Which value of x makes this equation true?

−4(3−x)+2x=8

Let's first write the equation given

x²+6x-13=0

They have told us to use "Completing the square" method.

So we need write x²+6x-13 as a whole square.

x²+6x-13=0

x²+(2*3*x)-9-4 = 0

x²+(2*3*x)-3²=4

Now we can write the LHS as:

(x - 3)²=2²

Hence,

x-3 can either be 2 or -2

Now,

x - 3=2

x=5

Or,

x - 3=-2

x=1

Therefore now we know that x can either be 1 or  5. So the correct answer is  Option B.

Step-by-step explanation:

x squared+6x-13=0

carry over that into the other side of the equal sign and then make the other side of the equal sign a perfect square

x squared +6x+3 squared=13+9(3 squared)

find the square root of both sides

(x+3)=class plus or minus

Given

Height of tank = 4 ft

Diameter = 2.2 ft

Gas is poured into the tank at a rate of 1.5 ft per minute.

Find

time taken to fill the empty tank.

Explanation

volume of cylindrical tank is given by

r = d/2 = 2.2 /2 = 1.1 ft

so ,

gas is poured at the rate of 1.5 ft per minute.

so ,

time taken to fill the empty tank =

Final Answer

Hence , the time to fill the empty tank is 10.1 minutes

Answer:

1111 in binary is 10001010111. Unlike the decimal number system where we use the digits 0 to 9 to represent a number, in a binary system, we use only 2 digits that are 0 and 1 (bits).

Answer:

\(f=-8\)

Step-by-step explanation:

\(8+4f=3f\)

\(8+4f-4f=3f-4f\) (Subtract \(4f\) from both sides of the equation to isolate \(f\))

\(8=-f\) (Simplify)

\(-f=8\) (Symmetric Property of Equality)

\(\frac{-f}{-1} =\frac{8}{-1}\) (Divide both sides of the equation by \(-1\) to get rid of \(f\)'s coefficient; remember that \(-f=-1*f\), so \(-f\) has a coefficient of \(-1\))

\(f=-8\) (Simplify)

Hope this helps!

Answer:

Step-by-step explanation:

Here you go mate

Step 1

8+4f=3f  Equation/Question

Step 2

8+4f=3f  Simplify

8+4f=3f

Step 3

8+4f=3f  Simplify by subtracting

f+8=0

Step 4

f+8=0  Subtract 8 frm sides

answer

f=-8

Hope this helps

Answer: 5

Step-by-step explanation:

Gerad's DVD club costs = Karen's DVD costs = y

Gerad - y = 2x + 10

Karen - y = x +15

2x + 10 = x + 15

x = 5

Answer:

0.4 is the whole number 5/12 is the fraction

Step-by-step explanation:

Answer:

C) 12 m

Step-by-step explanation:

Answer:

1,3,4,6

Step-by-step explanation:

The value of m∠Q is 148°.

What is tangent?

The straight line that "just touches" the curve at a given location is referred to as the tangent line to a plane curve in geometry. It was described by Leibniz as the path connecting two points on a curve that are infinitely near together.

Here, we have

Given: PR is ranger to circle Q at Point R. PS is tangent to circle Q at Point S.

We have to find the value of m∠Q.

We know that PR = PS

In ΔPRS

∠P + ∠R + ∠S = 180°

∴ ∠R = ∠S

∠P + ∠R + ∠R = 180°

38 + 2∠R  = 180°

2∠R  = 180° - 32°

2∠R = 148°

∠R  = 74°

∠S =  74°

∠PRQ = 90°

In ΔSRQ

∠SRQ = 90° - 74° = 16°

∠RSQ = 90° - 74° = 16°

∴ ∠SRQ + ∠RSQ + ∠RQS   = 180°

16° + 16° +∠RQS = 180°

∠RQS = 180° - 32°

∠RQS = 148°

m∠Q = 148°

Hence, the value of m∠Q is 148°.

To learn more about the tangent from the given link

https://brainly.com/question/31048699

#SPJ1

The value of sin(2x), cos (2x) and tan (2x) is 24/25, -7/25 and -24/7 respectively.

The value of the sin2x, cos2x, and tan2x  is calculated by applying trig ratios as follows;

Apply trigonometry identity as follows;

sin(2x) = 2sin(x)cos(x)

cos(2x) = cos²(x) - sin²(x)

tan(2x) = (2tan(x))/(1 - tan²(x))

If tan x = 4/3

then opposite side = 4

adjacent side = 3

The hypotenuse side  = 5 (based on Pythagoras triple)

sin x = 4/5 and cos x = 3/5

The value of sin(2x), cos (2x) and tan (2x) is calculated as;

sin (2x) = 2sin(x)cos(x) = 2(4/5)(3/5) = 24/25

cos (2x) = cos²(x) - sin²(x) = (3/5)² - (4/5)² = -7/25

tan (2x) = (2tan(x))/(1 - tan²(x)) = (2 x 4/3) / (1 - (4/3)²) = (8/3) / (-7/9)

= -24/7

Learn more about trig ratios here: https://brainly.com/question/10417664

#SPJ4

Answer:

22

Step-by-step explanation:

Just plug in

2(15 - 5) + 2 (Solve what's in the parenthesis)

2(10) + 2 (multiply 2*10)

20 + 2 (collect like terms)

22

The evaluation of the expression, 2(a - 5) + 2 when a = 15 is; 22

According to the question;

To evaluate 2(a - 5) + 2. when a = 15.

We have;

Read more;

https://brainly.in/question/19225277

The set of all possible outcomes is called the sample space. Thus in the context of a random experiment, the sample space is our universal set.

A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results. Depending on the experiment, a sample area could contain a variety of results.

The set of all potential outcomes or results of an experiment or random trial is referred to as the sample space in probability theory. The potential ordered outcomes, or sample points, are listed as elements in a set that is used to represent a sample space.

Learn more about sample space here

https://brainly.com/question/10558496

#SPJ4

Answer:

i would reword this to 6x+7=61

Step-by-step explanation:

So.  

move the 7 to the right side of the equation but as an opposite number so in this case its gonna be a negative

61-7=54

then you divide the number and get your missing numbers

54/6=9

d=9

plug it in

6(9)+7=61

Answer:

112 customers will pay cash next week

Step-by-step explanation:

1,100/138=7.97= approximately 8

Multiply the amount of customers who paid cash, 14 by 8.

.......................

Answer:

sorry error bessssssssss

Answer:

  c:  8,20,25

Step-by-step explanation:

You want to know which set of side lengths can form a triangle from the sets ...

A set of lengths can form a triangle if and only if the sum of the shorter two exceeds the longest.

In sets a, b, d, the sum of the shorter two is equal to the longest. These lengths will form a line segment, not a triangle.

A triangle can be formed by ...

  c: 8,20,25 . . . . . . 8+20=28 > 25

<95141404393>

The equation \(7.830 = 3.915(2)^D\) is the equation that can be solved to find the number of days (D) it takes for the water lily population to double.

Thus, option(B) is correct.

The general formula for population growth over time is given by:

\(P(t) = P(0) * (1 + r)^t\)

Where:

P(t) is the population at time t

P(0) is the initial population

r is the growth rate

t is the time period

In the context of the problem, the number of days it takes for the population to double. This means the final population (P(t)) will be twice the initial population (P(0)).

To find the equation(s) that can be solved to find the number of days (D) it takes the water lily population to double, we need to examine the given equations.

1. The equation \(2 = 3.915(1.106)^D\) is not solvable for D because it does not represent the doubling of the population.

2. The equation \(7.830 = 3.915(1.106)^D\) represents a specific value for the water lily population, but it does not indicate doubling.

3. The equation \(7.830 = 3.915(2)^D\) represents a specific value for the water lily population, the factor 2 is showing the doubling.

4. The equation \(2 = 1.106^D\) it does not indicate doubling either.

Learn more about Equation here:

https://brainly.com/question/29657992

#SPJ12

The P-value in each of the given situations for testing the null hypothesis H₀: p = 0.6 using a z-test can be determined as follows:

A. Hₐ: p > 0.6, z = 1.47: The P-value is the probability of observing a z-score greater than 1.47, which can be found by calculating the area under the standard normal curve to the right of 1.47.

B. Hₐ: p < 0.6, z = -2.70: The P-value is the probability of observing a z-score less than -2.70, which can be found by calculating the area under the standard normal curve to the left of -2.70.

C. Hₐ: p ≠ 0.6, z = -2.70: The P-value is the probability of observing a z-score less than -2.70 or greater than 2.70, which can be found by calculating the sum of the areas under the standard normal curve to the left of -2.70 and to the right of 2.70.

D. Hₐ: p < 0.6, z = 0.25: The P-value is the probability of observing a z-score less than 0.25, which can be found by calculating the area under the standard normal curve to the left of 0.25.

To determine the P-value, we need to calculate the corresponding areas under the standard normal curve based on the given z-scores. The P-value represents the probability of observing a z-score as extreme or more extreme than the given value, assuming the null hypothesis is true.

By using standard normal distribution tables or statistical software, we can find the probabilities associated with the given z-scores. These probabilities represent the P-values for each scenario, providing a measure of evidence against the null hypothesis.


To learn more about null hypothesis click here: brainly.com/question/30821298

#SPJ11

The given ordered pairs satisfy a linear function f(x) = mx + b.

As per the given data we have to determine the given ordered pairs satisfy a linear function.

If the information about the function is given in the algebraic form, then it is linear if it is of the form f (x) = mx + b.

Let the linear function be f (x)=a x + b

From the table f (4)=2 ; f (3)=4

a(4) + b = 2

4a + b = 2....(1)

a(3) + b = 4

3a + b = 4....(2)

Solving (1), (2)

4a - 3a + b - b = 2 - 4

a = - 2

Put a = - 2 in equation (2)

3(-2) + b = 4

b = 4 + 6

b = 10

Therefore f(x)= -2 x + 10

f(5)= -2(5) + 10

f(5)= -10 + 10

f(5)= 0

(x, y) = (5, 0)

f(4) = -2(4) + 10

f(4) = - 8 + 10

f(4) = 2

(x, y) = (4, 2)

So, ordered pairs satisfy the linear function

For more questions on linear function

https://brainly.com/question/29256039

#SPJ4

Answer:

im so sorry i have no idea

Step-by-step explanation:

The generating function for the sequence {an} is given by a(x) = (1 + 2x) / (1 - x - 6x^2). It captures the terms of the sequence {an} as coefficients of the powers of x.

To find the generating function of the sequence {an}, we can use the properties of generating functions and solve the given recurrence relation.

The given recurrence relation is: an = an-1 + 6an-2

We are also given the initial conditions: a0 = 1 and a1 = 3.

To find the generating function, we define the generating function A(x) as:

a(x) = a0 + a1x + a2x² + a3x³ + ...

Multiplying the recurrence relation by x^n and summing over all values of n, we get:

∑(an × xⁿ) = ∑(an-1 × xⁿ) + 6∑(an-2 × xⁿ)

Now, let's express each summation in terms of the generating function a(x):

a(x) - a0 - a1x = x(A(x) - a0) + 6x²ᵃ⁽ˣ⁾

Simplifying and rearranging the terms, we have:

a(x)(1 - x - 6x²) = a0 + (a1 - a0)x

Using the given initial conditions, we have:

a(x)(1 - x - 6x²) = 1 + 2x

Now, we can solve for A(x) by dividing both sides by (1 - x - 6x^2²):

a(x) = (1 + 2x) / (1 - x - 6x²)

Therefore, the generating function for the given sequence is a(x) = (1 + 2x) / (1 - x - 6x²).

Read more on Functions here: https://brainly.com/question/29890699

#SPJ11

The area of a desk pad eight yards wide and 4/5 yards long is given as follows:

A = 0.3 yd².

Considering a rectangle of length l and width w, we have that:

The dimensions for this problem are given as follows:

Hence the area is given as follows:

A = 0.375 x 0.8

A = 0.3 yd².

More can be learned about the area of a rectangle at https://brainly.com/question/25292087

#SPJ1

Answer:

75.9

Step-by-step explanation:

Answer:

1. Ce qui fait des énergies renouvelables une raison de se développer, c'est parce qu'elles utilisent une source qui peut être éternelle. Les combustibles fossiles sont notre principale énergie, mais cela ne durera pas éternellement.

2) Le courant alternatif rend cela possible.

Si vous recherchez un phénomène naturel, il peut s'agir du solaire, de l'hydroélectricité, du vent, de la biomasse, etc. Selon le contexte.

By the factor theorem P(10) = 0

A polynomial is a mathematical expression in which the power of the variable is greater than or equal to two.

Now, suppose (x - 10) divides evenly into some polynomial P(x). To detremine what is P(10), we notice that (x - 10) divides evenly into P(x). This means that (x - 10) is a factor of P(x).

Now, by the factor theorem, if (x - a) is  a factor of P(x), then P(a) = 0

So, now (x - 10) is a factor of P(x). So, it implies that by the factor theorem, P(10) = 0.

So, P(10) = 0

Learn more about factor theorem here:

https://brainly.com/question/30213721

#SPJ1

Answer:

Step-by-step explanation:

Proportional relationship:

We have:

Find the value of k:

or

Answer:

55

Step-by-step explanation:

Let,

Constant = k

k = h/mi

k = 110/2

k = 55 mi/h

Hence,

The constant of proportionality is 55