A tube of watercolor paints is $8.69, a paintbrush is $4.78, and a canvas is $6.32. If you pay with a $20 bill, how much money will the cashier give back to you?
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Answer:

(3a + 11) (3a - 11)

Step-by-step explanation:

:))

Answer: X= y^2

Step-by-step explanation:

Point d is at (5, -5), which is five units to the right of the origin on the x-axis and five units below the origin on the y-axis. Similarly, point e is at (7, 3), point f is at (-1, 5), and point G is at (-3, -3).

The given points, d (5, -5), e (7, 3), f (-1, 5), and G (-3, -3) form quadrilateral DEFG. To plot these points, we can first draw the x and y axes on a graph paper.

Then, we can plot each point by locating its x-coordinate on the x-axis and its y-coordinate on the y-axis.

After plotting the points, we can click on the "Graph Quadrilateral" button to see the quadrilateral DEFG. It should be a closed shape with four sides, connecting the four points in the given order.

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Answer:

4 , 24 , 144 , 864 , 5184

This is a sequence which is multiplied by 6 with the new digit.

First: 4

second: 4 * 6 = 24

third: 24 * 6 = 144

fourth: 144 * 6 = 864

fifth: 864* 6 = 5184

sixth: 5184 * 6 = 31104

seventh: 31104 * 6 = 186624

This sequence is never ending. Write the first 5 five in sequence that's the answer.

The solution to the system of equations is x = 1 and y = -3.

To solve the system of equations using the substitution or elimination method, let's start with the substitution method.

Given equations:

y = 4x - 7

4x + 2y = -2

We'll solve equation 1) for y and substitute it into equation 2):

Substituting y from equation 1) into equation 2):

4x + 2(4x - 7) = -2

4x + 8x - 14 = -2

12x - 14 = -2

Now, we'll solve this equation for x:

12x = -2 + 14

12x = 12

x = 12/12

x = 1

Now that we have the value of x, we can substitute it back into equation 1) to find y:

y = 4(1) - 7

y = 4 - 7

y = -3

Therefore, the solution to the system of equations is x = 1 and y = -3.

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The standard deviation of the data sample is 2.55.

The standard deviation of the data sample is calculated by applying the following formula;

S.D = √ (x -  μ)²/(n - 1)

where;

The given parameters;

mean,  μ = 64

x, = 12

number of samples = 9

The standard deviation of the data sample is calculated as;

S.D = √ (12 -  64)²/(9 - 1)

S.D = 2.55

Thus, the standard deviation of the data sample is calculated by applying the formula for standard deviation.

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Angles and lines come in many distinct varieties in geometry.

Geometry has several different kinds of lines and angles. The six different types of angles include reflex angle, complete angle, straight angle, acute angle, and obtuse angle. The various sorts of lines are transverse, parallel, perpendicular, vertical, horizontal, and vertical lines.

There are three ways to name an angle: by the vertex, by the angle's three points (the middle point must be the vertex), or by a letter or number put inside the angle's aperture.

You can create your address block for letters, envelopes, and other mail merges using Label Lines, a collection of fields. Use Label Lines rather of Acknowledgement, Company, and Address lines to skip blank lines in your labels and address blocks.

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66. For equation -1.48 = (x - 30)/4,  the value of  x is 24.08. 68. For equation 0.88 = 22,000.44/σ, the value of σ is 25,000.5.

An equation is a mathematical statement that shows the equality between two expressions, using symbols and mathematical operations. An equation typically contains variables, which are symbols representing unknown values, and constants, which are known values. The variables can be solved for using algebraic methods to find their specific value(s) that make the equation true.

Equations can take many forms, depending on the mathematical context. For example, a linear equation has the form y = mx + b, where y and x are variables, m is the slope of the line, and b is the y-intercept. Quadratic equations have the form ax² + bx + c = 0, where a, b, and c are constants and x is the variable. There are many other types of equations, such as trigonometric equations, logarithmic equations, and differential equations, each with their own specific form and properties.

66. -1.48 = (x - 30)/4

To solve for x, we can begin by multiplying both sides by 4:

-1.48 * 4 = x - 30

-5.92 = x - 30

Next, we add 30 to both sides to isolate x:

-5.92 + 30 = x

x = 24.08

Therefore, the solution is x = 24.08.

68. 0.88 = 22,000.44/σ

To solve for σ, we can begin by multiplying both sides by σ:

0.88σ = 22,000.44

Next, we divide both sides by 0.88 to isolate σ:

σ = 22,000.44/0.88

σ = 25,000.5

Therefore, the solution is σ = 25,000.5.

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The number of numbers circled with only one color found using arithmetic progression formula are 809 numbers

An arithmetic progression is a sequence of numbers in which the difference between any two consecutive terms in the sequence is constant

The given parameters are;

The set of the numbers written on the paper = Numbers from 1 to 2022

Numbers circled with red circles by Caitlin = All even numbers between 1 and 2022

Numbers Nicole circles using yellow = Numbers that are multiples of 5

Required; The number of numbers that are circled with one colour only

Solution; The even numbers are numbers that are a multiple of 2

The number of even numbers between 1 and 2022 are found using arithmetic progression formula as follows;

\( a_{n} = a_{1} + (n - 1)\cdot d\)

Where;

\(a_{1}\) = The first term = 2 (First even number)

d = The common difference = 2

n = The number of terms

Given that 2022 is an even number, we have;

\( a_{n} = 2022 = 2 + (n - 1)\cdot 2\)

Which gives;

\( \displaystyle {n = \frac{(2022 - 2)}{2} + 1 = 1011} \)

We note that 10 is the lowest common multiple of 2 and 5, which gives;

Multiples of 10 have two colors, therefore, the numbers that have only one color is given by the difference between the number of even numbers and the number of multiples of 10 as follows;

The number of multiples of 10 are;

\( \displaystyle {n = \frac{(2020 - 10)}{10} + 1 = 202} \)

Which gives;

The numbers having only one colour = 1011 - 202 = 809

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Answer:

A reflection, a rotation, and a translation will prove that shape 2 is congruent to shape 1.

Answer:

A reflection, a rotation, and a translation will prove that shape 2 is congruent to shape 1.

Step-by-step explanation:

There are 120 different combinations of 3 programmers that can be chosen to transfer to the new department

From the question, we have

Total number of programmers, n = 10

Numbers to programmers to select, r = 3

The number of ways of selection could be drawn is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 10 and r = 3

Substitute the known values in the above equation

Total = ¹⁰C₃

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 10!/(7! * 3!)

Evaluate

Total = 120

Hence, the number of ways is 120

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Answer:

x = 15

Step-by-step explanation:

The sum of the four angles of a quadrilateral add up top 360°

Given:

m∠A = (5x+14)°  

m∠b = 109°        

m∠C = (3x+8)°    

m∠D = 109°°

Here we are given actual values for two angles as 109°. Their sum is: 109 + 109 = 218°

The sum of the remaining two angles which are expressions in x should be:

360 - 218 = 142°

This is the sum of m∠A an m∠C

Substituting the terms for the two angle measures we get

(5x+14)  + (3x+8) = 142

5x+14  + 3x+8 = 142

Grouping like terms:

5x + 3x + 14 + 8 = 142

8x + 22 = 142

8x = 142- 22

8x = 120

x = 120/4

x = 15

Answer:

--------------------------

Find the difference of the initial and used amounts:

[i] … … … x + 3y - z = 9

[ii] … … … 2x + 9y + 4z = 12

[iii] … … … x + 4y + z = 7

Eliminate z by combining …

• … 4 times equation [i] and equation [ii] :

4 (x + 3y - z) + (2x + 9y + 4z) = 4•9 + 12

(4x + 12y - 4z) + (2x + 9y + 4z) = 36 + 12

6x + 21y = 48

2x + 7y = 16

• … equation [i] and equation [iii] :

(x + 3y - z) + (x + 4y + z) = 9 + 7

2x + 7y = 16

Since we ended up with 2 copies of the same equation, we have infinitely many solutions for x, y, and z. That is, we have infinitely many choices for x and y that satisfy 2x + 7y = 16, and consequently infinitely many choices for z to satisfy any of the 3 original equations.

We can parameterize the solution by letting, for instance, x = t; then the solution set is

x = t

2x + 7y = 16   ⇒   y = (16 - 2t)/7

x + 3y - z = 9   ⇒   z = t + 3 (16 - 2t)/7 - 9   ⇒   z = (t - 15)/7

where t is any real number.

The function f ( x ) = 2 x² + 5 will have the value 23 for f (- 3).

We are given the function:

f ( x ) = 2 x² + 5

We need to find the value of f ( -3 ).

We will do this by substituting the value of x = - 3 in the function and then evaluating the expression.

Putting x = -3 in the function, we get that:

f ( x = - 3 ) = 2 (- 3)² + 5

Solving the square, we get that:

f (- 3) = 2 ( 9 ) + 5

Simplifying the expression, we get that:

f (- 3) = 18 + 5

f (- 3) = 23

Therefore, we get that, the function f ( x ) = 2 x² + 5 will have the value 23 for f (- 3).

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Answer:

12,435 bats

Step-by-step explanation:

We need to figure out how many bats were produced.

First let's write the equation. Cost is $28 for each bat, and we start with fixed expenses of $58,780

y=28x + 58780

We are given y, total expenses at 406,960

so 406,960 = 28x + 58780

subtract 58780 from both sides

406,960 - 58,780 = 28x

348,180 = 28x

divide both sides by 28

12,435 = x

This means they produced 12,435 bats.

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Answer:

q=13

Step-by-step explanation:

Given q - 12 = 1

we need to find q

to do so we need to isolate the variable using inverse operations

so to get rid of the 12 we add 12 but whatever we do to one side we do to the other

so we add 12 to each side

-12+12 cancels our

1+12=13

we're left with

q=13

Answer:

Option 2 is right.

Answer:

B

Step-by-step explanation:

Take the sum of two lengths. If there is another length less than the sum then the three can make a triangle.

Answer:

Step-by-step explanation:

sin²β + sin²β×tan²β = tan²β

sin²β( 1 + tan²β ) = tan²β

~~~~~~~~~~~~~~~~

sin²β + cos²β = 1  

\(\frac{sin^2\beta }{cos^2\beta }\) + \(\frac{cos^2\beta }{cos^2\beta }\) = \(\frac{1}{cos^2\beta }\) ⇒ tan²β + 1 = sec²β ⇔ 1 + tan²β = sec²β

~~~~~~~~~~~~~~

1 + tan²β = \(\frac{1}{cos^2 \beta }\)

L.H. = sin²β ( \(\frac{1}{cos^2 \beta }\) ) = tan²β

R.H. = tan²β

Check the picture below, so Francesca's throw looks more or less like that, and it hits the ground when h(t) = 0

\(\stackrel{h}{0}=1+14t-5t^2\implies 5t^2-14t-1=0 \\\\\\ ~~~~~~~~~~~~\textit{quadratic formula} \\\\ \stackrel{\stackrel{a}{\downarrow }}{5}t^2\stackrel{\stackrel{b}{\downarrow }}{-14}t\stackrel{\stackrel{c}{\downarrow }}{-1}=0 \qquad \qquad t= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a}\)

\(t= \cfrac{ - (-14) \pm \sqrt { (-14)^2 -4(5)(-1)}}{2(5)} \implies t = \cfrac{ 14 \pm \sqrt { 196 +20}}{ 10 } \\\\\\ t= \cfrac{ 14 \pm \sqrt { 216 }}{ 10 }\implies t=\cfrac{ 14 \pm 6\sqrt { 6 }}{ 10 }\implies t=\cfrac{ 7 \pm 3\sqrt { 6 }}{ 5 }\implies t\approx \begin{cases} ~~ 2.870~\checkmark\\ -0.070 \end{cases}\)

so there are two valid values, however we can't use the negative one, since the phenomena is for seconds and we can't have negative seconds in this case.

Answer:

The answer is A

Step-by-step explanation:

Triangle DEF was rotated and dilated so that's why is looks different than triangle ABC, but it maintained the same shape that is presented in ABC and that is why A is the answer.

Answer:

e

Step-by-step explanation:

Answer:

B. 143.4 \(\text{mi} ^2\)

Step-by-step explanation:

In simple terms, surface area =  adding area of all surfaces

This figure has 6 sides.

Surface area = 2 * area of trapezium + 2* area rectangle + area of bottom rectangle + area top rectangle

Surface area = 2 * (\((\frac{a+b}{2}) * h + 2* (l*w) + l*w + l*w\))

= \(2 * (\frac{3+6}{2} * 2.6) + 2* (8*3) + 3*8 + 8*6\)

= \(2 * 11.7 + 2* 24 + 24 + 48\)

= 143.4 \(\text{mi}^{2}\)

Let me know if you need further explanation

Answer:

12344321

Step-by-step explanation:

Answer:

I won't do your homework for you, but I will walk you through one of them.

The answer for number 14 is 4/9 = 16/36

Step-by-step explanation:

1. We know both denominators. They are 9 and 36. 9 x 4 = 36.

2. Multiply that 4 in the numerators. 4 x 4 = 16

Answer:

1. 24

2. 6

3. 12

4. 40

5. 6

6. 20

7. 2

8. 16

9. 32

10. 4

11. 42

12. 45

13. 32

14. 16

15. 24

16. 63

17. 8

18. 40

19. 48

20. 35

Explaining it:

Divide the numerator or denominator by the first fraction blank.

Ex: say the first fraction is 2/8. The fraction on the other side is ?/24 ( the question mark will be the blank/ variable in this situation ). Divide that 24 by 8. You should get three. Then multiply that 3 bye two to get your ?/ answer.

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Answer: 4.3 mi

Step-by-step explanation:

From Oxford, getting to Kingswood takes 7.5mi, and getting to Norwood takes 11.8mi.  Thus, simply do 11.8-7.5 to get 4.3mi.

Hope it helps <3

Answer:

y>2x+1

Step-by-step explanation:

1. there is 'y=2x+1' graph is represented.

2. the shaded reqion is y>2x+1.

The correct linear inequality represented by the graph is y > 2x + 1. The correct option is C.

An inequality is a mathematical statement that compares two values or expressions and shows their relationship using the symbols < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to), or ≠ (not equal to).

To see why, note that the line shown in the graph has a y-intercept of 1 and a slope of 2 (i.e., it passes through the points (0,1) and (1,3)).

If we plug in any point above this line, we get a y-coordinate that is greater than 2x + 1. For example, if we plug in the point (2,6), we get:

6 > 2(2) + 1

6 > 5

All points above the line satisfy the inequality y > 2x + 1.

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a. The possible range of values in this row is from 210 to 219, inclusive.

To see why, note that the stem value is 21, so each leaf represents a number that should be added to 21. The smallest possible value is when the leaf is 0, which gives 21 + 0 = 210. The largest possible value is when the leaf is 9, which gives 21 + 9 = 219.

b. There are 6 data values in this row.

c. The actual values in this row are 210, 211, 213, 215, 217, 219.

In statistics, a leaf is the last digit or digits of a data point in a stem-and-leaf plot. A stem-and-leaf plot is a graphical display of data that shows the distribution of values by separating each value into two parts: a stem, which consists of the leading digits of the value, and a leaf, which consists of the final digit or digits of the value. The stem values are listed in a vertical column, and the leaves are listed in a row next to the corresponding stem. This type of plot allows us to see the shape of the data and the distribution of values within it.

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