Translate the phrase into an algebraic expression the quotient of b and 8

19/3

Step-by-step explanation:

10+9=3p

19=3p

19/3=p

Answer:

12+(-12)=0

-14+34=20

-65+42=-23

The first option, "one half," corresponds to the scale factor of 0.5.

Scale factor = Dimensions of the new shape Dimensions of the original shape is the fundamental formula used to calculate it. The formula is expressed as Scale factor = Larger image dimensions Smaller figure dimensions in the event that the original figure is enlarged.

We can contrast the side lengths of triangles D and D′ to determine the scaling factor.

Let's contrast the side lengths for the two triangles.

Triangle D has sides that are 4.2 in length, and triangle D′ has sides that are 2.1 in length.

Scale factor = (Side length of triangle D′) / (Side length of triangle D)

Scale factor = 2.1 / 4.2

Scale factor = 0.5

The first option, "one half," corresponds to the scale factor of 0.5.

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Answer:

(x-1)(4x-3)(x+3)

Step-by-step explanation:

The factor of the polynomial 4x³ + 5x² – 18x + 9 will be (4x – 3), (x + 3), and (x – 1).

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The polynomial is given below.

⇒ 4x³ + 5x² – 18x + 9

Then the factor of the polynomial will be

⇒ 4x³ – 3x² + 8x² – 6x – 12x + 9

⇒ x²(4x – 3) + 2x(4x² – 3) – 3(4x – 3)

⇒ (4x – 3)(x² + 2x– 3)

⇒ (4x – 3)(x² + 3x – x – 3)

⇒ (4x – 3)(x + 3)(x – 1)

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The percentage of races in will his finishing time is between 64.5 and 65.5 seconds is 68%.

According to the empirical rule, also known as the 68-95-99.7 rule, the percentage of values that lie within an interval with 68%, 95%, and 99.7% the values lies within one, two, or three standard deviations of the mean of the distribution.

\(\rm P(\mu - \sigma \ \ < X < \mu + \sigma) \ \approx 68\%\\\\P(\mu - 2\sigma < X < \mu + 2\sigma) \approx 95\%\\\\P(\mu - 3\sigma < X < \mu + 3\sigma) \approx 99.7\%\)

where we had were mean of the distribution of X is μ and the standard deviation from the mean of the distribution of X is σ (assuming X is normally distributed).

When Kiran runs the 400 meters dash, his finishing times are normally distributed with a mean of 65 seconds and a standard deviation of 0.5 seconds.

Then by the formula, we have

\(\rm P (65-0.5 < X < 65+0.5) = P(64.5 < X < 65.5) \approx 68\%\)

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Answer:

y= 1/2 X + 3/4

Step-by-step explanation:

..........

Step-by-step explanation:

So, the answer is

y=1/2 X + 3/4

1a. 128

1b. 81

1c. 64

1d. 25

1e. 343

1f. 100000

1g. 64

1h. 0

1i. 13

1j. 1

2a. 243

2b. 64

2c. 36

2d. 625

2e. 1331

2f. 10000000

2g. 81

2h. 0

2i. 17

2j. 1

Answer:

1 and 8 alternate exterior angles

4 and 5 - alternate interior angles

6 and 7 - vertical angles

4 and 8 - corresponding angles

3 and 5 - consecutive interior angles

1 and 2 - linear pair

Step-by-step explanation:

Answer: y=-3x+10

Step-by-step explanation:

M= 2-0/3-5 = -3

Y-1= -3(x-3)

-3x+9+1

Y=-3x+10

Answer:

the domain of the function is all real numbers less than or equal to 0

The given limit is: lim (x->0) (sin(9x) / x)

To estimate this limit, we can apply L'Hôpital's Rule since we have an indeterminate form (0/0 as x approaches 0). L'Hôpital's Rule states that if the limit of the ratio of the derivatives of the numerator and the denominator exists, then the limit of the original function exists and is equal to that value.

Taking the derivative of the numerator and the denominator with respect to x:

Numerator: d(sin(9x))/dx = 9cos(9x)
Denominator: d(x)/dx = 1

Now, we find the limit of the ratio of the derivatives:

lim (x->0) (9cos(9x) / 1)

As x approaches 0, cos(9x) approaches cos(0), which is 1. Therefore, the limit is:

lim (x->0) (9cos(9x) / 1) = 9(1) = 9

So, the limit exists and is equal to 9.

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They have a perimeter of 40 meters, and an area of 168 square meters. Therefore, either set of dimensions would work for Chase's fence.

Let's assume the rectangular plot of land has length L and width W. We can use the given information to set up the following system of equations:

2L + W = 40 (since there are three sides and the total length of fencing is 40 m)

LW = 168 (since the area of the land is 168 square meters)

Solving the first equation for W, we get:

W = 40 - 2L

we get:

L(40 - 2L) = 168

we get a quadratic equation:

\(2L^2\) - 20L + 84 = 0

Using the quadratic formula, we can solve for L:

L = (20 ± sqrt(\(20^2\) - 4(2)(84))) / (2(2))

L = (20 ± 4sqrt(11)) / 4

L = 5 ± sqrt(11)

Therefore, we have:

L = 5 + sqrt(11) or L = 5 - sqrt(11)

W = 30 - 2sqrt(11) or W = 30 + 2sqrt(11)

(5 + sqrt(11)) m by (30 - 2sqrt(11)) m

and

(5 - sqrt(11)) m by (30 + 2sqrt(11)) m

Note that both sets of dimensions satisfy the given conditions: they have a perimeter of 40 m (2L + W = 40) and an area of 168 square meters (LW = 168).

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Answer:

64

Step-by-step explanation:

140/56=2.5

160/2.5=64

Answer:

96% percent and fraction is 24/25

Answer: Down below

Step-by-step explanation:

64 % = 16 / 25

21 / 50 = 0. 42

9 / 25 = 36 %

2 / 5 = 40 %

/ = divide okay

Answer:

the length is 40 inches

the width is 14 inches

Step-by-step explanation:

We start by representation with variables

let l be the length and w the width

Length l is 2 inches less than 3 times width (3w)

l = 3w-2 ••••(i)

Mathematically,

we have the perimeter calculated as follows;

P = 2(l + w)

2(l + w) = 108

l + w = 108/2

l + w = 54 ••••••(ii)

Substitute equation i into ii

3w-2 + w = 54

4w = 54 + 2

4w = 56

w = 56/4

w = 14

Recall;

l + w = 54

14 + l = 54

l = 54-14

l = 40 inches

Answer:

The solution is: v = \(9\frac{1}{2}\)

Step-by-step explanation:

Given equation is:

\(\frac{4}{5}(v-7) = 2\)

The given equation is a linear equation in one variable. The solution requires isolating v on one side of the equation. Simple equality properties can be used to solve the equation.

So,

Multiplying both sides of equation with 5

\(5*\frac{4}{5}(v-7) =5* 2\\{4}(v-7) = 10\)

dividing both sides by 4

\(\frac{4(v-7)}{4} = \frac{10}{4}\\v-7 = \frac{5}{2}\\\)

Adding 7 on both sides

\(v-7+7 = \frac{5}{2}+7\\v = \frac{5+14}{2}\\v = \frac{19}{2}\\v = 9\frac{1}{2}\)

Hence,

The solution is: v = \(9\frac{1}{2}\)

Answer: 0,16,32,48,64

Step-by-step explanation: the equation 16b means you will multiple 16 by whatever is in the b box. For the first b is equal to 0 so 16x0 = 0, the second b is equal to 1 so 16x1 = 16

The discrete graph for the function rule is plotted and the coach will buy 8 basketballs for $128.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is the amount which a basketball coach spends at a sporting goods store and it depends on the number of basketballs the coach buys. The situation is represented by the function rule a = 16b.

The given equation is -

a = 16b

where -

[a] represents the amount spend by the basketball coach.

[b] represents the number of basketballs buyed.

The table is given as follows -

[b]                 [a]

0                    0

1                    16

2                   32

3                   48

4                   64

The graph of the representing the function rule - a = 16b is attached with the answer. The graph is discrete as number of basketballs cannot exist in fractions. This means the possible values of [b] will be whole numbers only.

PART - B

If coach spent $128, then the number of footballs bought will be -

b = 128/16

b = 8

Number of footballs bought were 8.

Therefore, the discrete graph for the function rule is plotted and the coach will buy 8 basketballs for $128.

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I think Landscape painting

Landscape painting was regarded as the highest form of Chinese painting, and generally still is. The time from the Five Dynasties period to the Northern Song period (907–1127) is known as the "Great age of Chinese landscape".

Landscape painting was regarded as the highest form of Chinese painting, and generally still is. The time from the Five Dynasties period to the Northern Song period (907–1127) is known as the "Great age of Chinese landscape".

The required slope (m) is -12 when the points given are (-3, 4) and (-3, -8).

In mathematics, a line's slope, also known as its gradient, is a mathematical expression of the line's steep slopes and orientation.

A line's steeper can be identified by looking at its slope.

The slope was calculated mathematically as "rise over run" (change in y divided by change in x).

So, the slope formula is:
m = y2 - y1/x2 - x1

Now, substitute the values and calculate the slope as follows:

m = y2 - y1/x2 - x1

m = -8 -4/-3+3

m = -12/0

m = -12

Therefore, the required slope (m) is -12 when the points given are (-3, 4) and (-3, -8).

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Answer:  16x^2 - 40x + 25

Step-by-step explanation:

The values of a for which the limit of r(x) exists, if r is a rational function  and is equal to r(a) are precisely those values of a such that q(a) is non-zero and p(x) and q(x) approach finite limits as x approaches a.

Let the rational function be expressed as:

r(x) = p(x)/q(x)

where p(x) and q(x) are polynomials and q(a) is non-zero.

If the limit of r(x) as x approaches a exists and is equal to r(a), then it must be the case that the numerator p(x) and denominator q(x) approach finite limits as x approaches a.

Therefore, we can write:

limx→a p(x) = p(a)

limx→a q(x) = q(a)

For the limit of r(x) to exist, it is also necessary that q(x) is not equal to zero in a neighborhood of a, except possibly at x=a.

Therefore, we can write:

q(x) ≠ 0 for x ≠ a

Putting these results together, we can conclude that limx→a r(x) exists and is equal to r(a) if and only if:

a is not a zero of q(x) (i.e., q(a) ≠ 0), and

p(x) and q(x) approach finite limits as x approaches a.

In summary, the values of a for which the limit of r(x) exists and is equal to r(a) are precisely those values of a such that q(a) is non-zero and p(x) and q(x) approach finite limits as x approaches a.

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Answer:

5/8 x 2 = 10/8 as simplified as 5/4 in fraction form.

5/8 x 2 = 1.25

in decimal form.

Step-by-step explanation:

The solution of the fraction is,

⇒ 5 / 4

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The fraction is,

⇒ 2 × 5/8

Now, We can simplify as;

The fraction is,

⇒ 2 × 5/8

Multiply as;

⇒ 10 / 8

⇒ 5 / 4

Thus, The solution of the fraction is,

⇒ 5 / 4

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Answer:

0.54 - Yes - repeating decimal

0.355555 - yes - repeating decimal

0.5473 - no - non-termination or repeating

0.254 - yes - terminating

Step-by-step explanation:

In the given game matrix, there is no saddle point, indicating the absence of a pure strategy that guarantees the best outcome for both players simultaneously. Players may need to consider mixed strategies or alternative approaches in this game.

In the given game matrix, the objective is to find the saddle point, if one exists, in pure or mixed strategies. The matrix is represented as follows:

A = 3 3       B = 1       C= 3 0

      1 3             2

                        3

To determine the saddle point, we need to find a value in the matrix that represents a minimum in its row and a maximum in its column at the same time. However, upon examining the matrix, we observe that there is no such value that satisfies this condition.

Consequently, we can conclude that there is no saddle point in this game matrix. A saddle point denotes an equilibrium point where both players have optimal strategies. In this scenario, the absence of a saddle point implies that there is no pure strategy that guarantees the best outcome for both players simultaneously. Instead, players may need to consider mixed strategies or alternative approaches to achieve their respective objectives in this game.

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Answer:

22 bicycles

Step-by-step explanation:

50 bicycles = $100.50

therefore 1 bicycle = $100.50 ÷ 50

= $2.01

so $45÷ $2.01 = 22 bicycles

because $2.01× 22= $44.22

$45.00- $44.22= $0.78

The statement "If x is a nontrivial solution of Ax=0​, then every entry in x is nonzero" is False.

A nontrivial solution means that there is at least one nonzero entry in x. However, it doesn't imply that every entry in x must be nonzero. It's possible to have a mixture of nonzero and zero entries in a nontrivial solution.

If x is a nontrivial solution of Ax=0, it means that x is a nonzero vector in the null space of A. This implies that A x = 0, which means that the linear combination of the columns of A given by x results in the zero vector.

However, this does not necessarily mean that every entry in x is nonzero. For example, consider the matrix A given by:

A = [1 0 1;

0 1 1;

1 1 2]

The null space of A contains the vector x = [-1; 1; 1], which is a nontrivial solution of Ax = 0. However, this vector has one entry that is zero and two entries that are nonzero.

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The total pieces at the fruit stand is 60.

Let the number of apples, bananas and oranges sold be 3x, 2x and 1x. We have actual number of bananas. So equating them to find the value of x.

2x = 20

x = 20/2

Performing division

x = 10

So, number of apples = 3x

Number of apples = 3×10

Number of apples = 30

Similarly, number of oranges = 10

Total number of fruits = sum of the number of apples, bananas and oranges

Total number of fruits = 30 + 20 + 10

Total number of fruits = 60

Thus, there are 60 fruits to sell.

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The center of the circle is at (2, -2).

To find the center of a circle, first use the equation

(x-h)^2 + (y-k)^2 = r^2,

where (h,k) is the center of the circle and r is the radius. Set both equations equal to each other and solve for h and k. To find the center of a circle with the equation

x² y² 4x 8y 11 0,

first rearrange the equation to standard form (x-h)² + (y-k)² = r²,

where h and k are the coordinates of the center and r is the radius. Then solve for h and k by completing the square. The equation becomes

(x-2)² + (y+2)² = 11,

so the center of the circle is at (2, -2).

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If there is a zero on the top of the fraction when calculating the slope, then the line is horizontal.

If the numerator (y2 - y1) is zero, it means that the y-coordinates of the two points on the line are the same. This indicates that the line is horizontal, because no matter how far apart the two points are horizontally (i.e., the difference between their x-coordinates), the vertical distance (y2 - y1) between them is zero.

In this case, the denominator (x2 - x1) will be non-zero, because the two points will have different x-coordinates, but since the numerator is zero, the overall fraction will be zero.

So, a zero on the top of the fraction indicates that the line has zero or undefined slope, which happens only for a horizontal or vertical line, respectively. Therefore, if there is a zero on the top of the fraction when calculating the slope, then the line is horizontal.

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