Indicate which formula you would use to solve for the missing side B and then write your answer correct to two decimal places.Write only the formula down.. Single line text.

Answer:

x = 16

Step-by-step explanation:

subtract 12 from both sides to isolate the variable and its coefficient

4x = 64

divide both sides by 4 to get x

x = 16

Answer:

x = 16

Step-by-step explanation:

4x+12=76

Step 1: Subtract 12 from both sides.

4x + 12 - 12 = 76 - 12

4x = 64

Step 2: Divide both sides by 4.

\(\frac{4x}{4} = \frac{64}{4}\)

x = 16

Answer:

A) 0.8131 ≈ 0.81

B) 0.6322 ≈ 0.63

C)  0.7639 ≈ 0.77

Step-by-step explanation:

A)

Total number of  units

= 55 + 32 + 17 + 3

 = 107

hence the probability that the failure involves a gas leak

= ( 55 + 32 ) / 107

= 0.8131

B) probability that there is evidence of electrical failure given tat there is a gas leak

P ( A / B ) = \(\frac{P(A n B)}{P(B)}\)

P( A∩B ) = 55/107 = 0.5140

P ( B ) = ( 55 + 32 ) / 107 = 0.8131

hence P ( A / B ) = 0.5140 / 0.8131 = 0.6322

A = failure due to electrical

B = failure due to gas leak

C)  Probability of a gas leak given that there is evidence of electrical failure

P ( B / A ) =  \(\frac{P(BnA)}{P(A)}\)

P ( B ∩ A ) = 0.5140

P( A ) = ( 55 + 17 ) / 107  = 0.6729

hence P ( B / A ) = 0.5140 / 0.6729 = 0.7639

Answer:

First equation: 4n^2=256

Second equation: 4n*2=64

Step-by-step explanation:

First equation:

4n^2 for n = 8.

Substitute 8 for n and solve:

4*(8)^2=4*64=256

4n^2=256

Second equation:

4n*2 for n = 8.

Substitute 8 for n and solve:

4*(8)*2=32*2=64

4n*2=64

I hope this helped you.

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Answer:

1024

Step-by-step explanation:

4 * 4 * 4 * 4 * 4

Answer:

z = 29

Step-by-step explanation:

z - 4 = 25

You were going the right way;you need to add that value to each side:

z - 4 ( +4 ) = 25 ( +4 )

z = 29

The equation of the line for the given graph will be y=0.35x+1

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.

\(\rm m =\dfrac{y_2-y_1}{x_2-x_1}\)

The slope of the line is,

m = (1.5-2)/(1-2)

m=0.5

The equation of the line passes through (2,2)(1.1.5) from the graph is,

y-2=0.5(x-2)

y-2=0.5x-1

y=0.35x+1

Thus, the equation of the line for the given graph will be y=0.35x+1

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Answer:

Quadrilaterals

Step-by-step explanation:

Answer: 2.68cm²

Step-by-step explanation:

The front face has surface area 4x11 = 44mm². The one facing the left has surface area 6x4 = 24mm². Finally, the one facing upwards has surface area 11x6 = 66mm². Adding these up, we get 134mm² for the three faces we can see. Double this for the ones which are hidden and we get 268mm², or 2.68cm².

Answer:

The vertex of the function is at (–3,–16)

The graph is increasing on the interval x > –3

The graph is positive only on the intervals where x < –7 and where

x > 1.

Step-by-step explanation:

The graph of \(f(x)=(x-1)(x+7)\) has clear zeroes at \(x=1\) and \(x=-7\), showing that \(f(x) > 0\) when \(x < -7\) and \(x > 1\). To determine where the vertex is, we can complete the square:

\(f(x)=(x-1)(x+7)\\y=x^2+6x-7\\y+16=x^2+6x-7+16\\y+16=x^2+6x+9\\y+16=(x+3)^2\\y=(x+3)^2-16\)

So, we can see the vertex is (-3,-16), meaning that where \(x > -3\), the function will be increasing on that interval

Given the following question:

Protein A = 75%

Protein B = 50%

Mixture = 70% = 1400

75% x + 50% (1400 - x) = 75.00%

Answer:

The same shape but not the same size

Step-by-step explanation:

       If two figures have the same shape and the same size, they are defined as congruent.

       As long as all the angles and sides are proportionally similar then the shapes have similarity.

The total number of people that were there altogether at the radio show is 175 people.

From the information, there were 5 people wearing boots at the rodeo for every 2 people who were not wearing boots.

It was also illustrated that there were 125 people wearing boots at the rodeo last night, those that aren't wearing boots will be illustrated by x.

2/5 = x/125

Collect like terms

5x = 125 × 2

5x = 250

Divide

x = 250/5

x = 50

Those not wearing boots = 50

Total number of people will be:

= Those wearing boots + Those not wearing

= 125 + 50

= 175

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Answer:

175

Step-by-step explanation:

Answer:

$574.86

Step-by-step explanation:

First you need to find 34% of 429 which is 145.86. Then you add the 145.86 to 429 which ends up being a total of $574.86.

Hope this helped :)

Answer:

111

Step-by-step explanation:

divide by 2 to find the radius

Answer:

centre = (5, - 6 ) , radius = 7

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

given

x² + y² - 10x + 12y + 12 = 0 ( subtract 12 from both sides )

x² + y² - 10x + 12y = - 12 ( collect terms in x/ y )

x² - 10x + y² + 12y = - 12

using the method of completing the square

add ( half the coefficient of the x/ y terms )² to both sides

x² + 2(- 5)x + 25 + y² + 2(6)y + 36 = - 12 + 25 + 36

(x - 5)² + (y + 6)² = 49 = 7² ← in standard form

with centre (5, - 6 ) and radius = 7

Answer:

Center = (5, -6)

Radius = 7

Step-by-step explanation:

To find the center and the radius of the circle represented by the given equation, rewrite the equation in standard form by completing the square.

To complete the square, begin by moving the constant to the right side of the equation and collecting like terms on the left side of the equation:

\(x^2-10x+y^2+12y=-12\)

Add the square of half the coefficient of the term in x and the term in y to both sides of the equation:

\(x^2-10x+\left(\dfrac{-10}{2}\right)^2+y^2+12y+\left(\dfrac{12}{2}\right)^2=-12+\left(\dfrac{-10}{2}\right)^2+\left(\dfrac{12}{2}\right)^2\)

Simplify:

\(x^2-10x+(-5)^2+y^2+12y+(6)^2=-12+(-5)^2+(6)^2\)

       \(x^2-10x+25+y^2+12y+36=-12+25+36\)

       \(x^2-10x+25+y^2+12y+36=49\)

Factor the perfect square trinomials on the left side:

\((x-5)^2+(y+6)^2=49\)

The standard equation of a circle is:

\(\boxed{(x-h)^2+(y-k)^2=r^2}\)

where:

Comparing this with the rewritten given equation, we get

Therefore, the center of the circle is (5, -6) and its radius is r = 7.

The second additional Polar representation of the point (3,-π/6) can be ($\frac{3\sqrt{6}}{2}$, $\frac{5\pi}{3}$) or ($\frac{3\sqrt{6}}{2}$, $-\frac{7\pi}{3}$).

We have a point in polar coordinates (3,-π/6) and we have to find two additional polar representations of this point. Let's recall the formula for converting from Cartesian to polar coordinates :x = rcosθy = rsinθAnd

the formula for converting from polar to Cartesian coordinates :r = √(x²+y²)θ = arctan(y/x)So, we can use the second formula to convert (3,-π/6) to Cartesian coordinates:$$x=3\cos(-\frac{\pi}{6})=3\cdot \frac{\sqrt{3}}{2}=\frac{3\sqrt{3}}{2}$$$$y=3\sin(-\frac{\pi}{6})=3\cdot \frac{-1}{2}=-\frac{3}{2}$$

Now we can use the first formula to convert back to polar coordinates:$$r=\sqrt{(\frac{3\sqrt{3}}{2})^2+(-\frac{3}{2})^2}=\frac{3\sqrt{6}}{2}$$$$\theta=\arctan(-\frac{3}{3\sqrt{3}})=-\frac{\pi}{3}$$

So, the first additional polar representation of the point (3,-π/6) is ($\frac{3\sqrt{6}}{2}$, $-\frac{\pi}{3}$).To find the second polar representation,

we need to add or subtract multiples of π to the angle until it is in the range [-2π, 2π].$$-\frac{\pi}{3}+2\pi=\frac{5\pi}{3}$$$$-\frac{\pi}{3}-2\pi=-\frac{7\pi}{3}$$

So, the second additional polar representation of the point (3,-π/6) can be ($\frac{3\sqrt{6}}{2}$, $\frac{5\pi}{3}$) or ($\frac{3\sqrt{6}}{2}$, $-\frac{7\pi}{3}$).

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Answer:

C(d) = 0.64c +37.95

Step-by-step explanation:

C(38) = 0.64(38) + 37.95 = $62.27

Answer:

424.8571428571429

Step-by-step explanation:

Answer:

Step-by-step explanation:

The data given illustrates that there's a constant ratio of 2 and y = 600(2)^x; 38400

The ratio based on the information given will be:

= 1200/600

= 2

Therefore, the constant ratio is 2.

In 6 years, the population will be:

= 600 × 2^6

= 600 × 64

= 38400

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the distance from the first plant to the last plant, ignoring the width of each plant stem, is 10.5 feet.

Why is it?

To find the distance from the first plant to the last plant, we need to add up the distances between each adjacent pair of plants. Since there are 8 plants, there are 7 pairs of adjacent plants, and each pair is separated by 1.5 feet.

So, the total distance from the first plant to the last plant is:

7 ×1.5 = 10.5 feet

Therefore, the distance from the first plant to the last plant, ignoring the width of each plant stem, is 10.5 feet.

Distance refers to the measurement of the physical space between two points or objects. It is a scalar quantity that only considers the magnitude of the separation between two points and does not take into account the direction of the separation.

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The correct option is not available among the choices provided (A. 49.4, B. 39.5, C. 55.2, D. 50.45).

To find the measure of angle A in triangle ABC using the Law of Sines, we can use the formula:

sin(A)/a = sin(B)/b = sin(C)/c

Given that a = 14, b = 17, and c = 22, we can substitute these values into the formula:

sin(A)/14 = sin(B)/17 = sin(C)/22

To find angle A, we need to solve for sin(A) and then take the inverse sine (arcsin) of that value.

First, let's find sin(B) using the given information:

sin(B)/17 = sin(A)/14

sin(B) = (17 * sin(A))/14

Next, let's find sin(C):

sin(C)/22 = sin(A)/14

sin(C) = (22 * sin(A))/14

Since the sum of angles in a triangle is 180 degrees, we can calculate angle C:

angle C = 180 - angle A - angle B

Now, we can substitute the expressions for sin(B) and sin(C) into the equation:

(22 * sin(A))/14 = (17 * sin(A))/14 + sin(B)

To solve for sin(A), we can multiply both sides of the equation by 14:

22 * sin(A) = 17 * sin(A) + 14 * sin(B)

22 * sin(A) - 17 * sin(A) = 14 * sin(B)

5 * sin(A) = 14 * sin(B)

sin(A) = (14/5) * sin(B)

Finally, we can take the inverse sine (arcsin) of sin(A) to find the measure of angle A:

A = arcsin((14/5) * sin(B))

Now, since the values of angles B and C are not provided, it is not possible to directly determine the measure of angle A using the given information.

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Answer:

7/20 is the fraction!!!!

Answer

\(\frac{35}{100}\) is equal to 35%.

Therefore , the solution of the given problem of equation comes out to be factor is (5b)(-5b+3).

A formula for connecting two statements using the equal sign (=) to denote equivalence is known as a mathematical equation. A mathematical equation in algebra is a statement that proves the equality of two mathematical expressions. For instance, the formula 3x + 5 = 14 places an equal sign between the variables 3x + 5 and 14. The mathematical relationship between the two sentences on either side of a letter is established. Most of the time, the symbol serves as both the one and only variable. for instance, 2x – 4 = 2.

Here,

the two numbers' primary factors are as follows:

-25\(b^{2}\) + 15b

Common prime factors can be multiplied to determine the GCF:

=> -25\(b^{2}\)  = -(5)(5) * \(b^{2}\)

=> 15b = (5)(3)b

The expression can be factored in the following fashion because the GCF is 5b:

=> -(5)(5) * \(b^{2}\) +  (5)(3)b

=> (5b)(-5b+3)

Therefore , the solution of the given problem of equation comes out to be factor is (5b)(-5b+3).

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Answer: Yes, this is a function!

Step-by-step explanation: Here are the requirements for determining if a 2-variable equation is a function or not.

2.

Each input should correspond to only one output

. In our case, any value of x you put into this equation only gives one value of y. We can verify this graphically using a simple test called the

vertical line test.

To do this, graph the function with the x axis being the horizontal axis and the y axis being the vertical axis (this matters!) In our case, this will be a parabola opening upwards. The test says that if I can draw vertical lines through every part of the graph and each vertical line only crosses the graph once, the equation is a function. In our case, I can draw vertical lines through everywhere in a parabola and they will only cross once. This shows that we have a function!

Hope this helps!

Bye for now,

Iz