Label the terms in the expression as constant, linear, and quadratic. 4x2 + 3x - 6

Final answer:

Geoff's garden exhibits exponential growth of dahlia bulbs, doubling each year. By following this pattern, Geoff should expect to have 768 bulbs in the eighth year.

Explanation:

Geoff’s dahlia bulbs are showing a pattern of doubling in quantity each year. This is an example of exponential growth, a concept commonly explored in mathematics. To determine the number of bulbs Geoff can expect in the eighth year, we need to continue this pattern.

In the first year, there are 6 bulbs. The second year has 12 bulbs which is 6 multiplied by 2. The third year has 24 bulbs, which is 12 multiplied by 2. This pattern suggests that every year, the number of bulbs is the previous year's total multiplied by 2.

By following this pattern, to find the number of bulbs in the eighth year, we calculate:

Fourth year: 24 bulbs × 2 = 48 bulbs

Fifth year: 48 bulbs × 2 = 96 bulbs

Sixth year: 96 bulbs × 2 = 192 bulbs

Seventh year: 192 bulbs × 2 = 384 bulbs

Eighth year: 384 bulbs × 2 = 768 bulbs

Therefore, Geoff should expect to have 768 bulbs in his garden in the eighth year if the pattern of doubling the number of bulbs each year continues.

The factored form of  −7ab+10 is (ab−5)(ab−2).

To factor the expression −7ab+10, we look for two binomials whose product gives the original expression. In this case, the factors are

(ab−5)(ab−2).

Expanding

(ab−5)(ab−2) using the distributive property, we get:

(ab−5)(ab−2)=(ab)(ab)−(ab)(2)−(5)(ab)+(5)(2)

Simplifying each term, we get:

−2ab−5ab+10

Combining like terms, we have:

−7ab+10

Therefore, the factored form of  −7ab+10 is (ab−5)(ab−2).

For this case we have the following definitions:

Answer:

x ----------------> Variable

3 ----------------> Coefficient

1 ----------------> Constant

[tex]3x ^ 2-4x + 1[/tex] -----------> Algebraic expression

2 ----------------> Degree

She will cover 35/8 miles.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given:

total distance in miles = 7/8 miles  per day

So, in 5 days in a week.

She will cover

=5*7/8

=35/8 miles.

Hence, She will cover 35/8 miles.

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Answer:

B

Step-by-step explanation:

The line segment XZ has a length of 16 units. Hence, the 3rd option is the correct choice. Computed using the tangent to the circle and the Pythagoras Theorem.

A tangent to a circle is always perpendicular to it, that is, the radius drawn from the center of the circle to the tangent, is always perpendicular to it.

According to the Pythagoras Theorem, in a right triangle, the square of the hypotenuse, that is, the side opposite to the right angle, is equal to the sum of the squares of the legs, that is, the other two sides.

In the question, we are asked to find the length of the line segment XZ.

Firstly, we name the center of the circle O.

The diameter of the circle is given to be 12 units.

Thus, its radius = 12/2 = 6 units,

Joining the radius OW, we get a right triangle OWZ, as the radius from the center of the circle to the tangent is always perpendicular.

In the right triangle OWZ, by Pythagoras Theorem, we can write:

OZ² = OW² + WZ² {Since, OZ is the hypotenuse},

or, (k + 6)² = 6² + (k + 4)² {Since, OZ = OY + YZ = Radius + k = 6 + k, and OW = Radius = 6},

or, k² + 12k + 36 = 36 + k² + 8k + 16 {Using the formula (a + b)² = a² + 2ab + b²},

or, k² + 12k - k² - 8k = 36 + 16 - 36 {Rearranging},

or, 4k = 16 {Simplifying},

or, k = 4 {Simplifying}.

Now, XZ = XY + YZ = Diameter + k = 12 + 4 = 16 units.

Thus, line segment XZ has a length of 16 units. Hence, the 3rd option is the correct choice. Computed using the tangent to the circle and the Pythagoras Theorem.

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Answer:  The 100th even natural number is 200.

Step-by-step explanation:  Given that the following arithmetic sequence represents the set of natural numbers :

2,  4,  6,  8,  10,  .  .  ..

We are given to find the 100th even natural number, i.e., the 100-th term of the sequence.

We know that

the n-th term of an arithmetic sequence with first term a and common difference d is given by

[tex]a_n=a+(n-1)d.[/tex]

For the given sequence, we have

a = 2  and  d = 4 - 2 = 6 - 4 =  .  .  .  =2.

Therefore, the 100-th term of the sequence will be

[tex]a_{100}=a+(100-1)d=2+99\times2=2+198=200.[/tex]

Thus, the 100th even natural number is 200.

Answer: 15

Step-by-step explanation: its 15

Answer:

the asnwer is 5

Step-by-step explanation:

i did this question

When a point is rotated 90 degrees counterclockwise about the origin, its new coordinates can be found by swapping the x and y coordinates and changing the sign of the new y coordinate. In this case, the new coordinates of point C would be (-3,-5).

When a point is rotated 90 degrees counterclockwise about the origin, its new coordinates can be found by swapping the x and y coordinates and changing the sign of the new y coordinate.

In this case, point C has coordinates (5,-3). When we rotate it, the new x coordinate becomes -3 and the new y coordinate becomes -5. Therefore, the new coordinates of point C would be (-3,-5).

Answer:

Frequency of [tex]d=2\sin (\frac{\pi t}{3})[/tex] is [tex]\frac{1}{6}[/tex].

Step-by-step explanation:

We have the harmonic equation as, [tex]d=2\sin (\frac{\pi t}{3})[/tex].

It is known that,

If a function f(x) has a period P, then the function cf(bx) has period [tex]\frac{P}{|b|}[/tex].

So, we have,

As the function [tex]\sin t[/tex] has [tex]2\pi[/tex], then [tex]d=2\sin (\frac{\pi t}{3})[/tex] will have period [tex]\frac{2\pi}{\frac{\pi}{3}}[/tex] = 6

Further, the frequency of a function is the reciprocal of its period.

Thus, the frequency of [tex]d=2\sin (\frac{\pi t}{3})[/tex] is [tex]\frac{1}{6}[/tex].

Answer:

Option C

Step-by-step explanation:

we need to find the solution(s) to the quadratic equation 50 – x^2 = 0

50 – x^2 = 0

Subtract 50 from both sides

– x^2 = -50

Now divide by -1 from both sides

x^2 = 50

To remove square , take square root on both sides

[tex]x=+-\sqrt{50}[/tex]

[tex]x=+-\sqrt{25*2}[/tex]

[tex]x=+-5\sqrt{2}[/tex]

Option C is the answer

To find the original weight of a bag of grapes before some were eaten, you divide the current weight of 5/8 lb by 4. The calculation reveals that the bag's original weight was 5 pounds.

The question asks us to calculate the original weight of a bag of grapes before it was partially eaten. After eating some of the grapes, the bag now weighs 5/8 of a pound. To find the original weight, we need to determine what weight, when multiplied by 4, would equal 5/8 of a pound. We do this by dividing the current weight by 4 to reverse the multiplication. Using the formula:

Original Weight = Current Weight / 4

So:

Original Weight = (5/8) lb / 4

When we do the calculation:

Original Weight = (5/8) lb / (4/1)

Original Weight = (5/8) lb \(1/4)

Original Weight = (5/32) lb

Since (5/32) lb is equivalent to 5 pounds (when multiplied by 4, it gives 20/32 lb, which simplifies to 5/8 lb), the original weight of the bag of grapes was 5 pounds.