(2, 7); m = -3
(Write an equation in point-slope form of the line that passes through the given point and has the given slope)

Answer:

Principal (amount invested) = $14,350

Step-by-step explanation:

Given the simple interest amount of $2,870 earned in 4 years at 5% interest rate:

In order to find the principal amount that was invested, we could use the simple interest formula and isolate the variable, P, algebraically.

I = P × r × t

where:

I = interest earned = $2,870

P  = principal amount invested = ?

r  = interest rate = 5% or 0.05

t = time = 4

Divide both sides by (r × t ) to isolate P :

[tex]\displaystyle\mathsf{\frac{I}{(r\:\times\:t)}\:=\:\frac{P\:\times\:r\:\times\:t}{(r\:\times\:t)}}[/tex]

[tex]\displaystyle\mathsf{P\:=\frac{I}{(r\:\times\:t)}}[/tex]

Substitute the given values into the formula for P:

[tex]\displaystyle\mathsf{P\:=\frac{I}{(r\:\times\:t)}\:=\:\frac{2870}{0.05\:\times\:4}}[/tex]

[tex]\displaystyle\mathsf{P\:=\frac{2870}{0.20}=14,350}[/tex]

Therefore, the principal amount invested is $14,350.

Answer:

w=[tex]\frac{V}{lh}[/tex]

Step-by-step explanation:

just divide lh from both sides

Answer:

Step-by-step explanation:

Total Number of possible outcomes = 52

Getting a jack from a deck of 52 cards for a certain event (A) = 4

The Probability (A) = 4/ 52

= 1 / 13 = 0.07

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Answer:

Step-by-step explanation:

what number is its own oppositie?

The number 0 is the only number that is its own opposite.

Answer:

0.5 ㏑ | 1-2x | +c

Step-by-step explanation:

Formula:  ∫ 1/ax+b dx = 1/a ln Iax+bI +c

The second derivative of the composition between two functions is described by the following expression:

[tex]\frac{d^{2}}{dx^{2}} (f\,\circ\,g\,(x)) = \frac{d^{2}f}{dg^{2}}\cdot \frac{dg}{dx} + \frac{df}{dg} \cdot \frac{d^{2}g}{dx^{2}}[/tex]

Mathematically speaking, a composition between two functions is defined by the following operation:

[tex]f\,\circ\,g\,(x) =f(g(x))[/tex] (1)

By Chain Rule we get the first and second derivatives of the composition:

First derivative

[tex]\frac{d}{dx} (f\,\circ\,g\,(x)) = \frac{df}{dg}\cdot \frac{dg}{dx}[/tex] (2)

Second derivative

[tex]\frac{d^{2}}{dx^{2}} (f\,\circ\,g\,(x)) = \frac{d^{2}f}{dg^{2}}\cdot \frac{dg}{dx} + \frac{df}{dg} \cdot \frac{d^{2}g}{dx^{2}}[/tex] (3)

The second derivative of the composition between two functions is described by the following expression:

[tex]\frac{d^{2}}{dx^{2}} (f\,\circ\,g\,(x)) = \frac{d^{2}f}{dg^{2}}\cdot \frac{dg}{dx} + \frac{df}{dg} \cdot \frac{d^{2}g}{dx^{2}}[/tex]

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Answer:

x = 10

Step-by-step explanation:

the unmarked angle in the triangle is the supplement to 6x - 7

180 - (6x - 7)

180 - 6x + 7

187 - 6x

The sum of the angles in a triangle is 180

therefor

(2x + 7) + 26 + (187 - 6x) = 180

Combine like terms

-4x + 220 = 180

Subtract 220 from both sides

-4x = -40

divide both sides by -4

x = 10

Answer: 15.00 units

Explanation: When we know the horizontal and vertical distances between two points we can calculate the straight line distance like this: distance = √ a2 + b2

Answer:

Step-by-step explanation:

The statement #5 and #7 give an outcome of the statement #8:

This is called transitive property of congruence:

Correct choice is C

Answer:

C. Transitive property of congruence

Step-by-step explanation:

Transitive property of congruence means, if one pair of lines or angles or triangles are congruent to a third line or angle or triangle, then the first line or angle or triangle is congruent to the third line or angle or triangle.

[tex]W = 23.7°[/tex]

Step-by-step explanation:

The formula given is the statement of Snell's law of refraction. We are given the following:

[tex]I_a = 1.0003[/tex]

[tex]I_w = 1.3[/tex]

[tex]A = 31.5°[/tex]

So we need to find the angle of refraction W. Starting with Snell's law,

[tex]\dfrac{I_w}{I_a} = \dfrac{\sin A}{\sin W} \Rightarrow \sin W = \left(\dfrac{I_a}{I_w}\right)\sin A[/tex]

Plugging in the given values, we get

[tex]\sin W = \left(\dfrac{1.0003}{1.3}\right)\sin{31.5°} = 0.402[/tex]

Solving for the angle W, we then get

[tex]W = \sin^{-1}(0.402) = 23.7°[/tex]

step:

20% = 20/100

of = ×

20/100 × $1575.00

answer : $315

Step:

20% = 20/100

of = ×

20/100 × $1575.00

Answer : $315

Answer:

147°

Step-by-step explanation:

Solving for x

To make a straight line the angles have to have a sum of 190. So 180°-33° would equal 147°

Answer:

x = 147°

Step-by-step explanation:

A line is 180°

180 - 33 = 147

Answer:

174 cm

Step-by-step explanation:

1.83 m to cm is 183.

So, 183 cm - 9 cm = 174cm

Hope you understand ^^

Answer:

174 cm

Step-by-step explanation:

1 meter is equal to 100 centimeter so 1.83m times 100 is equal to 183cm. so 183 cm-9cm=174 cm

Answer:

Step-by-step explanation:

[tex] = > b - \frac{7}{4} = - \frac{2}{3} [/tex]

[tex] = > b = - \frac{2}{3} + \frac{7}{4} [/tex]

[tex] = > b = \frac{ - 8 + 21}{12} [/tex]

[tex] = > b = \frac{13}{12} \: or \: 1 \frac{1}{12} [/tex]

Answer: x= 1/196

Step-by-step explanation:

Step-by-step explanation:

a= 3×(-2)+3=-6+3=3

b=3×(-1)+3=-3+3=0

c=3×1+3=3+3=6

d=2×3+3=6+3=9

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

a=3, b=0, c=6, d=9

Good work!

Answer:

[tex](x-1)^2(x+3)[/tex]

Step-by-step explanation:

For factorization the given expression you can use the Ruffini's rule.

First find the divisors of the independent term (these are the possible rational roots), in the given polynomial the independent term is [tex]3[/tex].

[tex]3 = \{\pm1,\pm3\}[/tex]

Now replace each number in the polynomial

[tex]P(1) = 1^3 + 1^2 - 5(1) + 3 = 0[/tex]

If the result is equal to 0 that's meaning that is a possible root of the polynomial. Then for know if is a root you have to divide the polynomial by [tex](x - \text{possible root})[/tex].

[tex](x^3 + x^2 -5x+3 )/ (x-1)[/tex]

In the first row are the coefficients of the given polynomial.

In the second row are the product between the coefficients and the independent term of the [tex]x-1[/tex].

The third row are the coefficients of the quotient polynomial (except the last that is the remainder).

[tex]\qquad 1\qquad 1\qquad-5\qquad \quad3\\1\qquad\qquad1\qquad \quad 2\qquad-3\\-------------\\ 0 \ \ \quad1 \qquad 2 \qquad -3 \qquad \quad 0[/tex]

Because the last term is the remainder and it's 0 you can factorizate [tex](x-1)[/tex] and the quotient polynomial is equal to

[tex]x^2 + 2x -3[/tex]

So our current expression is [tex](x-1)(x^2 + 2x -3)[/tex], however you can factorizate the quotient polynomial in:

[tex]x^2 +sx +rx +rs = x^2 + 3x -x + 3(-1) = (x + 3)(x -1)[/tex]

So the last expression is:

[tex](x-1)(x+3)(x-1) = (x-1)^2(x+3)[/tex]

Step-by-step explanation: (5√5)−2x+1=

1

5

(125x)−3

0.008x+1=

1

5

(125x)−3

Step 1: Flip the equation.

1

5

(125x)−3=0.008x+1

Step 2: Add 3 to both sides.

1

5

(125x)−3+3=0.008x+1+3

1

5

(125x)=0.008x+4

Step 3: Divide both sides by 1/5.

1

5

(125x)

1

5

=

0.008x+4

1

5

125x=0.04x+20

The  value of x is 46.

Exponents and powers can be used to represent extremely big or extremely small numbers in a more straightforward fashion.

The number of times a number is multiplied by itself is defined by the exponent. The power is an expression that displays the same number or factor being multiplied repeatedly.

Given:

[tex](5\sqrt{5} )^{-2x+1 }= 1/5 * 125^{x-3}[/tex]

ow, using exponents and powers

[tex](5\sqrt{5} )^{-2x+1 }= 1/5 * 125^{x-3}[/tex]

[tex](5\sqrt{5} )^{-2x+1 }= 1/5 * 5 ^{3(x-3)\\[/tex]

[tex](5\sqrt{5} )^{-2x+1 }= 5^{3x - 9 - 1}[/tex]

[tex](5\sqrt{5} )^{-2x+1 }= 5^{3x -10}[/tex]

[tex]5^{3/2(-2x+ 1)}= 5^{3x - 10}[/tex]

[tex]5^{-x+ 3/2}= 5^{3x -10}[/tex]

Now, Comparing

-x+ 3/2 = 3x- 10

-x - 3x = -10 - 3/2

-4x = -23/2

x= 46

Hence, the value of x is 46.

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Answer:

the ansewer is 56

Step-by-step explanation:

Answer:

In which town does the total number have meaning?

Answer: Town B

For Town A, it does not, cannot, does not.

For Town B, does, can, does.

Answer:

letter A

Step-by-step explanation:

3x=0

x=0

x-2=0

x=2

2x+7=0

2x=-7

x=-7/2

Answer:

25%

Step-by-step explanation:

25% of 12 is 3

25% of 8 is 2

5 people out of 20 people

5/20 = 25%

25% percent of the entire class is going on the field trip

percentage, a relative value indicating hundredth parts of any quantity.

Given,

There are 12 girls and 8 boys in Ms. Crabapple's class.

The total number of students

12+8=20

25% of the girls and 25% of the boys are going on a field trip to a nuclear power plant,

25% of the girls =0.25×12=3

25% of the boys =0.25×8=2

So the total number of students went to field trip

3+2=5

So out of 20 student, 5 students went to the field trip.

Which means 25% of the entire class is going on the field trip

Hence, 25% percent of the entire class is going on the field trip

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Answer:

The answer is 12/7.

Step-by-step explanation:

To get the answer, simply subtract -1 to 5/7

[tex]\frac{5}{7} - (-1)\\[/tex]

Find the least common denominator.

[tex]\frac{5}{7} - (-1) = \frac{5}{7} - \frac{(-7)}{7}[/tex]

= 12/7

To check, add -1 to 12/7.

[tex]\frac{12}{7} + (-1)[/tex]

Find the least common denominator.

[tex]\frac{12}{7} + (-1) = \frac{12}{7} + \frac{(-7)}{7}[/tex]

= 5/7

Answer:

Step-by-step explanation:

can u take good picture

Answer:

[tex] \: [/tex]

A. The sales tax will be $ 22.999425

so, the sales tax » $ 23

5.75 % of $ 399.99

B. The Total Purchase will be →

or

Answer:

0.2254

Step-by-step explanation:

multiply using long multuplication

Answer:

6

Step-by-step explanation:

[tex]45 \: min = 0.75 \: hour[/tex]

[tex]0.75 * 8 = 6 \: hours[/tex]

14(6x-2)=x-2

84x-28=x-2

84x-x= 28-2

83x = 26

x = 26/83

there are no corect answer below

ok done. Thank to me :>