Q5 Solve to find the values of a and b.
4a + 7b = 38
9a + 7b = 68​

The quotient include the following: D. \(\frac{x(2x-3)}{7}\)

In Mathematics and Geometry, a quotient is a mathematical expression that is simply used to represent the division of a number (numerator) by another number (denominator).

Based on the information provided above, we can logically deduce the following mathematical expression;

\(\frac{2x-3}{x} \div \frac{7}{x^2}\)

By rearranging the mathematical expression using the multiplication operation, we have:

\(\frac{2x-3}{x} \times \frac{x^{2} }{7}\\\\2x-3 \times \frac{x }{7}\\\\\frac{x(2x-3)}{7}\)

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Answer:

Snails and slugs are gastropods, which make up the largest class of mollusks with more than 60,000 species. Most of these species can be identified by their shells. Some dwell in ocean, others in the freshwater of rivers, ponds, and lakes. Land snails abound in tropical jungles and in damp temperate regions. All of them need calcium carbonate for building their shells, and so are not common in sandy soil. Slugs differ from snails in that they generally have only a small internal shell.

Snails move by sliding on their single foot. Specialized glands in the foot secrete mucus, which lubricates the path over which the snail crawls. Snails can only crawl. Even those that live in water can't swim. As they crawl they secrete a slime to help themselves move across surfaces. Snails and slugs travel at speeds that vary from slow (0.013 m/s) to very slow (0.0028 m/s).

The snail's head bears the mouth opening and one or two pairs of tentacles. The eyes are located at the base of the tentacles. Most snails live off plants and dead organic matter, although a few are carnivorous. Their radula is a tongue-like projection of their mouth which is lined with small sharp teeth. Some snails obtain food by using their radula to drill holes in the shells of other mollusks.

Freshwater snails and land snails have been eaten by people since prehistoric times. Today they are still regarded as a delicacy in many countries. The market supply comes largely from snails that are raised in captivity on special farms in southern France, Italy, and Spain. About 10,000 snails can be kept in a 9 square meter area, where they are fed meal, vegetables, and bran.

Angie

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

30 from the beginning of the week plus 50 that you bought.

80-x=30

50=x

Answer is D

Answer:50

Step-by-step explanation:

30+50=80

80-30=50

So he sell 50

Answer:

The number of possible numeric value for SAT are 8 possible numeric values

Step-by-step explanation:

A cryptarithm is a form of mathematical game where unknown numbers represented by letters of the alphabet are used to form mathematical equations

The given cryptarithm is SAT + SUN = 700

The parameters are;

The digits represented by the letters are different

Non of the digits represented by the letters equals 7 or 0

We have;

T + N = 10

1 + A + U = 10

1 + S + S = 7

Therefore, S = (7 - 1)/2 = 3

S = 3

A + U = 10 - 1 = 9

A + U = 9

Therefore, A = 4 or 5 (2 choices)

From T + N = 10

T = 1, 2, 8, or 9 (4 choices) similarly, N = 1, 2, 8, or 9 (4 choices)

Therefore, the number of numeric values that SAT represent is given as follows;

(S = 1 choice) × (A = 2 choices) × (T = 4 choices) = 1 × 2 × 4 = 8 numeric values

SAT has 8 possible numeric value

Ratio of rise to run between the points (-2, 8) and (4, -3) = -11/6

To find the ratio of rise to run between two points, we need to calculate the difference in the y-coordinates (rise) and the difference in the x-coordinates (run) between the two points.

Given points:

Point 1: (-2, 8)

Point 2: (4, -3)

Rise = difference in y-coordinates = y2 - y1 = -3 - 8 = -11

Run = difference in x-coordinates = x2 - x1 = 4 - (-2) = 6

Therefore, the ratio of rise to run can be calculated as:

Ratio of rise to run = Rise / Run = -11 / 6

Thus, the ratio of rise to run between the points (-2, 8) and (4, -3) is -11/6.

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The sequence\(f_n(x) = e^{-nx}\) does not converge uniformly to the limit function\(f(x) = 0\) on the interval \(I = [0, \infty)\).

To examine the uniform convergence of the sequence\(f_n(x) = e^{-nx}\) on the interval\(I = [0, \infty)\), we need to check if the sequence converges uniformly to a limit function on that interval.

For uniform convergence, we need the following condition to hold:

Given any\(\(\epsilon > 0\\)), there exists an \(\(N \in \mathbb{N}\\)) such that for all \(n > N\) and for all \(x \in I\), we have\(\(\left| f_n(x) - f(x) \right| < \epsilon\)\), where \(\(f(x)\)\) is the limit function.

Let's find the limit function\(\(f(x)\\)) of the sequence \(f_n(x) = e^{-nx}\) as \(n\) approaches infinity. Taking the limit as \(\(n\)\)goes to infinity

\(\[f(x) = \lim_{n \to \infty} e^{-nx}\]\)

We can rewrite this limit using the exponential function property:

\(\[f(x) = \exp\left(\lim_{n \to \infty} -nx\right)\]\)

Since the limit inside the exponential is\(\(-\infty\)\) as \(\(n\)\) goes to infinity, we have:

\[f(x) = \exp(-\infty) = 0\]

Therefore, the limit function \(f(x)\) is the constant function\(\(f(x) = 0\\)) on the interval \(I = [0, \infty)\).

To check for uniform convergence, we need to evaluate the difference \(\left| f_n(x) - f(x) \right|\) and see if it is less than any given \(\epsilon > 0\) for all \(n > N\) and for all \(x \in I\).

\(\[\left| e^{-nx} - 0 \right| = e^{-nx}\]\)

To make this expression less than\(\(\epsilon\),\) we need to find an \(N\) such that \(e^{-nx} \(< \epsilon\)\) for all\(n > N\) and for all\(\(x \in I\).\)

However, as \(\(x\)\) approaches infinity, \(e^{-nx}\) approaches 0. But for any finite \\((x\)\) in the interval \([0, \infty)\), \(e^{-nx}\)  will always be positive and never exactly equal to 0. This means we cannot find an\(\(N\)\)that satisfies the condition for uniform convergence.

Therefore, the sequence\(f_n(x) = e^{-nx}\) does not converge uniformly to the limit function \(f(x) = 0\) on the interval \(I = [0, \infty)\).

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Therefore, the directional derivative of f at P=(1,-1,-2) in the direction of A=3i+2j-6k is -2.

To find the directional derivative of f(x,y,z) at P=(1,-1,-2) in the direction of A=3i+2j-6k, we first need to find the gradient of f at P, which is given by:

grad(f) = ∇f = (∂f/∂x)i + (∂f/∂y)j + (∂f/∂z)k

Here, f(x,y,z) = xy + yz + zx, so we have:

∂f/∂x = y + z

∂f/∂y = x + z

∂f/∂z = x + y

Thus, at P=(1,-1,-2), we have:

∇f(P) = (∂f/∂x)i + (∂f/∂y)j + (∂f/∂z)k

= (y+z)i + (x+z)j + (x+y)k

= (0+(-2))i + (1+(-2))j + (1+0)k

= -2i - 1j + 1k

Next, we need to find the unit vector in the direction of A:

|A| = sqrt(3^2 + 2^2 + (-6)^2) = 7

u = A/|A| = (3/7)i + (2/7)j - (6/7)k

Finally, we can compute the directional derivative of f at P in the direction of A as:

(DAf) | 1(1,-1,-2) = ∇f(P) · u

= (-2i - 1j + 1k) · (3/7)i + (2/7)j - (6/7)k

= -6/7 - 2/7 - 6/7

= -2

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Answer:

16.8 cubic centimeter

Step-by-step explanation:

Dimensions of rectangular prism are:

\(4\ cm, 3\ cm , 1.4\ cm\)

To find:

The volume of rectangular prism in cubic cm ?

Solution:

The formula for volume of prism is given as:

\(V=l\times w\times h\)

Where \(l\) is the length of rectangular prism

\(w\) is the width of rectangular prism

\(h\) is the height of rectangular prism

Here we are given the three dimensions of prism as:

Length, \(l\) = 4 cm

Width, \(w\) = 3 cm

Height, \(h\) = 1.4 cm

Putting the values in formula for volume:

\(V=4\times 3\times 1.4\\\Rightarrow \bold{V =16.8\ cm^3}\)

So, volume is 16.8 cubic centimeter.

Answer:

16.8

Step-by-step explanation

(4 cm times 3 cm) = 12 cm times 1.4 = 16.8

hope i got it correct :)

If the sand falls at a rate of 16 cubic millimeters per second, a player would have approximately 6.25 seconds for their turn.

The rate of sand falling from the hourglass is given as 16 cubic millimeters per second. We need to find out the time available for a turn. Let's assume that the hourglass is filled with 'x' cubic millimeters of sand.

We can use the formula:

Volume = Rate x Time

Here, the volume of sand is 'x' cubic millimeters, the rate is 16 cubic millimeters per second, and we need to find the time available for a turn, which we can represent as 't' seconds.

So,

x = 16t

We can rearrange this equation to find 't':

t = x/16

This means that the time available for a turn is equal to the volume of sand in the hourglass divided by the rate at which the sand falls.

We don't know the exact volume of sand in the hourglass, but let's assume it's 100 cubic millimeters.

Then,

t = 100/16

t = 6.25 seconds

So, in this case, a player would have approximately 6.25 seconds for their turn before all of the sand falls to the bottom of the hourglass.

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Answer:

x=7

Step-by-step explanation:

2{x+8}+5{x-1}=60

Distribute

2x+16+5x-5 = 60

Combine like terms

7x +11 = 60

Subtract 11 from each side

7x+11-11 = 60-11

7x = 49

Divide each side by 7

7x/7 = 49/7

x = 7

Answer:

200

Step-by-step explanation:

We have the following ratio

dead batteries:total batteries

1:50

we then have the following ratio

x:10000

to solve this we mulitply the 1 from the first ratio by 200 (we do this because we multiplied 50 from the first ratio to get 10,000)

We get

200:10,000

200

Answer:

C(-7,-5)

Step-by-step explanation:

b is the mid point of AC

the coordinate of A ( 1,7)

the coordinate of B (-3,1)

XB=  (XA+XC)/2

-3 = (1+XC)/2

-6=1+XC

YB=(YA+YC) /2

1=(7+YC)/2

2=7+YC

YC=2-7

YC=-5

The inequality that shows the maximum weight capacity of the elevator is w≤ 2500

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign. The meaning of inequality is to say that two things are NOT equal. One of the things may be less than, greater than, less than or equal to, or greater than or equal to the other things.

To represent the weight limit for the elevator using inequality, we can write it out as

w ≤ 2500

This shows that the weight must not exceed 2500 pounds

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Answer:

The “center” of a data set is also a way of describing location. The two most widely used measures of the “center” of the data are the mean (average) and the median. To calculate the mean weight of 50 people, add the 50 weights together and divide by 50 .

Step-by-step explanation:

A state transition diagram shows how an object changes from one state to another, depending on events that affect the object. The correct answer is Option B.

State transition diagrams are utilized to model the behavior of objects in systems. Objects can experience multiple states, and state transition diagrams depict how an object transitions from one state to another, depending on the events that occur as a result of the system's execution. State transition diagrams, also known as state machines, state-chart diagrams, and state diagrams, are utilized in object-oriented software engineering and software engineering to describe object behavior and interactions with other objects.

A state transition diagram is useful for defining the states and transitions of a finite-state machine. When a system can be in one of a few discrete states, a state transition diagram is employed to represent the state transitions. State transition diagrams are helpful in system analysis, as they help users comprehend how the system works, and they may also be utilized as input to software testing tools. Additionally, state transition diagrams may be utilized to determine the number of states in a system or the minimum number of inputs required to transition from one state to another.

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Answer:

-10

-7

-4

-1

2

5

8

Step-by-step explanation:

an = a + (n - 1)d

Answer:

8.568cm

Step-by-step explanation:

IF Kenny leaves home and walks 10 blocks east and 24 blocks north to get to the movie theater, his distance from home to the theatre is gotten using the pythagoras theorem as shown;

d² = 23² + 10²

d² = 529 + 100

d² = 629

d = √629

d = 8.568

Hence the required distance is 8.568cm

Answer:

the multiples of five and eight are 40

Given:

Vertex: (-3, 3)

Focus: (-3, 2)

Let's find the distance from the point (x, y) to the focus of the parabola and the directrix.

To find the distance, apply the distance formula:

Thus, we have:

Distance from (x, y) to the focus:

Where:

(x1, y1) ==> (x, y)

(x2, y2) ==> (-3, 2)

Thus, we have:

Therefore, the distance from the point (x, y) to the focus is:

• The distance from the point to the directrix.

From the graph, the directrix is:

y = 4

Now, to find the distance, subtract the y-coordinate of the point from y = 4.

The distance is the absolute value of the result.

Thus, we have:

ANSWER:

Distance from the point to the focus:

Distance from the point to directrix:

Answer:

4/12 and 3/8

Step-by-step explanation:

Answer:

5,000.15

Step-by-step explanation:

The next three terms in the given geometric sequence are 24, 48, and 96

To find the next terms in the geometric sequence 3, 6, 12, we need to find the common ratio (r) first.

r = 6/3 = 2

Now we can use the formula for the nth term of a geometric sequence:

an = a1 * r^(n-1)

where n+1 is the nth term, a1 is the first term, r is the common ratio, and n is the term number.

Using this formula, we can find:

a4 = 24 (3 * 2^3)
a5 = 48 (3 * 2^4)
a6 = 96 (3 * 2^5)

Therefore, the next three terms in the sequence are 24, 48, and 96.

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The equation of the circle on the graph with center (0, 1) and point (3, 1) is x² + (y - 1)² = 9.

The standard form equation of a circle with center (h, k) and radius r is:

(x - h)² + (y - k)² = r²

From the image, the center of the circle is at point (0,1) and it passes through point (3,1).

Hence:

h = 3 and k = 1

Next, we need to find the radius of the circle, which is the distance between the center and the given point.

We can use the distance formula:

\(r = \sqrt{(x_2 - x_1)^2 + ( y_2 - y_1)^2}\)

Plugging in the coordinates (0, 1) and (3, 1), we have:

\(r = \sqrt{(3-0)^2 + ( 1-1)^2} \\\\r = \sqrt{(3)^2 + ( 0)^2} \\\\r = \sqrt{9} \\\\r = 3\)

So, the radius of the circle is 3.

Now we can substitute the values into the equation of a circle:

(x - h)² + (y - k)² = r²

(x - 0)² + (y - 1)² = 3²

Simplifying further, we get:

x² + (y - 1)² = 9

Therefore, the equation of the circle is x² + (y - 1)² = 9.

Option C) x² + (y - 1)² = 9 is the correct answer.

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Answer:62 miles/hour

Step-by-step explanation:372 miles / 6 hours = 62 miles/hour 62 * 15 = 930 A driver travels 372 miles in 6 hours. At that rate, the driver will travel 930 miles in 15 hours

Answer: 62 mph

Step-by-step explanation:

372/6=62

:)

Answer:

The percentage represented is 37.5%

Answer:

The answer is letter B.

With the coordinates (0, 1) ( 1, 4) (2, 7), Option B has a line of best fit represented by y = 3x + 1.

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.

The given linear equation is

y = 3x + 1

We need to find Which scatterplot represents the most likely line of best fit.

We will use the hit and trial method,

Let x = 0

y = 0 + 1

y = 1

Put x = 1

y = 3 + 1

  = 4

Put x = 2

y = 6 + 1

  = 7

So, we have some coordinates are which represent the line in option B.

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Answer:

Let's simplify step-by-step.

−3(x−4)+3(y−6)

Distribute:

=(−3)(x)+(−3)

(−4)+(3)(y)+(3)(−6)=−3x+12+3y+−18

Combine Like Terms:

=−3x+12+3y+−18=(−3x)+(3y)+( 12+18)=−3x+3y+−6

Answer:

=−3x+3y−6

Can I have a brainliest

Step-by-step explanation: