graph the line that passes through the points(0,-7) and (-6,-6) and determine the equation of the line

Answer:

48 cm²

Step-by-step explanation:

Area of trapezoid = \(\frac{a + b}{2}\) × h

Area = (8 + 16)/2 x 4

Area = 24/2 x 4

Area = 12 x 4

Area = 48 cm²

a) The inequality for the expression 2z + 9 is 2z + 9 > 13.

b) The inequality for the expression 3(z - 4) is 3z - 12 > -6.

c) The inequality for the expression 4 + 2z is 4 + 2z > 8.

d) The inequality for the expression 5(3z - 2) is 15z - 10 > 20.

a) To write an inequality for the expression 2z + 9, we can multiply the given inequality z > 2 by 2 and then add 9 to both sides of the inequality:

2z > 2 * 2

2z > 4

Adding 9 to both sides:

2z + 9 > 4 + 9

2z + 9 > 13

Therefore, the inequality for the expression 2z + 9 is 2z + 9 > 13.

b) For the expression 3(z - 4), we can distribute the 3 inside the parentheses:

3z - 3 * 4

3z - 12

Since we are given that z > 2, we can substitute z > 2 into the expression:

3z - 12 > 3 * 2 - 12

3z - 12 > 6 - 12

3z - 12 > -6

Therefore, the inequality for the expression 3(z - 4) is 3z - 12 > -6.

c) The expression 4 + 2z does not change with the given inequality z > 2. We can simply rewrite the expression:

4 + 2z > 4 + 2 * 2

4 + 2z > 4 + 4

4 + 2z > 8

Therefore, the inequality for the expression 4 + 2z is 4 + 2z > 8.

d) Similar to the previous expressions, we can distribute the 5 in the expression 5(3z - 2):

5 * 3z - 5 * 2

15z - 10

Considering the given inequality z > 2, we can substitute z > 2 into the expression:

15z - 10 > 15 * 2 - 10

15z - 10 > 30 - 10

15z - 10 > 20

Therefore, the inequality for the expression 5(3z - 2) is 15z - 10 > 20.

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Step-by-step explanation:

First get x on its own:

Subtract 3 from each side

y - 3 = 2x

Divide through by 2

y/2 - 3/2 = x

or x = y/2 - 3/2

Now simply switch labels: x↔y

y = x/2 - 3/2

Answer:

\(y=\frac{x}{2}+\frac{3}{2}\)

Step-by-step explanation:

To find inverse of an equation, replace the variables x with y and y with x:

x = 2y - 3

Now we get it in slope-intercept form:

x = 2y - 3

Add 3 to both sides.

x + 3 = 2y

Divide both sides by 2.

\(\frac{x}{2}+\frac{3}{2}=y\)

Swap left and right sides.

\(y=\frac{x}{2}+\frac{3}{2}\)

And this is the inverse of the equation y = 2x - 3.

I hope you find my answer helpful.

Answer:

m=-3

Step-by-step explanation:

Step-by-step explanation and Answer:

First, write statements! Then find out the operation. Very simple!

Number of burritos Chloe ate: 34

Number of burritos Lucy ate: 3

Number of burritos Chole ate more that Lucy: 34-3= 31

= Chloe ate 31 burritos more that Lucy.

The expression simplifies to |2x| = -2x, when x<0 by definition of absolute value

If x<0, then the expression |2x| simplifies to -2x.

The absolute value of a number is the distance of the number from zero on the number line.

Since x is negative in this case, 2x will be negative as well.

Taking the absolute value of -2x will give us the opposite of -2x, which is 2x.

However, since we know that x<0, this means that -2x will always be a positive number.

Hence, the expression simplifies to |2x| = -2x, when x<0.

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Complete question

Simplify the expression |2x|  when x is less than 0, x<0

Answer:

Samuel can type 40 words per minute

Step-by-step explanation:.

Then how many hours will it take for him to type 2.6 words times 10 to the power of five words

=> 2.6 words time 10 to the power of 5

=> 2.6 x 10^5

=> 2.6 x 100 000

=> 260 000 words in all.

Now, we need to find the number of words Samuel can type in a hour

=> 40 words / minutes , in 1 hour there are 60 minutes

=> 40 x 60

=> 2 400 words /hour

Now, let’s divide the total of words he need to type to the number of words he can type in an hour

=> 260 000 / 2 400

=> 108.33 hours.

The approximate solution of the linear system represented by the graph is, (5, 6)

The equation of a straight line is a relationship between x and y coordinates, The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.

Given that,

A graph in which two lines are intersecting each other,

basically solution of linear system means where both the lines will intersect,

So, in the graph it can be seen that lines are intersecting around x coordinate 5 and y coordinate 6,

Therefore, the solution is (5, 6)

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(a) Through the conditional probability formula:\(P(B ∩ A) = P(B | A) P(A),\)

\(P(B / A1) P(A1) = 0.50 x 0.20 = 0.10A2 = 0.30 x 0.30 = 0.09A3= 0.40 x 0.50 = 0.20\)

(b)Bayes' theorem gives

\(P(A2 | B) = p(B | A2) p(A2) / [p(B | A1) P(A1) + p(B | A2) P(A2) + p(B | A3) p(A3)]= 0.26Thus, P(A2 | B) = 0.26.\)

(c)the tabular approach can show us

Events      P(Ai)    P(B | Ai)   P(Ai ∩ B)   P(Ai | B)

A1          0.2     0.5       0.1        0.167

A2          0.3     0.3       0.09      0.307

A3          0.5     0.4       0.2        0.526

Therefore,\(P(A1 | B) = 0.167, p(A2 | B) = 0.307, p(A3 | B) = 0.526.\)

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Answer: See below

Step-by-step explanation:

The first is a beaker, it's used to measure liquid volume

The second is a ruler, it's used to measure length.

Last is a thermometer, it's used to measure temperature.

Suppose you look by eye at a star near the edge of a dusty interstellar cloud. The star will look dimmer than it would if it were outside the cloud.

Interstellar clouds are vast, dense regions of dust and gas that exist between stars. These clouds contain tiny solid particles of dust, which scatter and absorb light as it passes through them.

When we observe a star that is located near the edge of an interstellar cloud, the light from that star has to pass through a greater amount of dust before it reaches our eyes or telescopes. The dust scatters and absorbs some of the light, causing the star to appear dimmer than it would if it were outside the cloud.

This effect is similar to how the sun appears dimmer when it is viewed through a thick layer of clouds or fog. In both cases, the amount of light that reaches us is reduced due to the presence of a barrier that scatters and absorbs some of the light.

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The total amount accrued, principal plus interest, from simple interest on a principal of $9,100.00 at a rate of 2.5% per year for 3 years is $9,782.50.

Here, we have

Principle amount = P = £9100

interest rate = r = 2.5% per year

Time period = t = 3

Simple Interest = 9100 × 2.5% × 3 = £682.5

Total amount = Principal amount + Simple interest

                       = 9100 + 682.5

                       = £9782.5

Therefore, the total amount accrued, principal plus interest, from simple interest on a principal of £9,100.00 at a rate of 2.5% per year for 3 years is £9,782.50.

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complete question:

Colin invests £9100 into his bank account.

He receives 2.5% per year simple interest.

How much will Colin have after 3 years?

Give your answer to the nearest penny where appropriate.​

--- 3 to 2 (3:2) ---

The exact length of the sides of the quadrilateral are as follows:

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

Given, A quadrilateral ABCD with vertices A(4, 5), B(-3,3), C(-6,-13) and D(6,-2).

From the general formula of the distance between two coordinates in 2D plane.

Distance = √((x - x')² + (y-y')²)

For AB,

Distance = √((4  + 3)² + (5-3)²)

Distance = √49 + 4

Distance = √53

For BC,

Distance = √((-6 +3 )² + (-13-3)²)

Distance = √9 + 256

Distance = √264

Distance = 2√66

And the same process is to be continued For the CD and DA

While

CD = √265

DA = √53

Therefore, The exact length of the sides of the quadrilateral are as follows:

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Thus, the cardinal number of the set E is found to be: N(E) = 6.

A cardinal number describes or expresses how many of anything are present.

So all natural numbers are often refereed to as cardinal numbers. Cardinal numerals have been used for counting. When an ordinal number is an integer that represents the location or place of an object.

The description of a cardinal number is really a number that is used to express quantity in whole numbers. Decimals and fractions are not regarded as cardinal numbers. Natural numbers and numbering numbers constitute cardinal numbers. Each of them is a positive integer.

Given data:

N(CxE) = 18

C = {4, 5, 6)

In which N is the cardinal number, that is the total elements present in the set.

So,

N(C) = 3

Given that: N(CxE) = 18

The formula for the Cartesian product is:

N(CxE) = N(C) * N(E)

18 = 3* N(E)

N(E)  = 18 /3

N(E) = 6

Thus, the cardinal number of the set E is found to be: N(E) = 6.

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Complete questions:

Find N(E), Given That N(CxE) = 18 And C = {4, 5, 6).

Α. 6

B. 9

C. 3

D. 5

Answer:

20 blogs

Step-by-step explanation:

Step 1:  Determine the proportion of pop culture blogs:

First, we need to determine the proportion of pop culture blogs already written.  We can do this by dividing the number of pop culture blogs already written by the total number of blogs written:

The proportion of pop culture bloggers = Number of pop culture bloggers / Total number of bloggers

Proportion =  26 / (20 + 26 + 7 + 12)

Proportion = 26 / 65

Proportion = 0.4

Step 2:  Multiply the proportion of pop culture blogs by the number of upcoming blogs:

To determine the expected number of pop culture blogs that will be written given the data, we can multiply the proportion of pop culture blogs already written by the number of upcoming blogs:

Expected number of pop culture blogs = proportion of pop culture blogs *  number of upcoming blogs

Expected number = 0.4 * 50

Expected number = 20

Thus, you should expect 20 pop culture blogs to be written given the data.

The probability of pulling out a red pair of socks and sport shorts is 12/35.

We have,

10 pairs of socks, 6 are red, and 7 shorts, 4 of which are sport shorts.

So, The probability of pulling out a red pair of socks is given by:

= (number of red socks) / (total number of socks)

= 6 / 10

= 3 / 5

and, the probability of pulling out sport shorts is given by:

= (number of sport shorts) / (total number of shorts)

= 4 / 7

To find the probability of both events happening together

= P(red socks) x P(sport shorts)

= (3 / 5) x (4 / 7)

= 12 / 35

Therefore, the probability of pulling out a red pair of socks and sport shorts is 12/35.

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The length of side X in simple radical form with a rational denominator is 25/√3.

In Mathematics and Geometry, a 30-60-90 triangle is also referred to as a special right-angled triangle and it can be defined as a type of right-angled triangle whose angles are in the ratio 1:2:3 and the side lengths are in the ratio 1:√3:2.

This ultimately implies that, the length of the hypotenuse of a 30-60-90 triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30-60-90 triangle is √3 times the length of the shorter leg (adjacent side):

Adjacent side = 5/√3

Hypotenuse, x = 5 × 5/√3

Hypotenuse, x = 25/√3.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The answer to this question: B

The value of n can be determined by finding the number of visible arcs in the pattern, which is 30 in this case.

To determine the value of n, we need to find the relationship between the total length of visible areas and the number of circles (n).

In the given pattern, each circle contributes to the visible area twice: once as its circumference and once as the overlapping part with the adjacent circles. Since the circumference of each circle is 1 unit, the visible area contributed by each circle is 2 units.

Therefore, the total length of visible areas can be expressed as 2n. Given that the total length is 60 units, we can set up the equation:

2n = 60

Solving this equation, we find:

n = 60/2 = 30

Thus, the value of n is 30.

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Answer:

(x + 4)^2 + (y + 7)^2 = 36

Step-by-step explanation:

The given information describes a circle with its center at (-4, -7) and tangent to the vertical line x = 2. To determine the radius of the circle, we need to find the distance between the center and the tangent line.

The distance between a point (x1, y1) and a line Ax + By + C = 0 is given by:

d = |Ax1 + By1 + C| / sqrt(A^2 + B^2)

In this case, the equation of the line is x = 2, which can be written as 1x + 0y - 2 = 0. Therefore, A = 1, B = 0, and C = -2. The center of the circle is (-4, -7), so x1 = -4 and y1 = -7. Substituting these values into the formula, we get:

d = |1*(-4) + 0*(-7) - 2| / sqrt(1^2 + 0^2)

d = |-6| / sqrt(1)

d = 6

Therefore, the radius of the circle is 6 units. The equation of a circle with center (h,k) and radius r is given by:

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

Substituting the values we have found, we get:

(x + 4)^2 + (y + 7)^2 = 36

This is the equation of the circle that satisfies the given conditions.

The function A(x) that best describes the area of the cut mat is A(x) = 3.6x² + 8.2x + 14.

To find the function A(x), which represents the area of the cut mat, we need to subtract the area that is cut out from the total area of the mat.

The total area of the mat is given by the function M(x) = 3.6x² + 14.2x + 14.

The area that is cut out and removed from the middle of the mat is represented by the function N(x) = x + 5x = 6x.

To find A(x), we subtract N(x) from M(x):

A(x) = M(x) - N(x)

    = (3.6x² + 14.2x + 14) - (6x)

    = 3.6x² + 14.2x + 14 - 6x

    = 3.6x² + 8.2x + 14

Therefore, the function A(x) that best describes the area of the cut mat is A(x) = 3.6x² + 8.2x + 14.

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The graph given can be expressed as piecewise function as,

f(x) = 2x + 10, for [-6, -3)

     = -x + 1, for (-3, 2)

A piecewise function is a function which has different definitions of values for different intervals.

Given is a graph of a function.

The graph consists of two lines.

In the interval [-6, -3), the graph is a line with positive slope.

In the interval (-3, 2), the graph is a line with negative slope.

Now we have to find the equation of two lines.

The positive line passes through (-6, -2) and (-5, 0).

Slope of the line = (0 - -2) / (-5 - -6) = 2 / 1 = 2

Slope intercept form of the line is y = mx + c, where m is slope and c is y intercept.

y = 2x + c

Substitute a point (-5, 0), in the equation.

0 = (2 × -5) + c ⇒ c = 10

Equation is y = 2x + 10

The negative line passes through (0, 1) and (1, 0).

Slope = (0 - 1) / (1 - 0) = -1

y intercept = 1, since the line passes touches the Y axis at the point (0, 1).

Equation of line is y = -x + 1

So the function is, f(x) = 2x + 10, for [-6, -3)

                                    = -x + 1, for (-3, 2)

Hence the piecewise function is found.

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Answer:

y = 2x + 10 for -6 <= x < -3

y = -x + 1 for -3 < x < 2

Step-by-step explanation:

Answer:

b<−10

Step-by-step explanation:

Answer:

b<-10

Step-by-step explanation:

Inequality: -b-2>8

Step 1: Add 2 to both sides

-b-2+2>8+2

-b>10

Step 2: Divide both sides by -1

-b > 10

_      _

-1     -1

b<-10

Hope this helps you!!!!

The binomials represents the length of each of it sides = a + 5.

The given expression is;

a² + 10a + 25

It represents the area of square.

Since area of square = (side)²

Therefore,

(side)² = a² + 10a + 25

           =  a² + 5a + 5a + 25

           =  a(a+5) + 5(a+5)

           =   (a+5)(a+5)

           =   (a+5)²

⇒(side)² = (a+5)²

Taking square root both sides

Hence

side of square = a + 5

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