For the graph of function f shown below, which of the following is true?

Answer:

The graph of [tex]g(x) = (x - 1) (x + 4)^3(x +5)^2[/tex] crosses the x-axis at (1,0) and (-4, 0). It touches the x-axis at (-5, 0).

Step-by-step explanation:

g(x):

[tex]g(x) = (x - 1) (x - (-4))^3(x - (-5)^2[/tex].

There are three factors:

The first and second factors are raised to odd powers. The graph will cross the x-axis at all these two points:

The third factor is raised to an even power. The graph will touch the x-axis at that point.

Answer:

crosses at (1,0)

crosses at (-4,0)

touches at (-5,0)

Got correct on ed

Step-by-step explanation:

Answer:

[tex]\large\boxed{V=\dfrac{75\sqrt3}{2}\approx64.95}\\\boxed{S.A.=\dfrac{160+25\sqrt3}{2}}[/tex]

Step-by-step explanation:

The formula of a volume of a prism:

[tex]V=BH[/tex]

B - base area

H - height

In the base we have the equilateral triangle. The formula of an area of an equilateral triangle with side a:

[tex]A=\dfrac{a^2\sqrt3}{4}[/tex]

Substitute a = 5:

[tex]B=\dfrac{5^2\sqrt3}{4}=\dfrac{25\sqrt3}{4}[/tex]

H = 6.

Calculate the volume:

[tex]V=\left(\dfrac{25\sqrt3}{4}\right)(6)=\dfrac{75\sqrt3}{2}[/tex]

The formula of a Surface Area:

[tex]S.A.=2B+PH[/tex]

B - base area

P - perimeter of a base

H - height

Calculate P:  [tex]P=5+5+5=15[/tex]

Substitute:

[tex]S.A.=2\left(\dfrac{25\sqrt3}{4}\right)+(15)(6)=\dfrac{25\sqrt3}{2}+80=\dfrac{160+25\sqrt3}{2}[/tex]

Answer:

Step-by-step explanation:

D is correct.  The idea here is to ensure that the point on the post is equidistant from the bottom of the post (where it meets the ground), which in turn ensures that the angle between ground and post is 90° in at least two places on the ground.

The step that Sam must take first in order to make sure that the post of the fence is ⊥ to the bottom of the ground would be:

D). "Place the compass at the point off the ground, and swing an arc that intersects the ground in two places."

Learn more about 'arcs' here:

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Answer:

I only know how to do the first and second one i'm not sure about the rest:  V=Lwh

Step-by-step explanation:

so, (6)(6)(8)= 288ft^3

and (12)(16)(18)= 3456m^3

Hope i have helped you in some way!

Squares 1 and 2 have the same area because they're both (a+b) on a side.

Each of these squares is covered by four identical right triangle tiles, legs a,b, hypotenuse c.  

In the first picture we see the uncovered part of the square, not covered by triangular tiles, is two squares, area [tex]a^2+b^2[/tex].

In the second picture the uncovered part of the square is a smaller square, area [tex]c^2[/tex].

We just moved the tiles around on the square, so the uncovered part is the same in both cases.  So

[tex]a^2 + b^2 = c^2[/tex]

--------

The rectangular prism has a bottom rectangular base 6 by 8.  So  the diagonal is [tex]\sqrt{6^2+8^2}=\sqrt{100}=10[/tex].

The diagonal and the 7 cm side make a right triangle whose hypotenuse is the diagonal of the rectangular prism we seek.

[tex]\sqrt{10^2 + 7^2} = \sqrt{149}[/tex]

Answer: √149

Answer:

Option A. [tex]LN^{2}=33^{2}-11^{2}[/tex]

Step-by-step explanation:

we know that

In the right triangle MNL

Applying the Pythagoras Theorem

[tex]MN^{2}=ML^{2} +LN^{2}[/tex]

substitute the values

[tex]33^{2}=11^{2} +LN^{2}[/tex]

[tex]LN^{2}=33^{2}-11^{2}[/tex]

Answer:

2p, since twice as long would hint to multiplication.

Answer:

(5y+3)(y-1)

Step-by-step explanation:

5y^2-2y-3

I don't know if you like trial factors or not... but we can try that way

notice we have 5y^2

that can be written as 5y * 1y

Notice at the end we have -3

that can be written as -3*1

So possible answers could be:

(5y-3)(1y+1)   =5y^2+5y-3y-3=5y^2+2y-3

So this was almost right.

If we just switch the signs the - and + there we will have got it

(5y+3)(1y-1)=5y^2-5y+3y-3=5y^2-2y-3 which is good

So the answer is (5y+3)(y-1)

To factor the quadratic equation 5y^2-2y-3 completely, find two numbers that multiply to -15 and add to -2, and use them to rewrite the middle term before factoring by grouping. The factors obtained are (5y - 3)(y + 1).

The given quadratic equation to factor completely is 5y^2-2y-3. To achieve this, we are finding two numbers that multiply to the product of the coefficient of y^2 (which is 5) and the constant term (which is -3), and at the same time add up to the coefficient of the y term (which is -2).

The required pair of numbers is -3 and -1, because (-3)*(1) = -3 (the product of coefficient of y^2 and the constant term) and (-3)+(1) = -2 (the coefficient of the y term).

We rewrite the middle term and then factor by grouping:

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Answer:

The cost of the racquet is [tex]\$135[/tex]

Step-by-step explanation:

Let

x-----> the cost of the racquet

we know that

The racquet represent the 100%

so

using proportion

[tex]x/100\%=\$9.45/7\%[/tex]

[tex]x=100\%*(\$9.45)/7\%[/tex]

[tex]x=\$135[/tex]

Answer:

176

Step-by-step explanation:

To find a number from a known percentage and a number, divide the given number by the percent.

[tex]\frac{v}{p}[/tex]

Where [tex]v[/tex] is the value given and [tex]p[/tex] is the percentage.

[tex]\frac{44}{0.25}=176[/tex]

Answer:

176

Step-by-step explanation:

Answer:

(6x5) • 8

Step-by-step explanation:

We’ll I find it’s 6 dollars a day and their are 5 days that would be 30 but this went in for 8 weeks so it would be 30 x 8 which equal 240

Answer:

Required expression for amount spend on breakfast for 8 week is ( 6 × 5 ) × 8 and this amount is $ 240

Step-by-step explanation:

Given:

Amount spend on Breakfast using debit card = $6

Amount for breakfast spend for 5 mornings per week for past 8 weeks.

We need to write the multiplication expression for the given situation.

Amount spend on breakfast for a morning = $6

Amount spend on breakfast for 5 morning = 6 × 5

Amount spend on breakfast for 1 week = $ ( 6 × 5 )

Amount spend on breakfast for 8 week = ( 6 × 5 ) × 8

Required multiplication expression = ( 6 × 5 ) × 8

Answer of the multiplication = ( 6 × 5 ) × 8 = ( 30 ) × 8 = 240

Therefore, Required expression for amount spend on breakfast for 8 week is ( 6 × 5 ) × 8 and this amount is $ 240

Answer:

the slope intercept form is: y = x+2

Step-by-step explanation:

The general form of point slope form is : y-y₁ = m(x-x₁)

The given equation is: y – 3 = (x – 1)

comparing we get,

m = 1

and solving the equation;

y-3 = x-1

Adding +3 on both sides

y = x-1+3

y=x+2

The general formula of slope-intercept form is : y = mx+b

where m is the slope and b is the y-intercept

so, y = x+2

where m =1 and b=2

so, the slope intercept form is: y = x+2

Answer:

the answer is y = y= 1/2x+2

Step-by-step explanation:

Answer:

{x | x ≤ -20}

Step-by-step explanation:

x + 17 ≤ -3

Subtract 17 from each side

x + 17-17 ≤ -3-17

x  ≤ -20

Answer:

{x | x ≤ -20}

Answer: 72

Step-by-step explanation:

Rewriting input as fractions if necessary:

8/9, 7/8

For the denominators (9, 8) the least common multiple (LCM) is 72.

LCM(9, 8)

Therefore, the least common denominator (LCD) is 72.

Rewriting the original inputs as equivalent fractions with the LCD:

64/72, 63/72

Answer:

= 5.196 i

Step-by-step explanation:

The problem tells us to find the square root of -98 +71

√(-98 + 71)

= √(-27)

Which is an imaginary number

=√(-3^3)

Lets remember that, √(-1) = i

= i*3√(3)

= 5.196 i

Please see attached image for more information

Answer:

x^3-1

Step-by-step explanation:

f(x)=g(x)-1 since was shifted down 1 unit                                        x^3-1

f(x)=g(x)+1 would have been a shift up of 1 unit                             x^3+1

f(x)=g(x-1) shifted right 1 unit                                                            (x-1)^3

f(x)=g(x+1) shifted left one unit                                                        (x+1)^3

Anyways the answer is f(x)=x^3-1

1- Writing the system of equations:

The price of a cup of coffee is denoted by c while the price of a spaghetti is denoted by s

We are given that:

4 cups of coffee and 6 spaghetti cost $20.5

This means that:

4c + 6s = 20.5 ................> equation 1

We are also given that:

1 cup of coffee and 3 spaghetti cost $8.75

This means that:

c + 3s = 8.75 .................> equation 2

2- Solving the equations using substitution methods:

From equation 2:

c = 8.75 - 3s ................> I

Substitute with I in equation 1 and solve for s as follows:

4c + 6s = 20.5

4(8.75 - 3s) + 6s = 20.5

35 - 12s + 6s = 20.5

35 - 6s = 20.5

6s = 14.5

s = $2.41667

Substitute with s in I to get c:

c = 8.75 - 3s

c = 8.75 - 3(2.41667) = 1.4999 = $1.5

3- getting price for 1 cup of coffee and 1 spaghetti:

c + s = 1.5 + 2.41667 = $3.91667

Hope this helps :)

Answer: Last option

[tex]p = (0.9801) ^ {30}[/tex]

Step-by-step explanation:

the probability of a jaywalker being hit is

[tex]P = \frac{1}{100} = 0.01[/tex].

So the probability of a jaywalker not being hit is:

[tex]P '= 1-0.01[/tex]

[tex]P '= 0.99[/tex]

As in this experiment the probability of each trial is independent then, the probability that it is not a jaywalker will not be hit if it makes a round trip is:

[tex]P '= (0.99) (0.99) = 0.9801[/tex]

[tex]P '= 0.9801[/tex]

If this experiment is repeated for 30 days then the probability that it is not a jaywalker will not be hit if it makes a round trip is:

[tex]p = (0.9801) ^ {30}[/tex]

Answer:

[tex]\large\boxed{\dfrac{5}{4}}[/tex]

Step-by-step explanation:

[tex]a_1=20\\\\a_2=\dfrac{20}{2}=10\\\\a_3=\dfrac{10}{2}=5\\\\a_4=\dfrac{5}{2}\\\\a_5=\dfrac{\frac{5}{2}}{2}=\dfrac{5}{2}\cdot\dfrac{1}{2}=\dfrac{5}{4}[/tex]

Answer:

The answer would be B. 2x+4 / x

For this case we have that by definition of composition of functions that:

[tex](f_ {0} h_ {0} g) = f (h (g (x)))[/tex]

So:

[tex]h (g (x)) = 4 (x-2) -1 = 4x-8-1 = 4x-9[/tex]

So:

[tex]f (h (g (x))) = \frac {4x-9 + 4} {4x-9} = \frac {4x-5} {4x-9}[/tex]

ANswer:

[tex](f_ {0} h_ {0} g) = \frac {4x-5} {4x-9}[/tex]

Option D

Answer:

Step-by-step explanation:

[tex]14\leq2t+18\leq20\qquad\text{subtract 18 from all sides}\\\\14-18\leq2t+18-18\leq20-18\\\\-4\leq2t\leq2\qquad\text{divide all sides by 2}\\\\\dfrac{-4}{2}\leq\dfrac{2t}{2}\leq\dfrac{2}{2}\\\\-2\leq t\leq1\\\\\text{The third graph.}[/tex]

Answer:

The product is -x³ - 2x² + 13x + 26

Step-by-step explanation:

* Lets revise how to find the product of two binomials

- If (ax ± b) and (cx ± d) are two binomials, where a , b , c , d are constant

 their product is:

# Multiply (ax) by (cx) ⇒ 1st term in the 1st binomial and 1st term in the

  2nd binomial

# Multiply (ax) by (d) ⇒ 1st term in 1st binomial and 2nd term in

  2nd binomial

# Multiply (b) by (cx) ⇒ 2nd term in 1st binomial and 1st term in

  2nd binomial

# Multiply (b) by (d) ⇒ 2nd term in 1st binomial and 2nd term in

  2nd binomial

# (ax ± b)(cx ± d) = cx² ± adx ± bcx ± bd

- Add the terms adx and bcx because they are like terms

* Now lets solve the problem

- There are two binomials (13 - x²) and (x + 2)

- We can find their product by the way above

∵ (13)(x) = 13x ⇒ 1st term in the 1st binomial and 1st term in the

  2nd binomial

∵ (13)(2) = 26 ⇒ 1st term in 1st binomial and 2nd term in

  2nd binomial

∵ (-x²)(x) = -x³ ⇒ 2nd term in 1st binomial and 1st term in

  2nd binomial

∵ (-x²)(2) = -2x² ⇒ 2nd term in 1st binomial and 2nd term in

  2nd binomial

∴ The product of (13 - x²)(x + 2) = 13x + 26 - x³ - 2x²

- There is no like terms

- Lets arrange the terms from greatest power to smallest power

∴ The product is -x³ - 2x² + 13x + 26

Gregory has 2/3 of a pizza and gives 1/4 of an entire pizza to Marlene. By converting the fractions to a common denominator, we find that he gives away 3/8 of his portion of the pizza to Marlene.

Understanding fractions can sometimes be as easy as picturing how you would slice a pie and share it with friends.

Gregory has 2/3 of an entire pizza and decides to give 1/4 of an entire pizza to his friend Marlene.

To solve how much of his portion Gregory gives to Marlene, we need to figure out what fraction 1/4 represents out of the 2/3 that Gregory has.

If we think of the pizza being cut into 12 slices (since 12 is a common multiple of both 3 and 4), Gregory's 2/3 is equivalent to 8/12 of the pizza because (2/3) × (12/1) = 8/12.

Similarly, 1/4 of the pizza is equivalent to 3/12 of the pizza because (1/4) × (12/1) = 3/12.

Now we know that Gregory aims to give away 3/12 of the pizza, but we want to express this as a part of his original 8/12.

To find out what fraction of his part he gives away, we then calculate (3/12) ÷ (8/12).

When we divide these fractions, we can multiply by the reciprocal of the second fraction:

(3/12) × (12/8), which simplifies to 3/8.

Therefore, Gregory gives away 3/8 of his 2/3 of the pizza to Marlene.

The answer is C. (1, 12).

12 = 3 x [tex]4^{1}[/tex]

Answer:

Step-by-step explanation:

f(x)= 3 • 4^x

we can use the x coordinate of the points given in option to check what value do we get for y or f(x) .

so using the point from first option A :

x= 12

[tex]y=f(12)=3.4^{12}=50331648\neq 1[/tex]

for option B

x=0

[tex]y=f(0)=3.4^0=3[/tex]

option C

x=1

[tex]y = f(1)= 3.4^1=12[/tex]

so the correct option is C

Answer: $116,000

Step-by-step explanation:

Set up a ratio and then cross multiply and divide. See paper attached. (:

Final answer:

Ava's salary is calculated based on the given salary ratio of Paul to Ava (3:4). By dividing Paul's salary by 3, we find out how much one part of the ratio is worth and then multiply by 4 to find Ava's salary to be $116,000.

Explanation:

The question provided asks us to calculate Ava's salary based on the ratio of Paul to Ava's salaries which is 3:4. If Paul's salary is $87,000, we determine Ava's salary using the given ratio. Here is the step-by-step process:

Step 1: Understand the ratio, which tells us that for every 3 parts of Paul's salary, Ava gets 4 parts. This does not tell us the total amount, but how they share the total amount.

Step 2: Since Paul's salary is $87,000, and that represents 3 parts of the total, we divide $87,000 by 3 to find out what 1 part is: $87,000 / 3 = $29,000.

Step 3: Now that we know 1 part is $29,000, we can calculate Ava's salary which is 4 parts: $29,000 X 4 = $116,000.

Ava's salary is therefore $116,000.

Answer:

B. Rectangle

Step-by-step explanation:

All rectangles are parallelograms.

Answer:

Counting by hand

Dividing 15 by 2

Step-by-step explanation:

[tex]x=\ln 403.429[/tex]

Answer:

Step-by-step explanation:

45% off $25.60

= [tex]\frac{45}{100}[/tex] x $25.60

= $11.52 (Ans)

Answer:

$11.52

Step-by-step explanation:

$25.60 is 25.6 and 40% is 0.40

So do 25.6 * 0.40 and you get your answer of $11.52

Hope this helped ^-^