Work out the equation of the line which has a gradient of -2 and
passes through the point (1, 7)

Answer:

1/2 + 3/4 + 5/8

4/8 + 6/8 + 5/8 = 15/8 or 1 7/8 cups

Step-by-step explanation:

probably right dunno

This is one batch right? if so shud be right

A circle is a curve sketched out by a point moving in a plane. The radius and the diameter of the circle are 19.73 ft and 39.46 ft, respectively.

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.

Given that circumference of the circle as 124 ft. Therefore, the radius and the diameter of the circle can be written as,

Circumference of circle = 2 × π × (Radius of the circle)

124 ft = 2 × π × (Radius of the circle)

(Radius of the circle) = 124 ft/ (2 × π)

The radius of the circle = 19.73 ft

Diameter of circle = 2 × (Radius of the circle)

                              = 2 × 19.73 ft

                              = 39.46 ft

Hence, the radius and the diameter of the circle are 19.73 ft and 39.46 ft, respectively.

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Answer: jane has 1.5 meters of ribbon

Step-by-step explanation:

-5/3 is the constant of variation where y varies directly with x.

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

A DIRECT VARIATION is a mathematical relationship between two variables that can be stated mathematically by an equation in which one variable equals a constant times the other.  y = kx

⇒ 5 x+3 y=0

⇒ 3y= -5x

⇒ y = -5x/3

Thus, y  = -5/3 × x, here k is constant = -5/3

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The given equations have in one, (1/5) is the coefficient of x, in the second equation, (1/5) is the coefficient of (x + 2), while both equations equals 6. Therefore, the value of x is different in both equations which do not represent the same situation.

The given equations are presented as follows;

[tex]\frac{1}{5} \cdot x + 2 = 6...(1)[/tex]

[tex] \frac{1}{5} \cdot (x + 2) = 6...(2)[/tex]

Solving each equation for x gives;

For equation (1), x = 5×(6 - 2) = 20

x = 20

For equation (2), we have;

x = 6 × 5 - 2 = 28

x = 28

Given that the value of x in the given equations are different, the situations are different.

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The absolute value inequality to represent this situation is |d - 50| <= 5

The given parameters are

Margin = 5 feet

Depth = 50 feet

The absolute value inequality to represent this situation is

|d - Depth| <= Margin

So, we have:

|d - 50| <= 5

Hence, the absolute value inequality to represent this situation is |d - 50| <= 5

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The equation of the line in slope-intercept form passing through point (-3 , 1) and perpendicular to y = -(2/5)x - 4 is y = (5/2)x + 17/2

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The slope-intercept form of the equation of a line is given by the formula

y = mx + b

where m is the slope of the line

b is the y- intercept

If the line is perpendicular to y = -(2/5)x - 4, then their slopes are negative reciprocal of one another.

y = -(2/5)x - 4 : m = -2/5

m = 5/2

Substitute the values of the slope and the point to solve for the y-intercept, b.

y = mx + b

1 = 5/2(-3) + b

b = 17/2

Write the equation of the line by plugging in the value of the slope and y-intercept.

y = mx + b

y = (5/2)x + 17/2

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Using the combination formula, the committee can be selected in 1,211,760 ways.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

Combination formula is the number of different combinations of x objects from a set of n elements.

In this problem:

There are 10 sophomore, 8 junior, and 9 senior members in student council.

They are independent, so we can just multiply them, thus;

T = 18!/ 2! 16! x 12!/ 2! 10! x 10!/ 3! 7!

T  = 1,211,760

Hence, The committee can be selected in 1,211,760 ways.

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The slope - intercept form of the equation -4 x+3 y=1 is y = 4/3x + 1/3.

The equation given is -

-4 x+3 y=1

As we know the slope - intercept form is -

y = mx + c

-4 x+3 y=1

Dividing the equation with 3

⇒ -4/3x + y = 1/3

Now, rearranging the equation

y = 4/3x + 1/3

where slope = 4/3

y - intercept = 1/3

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Answer:

[tex]{ \tt{change = \frac{y_{b} - y _{a} }{x _{b} - x _{a} } }} \\ \\[/tex]

[tex]{ \tt{ change = \frac{16 - 2}{4 - 1} }} \\ \\ = { \tt{ \frac{14}{3} }} \\ \\ = 4 \frac{2}{3} [/tex]

For the data set 3, 6, 4, 13, 3, 7, 5, 13, 3, 7, 5, 15, 3, 8, 5, 27, 4, 8, 6, 6, 4, 11, the outliers are 3, 3, 3, 3, 15, and 27.

In statistics, outlier refers to the data point from a given data set that differs significantly from the other data points.

One way to determine the outlier in a given data set is to calculate the interquartile range.

1. Arrange the data set in ascending or descending order.

3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 8, 8, 11, 13, 13, 15, 27

2. Divide the data set into two sets and find the median.

{3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6} , {6, 6, 7, 7, 8, 8, 11, 13, 13, 15, 27}

Q1 median = 4

Q3 median = 8

3. Solve for the IQR.

IQR = Q3 - Q1

IQR = 8 - 4

IQR = 4

4. Determine the outlier if

high outlier ≥ Q3 + (1.5 x IQR) = 8 + (1.5 x 4) = 14

high outlier ≥ 14

low outlier ≤ Q1 − (1.5 x IQR) = 4 - (1.5 x 4) = 3

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The slope for equation y = -5x + 4 in slope - intercept form is -5 and y - intercept is (x, 4 ).

The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation. The slope, m, is a measure of how steep a line is.

The slope - intercept form is y = mx + c

5x + y = 4

Now, Rearrange the equation -

y = -5x + 4

m = -5 and y intercept = (x , 4)

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Answer:

Hello,

Step-by-step explanation:

[tex]x^2+6x-16\\\\=x^2+2*3x+3^2-9-16\\\\=(x+3)^2-25\\[/tex]

The statement "A 95% confidence interval for the population mean will be wider than a corresponding 99% confidence interval." is true.

It is defined as the sampling distribution following an approximately normal distribution for known standard deviation.

The formula for finding the confidence interval for population standard deviation as follows:

[tex]\rm s\sqrt{\dfrac{n-1}{\chi^2_{\alpha/2, \ n-1}}} < \sigma < s\sqrt{\dfrac{n-1}{\chi^2_{1-\alpha/2, \ n-1}}}[/tex]

Where s is the standard deviation.

n is the sample size.

α is the significance level.

σ is the confidence interval for population standard deviation.

Calculating the confidence interval for population standard deviation:

We know significance level = 1 - confidence level

The statement is:

A 95% confidence interval for the population mean will be wider than a corresponding 99% confidence interval.

As we know,

A 95% confidence interval is narrower than a 99% confidence interval.

Thus, the statement "A 95% confidence interval for the population mean will be wider than a corresponding 99% confidence interval." is true.

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the equation for y will be y = 4ˣ / 16 when the function y is defined as y = f ( g ( x ) ).

We are given the functions:

f ( x ) = 4ˣ

g ( x ) = x - 2

Now, we have a function y defined as:

y = f ( g ( x ) )

Now, we need to find the equation for y.

We know that:

f ( g ( x ) ) = 4⁽ ˣ⁻ ² ⁾

f ( g ( x ) ) = 4ˣ / 4²

f ( g ( x ) ) = 4ˣ / 16

Therefore, we get that, the equation for y will be y = 4ˣ / 16 when the function y is defined as y = f ( g ( x ) ).

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Answer:

Step-by-step explanation:

y = -3x + 7

since the slope of the line AB = (4 - 2) /( 3 - (-3)) = 1/3

slope of line perpendicular to AB will be -3

Answer:

$10

Step-by-step explanation:

Let's begin with adding all of the items Greg bought.

36.62 + 11.25 + 17.75 = 65.62

Let the money paid to the cashier be x.

Now, it's stated he paid 60 dollars to the cashier and that he also got $4.38 back from the cashier.

Then, it must be that x=65.62+4.38

x=70

The money he borrowed from friend = 70-60=10

Therefore, the money Greg borrowed from his friend to pay for all the items is $10.

Greg borrowed $1.24 from his friend.

A single unit's value may be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique. We typically utilise this technique for math computations.

This approach allows us to calculate both the value of many units from the value of one unit and the value of many units from the value of one unit.

Given:

Greg bought a blanket for $36.62,

a flag for $11.25,

and a glove for $17.75.

Total expense of the objects he brought

= 36.62+ 11.25 + 17.75

= $65.62

He paid $60 then

=65.62 - 60 = $5.62 remaining

Also, he got $4.38 in change from the cashier

= 5.62 - 4.38

= $1.24.

Hence, Greg borrowed $1.24 from his friend.

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The statement "If p || q , then ∠2 and ∠8 are supplementary" is false because " If p || q , then ∠2 and ∠8 are congruent"

Given,

The statement "If p || q , then ∠2 and ∠8 are supplementary"

In the figure

p is parallel to q.

∠2 and ∠8 are lie on the opposite sides of the transversal and both are nonadjacent exterior angle

So, ∠2 and ∠8 are alternate exterior angles

If p || q , then ∠2 and ∠8 are congruent.

Hence, The statement "If p || q , then ∠2 and ∠8 are supplementary" is false because " If p || q , then ∠2 and ∠8 are congruent"

The complete question is :

State whether the sentence is true or false. If false, replace the underlined word or number to make a true sentence.

If p || q , then ∠2 and ∠8 are supplementary .

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Answer:

1 7/8

Step-by-step explanation:

KCF method.

[tex]\sf 3 \dfrac{3}{8}-2\dfrac{1}{4} \div 1\dfrac{1}{2}= \dfrac{27}{8}-\dfrac{9}{4}\div\dfrac{3}{2} \\\\[/tex]

                       [tex]\sf = \dfrac{27}{8}-\dfrac{9}{4}*\dfrac{2}{3}\\\\=\dfrac{27}{8}-\dfrac{3}{2}\\\\=\dfrac{27}{8}-\dfrac{3*4}{2*4} \ [\text{LCM of 2 and 8 is 8}]\\\\=\dfrac{27}{8}-\dfrac{12}{8}\\\\=\dfrac{27-12}{8}\\\\=\dfrac{15}{8}\\\\=1\dfrac{7}{8}[/tex]

The lessons from Clare B. Dunkie's The Hollow Kingdom, and the quote it matches are:

One lesson that we see is that people who care about someone, are able to make sacrifices to ensure the wellbeing of that person. We see it with the narrator saying that the person loved another so much that they sacrificed their world for that person.

Another less is that nature can often help us gain the courage we need to do something. This is shown with the subject looking to the moon and stars to back her up.

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The 20th term of the arithmetic sequence is 122.

nth term = a1 + d(n - 1) so here:

20th term = -30 + 8(20 - 1)

- 30 +  152

[tex]a_{20}[/tex] = 122.

An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.

Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.

An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.

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The right angle triangle ΔJ K L with legs JK and KL has been plotted below where the third side will be √(16b² + a²).

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

Given the triangle  ΔJ K L

Base = a  and Perpendicular = 4b

By Pythagoras theorem,

Hyp² = Base² + Perp²

Hyp² = a² + (4b)²

LJ = √(16b² + a²).

Hence "The right angle triangle ΔJ K L with legs JK and KL has been plotted below where the third side will be √(16b² + a²)".

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The results of the expressions given are:

Part 1:

1)  -2

2) 12

3) 2

4) 11

5) -7

6) 7

7)  0

8)  0

9) - 6

10) - 10

Part 2:

1) 12

2) - 2

3)  2

4)  11

5) 5

6) 0

7) - 28

8) 0

9) - 17

10) -2

We solve the equations respecting the level of hierarchy:

Part 1:

1) -7+5= -2

2) 7+5 = 12

3) 7+ (-5) = 7 - 5 = 2

4) 2+9 = 11

5) 2+(-9) = 2 - 9 = -7

6) -2+9 = 7

7) 8+(-8) = 8 - 8 = 0

8) -5+5 = 0

9) -3+(-3) = - 3 - 3 = - 6

10) -5+(-5) = - 5 - 5 = - 10

Part 2:

1) 7- (-5) = 7 + 5 = 12

2) -7- (-5) = - 7 + 5 = - 2

3) 7- (+5) = 7 - 5 = 2

4) 2- (-9) = 2 + 9 = 11

5) -5- (-10) = - 5 + 10 = 5

6) 5-5 = 0

7) -8- (+20) = - 8 - 20 = - 28

8) -3- (-3) = - 3 + 3 = 0

9) -5- (+12) = - 5 - 12 = - 17

10) 8- (+10) = 8 - 10 = -2

We can say that they are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

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Answer: f(-1) = -12

Step-by-step explanation:

        To solve, we will substitute t for -1 into the function.

Given:

    h(t) = (t + 7)(t - 1)

Substitute:

    h(-1) = (-1 + 7)(-1 - 1)

Add and subtract:

    h(-1) = (6)(-2)

Multiply:

    f(-1) = -12

The definite integral that represents the area of the region under the given curves is:  [tex]\int\limits^3_{-3} {x^2-9} \, dx[/tex]

Given:

The points where the two intersect will be given by:

y₁ = y₂

=> x² + 2x + 3 = 2x + 12

=> x² + 3 = 12

=> x² = 9

=> x = ± 3

For x₁ = 3, y₁ = 2(3) + 12 = 18 => (x₁, y₁) = (3, 18)

For x₂ = -3, y₂ = 2(-3) + 12 = 6 => (x₂, y₂) = (-3, 6)

Now, for the area of the region under first curve [tex]y_1=x^2+2x+3[/tex]:

A₁ =  [tex]\int\limits^3_{-3} {x^2+2x+12} \, dx[/tex]

For the area of the region under the second curve [tex]y_2=2x+12[/tex]:

A₂ = [tex]\int\limits^3_{-3} {2x+12} \, dx[/tex]

For the required area of the region bounded by the two curves will be given by:

A = A₂ - A₁ = [tex]\int\limits^3_{-3} {x^2+2x+3 - (2x +12)} \, dx[/tex]

A = [tex]\int\limits^3_{-3} {x^2-9} \, dx[/tex]

Refer to the image for the area so bounded by the curves.

Hence, The definite integral that represents the area of the region under the given curves is:  [tex]\int\limits^3_{-3} {x^2-9} \, dx[/tex].

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Answer: $244.55

A = $250  ;  r=0.002   t= 11   [From 2007 to 2018 , t=2018-2007]

Range - { 4 , 0 , -4 , -3 } is the domain and range of each relation.

What does the math term domain mean?

What is domain and range mathematics?

A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.

Domain - { 0, 4 , -3 , -4 }

Range - { 4 , 0 , -4 , -3 }

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Answer:

if the peak level is 14949 above sea level , so the difference in elevation is 14949 + 39 =14988 feet

The equivalent expression by distributing the sign outside the parentheses: -(-8.2w+10) −(−8.2w+10) will be 16.4w - 20.

It should be noted that bwsed on the information given, the expression is illustrated as:

-(-8.2w+10) −(−8.2w+10)

The signs should be taken into consideration. This will be:

-(-8.2w+10) −(−8.2w+10)

= 8.2w - 10 + 8.2w - 10

= 16.4w - 20

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Answer:

see explanation

Step-by-step explanation:

a bit more info is needed so this may be wrong.

so first you add up the x values which is 12x+8x+x=21x

then you can see we have a problem, we dont know the x value so the answer would be 21x +3

but we can go a bit further to get an answer as 3(7x+1)

this is also known as factorisation.

so ans: 3(7x+1)