Find the least common multiple (LCM) of 10 and 8.

Answer:

Step-by-step explanation:

Put the coordinates of the points to the inequalities:

y ≤ x - 5; y ≥ -x - 4

-------------------------------------

(-5, 2) → x = -5, y = 2

2 ≤ -5 - 5

2 ≤ -10   FALSE

--------------------------------------

(5, -2) → x = 5, y = -2

-2 ≤ 5 - 5

-2 ≤ 0   TRUE

-2 ≥ -5 - 4

-2 ≥ -9   TRUE

---------------------------------------

(-5, -2) → x = -5, y = -2

-2 ≤ - 5 - 5

-2 ≤ -10   FALSE

---------------------------------------

(5, 2) → x = 5, y = 2

2 ≤ 5 - 5

2 ≤ 0    FALSE

Final answer:

Option b) (5, -2) is the only point that satisfies both inequalities, y ≤ x − 5 and y ≥ −x − 4, making it the correct answer.

Explanation:

The goal is to determine which point lies in the solution set of the given system of inequalities:

y ≤ x − 5

y ≥ −x − 4

Let's evaluate each option given for the system of inequalities:

(−5, 2): Plugging into the inequalities, y = 2 is not less than or equal to x − 5, because 2 is not ≤ (−5 − 5).

(5, −2): y = −2 is less than or equal to 5 − 5, and is also greater than or equal to −5 − 4. Therefore, (5, −2) satisfies both inequalities.

(−5, −2): y = −2 is not less than or equal to −5 − 5, thus not in the solution set.

(5, 2): y = 2 is not less than or equal to 5 − 5, hence it does not satisfy the first inequality.

The only point that satisfies both inequalities is option b) (5, −2).

Answer:

Is [tex]10^{6}[/tex] times greater

Step-by-step explanation:

Find the quotient of the two numbers

[tex]\frac{8*10^{5}}{8*10^{-1}}= \frac{8*10^{5}*10^{1} }{8}}=10^{6}[/tex]

therefore

Is [tex]10^{6}[/tex] times greater

[tex]8 \times 10^{5}[/tex] is 1,000,000 times as great as  [tex]8 \times 10^{-1}[/tex]

To determine how many times greater 8 x 105 is compared to 8 x 10-1, we can use the properties of exponents.

First, let's write each term in standard form:

[tex]8 \times 10^{5}[/tex]  = 800,000

[tex]8 \times 10^{-1}[/tex] = 0.8

Next, find the ratio of these two numbers:

Ratio = ([tex]8 \times 10^{5}[/tex] ) ÷ ([tex]8 \times 10^{-1}[/tex])

Using the division of exponents rule:

[tex]10^{5}[/tex] / [tex]10^{-1}[/tex]

= [tex]10^{5-(-1)}[/tex]

= [tex]10^{6}[/tex]

So, the ratio is 106, which is: 1,000,000.

Therefore, [tex]8 \times 10^{5}[/tex] is 1,000,000 times as great as [tex]8 \times 10^{-1}[/tex]

Question:

How many times is [tex]8 \times 10^{5}[/tex] greater than [tex]8 \times 10^{-1}[/tex]?

For this case we have the following functions:

[tex]m (x) = \frac {x + 5} {x-1}\\n (x) = x-3[/tex]

By definition we have to:

[tex](f * g) (x) = f (x) * g (x)[/tex]

So:

[tex](m * n) (x) = m (x) * n (x)\\(m * n) (x) = \frac {x + 5} {x-1} (x-3)\\(m * n) (x) = \frac {(x + 5) (x-3)} {x-1}[/tex]

By definition, the domain of a function is given by the values for which the function is defined.

The domain of m(x) is given by all reals except 1.

The domain of n(x) is given by all reals.

While the domain of [tex](m * n) (x)[/tex] is given by:

All reals, except the 1. With [tex]x = 1[/tex], the denominator is 0 and the function is no longer defined.

Answer:

Domain of[tex](m * n) (x)[/tex] is given by all reals except 1.

Here is a table that will help you understand. And the answer.

Hzhsususuhhhdhdhhddhdhhdjxxj

For this case, we must simplify the following expression:

[tex]\frac {(x + 8)} {4} - \frac {(x + 5)} {4}[/tex]

They are fractions with the same denominator, they can be subtracted in the traditional way. We must bear in mind that the law of the signs of multiplication states:

[tex]- * + = -[/tex]

So:

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

ANswer:

Option C

For this case we have by definition of properties of powers that:

To multiply powers of the same base, the same base is placed and the exponents are added. Also:

[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]

Now, applying the above properties, we can rewrite the given expression as:

[tex]3 ^ {-3-5} = 3 ^ {- 8} = \frac {1} {3 ^ 8}[/tex]

ANswer:

[tex]\frac {1} {3 ^ 8}[/tex]

Answer:

DDDDDDDDDDD for sure...

D it might look as if it were B but if it was you would cross multiply so it’s definitely D

Answer:

B

Step-by-step explanation:

To find the correct one plug in 4 into x and if you get 3, that's the correct one.

A. y(4) = -4^2 + 4*4 + 4 = -16 + 16 + 4 = 4 X

B. y(4) = -4^2 + 8 * 4 - 13 = -16 + 32 - 13 = 3

Answer:

7 years

Step-by-step explanation:

A = P (1 + r)^(n)

where A is the final amount, P is the initial amount, r is the interest rate, and n is the number of times of compounding.

Compounded quarterly means compounded 4 times per year.  So the effective interest rate per compounding is:

r = 0.07 / 4

r = 0.0175

Given that A = 8000 and P = 5000:

8000 = 5000 (1 + 0.0175)^n

1.6 = 1.0175^n

log 1.6 = n log 1.0175

n = (log 1.6) / (log 1.0175)

n ≈ 27.1

Rounding up to the nearest whole number, it takes 28 compoundings.  Since there's 4 compoundings per year:

t = 28 / 4

t = 7

It takes 7 years.

Answer:

B: 3z-4

Step-by-step explanation:

First you start with PEMDAS. Parenthesis first.

Distribute 4 to (2z-1)

You get 8z-4

Next combine like terms such as 8z and -5z.

You get 3z because 8-5 is 3.

then you add on the negative four and get 3z-4.

Answer:

b

Step-by-step explanation:

i got it right on edge :)

Answer:

The amount in the account at the end of the 2nd quarter is $1537.73 ⇒ 2nd answer

Step-by-step explanation:

* Lets revise the compound interest

- Compound interest can be calculated using the formula

 A = P (1 + r/n)^(nt)

Where:

• A = the future value of the investment, including interest

• P = the principal investment amount (the initial amount)

• r = the annual interest rate (decimal)

• n = the number of times that interest is compounded per unit t

• t = the time the money is invested for

* Now lets solve the problem

# P = $1500

# r = 5/100 = 0.05

# n = 4 ⇒ quarterly compound

# t = 1/2 ⇒ two quarters means 1/2 year

∴ A = 1500(1 + 0.05/4)^(4 × 1/2) = $1537.73

* The amount in the account at the end of the 2nd quarter is $1537.73

Answer:

The answer to your question is: D it has 3

Hope this helps!!!!

    - Aaliyah

Step-by-step explanation:

A data set has outliers if the data lie out side the interval

The interquartile range of a data set is

For option A, the required interval is [5.5, 25.5]. Since all the data lie in this interval, therefore this data set has no outliers.

For option B, the required interval is [-5, 19]. Since all the data lie in this interval, therefore this data set has no outliers.

For option C, the required interval is [-2.5, 17.5]. Since all the data lie in this interval, therefore this data set has no outliers.

For option D,

3, 6, 7, 7, 8, 8, 9, 9, 9, 10

(3, 6), 7, (7, 8),( 8, 9), 9,( 9, 10)

3 lies out side the interval [4,12]. It means this data set has an outlier, i.e,.

Therefore correct option is D.

Answer:

D

Step-by-step explanation:

Answer:

#3) 72; #4) 40,320; #5) 90.

Step-by-step explanation:

#3) The number of possible choices are found by multiplying the choices of flavors and the choices of toppings:

6*12=72.

#4) The ordering of 8 cards is a permutation, given by 8!=40,320.

#5) This is a permutation of 10 objects taken 2 at a time:

P(10,2) = 10!/(10-2)!=10!/8!=90.

P.S I had the same question once.

The number of choices which are possible for a single serving of frozen yogurt with one topping from a yogurt shop is 72.

Arrangement of the things or object is mean to make the group of them in a systematic order, in all the possible ways.

The number of possible ways to arrange is the n!. Here, n is the number of objects.

Let n is the total choices of selecting  6 different flavors of frozen yogurt and 12 different toppings. Thus,

n=6 x 12

n=72

These choice is equal to the possible choices for a single serving of frozen yogurt with one topping.

Thus, the number of choices which are possible for a single serving of frozen yogurt with one topping from a yogurt shop is 72.

Learn more about the arrangement here;

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Answer:

[tex]+2n^5 - 9n^2 + 5n[/tex]

Step-by-step explanation:

To solve the expression

[tex]-n(-2n^4+9n-5)[/tex]

first we will multiply -n with each term and then find their products.

When doing multiplication the powers will be added and co-efficient will be multiplied.

[tex]-n(-2n^4+9n-5)​\\-n(-2n^4) -n(+9n) -n(-5)\\+2n^5 - 9n^2 + 5n[/tex]

[tex]

d=295

t=120

s=d\div t= 295\div120\approx2.46\frac{\text{ft}}{\text{s}}

[/tex]

Answer:

27

Step-by-step explanation:

135 divided by 5 (divide both sides by 5)

Answer:

y=27

Step-by-step explanation:

First you have to leave y by itself. So since the y is with a constant (5) then that means that you have to bring 5 to both sides and divide it by 135.

5y=135, y=135/5=27

Answer:

The correct option is B.

Step-by-step explanation:

It is given that Alondra took out a car loan for $22,500 that has a 0% APR for the first 24  months and will be paid off with monthly payments over 5 years.

We know that

1 year = 12 months

Using this conversion we get

5 year = 60 months

It means total number of months in 5 years is 60. For first 24  months the APR is 0%. So, the number of months will Alondra be charged interest is

[tex]60-24=36[/tex]

Therefore the correct option is B.

Answer:

Step-by-step explanation:

If DMKT → FCBN, then

m∠D = m∠F, m∠M = m∠C, m∠K = m∠B and m∠T = m∠N

m∠K = 79° therefore m∠B = 79°.

Answer:

1.5 pound of beans are in each bag

Step-by-step explanation:

12/8=1.5

1.5 pounds of beans are in each bag.

Diving 12 by 8 will give you 1.5, the total number of pounds in any given cup. You can check this by multiplying 8 by 1.5, which gives you one-and-a-half pounds.

Answer:

in the graph

Step-by-step explanation:

the function g(t)= sin t is a periodic function with amplitude a0= 1 and period T0=2[tex]\pi[/tex]

For our case, the 5 that multiplies g (t) increases the amplitude so that a = 5 * 1 = 5 and  the 3 that multiplies the variable increases the period being T = 2[tex]\pi[/tex]*1/3 = 2[tex]\pi[/tex]/3

Answer:

The answer is B.

Slope=5

Y-intercept=-7

The volume of each sample is 0.10 liters of water from each water sample

For this case we must find the value of the variable "x" of the following expression:

[tex]4(10^{5x})=200[/tex]

We divide both sides of the equation by 4:

[tex]10 ^ {5x} = \frac {200} {4}\\10 ^ {5x} = 50[/tex]

We find ln on both sides of the equation to remove the exponent variable:

[tex]ln (10^{5x}) = ln (50)\\5x * ln (10) = ln (50)[/tex]

We divide both sides of the equation between 5 * ln (10):[tex]x = \frac {ln (50)} {5 * ln (10)}[/tex]

In decimal form we have:

[tex]x = 0.33979400[/tex]

ANswer:

[tex]x = 0.33979400[/tex]

Answer:

The name of the polygon is rectangle

Step-by-step explanation:

* Lets find the slope of the four sides and the length of two adjacent

 side to know what is the name of the figure

∵ The vertices are (1 , 3) , (3 , 4) , (5 , 0) , (3 , -1)

∵ The rule of the slope of a line which passes through the points

  (x1 , y1) and (x2 , y2) is m = (y2 - y1)/(x2 - x1)

- Let (x1 , y1) is (1 , 3) and (x2 , y2) is (3 , 4)

∴ m1 = (4 - 3)/(3 - 1) = 1/2

- Let (x1 , y1) is (3 , 4) and (x2 , y2) is (5 , 0)

∴ m2 = (0 - 4)/(5 - 3) = -4/2 = -2

- Let (x1 , y1) is (5 , 0) and (x2 , y2) is (3 , -1)

∴ m3 = (-1 - 0)/(3 - 5) = -1/-2 = 1/2

- Let (x1 , y1) is (3 , -1) and (x2 , y2) is (1 , 3)

∴ m4 = (3 - -1)/(1 - 3) = 4/-2 = -2

- The parallel lines have equal slopes

- The product of the slopes of the perpendicular lines is -1

∵ m1 = m3 and m2 = m4

∴ The sides contains points (1 , 3) , (3 , 4) and (5 , 0) , (3 , -1) are parallel

  and the sides contain points (3 , 4) , (5 , 0) and (3 , -1) , (1 , 3) are

  parallel

∵ m1 × m2 = 1/2 × -2 = -1

∴ The side contains points (1 , 3) , (3 , 4) is ⊥ to the line contains points

  (3 , 4) , (5 , 0)

∵ m3 × m4 = 1/2 × -2 = -1

∴ The side contains points (5 , 0) , (3 , -1) is ⊥ to the line contains points

  (3 , -1) , (1 , 3)

- Now lets find the length of the four sides by using the rule

 of the distance

- If a segment has two endpoints (x1 , y1) and (x2 , y2), then the length

 of the distance is √[(x2 - x1)² + (y2 - y1)²]

∵ The length of the side which contains points (1 , 3) and (3 , 4) is

 √[(3 - 1)² + (4 - 3)²] = √[4 + 1] = √5

∵ The length of the side which contains points (3 , 4) and (5 , 0) is

 √[(5 - 3)² + (0 - 4)²] = √[4 + 16] = √20 = 2√5

∵ The length of the side which contains points (5 , 0) and (3 , -1) is

 √[(3 - 5)² + (-1 - 0)²] = √[4 + 1] = √5

∵ The length of the side which contains points (3 , -1) and (1 , 3) is

 √[(1 - 3)² + (3 - -1)²] = √[4 + 16] = √20 = 2√5

∴ The four sides are not equal but each two opposite sides are equal

- From all above

# Each two opposite sides are parallel and equal

# Each two adjacent sides are perpendicular

∴ The name of the polygon is rectangle

Answer:

rectangle

Step-by-step explanation:

Answer:

[tex]82,8m^2 = S.A[/tex]

Step-by-step explanation:

Area of a Rectangle: [tex]hb\:or\:wb = A[/tex]

Area of a Triangle: [tex]\frac{1}{2}hb; \frac{1}{2}bh, or\: \frac{hb}{2} = A[/tex]

Need to know

- Two small triangles

- Two big triangles

12m² = Rectangle

26,4m² EACH = Big Triangles

9m² EACH = Small Triangles

[tex]2[9] + 2[26,4] + 12 = 18 + 52,8 + 12 = 82,8[/tex]

So, the surface area of the rectangular pyramid is 82,8m².

* The answer is not 85,31 because this rectangular pyramid has two slant heights. If we ONLY had 9 as ONE SLANT HEIGHT, then the answer would have been 85,31, otherwise it is incorrect.

I am joyous to assist you anytime.

A) The probability of selecting a hockey card, keeping it out, and then selecting another hockey car is 1/9

B) The probability of selecting a hockey card, keeping it out, and then selecting a football card is 1/4

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

A box has 3 hockey and 6 football cards.

So, the probability of selecting a hockey card, keeping it out, and then selecting another hockey card

= 3/9 x 2/8

= 6/72

= 1/9

and,  the probability of selecting a hockey card, keeping it out, and then selecting a football card

= 3/9 x 6/8

= 18/72

=1/4

Learn more about probability here:

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Final answer:

The probability of selecting a hockey card, keeping it out, and then another hockey card is 1/12, whereas the probability of selecting a hockey card and then a football card is 1/4.

Explanation:

The probability of selecting a hockey card, keeping it out, and then selecting another hockey card from a box containing 3 hockey and 6 football cards is calculated as follows. First, the probability of picking one hockey card (Event A) would be 3 out of the total of 9 cards, or 3/9. Then, since the card isn't replaced, there are now 2 hockey cards left out of 8 total cards. So, the probability of picking another hockey card (Event B) after the first pick would be 2/8.

The probability of both events A and B occurring is found by multiplying the two probabilities together:

P(A and B) = P(A)  imes P(B) = (3/9)  imes (2/8) = 1/12.

For selecting a hockey card and then a football card, the initial probability of picking a hockey card remains 3/9. After a hockey card has been picked and kept out, there are still 6 football cards left out of 8 total cards. The probability of now picking a football card would be 6/8.

The probability of picking a hockey card first and then a football card is therefore:

P(Hockey and then Football) = P(Hockey)  imes P(Football) = (3/9)  imes (6/8) = 1/4.

Answer:

It will take 4.858 years before the CD worth 8228.24

Step-by-step explanation:

* Lets revise the compound interest

- The formula for compound interest, including principal sum, is:

  A = P (1 + r/n)^(nt)

- Where:

• A = the future value of the investment/loan, including interest

• P = the principal investment amount (the initial deposit or loan amount)

• r = the annual interest rate (decimal)

• n = the number of times that interest is compounded per unit t

• t = the time the money is invested or borrowed for

- To find the time you can use the formula

  t = ln(A/P) / n[ln(1 + r/n)]

* Lets solve the problem

∵ P = $5600

∵ A = 8228.24

∵ r = 8/100 = 0.08

∵ n = 4

- Substitute all of these values in the equation of t

∴ t = ln(8228.24/5600) / 4[ln(1 + 0.08/4)] = 4.858 years

* It will take 4.858 years before the CD worth 8228.24

Answer:

R= q+c over 5y

Step-by-step explanation: Good luck sweetie!!

Answer:

[tex]g(x)=(x-8)^2-64[/tex]

Step-by-step explanation:

The given function is;

[tex]g(x)=-16x+x^2[/tex]

This is the same as;

[tex]g(x)=x^2-16x[/tex]

Add and subtract the square of half the coefficient of x.

[tex]g(x)=x^2-16x+(-8)^2-(-8)^2[/tex]

Observe that the first three terms is a perfect square trinomial.

[tex]g(x)=(x-8)^2-64[/tex]

The vertex form is [tex]g(x)=(x-8)^2-64[/tex]

The vertex (8,-64)

[tex]\bf \textit{Sum and Difference Identities} \\\\ sin(\alpha + \beta)=sin(\alpha)cos(\beta) + cos(\alpha)sin(\beta) \\\\ sin(\alpha - \beta)=sin(\alpha)cos(\beta)- cos(\alpha)sin(\beta) \\\\ cos(\alpha + \beta)= cos(\alpha)cos(\beta)- sin(\alpha)sin(\beta) \\\\ cos(\alpha - \beta)= cos(\alpha)cos(\beta) + sin(\alpha)sin(\beta) \\\\[-0.35em] ~\dotfill\\\\[/tex]

[tex]\bf cos(x)cos\left( \cfrac{\pi }{7} \right)+sin(x)sin\left( \cfrac{\pi }{7} \right)=-\cfrac{\sqrt{2}}{2}\implies cos\left( x-\cfrac{\pi }{7} \right)=-\cfrac{\sqrt{2}}{2} \\\\\\ x-\cfrac{\pi }{7}=cos^{-1}\left( -\cfrac{\sqrt{2}}{2} \right)\implies x-\cfrac{\pi }{7}= \begin{cases} \frac{3\pi }{4}\\\\ \frac{5\pi }{4} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf x-\cfrac{\pi }{7}=\cfrac{3\pi }{4}\implies x=\cfrac{3\pi }{4}+\cfrac{\pi }{7}~\hfill \stackrel{n ~\in~ \mathbb{Z}}{x=\cfrac{3\pi }{4}+\cfrac{\pi }{7}~~~~+2\pi n} \\\\[-0.35em] ~\dotfill\\\\ x-\cfrac{\pi }{7}=\cfrac{5\pi }{4}\implies x=\cfrac{5\pi }{4}+\cfrac{\pi }{7}~\hfill \stackrel{n ~\in~ \mathbb{Z}}{x=\cfrac{5\pi }{4}+\cfrac{\pi }{7}~~~~+2\pi n}[/tex]