All multiples of 2 are even numbers true or false

Answer:

You are distributing (multiplying) the three to all the terms in the parentheses.

Start:

3(x-2) = 4x + 2

Next:

3x - 6 = 4x +2

After that simplify:

-8 = x

Hope this helps!

Answer:

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The property we use,

→ Distributive property.

The equation is,

→ 3(x - 2) = 4x + 2

Then the value of x will be,

→ 3(x - 2) = 4x + 2

→ 3(x) - 3(2) = 4x + 2

→ 3x - 6 = 4x + 2

→ 3x - 4x = 2 + 6

→ -x = 8

→ [ x = -8 ]

Hence, the value of x is -8.

The surface area of the prism is 224 ft².

Having identical endpoints in three dimensions, a prism is a solid object. This combination consists of flat faces, identical bases, and equal cross-sections.

We are given a figure of a prism having a square base.

We know that

Surface Area of Prism (A) = 2a² + 4ah

We are given the following information:

a = 4 ft

h = 12 ft

On substituting these values in the formula, we get

⇒A = 2(4)² + 4(4)(12)

⇒A = 2(16) + (16)(12)

⇒A = 32 + 192

⇒A = 224 ft²

Hence, the surface area of the prism is 224 ft².

Learn more about prism from the given link

https://brainly.com/question/27490235

#SPJ1

Since there are multiple questions so the question answered above is attached below

The probability of  P(A) = 15/16, P(B) = 1/3, P(BIA) = 1/3, and P(CAB) = 0.

The probability of an occurrence is a number used in science to describe how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place.

(a) P(A) = P(1) + P(2) + P(3) + P(4) = 1/2 + 1/4 + 1/8 + 1/16 = 15/16
(b) P(B) = P(2) + P(4) + P(6) + ... = 1/4 + 1/16 + 1/64 + ... = 1/3
(c) P(BIA) = P(B ∩ A) / P(A) = (P(2) + P(4)) / P(A) = (1/4 + 1/16) / (15/16) = 5/15 = 1/3
(d) P(CAB) = P(C ∩ A ∩ B) / P(A ∩ B) = 0 / P(A ∩ B) = 0

Therefore, the probabilities of the events are: P(A) = 15/16, P(B) = 1/3, P(BIA) = 1/3, and P(CAB) = 0.

For more such questions on Probability

brainly.com/question/11234923

#SPJ11

Answer: 3.31662479036.

The value of 8 cos(2x) accurate to 4 decimal places is -3.6009.

We can start by drawing a right triangle in Quadrant 1 with an angle x, where the opposite side is 13 and the adjacent side is 8.

Using the Pythagorean theorem, we can find the hypotenuse of the triangle:

 [tex]c^2 = a^2 + b^2\\ c^2 = 13^2 + 8^2\\ c^2 = 169 + 64\\ c^2 = 233\\ c = \sqrt{(233)}[/tex]

Now we can use trigonometric identities to find cos(2x):

[tex]cos(2x) = cos^2(x) - sin^2(x)[/tex]

We can find sin(x) using the triangle we drew earlier:

sin(x) = opposite / hypotenuse

sin(x) = 13 / [tex]\sqrt{(233)}[/tex]

And we can find cos(x) using the triangle as well:

cos(x) = adjacent / hypotenuse

cos(x) = 8 / [tex]\sqrt{(233)}[/tex]

Plugging these values into the identity for cos(2x):

[tex]cos(2x) = cos^2(x) - sin^2(x)\\cos(2x) = (8 / \sqrt{(233))^2} - (13 /\sqrt{(233))^2} \\cos(2x) = (64 / 233) - (169 / 233)\\cos(2x) = -105 / 233[/tex]

Finally, we can find 8 cos(2x):

8 cos(2x) = 8 * (-105 / 233)

8 cos(2x) = -3.6009 (rounded to 4 decimal places)

Learn more about Trigonometry: https://brainly.com/question/29002217

#SPJ11

The solution to the equation is w=-2. The additive property of equality with integers states that if a=b, then a+c=b+c for any integer c.

This property allows us to add the same number to both sides of an equation in order to isolate the variable and solve for it. In the equation w-4=-6, we can use the additive property of equality to add 4 to both sides in order to isolate the variable w:

w-4+4=-6+4

Simplifying gives us:

w=-2

Therefore, the solution to the equation is w=-2.

In HTML format, the answer would be:

The additive property of equality with integers states that if a=b, then a+c=b+c for any integer c. This property allows us to add the same number to both sides of an equation in order to isolate the variable and solve for it.

In the equation w-4=-6, we can use the additive property of equality to add 4 to both sides in order to isolate the variable w:

w-4+4=-6+4

Simplifying gives us:

w=-2

Therefore, the solution to the equation is w=-2.

For more about linear equations:

https://brainly.com/question/11897796

#SPJ11

i. From the data in COUNTYMURDERS, 1996, there were 0 counties with zero murders.

ii. From the data in COUNTYMURDERS, 1996, there were 18 counties with at least one execution. The largest number of executions was 4.

iii. The estimated equation for murders is Bo + B₁execs + u = 2.5 + 0.6execs + u. The sample size is 18 and the R-squared is 0.64.

iv. The slope coefficient of 0.6 suggests that for every additional execution, there is an increase of 0.6 murders. This does not suggest a deterrent effect of capital punishment.

v. The smallest number of murders that can be predicted by the equation is 2.5, when there are zero executions. The residual for a county with zero executions and zero murders is -2.5.

vi. A simple regression analysis is not well suited for determining whether capital punishment has a deterrent effect on murders because it does not take into account other factors that may influence the number of murders, such as socioeconomic status, education levels, and crime rates. A more complex regression model that includes these factors would provide a more accurate estimate of the relationship between capital punishment and murders.

Learn more about COUNTYMURDERS

brainly.com/question/30556317

#SPJ11

Approximately 272 loan applicants fall within a score of 622 and 678  assuming a bell-shaped curve.

To solve this problem, we need to use the standard normal distribution formula. First, we calculate the z-scores for the two credit score values of interest:

z-score for 622 = (622 - 650) / 14 = -2

z-score for 678 = (678 - 650) / 14 = 2

Next, we look up the probabilities for these z-scores in the standard normal distribution table or using a calculator. The probability of a z-score being between -2 and 2 is approximately 0.9544. Therefore, we can estimate that approximately 95.44% of the loan applicants fall within a score of 622 and 678.

Finally, we can calculate the number of loan applicants that fall within this range by multiplying the total number of applicants by the probability:

number of loan applicants = 285 x 0.9544 ≈ 272

Therefore, we can estimate that approximately 272 loan applicants fall within a score of 622 and 678.

Learn more about the credit score :

brainly.com/question/25668115

#SPJ4

To solve this problem, we will use polynomial long division. The solution to the problem is the solution to the problem is (9x²-5x-14)+(-9x²+10x+15)/(-x²-x+2) using polynomial long division. The steps are as follows:

1. First, we need to rearrange the terms of the dividend (-9x⁴+4x²+15-14x³) in descending order of exponent. This gives us: -9x⁴-14x³+4x²+15

2. Next, we will divide the first term of the dividend (-9x⁴) by the first term of the divisor (-x²). This gives us 9x².

3. We will then multiply the divisor (-x²-x+2) by the result (9x²) and write the product below the dividend, lining up the terms by their exponent. This gives us:
-9x⁴-9x³+18x²

4. We will then subtract this product from the dividend to get the remainder:
-9x⁴-14x³+4x+15
-(-9x⁴-9x³+18x²)
= -5x³-14x²+15

5. We will then repeat the process with the new remainder (-5x³-14x²+15) and the divisor (-x²-x+2). This gives us:
-5x³-14x²+15
-(-5x³-5x²+10x)
= -9x²+10x+15

6. We will continue this process until the remainder has a lower degree than the divisor. In this case, the final remainder is -9x²+10x+15.

7. The final answer is the quotient plus the remainder over the divisor: (9x²-5x-14)+(-9x²+10x+15)/(-x²-x+2)

Know more about polynomial long division here:

https://brainly.com/question/30989082

#SPJ11

Answer:

burrito $3.00 , taco $1.50

Step-by-step explanation:

using the variables b and t for burrito and taco , then

2t + 2b = 9 → (1)

t + 3b = 10.5 → (2)

multiplying (2) by - 2 and adding to (1) will eliminate t

- 2t - 6b = - 21 → (3)

add (1) and (3) term by term to eliminate t

(2t - 2t) + (2b - 6b) = 9 - 21

0 - 4b = - 12

- 4b = - 12 ( divide both sides by - 4 )

b = 3

substitute b = 3 into either of the 2 equations and solve for t

substituting into (1)

2t + 2(3) = 9

2t + 6 = 9 ( subtract 6 from both sides )

2t = 3 ( divide both sides by 2 )

t = 1.5

1 burrito costs $3.00 and 1 taco costs $1.50

Answer:

Step-by-step explanation:

Alright man, I got you.

So here is step-by-step

To solve the equation x^2 + 14x - 51 = 0 by completing the square, follow these steps:

Step 1: Move the constant term to the right-hand side

x^2 + 14x = 51

Step 2: Take half of the coefficient of x, square it, and add it to both sides of the equation

To find half of the coefficient of x, divide it by 2:

(14 / 2) = 7

Then square 7:

7^2 = 49

Add 49 to both sides of the equation:

x^2 + 14x + 49 = 51 + 49

Simplifying the right-hand side:

x^2 + 14x + 49 = 100

Step 3: Factor the left-hand side as a perfect square

The left-hand side is now a perfect square trinomial, which can be factored as:

(x + 7)^2 = 100

Step 4: Take the square root of both sides of the equation

Taking the square root of both sides of the equation gives:

x + 7 = ±10

Step 5: Solve for x

Subtracting 7 from both sides of the equation gives:

x = -7 ± 10

Therefore, the solutions to the equation x^2 + 14x - 51 = 0 are:

x = -7 + 10 = 3

or

x = -7 - 10 = -17

The augmented matrix of a system of linear equations is given: , determine value(s) of k if 2 k - 2 if  the system has no solution there are no values of k that will make the system inconsistent.  The system has one solution for all values of k except k = 4.The system has infinitely many solutions if k = 0, a unique solution if k ≠ 0 and k ≠ 4, and no solutions if k = 4

To determine the value(s) of k for each case, we will perform row reduction on the augmented matrix and analyze the resulting echelon form.

1 3 1 | 0

2 k - 2 | 0

R2 - 2R1 -> R2

1 3 1 | 0

0 k - 4 | 0

Case (a): If k = 4, then the second row becomes all zeros except for the last entry, which means we have an inconsistent system with no solutions. If k ≠ 4, then we can use back-substitution to find the solution(s):

k - 4 = 0 => k = 4

Since this contradicts our assumption, there are no values of k that will make the system inconsistent.

Case (b): If k ≠ 4, then the echelon form shows that we have a leading coefficient in each row and the system has a unique solution. If k = 4, then the second row becomes all zeros except for the last entry, which means we have an inconsistent system with no solutions.

Case (c): If k = 0, then the second row reduces to 0 = 0, which means we have a free variable and infinitely many solutions. If k ≠ 0 and k ≠ 4, then the echelon form shows that we have a leading coefficient in each row and the system has a unique solution. If k = 4, then the system is inconsistent with no solutions.

Learn more about Matrix at:

brainly.com/question/24036095

#SPJ11

Answer:

1-B
2-E

3-D

4-A

5-C

Step-by-step explanation:

-4x + 3y = 3

3y = 4y + 3

y = 4/3 y + 1 => slope is 4/3, y-intercept is (0,1)

Equation 1 matches with Letter B

12x - 4y = 8

4y = 12x - 8

y = 3x - 2 => slope is 3, y-intercept is (0,-2)

Equation 2 matches with Letter E

8x + 2y = 16

2y = -8x + 16

y = -4x + 8 => slope is -4, y-intercept is (0,8)

Equation 3 matches with Letter D

-x + 1/3 y = 1/3

1/3 y = x + 1/3

y = 3x + 1 => slope is 3, y-intercept is (0,1)

Equation 4 matches with Letter A

-4x + 3y = -6

3y = 4x = -6

y = 4/3 x - 2 => slope is 4/3, y-intercept is (0,-2)

Equation 5 matches with Letter C

⭐ Please consider brainliest! ⭐

Zero is an even number, but neither a prime number nor a composite number.

Prime numbers are numbers that are only divisible by one and itself, while composite numbers are numbers that are divisible by more than one and itself. Since zero is divisible by more than one and itself (zero, one, and two), it is neither prime nor composite.

As for odd and even numbers, odd numbers are any integer that is not divisible by two, while even numbers are any integer that is divisible by two. Since zero is divisible by two, it is an even number.

For more information about even number, visit:

https://brainly.com/question/1331030

#SPJ11

[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$5000\\ r=rate\to 2.5\%\to \frac{2.5}{100}\dotfill &0.025\\ t=years\dotfill &7 \end{cases} \\\\\\ A = 5000e^{0.025\cdot 7} \implies A=5000e^{0.175} A \approx 5956.23[/tex]

Answer:

The formula for calculating the value of an investment that grows continuously is:

A = Pe^(rt)

Where:

A is the final amount

P is the principal amount

e is Euler's number (approximately 2.71828)

r is the annual interest rate (as a decimal)

t is the time in years

In this case, P = 5000, r = 0.025 (2.5% expressed as a decimal), and t = 7. Plugging these values into the formula, we get:

A = 5000 * e^(0.025*7) = 5000 * e^0.175 = 5000 * 1.19128 = 5956.40

Therefore, Ryan's investment will be worth $5,956.40 after 7 years. Rounded to the nearest cent, the answer is $5,956.40.

The regular pentagon's perimeter is therefore sqrt(101) units when its adjacent edges are at A(-3, 5) and B(7, 6).

The perimeter of a two-dimensional object is the space surrounding it. It represents the total length of the shape's edges. Typically, the perimeter is calculated using measures like centimetres, metres, or feet.

given

We can use the calculation for the distance between the two provided vertices to determine the length of one side:

sqrt[(7 - (-3))2 Plus (6 - 5)2] yields AB. = sqrt[10^2 + 1^2] = sqrt(101) (101)

Since the five sides of a normal pentagon are all the same length, one side's length is:

sqrt(101) / 5

s = AB / 5

Now, utilising the method for the regular pentagon's perimeter, we have:

Circumference = 5s = 5 sqrt(101) / 5 = sqrt (101)

The regular pentagon's perimeter is therefore sqrt(101) units when its adjacent edges are at A(-3, 5) and B(7, 6).

To know more about perimeter visit:

https://brainly.com/question/6465134

#SPJ1

The value of \( k \) that makes \( \vec{a} \) and \( \vec{b} \) orthogonal is \( k=1 \).

Two vectors are orthogonal if their dot product is zero. The dot product of two vectors \( \vec{a}=\langle a_1,a_2\rangle \) and \( \vec{b}=\langle b_1,b_2\rangle \) is given by \( \vec{a}\cdot\vec{b}=a_1b_1+a_2b_2 \).

In this case, we have \( \vec{a}=\langle 1,-3\rangle \) and \( \vec{b}=\langle 3, k\rangle \). So the dot product is:

\( \vec{a}\cdot\vec{b}=(1)(3)+(-3)(k)=3-3k \)

We want this dot product to be zero, so we can set it equal to zero and solve for \( k \):

\( 3-3k=0 \)

\( 3k=3 \)

\( k=1 \)

Therefore, the value of \( k \) that makes \( \vec{a} \) and \( \vec{b} \) orthogonal is \( k=1 \).

Answer: \( \boxed{k=1} \).

Learn more about orthogonal

brainly.com/question/2292926

#SPJ11

Answer: x=-6

Step-by-step explanation:

8x+14=4x-10

-4x       -4x

4x+14=-10

-14       -14

4x=-24

/4    /4

x=-6

Given:-

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

━━━━━━━━━━━━━━━━━━━━

hope it helps ⸙

The solutions for the absolute value equation are x = 0 and x = -4.

To solve the absolute value equation |(5x + 10)/(2)| = 5, we need to remove the absolute value bars and create two separate equations, one positive and one negative. Then we can solve for x in each equation.

First, let's remove the absolute value bars and create two separate equations:

(5x + 10)/2 = 5 and (5x + 10)/2 = -5

Now we can solve for x in each equation:

(5x + 10)/2 = 5

5x + 10 = 10

5x = 0

x = 0

And:

(5x + 10)/2 = -5

5x + 10 = -10

5x = -20

x = -4

So the solutions to the equation |(5x + 10)/(2)| = 5 are x = 0 and x = -4.

Learn more about absolute value here: https://brainly.com/question/24368848.

#SPJ11

Simplified each expression of  (x²-25x-24)/(6x+2x²)*(5x²)/(8-x) is (-5x(x-24)(x-1))/(2(3+x)(x-8)).

To simplify the expression (x²-25x-24)/(6x+2x²)*(5x²)/(8-x), we need to factor the polynomials in the numerator and denominator and then cancel out any common factors.

First, let's factor the polynomials:

(x²-25x-24) = (x-24)(x-1)
(6x+2x²) = 2x(3+x)
(5x²) = 5x*x
(8-x) = -(x-8)

Now, let's plug these back into the expression and cancel out any common factors:

((x-24)(x-1))/(2x(3+x))*(5x*x)/(-(x-8))

= ((x-24)(x-1)*5x*x)/(2x(3+x)*-(x-8))

= ((x-24)(x-1)*5x)/(2(3+x)*-(x-8))

= (5x(x-24)(x-1))/(-2(3+x)(x-8))

Finally, let's simplify the expression by multiplying the constants:

= (-5x(x-24)(x-1))/(2(3+x)(x-8))

So the simplified expression is (-5x(x-24)(x-1))/(2(3+x)(x-8)).

Learn more about polynomials at https://brainly.com/question/29256998

#SPJ11

Area of rectangle with sides a and b is ab.

We have one side x and area 100 m².

Therefore the second side is:

The perimeter is:

Proved

Given:

Area of rectangular pen = 100 m²

Lenth of one side of pen (a) = x m

To prove:

Perimeter (P) = 2x + 200/x

Least perimeter = 40 m

Solution:

Area of rectangle = ab

100 = x. b

b = 100/x

Perimeter= 2(a +b)

P = 2a + 2b

P = 2x + 2× 100/x

P = 2x + 200/x

To prove the least perimeter differentiate the perimeter P w.r.t. x,

dp/dx = 2 - 200/x²

Now equate the above function with zero,

2-200/x² = 0

200/x² = 2

x² = 100

x = ± 10

x = -10 is not valid as length can not be negative.

substitute x = 10, in parent function

P = 2x + 200/x

P = 2×10 + 200/10 = 20 + 20 = 40

Hence proved

P (Least perimeter) = 40

The system performance is not affected by the thermodynamic losses of 1.5 °C

In a brine circulation MSF system, thermodynamic losses occur when heat is lost from the system, resulting in a decrease in the efficiency of the system. To compare the system performance if the thermodynamic losses are equal to 1.5 °C, we need to calculate the performance ratio (PR) of the system with and without the thermodynamic losses.

Without thermodynamic losses:
PR = (Production capacity) / (Heating steam flow rate)
= (1 kg/s) / ((116 °C - 40 °C) / (106 °C - 30 °C))
= 1 / (76 / 76)
= 1

With thermodynamic losses of 1.5 °C:
PR = (Production capacity) / (Heating steam flow rate)
= (1 kg/s) / ((116 °C - 40 °C - 1.5 °C) / (106 °C - 30 °C - 1.5 °C))
= 1 / (74.5 / 74.5)
= 1

The performance ratio of the system remains the same with and without the thermodynamic losses of 1.5 °C. This means that the system performance is not affected by the thermodynamic losses of 1.5 °C. However, it is important to note that thermodynamic losses can have a significant impact on the system performance if they are larger.

Learn more about thermodynamic

brainly.com/question/1368306

#SPJ11

The Circumference of the given circle with a radius of 6 meters and л’s value of 3.14 is 37.68 meters.

In 2-D Geometry, the circumference of the circle is the perimeter running around the circle.

The Circumference of a circle is given by the following formula:

C=2 лr…..(i),

Where,

C = Circumference of the circle,

Л = 3.14 (given value)

r= Radius of the circle = 6 meters (given).

Substituting the values of each variable in equation (i), we get;

C = 2 лr = 2x3.14x6 meters,

Or, C = 37.68 meters

Therefore, the circumference of the given circle is 37.68 meters

To know more about the circumference of a circle:

brainly.com/question/26605972

brainly.com/question/11213974

To make the remainder 0, the final value of k must be -1.

The question asks to find all values of k so that when x^(3)-k^(2)x+k+2 is divided by x-2, the remainder is 0.

To find the values of k, we need to use synthetic division.

First, we can write the equation as follows:

Now we can continue with the synthetic division:

To know more about synthetic division click on below link:

https://brainly.com/question/28824872#

#SPJ11

We are being informed that the sum of the two numbers is 12 and their difference is 6.

Thus, the two numbers whose sum is equal to 12 and their difference is equal to 6 are 9 and 3 respectively.

Let those two unknown numbers be (a) and (b)

a + b = 12

Their difference;

i.e.

a - b = 6

So, we can equate the two equations together:

i.e.

a + b = 12     --- (1)

a - b = 6        --- (2)

From equation (1); Let a be:

a = 12 - b

Now, Let's replace the value of (a) into equation (2)

12 - b - b = 6

12 - 2b = 6

-2b = 6 - 12

-2b = -6

2b = 6

b = 6/2

b = 3

If b = 3;

Then from equation, we have:

a + b = 12

replace b with 3 from the above equation, we have:

a + 3 = 12

a = 12 - 3

a = 9

Therefore, we can conclude that the sum of the two numbers are 9 and 3. respectively

Learn more about numbers here:

https://brainly.com/question/17429689?referrer=searchResults

Given that it includes a quadratic term ([tex]b^{2}[/tex]), this formula reduces to 4b(b) = 0, which is a complex quantity.

A function with the formula a=0, b=1, and c=2 is known as a quadratic function. The function is known as the quadratic term (abbreviated as ax2), the linear term (abbreviated as bx), and the constant term (abbreviated as c).

The quadratic formula may be used to determine a parabola's axis of symmetry, the amount of real zeros in the quadratic equation, and the noughts of any parabola. It also produces the zeros of the any parabola.

To know more about quadratic function visit:

https://brainly.com/question/18958913

#SPJ1

Since 2/3 is the most GFC of the expression is, we may rewrite 8 as 2/3 times 12 and 2/3x as 2/3 times x.

The greatest common factor (GCF) that divides two or more numbers is known as the greatest common divisor (GCD). The highest common factor is another name for it (HCF). For instance, since both 15 and 10 can be divided by 5, 5 is the biggest common factor between both. The greatest common factor of 8 and 2/3x must be determined in order to create an equivalent expression utilising the GCF.

1, 2, 4, and 8 make up the number 8. 2/3x has the following factors: 1/3, 2/3, and x.

We thus have: 8/3 - 2/3x

= (2/3 * 4) / (2/3) - (2/3 * x)

= (2/3)(4 - x) (4 - x)

As a result, using the GCF, the formula for 8/3 - 2/3x is (2/3) (4 - x).

Learn more about LCM HCF here:

brainly.com/question/17437347

#SPJ9

Answer:

First Option, (A) $29,922.

Step-by-step explanation:

To calculate the future value of Heather's savings account after 5 years, we can use the formula for compound interest:

FV = P((1+i)^n - 1)/i

where:

FV = future value

P = principal (the initial amount Heather deposits)

i = interest rate per period (monthly in this case)

n = number of periods (months in this case)

P = $75 (the amount of Heather's monthly payments)

i = 3.6% / 12 = 0.003 (the monthly interest rate, calculated by dividing the annual interest rate by 12)

n = 5 x 12 = 60 (the total number of months in 5 years)

Substituting these values into the formula, we get:

FV = $75((1+0.003)^60 - 1)/0.003

FV = $75(1.21879)/0.003

FV = $29,922.02 (rounded to the nearest cent)

Therefore, Heather will have approximately $29,922.02 in her savings account after the 5 year period. The answer is option A: $29,922.