Factor the following trinomial: x2 + 8x + 15.

9514 1404 393

Answer:

  A. 5 should have been subtracted in step 4

Step-by-step explanation:

No question is stated, so there is no "answer."

__

If we assume the question is, "What error did Keith make?" then choice A properly describes it.

Step 4 should look like ...

  x -5 = 7y . . . . . . . 5 should be subtracted from both sides

and the final result should be ...

  g(x) = (x -5)/7

Answer:

10,000 + 7,000 + 500 + 70 +4

Step-by-step explanation:

The area for each part of the figure is given as follows:

The area of a right triangle is given by half the multiplication of it's sides.

Triangle A has the side lengths given as follows:

Hence the area is given as follows:

A = 0.5 x 4 x 10 = 20 units squared.

Triangle D is has the side lengths given as follows:

Hence the area is given as follows:

D = 0.5 x 2 x 6 = 6 units squared.

The total area is given by the sum of the areas of each part of the figure, hence:

20 + 2 + 4 + 6 = 32 units squared.

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Answer:

131072

Step-by-step explanation:

Answer: The answer is 131072.

Step-by-step explanation:

Using a calculator, we find that \(2^{17}=\boxed{131072}.\)

The woman will withdraw $300 given 6%   interest rate annually.

We can use the formula for simple interest to solve this problem:

I = Prt

where I is the interest earned, P is the principal (initial deposit), r is the annual interest rate as a decimal, and t is the time in years. Since the interest rate is given as an annual rate, we need to convert it to a daily rate by dividing by 365:

r = 0.06/365 = 0.00016438356

The time in years is 120/365 = 0.3287671233 years. Now we can plug in the values and solve for I:

I = 300 * 0.00016438356 * 0.3287671233 = 0.01699999999

The interest earned is $0.017, which is negligible. Therefore, the woman will withdraw the entire principal plus any interest earned, which is:

300 + 0.017 = $300.02

Rounding to the nearest dollar, the woman will withdraw $300.

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Without knowing the total number of coins or the ratio between one dollar and two dollar coins in the jar, we cannot accurately determine the number of two dollar coins.

Amadi has a jar with both one dollar and two dollar coins. The question is asking how many of the coins in the jar are two dollar coins.
To determine the number of two dollar coins, we need more information. The question does not provide any details about the total number of coins or the ratio between one dollar and two dollar coins in the jar. Without this information, it is not possible to give an accurate answer.
If we assume that the jar contains a total of 100 coins, we can use algebra to solve for the number of two dollar coins.

Let's say the number of two dollar coins is x. Then, the number of one dollar coins would be 100 - x.
Since the value of the two dollar coins is double the value of the one dollar coins, we can set up the equation 2x + 1(100 - x) = total value of coins.
Simplifying the equation, we get 2x + 100 - x = total value of coins.
Combining like terms, we have x + 100 = total value of coins.
Since we don't know the total value of coins, we cannot solve for x. Therefore, we cannot determine the number of two dollar coins without additional information.

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The translation direction is 5 units to the left.

To determine the translation direction and number of units, we can compare the original coordinates of point Q (Q(5, 4)) with the new coordinates of Q' after the translation (Q'(0, 4)).

By comparing the x-coordinates, we can see that the x-coordinate of Q' is smaller than the x-coordinate of Q, which means the triangle was translated to the left.

By comparing the y-coordinates, we can see that the y-coordinate of Q' is the same as the y-coordinate of Q, which means there was no vertical translation.

Therefore, the translation direction is 5 units to the left.

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\(\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ n\theta = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\ \theta = \stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ n=5 \end{cases}\implies 5\theta =180(5-2) \\\\\\ 5\theta =180(3)\implies 5\theta =540\implies \theta =\cfrac{540}{5}\implies \theta =108\)

Answer:

6(4)-4=3(4)+8

24-4=12+8

20=20

Step-by-step explanation:

To prove x=4, substitute four into the equation

6(4)-4=3(4)+8

24-4=12+8

20=20

Therefore x=4 is proved

Answer:

(Answer in Image)

Step-by-step explanation:

6x-4=3x+8

6x-4-3x=3x+8-3x                    subtract -3x on both sides

3x-4=8                                    

3x-4+4=8+4                               add four on both sides

3x=12                                      simplify

3/3x=12/3                                       divide both sides by 3

x=4

Answer:

Time = X = 37.14 minutes

Distance they covered= 33.42 miles.

Step-by-step explanation:

Distance= speed * time

And the distance traveled by the two need to be equal.

Speed of storm = 33 mph

Speed of van = 54 mph

But storm is 13 miles away from van.

So

54*x = 33*x+ 13

54x-33x = 13

21x = 13

X= 0.62 hours

X = 37.14 minutes

54 *0.62= 33.42 miles.

Answer:

0 hundreds

0 tens

7 ones

.

4 tenths

0 hundredths

8 thousandths

Standard form=7.408

Step-by-step explanation:

Lets first solve (7x1)+(4x1/10)+(8x1/1000)

7+0.4+0.008

Simplify:

7.408

Answer:

1 cm = 3 feet.

Step-by-step explanation:

Divide 15 by 5 to get 3; on the blueprint, every centimeter represents 3 feet.

The scale of scale factor of the blueprint is 1 cm = 3 feet.

The scale factor defines a variable in a ratio of two different measurements.

Sometimes drawings of large models are represented in a scale factor of a smaller unit.

Given, On a blueprint, the length of a wall is 5 centimeters and the actual length of the wall is 15 feet.

Therefore, The scale factor of the blueprint is,

= (5/15).

= 1/5.

So, It can be written as 1 cm = 3 feet.

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Answer:

Step-by-step explanation:

DO YOU MEAN :

\(4x + 5y = 7\\ 3x - 2y = -12\\Multiply-equation 1 -by -the-coefficient-of-x-in-equation-2\\multiply-equation-2 -by-the-co-efficient -of x -in-equation- 1\\\\3(4x + 5y = 7)\\4( 3x - 2y = -12)\\\\12x +15y=21\\12x -8y=-48\)

Answer:

C.  

x ≈ 2.50

Step-by-step explanation:

The value of x in the given equation \(-3(-x) -6 = -3x+ 10\) is 2.66

A line graph is a type of chart used to show information that changes over time. We plot line graphs using several points connected by straight lines. We also call it a line chart. The line graph comprises of two axes known as 'x' axis and 'y' axis. The horizontal axis is known as the x-axis.

According to the given question.

We have a equation

\(-3(-x)-6 = -3x +10\)

To draw a graph for the above equation we have to simplify the given equation.

Therefore,

\(-3(-x) -6 = -3x + 10\)

⇒ \(+3x-6 = -3x + 10\)

⇒\(3x+3x = 10 + 6\)

⇒ \(6x = 16\)

⇒ \(x = \frac{16}{6}\)

⇒ \(x = 2.66\)

After solving the above equation for x we have,

x = 2.66

⇒ A line which is parallel to y axis.

Therefore, we draw a line graph at a point x = 2.66 which is parallel to y axis.

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Answer:

volume of a brick: 10(7)(5) = 350 \(in^3\)

14000/350 = 40 bricks

After 18 years, the investment compounded periodically (quarterly) will be worth $1,230.23 more than the investment compounded annually.

Compounded interest refers to the interest system that charges interest on both principal and accumulated interest.

The period of compounding in a year determines the worth of the future value.

The future value can be ascertained using an online finance calculator as follows:

Interest periods: = 4 times yearly (Quarterly)

Principal = $5,000

Annual interest rate = 9%

Number of years: 18

N (# of periods) = 72 quarters (18 years x 4)

I/Y (Interest per year) = 9%

PV (Present Value) = $5,000

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $24,815.83

Total Interest = $19,815.83

Interest periods: = Annually

N (# of periods) = 18 years

I/Y (Interest per year) = 9%

PV (Present Value) = $5,000

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $23,585.60

Total Interest = $18,585.60

Difference in Future Values $1,230.23 ($24,815.83 - $23,585.60)

Thus, an investment compounded periodically earns more than an investment compounded annually.

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The absolute value of the Rational number -474/513 is 474/513.

To find the sum of the rational numbers -8/9 and -2/57, you need to have a common denominator. The least common multiple (LCM) of 9 and 57 is 513. So, you can rewrite the fractions with a common denominator:

-8/9 = (-8/9) * (57/57) = -456/513

-2/57 = (-2/57) * (9/9) = -18/513

Now, you can add the fractions:

-456/513 + (-18/513) = (-456 - 18)/513 = -474/513

To find the absolute value of the rational number -474/513, you simply ignore the negative sign and take the value as positive:

| -474/513 | = 474/513

Therefore, the absolute value of the rational number -474/513 is 474/513.

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Answer:

first and third expressions

Step-by-step explanation:

using the rule of exponents

\(\frac{a^{m} }{a^{n} }\) = \(a^{m-n}\)

then

\(\frac{3^{\frac{4}{9} } }{3^{\frac{2}{9} } }\)

= \(3^{\frac{4}{9}-\frac{2}{9} }\) ← first expression

= \(3^{\frac{2}{9} }\) ← third expression

The probability that (50) dies within 10 years and dies after (40) is at least 0.02 but less than 0.04. So the answer is B. At least .02 but less than .04.

To calculate the probability that (50) dies within 10 years and dies after (40), we need to find the joint probability of the two events happening together.

Let X and Y be the future lifetimes of (40) and (50), respectively. We want to find P(Y≤10 and X<Y). Using the Law of Total Probability, we can write:

P(Y≤10 and X<Y) = ∫P(Y≤10 and X<Y|X=t) fX(t)dt

where fX(t) is the probability density function of X.

Since the force of mortality for (40) is constant, the probability density function for X is given by:

f X (t)=ue −ut

where u=0.05.

For (50), we have the survival function S(y) = 1 - y/10. So, the probability density function for Y is:

fY(y) = S'(y) = 1/10

Now, we can substitute these expressions into the integral and simplify:

P(Y≤10 and X<Y) = ∫P(Y≤10 and X<Y|X=t) fX(t)dt

= ∫∫P(Y≤10 and X<Y|X=t) fY(y)fX(t)dydt

= ∫∫P(Y≤10 and t<Y) (1/10)(0.05)e^(-0.05t)dydt

= (1/10)∫e^(-0.05t) ∫1≤y≤10 e^(0.1y) dydt

= (1/10)∫e^(-0.05t) (e - e^(-t/10)) dt

Evaluating this integral, we get:

P(Y≤10 and X<Y) ≈ 0.0286

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Answer:

p = 23

Step-by-step explanation:

using the rules of exponents

• \((a^m)^{n}\) = \(a^{mn}\)

• \(a^{m}\) × \(a^{n}\) = \(a^{(m+n)}\)

then

\((x^3)^{5}\) (\(x^{8}\) )

= \(x^{3(5)}\) × \(x^{8}\)

= \(x^{15}\) × \(x^{8}\)

= \(x^{(15+8)}\)

= \(x^{23}\)

= \(x^{p}\) ← with p = 23

Answer:

The correct answer is the last one

Step-by-step explanation:

Answer:

Domain { -3,1,5,6,9}

Range { -8,-6,3,5,7}

Step-by-step explanation:

The domain is the inputs

Domain { 6,9,-3,1,5}

We normally put them in order from smallest to largest

Domain { -3,1,5,6,9}

The range is the outputs

Range { -8,-6,3,5,7}

The domain is the set of all x-coordinates.

So here, the domain is {6, 9, -3, 1, 5} which we

can write in ascending order as {-3, 1, 5, 6, 9}.

Note that the domain is usually written in ascending order.

In other words, from least to greatest.

Next, the range is the set of all y-coordinates.

So here, the range is {-8, 3, 5, -6, 7} which we

can write in ascending order as {-8, -6, 3, 5, 7}.

Like the domain, the range is usually written in ascending order.

Proof -

So, in the first part we'll verify by taking n = 1.

\( \implies \: 1 = {1}^{2} = \frac{1(1 + 1)(2 + 1)}{6} \)

\( \implies{ \frac{1(2)(3)}{6} }\)

\(\implies{ 1}\)

Therefore, it is true for the first part.

In the second part we will assume that,

\( \: { {1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} = \frac{k(k + 1)(2k + 1)}{6} }\)

and we will prove that,

\(\sf{ \: { {1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k + 1)(k + 1 + 1) \{2(k + 1) + 1\}}{6}}}\)

\( \: {{1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k + 1)(k + 2) (2k + 3)}{6}}\)

\({1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{k (k + 1) (2k + 1) }{6} + \frac{(k + 1) ^{2} }{6} \)

\({1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{k(k+1)(2k+1)+6(k+1)^ 2 }{6} \)

\({1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)\{k(2k+1)+6(k+1)\} }{6}\)

\({1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)(2k^2 +k+6k+6) }{6} \)

\({1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)(2k^2+7k+6) }{6} \)

\({1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)(k+2)(2k+3) }{6} \)

Henceforth, by using the principle of mathematical induction 1²+2² +3²+....+n² = n(n+1)(2n+1)/ 6 for all positive integers n.

_______________________________

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Answer:

B

Step-by-step explanation:

Answer:

1 week, 14 days, 24 hours = 1 day,

= 4 days + 7 days + 10 hours + 16 hours

= 11 days + 26 hours

= 11 days 26 hours

Answer:

1 week 5 days 2 hours

Step-by-step explanation:

10 hours + 16 hours = 26hrs = 1 day 2 hours

4 days + 7 days + 1 day 2hrs = 12 days 2 hrs

7 days in a week so 12 days = 1 week 5 days

The computer can occupy a maximum of 1200 bytes of memory.

To determine the maximum memory capacity of a computer that can execute 300 instructions, we need to consider the representation of integers and the storage requirements for instructions.

If each instruction is stored in the entire memory word, it implies that each instruction occupies one memory word. Therefore, the number of instructions executed (300) directly corresponds to the number of memory words required.

The memory capacity of a computer is typically measured in bytes. However, since we are assuming each instruction occupies one memory word, we can consider the memory capacity in terms of memory words.

Hence, the maximum memory capacity this computer can occupy would be 300 memory words.

To convert this capacity into bytes, we need to know the size of a memory word. If we assume the computer uses a 32-bit word size, which is common in many systems, each memory word would consist of 4 bytes (32 bits / 8 bits per byte). Therefore, the maximum memory capacity in bytes would be:

300 memory words * 4 bytes per word = 1200 bytes.

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a) The probability that a randomly chosen adult female is taller than 150 cm, using the normal distribution, is of: 0.9452 = 94.52%.

b) Sarah's adult height will be estimated as: 164 cm.

The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is obtained by the rule presented as follows:

\(Z = \frac{X - \mu}{\sigma}\)

The mean and the standard deviation of the heights are given as follows:

\(\mu = 162, \sigma = 7.5\)

For item a, the probability that a randomly chosen adult female is taller than 150 cm is one subtracted by the p-value of Z when X = 150, hence:

\(Z = \frac{X - \mu}{\sigma}\)

Z = (150 - 162)/7.5

Z = -1.6

Z = -1.6 has a p-value of 0.0548.

1 - 0.0548 = 0.9452 = 94.52%.

The 60th percentile is X when Z = 0.253, hence:

0.253 = (X - 162)/7.5

X - 162 = 0.253 x 7.5

X = 164 cm.

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