an outcome or set of outcomes of an experiment or situation​

The solution to the equation X=(3x+10) is -5, which was found by isolating x on one side of the equation.

To solve the equation X = 3x + 10 for x, you begin by isolating the variable. First, subtract 3x from both sides, yielding -2x = 10. To find the value of x, divide both sides by -2. This results in x = -5. So, the solution for x in the given equation X = 3x + 10 is x = -5. This process involves balancing both sides of the equation to isolate the variable, and by subtracting 3x and then dividing by -2, we find that x equals -5, making it a clear and concise solution to the equation.

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Answer:

a(n) = a(1)*(1/4)^(n - 1)

Step-by-step explanation:

The first four terms of this sequence are 64, 16, 4, 1.

Let the common ratio be r.  Then 64r = 16, and r = 1/4.

The first term is  64.

The general term is then

a(n) = a(1)*(1/4)^(n - 1)

Answer:

see explanation

Step-by-step explanation:

These are the terms of an arithmetic sequence with n th term

[tex]a_{n}[/tex] = a + (n - 1)d

where a is the first term and d the common difference

d = 25 - 20 = 30 - 25 = 5 and a = 20, hence

[tex]a_{n}[/tex] = 20 + 5(n - 1) = 20 + 5n - 5 = 5n + 15 ← n th term formula

Answer:

The length of the ladder is [tex]16\ ft[/tex]

Step-by-step explanation:

Let

L ----> the length of the ladder

we know that

Applying the Pythagoras theorem

[tex]L^{2}=15^{2} +6^{2}[/tex]

[tex]L^{2}=261[/tex]

[tex]L=\sqrt{261}\ ft[/tex]

[tex]L=16\ ft[/tex]

Answer:

Answer:

The length of the ladder is  

Step-by-step explanation:

Let

L ----> the length of the ladder

we know that

Applying the Pythagoras theorem

Step-by-step explanation:

Answer:

3-x/x(x-1)

Step-by-step explanation:

Given

2/(x^2-x)-  1/x

To simplify, we can take x as common from the denominator of first term

=  2/(x(x-1))-  1/x

Taking LCM of denominators and then using the rules of addition and subtraction of numerators using denominator’s LCM

=  (2(1)-(x-1))/(x(x-1))

Solving the brackets

=(2-x+1)/(x(x-1))  

=  (-x+3)/(x(x-1))

The term can also be written as:

=  (3-x)/(x(x-1))

 (3-x)/(x(x-1)) is the correct answer ..  

To simplify the expression 2/x^2 - x - 1/x, we need to find a common denominator for the two fractions in the expression, which is x(x+1). The simplified form is (x + 2)/(x(x+1)).

To simplify the expression 2/x^2 - x - 1/x, we need to find a common denominator for the two fractions in the expression. The common denominator is x(x+1). Multiplying the numerator and denominator of the first fraction by x+1 and the numerator and denominator of the second fraction by x, we get:

So, the simplified form of 2/x^2 - x - 1/x is (x + 2)/(x(x+1)).

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ANSWER

A. (0.4, 1)

EXPLANATION

The given system of equations is:

y=-5x+3

y=1

We equate the two equations to obtain;

[tex] - 5x + 3 = 1[/tex]

Group the similar terms to obtain;

[tex] - 5x = 1 - 3[/tex]

[tex] - 5x = - 2[/tex]

We divide both sides by -5 to get,

[tex]x = \frac{ - 2}{ - 5} [/tex]

[tex]x = \frac{ 2}{ 5} [/tex]

[tex]x = 0.4[/tex]

Therefore the solution is (0.4,1)

Answer:

[tex]\large\boxed{A.\ (0.4,\ 1)}[/tex]

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y=-5x+3\\y=1\end{array}\right\\\\\text{Put the value of y from the second equation to the first equation:}\\\\1=-5x+3\qquad\text{subtract 3 from both sides}\\\\-2=-5x\qquad\text{divide both sides by (-5)}\\\\\dfrac{-2}{-5}=x\to \boxed{x=0.4}[/tex]

Answer:

[tex]Log_41024=5[/tex]

Step-by-step explanation:

The change of form formula (exponential to logarithm) is:

[tex]a^x=b\\Log_ab=x[/tex]

Looking at the problem given, we can simply write the logarithmic form as:

[tex]4^5=1024\\Log_41024=5[/tex]

This is the answer.

Answer:

The product of two rational numbers is a rational number

Step-by-step explanation:

I'll quickly recap the proof: a rational number is, by definition, the ratio between two integers. So, there exists four integers m,n,p,q such that

[tex]a=\dfrac{m}{n},\quad b=\dfrac{p}{q}[/tex]

If we multiply the fractions, we have

[tex]ab = \dfrac{mp}{nq}[/tex]

Now, mp and nq are multiplication of integers, and thus they are integers themselves. So, ab is also a ratio between integer, and thus rational.

Answer:

the product of two rational numbers is a rational number!

Step-by-step explanation:

For this case we propose a rule of three, and thus find the grams of medication.

150lb -----------> 24g

120lb -----------> x

Where the variable "x" represents the grams of medicine that a 120-pound woman should receive

[tex]x = \frac {120 * 24} {150}\\x = 19.2[/tex]

Thus, a woman of 120 pounds should receive 19.2 grams of medication.

Answer:

19.2 grams

Answer:

For the equation

[tex]y=\frac{x-6}{x^2+5x+6}[/tex]

There are vertical asymptotes at x=-2 and x=-3

There are no holes

Step-by-step explanation:

The equation for this graph can be factored in its denominator to get

[tex]y=\frac{x-6}{(x+2)(x+3)}[/tex]

This means that there are VA's at x=-3 and x=-2

(There are no holes as there is not a factor that cancels out.)

A function assigns the values. The asymptotes and the holes for the graph lie at x=-2 and x=-3.

A function assigns the value of each element of one set to the other specific element of another set.

The vertical asymptotes and the holes for the graph can be found by factorizing the denominator of the given function. Therefore, the factorisation of the denominator is,

x² + 5x + 6 =0

x² + 2x + 3x +6 =0

x(x+2)+3(x+2)=0

(x+2)(x+3)=0

x = -2, -3

Hence, the asymptotes and the holes for the graph lie at x=-2 and x=-3.

Learn more about Function:

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You would have to combine terms that are the same

6x + 2x = 8x

9-1 = 8

8x + 8 =24

This is simplified enough so your answer is 8x + 8 = 24

Thanks

Answer:

B

Step-by-step explanation:

B is the only graph that starts at both intervals of 2, which would be 2, and -2

Answer:

It has no amplitud and the period is 5pi/2

Step-by-step explanation:

Given a function of the following type:

f(t) = AtanB(t + C)

The function has no amplitud, given that it doesn't have maximum or minimum value.  And the period is given by: pi/B

In this case, we have f(t)= -tan0.4t. Then:

B = 0.4

⇒ Period = pi/0.4 = 5pi/2

Therefore, the answer is: It has no amplitud and the period is 5pi/2

Answer:

The equation of the parabola is (y + 3)² = -6(x - 7/2)

Step-by-step explanation:

* Lets revise the equation of a parabola

- If the equation is in the form (y − k)² = 4p(x − h), then:

• Use the given equation to identify h and k for the vertex, (h , k)

• Use the value of k to determine the axis of symmetry, y = k

• Use h , k and p to find the coordinates of the focus, (h + p , k)

• Use h and p to find the equation of the directrix, x = h − p

* Now lets solve the problem

∵ The directrix ⇒ x = 5

∴ The form is (y − k)² = 4p(x − h)

∵ The directrix is x = h - p

∴ h - p = 5 ⇒ (1)

∵ The focus is (h + p , k)

∵ The focus is (2 , -3)

∴ k = -3

∴ h + p = 2 ⇒ (2)

- Add (1) and (2) to find h

∴ 2h = 7 ⇒ ÷ 2 for both sides

∴ h = 7/2

- Substitute this value in (1) or (2) to find p

∴ 7/2 + p = 2 ⇒ subtract 7/2 from both sides

∴ p = -3/2

* Now we can write the equation

∴ (y - -3)² = 4(-3/2) (x - 7/2)

∴ (y + 3)² = -6(x - 7/2) ⇒ in standard form

* The equation of the parabola is (y + 3)² = -6(x - 7/2)

Answer:

Step-by-step explanation:

11 cm. Simply divide 440 by 40, and you'll get your answer.

Answer:

1 centimeter = 40 kilometers

? centimeter = 440 kilometers

The simple way to do this is to set it as a ratio as shown above. From 40 to 440, there is a increase in 11 times. (40 x 11 = 440)

So, you would do 1 x 11 = 11. This means 11 centimeters is equal to 440 kilometers.

11 centimeter = 440 kilometers

Answer:

A equals 254.46

C equals 56.54

Step-by-step explanation:

Area

pie (3.14) times the radius (9) times ^2 is equal to

254.46

Circumference

(2) times pi (3.14) times radius of (9) to get

56.54

Area of a circle formula = [tex]\pi[/tex]r² where r means radius and [tex]\pi[/tex] means 3.14

3.14(9)^2 = 254.34 = area

Circumference formula: 2[tex]\pi[/tex]r

2(3.14)(9) = 56.52 = circumference

Hello There!

75% of 180 is 135.

Converting Percent To Decimal.

p = 75%/100 = 0.75

Y = 0.75 * 180

Y = 135

Make a proportion ([tex]\frac{part}{whole}[/tex])...

The whole is 180 but we need to find the part which would be x

75 % is also a part of 100% (the whole)

The proportion would look like this...

[tex]\frac{x}{180} =\frac{75}{100}[/tex]

Now cross multiply to solve for x. The work for this is below.

100x = 13500

To isolate x divide 100 to both sides

100x/100 = 13500/100

x = 135

So...

135 is 75% of 180

Hope this helped!

Answer:

See below

Step-by-step explanation:

The given inequality is  

[tex]y\:>\:-5x+1[/tex]

The corresponding linear equation is y=-5x+1.

This line is of the form y=mx+b

The slope of this line is m=-5 and b=1 is the y-intercept.

Since the inequality sign is '>' the boundary line is a dashed line.

We test the origin to see if the inequality will be satisfied.

[tex]0\:>\:-5(0)+1[/tex]

[tex]0\:>\:1[/tex]

This statement is false so we shade above the dashed line.

The graph of the inequality is shown in the attachment.

Answer:

4x^3 -x^2 -6x +10

Step-by-step explanation:

You can perform the division of (4x^4 +11x^3 -9x^2 -8x +30)/(x +3) by polynomial long division or by synthetic division. The latter is shown below.

The result of the division is ...

4x^3 -x^2 -6x +10

m=9-5 so answer is m=4

Answer:

[tex]m=4[/tex]

Step-by-step explanation:

We have been given an equation. We are asked to find the value of m for our given equation.

[tex]\frac{6.22\times 10^9}{1.79\times 10^5}=3\times 10^m[/tex]

Let us solve left side of our given equation using exponent property for quotient [tex]\frac{a^b}{a^c}=a^{b-c}[/tex].

[tex]\frac{6.22\times 10^9}{1.79\times 10^5}=\frac{6.22}{1.79}\times 10^{9-5}[/tex]

[tex]\frac{6.22\times 10^9}{1.79\times 10^5}=3.18\times 10^{4}[/tex]

Therefore, the value of m would be 4 for our given equation.

Answer:

[tex](\frac{y^{4}}{10})^{3}[/tex]

Step-by-step explanation:

we have

[tex]0.001y^{12}[/tex]

we know that

[tex]0.001=\frac{1}{1,000}=\frac{1}{10^{3}}=(\frac{1}{10})^{3}[/tex]

[tex]y^{12}=(y^{4})^{3}[/tex]

substitute

[tex]0.001y^{12}=(\frac{1}{10})^{3}(y^{4})^{3}=(\frac{y^{4}}{10})^{3}[/tex]

The expression 0.001y12 can be written as the cube of a monomial by taking the cube root of each term. The final expression is (0.1y4)^3.

The given expression is 0.001y12. This can be written as the cube of a monomial in the form (_)^3 by finding the cube root of each term. The cube root of 0.001 is 0.1 (as 0.1^3 = 0.001) and the cube root of y12 is y4 (as (y4)^3 = y12). Hence, the monomial that can be cubed to get 0.001y12 is 0.1y4, and the final expression is (0.1y4)^3.

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Answer:

4x - 3)(3x^2 - 1).

Step-by-step explanation:

To factorize the expression 12x^3 - 9x^2 - 4x + 3, we can start by grouping the terms:

(12x^3 - 9x^2) - (4x - 3)

Now, we can factor out common terms from each group:

3x^2(4x - 3) - 1(4x - 3)

Notice that the expression (4x - 3) is common to both terms. We can now factor it out:

(4x - 3)(3x^2 - 1)

Therefore, the factored form of 12x^3 - 9x^2 - 4x + 3 is (4x - 3)(3x^2 - 1).

Answer:

slightly more than 15

Step-by-step explanation:

5[tex]\pi[/tex] ≈ 5(3.14) ≈ 15.7 (slightly more than 15)

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:x

Step-by-step explanation:

solve for the x value in the first equation one and plug it into the second equation in order to find the value of the y

3x -6y = 27

3x+4y=17

solution

3x-6y =27 solve for x

3x-6y + 6y = 27 +6y

3x=27 +6y

usually you would simplify to solve for x

but in this case I would leave it as 3x because the second equation requires the value of 3x

so substituting the 27 +6y for 3x

you end up with the equation of 27+6y + 4y = 17 (combine the like terms)

27+10y = 17  

subtract the 27 form both sides 10y = 17-27 which simplifies to 10y = 10

divide both sides by 10 and you get y = -1

you then take the value of y which is -1  : y = -1        

3x-6y = 27

3x - 6(-1) = 27  :substitute -1 into the top equation

3x +6 = 27 :  multiply the -6(-1)

3x=27-6 :subtract both sides by -6

3x = 21 divide both sides by 3

x = 7

Answer:

Option A. [tex]30\ days[/tex]

Step-by-step explanation:

step 1

Find the area of the brownie pan

The area of the trapezoid is equal to

[tex]A=\frac{1}{2}(30+42)(25)=900\ cm^{2}[/tex]

step 2

To calculate the number of days, divide the total area of the brownie pan by 30 square centimeters of brownie

so

[tex]900/30=30\ days[/tex]

Answer: A: 30 days

Step-by-step explanation:

Answer:

1. 14/15

2. 5 7/8

3. 81.25%

Step-by-step explanation:

1. (fraction) 7/9 divided by 5/6 (fraction)

7/9 ÷ 5/6 =

= 7/9 * 6/5

= (7 * 6)/(9 * 5)

= 42/45

= 14/15

2.

1 3/8 + 4 1/2 =

= 1 + 3/8 + 4 + 1/2

= 1 + 4 + 3/8 + 4/8

= 5 + 7/8

= 5 7/8

3.

percent = part divide by whole times 100

13/16 * 100 =

= 81.25%

Answer/Step-by-step explanation:

1. 14/15

7/9 divided by 5/6

7/9 X 6/5: multiply by the reciprocal

7/3 X 2/5: reduce the numbers

7/3 X 2/5=14/15

2. 1 3/8 + 4 1/2

1+4: add all whole numbers first

3/8 +1/2 : then add the fractions

5 7/8: is your final answer in its simplest form

3. Convert fraction 13 / 16 to a Answer: 81.25%

Answer:

Mean

Step-by-step explanation:

Means tell the average of something

Answer:in order to get a more accurate result, the teacher would not add in the score

Step-by-step explanation:

im pretty sure the correct answer is D

Answer:

Answer: Two students are the same age but have different heights.

Step-by-step explanation:

Answer:

[tex](7x)^{\frac{2}{3}}[/tex]=[tex]\sqrt[3]{49x^{2} }[/tex]

Step-by-step explanation:

We have been given the expression;

7 times x to the two thirds power which can be written mathematically as;

[tex](7x)^{\frac{2}{3}}[/tex]

To express the above expression as a radical, we need to recall that;

[tex]a^{\frac{b}{n}}=\sqrt[n]{a^{b}}[/tex]

Therefore;

[tex](7x)^{\frac{2}{3}}=\sqrt[3]{(7x)^{2} }\\\\=\sqrt[3]{49x^{2} }[/tex]

Answer:

19°

Step-by-step explanation:

In triangle ABC, ∠A=120°, a=8, b=3.

Use the sin rule:

[tex]\dfrac{a}{\sin \angle A}=\dfrac{b}{\sin \angle B}\\ \\\dfrac{8}{\sin 120^{\circ}}=\dfrac{3}{\sin \angle B}\\ \\8\sin \angle B=3\sin 120^{\circ}\\ \\8\sin \angle B=3\cdot \dfrac{\sqrt{3}}{2}\\ \\\sin \angle B=\dfrac{3\sqrt{3}}{16}\approx 0.3248\\ \\\angle B\approx 18.95^{\circ}\approx 19^{\circ}[/tex]