What does b represent in the equation of a line in the form y = mx + b?The y-intercept
The value of x when y = 0
The slope
The x-intercept

Answer: 33 pages in 1 hour

Step-by-step explanation:

You could cross multiply

[tex]\frac{11}{1/3}[/tex] = [tex]\frac{x}{1}[/tex]

11=1/3x

x=33

The exponential number 7⁴ we get expression as 2401.

Given that,

The exponential number is 7⁴.

We have to find the expression.

A number's exponent tells us how many times it has been multiplied by itself.

Exponent-related issues are resolved utilising exponentiation rules or exponentiation attributes.

How many times we must multiply the reciprocal of the base is indicated by a negative exponent is the exponential with negative symbol

A fractional exponent is one where the exponent of a number is a fraction.

Take the exponential number.

7⁴

7×7×7×7

2401

Therefore, The exponential number 7⁴ we get expression as 2401.

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Answer:

Step-by-step explanation:

no because (-2X1, Y1), and-2X3, y3), arent congruent so the whole problem is not congruent

The amount of money that Malachy get is £123 .

In the question ,

it is given that ,

£410 is divided between Gordon, Malachy and Paul .

also given that Malachy gets three times as much as Paul ,

let the amount that Paul get = x .

So , the amount that Malachy get = 3x

it is given that Gordon gets twice as much as Malachy ,

that means , the amount that Gordon get = 2(3x) = 6x

given the total amount is £410 ,

So, equation representing the total amount is

x + 3x + 6x = 410

4x + 6x = 410

10x = 410

x = 410/10

x = 41

So , the amount that Paul get = £41 ,

amount that Malachy get = 3(41) = £123

amount that Gordon get = 6(41) = £246

Therefore ,  The amount of money that Malachy get is £123 .

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a)  no solution

b) only one solution

c) only one solution

d) infinite many solution.

e)  only one solution

f) no solution

g) infinite many solution.

h)  infinite many solution.

i)  no solution

j) only one solution

k) infinite many solution.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

We know depending upon the types of lines there are different type of solution

if there are two equations

[tex]a_1 x+ b_1 y+ c_1= 0[/tex] and [tex]a_2 x+ b_2 y+ c_2= 0[/tex]

For Intersecting Lines

[tex]a_1/a_2[/tex] ≠ [tex]b_1/b_2[/tex]

and, have only one solution

For parallel lines:

[tex]a_1/a_2[/tex] = [tex]b_1/b_2[/tex] ≠ [tex]c_1/c_2[/tex]

and, have no solution

For co- incident line

[tex]a_1/a_2[/tex] = [tex]b_1/b_2[/tex] = [tex]c_1/c_2[/tex]

and, have infinite many solution.

a) y= -5x + 4  --> 5x + y = 4

5x+y= -3

So, [tex]a_1/a_2[/tex] = [tex]b_1/b_2[/tex] ≠ [tex]c_1/c_2[/tex]

and, have no solution

b) y=3/4 x+5

y= 4/3 x + 5

so, [tex]a_1/a_2[/tex] ≠ [tex]b_1/b_2[/tex]

and, have only one solution

c) y= -3/4x+5

y=3/4x+5

[tex]a_1/a_2[/tex] ≠ [tex]b_1/b_2[/tex]

and, have only one solution

d) y= 3/4 x + 5

y= 5+ 3/4x

So, [tex]a_1/a_2[/tex] = [tex]b_1/b_2[/tex] = [tex]c_1/c_2[/tex]

and, have infinite many solution.

e) y= 3/4x +5

y=  x + 2

So, [tex]a_1/a_2[/tex] ≠ [tex]b_1/b_2[/tex]

and, have only one solution

f) y= 3/4x + 5

y= 3/4x + 2

So, [tex]a_1/a_2[/tex] = [tex]b_1/b_2[/tex] ≠ [tex]c_1/c_2[/tex]

and, have no solution

g) 6x -y = 5

-6x + y= -5

So, [tex]a_1/a_2[/tex] = [tex]b_1/b_2[/tex] = [tex]c_1/c_2[/tex]

and, have infinite many solution.

h) 2x- y +5 =0

2x- y+ 5 =0

So, [tex]a_1/a_2[/tex] = [tex]b_1/b_2[/tex] = [tex]c_1/c_2[/tex]

and, have infinite many solution.

i) 4x- y+ 5 =0

4x- y +3 = 0

So, [tex]a_1/a_2[/tex] = [tex]b_1/b_2[/tex] ≠ [tex]c_1/c_2[/tex]

and, have no solution

j) 3x- y +5 = 0

2x -y +5 =0

So, [tex]a_1/a_2[/tex] ≠ [tex]b_1/b_2[/tex]

and, have only one solution

k) 2x+ y -1 = 0

2x + y- 1= 0

So, [tex]a_1/a_2[/tex] = [tex]b_1/b_2[/tex] = [tex]c_1/c_2[/tex]

and, have infinite many solution.

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Answer:

(3b + 2y)(2x - 3m)

Step-by-step explanation:

6xb + 2xy - 9mb - 6my ( factor first/second and third/fourth terms )

= 2x(3b + y) - 3m(3b + 2y) ← factor out (3b + 2y) from each term

= (3b + 2y)(2x - 3m)

Answer:

Step-by-step explanation:

gradient of L:

4-(-1)/6-4

=5/2

Gradient of m=perpendicular gradient=m1xm2= -1

5/2m2=-1

5m2=-2

m2=  2/5

y intercept given=8

equation:

y= -2/5x+8

y will be0 when line crosses x-axis

input y as 0

0= -2/5x+8

2/5x=8

2=40x

x= 20

coordinate=(-20,0)

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Answer:

Step-by-step explanation:

75 = 64 + 8 + 2 + 1 = 1*2^6 + 1*2^3 + 1*2^1 + 1*2^0

There is no power 5, 4, or 2 so zeros go in those slots.

75 = 1001011 (Base 2)

[tex]\boldsymbol{\sf{\dfrac{5}{3}x+4=\dfrac{2}{3}x }}[/tex]

Subtract 2/3x on both sides.

[tex]\boldsymbol{\sf{\dfrac{5}{3}x+4-\dfrac{2}{3}x=0 }}[/tex]

Combine 5/3x and -2/3x to get x.

[tex]\boldsymbol{\sf{x+4=0 }}[/tex]

Subtract 4 from both sides. Any value subtracted from zero results in its negative value.

[tex]\boldsymbol{\sf{x=-4 }}[/tex]

Answer:

x = - 4

Step-by-step explanation:

[tex]\frac{5}{3}[/tex] x + 4 = [tex]\frac{2}{3}[/tex] x ( multiply through by 3 to clear the fractions )

5x + 12 = 2x ( subtract 2x from both sides )

3x + 12 = 0 ( subtract 12 from both sides )

3x = - 12 ( divide both sides by 3 )

x = - 4

The new volume of the container will be 120 ft³

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

Given a container with dimensions 3ft by 4ft by 5ft

Its volume need to be twice.

Volume of container = length*width*height

Original volume = 3*4*5 = 60 ft³

After doubling = 60*2 = 120 ft³

New dimensions are = 4ft by 5ft by 6ft

Hence, The new volume of the container will be 120 ft³ and New dimensions are 4ft by 5ft by 6ft

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According to the area of triangle, the value of x is 8.6 and the value of y is 10.5

Area of triangle:

The area of the triangle is defined as the region enclosed by its perimeter or the three sides of the triangle.

Given,

Here we have the triangle with side values and height.

Now, we have to find the value of x and y in the triangle.

We know the formula of the triangle is,

A = 1/2 b x h

Here the value of b is x + 9 and the value of h = 6

So, the area of the triangle is,

=> [(x + 9) x 6]/2

=> 2 = 6x + 54

=> 6x = 52

=>  x = 52/6

=> 8.6

Now, the value of y is calculated by using the Pythagoras theorem,

=> y² = (8.6)² + 6²

=> y² = 73.96 + 36

=> y² = 109.96

=> y = √109.96

=> y = 10.5

Therefore, the value of y is 10.5

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Weight of water will a 55 gallon tank hold 440 lbs.

If a 45 gallon hot water tank holds 360 lbs.

45 gal⇒  360 lb

55 gal ⇒ x lb?

Ratio

45 : 360 = 55 : x

Ratios are used to compare two numbers by dividing them. If you want to compare one data point (A) to another (B), your formula would be A/B. This signifies that you are dividing data A by data B. If A is five and B is ten, your ratio will be 5/10.

Here,

do the relation

[tex]\frac{45}{360} = \frac{55}{x}[/tex]

solve the x

[tex]x = \frac{55 * 360}{45} \\ = 440[/tex]

Hence weight of water will a 55 gallon tank hold 440 lbs.

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Answer:

L = 22     W = 4

Step-by-step explanation:

It says that the length is 6 more than 4 times its width, this means

4W + 6 = L

Perimeter is 52, this means

2W + 2L = 52

and Area is 88, this means

W*L = 88

2W = 52 - 2L

W = 26 - L

4(26 - L) + 6 = L

104 - 4L + 6 = L

104 + 6 = L + 4L

110 = 5L

L = 22

W = 26 - 22

W = 4

The total surface are of cuboid is 304 cm square.

What is total surface area of cuboid?

The area of a cuboid refers to the surface area as the cuboid is a three dimensional solid. Thus, the area of cuboid can be calculated using the formula of area of rectangle, since the faces of a cuboid are in a rectangular shape.

The Total surface area of a cuboid (TSA) is equal to the sum of the areas of it’s 6 rectangular faces, which is given by:

Total Surface Area of a Cuboid (TSA) = 2 (lw + wh + lh) square units

The above formula gives the total surface area of a cuboid having all six faces.

Given, length = 10cm , width = 6 cm , height = 7cm

Total surface area = 2[10(6)+6(7)+10(7)]

=2(60+42+70)

=2(152)

=304.

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Using Z- distribution it is found that the mean length of jail time has increased because the test statistics is greater than the critical value.

Z- distribution: It is a special normal distribution where the mean is 0 and standard deviation is 01.

                             z = (x -μ) / σ

At the Null hypothesis, it is tested if the mean length of jail time is still of 2.5 years.,          

            i.e.,  H₀ :μ = 2.5

Null hypothesis : It refers to a hypothesis that states that there is no relationship between two population parameters.

At the alternative hypothesis, it is tested if it has increased

                 i.e., H₁ :μ>2.5

Alternative Hypothesis:   The alternative hypothesis states the research prediction of an effect or relationship.

we have the standard deviation for population thus the z- distribution is used.  The test statistics is :

                 z= ⁻ₓ -μ /σ /√n

where, x is the sample mean

           μ is the value tested at the null hypothesis.

           σ is the standard deviation of sample.

           n is the sample size.

For this problem the values of parameter are:

         x= 5 ,σ =1.4 ,μ = 2.5 and n = 27

hence the value is :

              z= ⁻ₓ -μ /σ /√n

                 = 5 - 2.5 / 1.4 ÷ √27

                 = 2.5 × √27 /1.4

                 = 9.27

The critical value for a right tailed test as we are testing if the mean is greater than a value with a significance level of 0.05 is of 2*= 1.645.

since, the test statistics is greater than the critical value, it can be concluded that the mean length of jail time has increased.

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The approximate value of the account after 5 years will be $6778.

Given that,

Mario put $6,000 into a savings account that accrues interest at a rate of 5% per year.

The amount is given by,

A= p(1 + r)^t

P = 6000

R = 5%

T= 2.5 years

R = Rate of Interest

T= Time

P = Principal Amount

By substituting we get,

A= p(1 + r)^t

A = 6000(1 + 0.05)^2.5

A = 6000(1.05)^2.5

A = 6000 * 1.129

A = 6778.35

As a result, the account will roughly be worth $6778 after five years.

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The P(a, b and c)  is 0.0432 when P(a) = 0.90, p(b) = 0.96, p(c) = 0.05.

From the given question, we know that

Probability of event 'a' occurring, P(a) = 0.90

Probability of event 'b' occurring, P(b) = 0.96

Probability of event 'c' occurring, P(c) = 0.05

We have been told that these three events are independent.

Thus, we can use the multiplication rule of probability, which states that the probability of three independent events a, b, and, c occurring is equal to the products of the probability of each individual event occurring.

p(a, b and c) = p(a) × p(b) × p(c)

                    = 0.90 × 0.96 × 0.05

                    = 0.0432

Hence, the probability(a, b, and c) is 0.0432.

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Answer:

Only the third one is incorrect. First 2 and last 1 are correct.

Answer:

9

Step-by-step explanation:

given 2 sides of a triangle then the third side x lies within the limits

difference of 2 sides < x < sum of 2 sides , that is

6 - 4 < x < 6 + 4

2 < x < 10

then the largest possible length is 9

Using the theories of probability, we got that  5/9 is the probability that one letter is from each sister's name if the letters from their names are placed on identical cards so that each of cards contains one letter. without replacement.

We know very well that if we want to count number of ways  by which r object can be chosen from n objects ,this can be done in [tex]^nC_r[/tex] ways which is equivalent to =(n!/(r!.(n-r)!)

Here are the same case, we have 10 cards, in each of the card there is letter written on it. So number of ways to choose two cards such that it contains any letter is can be done  in  [tex]^1^0C_2[/tex] ways which is equivalent to 45 ways.

Similarly, number of ways of choosing card which contains only Cybil`s name =[tex]^5C_2[/tex] ways=10 ways.

Similarly, number of ways of choosing card which contains only Ronda`s name =[tex]^5C_2[/tex] ways=10 ways.

So  the number of ways containing one letter from each name  =  45 - 10 - 10 = 25

So....the probability of choosing one of these sets  =  25 / 45  =  5 / 9 =0.55

Hence, Cybil and Ronda are sisters. the letters from their names are placed on identical cards so that each of cards contains one letter. without replacement, two cards are selected at random from the cards.  the probability that one letter is from each sister's name is = 5/9.

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(Complete question) is:

cybil and ronda are sisters. the 10 letters from their names are placed on 10 identical cards so that each of cards contains one letter. without replacement, two cards are selected at random from the 10 cards. what is the probability that one letter is from each sister's name? express your answer as a common fraction.

Answer:

14x + 8 for the first column and the second one is i think its 2 (7x + 4)

Step-by-step explanation:

sorry if this is not what your looking for

The point(0,3) is not a part of any quadrant. option D is the correct answer

The points on the x-axis and the y-axis are not a part of any quadrant.

From the question, we have

The point(0,3) is not a part of any quadrant.

Cartesian Coordinate System:

A point in a plane can be found using the coordinate system by connecting two perpendicular lines. In two dimensions, points are represented as coordinates (x, y) with respect to the x- and y-axes. We will study the Cartesian Coordinate System in this article. Axes and quadrants make up a plane. The coordinate axes are the name of the axes. Axes and quadrants make up a plane. The coordinate axes are the name of the axes. A rectangular system's reference lines, the vertical and perpendicular axes, are used to measure distances.

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The marked price of the wrist watch after the trader sold a wrist watch for $3150 after giving a 10% discount is $3500.

First, let us understand the percentage:

A percentage is a fraction of a whole expressed as a number between 0 and 100. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent, and nothing is zero percent.

To determine a percentage, we need to divide the portion of the whole by the whole itself and multiply by 100.

Let the marked price be x.

So,

According to the question;

x - x * 10% = 3150

x - x * 10/100 = 3150

100x - 10x / 100 = 3150

90x = 3150 * 100

x = 3150 * 100 / 90

x = 3500

So, the marked price is $3500.

Thus, the marked price of the wrist watch after the trader sold a wrist watch for $3150 after giving a 10% discount is $3500.

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Answer:

= 27

Step-by-step explanation:

36×3/4

36 × 3

--

4

9 × 3

= 27

Answer:

[tex]\frac{\sqrt{2} }{3}[/tex]

Step-by-step explanation:

Answer: y= -2/4x - 3

Step-by-step explanation:

b=y-intercept

Equation for slope-intercept form: y=mx+b

Locate the y-int/b: -3=b

Identify the slope/m: -2/4= 2 down, 4 to the right

Insert slope and y-int into slop-intercept form: y= -2/4x - 3

The degree of a function has no effect by the dilation of the function.

and the degree of the dilated function is same as the degree of the original function.

Dilation is defined as, when a function is multiplied by any number, the graph of the function retain a new shape, either by stretch or by compression in different directions.

Now, when a function is dilated it is either stretched or compressed in upward or downward direction.

It does not affect the degree of the function as the number of roots will be same as original function.

So, the degree of the dilated function is same as the degree of the original function.

Hence, the degree of the dilated function is same as the degree of the original function.

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2. The equation is given as follows: x + 4x = 25.

3. The constrains are given as follows: 0 ≤ x ≤ 25, 0 ≤ y ≤ 75.

The time spent running is given by:

Running = 4x.

The time spent walking is one-fourth of the time spent walking, hence it is given by:

Walking = 4x/4 = x.

The total time is the sum of the times spent running and walking, hence the expression is presented as follows:

x + 4x = 25.

The variables are given as follows:

You can accept at most 25 out-of-state hires, hence:

0 ≤ x ≤ 25

(as the number cannot be negative).

The company plans to have three times as many in-state hires, hence:

0 ≤ y ≤ 75.

As:

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Answer:

45mi/h

Step-by-step explanation:

4 to 8 = 4 hours

v = space / time

v = 180/4 = 45 mi/h

The number of bottles of soda purchased are 4 and the number of bottles of juice purchased are 10.

Given,Parker went to the grocery store and bought bottles of soda and bottles of juice.

Each bottle of soda has 50 grams of sugar and each bottle of juice has 10 grams of sugar.

Parker purchased a total of 14 bottles of juice and soda which collectively contain 300 grams of sugar.

we are asked to determine  the number of bottles of soda purchased,x, and the number of bottles of juice purchased, y.

So, the total number of bottles:x+y=14

x=14-y ...eq(1)

As, Each bottle of soda has 50 grams of sugar and each bottle of juice has 10 grams of sugar.

50x+10y=300

Substituting the value of x from eq(1)

⇒ 50(14-y) + 10y = 300

⇒ 700 - 50y + 10y = 300

⇒ -40y = 300 - 700

⇒ -40y =-400

y = 400/40

y = 10

The number of juice bottles = 10.

Now, to get the number of bottle of soda by substituting the value of y  in equation (1):

x = 14-y

x = 14 - 10

x = 4

The number of soda bottles = 4.

Therefore, the number of bottles of soda purchased are 4 and the number of bottles of juice purchased are 10.

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