If f(x) = 4 – x2 and g(x) = 6x, which expression is equivalent to (9 - 1)(3)?

Answer:

0

Step-by-step explanation:

Quadratic equation

[tex]x=\frac{-b+-\sqrt{b^{2}-4*a*c} }{2*a}[/tex]

The discriminant is the part of the quadratic formula within the square root symbol: [tex]{b^{2}-4*a*c}[/tex].  The discriminant indicates if there are two solutions, one solution, or none.

The discriminant can be positive, zero or negative which determines how roots exist for the given quadratic equation.

So, a positive discriminant tell us that the quadratic has two different real solutions.

A discriminant of zero tell us that the quadratic has two real and equal solutions.

And a negative discriminant tell us that none of the solutions are real numbers.

In this case: 25x^2-10x+1=0

We can see that

a= 25    b=-10   c=1

Using:  [tex]{b^{2}-4*a*c}[/tex]

We have  [tex]-10^{2}-4* 25*1 =100-100=0[/tex]

the answer is zero, so the quadratic has two real and equal solutions

Answer:

What is the value of the discriminant of f?

0

How many x-intercepts does the graph of f?

1

Step-by-step explanation:

I promise you i just got this question and this is the answer

Answer: b. The slope is -0.5. Starting at 4.0, the GPA will decrease by 0.5 for every text sent in class.

Step-by-step explanation:

We know that the equation of a line in intercept form is given by :-

[tex]y=mx+c[/tex], where m is the slope and c is the y-intercept.           (i)

Given : Sloane believes there is a correlation between the number of texts sent in class and GPA. She collected data and found that the line of best fit for the data can be modeled by the equation :-

[tex]y = 4.0-0.5x[/tex]

When we compare it to (i), we get

m=-0.5 and c=4.0

It means the slope is -0.5 and the function is starting at 4.0 and the GPA will decrease by 0.5 for every text sent in class (since its negative).

The correct option is B which is ''The slope is −0.5. Starting at 4.0, the GPA will decrease by 0.5 for every text sent in class''.

Given

The data can be modeled by the equation;

[tex]\rm y = 4.0 - 0.5x[/tex]

The standard form of the linear equation is;

[tex]\rm y = mx+c[/tex]

Where m is the slope of the equation and c is the intercept.

On comparing the given equation with the standard equation;

[tex]\rm y = 4.0 - 0.5x\\\\y = -0.5x+4.0[/tex]

The slope of the line m is -0.5 and intercept c is 4.0.

Hence, the slope is −0.5. Starting at 4.0, the GPA will decrease by 0.5 for every text sent in class.

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Answer:

C

Step-by-step explanation:

Note that C is exactly -1/4(4x-8) = -1/4*4x -1/4*(-8) = -x+2, so the system with C is the same equation twice, and obviously has an infinite number of solutions.

Answer:

x=1

Step-by-step explanation:

Since you know two sides and are trying to find the missing side, you can use the Pythagorean Theorem. So fashion the equation like this:

x^2 + 3^2 = sqrt10^2. After simplify, which leads to x^2 + 9 =10. Then have the variable to one side by subtracting 9 on both sides. This leads to x^2=1. Finally, square root both sides which leads to 1. Note that any root of 1 is 1. So your answer becomes x=1.

Hope this helps!

Answer:

-16 cents

Step-by-step explanation:

We are given that on  three rolls of a single​ die, you will lose ​$19 if a 3 turns up at least​ once, and you will win ​$5 otherwise.

We are to find the expected value of the game.

P (at least one 5 in three rolls) = 1 - P (no. of 3 in three) = [tex]1-(\frac{3}{6} )^2[/tex] = 0.875

P (other results) = 1 - 0.875 = 0.125

Random game value = -19, +5

Probabilities: 0.875, 0.125

Expected game value (X) = 0.875 × (-19) + 0.125 × (5) = -16 cents

Therefore, every time you play the game, you can expect to lose 16 cents

Answer:

It is expected to lose 5.10 dollars

Step-by-step explanation:

The probability of getting a 3 by throwing a die once is 1/6.

By throwing it 3 times the probability of not getting a 3 is:

[tex]P=(\frac{5}{6}) ^ 3 =0.5787[/tex]

Then the probability of obtaining a three at least once in the 3 attempts is:

[tex]P'=(1-0.5787)=0.421[/tex]

So if X is the discrete random variable that represents the amount gained in a single move of this game, the expected gain E(X) is:

[tex]E(X)=P'*(X') + P*(X)[/tex]

[tex]E(X) =0.421'*(-19) + 0.5787*(5)\\\\E(X) =-\$5.10[/tex]

[tex]4x^2-12x+29=20 \\4x^2-12x+9=0\\(2x-3)^2=0\\2x-3=0\\2x=3\\x=\dfrac{3}{2}[/tex]

With these kind of equations you want to use the quadratic formula. These problems take time, so don't fret you'll get there! :)

Quadratic formula:

-b +- √b^2-4(a)(c)  

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

2(a)

Next find your a, b, and c!

a= 4

b=12

c=29

Time to plug those answers in.

12 +- √(-12)^2-4(4)(9)

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

2(4)

Next solve everything in the radical first! Then the bottom.

12 +- √144-144

----------------------- ~ x=12/8 ~ x=3/2

8

You get: x=3/2!

Answer:

They are adding 16 to the number each time. So the next number in the sequence would be 78.

Step-by-step explanation:

d(1) = 14

d(n) = d (n-1) + 16

14 + 16 = 30

30 + 16 = 46

46 + 16 = 62

62 + 16 = 78 and so on...

The recursive formula of the arithmetic sequence is [tex]d_{n}=d_{n-1} +16[/tex].

A recursive formula is a formula that defines any term of a sequence in terms of its preceding term(s).

The recursive formula of an arithmetic sequence is, [tex]a_{n}=a_{n-1} +d[/tex]

From the question

14, 30, 46, 62, .......

d = [tex]62-46 =46-30=30-14=16[/tex]

d = 16

As per sequence

d(1) = 14

[tex]d_{n}-d_{n-1} =d=16[/tex]

[tex]d_{n}=d_{n-1} +16[/tex]

The recursive formula of the arithmetic sequence is [tex]d_{n}=d_{n-1} +16[/tex].

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Answer:

g(x) is option 1 or g(x) = (x + 7)^2 + 5

A quadratic equation has the general form of:

y=ax² +bx + c

It can be

converted to the vertex form in order to determine the vertex of the parabola.

It has the standard form of:y =a(x+h)² + k

where hand k represents the vertex, h represent the point in the x axis and k is thepoint in the y axis. Therefore, from the details given in the problem, the equation that represents

g(x) is option 1 or g(x) = (x + 7)^2 + 5

Answer:

Part 1) The solution of the absolute value is  (-∞,-6)∪ (2,∞)

Number line with open circles on negative 6 and 2, shading going in the opposite directions

Part 2) The graph in the attached figure

Step-by-step explanation:

we have

[tex]\left|2x+4\right|>8[/tex]

we know that

The absolute value has two solutions  

step 1

Find the positive case

[tex]+(2x+4)>8[/tex]

[tex]2x>8-4[/tex]

[tex]2x>4[/tex]

[tex]x>2[/tex]

The solution is the interval ----> (2,∞)

All real numbers greater than 2

step 2

Find the negative case

[tex]-(2x+4)>8[/tex]

Multiply by -1 both sides

[tex](2x+4)<-8[/tex]

[tex]2x<-8-4[/tex]

[tex]2x<-12[/tex]

[tex]x< -6[/tex]

The solution is the interval ----> (-∞,-6)

All real numbers less than -6

therefore

The solution of the absolute value is

(-∞,-6)∪ (2,∞)

Number line with open circles on negative 6 and 2, shading going in the opposite directions

step 3

using a graphing tool

see the attached figure

Answer:

The x-term inside the radical has a negative coefficient

Step-by-step explanation:

The argument of a square root should be ALWAYS greater or equal to zero. If the domain of the function is x<7, rearranging, we have: 0<x-7

Therefore the argument is: x-7, and the function is: y = √(x-7)

The statement "The x-term inside the radical has a negative coefficient" is the right answer.

Answer:

C). This is an example of causation

Step-by-step explanation:

Causation : It can be defined as the one event is the result of the other event. It is simply the cause and its effect. There is a causal relation between the two events.

Correlation : It can described the direction of the relation between two or more events or variables.

The conclusion of the experiment is that the plant that received more than two hours of sunlight in each day grew more than the plants that received less than two hours of sunlight in each day.

This is the cause of one event and its effect on the other event.

So option C is correct because sunlight causes plants to grow.

So option C). This is an example of causation.

Answer:

C( This is an example of causation

Answer:

A: Step 1: 6x − 10 = 1; Step 2: 6x = 11

Step-by-step explanation:

First: remove parentheses by multiplying factors.

6x - 10 = 1

Second: Move the constants to the right side of the equation

6x = 1 + 10

6x = 11

Answer: The correct answer is "Step 1: 6x − 10 = 1; Step 2: 6x = 11"

Step-by-step explanation:

Answer:

The farthest Left

Step-by-step explanation:

The second equation, y<x+1, means that every y value will be less than the x value +1. Since it is less than, and not less than or equal to, the graph is represented by the dotted line and not a solid line. Moving on to the next problem, we have to get it in slope-intercept form. We start with x-4y is less than or equal to 4. We need to separate the x and y, so we add 4u to the negative 4y, cancelling it out, but what we do to one side, we have to do to the other, so we add 4y, making our equation x is less than or equal to 4y + 4. Next, we need to get the y by itself, so we subract 4 from the y side, cancelling it out and subtract it from the other side, which leaves us with x-4 is less than or equal to 4y. 4y is just 4 times y so we divide it by four on both sides to get y is greater than or equal to 1/4x-1. Since the solution can be equal to, we make the line solid and when we plot both lines, we get the graph furthest to the left.

Answer:

120

Step-by-step explanation:

<2 = 120 degrees

<3 = <2  vertical angles

Assuming b is parallel to c

<3 = <6  alternate interior angles

<6 = <7 vertical angles

<2 = <7 =120

Step-by-step explanation:

The expected value is the sum of each outcome times its probability.

E = (0.70)(50000) + (0.05)(0) + (0.25)(-3500)

E = 34125

The store is expected to gain $34,125.

To calculate the expected gain or loss for the new store, we multiply each possible outcome by its probability, then sum these values. This results in an expected gain of $34,125 for the store.

The problem requires calculating the expected value of the coffee franchise's new store opening. We use probability and finance to estimate the expected gains or losses.

The expected value (EV) is calculated as follows:

Multiply each outcome by its respective probability.

Sum these products to get the EV.

So, the expected value is:

EV = (0.70 imes $50,000) + (0.05 imes $0) + (0.25 imes -$3,500)

EV = $35,000 + $0 - $875

EV = $34,125

This implies an expected gain of $34,125 for the new store.

Answer:

Option D (r(t) = 3.50t +25 ; r(8) = 53)

Step-by-step explanation:

The fixed cost to rent the kayak $25. This is the cost which remains fixed irrespective of the usage of the kayak. The variable cost of using the kayak is the cost which depends on the usage of the kayak. It is mentioned that the kayak is used for 4 hours and the company charges $3.5 for every half hour. The cost function is given by:

r(t) = 25 + 3.5t ; there r is the total cost of using the kayak and t is the number of half-hours the kayak is used.

4 hours means that there are 8 half-hours. Therefore, t=8. Put t=8 in r(t).

r(8) = 25 + 3.5*(8) = 25 + 28 = 53.

Therefore, Option D is the correct answer!!!

Answer:

The Answer would be D.

r(t) = 3.50t +25

r(8) = 53

Step-by-step explanation:

The Rental Company charges a fixed price of $25 to rent the kayak, as well as an additional $3.50 for each half hour. So the only variable we are looking at would be the amount of time the kayak was rented. We can model this question with the following equation.

[tex]f(x) = 25 + 3.50x[/tex]

with x being the time the kayak was rented in 30 min intervals. Since the kayak was rented for 4 hours we can multiply this by 2 to get 8 (30 min intervals). Now we can plug this into the formula and solve it.

[tex]f(8) = 25 + 3.50(8)[/tex]

[tex]f(8) = 25+  28[/tex]

[tex]f(8) = 53[/tex]

So to rent the kayak for 4 hours it would cost $53

Answer:

The patient must take [tex]2\frac{1}{2}\ tablets[/tex] per day

Step-by-step explanation:

we know that

12 1/2 grains (gr) of aspirin is equal to 12.5 grains

using proportion

Let

x -----> the number of aspirin tablets

[tex]\frac{1}{5} \frac{tablet}{gr} =\frac{x}{12.5} \frac{tablets}{gr} \\ \\x= 12.5/5\\ \\x=2.5\ tablets[/tex]

Convert to mixed number

[tex]2.5=2\frac{1}{2}\ tablets[/tex]

The simplified form of the fraction 11/5 is determined as 2 1/5.

Simplification refers to the process of reducing an expression, equation, or fraction into its simplest or most concise form.

Fractions can be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD). This reduces the fraction to its simplest form.

The given fraction expression;

11/5

This expression is simplified as follows;

11/5 = 2 remainder 1

The final expression becomes;

11/5 = 2 1/5

Thus, the simplified form of the expression 11/5 is determined as 2 1/5.

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Thus, based on the observed pattern and the linear model, we can expect the Photography Club to have 13 members in the sixth month.

Based on the updated coordinate points provided for the graph, which are (1,4), (2,5), (3,7), (4,9), and (5,11), we can describe the data and predict the number of members for the sixth month as follows:

1. Describe the Data:

  - At month 1, there are 4 members.

  - At month 2, there is an increase to 5 members.

  - At month 3, there are 7 members.

  - At month 4, there are 9 members.

  - At month 5, there are 11 members.

2. Identify the Pattern:

  - From month 1 to 2, the increase is 1 member.

  - From month 2 to 3, the increase is 2 members.

  - From month 3 to 4, the increase is 2 members.

  - From month 4 to 5, the increase is 2 members.

3. Predict the Number of Members for the Sixth Month:

  - We observe that after the first month, the number of members increases by 2 each month.

  - Assuming the pattern continues, we can predict that in the sixth month, the number of members will increase by 2 from the fifth month.

Therefore, the predicted number of members for the sixth month would be:

[tex]\[ 11 \text{ members at month 5} + 2 \text{ increase} = 13 \text{ members at month 6} \][/tex]

We can plot the provided data points and extend the line to the sixth month to visually confirm our prediction. Let's do that.

The linear model fitted to the given data points predicts approximately 12.6 members for the sixth month. Since the number of members must be a whole number, we can round this to 13 members.

Answer:

The turns of a graph is represented by the number of maximum or minimum that the function has.

If we differenciate f(x) we get:

f'(x)=4x^3+6x

f'(x)=2x(2x^2 + 3)

Therefore f'(x) =0, when x=0. Given that negative roots are not defined.

Therefore, the number of turns will be given by the number of solutions of f'(x) which is 1.

Attached you find the graph of the function which confirms the number of turns.

If the function had other solutions, the maximum number of turns it could have is 3! because f'(x) is a third degree polynomial, therefore it can't have more than 3 solutions!

[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-b^2}=a \qquad \begin{cases} c=\stackrel{hypotenuse}{61}\\ a=adjacent\\ b=\stackrel{opposite}{11}\\ \end{cases} \\\\\\ \sqrt{61^1-11^2}=a\implies \implies \sqrt{3600}=a\implies 60=a[/tex]

Answer:

A Secant is a line in the plane of a circle that intersects the circle at exactly two points

Step-by-step explanation:

A line intersecting in two points is called a secant line, in one point a tangent line and in no points an exterior line. A chord of a circle is the line segment that joins two distinct points of the circle. A chord is therefore contained in a unique secant line and each secant line determines a unique chord.

Answer:

-1/3 is the slope perpendicular

Step-by-step explanation:

When we have 2 points, we can use the formula

m = (y2-y1)/(x2-x1) to find the slope

m = (1-7)/(3-5)

   =-6/-2

    =3

The slope is 3

We want a slope perpendicular

Remember that is the negative reciprocal

- (1/3)

-1/3

Two lines are perpendicular when,

[tex]a_1=-a_2^{-1}[/tex]

Now solve for [tex]a_2[/tex] to get [tex]a_2=-a_1^{-1}[/tex]

First we calculate the slope [tex]a_1[/tex] from the given points [tex]E(x_1,y_1),F(x_2,y_2)\longrightarrow E(5,7),F(3,1)[/tex].

[tex]a_1=\dfrac{\Delta{y}}{\Delta{x}}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{1-7}{3-5}=\dfrac{-6}{-2}=3[/tex]

Now use the first formula and insert the data in it to find the value of the second slope [tex]a_2[/tex],

[tex]a_2=-3^{-1}=\boxed{-\dfrac{1}{3}}[/tex]

And that's it.

Hope this helps.

r3t40

Answer:

Option A. 93.5°

Step-by-step explanation:

we know that

The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.

so

∠C=(1/2)[83°+2(52°)]

∠C=(1/2)[83°+104°]

∠C=(1/2)[187°]

∠C=93.5°

Answer: 10

Step-by-step explanation:

if we know a-b=5, to get the answer of 2(a-b) multiply 5 by 2.

Answer:

10

Step-by-step explanation:

a-b=5

Multiply each side by 2

2(a-b) = 2*5

2 (a-b) = 10

G -1/6= 1/6

Move -1/6 to the other side

sign changes from -1/6 to 1/6

G-1/6+1/6=1/6+1/6

G = 2/6

Reducing: divide by 2 for 2/6

2/2= 1

2/6= 3

Answer : G= 2/6= 1/3

Answer:

Yes

Step-by-step explanation:

To be a solution of the system, it has to satisfy both the equations.

Let's check first one:

3x - 2y = -1

3 (1) - 2(2) = 3 - 4 = -1

So correct (satisfies).

Now, 2nd one:

y = -x + 3

y = -(1) + 3

y = -1 +3

y = 2

Yes, this is satisfied.

Hence, (1,2) IS A SOLUTION OF THE SYSTEM

Answer:

x=-7

Step-by-step explanation:

The sum of the angles of a triangle are 180 degrees

40 + x+57 + 90 =180

Combine like terms

187 +x = 180

Subtract 187 from each side

187-187 +x = 180-187

x = -7