factor the following by taking on the greatest common factor 14a^3 + 35a^2 +42a

Answer:

x = 29°

Step-by-step explanation:

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$27.00-6.00=21.00

21.00-11.00=10.00

A

Answer:

8a. x = 16√3

8b. y = 8√3

Step-by-step explanation:

8a. Determination of the value of x

Adjacent = 24

Hypothenus = x

Angle θ = 30°

The value of x can be obtained by using cosine ratio as illustrated below:

Cos θ = Adjacent /Hypothenus

Cos 30 = 24 / x

√3/2 = 24/x

Cross multiply

x × √3 = 2× 24

x × √3 = 48

Divide both side by √3

x = 48/√3

Rationalise

x = 48/√3 × √3/√3

x = 48√3 / √3 × √3

x = 48√3 / 3

x = 16√3

8b. Determination of the value of y

Opposite = y

Adjacent = 24

Angle θ = 30°

The value of y can be obtained by using Tan ratio as illustrated below:

Tan θ = Opposite / Adjacent

Tan 30 = y / 24

1 / √3 = y /24

Cross multiply

y × √3 = 1 × 24

y × √3 = 24

Divide both side by √3

y = 24 /√3

Rationalise

y = 24 /√3 × √3/√3

y = 24 ×√3 / √3 × √3

y = 24√3 / 3

y = 8√3

The value of expression 50% of 36 is,

⇒ 50% of 36 = 18

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

The expression is,

⇒ 50% of 36

Now, We can simplified as;

The expression is,

⇒ 50% of 36

By definition of percent we get;

⇒ 50/100 × 36

⇒ 1/2 × 36

⇒ 36/2

⇒ 18

Thus, The value of 50% of 36 is,

⇒  50% of 36 = 18

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Based on the information given, the price of the zero coupon bond is $692.04.

To calculate the price of a zero coupon bond, we need to use the following formula:

\(\sf P =\dfrac{F}{1+r\div n}^{(nt)\)

Where:

Also, the annual interest rate is 7.50%, which is the market interest rate, and the compounding is semiannual, which means n = 2. Finally, the time to maturity is 5 years.

Plugging in the values into the formula, we get:

\(\sf P = \dfrac{1000}{(1+0.075\div2)^{(2\times5)}}\)

\(\sf P = \dfrac{1000}{(1.0375)^{10}}\)

\(\sf P = \dfrac{1000}{1.4450}\)

\(\sf P = \$692.04 \ \ (rounded \ to \ the \ nearest \ cent)\)

Therefore, the price of the zero coupon bond is $692.04.

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here is the answer 1,000,700

The standard form of "one million seven hundred" is 1,000,700.

The standard form of a number refers to the representation of a number using digits and place value notation. It is also known as the decimal form or the base-10 form.

We have,

"one million seven hundred"

In standard form, numbers are written using place value notation, where each digit is assigned a position based on its place value.

In the case of "one million seven hundred," the digit 1 represents one million, the digit 7 represents seven hundred, and the remaining zeroes represent placeholders for the tens, ones, and smaller place values.

So, by combining the place values, we can express "one million seven hundred" in standard form as 1,000,700, where the 1 represents one million, the 0s serve as placeholders for the smaller place values, and the 7 represents seven hundred.

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It took Emily 33.4 minutes to make dinner.

A mixed number is a kind of fraction that also has a proper fraction and a whole number. The number of whole units is represented by the whole number, and the fraction of a unit is represented by the proper fraction.

To solve the problem, we have to convert the mixed number  \(9 \frac{1}{10}\)   to a decimal number:

⇒ \(9 \frac{1}{10} = 9 +\frac{1}{10} = \frac{(9*10)+1}{10}\)

⇒ \(\frac{91}{10}\)  =  9.1

This means that Emily finished making dinner 9.1 minutes sooner than the cake.

To find out how long it took Emily to make dinner, we can subtract 9.1 from the cake baking time:

⇒ 42.5 - 9.1 = 33.4 minutes

Therefore, it took Emily 33.4 minutes to make dinner.

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Answer: 18.78 cubic feet

Step-by-step explanation:

The detailed analysis is attached below.

Answer:

4 1/2 flowers

Step-by-step explanation:

2 + 3 = 5 and 4 x 5 = 20 and plus half a flower.

The value of covariance cov(y1, y2) is -0.222

                      y1      

y2         0         1         2          Total

0          1/9      2/9     1/9          4/9

1          2/9      2/9      0            4/9

2          1/9        0       0            1/9

Total   4/9       4/9     1/9          1      

  marginal distribution of y2:

y2      P(y2)      y2P(y2)      y2^2P(y2)

0         4/9        0.0000        0.0000

1          4/9         0.4444        0.4444

2          1/9         0.2222        0.4444

total      1          0.66667       0.88889

E(y2) = 0.6667

E(y2^2) = 0.8889

Var(y2) = E(y2^2)-(E(y2))^2=0.4444

marginal distribution of y1  

y1       P(y1)       y1P(y1)      y1^2P(y1)

0         4/9       0.0000      0.0000

1          4/9        0.4444       0.4444

2          1/9         0.2222      0.4444

total  1.00          0.6667      0.8889

E(y1) = 0.6667

E(y1^2) = 0.8889

Var(y1)= σy = E(y1^2)-(E(y1))^2 = 0.4444

E(XY) =∑xyP(x,y)=0.2222

Cov(y1,y2) = -0.222

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Answer: \(m\angle DE F=90^{\circ}\)

Step-by-step explanation:

The slope of \(DE\) is \(\frac{7-3}{5-4}=4\).

The slope of \(EF\) is \(\frac{3-2}{4-8}=-\frac{1}{4}\).

Thus, \(DE \perp EF\), meaning \(m\angle DE F=90^{\circ}\).

Answer:

b=43 i think

Step-by-step explanation:

If this is a 1 attempt thing do not trust me but just know that is 180 degrees so a+b+c=180 will be your formula

It has taken me 32 minutes to drive 48 km. If the total length of my journey is 146 km and I maintain the same speed,  then you can estimate that you will be driving for approximately 65.344 minutes longer to complete the remaining 98 km of your journey.

To estimate how much longer you will be driving for, we can use the concept of proportionality. We know that the time taken to drive 48 km is 32 minutes. Let's use this information to find the time it would take to drive 146 km.

We can set up a proportion to find the time:

(time taken for 48 km) / (48 km) = (time taken for 146 km) / (146 km)

Let's solve for the time taken for 146 km:

(time taken for 146 km) = (time taken for 48 km) * (146 km / 48 km)

Substituting the given values:

(time taken for 146 km) = 32 minutes * (146 km / 48 km)

Calculating the value:

(time taken for 146 km) ≈ 32 minutes * 3.042

(time taken for 146 km) ≈ 97.344 minutes

Therefore, it would take approximately 97.344 minutes to drive 146 km at the same speed.

To estimate how much longer you will be driving for, we can subtract the initial time of 32 minutes from the estimated time of 97.344 minutes:

Additional time = 97.344 minutes - 32 minutes

Additional time ≈ 65.344 minutes

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Answer:

Step-by-step explanation:

A. 60 + 30 = 90

B. 690000

C. 90 x 2000 = 180000

Answer:

(x+1)(x+3)

Step-by-step explanation:

Let's factor x^2+4x+3

x^2+4x+3

The middle number is 4 and the last number is 3.

Factoring means we want something like

(x+_)(x+_)

Which numbers go in the blanks?

We need two numbers that...

Add together to get 4

Multiply together to get 3

Can you think of the two numbers?

Try 1 and 3:

1+3 = 4

1*3 = 3

Fill in the blanks in

(x+_)(x+_)

with 1 and 3 to get...

(x+1)(x+3)

Setting h=0 and solving for t we get:

Since t<0 does not have real meaning, we get that:

Answer: 6.5 seconds.

Answer:

Diameter of wheel in millimetres is 660.4

Step-by-step explanation:

Diameter of wheel in inches = 26

given

1 inch = 25.4 millimeters

multiplying RHS and LHS by 26

26*1 inch = 26*25.4 millimeters

=>26 inch = 660.4 mm.

Thus, diameter of wheel in millimetres is 660.4

The distance between the fire and station B is 10.7miles

The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.

The angle at A = 90- 35

= 55°

The angle at B = 90-49

= 41°

Angle at the fire = 180-(41+55)

= 180-96 = 84°

Using sine rule

sin84/13 = sin55/x

xsin84 = 13sin55

0.995x = 10.65

x = 10.65/0.995

x = 10.7 miles

Therefore the distance between the fire and station B is 10.7 miles.

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Answer:

\( f(t) = 13,500(0.89)^t \)

Step-by-step explanation:

The formula for the exponential function is given as \( f(t) = a(b)^t \)

Where,

base value = a = $13,500

b = 1 - % decrease = 1 - 11% = 1 - 0.11

b = 0.89

Substitute the values of a and b into the exponential function, \( f(t) = a(b)^t \), respectively.

Thus:

\( f(t) = 13,500(0.89)^t \)

The height of the building is 242.59 feet.

Let's denote the height of the building as h.

angle of elevation is 35 degrees.

Using the tangent function,

tan(35°) = h / x

h = x tan(35°)

From the second observation point, which is 150 feet closer to the building,

The adjacent side is now (x - 150) since we moved closer to the building.

So, tan(51°) = h / (x - 150)

Now, tan(51°) = (x tan(35°)) / (x - 150)

1.2348 = x (0.7002)/ x-150

1.2348x - 185.22 = 0.7002x

x= 346.4646 feet

and, h = 364.4646 x 0.7002 =  242.59 feet

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Answer:

rectangle= 22*9 = 198ft

triangle=11*10 = 110 ft

110+ 198 = 308 polygon

Answer:

The triangles are similar.

Explanation:

Similar triangles have 3 pairs of congruent angles. In this diagram, we can see that the triangles WXP and WYZ share angle W, which is congruent to itself; therefore, they have at least 1 pair of congruent angles. We are given that angle X is congruent to angle Y, so that is a second pair of congruent angles. Finally, we know that angle P is congruent to angle Z because if two pairs of corresponding angles are congruent, then the third pair must also be congruent because the measures of the interior angles of both triangles have to add to 180°.

Answer:

$ 25.86 is the answer

Step-by-step explanation:

Jenny will need to invest approximately $15,112.18 in order to reach her retirement goal of $60,000 with a 9% return on her investment.

To calculate how much money Jenny will need to invest in order to reach her retirement goal, we can use the concept of compound interest.

Given:

Current age: 49 years

Retirement age: 65 years

Additional funds needed for retirement: $60,000

Expected return on investment: 9% (expressed as a decimal: 0.09)

The compound interest formula for determining an investment's future worth is as follows:

FV = PV * (1 + r)ⁿ

Where:

FV = Future Value (the desired amount at retirement)

PV = Present Value (the initial investment)

r = Interest rate per period

n = Number of periods

In this case, Jenny has 16 years until retirement (65 - 49 = 16), and she wants to accumulate an additional $60,000.

Let's plug the values into the formula:

$60,000 = PV * (1 + 0.09)¹⁶

Now, we can solve for PV:

PV = $60,000 / (1 + 0.09)¹⁶

we find:

PV ≈ $15,112. 18

Therefore, Jenny will need to invest approximately $15,112.18 in order to reach her retirement goal of $60,000 with a 9% return on her investment.

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