Is an example of distributive law *?.

Julian's average speed for the whole journey was 8 miles per hour.

To find Julian's average speed for the whole journey, we can use the formula:

average speed = total distance / total time

We know that Julian walked from his house to the library for 2 hours at a speed of 4 miles per hour and then returned home by bicycle at a speed of 12 miles per hour.

To find the total distance, we can add the distance he walked to the distance he rode his bicycle:

total distance = distance walked + distance rode by bicycle

To find the distance he walked, we can use the formula:

distance = speed x time

distance walked = 4 miles/hour x 2 hours = 8 miles

distance rode by bicycle = 12 miles/hour x 2 hours = 24 miles

total distance = 8 miles + 24 miles = 32 miles

We know that Julian walked for 2 hours and rode for 2 hours, so we can add those times to find the total time:

total time = time walked + time rode by bicycle = 2 hours + 2 hours = 4 hours

Now we can use the formula to find Julian's average speed for the whole journey:

average speed = total distance / total time = 32 miles / 4 hours = 8 miles/hour

Therefore, Julian's average speed for the whole journey was 8 miles per hour.

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The descriptors that are applicable for factor by grouping is 4 terms and 3 terms.

What is group factorization?

Factorization by grouping requires that we first group the terms according to their common factors. Method of factorization by term grouping:

(i) A factor can be extracted from each group of the supplied expression's groupings.

(ii) Factorize each group.

(iii) Next, eliminate the factor shared by the newly created group.

To factorize 4 terms use the method -

The first step is to group the first and last two terms together.

Then create a GCF by factoring each individual binomial.

Factor out the common binomial in step three.

To factorize 3 terms use the method -

Factoring out the GCF of the full phrase is the first step (from all 3 terms). There might not always be a GCF to account for (that is, the GCF is 1).

Next, select two terms to think about jointly (we may need to split a term into two parts). Subtract the two terms' GCFs.

Consider the remaining terms along with the factored pair and determine if there is any additional factoring that can be done (if anything).

A binomial cannot be factored by factor by grouping method as it contain only two terms which doesn't require further factoring using grouping method.

Both terms are not always perfect squares, there can be times when the factors are written as roots.

Therefore, descriptors are 4 terms and 3 terms.

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Answer:

5

Step-by-step explanation:

Therefore, there are no solutions to the given quadratic equation. 57 and −2. Yes, there are two real roots in the given equation.

The formula for determining the roots is x = (-b  (b2 - 4ac))/2a. D = b2 minus 4ac is the discriminant. The equation has two real and distinct roots if D is greater than zero.

As a result, this equation does not have any actual roots.

Quadratic equations can be solved in three basic ways: completing the square, using the quadratic formula, and factoring.

When a given quadratic equation is multiplied by ax 2 + bx + c=0, we obtain a=2, b=7, and c=5.

Now, x x x using the quadratic formula.

= \s2×3 \s−7± \s7 \s2 \s −4×3×−5

= \s6 \s−7± \s49+60

= \s6 \s−7± \s109

= \s6 \s−7+ \s109

​ \s and x= \s6 \s−7− \s109

=0.57 and x=−2.91

Therefore, 0.57 and 2.91 are the answers to the given quadratic equation.

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Full Question = Solve the following equations.

3x 2 +7x−5=0

Show all your working and give your answer correct to 2 decimal places.

Answer: 20 000 000

(the first value is two because the one after the second one (9) is greater than 5 therefore you should add 1 to the the number in front)

The slope of the equation y=-2x+10 is -2.

The slope of a line is a measure of its steepness and direction. In the equation y = -2x + 10, the slope is -2.

To understand this, let's first look at the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis).

In this case, the equation is already in the slope-intercept form and we can see that the slope is -2. The negative sign indicates that the line is sloping downward. The bigger the absolute value of the slope, steeper the line is.

In other words, the slope of a line tells us how much y changes for each unit of change in x. In this case, the slope is -2, which means that for each unit increase in x, y decreases by 2 units.

It's also worth noting that, if the slope is positive, the line will rise from left to right, if the slope is negative, the line will fall from left to right.

Therefore, The slope of the equation y=-2x+10 is -2.

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We know that 1 hour = 60 minutes.

Set equal proportions for both Laisha and Jefford to find the distance x and y they bike in 60 minutes:

Laisha will bike farther by:

A bar graph would be the best graphical representation to display the data. The correct answer would be an option (D).

A random sample of 130 purchases from a particular pharmacy was taken. The type of item purchased was recorded, and a table of the data was created.

Item Purchased      Health & Medicine     Beauty     Household     Grocery

Number of Purchases       55                       23               22               30

A bar graph would clearly and effectively show the number of purchases for each category of item (Health & Medicine, Beauty, Household, and Grocery) and allow for easy comparison between the categories.

Thus, a bar graph would be the best graphical representation to display the data.

Hence, the correct answer would be option (D).

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The required point that is not always true for parallelograms is the diagonals are perpendicular.

A parallelogram is a quadrilateral consisting of pairs of parallel sides.

Here,
For any parallelogram, the point that remains always the same,
(1)  opposite angles are congruent
(2) opposite sides are congruent
(3) the diagonals bisect each other

Thus, the required point that is not always true for parallelograms is the diagonals are perpendicular.

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The side length UX which have the segment UW tangent to the circle is equal to 3.4.

The tangent to a circle theorem states that a line is tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency

Considering the triangle ∆UVX; we will observe that the side XV consists of the circle diameter which is perpendicular to the side UV tangent to the circle, this implies the ∆UVX is a right triangle and we can solve for the side length UX using the Pythagoras rule as follows;

UX² = 3² + 1.6²

UX² = 9 + 2.56

UX² = 11.56

UX = √11.56 {take square root of both sides}

UX = 3.4.

In conclusion, we have the length of side UX = 3.4 which have the segment UW tangent to the circle.

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The distance, y, in miles, covered by a car during a specific period, x, in hours and The distance, y, in miles, a car travels in a given period of time, x, in hours

The following graph displays the distance travelled as a linear function of time, D (in miles), and (in hours): To view a larger version of the graph, click on it.) Find AD and 4 values between the specified start and finish times for each interval: Fill in your responses in the appropriate columns in the table below: AD t =1tot=3.5, 0.5 to t =3.5, t=2tot=4, and AD t =3tot=4

b) In light of your findings in (a), it is evident that the average rate of change of D is constant. Decide on ALL that apply (more than one may apply) A It symbolises the car's velocity: B. The angle of the line's slope: C. The average speed of the car throughout the first two hours.

Therefore the correct answer is option A ) It travels for 3 hours, then stops for 2 hours, and finally travels again for 2 hours.

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Answer:

X = 5

Step-by-step explanation:

this must form a triangle so simply using the same value of x equally in each equation.

It depends on the values of a,b,d and e in the equations , different values may lead to different answers.

What is linear equation ?

A linear equation is an equation in which the highest power of the variable is 1. Linear equations can be written in the form of y = mx + b, where m is the slope of the equation, x is the variable, and b is the y-intercept, the point where the line crosses the y-axis. These equations are called linear because they describe a straight line when graphed.

It depends on the specific equations and the values of a, b, d and e in the system of equations. Multiplying both sides of an equation by a non-zero constant does not change the solution set of the equation.

However, if Jim wants to use the method of elimination, which is multiplying one equation by a constant and adding or subtracting it from the other equation, then it is important to ensure that the coefficients of one variable in the two equations are opposite in sign after the multiplication. This will enable him to eliminate one variable and find the value of the other variable.

It depends on the values of a,b,d and e in the equations , different values may lead to different answers.

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Answer:

Step-by-step explanation:

The measure of an angle is  5π/12 radians

Let us assume that the complement of the angle measures x degrees.

We have been given the measure of the angle is five times its complement.

So we get the measure of the angle = 5 × x

We know that two angles are complementary when their measures add to 90 degrees (π/2 radians).

So from the definition of complementary angles we get an equation,

x + 5x = π/2

We solve above equation to find the value of x.

x + 5x = π/2

6x = π/2

x = π/12 radians

This means, the measure of complement of angle is π/12 radians.

So, the measure required angle would be,

5 × π/12 = 5π/12 radians

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The comple question is:

An angle is equal to 5 times its complement determine its measure?.

The domain of function, (cd)(x) is all real values of x except x = 2, i.e., (−∞,2)∪(2,∞).

The domain of a function is defined as a set of values accepted by function. In this case, we have a rational function. A rational function will only be defined if the denominator is not equal to zero. We have, two functions, c(x) = 5/ x - 2 and

d(x) = x + 3. We should determine the domain of (cd) (x). The product of two is (cd) (x) = c(x) . d(x)

=> (cd)(x) = (5/(x - 2) )(x + 3) = 5(x+3)/(x -2)

Which is a rational function. So, the function will be defined if the denominator is not equal to zero, i.e., x - 2 ≠ 0 => x ≠ 2. Thus, domain set of function contains all real numbers values except 2. Therefore, the required domain of function (cd) (x) is all real values of x except 2.

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Complete question:

If c(x) = 5 / x - 2 and d(x) = x + 3. What is the domain of (cd)(x)?

The percentage error is 8.3%. ((60 - 55) / 60) x 100 = 8.3%.

(60 - 55) / 60 = 0.083

0.083 x 100 = 8.3

Brianna estimated that he would spend $60 hopping for school supplies before the start of the school year. However, she actually spent $55. To calculate the percent error for her estimate, we first subtract the actual amount spent ($55) from the estimated amount ($60). This gives us 0.083, which is then multiplied by 100 to get 8.3%. This means that Brianna's estimate was 8.3% off from the actual amount spent. This result can help her understand how close her estimate was to the actual amount spent and can help her improve her estimating skills in the future.

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The difference between the polynomials to subtract the terms with the same degree in order to calculate the difference between two polynomials.

For instance, you would deduct 4x2 from 3x2 (which is -x2) and then deduct 2x from 5 to find the difference between 4x2 + 2x - 7 and 3x2 + 5. (which is 3x). -x2 + 3x - 7 is the difference between the two polynomials.

A polynomial is a type of equation where each variable's exponent must be a whole number.

Expressions of the type polynomials exist. Sums (and differences) of polynomial "terms" are polynomials.

To be a polynomial term, any variables in the expression must have whole-number powers (or else the "understood" power of 1, as in x1, which is normally written as x)

A polynomial term can also be a simple number. In particular, an expression must not contain any square roots of variables, any fractional or negative powers on the variables, and any variables in any fractions' denominators in order to qualify as a polynomial term.

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The graph of the piece-wise function f(x) is given by the image presented at the end of the answer.

A piece-wise function is a function that has different definitions, depending on the input of the function.

The extreme points of the function in this problem are given as follows:

Hence the graph of the function in this problem is composed as follows:

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The expression can be simplified by combining any like terms, which in this case are 5g and 5g. When added together, they become 10g.

The expression 5g5g–10g can be simplified by performing the following steps:

1. Multiply 5g and 5g, to get 25g2.

Subtract 10g from 25g, to get 15g.

3. Simplify to 10g.

Simplifying the expression 5g5g–10g involves combining like terms. Like terms are terms that have the same variable, in this case the letter g. To simplify, first we need to multiply the two 5g terms together, giving us 25g. Then, we subtract 10g from 25g, to get 15g. Finally, we can simplify further by combining any remaining like terms, which in this case there are none. Therefore, when all is said and done, the expression can be simplified to 10g. This is because 10g is the only like term in the expression.

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A. Kevin will have $5040 if he use Bet Bank.

B. Kevin will have $14,707.7 if he use Primo Bank.

C. Kevin would use Primo Bank due to high amount generation.

The formula to be used for simple interest is -

SI = PRT/100, where SI is simple interest, P is principal, R is rate of interest and T is time.

The formula for compound interest is -

A = [tex] {P(1 + r)}^{n} [/tex], where n is times interest is calculated.

To answer first part -

SI = 8000 × 9 × 7/100

Performing multiplication

SI = 504,000/100

SI = $5040

Amount generated = 8000 + 5040

Performing addition

Amount generated = $1340

To answer second part -

A = 8000(1+ 7/100)⁹

Convert rate to decimal

A = 8000 (1+0.07)⁹

Performing addition

A = 8000 × 1.07⁹

Taking power

A = 8000 × 1.84

Performing multiplication

A = $14,707.7

The money generated in Primo Bank is more. Hence, Kevin must choose this bank.

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The 12th term of the geometric  sequence is -341796875.

The common ratio (r) is:

[tex]\frac{a_{1} }{a_{2} } =-\frac{35}{7} =-5[/tex]

[tex]\frac{a_{3} }{a_{2} } =\frac{175}{-35} =-5[/tex]

(r)=-5

The sum is :

[tex]S_{n}[/tex]=a·{[tex]\frac{1-r^{n} }{1-r^{} }[/tex]}

[tex]S_{3}[/tex]= 147

So. The general form is:

[tex]a_{n}[/tex]=7·-[tex]5^{n-1}[/tex]

Now, The nth term is:

[tex]a_{1}[/tex]=7

[tex]a_{2}[/tex] = [tex]a_{1}[/tex]·[tex]r^{n-1}[/tex] = 7· [tex]-5^{2-1}[/tex] = 7 · [tex]-5^{1}[/tex] = 7 · -5 = -35

[tex]a_{3}[/tex] = [tex]a_{1}[/tex]·[tex]r^{n-1}[/tex] = 7· [tex]-5^{3-1}[/tex] = 7 · [tex]-5^{2}[/tex] = 7 · 25 = 175

[tex]a_{4}[/tex] = [tex]a_{1}[/tex]·[tex]r^{n-1}[/tex] = 7· [tex]-5^{4-1}[/tex] = 7 · [tex]-5^{3}[/tex] = 7 · -125 = -875

[tex]a_{5}[/tex] = 4375

[tex]a_{6}[/tex] = -21875

.......  so, [tex]a_{12}[/tex] = - 341796875

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Answer: (Only for homework, no tests, please!)

Step-by-step explanation:

Hello! An easy way to help you solve this is to use graph paper.  Make a coordinate grid using a ruler to help you form the trapezoid and plot the points at the proper coordinates.  It should look something like this but with a line going through BC and AD.  Draw the midpoint of line segments AD and BC by measuring their lengths with a ruler and divide the length in half to plot the points.  Connect the midpoints with a ruler to form the midsegment.  Hope this helps you with your homework!

In the last basketball game, the ratio of baskets made to the total shots taken was 4:7 and if the team shot a total of 56 baskets in the game then the total basket they made is 40.

The ratio is 4:7, this means that for every 7 shots taken, 4 of them were made. If the team shot a total of 56 shots in the last game, then they made

(4/7) ×56 = 40 baskets.

This calculation can be broken down into simpler terms. For every 7 shots, 4 shots were made. Therefore, for 56 shots, 40 shots were made. Therefore, the team made 40 baskets in the last game.

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Answer:

r.a) (3) = r(a(3)) = r(3) = -2(3)² - 2 = -2(9) - 2 = -18 - 2 = -20

(q-r) (3) = q(3) - r(3) = -3 + 1 - (-18) = -2

So, (r.a) (3) = -20 and (q-r) (3) = -2

Step-by-step explanation:

The equation of the line that passes through (-3, 5) and is perpendicular to the line y = -3x - 1 is y = (1/3)x + (20/3).

What is the equation of the line?

The equation of a straight line is y=mx+c y = m x + c m is the gradient and c is the height at which the line crosses the y -axis, also known as the y-intercept.

To write an equation of the line that passes through (-3, 5) and is perpendicular to the line y = -3x - 1, we can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.

First, we need to find the slope of the line that passes through (-3, 5). Since the line is perpendicular to y = -3x - 1, we know that the slope of the line is the negative reciprocal of -3, which is 1/3. So the slope of the line is 1/3.

Next, we can use the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Plugging in the point (-3, 5) and the slope 1/3, we get:

y - 5 = (1/3)(x + 3)

Simplifying we get:

y = (1/3)x + (20/3)

Hence, the equation of the line that passes through (-3, 5) and is perpendicular to the line y = -3x - 1 is y = (1/3)x + (20/3).

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Figure B's cone has a volume of 678.24 cu ft.

The Volume of Cone in figure B is 678.24 cu ft.

Given:

Figure A~ Figure B

Figure A: where V = 25.12 cu ft and r = 2 feet

Figure B: r= 6 ft

Now, the formula for volume of cone

= 1/3 πr²h

As, Figure A and B are similar

So, [tex]r(B) / r(A) =h(A) / h(B)\\[/tex]

                       [tex]= 6/2[/tex]

                       =3

Now, r(B) = 3 r(A)

and, h(B) = 3 h(A)

So, the volume of figure B is

V = 1/3 π(3 r(A))² (3h (A))

[tex]V = 1/3 \times 27\times 3\times \pi r^2(A) h(A)[/tex]

V = 27 πr(A)²h(A

V = 27 V(A)

V = 27 * 25.12

V = 678.24 cu ft

Thus, the volume is 678.24 cu ft.

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The percent error for Anita's measurement is 8%

To calculate the percent error, you need to find the difference between the measured value and the actual value, then divide that by the actual value and multiply by 100. The formula for percent error is:

% error = (|measured value - actual value| / actual value) x 100

In this case, the measured value is 0.46 cubic centimeter and the actual value is 0.50 cubic centimeter.

% error = (|0.46 - 0.50| / 0.50) x 100

% error = (0.04 / 0.50) x 100

% error = 0.08 x 100

% error = 8%.

Hence, Anita's measurement using the water displacement method has a percent error equivalent to 8%.

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Answer:

A = - 12 , B = - 8 , C = - 4

Step-by-step explanation:

substitute the value of x above the letters into the equation and solve for y

x = - 2

2(- 2) - y = 8

- 4 - y = 8 ( add 4 to both sides )

- y = 12 ( multiply both sides by - 1 )

y = - 12 ← value of A

x = 0

2(0) - y = 8

0 - y = 8- y = 8 ( multiply both sides by - 1 )

y = - 8 ← value of B

x = 2

2(2) - y = 8

4 - y = 8 ( subtract 4 from both sides )

- y = 4 ( multiply both sides by - 1 )

y = - 4 ← value of C