Calculate the area of triangle abc with altitude bd, given a (-6,0) b (0,0) c (o,6) and d (3,-3)

For f(x) we have:

And for g(x):

The domain of a function is the set of inputs that we can use on the function, and the range is the set of outputs.

a) f(x) = -2x

This is just a linear equation, as you can see, for no value of x we have a problem, then the domain is the set of all real numbers.

Similar for the range, it covers the set of all real numbers, then:

b) g(x) = 0.5*x² + 5

This is a quadratic function, so the domain is the set of all real numbers again.

Now the range will have a minimum, which is at the vertex of the parabola.

For the parabola the vertex is at x = 0:

g(0) = 0.5*0² + 5 = 5

Then the range is the set of all real numbers equal to or larger than 5.

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Answer:

4 is the smallest possible number of integers in the list.

Answer:

Step by Step Solution

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Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

c-((4+w)/(w+3))=0

STEP

1

:

4 + w

Simplify —————

w + 3

Equation at the end of step

1

:

(w + 4)

c - ——————— = 0

w + 3

STEP

2

:

Rewriting the whole as an Equivalent Fraction

2.1 Subtracting a fraction from a whole

Rewrite the whole as a fraction using (w+3) as the denominator :

c c • (w + 3)

c = — = ———————————

1 (w + 3)

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2 Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

c • (w+3) - ((w+4)) cw + 3c - w - 4

——————————————————— = ———————————————

1 • (w+3) 1 • (w + 3)

Equation at the end of step

2

:

cw + 3c - w - 4

——————————————— = 0

w + 3

STEP

3

:

When a fraction equals zero :

3.1 When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

cw+3c-w-4

————————— • w+3 = 0 • w+3

(w+3)

Now, on the left hand side, the w+3 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

cw+3c-w-4 = 0

Solving a Single Variable Equation:

3.2 Solve cw+3cw-4 = 0

In this type of equations, having more than one variable (unknown), you have to specify for which variable you want the equation solved.

We shall not handle this type of equations at this time.

Answer:

w = (4 - 3C)/(C - 1).

Step-by-step explanation:

C=(4+w)/(w+3)

Multiply both sides of the formula by  w+3:-

C(w + 3) = 4 + w

Cw + 3C = 4 + w

Cw - w = 4 - 3C

w(C - 1) = 4 - 3C

w = (4 - 3C)/(C - 1).

Answer:

A

Step-by-step explanation:

By using greatest common factor you are able to take a 2 out of all the numbers

Second time john wins the race because he runs in the race with constant speed as same speed they run in 1st race.

According to the statement

We have given that the John and Peter, are running a 100-meter race.

In the first race that they run John beats Peter by 5 meters. and the next time they race John stands 5 meters behind the starting line.

Here the both participant's speed remain same in both races.

So, We have to find that the If they run at the constant speed as the first race, who will win the second race

So, for this purpose

According to the statement

in first race john beats the peter and wins the race and if they start the second race with the same speed then it is clear that the second time john won the race.

So, Second time john wins the race because he runs in the race with constant speed as same speed they run in 1st race.

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The measure of angle D in the inscribed triangle is as follows;

∠D = 63 degrees

The circle theorem can be use to find the ∠D as follows;

The triangle BCD is inscribed in the circle.

Using circle theorem,

The angle of each triangle is double the angle of the arc it create.

Therefore,

arc BC = m∠D

m∠B = 134 / 2 = 67 degrees.

Therefore, using sum of angles in a triangle.

67 + 50 + m∠D = 180

m∠D = 180 - 50 - 67

m∠D = 63 degrees.

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Answer: D

Step-by-step explanation:

As the circumference of a circle is 360 degrees, this means arc BC is 64 degrees.

So, we can conclude that arc AB measures 180-64=116 degrees.

Thus, angle AOB is also 116 degrees.

Answer:

D) 116°

Step-by-step explanation:

If arcBAC measure 296°,

And arcAC measure 180°,

You can get arcAB measure 116°,

Because the arc equals the measure of the central angle,

<AOB=116°

Hope this helps <3

Answer:

-1/2

Step-by-step explanation:

cos(x+pi) = -cos(x), so the answer is -1/2.

Answer: -9/4.

The slope formula of the line passing through the points

The results of the survey best illustrate the framing effect.

People make choices based on whether possibilities are given with positive or negative connotations, such as as a gain or a loss, according to a cognitive bias known as the framing effect.

When provided with a positive frame, people tend to avoid danger, but when offered with a negative frame, they tend to seek out hazards.

The scenario of framing effect defines gain and loss as descriptions of results.

The idea aids in the development of framing effect understanding in social movements as well as in the creation of political opinion, where spin plays a significant role in political opinion polls that are framed to encourage a response advantageous to the group that commissioned the poll. It has been asserted that the framing effect is invalidating political polls.

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Answer:

Step-by-step explanation:

Answer:

35.7 megabytes

Step-by-step explanation:

Let's first find 10% of the percent needed. If it is 234 megabytes and 10% has downloaded so far, we conclude that 10% of the download is 23.4 megabytes (since we move the decimal point one spot to the left to find ten percent).

To get to 15% of the percent needed, let's split 10% in half to get the amount of megabytes per every 5%.

23.4/2 = 11.7

We can now conclude that 5% = 11.7. Therefore, 15% will equal (23.4 + 11.7) 35.1 megabytes.

To find the remaining 3.5% left of the percent needed, we use a calculator.

3.5% x 18 = 0.63.

We will add that to the 35.1 megabytes, but we need to round to the nearest tenth, as the question stated. Therefore, we round to 0.6, add it to 35.1, to get a total of 35.7 megabytes.

For 18.5% of the download, it will be 35.7 megabytes.

Answer:27 < AB < 81

Step-by-step explanation:

Answer:

27 < AB < 81

Step-by-step explanation:

in a triangle the sum of any 2 sides must be larger than the third side.

that must be true for every pair of sides you pick.

simply because, if that is not fulfilled, the third side would be too long, and the other 2 sides cannot connect to the endpoints of the third side.

so,

AC + CB = 81 must be longer than AB. otherwise the triangle cannot "close".

AC + AB = 27 + AB must be longer than CB = 54.

so, AB must be longer than 27.

CB + AB = 54 + AB must be longer than AC = 27. but that is always true, as CB alone is already larger.

so only the other 2 conditions need to be true.

hence the answer.

Answer:

Step-by-step explanation:

I assume that QP = 18 cm and m∠Q = 72°

Answer:

[tex]\fbox {P = 6.76 cm}[/tex]

Step-by-step explanation:

Finding the missing angle :

Applying the Law of Sines :

[tex]\boxed {\frac{sin P}{P} = \frac{sin R}{PQ}}[/tex]

Substituting the known values :

The number of robots have have for a city of 75 square miles would be 10 robots.

The first step is to determine how many robots are needed for 1 square mile: 4/30.

The second step is to multiply this fraction by 75

4/30 x 75 = 10 robots

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Based on the given task content; the five consecutive odd integers preceding -31 are: -21, -23, -25, -27, -29

Odd integers preceding -31

= -1, -3, -5, -7, -9, -11, -13, -15, -17, -19, -21, -23, -25, -27, -29

Therefore, Five consecutive odd integers preceding -31 are: -21, -23, -25, -27, -29

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Answer: Choice B

All real numbers except 2 and 5

===========================================================

Explanation:

Factor the denominator.  We need to find two numbers that multiply to 10 and add to -7.

Through trial and error, those two numbers are -2 and -5

-2 times -5 = 10

-2 plus -5 = -7

This means the denominator [tex]\text{x}^2 - 7\text{x} + 10[/tex] factors to [tex](\text{x}-2)(\text{x}-5)[/tex]. You can use the FOIL rule to confirm this.

Then each piece is set equal to zero to solve for x

x-2 = 0 leads to x = 2

x-5 = 0 leads to x = 5

------------

In short, if x = 2 or x = 5, then it causes the the denominator [tex]\text{x}^2 -7\text{x}+10[/tex] to turn into 0.

Dividing by 0 is not allowed; therefore, x = 2 nor x = 5 is allowed in the domain. Any other x value is valid.

Hello,

2x² - 8x = 0

2x × x - 2x × 4 = 0

2x(x - 4) = 0

2x = 0 or x - 4 = 0

x = 0 or x = 4

The stores that will be in the sample are - 00, 02, 05, 08, 11, 14, 17, 20, 23.

What comprises the sample?

An analytical subset of a larger population is referred to as a sample in statistics. A sample are used in research so that it can be done quickly and with more manageable data. However, obtaining such a sample may be costly and time-consuming. Randomly generated samples do not have significant bias if they are large enough.

Stores in the Sample

Since it is given that the sample is made up of every third store, starting from the first retail store. The stores have been numbered systematically from 00 to 23.  Since a systematic sampling is done, after picking the first store, the third store will be picked, that is, 02, and then 05, and so on till 23.

Thus, the following retail stores will be present in the sample,

00, 02, 05, 08, 11, 14, 17, 20, 23

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Replace x with the value in the table and solve for y

-3:  2(-3)/3 + 4 = -6/3 + 4 = -2+4 = 2

0:  2(0)/3 +4 = 0/3 + 4 = 0+4 = 4

3: 2(3)/3 + 4 = 6/3 + 4 = 2 + 4 = 6

6:  2(6)/3 + 4 = 12/3 + 4 = 4+4 = 8

Answer:

When x = -3:

y = 2(-3)/3 + 4

y = 2

When x = 0:

y = 2(0)/3 + 4

y = 4

When x = 3:

y = 2(3)/3 + 4

y = 6

When x = 6:

y = 2(6)/3 + 4

y = 8

Answer:

Step-by-step explanation:

What is the length of the apothem, rounded to the nearest inch? recall that in a regular hexagon, the length of the radius is equal to the length of each side of the hexagon. 4 in. 5 in. 9 in. 11 in.

Answer:

9

Step-by-step explanation:

apothem (AB)

1/2 of the length (10) is 5

AB^2 + 5^2 = 10^

AB^2 = 100-25

Square root of AB^2 = square root of 75

AB = 8.66

8.66 is about 9

The slope of the parallel line is 0 and the slope of the perpendicular line is undefined

The equation is given as:

y = 1

A linear equation is represented as:

y = mx + c

Where:

m represents the slope

By comparison, we have:

m = 0

The slope of the parallel line is:

Slope = m

This gives

Slope = 0

The slope of the perpendicular line is:

Slope =-1/m

This gives

Slope = -1/0

Slope = undefined

Hence, the slope of the parallel line is 0 and the slope of the perpendicular line is undefined

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The linear inequality in standard form is: x + y < -2 or x + y + 2 < 0

To determine what sign to use, follow these rules:

The graph given has the following features:

Find the slope:

Slope (m)= rise/run = -(2 units) / (2 units).

Slope (m) = -1.

The y-intercept (b) = -2.

Substitute m = -1 and b = -2 into y < mx + b:

y < (-1)x + (-2)

y < -x - 2

Rewrite

x + y < -2

x + y + 2 < 0

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The equation that describes how the parent function, y = x³, is vertically stretched by a factor of 4 is y = 4x³.

When an equation is vertically stretched, it means that the parent equation has been multiplied by a number that is more than one.

This means that the equation is multiplied by some factor.

It is given that we should describe how the parent function is vertically stretched by a factor of 4.

The parent function is given as y = x³.

Since the equation is said to be vertically stretched by a factor of 4, we must multiply the parent equation by 4 to stretch it.

Therefore, we have found the equation that describes how the parent function, y = x³, is vertically stretched by a factor of 4 to be y = 4x³.

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Answer: C

Step-by-step explanation:

Just C

The probability that the child has measles is gotten as; 0.35

F is the event of a child being sick with flu.

M is the event of a child being sick with measles.

A is the event that the doctor finds a rash.

B1 is the event that the child has measles

S is the sick children.

P(R|M) = 0.93.

P(R|F) = 0.09

P(S|F) = 0.95

P(S|M) = 0.05

Thus, the probability that the child has measles is;

P(M|R) = [(0.05 * 0.93)/[(0.05 * 0.93) + (0.95 * 0.09)]

P(M|R) = 0.35

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Answer:

Scenario 1: Cameron works at a local grocery store after school. He is paid $8 for each hour(h) he works. And ammount of money can be (m)

considering theres no like first hour pay or something then it would be

Equation: m = 8h

Scenario 2: At a local bakery, one box of doughnuts(b) costs $5(c). Two boxes of doughnuts cost $10.

Equation: c = 5b where b is the ammount of doughnut boxes and c is the cost

Scenario 1a: Jim goes to the gym for 10 hours(h) It costed him $20(c) for those 10 hours.

Equation:  c = 2h

Scenario 1b: Kayla goes to a for a ride on her bike and traveled 15 miles(m) and was out for 30 minutes. (t)

Equation: t = 2m

Answer:

y = 60

Step-by-step explanation:

"The ratio of y to x is 3"

This means that, [tex]y\div x=3[/tex]

"The sum of y and x is 80"

This means,  [tex]x+y=80[/tex]

If [tex]y\div x=3[/tex], then [tex]y = (3*x)[/tex].

We can plug this into the other equation by substitution:

[tex]x + (3 * x)=80[/tex]

This simplifies to:

[tex]4x = 80[/tex]

Which we can solve out and get:
[tex]x=20[/tex].

We solved for x, but we need the value of y.

So, we go back to the equation we first derived: "[tex]y = (3*x)[/tex]".

And now we substitute the value of x, into this.

[tex]y = (3 * (20))[/tex]

By solving this out, we get:
[tex]y=60[/tex]

So, the value of y is 60.

Answer:

26.1 to the nearest  tenth.

Step-by-step explanation:

tan 43 = x / 28

x = 28 tan 43

  = 26.1102

The error made while find the mean absolute deviation was: C. When calculating the distances to the mean, the student forgot to take the absolute values.

The mean absolute deviation is simply the average of the sum of the "absolute difference" of the mean and each data point.

In the calculation of the student, after getting the difference of the mean and each data point, the student failed to take the absolute value, and still kept the minus sign included.

Therefore, the error was: C. When calculating the distances to the mean, the student forgot to take the absolute values.

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The given triangle is a right triangle

The coordinates are given as:

D (0,n), E(m,n), F(m,0)

The length is calculated using:

[tex]l=\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2[/tex]

So, we have:

[tex]DE=\sqrt{(0-m)^2 + (n-n)^2} = m[/tex]

[tex]DF=\sqrt{(0-m)^2 + (n-0)^2} = \sqrt{m^2 + n^2[/tex]

[tex]EF=\sqrt{(m-m)^2 + (n-0)^2} = n[/tex]

The slope is calculated using:

[tex]m = \frac{y_2 -y_1}{x_2 - x_1}[/tex]

So, we have:

[tex]DE = \frac{n -n}{0- m} = 0[/tex]

[tex]DF = \frac{n -0}{0- m} = -\frac nm[/tex]

[tex]EF = \frac{n -0}{m- m} = \mathbf{unde fined}[/tex]

This is calculated using

[tex]m = 0.5 * (x_1 + x_2, y_1 + y_2)[/tex]

So, we have:

[tex]DE = 0.5 * (0 + m, n+ n)=(0.5m, n)[/tex]

[tex]DF = 0.5 * (0 + m, n+ 0)=(0.5m, 0.5n)[/tex]

[tex]EF = 0.5 * (m + m, n+ 0)=(m, 0.5n)[/tex]

In (a), we have:

Lengths

[tex]DE= m[/tex]

[tex]DF = \sqrt{m^2 + n^2[/tex]

[tex]EF= n[/tex]

Slope

[tex]DE = 0[/tex]

[tex]DF = -\frac nm[/tex]

[tex]EF = \mathbf{unde fined}[/tex]

The sides are not equal.

However, the 0 and the undefined slope implies that the triangle is a right triangle because the sides are perpendicular

It should be noted that the triangle cannot be graphed because the coordinates are not numeric

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