Solve the formula for f2

f =

f1f2/

f1 + f2

The first equation we are asked to graph is the simple equation:

x = -1

So, we create a table for it that has in the first column the x values, and in the second column the associated y values.

SInce the equation says x = -1 no matter what the value of y is, we can write any y values in the column for y

We end up with pairs of points of the form:

(-1, 0)

(-1, 2)

(-1, 3)

(-1, 5)

(-1, -4)

and so forth, with all os them having a -1 in the first coordinate (the x-coordinate)

Notice that such points give us a vertical line when we join them, it is a vertical line going through the X = -1 point on the x-axis.

where the line x = -1 is plotted in red.

Now, for the second line that reads:

2 x - 5 y = 5

we solve for y in order to make our calculations easier:

add 5 y to both sides:

2 x = 5 + 5y

subtract 5 from both sides:

2 x - 5 = 5 y

now diide both sides by 5:

y = (2 x - 5) / 5

So, let's find at least three points that define our line

Notice that when x = 5 , we get:

y = (10 - 5) / 5 = 5 / 5 = 1

So we draw the point (5, 1) on the x-y plane

When x = 0 we get:

y = (2 (0) - 5) / 5 = - 5/5 = -1

So we draw the point (0, -1) on the plane

And finally, we use the point x = -5 and get:

y = (2 (-5) - 5) / 5 = -15/ 5 = -3

So we draw the point (-5, -3) on the plae.

Then we draw a line connecting the three points we found, as shown below:

Answer:

180 is a straight angle so B

Answer:

X=1

Step-by-step explanation:

6x+12-3=15

6x+9=15

6x+9-9=15-9

6x=6

X=1

Answer:

see below

Step-by-step explanation:

15=3(2x+4)-3

Distribute

15 = 6x +12 - 3

Combine like terms

15= 6x +9

Subtract 9 from each side

15 -9 = 6x+9-9

6 = 6x

Divide each side by 6

6/6 = 6x/6

1 =x

Answer:70

Step-by-step explanation:910/13=70 so he gives away 70 loafs of bread.

Answer:

49z^10 dm^2

Step-by-step explanation:

The rate of change of the function g(x) in the interval -9 ≤ x ≤ -1 is  1

The rate of change of a function y = f(x) on the interval [a, b] is given by the formula below:

R = (f(b) - f(a))/(b - a)

Here the function is g(x) = -x² − 9x + 27 and the interval is [-9, -1], we can evaluate g(x) in both ends of our interval, then we will get the two values needed for the numerator, here we will get:

g(-1) =  -(-1)² − 9*-1 + 27 = -1 + 9 + 27 = 35

g(-9) = -(-9)² -9*-9 + 27 = 27

Replacing that in the formula we can get the rate of change is:

R = (35 - 27)/(-1 + 9) = 8/8 = 1

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Answer: a:b. 3:7 this the right answer

[~S & (R V S)] ≡ (Q ⊃ S) is true when A = T, S = F, R = F, and Q = T by substituting the propositional variables.

A truth table is a table used to determine the truth values of a compound proposition, which is a logical statement made up of simpler propositions using logical operators such as "and" (represented by "&"), "or" (represented by "V"), "not" (represented by "~"), conditional (represented by "⊃"), and biconditional (represented by "≡").

Let's substitute the given truth values for the propositional variables in the given statement:

[~F & (F V F)] ≡ (T ⊃ F)

Using the truth table for conjunction (represented by "&") and disjunction (represented by "V"), we can simplify the left-hand side of the equivalence:

[T & F] ≡ (T ⊃ F)

Using the truth table for conditional (represented by "⊃"), we can simplify the right-hand side of the equivalence:

F ≡ F

Since both sides of the equivalence have the same truth value, the statement is true.

Therefore, [~S & (R V S)] ≡ (Q ⊃ S) is true when A = T, S = F, R = F, and Q = T.

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Answer: Hello your question has some missing data that I was able to find and attach below

A recent 10-year study conducted by a research team at the Great Falls Medical School was conducted to assess how age, systolic blood pressure, and smoking relate to the risk of strokes. Assume that the following data are from a portion of this study. Risk is interpreted as the probability (times 100) that the patient will have a stroke over the next 10-year period. For the smoking variable, define a dummy variable with 1 indicating a smoker and 0 indicating a nonsmoker.

answer :

The condition : Client age ≤ 31.26 years

Step-by-step explanation:

First step : perform a regression analysis via excel ( result attached below )

P-value = 2.06E-07

Next determine the condition on which the company will sell its policy

Y = - 91.7595 +  1.0767x1 + 0.2518x2 + 8.7399x3

1  < -91.7595 + 1.0767x1 + 0.2518*200 + 8.7399*1

make X1 subject of equation above

X1 < 31.26

Answer:

R=50

x=65

x-15=50+2x=180

Answer:  The answer is:  " m∡R = 20° " .

__________________________

Step-by-step explanation:

__________________________

Note that ∡R and ∡Q are "supplementary angles".

In these particular case:

  " m∠R + m∠Q = 180 " ;

We are given (in the picture):

_____________________________

" m∠R = (x - 15) " :

and " m∠Q = 2x " ;

_____________________________

So we plug in these values:

_____________________________

→ m∠R + m∠Q = 180  ;

  → (x - 15) + 2x = 180 ;

  → x - 15 + 2x = 180 ;

  → combine the "like terms" on the "left-hand side of the equation" :

   x + 2x = 1x + 2x = 3x ;

  Rewrite as:  3x - 15 = 180 ;

Now add "15" to each side of the equation:

       3x - 15 + 15 = 180 + 15 ;

 to get:

       3x = 195 ;

Now, divide each side of the equation by "3" ; to isolate "x" on the left-hand side of the equation; and to solve for " x" ;

       3x / 3 = 195/3 ;

    to get:  x = 65 ;

Now, we are to solve for:  m∡R ; which is:  " (x - 15) " ;

 So we substitute "65" ; for "x" ;

→  m∡R = x - 15 = 65 - 15 = 50 ;

The answer is:  " m∡R = 50.°

__________________________________

Note:  Alternate method:

Above; when we have:

 "3x - 15 = 180 " ;

we can divide each side of the equation by "3";

 to get:

   1x - 5 = 60 ;

 → x - 5 = 60 ;

Add "5" to each side of the equation:

     x - 5 + 5 = 60 ;

 → x = 60 ;

and then continue acordingly.

__________________________

Best wishes!

Answer:

144ft^3

Step-by-step explanation:

To start, we have your formula: \(V=\frac{1}{2} (bh) (l)\)
b = base length of the triangle.
h = height of the triangle.
l = length of the prism

Fill in for each of those values:
\(V = \frac{1}{2} (6x6)(8)\)

\(V=\frac{1}{2} (36)(8)\)

\(V=(18)(8)\)

\(V=144\)

Your answer, because it is a 3D shape, should be cubed, so:
\(V=144ft^{3}\)

Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x:

2x² - x - 10 = 0

This equation can be factored as:

(2x + 5)(x - 2) = 0

Setting each factor equal to zero, we get:

2x + 5 = 0 => 2x = -5 => x = -5/2

x - 2 = 0 => x = 2

Therefore, the x-intercepts of the graph of f(x) are x = -5/2 and x = 2.

Part B: The vertex of the graph of f(x) can be determined using the formula x = -b/2a, where a and b are the coefficients of the quadratic equation in standard form (ax² + bx + c = 0).

In this case, a = 2 and b = -1. Plugging these values into the formula, we have:

x = -(-1) / (2 * 2) = 1/4

To determine if the vertex is a maximum or a minimum, we can examine the coefficient of the x² term. Since the coefficient a is positive (a = 2), the parabola opens upwards, and the vertex represents a minimum point

Therefore, the vertex of the graph of f(x) is (1/4, f(1/4)), where f(1/4) can be obtained by substituting x = 1/4 into the equation f(x).

Part C: To graph f(x), we can follow these steps:

Plot the x-intercepts: Plot the points (-5/2, 0) and (2, 0) on the x-axis.

Plot the vertex: Plot the point (1/4, f(1/4)) as the vertex, where f(1/4) can be obtained by substituting x = 1/4 into the equation f(x).

Determine the direction of the graph: Since the coefficient of the x² term is positive, the graph opens upwards from the vertex.

Determine additional points: Choose a few x-values on either side of the vertex and calculate their corresponding y-values by substituting them into the equation f(x). Plot these points on the graph.

Draw the graph: Connect the plotted points smoothly, following the shape of the parabola. Ensure the graph is symmetrical with respect to the vertex.

The answers obtained in Part A (x-intercepts) and Part B (vertex) provide crucial points to plot on the graph, helping us determine the shape and position of the parabola.

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The x-intercepts from the graph attached are

The vertex  from the graph attached is

Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x:

2x² - x - 10 = 0

x = (-b ± √(b² - 4ac)) / (2a)

a = 2, b = -1, c = -10

Plugging these values into the quadratic formula:

x = (-(-1) ± √((-1)² - 4 * 2 * (-10))) / (2 * 2)

x = (1 ± √(1 + 80)) / 4

x = (1 ± √81) / 4

x = (1 ± 9) / 4

x₁ = (1 + 9) / 4 = 10 / 4 = 2.5

x₂ = (1 - 9) / 4 = -8 / 4 = -2

Therefore, the x-intercepts of the graph of f(x) are 2.5 and -2.

Part B

To find the coordinates of the vertex, we can use the formula:

x = -b / (2a)

x = -(-1) / (2 * 2) = 1 / 4 = 0.25

we substitute this value back into the original function:

f(0.25) = 2(0.25)² - 0.25 - 10

f(0.25) = 0.125 - 0.25 - 10

f(0.25) = -10.125

Therefore, the vertex of the graph of f(x) is located at (0.25, -9.125).

Part C: The steps to graph f(x) include:

Plotting the x-intercepts: Based on the results from Part A, we know that the x-intercepts are 2.5 and -2. We mark these points on the x-axis.

Plotting the vertex: Using the coordinates from Part B, we plot the vertex at (0.25, -9.125). This represents the minimum point of the graph.

Drawing the shape of the graph: Since the coefficient of the x² term is positive, the graph opens upward. From the vertex, the graph will curve upward on both sides.

Additional points and smooth curve: To further sketch the graph, we can choose additional x-values and calculate their corresponding y-values using the equation f(x) = 2x² - x - 10. Plotting these points and connecting them smoothly will give us the shape of the graph.

By using the x-intercepts and vertex obtained in Part A and Part B, we have the necessary information to draw the graph accurately and show the key features of the quadratic function f(x)

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Answer: 24

Step-by-step explanation:

Since n is 5 you will multiply 9x5 which you’ll get 45 than you move on to 3m so m=7 so than you will multiply 3x7 which equals 21. The final step is just subtract the two numbers.

9x5 - 3x7= 45 - 21= 24

9x5= 45

3x7= 21

Answer:

B

Step-by-step explanation:

Cos is the adjacent side over the hypotenuse.  The adjacent side to <E is side ED.  The hypotenuse is side EF.  ED/EF.  They do not go right out and give you this choice, but you see that B says the same thing.

Answer:

  B. 3x¹¹ +9x⁷ +5x³ −x +4

Step-by-step explanation:

You want to identify the polynomial that has terms written in descending order of their degree.

The degree of a term is the exponent of x in that term. In the given polynomial, the term degrees are 3, 1, 7, 0, 11.

When these are put into descending order, that order is ...

  11, 7, 3, 1, 0

The answer to this question will be the polynomial with terms written in the order of their degree as shown above:

  3x¹¹ +9x⁷ +5x³ −x +4

__

Additional comment

When the exponent of x is 0, the value of the term x^0 is 1. That is why we can say the constant term is a term that has the variable to degree 0.

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A. The null hypothesis H₀ and the alternative hypothesis H₁ are:

H₀: μ = 35 minutes       H₁: μ > 35 minutes

B. If the consultant decides not to reject the null hypothesis, she might be making a Type II error.

C. A Type II error would be failing to reject the hypothesis that μ is = to 35 minutes when, in fact, μ is 43 minutes.

A Type II error occurs when the null hypothesis is false, but the test does not reject it.

In this case, the consultant would be concluding that the mean shopping time is 35 minutes, when in fact it is greater than 35 minutes.

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The length of the straw is √110 inches.

What is rectangle ?

Rectangle can be defined as opposites sides are equal and the area of rectangle is product of length and breadth.

We can use the Pythagorean theorem to find the length of the diagonal of the rectangular box, which will be the length of the straw.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the rectangular box forms a right triangle, and the length of the hypotenuse is the length of the diagonal from the bottom left corner to the top right back corner, which is the length of the straw.

The lengths of the other two sides of the triangle are the dimensions of the rectangular box:

The width is 2 inches, which is the length of one leg of the right triangle.

The height is 5 inches, which is the length of the other leg of the right triangle.

So we can use the Pythagorean theorem as follows:

length of straw = √(2*2 + 5*5 + 9*9)

= √(4 + 25 + 81)

= √110

Therefore, the length of the straw is √110 inches.

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For this problem, we are given the attendance graph of three sports centers in the span of 7 months. We need to identify which of the three centers had the largest increase in attendance during this time.

To solve the problem, we need to compare the attendance of each sports center in month 7 with their attendance in month 1.

The Coors field seems to have a growth in attendance of 2.5 horizontal bars, the Petco Park seems to have a growth in attendance of 4.8 bars and the Turner field seems to have a growth in attendance of 3.9 bars. With thi,s we conclude that Petco Park saw the highest growth in attendance.

The answer is Petco Park.

Answer:

h=-2

Step-by-step explanation:

the graph was shifted 2 units left

Answer:

the answer is 2

Step-by-step explanation:

Answer:

Step-by-step explanation:

It is 2, because it is the only factor that can go with both of the numbers.

Answer:

\(a. {( \sqrt{36} )}^{2} = 36\)

\(b. ({ \sqrt{ \frac{25}{81} } })^{2} = \frac{25}{81} = 0.3086\)

\(c. {( \sqrt{1.99} )}^{2} = 1.99\)

\(d. {( \sqrt{x} })^{2} = x\)

The square exponent is removed with the root .

Answer:

Sana takes 10 minutes longer than Ali in bathroom

Step-by-step explanation:

Given:

Ali Showers, brushes teeth 20 minutes

Thus, Ali takes 20 minutes time in bathroom

Sana Takes a bath, brushes teeth ½ hour

1 hour has 60 minutes

1/2 hour has 60/2=30 minutes

Thus, Sana takes 30 minutes time in bathroom.

Time, taken more by sana than Ali = 30 minutes - 20 minutes = 10 minutes

.

Thus, Sana takes 10 minutes longer than Ali in bathroom.

The possible values of x, given the number of bets are $54,999, $14,999, and -$1.

The expected winnings would be -$0.97.

The possible values of the net winning would be the amount you win at net if you win first prize, second prize, or nothing.

The possible values would therefore be:
$54,999, $14,999, and -$1.

These show that if you win the first or second prize, you will deduct the $ 1 you bet. And if you win nothing, you would have lost $ 1.

The expected winnings would be:

= ∑ ( Probability of event x Potential net win / loss)
= ( 1 / 3, 000, 000 x 54, 999 ) + ( 2 / 3, 000, 000 x 14, 999 ) + ( 2,999, 997 / 3, 000, 000 x - 1 )

= - $ 0.97

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Answer:

$100

Step-by-step explanation:

since 1 hockey mask costs $10 and you need 10 masks you can multiply 10x10 and you will get 100

Answer:

0-y=3/4(x-2)

Step-by-step explanation:

Answer:

8/69

Step-by-step explanation:

1.6÷13.8

convert the decimal into fraction so 8/5 ÷ 13.8 and 8/5÷69/5 multiply by the reciprocal and reduce the number and you will get 8×1/69

Remember that

A regular hexagon can be divided into 6 equilateral triangles

the measure of each interior angle in a regular hexagon is 120 degrees

so

see the attached figure to better undesrtand the problem

each equilateral triangle has three equal sides

the length of each side is given and is 12 units

Part A) Perimeter

the perimeter is equal to

P=6(12)=72 units

Part B

Find the area

Find the height of each equilateral triangle

we have

tan(60)=h/6

Remember that

therefore

the area of the polygon is

applying Pythagorean Theorem

12^2=6^2+h^2

h^2=12^2-6^2

h^2=108

h=6√3 units

Answer:

They are intersecting.

Step-by-step explanation:

Since their slopes can't be the same (because their product couldn't be negative in that case), they have to intersect at one point or another.

Answer:

D. 3x^2 -6 is the correct answer.

Step-by-step explanation: