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Question: What is the solution to this quadratic?

In the given scenario, the explanatory variable is the type of equipment used every year, while the response variable is the amount of improvement in the golfer's game.

The explanatory variable is the variable that is believed to have an effect on or be able to explain the changes in the response variable. In this case, the golfer wants to determine if the type of equipment used can be used to predict the amount of improvement in their game.

Therefore, the type of equipment used every year is the explanatory variable because it is being considered as a potential factor that may influence the amount of improvement in the golfer's game.

On the other hand, the response variable is the variable that is being observed or measured to determine the outcome or the effect of the explanatory variable.

In this scenario, the response variable is the amount of improvement in the golfer's game. The golfer is interested in assessing how the type of equipment used relates to the changes or improvements in their game performance.

Thus, the amount of improvement in the golfer's game is the response variable in this context.

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Answer:

Step-by-step explanation:

<NOC is 31 because it is a vertical angle to <BOK, which is also 31

<DOC is 62 because it is two times the bisected <NOC. 2*31=62

<DON is 31 because it is the bisected angles <DON and <NOC are equal.

<TOC is 118 because <KOT and <NOC are both 31 degrees. Since they lie on a line together, the three angles should add up to 180 degrees. 180-31-31 = 118

I hope this helps! :)

Answer:

False.

Step-by-step explanation:

Using the property of distribution, (a + b)² will be a² + b², never a² + b.

No, for any two integers a and b, (a + b)² ≠ a² + b is a false statement.

For the given two integers a and b,

The given expression

(a + b)² = a² + b (false statement)

The correct statement is-

(a + b)² = (a + b)(a + b)

(a + b)² = a² + b² +  2ab

Thus, no, for any two integers a and b, (a + b)² ≠ a² + b.

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The length of sides BC and XC in the triangle are 8.66 and 10 units respectively

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

Trigonometric ratio is used to show the relationship between the sides and angles of a right triangle.

From the triangle shown, using trigonometric ratio:

sin(30) = 5/XC

XC = 10

Also:

tan(30) = 5/BC

BC = 8.66

The length of BC and XC are 8.66 and 10 units respectively

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Answer:

Step-by-step explanation:

AAS theorem: If two angles and a non-included side of one triangle are congruent to corresponding two angles and a non-included side of second triangle, then the triangles are congruent.

~~~~~~~~~~~~~

1). ∠N ≅ ∠L   Given

2). JK ≅ MK  Given

3). ∠JKN ≅ ∠MKL   Vertical

4). ΔJKN ≅ ΔMKL   AAS theorem of congruence.

Answer:  14,533.79 don´t take my word for it

Step-by-step explanation:

Future Value of Annuity Due

P = 2,000

r = 5.5% (0.055)

n = 6

1.055 * (2,000 * [(1 + 0.055)^6 - 1)/(0.055)])

= 14,533.79

Answer:

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

Let Anita be x now.

Her mother is 5 times older and in two years time she will be 5x + 2.

Rita is half the age of Anita and in two years time she will be (x/2) + 2.

The sum of ages after two years will be 58:

Anita is 8 years old.

Answer:

1/15

Step-by-step explanation:

Answer:

0.06

Step-by-step explanation:

Turn 1/3 to a decimal, which becomes .3

Then you do .3/5 which equals 0.06

Hope this helps.

Answer:

\(x^3-10\)

Step-by-step explanation:

Let the number be x.

"A number cubed" refers to x³.

"Difference" means to subtract, so the answer is \(x^3-10\).

Answer:

207

Step-by-step explanation:

Denise has 46(7/2) = 161 cherries.

So, they have a total of 161 + 46 = 207 cherries

Since $f(x)$ is an odd function, we have $f(x) = -f(-x)$ for all $x$ in the domain of $f(x)$. Therefore,

\begin{align*}

\int_{-5}^5 f(x) dx &= \int_{-5}^0 f(x) dx + \int_0^5 f(x) dx \

&= \int_{5}^0 -f(-x) dx + \int_0^5 f(x) dx &\quad\text{(using substitution)} \

&= \int_{0}^5 f(-x) dx + \int_0^5 f(x) dx \

&= 2\int_0^5 f(x) dx \

&= 2\cdot \frac{1}{5}\int_{-5}^5 f(x) dx \

&= 2\cdot \frac{1}{5} \cdot 3 \

&= \frac{6}{5}.

\end{align*}

Thus, the average value of $f$ on the interval $[-5,5]$ is $\frac{1}{10} \int_{-5}^5 f(x) dx = \frac{6}{5}\cdot\frac{1}{10} = \boxed{\frac{3}{5}}$.

The rules AAS, ASA, SSS and SAS are congruence rule of triangle  and the each rules has been explained

The rules AAS, ASA, SSS and SAS are congruence rule of triangle

SSS rule is side-side-side rule, it states that if three sides of the one triangle and three sides of the other triangles are equal, then both triangles are congruent

SAS rule is side-angle-side rule, it states that if two sides and one included angles between the sides of the one triangle is equal to  the two sides and one included angles between the sides of the other triangle, then both triangles are congruent

ASA rule is angle-side-angle rule, it states that if two angles and one included side between the angle of the one triangle is equal to the two angles and one included sides between the angles of the other triangle, then both triangles are congruent

AAS rules is angle-angle-side rule, it states that if two angles and one non included sides of the one triangle is equal to the two angles and one non included sides of the another triangle, then both triangles are congruent

Therefore, the AAS, ASA, SSS and SAS are the rules of congruence of the triangle

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Answer:

$60

Step-by-step explanation:

because 30 is 50% percent of 60

The distance from the point on the ground to the base of the tree is given as follows:

20.5 feet.

The three trigonometric ratios are defined as follows:

For the angle of 38º, we have that:

Hence the distance is obtained as follows:

tan(38º) = 16/d

d = 16/tangent of 38 degrees

d = 20.5 feet.

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The solution for each inequality is:

x ∈ (-∞, 22]

x ∈ (4/3, ∞)

x ∈ (1, 2)

x ∈ (-∞, -1) U (6, ∞)

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

1)

Starting with the inequality:

√(2x+5) ≤ 7

Squaring both sides, we get:

2x + 5 ≤ 49

Subtracting 5 from both sides:

2x ≤ 44

Dividing both sides by 2:

x ≤ 22

So the solution is:

x ∈ (-∞, 22]

2)

Starting with the inequality:

√(2x-1) > √(3-x)

Squaring both sides, we get:

2x - 1 > 3 - x

Adding x and 1 to both sides:

3x > 4

Dividing both sides by 3:

x > 4/3

So the solution is:

x ∈ (4/3, ∞)

3)

Starting with the inequality:

√(3x-2) < x

Squaring both sides, we get:

3x - 2 < x^2

Subtracting 3x and adding 2 to both sides:

0 < x^2 - 3x + 2

Factoring the right side:

0 < (x - 1)(x - 2)

So the solution is:

x ∈ (1, 2)

4)

Starting with the inequality:

√(5x+6) > x

Squaring both sides, we get:

5x + 6 > x^2

Subtracting 5x and 6 from both sides:

0 > x^2 - 5x - 6

Factoring the right side:

0 > (x - 6)(x + 1)

So the solution is:

x ∈ (-∞, -1) U (6, ∞)

Thus,

The solution for each inequality is:

x ∈ (-∞, 22]

x ∈ (4/3, ∞)

x ∈ (1, 2)

x ∈ (-∞, -1) U (6, ∞)

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Answer: 500 W (watt)

Step-by-step explanation:

Power = P = Work / time = W/t

W = Fd = Force x distance = 400N x 5m = 2000J

P = 2000J/4s = 500 W

Answer:

Most people use about 30 gallons of water for a bath, according to industry estimates. When filled to capacity (just below the overflow), a standard bathtub holds 42 gallons, but some of that water will be displaced when you get into the tub.

Step-by-step explanation:

Answer:

To start, the standard bathtub will hold roughly around 80 gallons (302 liters) of water. Much smaller bathtubs can only hold around 40 gallons (150 liters) of water, which typically are more suited for smaller children or function more as a shower space.

Answer:

To find a formula for the nth term of the given sequence, we can analyze the pattern and identify the relationship between the terms.

If we observe the numerator of each term, we can see that it follows the pattern 7, 10, 13, 16, 19, ... This is an arithmetic sequence with a common difference of 3.

If we examine the denominator of each term, we can see that it follows the pattern 1, 2, 6, 24, 120, ... This is not a common arithmetic sequence, but it can be described as a factorial sequence.

The nth term of a factorial sequence can be represented as n!, where n! denotes the factorial of n.

Combining these patterns, we can express the nth term of the given sequence as:

an = (3n + 4)/(n!)

Therefore, the formula for the nth term of the sequence is (3n + 4)/(n!).

Step-by-step explanation:

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The expression a⁷- a is divisible by 7 if a is an integer.

Given that,

7 divides a^7−a

To find that if a is an integer, then 7 divides a^7 -a or a⁷- a is divisible by the number 7

We can write, where k is an integer

a^7−a=7k

a(a^6−1)=7k

Now if a=k then

a^6−1=7

a^6=8

and a=±1.414 so a^7−a=9.898

If a is not equal to k then

a(a^6−1)=a(a^3+1)(a^3−1)=7k

since a(a+1)(a−1) is the not product of 3 consecutive integers, the expression is divisible by 7.

Hence, The expression a⁷- a is divisible by 7 if a is an integer.

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So to find the sale price of any item with a regular price of $45, you would multiply $45 by 0.8889 to get $40.

Proportion refers to the relationship between two ratios or two fractions. It indicates that two ratios or fractions are equal to each other. Proportions are commonly used in mathematics and everyday life to compare different quantities or to solve problems related to ratios and fractions.

Here,

To find the sale price, you multiply the regular price by a constant of proportionality. The constant of proportionality is equal to the ratio of the sale price to the regular price.

For example, if the regular price is $10 and the sale price is $8, then the constant of proportionality is:

$8/$10 = 0.8

So to find the sale price of any item with a regular price of $10, you would multiply $10 by 0.8 to get $8.

Looking at the table provided, we can see that the sale price is always less than the regular price. We can calculate the constant of proportionality for any pair of regular and sale prices. For example, for the first pair (regular price $25, sale price $24), the constant of proportionality is:

$24/$25 = 0.96

So to find the sale price of any item with a regular price of $25, you would multiply $25 by 0.96 to get $24.

Similarly, for the second pair (regular price $45, sale price $40), the constant of proportionality is:

$40/$45 = 0.8889 (rounded to four decimal places)

So to find the sale price of any item with a regular price of $45, you would multiply $45 by 0.8889 to get $40.

We can repeat this process for each pair of regular and sale prices to find the constant of proportionality for each pair.

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Answer:

22 feet

Step-by-step explanation:

6+5+6+5

= 11+11

= 22

Answer:

check A and C

Step-by-step explanation:

Answer:

Right angle, suppemantary angle, complemantary angle.

Step-by-step explanation:

Ive dont this lesson befoe

Answer: 0.71

Step-by-step explanation:

Since we have just two flavors, the probability of a cup drink being cola flavour will be calculated below:

P(R) + P(C) = 1

0.29 + P(C) = 1

P(C) = 1 - 0.29

P(C) = 0.71

Therefore, the probability of a cup drink being cola flavour is 0.71.

The power generated by the student after 4 seconds is one-fourth of the power generated by the student after 2 seconds.

Power generated by a student when standing up from a chair depends on the height, mass, and acceleration of the student.

If we assume that all other factors remain constant, the power generated by a student can be calculated using the equation:

Power = Work done / time Taken

The energy required to lift a student of mass m to a height h is given by the equation:

mgh, where g is the acceleration due to gravity.

Therefore, the work done in lifting the student from a chair is given by the equation:

mgh.

The acceleration of the student is given by the equation:

a = (final velocity - initial velocity) / time Taken.

For the student standing up from a chair, the initial velocity is zero.

Therefore, the acceleration is given by the equation:

a = (2h / timeTaken²)

The power generated by the student after 2 seconds is:

P1 = (mgh / 2) × (2h / 2²)

P1 = (mgh² / 4)

The power generated by the student after 4 seconds is:

P2 = (mgh / 2) × (2h / 4²)

P2 = (mgh² / 16)

Comparing P1 and P2, we can see that the power generated by the student after 4 seconds is:

P2 = P1 / 4

Therefore, the power generated by the student after 4 seconds is one-fourth of the power generated by the student after 2 seconds.

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Answer:

Slope = rise/run

Rise = 0

So zero divided by any run is 0.

B

Answer:

B

Step-by-step explanation:

slope or gradient = rise/run

rise=0 0/anything= 0

Line B has no graidient so it is considered as 0.

The total number of smoothies that Autumn can make with the yoghurt is 165.

We know that the total number of cups of yoghurt that Autumn needs to make smoothies is 55. Each smoothie uses 1/3 cup of yogurt. We need to calculate the total number of smoothies that Autumn can make with the yogurt.

Let the total number of smoothies be represented by the variable "N''. We will use the unitary method. The total number of smoothies that can be made is the ratio of the total number of cups of yoghurt to the fraction of a cup used to make one smoothie.

N = 55/(1/3)

N = 55*3

N = 165

Hence, Autumn can make 165 smoothies from 55 cups of yogurt.

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New function that is a horizontal stretch of F(x)=\((x+2)^{3} + 5\) is F(\(\frac{x}{k}\))=\((\frac{x}{k} +2)^{3} + 5\)

The point (x, y) on the graph of f(x) is changed to the point (x/k, y) on the graph of g when the graph is stretched or contracted horizontally by a factor of 1/k (x).Only when the input value is also increased by a, can a graph be stretched horizontally by a factor of 1/a. The x-coordinates should be multiplied by a once f(x) has been stretched horizontally to f(ax). Keep the y-intercepts where they are. The resulting function might have a different domain, but it will have the same range. If a point (m, n) is stretched horizontally, it becomes (am, n).

F(x)=\((x+2)^{3} + 5\)

F(\(\frac{x}{k}\))=\((\frac{x}{k} +2)^{3} + 5\)ch visit :
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The maximum height will be achieved by the rocket in 1.5 seconds.

And the maximum height of the rocket will be 39 ft.

A function of the form f(x) = ax² + bx + c is called a parabolic function.

The given parabolic function is,

h(t) = -16t²+48t+3       (1),

Initial velocity is 48 feet per second,

And initial height = 3 feet

Differentiate with respect to t,

h'(t)= -32t+48

To find time to substitute this expression to zero.

-32t+48=0

t = 1.5 seconds

For maximum height, substitute this value in equation (1).

h(t) = -16(1.5)²+48(1.5)+3

      = -36+72+3

      = 39ft

Therefore, The rocket reaches the maximum height in 1.5 seconds, and the maximum height of the rocket will be 39ft.

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Answer: f⁻¹(x)=x/5

Step-by-step explanation:

To find the inverse function, you replace the y with x, and x with y.

x=5y

y=x/5

f⁻¹(x)=x/5