given the function f ( x ) = 4 x 2 + 7 x − 5 . Calculate the following values:

Answer:

x = 6

Step-by-step explanation:

This is a bit of a tricky equation, and it's what we call an exponential equation since it involves some exponents. The way we begin to solve these kinds of problems is make the base on each side of the equals sign the same. On one side, we have 9 as our base, and on the other side, we have 3 as our base. 9 = 3², so we can rewrite our equation as shown below:

(3²)⁴ˣ⁻¹⁰ = 3⁵ˣ⁻²

From there, we can use the exponent rule (xᵃ)ᵇ = xᵃᵇ to simplify the left side of the equation.

3²⁽⁴ˣ⁻¹⁰⁾ = 3⁵ˣ⁻²

3⁸ˣ⁻²⁰ = 3⁵ˣ⁻²

Since our bases are now the same, we can take just the exponents and turn it into a new equation as shown below:

8x - 20 = 5x - 2

Hopefully at this point, this problem becomes easy for you, but I'll show how I solved this new equation below in case it doesn't make sense.

8x - 20 = 5x - 2

8x - 20 - 5x = 5x - 2 - 5x

3x - 20 = -2

3x - 20 + 20 = -2 + 20

3x = 18

3x/3 = 18/3

x = 6

Hopefully that's helpful! Let me know if you need more help. :)

To find the equation of the line, parallel to the line y=-ax+b, that passes through the point (-1,2), you have to keep in mind that the slope of two parallel lines is equal.

The slope of the known line is the coefficient of the x-term. in this case, the slope is equal to "-a"

Once you have determined the slope of the line, you can use the point-slope form to find the equation of the line:

Where

m is the slope of the line

(x₁,y₁) are the coordinates of one point of the line:

The coordinates of the point of the line are x₁= -1 and y₁= 2 and the slope is m=-a, so that:

So, the equation of the line, parallel to y=-ax+b, passes through the point (-1,2) is y-2=-a(x+1)

Answer:

they either scored 18 or 9 points from the field goals but i think it is the 9 point if i'm wrong then it is the other one

Step-by-step explanation:

Answer:

3x3=9

Step-by-step explanation

The answer is 9 because the field goal is worth 3 points per goal and 3 x 3 =9

Answer: \(5\sqrt 5\)

Step-by-step explanation:

Sol \(\sqrt 125\) = \(\sqrt{25.5}\)

= \(\sqrt{25}\)  x  \(\sqrt{5}\)

\(5 \sqrt{5}\)

Answer:

At t = 9, Whitney's acceleration will be -0.2 miles per minute.

Step-by-step explanation:

Remember that the acceleration is the derivative of velocity.

Since we want to find Whitney's acceleration at t = 9 and we are given the velocity function, we can simply find the derivative of the point at t = 9. In other words, a(9) = v'(9).

For the interval (7, 11), we simply have a line. So Whitney's acceleration at t = 9 will be equivalent to the slope of that line.

We have the two points (7, 0.8) and (11, 0). So, the slope between them is:

\(\displaystyle m=\frac{0-0.8}{11-7}=\frac{-0.8}{4}=-\frac{1}{5}\)

So, a(t) = v'(t) = -0.2 ∀t ∈ {t | 7 < t  < 11}. Then at t = 9, Whitney's acceleration will be -0.2 miles per minute.

We have that the cost is $80 plus $3 per mile, and also we now that the car is 20 to 30 miles from the car repair shop. So we have that Trini have to pay

So the answer is: b.140 greater than sign M greater than sign 150.

Answer:

110

Step-by-step explanation:

Know the angle for BCD which is 130.

Subtract 180 from 130 and you get angle c for the triangle which is 50

Already knowing B and C, add them both which comes up to 70

All triangle angles equal 180 so subtract 70 for 180 and you get 110

A graph of the resulting triangle after a rotation of -180° about the origin is shown below.

In Mathematics and Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).

Furthermore, the mapping rule for the rotation of triangle TOP 180° counterclockwise or -180° about the origin is given by this mathematical expression:

(x, y)                                            →            (-x, -y)

Coordinates of point T (6, 0)  →  Coordinates of point T' = (-6, 0)

Coordinates of point O (-2, -5)  →  Coordinates of point O' = (2, 5)

Coordinates of point P (-2, 5)  →  Coordinates of point P' = (2, -5).

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Work Hard and poop on em

Answer:

Unlabeled side length = 15.00 units

Step-by-step explanation:

Because this is a right triangle, we can find the unlabeled side length using the Pythagorean theorem, which is

a^2 + b^2 = c^2, where

In the triangle, we're given that the legs are 12 and 9 units and the unlabeled side is the hypotenuse, which we must find:

Step 1:  Plug in 12 for a and 9 for b and simplify:

12^2 + 9^2 = c^2

144 + 81 = c^2

225 = c^2

Step 2:  Take the square root of both sides to solve for c, the hypotenuse (aka the unlabeled side):

± √225 = √(c)^2

± 15 = c

15.00 units = c

Although taking the square root of a number produced both a positive and negative answer since squaring both a positive and negative answer gives us a positive answer (e..g, 15 * 15 = 225 and -15 * -15 = 225), you can't have a negative measure.  Therefore, c, the unlabeled side length = 15.00 units.

Answer:

20.599

Step-by-step explanation:

Answer:

12.325 + 8.274 = 20.599

A²+B²= C²

31²+ 21²= z²

961+441 = z²

1402= z²

z= 37.443290454

Answer:

B

Step-by-step explanation:

To find the equation, we can use the point-slope form:

\(y-y_1=m(x-x_1)\)

Where m is the slope and (x₁, y₁) is a point.

First, we will need to find the slope. Since we have two points, we can use the slope formula:

\(\displaystyle m=\frac{y_2-y_1}{x_2-x_1}\)

Let (2, -1) be (x₁, y₁) and let (0, 5) be (x₂, y₂). Substitute and evaluate:

\(\displaystyle m=\frac{5-(-1)}{0-2}=6/-2=-3\)

Therefore, the slope m is -3.

Now, we can use the point-slope form. We also need a point. Let’s use (2, -1) for consistency. So, we will substitute -3 for m and (2, -1) for (x₁, y₁). This yields:

\(y-(-1)=-3(x-2)\)

We will now convert this to slope-intercept form. Simplify the left and distribute the right:

\(y+1=-3x+6\)

Subtract 1 from both sides. Therefore, our equation is:

\(y=-3x+5\)

Thus, our answer is B.

We have found that: AB = (BD/2) * (XZ/AY) and we can solve for BD:

BD = 2 * AB * AY / XZ

What is triangle?

A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.

Since BD is a median of triangle ABC, it divides side AC into two equal parts. Let's label the midpoint of AC as M. Similarly, YW is a median of triangle XYZ and it divides side XZ into two equal parts, with the midpoint labeled as N.

Since AABC~AXYZ, we know that the corresponding sides are proportional. Thus,

AB/AX = AC/AY = BC/BZ

Since AB = BC (given that B is a vertex of both triangles), we have:

AB/AX = AC/AY

We can rewrite this equation as:

AB/AC = AX/AY ----(1)

Since BD is a median of triangle ABC, we have:

BD = 1/2 AC ----(2)

Similarly, since YW is a median of triangle XYZ, we have:

YW = 1/2 XZ ----(3)

From equation (1), we have:

AB/AC = AX/AY

Multiplying both sides by AC, we get:

AB = AX * (AC/AY)

Now, using equation (2), we can substitute AC/2 for BD:

AB = AX * BD/AY

Finally, using equation (3), we can substitute XZ/2 for YW:

AB = (BD/2) * (XZ/AY)

Therefore, we have found that:

AB = (BD/2) * (XZ/AY)

Hence, we can solve for BD:

BD = 2 * AB * AY / XZ

Note that we need to know the actual values of AB, AY, and XZ to find BD.

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An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.

We know that,

An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.

The explicit formula for any arithmetic series is given by the formula,

a_n = a_1 + (n-1)d

where d is the difference and a₁ is the first term of the sequence.

The major distinction between recursive and explicit formulas is that a recursive formula returns the value of a particular term depending on the preceding term, whereas an explicit formula returns the value of a given term based on its location.

When the value of the first term and the common difference is known then an explicit formula is used, while the recursive formula will be used when the value of the previous value is known and the value of the common difference is known.

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complete question:

what is the difference between the explicit formula and recursive formula for sequences when would you use one over the other​

Answer:

x = 7

Step-by-step explanation:

3x-5=x+9 (Adding 5 and -x to both signs of = Sign)

2x = 14

x = 7

Step-by-step explanation:

The y-intercept of a function can be found by looking at the point where the x-coordinate is 0. In this case, the y-intercept of the function is -3, as the point (0,-3) is on the graph.

The slope of a function can be found by looking at the change in y divided by the change in x between two points on the graph. In this case, we can use the points (0,-3) and (1,-1) to find the slope. The change in y is -1 - (-3) = 2 and the change in x is 1 - 0 = 1. So the slope is 2/1 = 2.

Therefore, the equation of the function can be written in slope-intercept form as y = mx + b, where m is the slope and b is the y-intercept. So the equation of the function is:

y = 2x - 3

It's the equation of a line that pass through (0,-3) and (1,-1) and (2,1) and (3,3) and (4,5)

Answer:

Its is the second one

Step-by-step explanation:

Remember: rise over run

The b of the equation is -2 because that is how far it goes down on the y axis.

The slope is 3x.

Put the slope like this 3/1= rise/run

Sorry for the delayed response!  

Answer:

So 3/7 is the fraction of the money John received.

Step-by-step explanation:

3:4, so John is 3 and Peter is 4.

Now add these up for the denominator which is 3+4=7

and put Johns value over it, Johns value is 3.

So 3/7 is the fraction of the money John received.

Using the permutation formula, it is found that there are 57,120 ways to fill the 4 positions.

There are different roles, hence the order is important, which means that the permutation formula is used.

The number of possible permutations of x elements from a set of n elements is given by:

\(P_{(n,x)} = \frac{n!}{(n-x)!}\)

In this problem, 4 roles are chosen from a set of 17, hence the number of ways is given by:

\(P_{17,4} = \frac{17!}{13!} = 57120\).

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The probability of Miguel selecting a tile number less than 3 from each bag -1 is 1/5 and bag-2 is 2/5.

The given tiles in bag-1 = {2, 4, 5, 8, 9}

Total number of tiles in bag-1 = 5

The number of tiles less than number 3 in the bag - 1 = 1

The probability of Miguel selecting a tile number less than 3 =

number of tiles less than 3 / total number of tiles = 1/3

The given tiles in bag-2 = {0, 1, 3, 6, 7}

Total number of tiles in bag-2 = 5

The number of tiles less than number 3 in the bag-2 = 2

The probability of Miguel selecting a tile number less than 3 =

number of tiles less than 3 / total number of tiles = 2/3

From the above analysis, we solved the problem.

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We can see here that the probability that a student chosen at random from this school will be enrolled in both a foreign language course and a psychology course is 0.1.

Probability is a branch of mathematics that deals with numerical descriptions of the likelihood that an event will occur or that a statement is true. The probability of an event is a number between 0 and 1, where, generally speaking, 0 indicates the event's impossibility and 1 indicates its certainty.

Let's look at the provided information.

We see that 18% of the student are enrolled in a psychology course.

Let P(A) be the student that is enrolled in psychology course.

Thus: P(A)=18%=0.18

28% students are enrolled in a foreign language course.

Let P(B) indicate the percentage of students enrolled in foreign language course.

Thus: P(B)=28%=0.28.

36% are enrolled in either a psychology course or a foreign language course or both.

That means P(A∪B) = 36% = 0.36

Looking for the probability that a student chosen at random from the school will be enrolled in both a foreign language course and a psychology course, we have:

Thus, we need to find P(A∩B).

P(A∪B) = P(A)+P(B)-P(A∩B)

0.36 = 0.18 + 0.28 - P(A∩B)

0.36 = 0.46 - P(A∩B)

P(A∩B) = 0.1

Thus, we see that the required probability is 0.1.

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Answer:

The equations are:

\(4H + 3P = 13.75\)

\(2H + 5P = 11.25\)

\(Hotdog = 2.50\)

\(Pretzel = 1.25\)

Step-by-step explanation:

Let:

\(H = hot\ dog\)

\(P =Pretzel\)

For Tina:

\(4H + 3P = 13.75\)

For Doug:

\(2H + 5P = 11.25\)

Solving for the price of both items:

We have:

\(4H + 3P = 13.75\) --- (1)

\(2H + 5P = 11.25\) --- (2)

Multiply (2) by 2

2 * (\(2H + 5P = 11.25\))

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

\(4H + 10P = 22.50\) --- (3)

Subtract (3) from (1)

\(4H + 3P = 13.75\)

\(4H + 10P = 22.50\)

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

\(4H - 4H + 3P - 10P = 13.75 - 22.50\)

\(3P - 10P = 13.75 - 22.50\)

\(-7P = -8.75\)

Solve for P

\(P = \frac{-8.75}{-7}\)

\(P = 1.25\)

Substitute 1.25 for P in (2)

\(2H + 5P = 11.25\)

\(2H + 5 * 1.25 = 11.25\)

\(2H + 6.25 = 11.25\)

Collect Like Terms

\(2H = 11.25-6.25\)

\(2H = 5\)

Solve for H

\(H = \frac{5}{2}\)

\(H = 2.50\)

The solutions of the given equations are x = 0 and x = -36.

We have,

To solve these equations:

9x - 7 = -7

We can add 7 to both sides to isolate the variable:

9x - 7 + 7 = -7 + 7

Simplifying the left-hand side and the right-hand side, we get:

9x = 0

Finally, dividing both sides by 9, we get:

x = 0

Next, to solve:

-1 = 5 + x/6

We can begin by subtracting 5 from both sides:

-1 - 5 = 5 + x/6 - 5

Simplifying the left-hand side and the right-hand side, we get:

-6 = x/6

Finally, multiplying both sides by 6, we get:

-36 = x

Thus,

The solutions of the given equations are x = 0 and x = -36.

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The complete question.

9x - 7 = -7

-1 = 5  + x/6

Answer:

1) 38

2) 56

3) 86

4)  37

5) 6 i think

6) 93

Step-by-step explanation: sorry if any of these are wrong

Answer:

The answer is 38. Sorry if it's wrong.

The value of the equation that defines the function is f(x) = 3(5/3)ˣ

From the question, we have the following parameters that can be used in our computation:

(0, 3) and (1, 5)

An exponential function is represented s

y = abˣ

Where,

a = y when x = 0

So, we have

y = 3bˣ

Using the other point, we have

3b = 5

This gives

b = 5/3

So, we have

f(x) = 3(5/3)ˣ

Hence, the equation defining f is f(x) = 3(5/3)ˣ

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There is only 1 possible 11-card hand that can be formed from a 20-card deck.

To determine the number of 11-card hands possible with a 20-card deck, we can use the concept of combinations.

The number of combinations, denoted as "nCk," represents the number of ways to choose k items from a set of n items without regard to the order. In this case, we want to find the number of 11-card hands from a 20-card deck.

The formula for combinations is:

nCk = n! / (k!(n-k)!)

Where "!" denotes the factorial of a number.

Substituting the values into the formula:

20C11 = 20! / (11!(20-11)!)

Simplifying further:

20C11 = 20! / (11! * 9!)

Now, let's calculate the factorial values:

20! = 20 * 19 * 18 * ... * 2 * 1

11! = 11 * 10 * 9 * ... * 2 * 1

9! = 9 * 8 * 7 * ... * 2 * 1

By canceling out common terms in the numerator and denominator, we get:

20C11 = (20 * 19 * 18 * ... * 12) / (11 * 10 * 9 * ... * 2 * 1)

Performing the multiplication:

20C11 = 39,916,800 / 39,916,800

Finally, the result simplifies to:

20C11 = 1

Consequently, with a 20-card deck, there is only one potential 11-card hand.

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Answer: A

Step-by-step explanation:

Volume= LxWxH so we get 20x28x24 as given.

Volume= 13,440 which is the volume of the box given. ANd so if the box is 10,500cubic inches, we subtract to find the difference.

13,440-10,500= 2,940 Cubic Inches

Option A

Answer:

Part A:  13440 cubic inches.

Part B: A - 2940 cubic inches.

Step-by-step explanation:

The volume of the box = 24x20x28 = 13440 cubic inches.

The problem tells us that his gift is 10,500 cubic inches. So subtract that from the volume of the box.

13440-10500 = 2940 cubic inches. The answer is A.

Answer:

The parents must deposit $9612.75 when their child is born.

Step-by-step explanation:

Hope this helps!