Find the slope of the line passing through the two points.
(–7, 8), (–4, 3)

The number of k-element subsets of a set of n elements is given by

... C(n, k) = n!/(k!(n-k)!)

a) C(100, 99) = 100!/(99!×1!) = 100

b) C(100, 98) = 100!/(98!×2!) = 100*99/2 = 4950

c) C(100, 2) = 100!/(2!×98!) = 4950 . . . . same as  (b)

Answer:

See the attached

Step-by-step explanation:

An exponential function has the variable in the exponent.

Answer:

Exponential functions: [tex]f(x)=8e^x[/tex],[tex]f(x)=e^{-3x}[/tex] and [tex]f(x)=20^{\frac{x}{3}}[/tex]

Non-exponential functions: [tex]f(x)=5x^{\frac{3}{7}}[/tex], [tex]f(x)=4x^3-6x[/tex] and [tex]f(x)=\sqrt{x}+3x[/tex]

Step-by-step explanation:

The general form of an exponential function is

[tex]f(x)=ab^x[/tex]

where, a is initial value and b is growth factor.

It means the variable term i.e., x must be the exponent . In other words we can say that the variable term must be in the power of constant terms.

We need to check whether the given function is an exponential function or not.

The given function is

[tex]f(x)=8e^x[/tex]

It is an exponential function with initial value 8 and growth factor e≈2.718.

Similarly,

[tex]f(x)=e^{-3x}[/tex] and [tex]f(x)=20^{\frac{x}{3}}[/tex] are exponential functions.

[tex]f(x)=5x^{\frac{3}{7}}[/tex], [tex]f(x)=4x^3-6x[/tex] and [tex]f(x)=\sqrt{x}+3x[/tex] are non-exponential functions.

Answer,

C. 1650

Explanation,

495/6 = 82.5

82.5 x 20 = 1650

Hope this helps :-)

These are three equations and three answers.

Answers:

Explanation:

Equation A: 20 - 4x = 12 - x + 8 - 3x

The objective is clearing the unknown, which is to isolate it in one side of the equation.

These are the steps and properties that you need to use:

1.  Combine like terms on right side:

20 - 4x  = 20 - 4x

2. Use addition property of equality (add 4x on each side).

20 = 20 ↔ identity

Conclusion: you have gotten a condition that is always true, no matter the value of x, which means that the equation has infinite solutions and it is an identity.

Equation B: 5x + 4x - 3  =  24 + 8x (note that I placed the equal sign as it was missing)

1.  Combine like terms on each side:

9x - 3 = 24 + 8x

2. Subtraction property and addition propertiy of equality (subtract 8x and add + 3 on both sides)

x = 27 ↔ solution (neither contradiction nor identity)

Conclusion: the solution is x = 27.

Equation C: 5x + 6 = 2x + 6 + 3x - 15 (note that I placed the equal signs as it was missing)

1. Comitne like terms on the right side:

5x + 6 = 5x - 9

2. Subtraction property of equality (subtract 5x from each side)

6 = - 9 ↔ contradiction

Conclusion: the equation does not have a solution since the final equality is always false (a condradiction or absurd).

For your information, when the variable (x) dissapears and fhe final equality is always true (for example 0 = 0, or 20 = 20), the equation is an identity.

A) 20-4x=12-x+8-3x

Bring all x values at one side and all numerical values to the other side of the equal sign and solve. Also, do not forget to change the sign when you change the side.

-4x + x + 3x = -20 + 12 + 8

-4x + 4x = -20 + 20

0 =0 No solution

B) 5x+4x-3+24+8x

this expression can only be simplified to 17x + 21 and not solved because there is no equal sign here

C) 5x +6+2x+6+3x-15

this expression can only be simplified to 10x - 3 and not solved because there is no equal sign here

Also, neither of these is an identity or contraction.

As t/3 it means that 0.5% every 3 years.

So n will be 3 years , 36 months

Solution:

The Given model to Predict the population

[tex]P=P_{0}(1.005)^{\frac{t}{3}[/tex]

                               ----------------------------------(1)

The population increases by 0.5 % every n months.

Initial Population = 215

Final Population

[tex]=215+215\times \frac{0.5}{100}\\\\=215+1.075\\\\=216.075[/tex]

Substituting the value of , Initial and final Population in equation 1,

[tex]216.075=215\times (1.005)^{\frac{t}{3}}\\\\  (1.005)^{\frac{t}{3}}=\frac{216.075}{215}\\\\  (1.005)^{\frac{t}{3}}=(1.005)^{1}\\\\ \frac{t}{3}=1\\\\ t=3[/tex]

t=3 years =36 months

The value of n is equal to 36 months.

C

given 1 /( 3 + √2 )

then rationalise the denominator by multiplying the numerator/ denominator by the conjugate of the denominator

the conjugate of 3 + √2 is 3 - √2

1 / (3 + √2 ) × (3 - √2 ) / (3 - √2 )

= (3 - √2 ) /( 9 - 2 ) = (3 - √2 ) / 7

The fraction [tex]\frac{1}{3+\sqrt{2}}[/tex] can be written as [tex]\frac{3-\sqrt 2}{7}[/tex]. Option C is correct.

Fraction simplification is a method of fraction reduction that entails making a fraction as simple as possible.

This is accomplished by dividing the numerator and denominator by the biggest integer that divides both integers exactly.

Given fraction;

[tex]\frac{1}{3+\sqrt{2}}[/tex]

Multiplying the numerator and denominator by the conjugate of the denominator will rationalize the denominator;

The conjugate of the denominator (3 + √2) is 3 - √2;

Apply the rationalization of fraction;

[tex]\frac{1}{3+\sqrt{2}} \\\ \frac{1}{3+\sqrt{2}} \times \frac{3-\sqrt2}{3-\sqrt 2} \\\\ \frac{3-\sqrt 2}{9-2} \\\\\ \frac{3-\sqrt 2}{7}[/tex]

Hence option C is correct.

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A

reducing one side by 2 is expressed as (x - 2) ← length

increasing the other side by 2 is expressed as (x + 2 ) ← width

the area of new patio = (10 - 2 )(10 + 2) 8 × 12 = 96 ft²

Answer: A. lw = (x + 2)(x – 2); 96 square feet

Step-by-step explanation:

Given: Stephon has a square brick patio. He wants to reduce the width by 2 feet and increase the length by 2 feet.

Let x be the side-length of the patio, then

The length of the patio after change = x+2

The width of the patio  after change = x-2

Then the area of the patio is given by :-

[tex]A=lw\\\Rightarrow\ A=(x+2)(x-2)[/tex]

If the original patio measures 10 feet by 10 feet.

Then the area of the patio= [tex](10+2)(10-2)=(12)(8)=96[/tex] square feet.

Hence, A is the right answer.

You can see that this line passe through the points (-4,-2) and (4,3).

The slope of the line passing through the points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is

[tex]\dfrac{y_2-y_1}{x_2-x_1}.[/tex]

Thus, the slope is

[tex]\dfrac{3-(-2)}{4-(-4)}=\dfrac{5}{8}.[/tex]

Then the equation of the line is

[tex]y-3=\dfrac{5}{8}(x-4),\\\\y=\dfrac{5}{8}x+\dfrac{1}{2}.[/tex]

Answer: correct choice is C.

109.93 lbs

since the quantities vary directly, then

w(moon) = kw(earth ) ← ( k is the constant of variation )

to find k use the given condition

k = w( moon ) / w( earth ) = [tex]\frac{25.66}{150.94}[/tex]

given w(earth) = 218.24

w(moon) = [tex]\frac{25.66(218.24)}{150.94}[/tex] = 109.93

The absolute value of a number is that number with a positive sign.

|10| = 10

|-7| = 7

Answer:

Option D [tex]BC=63\ in[/tex]

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

In this problem

[tex]\frac{DC}{ML}=\frac{BC}{KL}[/tex]

substitute the given values and solve for BC

[tex]\frac{56}{8}=\frac{BC}{9}[/tex]

[tex]BC=56(9)/8\\BC=63\ in[/tex]

To convert the density of the textbook to slug/in³, we first convert the density from g/cm³ to kg/m³ and then use the given conversion factors to convert it to slug/in³.

To convert the density of the textbook to slug/in³, we need to use the given conversion factors: 1 slug = 14.59 kg and 1 in = 2.54 cm. First, we need to convert the density from g/cm³ to kg/m³ by dividing by 1000. Then, we can convert from kg/m³ to slug/in³ using the given conversion factors. Let's calculate:

Given density = 3 g/cm³

Step 1: Convert g/cm³ to kg/m³

Density in kg/m³ = 3 g/cm³ / 1000 = 0.003 kg/m³

Step 2: Convert kg/m³ to slug/in³

Density in slug/in³ = 0.003 kg/m³ × (1 slug / 14.59 kg) × (1 in³ / (2.54 cm)³)

Performing the calculations gives us the density of the textbook in slug/in³.

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Answer:

  C.  -20

Step by step explanation:

It appears you want the value of the expression -5² +8|-1| +(-3).

The order of operations tells us that the first step is to evaluate expressions in parentheses. Here, the absolute value symbols effectively serve as parentheses, so we start there.

|-1| signifies the absolute value of -1, its magnitude, or positive value. That simplifies to 1. So, your expression is ...

  -5² +8·1 -3

The next step is to evaluate the term with an exponent: -5² = -(5·5) = -25.

  = -25 +8·1 -3

Now, we perform the multiplication:

  = -25 +8 -3

And finally, the addition/subtraction

  = -17 -3

  = -20

__

Additional comment

The expression you show in the problem statement looks like the first term is negative fifty-two. That is very different from negative five squared. An exponent is indicated using a caret (^), as -5^2, or using a superscript font, as -5². Please be careful to use appropriate math symbols where exponents are involved.

The value of F(8) is 64.

Given that,

Based on the above information, the calculation is as follows:

[tex]F(8) = 8 \times 8[/tex]

= 64

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Answer:125a6

-64q12

-c^30d^9f^18g^3

Step-by-step explanation:

Got it right on edgy

Hey!

This question is super easy to me. This question is going to be used their order of operations.

Order of operations stands for

↓

P-Parenthesis

E-Exponents

M-Multiply

D-Divide

A-Add

S-Subtract

(9+15)/3+2

24/3+2

8+2

=10

Answer⇒⇒⇒⇒⇒=10

Hope this helps!

Thank you for posting your question at here on Brainly.

-Charlie

Answer:

10

Step-by-step explanation:

(9+15) ÷ 3 + 2 = 10

Remark

Answer: The second one. The second step removes the brackets on the right. It uses the distributive property which puts back the common factor that was taken out of the two terms 6x and 24. Quite often the distributive property is useful when presenting a problem to be solved.

The associative property is more of an order thing and that is very useful sometimes as well what it says is that if you have three numbers a + b + c the order which you combine things does not matter.

For example 3 + 4 + 5 could be combined as 3 + 4 = 7;  7 + 5 = 12 or 3 + 5 = 8, 8 + 4 = 12.  

The associative property is useful when adding fractions.

After the 10% discount on marked price (P), the selling price is ...

... P×(100% -10%) = 0.90P

After a markup off 35% on cost, the value is

... $70×(100% +35%) = 1.35×$70 = $94.50

The retailer wants these two values to be equal:

... 0.90P = $94.50

... P = $94.50/0.90 = $105.00 . . . . . divide by the coefficient of P

The marked price should be $105.00.

To make a 35% profit on the cost, the retailer should mark the sunglasses at a price of $85.05.

To determine the price at which the retailer should mark the sunglasses, we need to calculate the original price and then apply the discount. First, let's find the 35% profit on the cost, which is $70. 35% of $70 is 0.35 * 70 = $24.50.

To make a profit of $24.50, the original price should be $70 + $24.50 = $94.50. To sell the sunglasses at a 10% discount, the marked price will be 90% of $94.50. 90% of $94.50 is 0.90 * 94.50 = $85.05.

Therefore, the retailer should mark the sunglasses at a price of $85.05.

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To know which of the following expressions are polynomials, let us look at the definition of a polynomial:

Polynomial is derived from poly- (which means "many") and -nomial (meaning "term"), so it says "many terms".

For an instance: [tex]2x^2y+2y^2[/tex] is a polynomial, but [tex]4xy^2[/tex] is not a polynomial because it contains single term only.

We must keep in mind that in polynomial it can have variables, constants, and exponents but it can never have division by a variable.

Now lets, look at the

[tex]30y^2[/tex] since it has got one term it can not be a polynomial.

[tex]30y^2+x[/tex]: it has got more than one term therefore, it is a polynomial.

[tex]30y^2x[/tex]: again it has got just one term so it is not a polynomial.

[tex]30y^2+x^{12}[/tex]: Since it has got more than one term, so again it is a polynomial.

The correct polynomial expressions are 30y²+x and 30y². Option A and D is the correct answer.

Polynomials are expressions that consist of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and exponentiation.

30y²+x: This expression is a polynomial because it consists of a constant term (30), a variable term (y²) raised to a non-negative integer exponent, and an additional variable term (x).

30y²: This expression is a polynomial because it consists of a constant term (30) and a variable term (y²) raised to a non-negative integer exponent.

These expressions are considered polynomials because they consist of variables, constants, and non-negative integer exponents, and they involve the appropriate mathematical operations of addition and multiplication.

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The complete question is, "Which expressions are polynomials? Select each correct answer.

a.  30y²+x

b. 30y²+x (¹/²)

c. (30y²) ÷ x

d. 30y²"

The multiples for 6 : 6, 12, 18, 24, 30,36, 42, 48

The multiples for 8 : 8, 16, 24, 32, 40, 48, 56, 64

Hope this helps

After the 15% discount, Maria pays 85% of the cost. That cost is the sum of the fixed cost and the variable (per visit) cost.

... (updated cost) = 0.85×($150 +$30×a)

... (updated cost) = 127.50 +25.50a . . . . in dollars

The term sin(x+[7pi/4]) can be rewritten in terms of sin(x) and cos(x) using the formula for sine of the sum of two angles. Given A = x and B = 7pi/4, the equation can be simplified to sin(x + [7pi/4]) = sin(x)(√2/2) - cos(x)(√2/2).

To rewrite the term sin(x+[7pi/4]) in terms of sin(x) and cos(x), we can use the formula for sine of the sum of two angles. The formula is given by:

sin(A + B) = sinAcosB + cosAsinB

Substituting our given values into this formula, where A = x and B = 7pi/4, we get:

sin(x + [7pi/4]) = sin(x)cos(7pi/4) + cos(x)sin(7pi/4)

Note that cos(7pi/4) = √2/2 and sin(7pi/4) = -√2/2. Therefore:

sin(x + [7pi/4]) = sin(x)(√2/2) - cos(x)(√2/2)

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Copy down y = 2x - 8.  Note that any line parallel to this will have exactly the same form,  although the constant (representing the y-intercept) may be different.

Knowing that this line passes through (3,10), all we have to do is find the value of the constant of this new, parallel line.  Substitute 10 for y and 3 for x, obtaining 10 = 2(3) + b.  Then 10-6 = b, or b = 4, and:

y =2x + 4 (answer).  Again, note how the form of this new equation is exactly the same as the form of the given equation; only the constant (the y-intercept) is different.

Answer:

y=2x+4

Step-by-step explanation:

The equation we have is y=2x-8, so we subsitute the values and 8 is equal to b. After you substitue you solve it. b=4. So, the answer is y=2x+4

Hope this helped :) *also sorry if I spelled some words wrong*

we are given that the English Aplhabet has 26 letters. we let g represent the number of letters in the Greek alphabet. From the statement given, English alphabet which is 26 = 20 + 1/4 *g. The expression which is similar to this is in option A. 1/4g + 20 = 26.

Put 5 where x is in the equation and do the arithmetic.

y = 1.923×3.772⁵ ≈ 1468.377444

The most appropriate answer is ...

... D. 1468

Answer:

the value of y when x= 5 is 1468

Step-by-step explanation:

Suppose the exponential regression equation for some data is given by y=1.923*3.772^x

We need to find out the value of y when x= 5

Plug in 5 for x  and find out y

y=1.923*3.772^x

y=1.923*3.772^5=1468.37744

So the value of y when x= 5 is 1468

Let's evaluate the quantity within the parentheses.  (11 - 3^2) becomes (2).  Then we have:

(72 divided by 2) / 3, or 36/3, or 12.