If Georgina travels 455 km in 7 hours how far will she travel in 9 hours at the same rate

Answer: D: The minimum value of A occurs 7 units lower than minimum of function B.

Step-by-step explanation: The minimum of function A is at (3,-2), while the minimum of function B would be at (-3,5). So, you do 5-(-2) to get 7.

The minimum value of A occurs 7 units lower than the minimum of function B.

We have given that,

Statement best compares the two functions

The maxima and minima of a function, known collectively as extrema, are the largest and smallest value of the function, either within a given range, or on the entire domain.

The minimum of function A is at (3,-2), while the minimum of function B would be at (-3,5). So, you do 5-(-2) to get 7.

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Answer:

B (1, -3)

Step-by-step explanation:

Step 1:  Use the midpoint formula to find the coordinates of the endpoint:

Normally, we find the midpoint of a segment using the midpoint formula, which is given by:

M = (x1 + x2) / 2, (y1 + y2) / 2, where

Since we're solving for the coordinates of an endpoint, we can allow (-5, 7) to be our (x1, y1) point and plug in (-2, 2) for M to find (x2, y2), the coordinates of the endpoint B:

x-coordinate of B:

x-coordinate of midpoint = (x1 + x2) / 2

(-2 = (-5 + x2) / 2) * 2

(-4 = -5 + x2) + 5

1 = x2

Thus, the x-coordinate of the endpoint B is 1.

y-coordinate of B:

y-coordinate of midpoint = (y1 + y2) / 2

(2 = (7 + x2) / 2) * 2

(4 = 7 + x2) -7

-3 = y2

Thus, the y-coordinate of the endpoint B is -3.

Thus, the coordinates of the endpoint B are (1, -3).

Answer:

13.27 cm

Step-by-step explanation:

I am using (xy) to mean the length of the side xy

7^2 + (xy)^2 = 15^2

49 + (xy)^2 = 225

(xy)^2 = 225-49

(xy)^2 = 176

Side (xy) = sqrt(176) = 13.2664991614 = 13.27 cm

The method used is Distributive Property.

The Distributive Property is an algebraic property that is used to multiply a single value and two or more values within a set of parenthesis.

Given:

(2x² - 1)(3x+2) = (2x²)(3x) + (2x²)(2) + (-1)(3x)+(-1)(2)

Here the property used is Distributive property.

Because distributive property in this way

a*(b+c)= a*b+ a*c

This is how a is being multiplied by with b and c.

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first row is 7 and second row is 30 and then 75

Answer:

40 and 10

Step-by-step explanation:

1. if the length is 'l' and height is 'h', then according to the condition 1/4*l=h.

2. if the given area is 400, it means, h*l=400;

3. if to substitute h=1/4*l into the formula of the area, then

l*l*1/4=400; ⇔ 1/4*l²=400;

4. if to calculate the value of the 'l', then l=40 (the required length).

5. if to substitute l=40 into 1/4*l=h, then h=10 (the required height).

Answer:

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

Initial value of the toy is €450.

After 10% increase the value is:

After further 10% decrease the value becomes:

The final value of the toy is €445.50.

Answer:

x < -6

Step-by-step explanation:

-5x - 8 > 22

Add 8 to both sides:  -5x > 30

Divide both sides by 5:  -x > 6

Divide both sides by -1 (reverse sign):  x < -6

Answer:

x < -6

Step-by-step explanation:

First we want to move all terms not containing x to the right side

-5x > 22 + 8

-5x > 30

Then we want to divide

-5x/5 < 30/-5

30/-5

x < - 6

The term “inverse” in mathematics generally refers to an operation that undoes or reverses another operation. However, the phrase "inverse of maths tools" doesn't really make sense because “maths tools” is not a specific mathematical operation.

Mathematical tools can refer to various instruments or techniques used in mathematics, such as calculators, rulers, compasses, graph paper, software, etc. Each of these tools has its own purpose and may or may not have an inverse operation or tool associated with it.

For example, the inverse of addition is subtraction, the inverse of multiplication is division, and the inverse of differentiation is integration. However, it's not clear what the inverse of a “maths tool” would be.

Therefore,  a) The inverse of “Add 25” would be “Subtract 25.”What is the  b) The inverse of “Divide -18” would be “Multiply -18.” c) The inverse of “Subtract 3” would be “Add 3.” d) The inverse of “Multiply 14” would be “Divide 14.”

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Answer:

corporate team-building event cost will cost $98

Step-by-step explanation:

A corporate team-building event costs $32, plus an additional $1 per attendee.

Let cost be C

The expression for the above statement

C($)= 32+n(1)

Where n is the number of attendees

So a situation where there are 66 attendees, the total cost will be

C($) = 32 +66(1)

C($) = 32+66

C($)= 98

a. We can start by factoring out the greatest common factor of the three terms, which is 2: 2(x² - 3x - 10)

b. 2x² - 6x - 20 can be factorized as 2(x - 5)(x + 2).

The factorization method uses basic factorization formula to reduce any algebraic or quadratic equation into its simpler form, where the equations are represented as the product of factors instead of expanding the brackets. The factors of any equation can be an integer, a variable, or an algebraic expression itself.

a. To fill in the gaps, we need to factorise the quadratic expression 2x² - 6x - 20. We can start by factoring out the greatest common factor of the three terms, which is 2:

2(x² - 3x - 10)

b. To factorise 2x² - 6x - 20 into a(x+b)(x+c), we need to find values for a, b, and c such that:

a(x+b)(x+c) = 2x² - 6x - 20

Expanding the right-hand side of the equation gives:

a(x² + bx + cx + bc) = 2x² - 6x - 20

We can simplify the left-hand side by grouping the "x" terms together:

a(x² + (b+c)x + bc) = 2x² - 6x - 20

Since this equation must hold for all values of x, we can equate the coefficients of x², x, and the constant term separately:

Coefficient of x²: a = 2

Coefficient of x: a(b+c) = -6

Constant term: abc = -20

From the first equation, we know that a = 2. Substituting this into the second equation gives:

2(b+c) = -6

b + c = -3

To solve for b and c, we can use the third equation:

2bc = -20

We need to find two values of b and c that multiply to -10 (since 2 is already determined) and add up to -3. One possible pair of values is -5 and 2, since (-5)(2) = -10 and (-5) + 2 = -3. Therefore, we have:

b = -5, c = 2

Substituting these values into the factored form, we get:

2x^2 - 6x - 20 = 2(x - 5)(x + 2)

Therefore, 2x² - 6x - 20 can be factorised as 2(x - 5)(x + 2).

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The solution to the inequality expression is -8/9 ≤ x ≥ 4/9

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

|3x + 6/9| ≥ 2

Expand the inequality expression

So, we have

-2 ≤ 3x + 6/9 ≥ 2

Subtract 6/9 from both sides

So, we have

-24/9 ≤ 3x ≥ 12/9

Divide through the equation by 3

-8/9 ≤ x ≥ 4/9

Hence, the solution to the inequality expression is -8/9 ≤ x ≥ 4/9

The graph is attached

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Typically, linear equations are written in slope-intercept form:

\(y=mx+b\)

To find the equation of a line given a point and the slope:

We're given:

\(y=mx+b\)

⇒ Plug in the slope, \(\dfrac{1}{5}\):

\(y=\dfrac{1}{5}x+b\)

⇒ Plug in the point (-5,-4) and solve for b:

\(-4=\dfrac{1}{5}(-5)+b\\\\-4=-1+b\\\\b=-3\)

⇒ Therefore, the y-intercept of the line is -3. Plug this back into our original equation as b:

\(y=\dfrac{1}{5}x-3\)

\(y=\dfrac{1}{5}x-3\)

If Yin makes the maximum salary contribution to her 401(k), she will have made a total of $7,950.

Divide the part by the entire and multiply the result by 100 to obtain the percentage. A number can be expressed as a fraction of 100 by using the percentage, in other words.

If, for instance, there were 50 students in the class and 35 of them passed the test, and you want to know what percentage of those students passed the test, you may determine it by using the formula below.

% = (Number of students who passed / Total number of students) x 100 % = (35 / 50) x 100 % = 0.7 x 100 %

Percentage = 0.7 x 100

Percentage = 70%

If Yin may contribute up to 15% of her annual earnings to her 401(k) and her beginning salary is $50,000, her maximum annual contribution would be:

Maximum donation is = 15% of $50,000.

Maximum donation is 0.15 times $50,000.

Maximum annual contribution =  $7,500

Given that Yin's company will match up to 6% of her contributions, the maximum amount they might contribute annually is:

6% of $50,000 is the employer's contribution.

Employer contribution equals 0.6 times $50,000.

Annual employer contribution equals $3,000.

Hence, Yin's company will pay an additional $3,000 year if she contributes the maximum of $7,500 to her 401(k). Yin will contribute a total of $10,500 per year to her 401(k) ($7,500 + $3,000). (k).

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Answer:

Intersecting (fourth answer choice)

Step-by-step explanation:

First, let's convert both lines to slope-intercept form, whose general equation is y = mx + b, where

Converting y - 3x = 4x to slope-intercept form:

(y - 3x = 4x) + 3x

y = 7x

Thus, the slope of this line is 7 and the y-intercept is 0.

Converting 6 - 2y = 8x to slope-intercept form:

(6 - 2y = 8x) - 6

(-2y = 8x - 6) / -2

y = -4x + 3

Thus, the slope of this line is -4 and the y-intercept is 3.

Checking if y = 7x and y = -4x + 3 are perpendicular lines:

We can show this in the following formula:

m2 = -1 / m1, where

Thus, we only have to plug in one of the slopes for m1.  Let's do -4.  

m2 = -1 / -4

m2 = 1/4

Thus, the slopes 7 and -4 are not negative reciprocals of each other so the two lines are not perpendicular.

 Checking if y = 7x and y = -4x + 3 are parallel lines:

The slopes of parallel lines are equal to each other.

Because 7 and -4 are not equal, the two lines are not parallel.

Checking if the lines intersect:

Method to solve the system:  Elimination:

We can multiply the first equation by -1 and keep the second equation the same, which will allow us to:

-1 (y = 7x)

-y = -7x

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

    -y = -7x

+

    y = -4x + 3

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

(0 = -11x + 3) - 3

(-3 = -11x) / 11

3/11 = x

Now we can plug in 3/11 for x in y = 7x to find y:

y = 7(3/11)

y = 21/11

Thus, x = 3/11 and y = 21/11

We can check our answers by plugging in 3/11 for x 21/11 for y in both y = 7x and y = -4x + 3.  If we get the same answer on both sides of the equation for both equations, the lines intersect:

Checking solutions (x = 3/11 and y = 21/11) for y = 7x:

21/11 = 7(3/11)

21/11 = 21/11

Checking solutions (x = 3/11 and y = 21/11) for y = -4x + 3:

21/11 = -4(3/11) + 3

21/11 = -12/11 + (3 * 11/11)

21/11 = -12/11 + 33/11

21/11 = 21/11

Thus, the lines y = 3x = 4x and 6 - 2y = 8x are intersecting lines (the first answer choice).

This also means that lines are not skew since lines had to be neither perpendicular nor parallel nor intersecting to be skew.

Answer:

1) 5/1 is the slope, and 10 is the y intercept.

2) Inital amount is the y intercept, and 10 is the rate of change.

3) Should be easy from there! Just graph (0,10), and go up 5, right 1, and repeat.

Step-by-step explanation:

This is in slope intercept form! Where 5 is the slope, and 10 is the y intercept. The rate of change is another way of saying slope, and the inital amount is your starting value, or y intercept.

Answer:

Factors of the term \(4x^2 + 12xy + 9y^2\) are \(\mathbf{(2x+3y)(2x+3y)\:or\:(2x+3y)^2}\)

Step-by-step explanation:

We need to factor the term \(4x^2 + 12xy + 9y^2\)

We can factor the term by breaking the middle term.

Middle term 12xy should be broken is such a way that:

Now, if we break 12xy into 6xy and 6xy

So, our both conditions are fulfilled.

Breaking the middle terms and finding factors

\(4x^2+12xy+9y^2\\=4x^2+6xy+6xy+9y^2\\=2x(2x+3y)+3y(2x+3y)\\=(2x+3y)(2x+3y)\\=(2x+3y)^2\)

So, factors of the term \(4x^2 + 12xy + 9y^2\) are \(\mathbf{(2x+3y)(2x+3y)\:or\:(2x+3y)^2}\)

Answer:

Part A:  $45, Part B:  $8

Step-by-step explanation:

Part A: 60 - 10 = 50

50 * 0.30 = 15

60 - 15 = $45

Part B:  60 * 0.30 = 18

18 - 10 = $8

Answer: part a: $35

part b $32

Step-by-step explanation:

Answer: not related

Step-by-step explanation: Statistical tests are employed when trying to establish the existence or non-existence of relationship between two variables. Variables may be numerical or categorical, in most cases, regression is employed in establishing relationship between. numerical variables. However, the Chisquare test of independence is employed when analysing and trying to establish if a relationship exists between two categorical variables. With the null hypothesis maintain that both variables are independent are hence unrelated while the alternative hypothesis states otherwise.

Answer:

Outcome Y is independent of Factor X.

Step-by-step explanation:

The null hypothesis for the Chi-Square Tables Test is:

Outcome Y is independent of Factor X.

Answer: 28 cm

Step-by-step explanation:

x - the length of the shorter piece

2x - the length of the longer piece

Together they are 42 cm long.

Compose te equation:

2x + x = 42

3x = 42

x = 14 cm

The shorter piece is 14 cm, the longer piece is twice longer, 2x, or 2( 14 ).

Two times longer than 14 is 28. The longer piece is 28 cm.

2. Coco, the wonder cat, is watching a spider on a wall that is 18 feet wide and 12 feet tall. The spider moves along for 10 seconds along a path describe by the parametric equations x(t)=.3(t-2.5)^2+2 and y(t)=1.5 sin t+6 and if the lower left corner is taken as the origin. Coco can reach 3 feet up and can move freely from side to side (Set your calculator to Radian mode—not degree mode—for this problem). a. What is the closest that Coco can come to the catching the spider. When does this happen? Given answers to the nearest tenth. Explain your reasoning and how you arrived at this answer b. How close does the spider get to the origin? Show/explain how you arrived at this answer.

Answer:

Step-by-step explanation:

a. What is the closest that Coco can come to the catching the spider. When does this happen?

From the given information;

Coco can reach 3 feet up and can move freely from side to side; thus as long as  Coco can move freely about any region on the line y =3 , thus we want the closest that Coco can come to the catching the spider at that line.

So; Sin(t) has  a minimum value of -1

y(t) has a minimum value of 4.5

Thus; the  closest that Coco can come to the catching the spider is :

y = (4.5 -3) ft

y = 1.5 ft

b. How close does the spider get to the origin?

The spider location away from the origin  is:

z² = x² + y²

x(t)=0.3(t-2.5)^2+2

y(t)=1.5 sin t+6

∵

z² = (0.3(t-2.5)²+2)² + ( 1.5 sin t + 6)²

As we know that z will be minimum when z² is minimum; then:

\(\dfrac{dz}{dt}=0 \Longrightarrow 2(0.3 (t - 2.5)^2+2) \times 0.6(t-2.5)+2(1.5 \ sin t+ 6) \times 1.5 cos \ t\)

z = 5.5 ft

So, z is minimum at about 5.5 ft.

Thus; the spider is 5.5 ft close to the origin.

Answer:

517

Step-by-step explanation:

Answer:

517

Step-by-step explanation:

43×12+3-2 = 516+3-2

Do the multiplication/division before the addition/subtraction

516+3-2 = 519-2

Work from left to right

519-2 = 517

Given statement solution is :- The present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

To calculate the present value of an investment with compound interest, we can use the formula for the present value of an annuity:

PV = A *\((1 - (1 + r)^(-n)) / r\)

Where:

PV = Present value

A = Annual payment or cash flow

r = Interest rate per period

n = Number of periods

In this case, the annual payment (A) is R13,000, the interest rate (r) is 10% per year, and the investment is made for 8 years (n).

Using the formula and substituting the given values, we can calculate the present value:

PV = \(13000 * (1 - (1 + 0.10)^(-8)) / 0.10\)

Calculating this expression:

PV = \(13000 * (1 - 1.10^(-8)) / 0.10\)

= 13000 * (1 - 0.46318) / 0.10

= 13000 * 0.53682 / 0.10

= 6977.66 / 0.10

= 69776.6

Therefore, the present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

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Answer: 20

Step-by-step explanation:

Multiply 2.4*10-4

Calculate 24-4

the answer is (12x^10000)/5

Simplifying, the exponents expression, we have 63y/xu⁴

Exponents are the powers to which a particular number is raised.

Given the expression 3y⁻⁴ . 3y⁵x⁸u⁻⁵.7x⁻⁹. To simplify the expression, we use the product rule of exponents which states that for a given base x, xᵃ xᵇ = xᵃ⁺ᵇ.

So, applying this rule to the expression and collecting common bases, we have that

3y⁻⁴ . 3y⁵x⁸u⁻⁵u.7x⁻⁹ = 3y⁻⁴ × 3y⁵ × x⁸ × 7x⁻⁹ × u⁻⁵ × u

= 3 × 3 × y⁻⁴ × y⁵ × 7 × x⁸ × x⁻⁹ × u⁻⁵ × u

Applying the product rule, we have that

= 3 × 3 × y⁻⁴ ⁺ ⁵ × 7 × x⁸ ⁺(⁻⁹) × u⁻⁵ ⁺ ¹

= 3 × 3 × y⁻⁴ ⁺ ⁵ × 7 × x⁸ ⁻ ⁹ × u⁻⁵ ⁺ ¹

= 3 × 3 × y × 7 × x⁻¹ × u⁻⁴

= 3 × 3 × 7 × y × x⁻¹ × u⁻⁴

Using the reciprocal rule that x⁻ⁿ = 1/xⁿ, we have that

= 3 × 3 × 7 × y × x⁻¹ × u⁻⁴

= 63 × y × 1/x × 1/u⁴

= 63y/xu⁴

So, simplifying, we have 63y/xu⁴

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The mode of the given observations 2, 5, 3, 2, 4, 6, 2, 4 is 2, so the correct answer is 1) 2.

To find the mode of a set of observations, we need to identify the value that appears most frequently.

Let's analyze the given observations: 2, 5, 3, 2, 4, 6, 2, 4.

Looking at the observations, we can see that the number 2 appears three times, while the numbers 5, 3, 4, and 6 appear only once each.

Since the number 2 appears more frequently than any other number in the set, the mode of these observations is 2.

Therefore, the correct answer is 1) 2.

The mode is a measure of central tendency that represents the most commonly occurring value in a data set.

It can be useful in identifying the most frequent value or category in a dataset.

In this case, the mode of the given observations is 2 because it appears more frequently than any other number.

It's important to note that a dataset can have multiple modes if there are two or more values that occur with the same highest frequency. However, in this specific case, the number 2 is the only value that appears more than once, making it the mode.

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