Simplify
2a - 5 + 3a + 4

Answer:

Exact Form:  x  =  1 /15

Decimal Form:  x  =  0.0 6

Answer:

yes

Step-by-step explanation:

4 x 15 - 20 = 40

60 - 20 = 40

Answer:

Gain= $93.01

ROI= 212.59%

Step-by-step explanation:

Given data

Cost of apple share in 2018 = $43.75

Sale price of apple share= $136.76

1. Her gain is

Gain= Sales price- Cost price

Gain = 136.76-43.75

Gain= $93.01

2. ROI is

ROI= Gain/cost*100

ROI= 93.01/43.75*100

ROI=2.1259*100

ROI= 212.59%

The equation for the plane tangent to each surface - -10x + 6y + z - 5 = 0

What is Plane Tangent?

a tangent is a line that touches a curve at exactly one point without intersecting it. Similarly, a plane tangent is a plane that touches a surface at only one point without intersecting it further. This concept is commonly used in calculus and differential geometry to study the behavior of curves and surfaces.

We usually use partial derivatives of the equation of the surface to find the equation of the plane tangent to the surface at a point. The normal vector to the surface at that point is obtained by taking the cross product of the partial derivatives evaluated at that point. Then, using the coordinates of the point and the normal vector, we can determine the equation of the plane using the point-normal form or the general form of the plane equation.

It is important to note that the tangent plane equation depends on the specific point on the surface where the tangent plane is desired. Different points on the surface will have different tangent planes associated with them.

To find the equation for the plane tangent to the surface z = f(x, y) at a point (a, b, c), we need to use the partial derivatives of f with respect to x and y at the point (a, b) to find the normal vector to the plane.

Then we can use the point-normal form of the equation of a plane to write the equation.

First, we need to find the partial derivatives of f(x, y) = x^2 + y^3 - 6xy with respect to x and y:

fx = 2x - 6y

fy = 3y^2 - 6x

Then we can evaluate these partial derivatives at the point (1, 2) to get the normal vector:

n = <fx(1, 2), fy(1, 2)> = <2(1) - 6(2), 3(2)^2 - 6(1)> = <-10, 6>

So the equation of the plane tangent to the surface z = f(x, y) = x^2 + y^3 - 6xy at the point (1, 2, 3) is:

-10(x - 1) + 6(y - 2) + (z - 3) = 0

Simplifying, we get:

-10x + 6y + z - 5 = 0

So the equation of the plane tangent to the surface z = x^2 + y^3 - 6xy at the point (1, 2, 3) is -10x + 6y + z - 5 = 0

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Answer:

supplementary angles

Step-by-step explanation:

they are on the same line, so they sum up to 180°

Answer:

17

Step-by-step explanation:

Simply plug x=3 into the equation f(x):

f(x) = 5(3)+2

f(x) = 15+2

f(x) = 17

Answer:

okay well all i can explain is the image on the far left, the answer would be x=112 and then for the one on the far right (im not sure ) i think its 17

explanation: so a straight line had 180 degress and the outside angle is 126 meaning that if you do 180-126 you can find the amount of the inside angle on the bottom right. When you do this you get 54 degress. Then remember that a triangle has a total of 180 degrees all added up so the final angle inside the triagle is 80 minus the sum of the other two angles. 58+54=112 and 180-112=68. remember that 68 is the angle on the INSIDE and x is clearly on the outside meaning that you would need to do 180-68. your final answer would be 112. (and im really sorry i couldn't answer the other ones they're too blurry  :(

Answer:

speed=distance / time

speed=(4/3) / (1/10)

speed=13.33miles per hour

Answer:

124250cm, 1242.5m or 1.2425km

Step-by-step explanation:

0.6% = 6/100

6/100 = 0.006

0.006*1.25 = 0.0075

1.25km = 1250m = 125000cm

0.0075km = 7.5m = 750cm

125000 - 750 = 124250

Therefore:

The answer is 124250cm, 1242.5m or 1.2425km

Sub to oTechz :)

Answer:

The chord is drawn below

Step-by-step explanation:

In a normal population with a mean (μ) of 10 and a standard deviation (σ) of 7, we are asked to calculate probabilities for different scenarios.

(a) To find the proportion of the population less than 18, we need to calculate the cumulative probability up to that value using the standard normal distribution. By standardizing the value of 18 and looking up its corresponding cumulative probability in the standard normal distribution table, we can determine the proportion.

(b) For the probability that a randomly chosen value will be greater than 3, we again need to standardize the value of 3 and find its corresponding cumulative probability in the standard normal distribution table. Since we are looking for values greater than 3, we subtract the cumulative probability from 1 to obtain the probability.

Using the mean and standard deviation provided, along with the standard normal distribution, we can calculate the desired probabilities by finding the corresponding cumulative probabilities and rounding the answers to four decimal places.

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Answer:

0.0312

Step-by-step explanation:

You subtract 29.12 by 26 which equals 3.12

Then you divide by 100 which equals 0.0312

Answer:

12

Step-by-step explanation:

The interest cost and the total amount due on a six month loan is  $1500 and total amount due is $1599

SI is equal to 100. r = 10% T=6 months, or 6/12 years.

Idea employed: SI = Prt/100. Interest rate in principle.

Calculation: P = (100 100 12)/(10 6) 100

= (P 10 6)/(12 100)

P = 2000.

For instance, if your current APR is 17.99% and you currently owe $500 on your credit card over the course of the month, you can get your monthly interest rate by dividing 17.99% by 12, which is roughly 1.49%. Then multiply $500 by 0.0149 to get a monthly payment of $7.45.

annual interest = $1,599

 full amount due = ($1,500 + $99).

= $1599

Hence we get the required  answers.

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Answer:

-2

Step-by-step explanation:

Let f(x)=y.

\(x=6y+12 \\ \\ x-12=6y \\ \\ y=f^{-1}(x)=\frac{x}{6}-2\)

By considering the given information that angles 21 and 23 are supplementary and analyzing the properties of supplementary angles and parallel lines, we have proven that segment HI is parallel to segment JK.

To prove that segment HI is parallel to segment JK based on the given information that angles 21 and 23 are supplementary, we can utilize the properties of supplementary angles and parallel lines.

First, let's examine the given figure and information.

We have a capital letter A with serifs, where segment HI represents one of the serifs, and segment JK represents a horizontal line within the letter A.

To begin the proof, we'll make use of the fact that angles 21 and 23 are supplementary.

Supplementary angles are defined as two angles whose measures sum up to 180 degrees.

We can observe that angle 21 is an interior angle of triangle AHI, and angle 23 is an interior angle of triangle AJK.

Since angles 21 and 23 are supplementary, their sum is equal to 180 degrees.

Now, let's assume that segments HI and JK are not parallel.

In this case, if we extend lines HA and JA, they will eventually intersect at point P.

Since the angles formed at the point of intersection are supplementary (angle 21 + angle 23 = 180 degrees), it would imply that angle 21 and angle PJK, as well as angle 23 and angle PHI, are also supplementary.

However, this leads to a contradiction. In the original figure, we can observe that angle 21 and angle PJK do not form a supplementary pair since angle PJK is a right angle (90 degrees) in the letter A.

Therefore, our assumption that segments HI and JK are not parallel must be incorrect.

Consequently, we can conclude that segment HI is indeed parallel to segment JK.

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The first five terms of the sequence are 27, 22, 17, 12, and 7.

To find the first five terms of the sequence given by a₁=27 and d=-5,

we can use the formula for the nth term of an arithmetic sequence:

\(a_n=a_1+(n-1)d\)

Substituting the given values, we have:

\(a_n=27+(n-1)(-5)\)

Now, we can calculate the first five terms of the sequence by substituting the values of n from 1 to 5:

\(a_1=27+(1-1)(-5)=27\)

\(a_1=27+(2-1)(-5)=22\)

\(a_1=27+(3-1)(-5)=17\)

\(a_1=27+(4-1)(-5)=12\)

\(a_1=27+(5-1)(-5)=7\)

Therefore, the first five terms of the sequence are 27, 22, 17, 12, and 7.

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Answer:

The answer is B,C,D and E

The points that show the proportionality rate 1/3 are (3, 1), (9, 3), (12, 4) and (18, 6).

A proportional relationship is a relationship between two expressions and where changes in one expression means some constant change in the other expression as well. Generally, it is represented as x/y = k, where x and y are two expressions and k is constant.

We have constant of proportionality is 1/3.

And the proportionality is represented as x/y = k, where x and y are two expressions and k is constant.

So, x / y = 1/3

A) (5,8)

x/y = 5/8 ≠ 1/3

B) (3,1)

x/y = 1/3

C) (9,3)

x/y = 3/9 = 1/3

D) (12,4)

x/y = 4/12 = 1/3

E) (18,6)

x/y = 6/18 = 1/3

Therefore, B, C, D and E are the answers.

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Answer:

6(9+7)

Step-by-step explanation:

SEE THE IMAGE FOR SOLUTION

HOPE IT HELPS

HAVE A GREAT DAY

A circle can be defined as a geometric shape consisting of all points in a plane that are equidistant from a given point, which is known as the center. The distance between the center of the circle and any point on the circle is referred to as the radius.

In order to find the center and radius of a circle, we need to have three points on the circle's circumference, and then we can use algebraic formulas to solve for the center and radius. Let's look at the given problem to find the center and radius of the circle that passes through the points (-1,5), (5,-3), and (6,4).

Center of the circle can be determined using the formula:

(x,y)=(−x1−x2−x3/3,−y1−y2−y3/3)(x,y)=(−x1−x2−x3/3,−y1−y2−y3/3)

Let's plug in the values of the given points and simplify:

(x,y)=(−(−1)−5−6/3,−5+3+4/3)=(2,2/3)

Next, we need to find the radius of the circle. We can use the distance formula to find the distance between any of the three given points and the center of the circle:

Distance between (-1,5) and (2,2/3) =√(x2−x1)2+(y2−y1)2=(2+1)2+(2/3−5)2=√10.111

Distance between (5,-3) and (2,2/3) =√(x2−x1)2+(y2−y1)2=(5−2)2+(−3−2/3)2=√42.222

Distance between (6,4) and (2,2/3) =√(x2−x1)2+(y2−y1)2=(6−2)2+(4−2/3)2=√33.361

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Metric System is a decimal system of measurement that is based on the meter, kilogram, and second and is used in most countries around the world. It is also known as the International System of Units (SI).

The Metric System is the most common measuring system used in the world today. It is a decimal system based on the meter, kilogram, and second and is officially known as the International System of Units (SI). This system was initially developed in France in the late 18th century and is now used in most countries around the world. The Metric System is based on powers of 10 and each unit is related to the next unit by a factor of 10. For example, a kilometer is equal to 1000 meters, a milliliter is equal to 0.001 liters, and a centimeter is equal to 0.01 meters. The Metric System is used to measure length, area, mass, weight, temperature, and volume. It is used in many different industries and applications including science, engineering, medicine, and agriculture. The Metric System has become the international standard for scientific measurements and is accepted by most countries as the preferred system of measurement. The Metric System is also easier for students to learn and use than other systems of measurement.

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The inverse of the given matrix is not defined.

To find the inverse of a matrix, we need to check if the matrix is invertible or non-singular. For a square matrix to be invertible, its determinant must be non-zero.

Let's calculate the determinant of the given matrix:

Det(Matrix) = (1 * 0 * 2) + (2 * 2 * 1) + (1 * 3 * 8) - (2 * 0 * 1) - (1 * 2 * 8) - (1 * 3 * 0)

= 0 + 4 + 24 - 0 - 16 - 0

= 12

Since the determinant of the given matrix is non-zero (12 ≠ 0), it implies that the matrix is invertible.

Next, we can proceed to find the inverse of the matrix by using the formula:

Matrix^(-1) = (1/Det(Matrix)) * Adjoint(Matrix)

However, before calculating the adjoint of the matrix, let's check for any possible errors in the matrix elements. The elements of the matrix you provided are not consistent, and it seems there might be a mistake. The matrix you provided (121, 302, 182) does not conform to the standard 3x3 matrix format.

In conclusion, based on the given matrix, the inverse is not defined. Please make sure to provide a properly formatted 3x3 matrix to find its inverse.

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Answer: $13.5

Step-by-step explanation:

1. 15 x 10 =150

2. 150/100=1.5

3. 15.00 - 1.50= 13.5

Answer:

cosC = \(\frac{7}{25}\)

Step-by-step explanation:

cosC = \(\frac{adjacent}{hypotenuse}\) = \(\frac{BC}{AB}\) = \(\frac{7}{25}\)

Answer: - 1°F

Step-by-step explanation:

Given that:

At 8a.m:

Temperature = 3°F below 0

By 1p.m ; Temperature rose by 14F ;

By 10pm ; temperature dropped by 12F

Temperature at 10 pm:

3°F below 0 = - 3°F

Temperature at 1pm: temperature increased by 14°F

-3°F + 14°F = 11°F

Temperature at 10pm: temperature dropped by 12°F

11°F - 12 = - 1°F

The amount produced is the independent variable and the number of truckers is the dependent variable. So, option 2 is the correct answer.

Independent variables are those variables that do not require any other quantity/variable in order to determine their value. On the other hand, dependent variables do require another such variable.

In the given problem, the amount of product does not depend on any other factor. This means it is independent of any other variable. Meanwhile, the number of truckers depends on the amount produced. This makes it the dependent variable. So, option 2 is the answer here.

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(9) The exact value of the cosine ratio for the given point is approximately 0.39.

(10) The measure of the principal angle to the nearest tenth of radians for the given point is approximately 3.7 radians.

Question 9:

The point P(3.00,−7.00) is on the terminal arm of an angle in standard position. To determine the exact values of the cosine ratio, we need to find the value of the adjacent side and hypotenuse. The distance between the origin and P can be found using the Pythagorean theorem: √(3^2 + (-7)^2) = √58. Therefore, the hypotenuse is √58. The x-coordinate of P represents the adjacent side, which is 3. The cosine ratio can be found by dividing the adjacent side by the hypotenuse: cosθ = 3/√58 ≈ 0.39.

Therefore, the exact value of the cosine ratio for the given point is approximately 0.39.

Question 10:

The point P(−9.00,−5.00) is on the terminal arm of an angle in standard position. To determine the measure of the principal angle, we need to find the reference angle. The reference angle can be found by taking the inverse tangent of the absolute value of the y-coordinate over the absolute value of the x-coordinate: tan⁻¹(|-5/-9|) ≈ 0.54 radians. Since the point is in the third quadrant, we need to add π radians to the reference angle to get the principal angle: π + 0.54 ≈ 3.69 radians.

Therefore, the measure of the principal angle to the nearest tenth of radians for the given point is approximately 3.7 radians.

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The height of the tower is  144 feet

The tangent of an angle is a trigonometric function that relates the ratio of the length of the side opposite to the angle and the length of the adjacent side in a right triangle. In other words, the tangent of an angle is the ratio of the opposite side to the adjacent side of a right triangle. It is denoted by the symbol "tan" and can be expressed mathematically as:

tan(θ) = opposite / adjacent

Tan 30 = H/250

H = 250 Tan 30

H = 144 feet

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