Solve the system by using substitution

Answer:

x=30 degrees

Step-by-step explanation:

there are 3theorems that can be used for this

vertical angle theorem: vertical angles congruent

triangle sum theorem: all angles in triangle add up to 180 degrees

straight line?? i forgot the name: a straight line is 180 degrees

refer to image attached

measure of angle BAC is 36 degrees by vertical angle theorem.

look at the angle 105 degrees. it and a unknown degree to the left equal 180 because it makes a straight line. so measure of angle BDC is 180-105 degrees. measure of angle BDC is 75 degrees

then sum of all the angles in triangle ABD is 180

36 +(39+x) +75=180 degrees

solve equation

x +150=180

x=30 degrees

hope this helps !!

Answer:

4 x  +  3 y  +  9  =  0

Step-by-step explanation:

Answer:

equation of the line is

y =3/4 x+15

Step-by-step explanation:

Equation of a line is

y = mx+ b

to find m = y2-y1/ x2-x1

=0-3/ -8-(-4)

=-3/-4 =3/4

if the line is passing through (-4,3) the intercept b is

y= mx+b

3= 3*(-4) +b

b= 15

y =3/4 x+15

We can check this by plugging in the other points (-8,0).

y = 3/4x + 6

0 = 3/4(-8) + 6

0 = -6 + 6

0 = 0

which means our equation is correct.

Answer:

-498

Step-by-step explanation:

Using BODMAS:

6+4×(18+(-32))×(7-(-2))​

6+4×(-14)×(9)

6+4×-126

= -498

Answer:

(3,0)

Step-by-step explanation:

You want the x-intercept so you have to find the values until the x value is 0 or above. If you put the points into a chart it will look like this:

x   l   y  

-21 l -64             You add 6 to each x value to get the next value. -15+6=-9

-15 l -48             You add 16 to each y value to get the next value. -48+16=-32

-9  l -32              -9+6=-3         -32+16=-16  

-3  l -16               -3+6=3          -16+16=0

3  l  0

The answer is (3,0). I got it right on Khan Academy.

Answer:

(x+4)

Step-by-step explanation:

Since area is width times length, you can just factor the area to get the width and length

You factor to get (x+4)(x+7)

Since (x+7) is the length, (x+4) must be the width

Answer:

(x + 4) m

Step-by-step explanation:

\(Area \: of \: rectangle = length \times width \\ \\ width = \frac{Area \: of \: rectangle}{length} \\ \\ = \frac{ {x}^{2} + 11x + 28 }{x + 7} \\ \\ = \frac{ {x}^{2} + 7x + 4x + 28}{x + 7} \\ \\ = \frac{ x({x} + 7) + 4(x + 7)}{x + 7} \\ \\ = \frac{ ({x} + 7) (x + 4)}{x + 7} \\ \\ = (x + 4) \: m \\ \\ \red{ \boxed{\bold {\therefore \: width \: = (x + 4) \: m}}} \)

Answer:

118.7 inches squared.

Step-by-step explanation:

The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.

Diameter is the length across the entire circle, the line splitting the circle into two identical semicircles.

The expression for solving the area of a circle is A = π × \(r^{2}\).

To solve for the semicircle above, we can divide the diameter into 2 to get the radius.

So, the radius of the upper semicircle is 6 inches.

If the radius of a circle is 6 inches, then you can substitute r for 6 into the formula.

This simplifies to A = 36π. If a semicircle if half the size of a normal circle, then it will be A = 18π, because 36 ÷ 2 = 18.

To solve for the lower semicircle, we can do the same this as we did above.

But wait, we don't know the radius or diameter!

No worries! To solve for the diameter of the circle, we can take the line that is parallel to the semicircle (the one that has a length of 12in) and subtract 6 from it. We subtract 6 from it because the semicircle takes up the remaining length of the line, not including the 6in.

To solve for the lower semicircle, we can divide the diameter by 2 to get the radius.

So, the radius of the circle is 3.

Now we can insert 3 into the expression.

This simplifies to A = 9π. If a semicircle if half the size of a normal circle, then it will be A = 4.5π because like above, 9 ÷ 2 = 4.5.

Adding the two semicircles together:

So, the area of both semicircles is approximately 70.6858 square inches.

To solve for the area of a rectangle we use the expression:

Inserting the dimensions of the rectangle:

So, the area of the rectangle is 48 square inches.

Adding the two areas together:

Therefore, the area of the entire figure, rounded to the nearest tenth is \(118.7\) \(in^{2}\).

Answer:

the anwer is b

I did the math

Answer: sqrt(182)

Step-by-step explanation:

Answer:

C) 3y -2x= -5

Step-by-step explanation:

(1,1), (4,3)

slope= y2-y1/ x2-x1

slope= 3-1/4-1= 2/3

(4,1)

Substitute into y=mx+b

1= 4(2/3)+b

1= (8/3) +b

-5/3= b

3(y= 2/3x -5/3)

3y= 2x -5

3y -2x= -5

Answer:

a quadratic function

Step-by-step explanation:

A quadratic function is a second-degree polynomialfunction, and when graphed is called a parabola.

Answer:

see explanation

Step-by-step explanation:

5 : 15 ( divide both parts by 5 )

= 1 : 3

3 : 9 ( divide both parts by 3 )

= 1 : 3

9 : 3 ( divide both parts by 9 )

= 1 : \(\frac{1}{3}\)

25 Kg : 100 Kg ( divide both parts by 25 Kg )

= 1 : 4

Answer: There are 0.4 ounces left in the can.

Step-by-step explanation:

The data we have is:

Chester weighs 6.8 pounds.

Chester can eat 3/4 of an ounce for each pound of body weight.

Then Chester can eat 6.8 times 3/4 of an ounce:

6.8*(3/4) ounces = 5.1 ounces

Then Chester should eat 5.1 ounces of canned food.

If the can has 5.5 ounces, then the amount that will be left in the can is:

5.5 oz - 5.1 oz = 0.4 oz

There are 0.4 ounces left in the can.

the average radiation pressure on an ideal reflector due to an EM wave whose rms magnetic field strength is 0.050 m is 0.000079 N/m². The radiation pressure on an ideal reflector due to an EM wave with an rms magnetic field strength of 0.050 m is 0.000079 N/m².

The average radiation pressure on an ideal reflector due to an EM wave whose rms magnetic field strength is 0.050 m is 0.000079 N/m².Main Answer:The average radiation pressure on an ideal reflector due to an EM wave whose rms magnetic field strength is 0.050 m is 0.000079 N/m².

Given parameters: Magnetic field strength, B = 0.050 m Also, the formula for the radiation pressure is given by: P = (2E/c) Where, E = Electric field strength c = Speed of light So, the electric field strength is given as E = Bc

The magnetic field strength is given as B = 0.050 m Speed of light, c = 3 × 10⁸ m/s Putting values in E = Bc; E = 0.050 × 3 × 10⁸ = 15 × 10⁶ V/m Therefore, the radiation pressure is given by: P = (2E/c) = (2 × 15 × 10⁶) / (3 × 10⁸) = 0.0001 N/m² = 0.000079 N/m²

An electromagnetic wave comprises an oscillating magnetic field and an oscillating electric field that travel perpendicular to each other and perpendicular to the direction of the wave's movement.

The formula for calculating the radiation pressure is given by the formula P = (2E/c). P represents radiation pressure, E represents Electric field strength and c represents the speed of light.

In the given question, the magnetic field strength is given as B = 0.050 m.

Using E = Bc, we have E = 0.050 × 3 × 10⁸ = 15 × 10⁶ V/m.
Substituting the value of E in the formula P = (2E/c) gives P = (2 × 15 × 10⁶) / (3 × 10⁸) = 0.0001 N/m² = 0.000079 N/m².

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Answer:

\(x = [2644,8418)\)

Step-by-step explanation:

Given

\(f(x) = 86.3ln\ x - 680\)

\(x < 8418\)

Required

The domain of the function

The maximum value of x has been given.

So, the next step is to calculate its minimum value.

Since f(x) represents the % moisture. This value cannot go less than 0.

So, we set f(x) to 0; in order to calculate the minimum of x.

This gives:

\(f(x) = 0\)

\(86.3ln\ x - 680 = 0\)

Add 680 to both sides

\(86.3ln\ x - 680 + 680= 0 + 680\)

\(86.3ln\ x = 680\)

Divide both sides by 86.3

\(ln\ x = \frac{680}{86.3}\)

\(ln\ x = 7.88\)

Take exponent of both sides

\(e^{(ln\ x)} = e^{7.88\)

\(x = e^{7.88\)

\(x = 2644\)

Hence, the domain is:

\(x = [2644,8418)\)

or

\(2644 \le x< 8418\)

Using the range to compare the variability of data sets is a rather insensitive measure of data variance is the correct answer.

In this question,

The range tells you the spread of your data from the lowest to the highest value in the distribution. The range is the difference between the smallest and highest numbers in a list or set. To find the range, first put all the numbers in order. Then subtract (take away) the lowest number from the highest.

Data variability also known as spread or dispersion, refers to how spread out a set of data is. Variability gives users a way to describe how much data sets vary and allows users to use statistics to compare their data to other sets of data.

Thus the disadvantage of using range is that it does not measure the spread of the majority of values in a data set, it only measures the spread between highest and lowest values.  

The options are a) It is a rather insensitive measure of data variance, b) It is hard to compute, c) It is a sensitive measure of data variance, d) It does not have any variance.

Hence we can conclude that using the range to compare the variability of data sets is a rather insensitive measure of data variance.

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The answer to this question is c.The use of a correlation coefficient.

The use of a correlation coefficient would tell you that an association claim is being made in a research study. A correlation coefficient is a statistical measure that shows the strength and direction of a relationship between two variables. It ranges from -1 to 1, with 0 indicating no relationship and -1 or 1 indicating a perfect negative or positive relationship, respectively.

A scatterplot or bar graph may be used to visually display the relationship between two variables, but they do not necessarily indicate that an association claim is being made. The measurement of two variables is necessary for any type of research study, but it does not inherently imply that an association claim is being made.

Interrogation of internal validity is a process used to ensure that the study's results accurately reflect the relationship between the variables being studied. It is important for any research study but does not specifically indicate that an association claim is being made.

Therefore,the answer to this question is c.The use of a correlation coefficient.

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Answer:

The numbers are 37, 39 and 41.

Step-by-step explanation:

Let the smallest number be \(x\\\).

Then the other numbers will be \(x+2, x+4\) (as they are consecutive odd numbers, their difference will be 2).

As per the given statement:

LHS(Left Hand Side) : Sum of five times the smaller number and twice the larger number.

i.e. five times the smaller number = \(5\times x\)

twice the larger number = \(2 \times (x+4)\)

Their sum:

The Left Hand Side becomes:

\(5x+2(x+4)\)

RHS(Right Hand Side):

33 more than six times the median number:

i.e. \(6\times(x+2) +33\)

Equating LHS and RHS:

\(5x+2(x+4) = 6x+12 +33\\\Rightarrow 7x+8=6x+47\\\Rightarrow \bold{x =37}\)

Therefore, the numbers are 37, 39 and 41.

The correct option is option (A) . Using Scatter plots,

Visulazation by scatter plots show the association and the distribution of Y changes as X changes.

Scatter plots:

A scatterplot plots pairs of numeric data using one variable on each axis to explore the relationship between them. If the variables are correlated, the points are along a straight line or curve.

A correlation exists between two variables if one of them is related to the other in some way. A scatterplot is a great place to start. A scatterplot (or scatterplot) is a graph of paired (x,y) sample data with a horizontal x-axis and a vertical y-axis. Each unique (x,y) pair is represented as one point.

Thus, the Visual examination of a scattergram indicates the existence of an association between variables and change in Y with change in X .

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Answer:

Chart:

x           y

-6         11

3           5

15         -3

-12        15

Step-by-step explanation:

The only things you can plug in are the domain {-12, -6, 3, 15}

Plug in the domain into equation to find y.

-6 :

y = -2/3 (-6) +7

y = +47

y=11

(-6,11)

3:

y = -2/3 (3) +7

y = -2 +7

y = 5

(3, 5)

15:

y = -2/3 (15) +7

y =  -10 +7

y = -3

(15 , -3)

-12:

y = -2/3 (-12) +7

y = 8 + 7

y= 15

(-12,15)

Answer:

1) 11

2) 3

3) -3

4) -12

Step-by-step explanation:

eq(1):

\(y = \frac{-2}{3} x + 7\\\\y - 7 = \frac{-2}{3} x\\\\x = (y - 7)\frac{-3}{2} \\\\x = (7-y)\frac{3}{2} ---eq(2)\)

1) x = -6

sub in eq(1)

\(y = \frac{-2}{3} (-6) + 7\\\\y = \frac{12}{3} + 7\\\\y = 4+7\\\\y = 11\)

2) y = 5

sub in eq(2)

\(x = (7-5)\frac{3}{2} \\\\x = 3\)

3) x = 15

sub in eq(1)

\(y = \frac{-2}{3} 15 + 7\\\\y = \frac{-30}{3} +7\\\\y = -10 + 7\\\\y = -3\)

4)

sub in eq(2)

\(x = (7-15)\frac{3}{2} \\\\x = -8\frac{3}{2}\\ \\x = -12\)

Vertex Vertex Vertex

Answer:

An angle can be formed when two rays meet at a common point. The rays are the sides of the angle. The point of the end of two rays is called the vertex.

Step-by-step explanation:

The given information provides a square thin plane lamina with side length 4 cm, which is earthed along three sides.

(i) Deriving expressions for the potential and electric field strength:

Electric Field Strength (E):

E = -∇V, where ∇ represents the gradient operator and V(x, y) = sin(πx/2a)sin(πy/2a).

Now, let's calculate the components of the electric field E using the partial derivatives:

E = -(∂V/∂x)î - (∂V/∂y)ĵ

= -[(πcos(πx/2a))/2a]î - [(πcos(πy/2a))/2a]ĵ

= -(π/2a)cos(πx/2a)î - (π/2a)cos(πy/2a)ĵ.

(ii) Calculating the values at the center of the plate:

Voltage at the center of the square:

V(x, y) = sin(πx/2a)sin(πy/2a)

V(0.02, 0.02) = sin(π/4)sin(π/4) = 0.5V.

Vector E field at the center of the square:

E = -(π/2a)cos(πx/2a)î - (π/2a)cos(πy/2a)ĵ

E(0.02, 0.02) = -(π/2(0.04))cos(π/4)î - (π/2(0.04))cos(π/4)ĵ

= -19.63î - 19.63ĵ V/m.

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\( {n}^{2} - 11n + 10 = \)

\((n - 1)(n - 10)\)

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

Answer:

x = 10.8

Step-by-step explanation:

9 ÷ x = x ÷ (9 + 4)

9 × (9 + 4) = x × x

9 × 13 = x²

117 = x²

x = 10.81665383

In a regression analysis, the error term ε is a random variable with a mean or expected value of zero. The correct option is a.

The average of a group of variables is referred to as the mean in mathematics and statistics. There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.

Given:

Analysis is a regression analysis.

And the error term in regression analysis:

The error term, which refers to the total of the deviations within the regression line and explains the discrepancy between the theoretical value of the model and the actual observed results, denotes the margin of error inside a statistical model.

ε = Epsilon or error term.

The variation in the dependent variable that the independent factors do not explain is taken into account by the error term.

The values of the error term should be determined by random chance.

The average value of the error term must be equal to zero in order for your model to be impartial.

Therefore, error term is zero.

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Answer:

6.4

Step-by-step explanation:

70.4/11

= 6.4

Answer:

b)

x= 5

Step-by-step explanation:

4x = 20

:4

x=5

Throwing a coin until it lands tails is an example of a discrete random variable which does not have a finite expectation.

For the given question,

A discrete random variable is a type of variable whose value depends upon the numerical outcomes of a certain random phenomenon. Discrete random variables are always whole numbers, which are easily countable.

It is a variable that can take on a finite number of distinct values and takes numerous values. It is also known as a stochastic variable. When you consider probabilistic experiments with infinite outcomes, it is easy to find random variables with an infinite expected value.

Let X be a random variable that is equal to 2ⁿ with probability 2⁻ⁿ (for positive integer n). Then,

\(E(X)=\sum_{n:1}^{\infty} |2^{-n}2^{n}|\)

⇒ \(E(X)=\sum_{n:1}^{\infty} (1)\)

⇒ \(E(X)=\infty\)

Consider the following example,

You throw a coin until it lands tails.

Let n be the number of heads

Then number of heads can be found by, 2ⁿ

Now, the expected value function is

\(E(X)=\frac{1}{2}(2^{0} )+ \frac{1}{4}(2^{1} )+....\)

⇒ \(E(X)=\sum_{n:1}^{\infty} |2^{-n}2^{n-1}|\)

⇒ \(E(X)=\sum_{n:1}^{\infty} \frac{1}{2}\)

⇒ \(E(X)=\infty\)

Since the number of outcomes is infinite. The probability of each outcome decreases exponentially.

Hence we can conclude that throwing a coin until it lands tails is an example of a discrete random variable which does not have a finite expectation.

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-3(X - 4) = – 3x + 12 infinite solutions

4(x + 1) = 3x + 4 one solution

-2(x-3) = 2x - 6 one solution

6(x + 5) = 6x + 11 no solution

5(x-2)=5x-7 no solution

Answer:

The equation in the slope-intercept form is

y = -5x - 41

Step-by-step explanation:

The given equation in the question is;

y = -5x + 2

The equation of a straight line graph can be written in the form;

y = mx + c

where m is the slope and c is the intercept

From here, we can see that the slope m is -5

Since the line is parallel to the new line we are trying to write its equation, it means that they have the same value of intercept.

Hence, the slope of the new line is also -5

Now, we can write the equation of the new line as;

y = -5x + c

we need to get the value of c here however

To get the value of c, we need to input the value of x and y

From the graph, x = -7 and y = -6

Substituting these values, we have;

-6 = -5(-7) + c

-6 = 35 + c

c = -6 -35

c = -41

So the equation of the new line will be;

y = -5x - 41

The equivalent equation to represents the lateral area for 'r' as radius of the base and 's' as the slant height of the cone are given by  LA/r = s and LA/s = r.

The formula for the lateral area of a right cone is LA = rs,

where r is the radius of the base and s is the slant height of the cone.

To find the equivalent equations,  manipulate the given formula.

Dividing both sides of the equation by r, we get,

LA/r = s

Multiplying both sides of the equation by r, we obtain,

LA = rs

These two equations are equivalent.

The first equation (LA/r = s) expresses the slant height of the cone in terms of the lateral area and the radius,

while the second equation (LA = rs) directly relates the lateral area to the radius and slant height.

Therefore, equivalent equation to represents the lateral area are LA/r = s and LA/s = r.

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The above question is incomplete, the complete question is:

The formula for the lateral area of a right cone is LA = rs, where r is the radius of the base and s is the slant height of the cone. Which are equivalent equations?