(b) 3(27) = 3(25 + 2)

Answer:

c. x² + 2x -5 = 0

Step-by-step explanation:

 Given expression;

         \(\frac{5}{x}\)   = \(\frac{x + 2}{3}\)  

Unknown:

 The quadratic equation equivalent to this expression:

Solution:

  The common denominator here is 3x;

    So, multiply both sides by 3x

          \(\frac{5}{x}\) x 3x  =  \(\frac{x + 2}{3} x\) 3x

          5 x 3 = (x + 2)x

           15 = x² + 2x

     So;

          x² + 2x - 15

The quadratic expression is x² + 2x - 15

The values of the trigonometric ratios are: a) - 7/5, b) -75 c ) -1/5  d ) -25/12

Trigonometric ratios are measurements of the lengths of two sides of a triangle. There are three basic trigonometric ratios: sine, cosine, and tangent.  Sine ratios are the ratios of the length of the side opposite the angle they represent over the hypotenuse

the give parameters are:

tanα = -4/3 where π/2 <α<π and sinβ = √3/2, 0<β<π/2

a)  sin(α+β)

Using the trig ratios tan = opp/adj

but from pyth. rule, 4² + 3² = h²

16+9 = h²

h = √25 = 5

Now from trig Sin(α+β)

4/5 + 3/5

=- 7/5

b) cos(α+β)

cos = ad/hypo

4/5 + 3/5

= -7/5

c) Sin(α-β)

4/5 - 3/5

-1/5

d) tan(α-β)

= -4/3 - 3/4

= (-16 - 9)/ 12

-25/12

Learn more about trigonometric ratios on https://brainly.com/question/23130410

#SPJ1

Answer: 538

Step-by-step explanation: en verdad no sé pero eso fuelo que me salio

Answer:

$127.80

Step-by-step explanation:

Please let me know if you want me to add an explanation as to why this is the answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)

2/6 is the equivalent fraction for the fraction represented on the given number line. So, B is the correct option

What is an equivalent fraction ?

According to equivalent fractions, two or more fractions are considered to be equal if, following simplification, both provide the same fraction. Let's imagine that a/b and c/d are two fractions. If these fractions are simplified to produce comparable fractions, such as e/f, they are then equal to one another.

For instance, if we simplify 5/15, the resulting fraction is the same as 1/3, hence that is the equivalent fraction of 1/3.

The fractions with distinct numerators and denominators but the same value are said to be equivalent fractions. For instance, since 2/4 and 3/6 both equal the 12, they are identical fractions. An element of a whole is a fraction. The same amount of the whole is represented by equivalent fractions.

as 2/6 can further reduced to 1/3 which is represented on to the number line  as 1/3 which is equal to 2/6

Learn more about equivalent fraction from the link below

https://brainly.com/question/29769027

#SPJ1

The investment amount is $37263.09.

Interest that compounded continuously to the principal amount. This interest rate provides exponential growth to period of time.

Formula of continuous compound interest rate;

P(t) = P₀ \(e^{rt}\) , where P₀ is the principal amount, r is the interest rate and t is the time period.

Given that the Alang is going to invest with the continuous compound interest rate 5.7%.

Using the formula of continuous compound interest rate,

P(t) = P₀ \(e^{rt}\)

P(t) = $113000 x    \(e^{(5.7)(5)}\)

P(t) = $37263.09

Therefore, the investment amount is $37263.09.

To learn more about the continuous compound interest;

https://brainly.com/question/18722165

#SPJ1

The graph of the function y = 5|x - 4| is added as an attachment

From the question, we have the following parameters that can be used in our computation:

y = 5|x - 4|

The above function is an absolute value function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking not of the above transformations rules

The graph of the function is added as an attachment

Read more about functions at

brainly.com/question/2456547

#SPJ1

The surface area of the right rectangular prism is given as follows:

358 m².

The surface area of a prism is obtained with the sum of the areas of each part of the prism.

The parts that compose the prism are given as follows:

The area of a rectangle is given by the multiplication of each of the dimensions of the rectangle.

Hence the surface area of the prism is calculated as follows:

S = 2 x (7 x 12 + 5 x 12 + 5 x 7) = 358 m².

(multiplication by two due to the two rectangles with each of the dimensions).

The prism is given by the image shown at the end of the answer.

More can be learned about surface areas at https://brainly.com/question/16519513

#SPJ1

The equation to show the perimeter of the rectangle is P = 2(2w + 5)

From the question, we have the following parameters that can be used in our computation:

Length = 5 more than the width

Also, we have

Perimeter = 58

This means that

P = 2(w + 5 + w)

P = 2(2w + 5)

In (a), we have

P = 2(2w + 5)

This gives

2(2w + 5) = 58

So, we have

2w + 5 = 29

2w = 24

w = 12

Next, we have

l = 12 + 5

l = 17

Lastly, we have

Area = 17 * 12

Area = 204

Read more about area at

https://brainly.com/question/24487155

#SPJ1

Answer:

area = 132 cm²

Step-by-step explanation:

area of rectangle = 7 x 12 = 84

area of one triangle = 8 x 6 x 0.5 = 24

total area = 84 + 24 + 24 = 132 cm²

Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

Answer:

Step-by-step explanation:

gain

loss

gain loss

gain

Answer:

Gains : +1,+10,+3

loss: -3,-5,-9,-100

Step-by-step explanation: I think this question is basically just asking about givings examples of positive and negative numbers

Answer: 64cm

Step-by-step explanation:

Answer:

B. 64cm

Step-by-step explanation:

Answer:

To determine the amount of engine oil needed, we need to find 5% of 3.8 gallons:

0.05 x 3.8 = 0.19

So, 0.19 gallons of engine oil should be added to the jerry can.

The values of x, y , and z in the matrix equation is 3, 4, 0 respectively.

The solution of the matrix equation is calculated by applying Cramer's rule as shown below;

[ 1     1     -1 ]  [ 7 ]

[ 2    3     0 ] [ 18 ]

[ -5   -7    -1 ] [ -43 ]

The determinant of the matrix is calculated as follows;

[ 1     1     -1 ]  

[ 2    3     0 ]

[ -5   -7    -1 ]

Δ = 1 (-3 - 0) - 1(-2 - 0 )  - 1(-14 + 15)

Δ = -2

The x determinant of the matrix is calculated as follows;

[ 7     1     -1 ]  

[ 18    3     0 ]

[ -43   -7    -1 ]

Δx = 7 (-3 - 0) - 1 (-18 - 0 )  - 1(-126 + 129)

Δx = -6

The y determinant of the matrix is calculated as follows;

[ 1     7     -1 ]  

[ 2    18     0 ]

[ -5   -43   -1 ]

Δy = 1 (-18 - 0 )   - 7(-2 - 0 )  -1(-86 + 90)

Δy = -8

The z determinant of the matrix is calculated as follows;

[ 1     1     7 ]  

[ 2    3    18 ]

[ -5   -7   -43]

Δz = 1 (-129 + 126) - 1(-86 + 90) + 7(-14 + 15)

Δz = 0

The values of x, y , and z is calculated as;

x = Δx/Δ = -6/-2 = 3

y = Δy/Δ = -8/-2 = 4

z = Δz/Δ = 0/-2 = 0

Learn more about matrix equation here: https://brainly.com/question/11989522

#SPJ1

The percent of the bags of chips weigh less than 176 grams is b 16%

From the question, we have the following parameters that can be used in our computation:

Mean = 180

Standard deviation = 4

Bags of chips weigh less than 176 grams

This means that

x = 176

So, the z-score is

z = (176 - 180)/4

Evaluate

z = -1

The percent of the bags of chips weigh less than 176 grams is represented as

P = P(z < -1)

Using a graphing calculator, we have

Percentage = 0.15866

So, we have

Percentage = 16%

Hence , the percentage is 16%

Read mroe about z-scores at

brainly.com/question/25638875

#SPJ1

The length of the perpendicular from the point (1, -3) to the line 5x + 12y + 5 = 0 is 2 units.

To find the length of the perpendicular from a point to a line, use the formula:

D = |Ax₁ + By₁ + C| / √(A² + B²)

Where A, B, and C = coefficients of the line equation Ax + By + C = 0, and (x1, y1) is the point from which the perpendicular is drawn.

Given the line equation 5x + 12y + 5 = 0 and the point (1, -3), substitute these values into the formula:

D = |(51) + (12-3) + 5| / √(5² + 12²)

D = |5 - 36 + 5| / √(25 + 144)

D = |-26| / √(169)

D = 26 / 13

D = 2 units.

Therefore, the length of the perpendicular from the point (1, -3) to the line 5x + 12y + 5 = 0 is 2 units.

Find out more on length here: https://brainly.com/question/30043623

#SPJ1

The amount of a decaying substance with half life τ that remains after a time t, if the initial amount of that substance is A_0, is given by the formula:

If the half life of that substance is 12 days, and the initial amount of that substance is 4.5 grams, then A_0=4.5 and τ=12. Substitute those values as well as t=20 to find the remaining amount after 20 days:

To the nearest tenth of a gram, the remaining amount after 20 days, is:

Answer: ∠BEA

Step-by-step explanation:

Congruent: Same Angle Measure

Starting: ∠BHK

Congruent Angle: ∠BEA

One of the trigonometric identities is :

From the problem, we have :

Applying the identity above,

Note that :

The identity will be :

The answer is -cos x

Answer:

r = -140

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.  Not sure if this was the answer you were looking for.

The completed list of numbers would be: 1, 1, 1, 2, 1, 4, 1, 2

By examining the given list of numbers 1, 1, 1, 2, 1, 4, 1, we can observe a pattern emerging.

The pattern seems to involve alternating sequences. The first sequence is the number 1 repeated three times (1, 1, 1). The second sequence is a number that follows the pattern of increasing by 1 each time (2). The third sequence is the number 1 repeated once (1). The fourth sequence is a number that follows the pattern of doubling each time (4). This pattern of alternating sequences continues.

Based on this pattern, we can predict that the next number in the sequence will follow the alternating sequence pattern. Since the last number in the sequence is 1, the next sequence will involve a number that follows the pattern of increasing by 1. Therefore, the next number in the sequence would be:

1 + 1 = 2

Hence, based on the observed pattern, the next number in the sequence is 2.

Therefore, the completed list of numbers would be:

1, 1, 1, 2, 1, 4, 1, 2

For more such questions on numbers visit:

https://brainly.com/question/24644930

#SPJ8

Answer:

-200.5

Step-by-step explanation:

that’s just the right answer lol

Answer:

Step-by-step explanation:

The figure shown is represented as a right triangle, which means that the sum of the angles within should add up to 90°. So if we take 32° (one of the angles given) and subtract it from 90°, we should be left with 58°.

This means that the value of the equation that contains "x" must equal 58°. Therefore, (6 x 9 + 4)° must equal 58.° Which means that the value of x = 9.

Answer:

25 gallons of the 70% and 75 gallons of the 30%

Step-by-step explanation:

First, make three baskets. One having x, the second having 100-x, and the third having 100. The reason you have 100-x is because you are adding two unknown numbers, and when you add them they equal 100. And if they add to be 100, 100-x=100-x. To continue, under each basket, write the number of the percent. So the first basket would have 70 under it, the second one would have 30 under it, and the third one would have 40 under it. Then multiply the number inside the basket by the number under. Then you would get 70x+3,000+30x=4,000. Next, 40x+3,000=4,000. Then 40x=1,000. x=25. That's the first basket. For the second, you do 100-25 because of the equation inside the second basket, which is 75. Hope this helps!

The length of BD is 22.

In the given scenario, let's consider the following information.

AD = 8

AE = 6

EC is 12 more than BD.

To find the length of BD, we can utilize the Intercepted Arcs Theorem, which states that when two secants intersect outside a circle, the measure of an intercepted arc formed by those secants is equal to half the difference of the measures of the intercepted angles.

From the given information, we know that AD = 8 and AE = 6.

Since these are the lengths of the secants, we can use them to calculate the intercepted arcs.

First, let's find the intercepted arc corresponding to AD:

Intercepted Arc ADB = 2 \(\times\) AD = 2 \(\times\) 8 = 16

Similarly, we can find the intercepted arc corresponding to AE:

Intercepted Arc AEC = 2 \(\times\) AE = 2 \(\times\) 6 = 12

Now, we know that EC is 12 more than BD.

Let's assume the length of BD as x.

BD + 12 = EC

Now, let's consider the intercepted arcs theorem:

Intercepted Arc ADB - Intercepted Arc AEC = Intercepted Angle B - Intercepted Angle C

16 - 12 = Angle B - Angle C

4 = Angle B - Angle C.

Since Angle B and Angle C are vertical angles, they are congruent:

Angle B = Angle C.

Therefore, we can say:

4 = Angle B - Angle B

4 = 0

However, we have reached an inconsistency here.

The equation does not hold true, indicating that the given information is not consistent or there may be an error in the problem statement.

As a result, we cannot determine the length of BD based on the given information.

For similar question on length.

https://brainly.com/question/30582409  

#SPJ8

The value of x is 63

To determine the value of the variable, we have that;

From the information given, we have that;

x and x - 36 are complementary angles

Now, equate the angles to 90 degrees, we have;

x + x - 36= 90

collect the like terms, we get;

2x = 90 + 36

add the terms

2x =1 26

Divide by the coefficient

x = 63

Learn more about angles at: https://brainly.com/question/25716982

#SPJ1

Complete question:

The angles X,(x-36)  are complementary. What is the value of x

Answer:

Step-by-step explanation:

-3x + 4y = 12

12(1/4x - 1/3y = 1)

-3x + 4y = 12

 3x - 4y = 12

there is no solution

Answer:

D) 21

Step-by-step explanation:

the sum of the two shorter sides must be greater than the longer side of a triangle