Queensbury, New York is a 200 mile drive from New York City. If Laura had driven 140 miles of it already, what percent has she driven?

The sum of two polynomials 4x³ + 2x² - 4x³ and 7x³ - 4x² + 7x + 8 is equal to 11x³ - 2x² + 3x + 8.

To add the polynomials 4x^3 + 2x^2 - 4x + 3 and 7x^3 - 4x^2 + 7x + 8, we first arrange them in descending order of powers of x:

4x^3 + 2x^2 - 4x + 3

7x^3 - 4x^2 + 7x + 8

Adding

11x^3 - 2x^2 + 3x + 11

Therefore, the sum of the two polynomials is 11x^3 - 2x^2 + 3x + 11.

Placing it in the grid:

| 11 | -2 | 3 | 11 |

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Answer:

yep

Step-by-step explanation:

Answer: Yeah-     I

..................................I

Answer:

The answer is C

Step-by-step explanation:

If this is the graph of f(x) =a^(x+h)+k then h<0 and k> 0.Hence option C is correct.

A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.

A function is a statement, rule, or law that specifies the connection between two variables. Functions are common in mathematics and are required for the formulation of physical connections.

If f(x) = a(x+h) + k is the graph, then h<0 and k> 0.

Therefore, choice D is right.

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Answer:

he was supposed to add three on both sides

Step-by-step explanation:

xddudududududdudididididididididi

Answer: 4/35

Step-by-step explanation:

Number of red marbles = 4

Number of blue marbles = 5

Number of green marbles = 6

Total number of marbles = 4+5+6 = 15

When a red marble is picked, the probability is 4/15, then to pick a green marble after that, we have 14 marbles left and probability of picking green is 6/14.

Now, probability of choosing a red marble from the bag, not putting it back, and then choosing a green marble will be:

= 4/15 × 6/14

= 24/210

= 4/35

Answer

260 kilograms

Step-by-step explanation:

the correct answer is 260 kg

Answer: 12.6 kg

Step-by-step explanation: add the amounts of food for her farm, and just search for how many kg are in 1,260 grams

The Equation of the Line is y = 0 which is the equation is of the X-axis

What is Slope of Line?

The slope is defined as the ratio of "rise" divided by "run" between two points on a line, or the ratio of altitude change to horizontal distance between any two locations on the line.

We are given that the slope of the line is 0

and, the intercept point is (4, 0)

Equation of line: y - y1 = m (x - x1)

y - 0 = 0

y = 0

Implies that the equation is of the X-axis

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Given:

Write the abve expression in the for of y=mx+c, then m will be the slope of the equation.

Compare the above expression with y=mx+c. The slope of the given equation is 2/3, and the correct option is option C.

The altitude of Polaris, also known as the North Star, refers to its angle above the horizon when observed from a specific location on Earth.

The altitude of Polaris varies depending on the observer's latitude.

For an observer at the North Pole (latitude 90 degrees), Polaris appears directly overhead, at an altitude of 90 degrees. This means Polaris is at the zenith, the highest point in the sky.

For observers at other latitudes in the Northern Hemisphere, Polaris will appear lower in the sky. The altitude of Polaris is equal to the observer's latitude. For example, if you are at a latitude of 40 degrees north, Polaris will have an altitude of approximately 40 degrees above the horizon.

It's important to note that the altitude of Polaris remains relatively constant throughout the night and throughout the year due to its proximity to the celestial north pole. This makes it a useful navigational reference point for determining direction and latitude in the Northern Hemisphere.

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Answer:

2. It's sides are 3 times as long as those of the origanal square.

Step-by-step explanation:

The scale factor is 3. So the scale of the sides of the orig. square to the image is 1:3. So, it is 3 times as large as the preimage.

Answer:

x = -1 and 5

Step-by-step explanation:

Solve:  \(-16x^2+64x+80=0\)

Factor out common value of 16:

\(\implies 16(-x^2+4x+5)=0\)

Divide both sides by 16:  

\(\implies -x^2+4x+5=0\)

Change signs:

\(\implies x^2-4x-5=0\)

Break expression into groups:

\(\implies x^2+x-5x-5=0\)

\(\implies( x^2+x)-(5x+5)=0\)

Factor parentheses:

\(\implies x(x+1)-5(x+1)=0\)

Factor out common term \(x+1\):

\(\implies (x+1)(x-5)=0\)

Therefore,

\(x+1=0\)  and  \(x-5=0\)

So \(x=-1\) and \(x=5\)

\(\\ \tt\hookrightarrow -16x^2+64x+80=0\)

\(\\ \tt\hookrightarrow 16x^2-64x-80=\)

\(\\ \tt\hookrightarrow 16(x^2-4x-5)=0\)

\(\\ \tt\hookrightarrow x^2-4x-5=0\)

\(\\ \tt\hookrightarrow x^2-5x+x-5=0\)

\(\\ \tt\hookrightarrow x(x-5)+1(x-5)=0\)

\(\\ \tt\hookrightarrow (x+1)(x-5)=0\)

So, y = (1/2)(x + 8) is the equation of the linear function.

To write the equation of a linear function with a given x-intercept and y-intercept, we can use the point-slope form of a linear equation:

y - y1 = m(x - x1)

In this case, we are given that the x-intercept is (-8, 0) and the y-intercept is (0, 4). We can use the coordinates of the x-intercept as (x1, y1) and the slope of the line as m to write the equation:

y - 0 = m(x - (-8))

y = m(x + 8)

We can then substitute the y-intercept into this equation to find the value of m:

4 = m(0 + 8)

4 = 8m

m = 1/2

Substituting the value of m back into the equation, we get:

y = (1/2)(x + 8)

This is the equation of the linear function.

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y - y1 = m(x - x1)

y - 0 = m(x - (-8))

y = m(x + 8)

We can then substitute the y-intercept into this equation to find the value of m:

4 = m(0 + 8)

4 = 8m

m = 1/2

Substituting the value of m back into the equation, we get:

y = (1/2)(x + 8)

Form the given five quadratics , the one representing the repeated roots is equal to option d. 25x² - 30x + 9 and repeated roots are 3/5 or 3/5.

Quadratics representing repeated roots has discriminant equals to zero.

Standard quadratic equation is:

ax² + bx + c = 0

Discriminant 'D' = b² - 4ac

option a. -x²+ 18x + 81

Discriminant

'D' = 18² - 4(-1)(81)

      = 324 + 324

      = 648

D>0 has distinct roots.

option b. 3x²- 3x - 168

Discriminant

'D' = (-3)² - 4(-3)(-168)

      = 9 - 2016

      = -2007

D< 0 has distinct roots.

option c. x²- 4x -  4

Discriminant

'D' = (-4)² - 4(1)(-4)

      = 16 + 16

      = 32

D>0 has distinct roots.

option d. 25x²- 30x + 9

Discriminant

'D' = (-30)² - 4(25)(9)

      = 900 - 900

      = 0

D = 0 has repeated roots.

Repeated roots are:

x = ( -b ±√D ) / 2a

  = [-(-30)±√0 ]/ 2(25)

  = 30/ 50

  = 3/5.

option e.  x² - 14x + 24

Discriminant

'D' = (-14)² - 4(1)(24)

      = 196 - 96

      = 100

D>0 has distinct roots.

Therefore, the quadratics which represents the repeated roots are given by option d. 25x² - 30x + 9 and its repeated roots are 3/5 or 3/5.

The above question is incomplete, the complete question is:

One of the five quadratics below has a repeated root. (There other four have distinct roots.) What is the repeated root?

a. -x²+ 18x + 81

b. 3x² - 3x - 168

c. x² - 4x - 4

d. 25x² - 30x + 9

e. x² - 14x + 24

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To show that the vector field F(x, y, z) = (-2y, -2x, 7z) is a gradient vector field, we need to find a scalar function V(x, y, z) such that its gradient, ∇V, is equal to F. We can determine the function V by integrating the components of F with respect to their respective variables.

Let's find the function V(x, y, z) by integrating the components of F(x, y, z) = (-2y, -2x, 7z) with respect to their variables.
∫-2y dx = -2xy + g(y, z)
∫-2x dy = -2xy + h(x, z)
∫7z dz = 7/2 z^2 + k(x, y)
We can see that -2xy is a common term in the first two integrals. Similarly, we observe that there are no common terms between the first and third integrals, as well as the second and third integrals. Therefore, we can assume that g(y, z) = h(x, z) = 0, since they will cancel out in the subsequent calculations.
Now, we can rewrite the integrals:
∫-2y dx = -2xy + C1(y, z)
∫-2x dy = -2xy + C2(x, z)
∫7z dz = 7/2 z^2 + C3(x, y)
By comparing these integrals with the components of the gradient vector, we can conclude that ∇V = (-2y, -2x, 7z), where V(x, y, z) = -xy + 7/2 z^2 + C.
To determine the constant C, we use the condition V(0, 0, 0) = 0:
V(0, 0, 0) = -(0)(0) + 7/2 (0)^2 + C = 0
C = 0
Therefore, the function V(x, y, z) that satisfies V(0, 0, 0) = 0 is V(x, y, z) = -xy + 7/2 z^2. Thus, the vector field F(x, y, z) = (-2y, -2x, 7z) is indeed a gradient vector field F = ∇V.

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The graph of the function is attached below and the solution of the system is, (-2,5) and (2,-3)

Graph:

A graph consists of points, called vertices, and lines between those points, called edges.

Given,

Here we have the following functions,

f(x) = -2x + 1

g(x) = x² - 2x - 3

And we need to find the solution of the system and we have also plot the graph for the functions.

The graph of the given function is attached below.

The solution of the function s calculated as,

By looking at the graph we have identified that there are two point that intersect both lines.

At hose points are referred as the solutions of the function,

Therefore, the solution of  the function is (-2,5) and (2,-3).

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Answer:

$2.10

Step-by-step explanation:

change the rate of sales tax to a decimal by dividing by 100, so 3%=.03

multiply the price by .03

Answer:

2.10

Step-by-step explanation:

You do 3% of 70 which equals 2.10

Therefore, the sum of the distances traveled by the tips of both hands in one $24$-hour period is approximately $15.708$ meters.

To start, we need to find the length of each hand. The minute hand measures $10$ cm, which is equivalent to $0.1$ meters, and the hour hand measures $5$ cm, or $0.05$ meters.
Now, let's consider the distance each hand travels in one hour. The minute hand travels the circumference of the clock face, which has a diameter of $20$ cm or $0.2$ meters. The formula for the circumference of a circle is $2\pi r$, so the distance traveled by the minute hand in one hour is $2\pi(0.1) = 0.2\pi$ meters.
The hour hand travels the circumference of a circle with a diameter of $10$ cm or $0.1$ meters. Since the hour hand takes $12$ hours to complete one full revolution around the clock face, it travels $\frac{1}{12}$ of the circumference in one hour. Therefore, the distance traveled by the hour hand in one hour is $\frac{1}{12} \cdot 2\pi(0.05) = \frac{\pi}{120}$ meters.
To find the total distance traveled by both hands in $24$ hours, we can add up the distance traveled by each hand in one hour and multiply by $24$.
Total distance = $24\left(0.2\pi + \frac{\pi}{120}\right) \approx 15.708$ meters
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Answer:

1800

Step-by-step explanation:

Answer: The roses costed $9

Step-by-step explanation:

3 multiplied by 3 equals 9

1 multiplied by 6 equals 6

9+6=15

Answer:

f^-1(x)=x/3-1/3

Step-by-step explanation:

The given statement " If two sounds can form a minimal pair, they are allophones of two distinct phonemes." is true. because when two sounds can form a minimal pair, it demonstrates that the difference between the sounds is crucial for distinguishing the meaning of the words in the language as a result these sounds cannot be considered as allophones of the same phoneme, as they do not share the same underlying representation.

A minimal pair refers to two words that differ in only one sound but have different meanings. For example, "bat" and "pat" differ only in their initial consonants, /b/ and /p/, but have distinct meanings. This difference in meaning indicates that the two sounds are part of separate phonemes.

Phonemes are the basic, abstract units of sound in a language that can change the meaning of a word when substituted for one another. Allophones, on the other hand, are the various concrete realizations of a phoneme that do not change the meaning of a word. They are considered to be different surface forms of the same underlying phoneme.

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Answer:

Step-by-step explanation:

(-2g+7)-(g+11)

-2g+7-g-11

-3g-4

Answer:

See the expression below

Step-by-step explanation:

Given data

We have the expression  

-4x+y=11-----------1

from 1 make y subject of formula we have

y=100+4x

Make x subject of the formula we have

-4x=11-y

divide both sides by -4

x=(11-y)/-4

By using the definition of continuity and exploiting the fact that f(0) = 1, we were able to prove the existence of an open interval (a, b) containing 0 such that for any real number r within this interval, the function value f(r) is greater than 0.

First, let's recall the definition of continuity at a point. A function f is continuous at a point c if, for any positive number ε, there exists a positive number δ such that whenever x is within δ of c, the value of f(x) will be within ε of f(c).

Now, since f is continuous at 0, we can say that for any positive ε, there exists a positive δ such that if |x - 0| < δ, then |f(x) - f(0)| < ε.

Since f(0) = 1, the above inequality simplifies to |f(x) - 1| < ε.

We want to find an open interval (a, b) containing 0 such that for any r within this interval, f(r) > 0. Let's consider ε = 1 as an arbitrary positive number.

From the definition of continuity at 0, we can find a positive δ such that if |x - 0| < δ, then |f(x) - 1| < 1. This implies -1 < f(x) - 1 < 1, which further simplifies to 0 < f(x) < 2.

Now, consider the interval (a, b) = (-δ, δ). Since δ is positive, it ensures that 0 is within this interval. Also, since f(x) is continuous on this interval, we can conclude that f(r) > 0 for all r within (-δ, δ).

To prove this, let's take any r within (-δ, δ). Since r is within this interval, we have -δ < r < δ, which implies |r - 0| < δ. By the definition of continuity at 0, we know that |f(r) - 1| < 1. Therefore, 0 < f(r) < 2, and we can conclude that f(r) > 0.

Hence, we have shown that there exists an open interval (a, b) containing 0 such that for all r within this interval, f(r) > 0.

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Three labeled points on the line are (-2, -2m), (0, 0), and (2, 2m), where m is the slope of the line.

A line passing through the origin but not contained in any of the three coordinate planes can be represented by the equation y = mx, where m is the slope of the line. Since the line passes through the origin, the y-intercept is 0.

To find labeled points on the line, we can choose different values for x and calculate the corresponding y-values using the equation y = mx. Let's choose three values for x: -2, 0, and 2.

For x = -2:

y = m(-2) = -2m

So, one labeled point on the line is (-2, -2m).

For x = 0:

y = m(0) = 0

Another labeled point on the line is (0, 0).

For x = 2:

y = m(2) = 2m

So, the third labeled point on the line is (2, 2m).

These three labeled points (-2, -2m), (0, 0), and (2, 2m) lie on the line passing through the origin, and they are not contained in any of the coordinate planes.

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Answer:

15

Step-by-step explanation:

(-7,0) and (8,0) are on the opposite side of origin of x axis

d = 8 - -7 = 15

Answer:

if I have to calculate the average then it's a

add all of them and divide by 10

answer is 29.7

Answer:

12) z = 64

15) q = 75

Step-by-step explanation:

12) 40/65 = z/10⁴

Cross Multiply

65 × z = 40 × 104

65z = 4160

z = 4160 / 65

z = 64

15)32.5/25 = 97.5/q

Cross Multiply

25 × 97.5 = 32.5× q

q = 25 × 97.5/32.5

q = 2437.5 /32.5

q = 75

Answer:

Step-by-step explanation:

Since it's a triangle all it's interior angles sum up to 180°

The triangle is isosceles which means two of it's angles are equal

From the question

\(m\angle B = m\angle C = 41 \degree\)

So to find \(m \angle A\) add up all the angles and equate it to 180° and solve for A

That's

\(m\angle A + m\angle B + m\angle \: C = 180 \\ m\angle A = 180 -m\angle B - m\angle \: C \\ m\angle A = 180 - 41 - 41 \\ = 180 - 82\)

We have the final answer as

\(m\angle A = 98\)

Hope this helps you