supplimentary

Step-by-step explanation: 180 - 96.7 = 83.7

The two teachers have 16 and 64 homework papers to return, totalling in 80.

They also have 14 and 60 quizzes to return, totalling in 74.

The ratio of homework papers to quizzes that need to be returned is 80:74

In total, there are 80 homework papers and 74 quizzes to be returned. The ratio for the total would be 80 : 74 (or 80/74), and 40 : 37 (or 40/37) simplified.

For Ms. G alone, the ratio would be 16 : 14 (or 16/14), and 8 : 7 (or 8/7) simplified.

For Ms. M alone, the ratio would be 64 : 60 (or 64/60), and 16 : 15 (or 16/15) simplified.

Hope this helps!! :)

Answer:

10[tex]\leq[/tex]D+R

D[tex]\geq[/tex]R/3 (or 3D[tex]\geq[/tex]R)

Step-by-step explanation:

Say that D = Decaf and R = Regular

10[tex]\leq[/tex]D+R

D[tex]\geq[/tex]R/3 (or 3D[tex]\geq[/tex]R)

Maria had 2 yards of trim when she started.

Step-by-step explanation:

Step 1:

All of the sides of the triangle is 22 inches long each.

The total length of the sides of the triangle [tex]= 3(22) = 66.[/tex]

So the total length of the trim for the banner is 66 inches long.

If Maria still has [tex]\frac{1}{2}[/tex] a foot of trim left, she had 6 inches of the trim left.

The length of the trim when she started[tex]=66 +6 = 72[/tex] inches.

Step 2:

Now we need to convert the 72 inches into yards.

We have 1 inch = 0.0277778 yards.

So 72 inches [tex]= 0.0277778(72) = 2.[/tex]

So Maria had 2 yards of trim when she started.

Answer:

682,500 people

Step-by-step explanation:

so just find how many people per year it grows by then add that number 15 times to 300,000

so 8.5% of 300,000 is 25,500 people

now multiply that by 15 to get 382,500

add that to 300,000

Final answer:

Using the exponential growth formula, the population of a city with an initial population of 300,000 and an annual growth rate of 8.5% will be approximately 962,100 after 15 years.

Explanation:

To calculate the future population of a city with an initial population of 300,000 people and an annual growth rate of 8.5% over 15 years, we use the formula for exponential growth:

P = P_0 (1 + r)[tex]^{t}[/tex]

where:

P is the future population,

P_0 is the initial population (300,000),

r is the annual growth rate (expressed as a decimal, so 8.5% becomes 0.085), and

t is the number of years (15).

Substituting the values we get:

P = 300,000 (1 + 0.085)¹⁵

Calculating this, we find:

P = 300,000 (1.085)¹⁵

P = 300,000 (3.207)

P ≈ 962,100

Therefore, after 15 years, the population is expected to be approximately 962,100, rounding to the nearest whole number.

The question means in Portuguese: In a certain addition of three consecutive natural numbers, the smallest is 49. What should the sum be?

English: Since 49 is the smallest number, the next number up and the next number up give us the 3 consecutive numbers. So 49+50+51 is 150.

Portuguese: Como 49 é o menor número, o próximo número acima e o próximo número acima nos dão os 3 números consecutivos. Então 49 + 50 + 51 é 150.

Answer:           Equivalent fractions are fractions with different numbers representing the same part of a whole. They have different numerators and denominators, but their fractional values are the same.

Step-by-step explanation :   For example, think about the fraction 1/2. It means half of something. You can also say that 6/12 is half, and that 50/100 is half. They represent the same part of the whole. These equivalent fractions contain different numbers but they mean the same thing: 1/2 = 6/12 = 50/100

Multiply both the numerator and denominator of a fraction by the same whole number. As long as you multiply both top and bottom of the fraction by the same number, you won't change the value of the fraction, and you'll create an equivalent fraction.

Find fractions equivalent to 3/4 by multiplying the numerator and denominator by the same whole number ! Again, hoped this helped. If you do used, don't word for copy. Make it into your own words.

Equivalent fractions are fractions with different numbers representing the same part of a whole. They have different numerators and denominators, but their fractional values are the same.

For example, think about the fraction 1/2. It means half of something. You can also say that 6/12 is half, and that 50/100 is half. They represent the same part of the whole. These equivalent fractions contain different numbers but they mean the same thing: 1/2 = 6/12 = 50/100

Answer: 24

Step-by-step explanation:

Based on the inscribed angle theorem, the measure of angle CAB in circle (O) is: A. 24 degrees.

According to the inscribed angle theorem, the measure of an inscribed angle whose vertex lies on a circle is always half the measure of the intercepted arc that is subtended at a point on the circle.

Given the following data:

Based on the inscribed angle theorem, we have:

∠CAB = ∡CB/2

∠CAB = 48/2

∠CAB = 24 degrees.

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Answer:

Step-by-step explanation:

A. The regular cost is 55 per person. Using the given variable definitions, that cost can be expressed as ...

  y = 55x

__

B. The party special cost is 46 per person, with an added fee of 45. That cost can be expressed as ...

  y = 46x +45

_____

As you know, the cost of a purchase is the product of the cost of an item and the number of items. Here, the cost of entry is the cost of the item of interest, and the number of persons needing entry is the number of items. The party special has the addition item of a private room, so its cost is added to the total for the party special.

Answer:

7*(2a-1)

Step-by-step explanation:

Answer:

7*(2a+1) / 2*(7a+1)

Step-by-step explanation:

Answer:

10.92m

Step-by-step explanation:

See attached picture for more illustration

Using SOH CAH TOA,

Tan 20° = opposite / adjacent

Tan 20° = x / 30

x = 30 * tan20

x = 10.919m = 10.92m

The height of the tree is 10.92m

Final answer:

The height of the cat in the tree is 10.44m

Explanation:

The question involves finding the height of a cat caught in a tree using trigonometry, specifically the tangent function. If the firefighter is standing 30m from the base of the tree and the angle to the cat is 20 minutes (which should be converted to degrees for typical trigonometric calculations), we can calculate the height of the cat in the tree. First, we need to convert the angle from minutes to degrees. Since 1 degree = 60 minutes, 20 minutes is equal to 20/60 degrees or approximately 0.33 degrees.

To find the height of the cat, we can use the tangent function (tan) in trigonometry, which is the ratio of the opposite side (the height of the cat in the tree, which we're trying to find) to the adjacent side (the distance from the firefighter to the base of the tree). Thus, the formula becomes height = tan(angle) × distance.

Using the formula:

distance = 30m

angle = 0.33 degrees

height = tan(0.33 degrees) × 30

Tan(20') x Distance

Calculating: Height = Tan(20') x 30m = 10.44m

Answer:

3,854

Step-by-step explanation:

There’s 82 kids each learned 47 lines you would multiply

The children learned a total of 3854 lines of the song. This is found by multiplying the number of children by the number of lines in the song.

This problem involves simple multiplication. Since each child needs to learn one line of the song, and the fun song has 47 lines, to find the total number of lines the children learned altogether, you simply multiply the number of children by the number of lines in the song. Therefore, 82 (number of children) x 47 (number of lines in the song) equals 3854. So, the children learned 3854 lines in total.

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Answer:

24x − 8y

Step-by-step explanation:

8(3x-y)

apply distributive property;

1. 8 (3x) + 8 (−y)

multiply 3 by 8 ;

2. 24x + 8 (-y)

multiply -1 by 8;

3. 24x - 8y

Regroup terms ;

4. 24x − 8y

Answer:

D:step 4

Step-by-step explanation:

The factored forms are [tex]\((p + 4c)(p - 4c - 1)\)[/tex] for the first expression and [tex]\(-(x - 7)(y - 7)\)[/tex] for the second expression.

Let's factor the given expressions:

1. [tex]\(p^2 - 16c^2 - p - 4c\)[/tex]:

  To factor this quadratic expression, we can use the difference of squares formula, [tex]\(a^2 - b^2 = (a + b)(a - b)\)[/tex]. In this case, [tex]\(p^2 - 16c^2\)[/tex] is a difference of squares, so we can factor it as [tex]\((p + 4c)(p - 4c)\)[/tex]. The remaining terms are [tex]\( - p - 4c\)[/tex], and thus, the factored form is [tex]\((p + 4c)(p - 4c) - (p + 4c)\)[/tex]. Factoring out the common factor of -1 from the last two terms gives us the final factored expression: [tex]\((p + 4c)(p - 4c - 1)\)[/tex].

2. [tex]\(x^2 - 7x + 7y - y^2\)[/tex]:

  This expression is a quadratic trinomial, and to factor it, we need to find two binomials whose product equals the given expression. The expression can be rewritten as [tex]\(x^2 - 7x - y^2 + 7y\)[/tex]. Now, we can group the terms as [tex]\((x^2 - 7x) - (y^2 - 7y)\)[/tex]. Factoring out \(x\) from the first group and y from the second group, we get [tex]\(x(x - 7) - y(y - 7)\)[/tex]. Now, we notice that both terms have a common factor of -1, so we can factor that out to obtain the final result: [tex]\(-(x - 7)(y - 7)\)[/tex].

Answer:

  31.205

Step-by-step explanation:

The perimeter is the sum of the side lengths:

  8.73 +12.4 +10.075 = 31.205

_____

If you're after an answer that has the appropriate precision (assuming these are measured values), that would be one that is rounded to 1 decimal place: 31.2.

.answer:

120

step-by-step explanation:

10+10+10+10=40

8+8+8+8.     =32

12+12+12+12=48

add everything up (the numbers that we got) and you would get 120cm

Answer:

960

Step-by-step explanation:

You multiply the base x height x width. So you do 10 x 8 x 12 = 960 cm.

Answer:

8y - 16

Step-by-step explanation:

Step 1:  Distribute

32 + 8(y - 6)

32 + 8y - 48

8y - 16

Answer:  8y - 16

If needed solve for y:

8y - 16 + 16 = 0 + 16

8y / 8 = 16 / 8

y = 2

Answer:

8y - 16  

Step-by-step explanation: