Finish the patterns
12, _ , _ , _ , 60
1, 3, 5 , 7, _
9, _, _ ,_, 81
_,_,15,_.20

The length of line JM would be = 19.2.

To calculate the missing length of the given figure above, the following steps should be taken as follows:

The formula that should be used is given as;

= GJ/GM = HK/HN

where;

GJ = 16

GM = 16+X

HK = 15

HN = 15+18 = 33

That is;

16/16+x = 15/33

16×33 = 15(16+X)

528 = 240+15x

528-240 = 15x

15x = 288

X = 288/15

= 19.2

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Answer:

[tex]\displaystyle x_1=2,\,x_2=-\frac{1}{2}[/tex]

[tex]\displaystyle y_1=1,\,y_2=-\frac{3}{2}[/tex]

Step-by-step explanation:

[tex]\displaystyle x+2y^2=4\\x+2(x-1)^2=4\\x+2(x^2-2x+1)=4\\x+2x^2-4x+2=4\\2x^2-3x-2=0\\\\x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x=\frac{-(-3)\pm\sqrt{(-3)^2-4(2)(-2)}}{2(2)}\\ \\x=\frac{3\pm\sqrt{9+16}}{4}\\ \\x=\frac{3\pm\sqrt{25}}{4}\\ \\x=\frac{3\pm5}{4}\\\\x_1=\frac{3+5}{4}=\frac{8}{4}=2,\,x_2=\frac{3-5}{4}=\frac{-2}{4}=-\frac{1}{2}[/tex]

[tex]\displaystyle y_1=2-1=1, y_2=-\frac{1}{2}-1=-\frac{3}{2}[/tex]

Answer:

(2, 1) (-0.5, -1.5)

Step-by-step explanation:

[tex]\begin{cases}x + 2y^2 = 4\\y = x - 1\end{cases}[/tex]

From here, we can substitute [tex]y = 2x - 1[/tex] into the first equation.

[tex]x + 2(x - 1)^2 = 4\\x + 2(x^2 - 2x + 1) = 4\\x + 2x^2 - 4x + 2 = 4\\2x^2 - 3x + 2 = 4\\2x^2 - 3x - 2 = 0\\x = 2, -\frac12[/tex]

Substituting back into the second equation to find the corresponding y values:

[tex]y(x = 2) = 2 - 1 = 1\\y(x = -\frac12) = -\frac12 - 1 = -1.5[/tex]

Answer:

Step-by-step explanation:

We know that the bag has dark chocolates and milk chocolates, and the probability of randomly choosing a dark chocolate is g. And, we know that there are 18 dark chocolates in the bag and each is equally likely to be chosen.

Now, let's use this information to find the number of milk chocolates. If there are n total chocolates in the bag, then the probability of choosing a dark chocolate is g, and the probability of choosing a milk chocolate is 1-g. We can write these probabilities as:

g = 18/n

1-g = (n-18)/n

So, if we equate the two expressions, we get:

18/n = (n-18)/n

That means:

18 = n - 18

And finally:

n = 36

So, there must be 36 chocolates in the bag, and 18 of them are dark chocolates, which means there must be 18 milk chocolates!

The total distance Sam will travel is 56 miles.

A Fraction is a number that is a part of a whole. It is denoted by [tex]\frac{a}{b}[/tex] form. In which the upper part 'a' denotes the numerator and the lower part 'b' denotes the denominator.

Let d be the total distance travelled by Sam.

Then, he travelled 12 miles plus 1/4 total distance = 12+ [tex]\frac{1}{4}[/tex](d)

He still needs to travel = [tex]\frac{3}{8}[/tex](d)+9

Total distance,d = 12+[tex]\frac{1}{4}[/tex](d)+[tex]\frac{3}{8}[/tex](d)+9

                       d = 12+9+[tex]\frac{5}{8}[/tex](d)

                       d = [tex]\frac{96 +72+5d}{8}[/tex]

                     8d = 96+72+5d

               8d-5d = 168

                       d = [tex]\frac{168}{3}[/tex]

                       d= 56 miles.

Hence, total distance Sam will travel today is 56 miles.

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[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \pounds 200\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ t=years\dotfill &1 \end{cases} \\\\\\ A = 200[1+(0.03)(1)] \implies A = 206[/tex]

Answer: 149 - m

He gave some away so we subtract

Answer:

Step-by-step explanation:

0.96!

0.5568 divided by 0.58 is approximately 0.9593.

Here, we have,

To divide 0.5568 by 0.58, you can follow these steps:

Step 1: Write down the dividend (the number being divided), which is 0.5568.

Step 2: Write down the divisor (the number you're dividing by), which is 0.58.

Step 3: To simplify the division, you can multiply both the dividend and divisor by a power of 10 to remove the decimal places. In this case, we can multiply both numbers by 100 to move the decimal point two places to the right.

0.5568 * 100 = 55.68 (new dividend)

0.58 * 100 = 58 (new divisor)

Step 4: Divide the new dividend by the new divisor:

55.68 / 58 ≈ 0.95931034

Step 5: Round the result to the desired number of decimal places. In this case, since the original dividend had four decimal places, we can round the result to four decimal places:

0.9593

Therefore, 0.5568 divided by 0.58 is approximately 0.9593.

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When YQ and XP are altitudes to the congruent sides of isosceles triangle, the true statement are:

WXY = WXY

PXY = QYX

Isosceles triangle has three sides out of which two are equal. It has two congruent sides. The angle opposite to base is vertex. It should be noted that the two sides of the triangle are congruent and the angles opposite to these sides are also congruent

From the information WXY is an isosceles triangle.

WXY = WXY

XY = XY

QXY == PYX (property of congruent triangle}

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By applying the transformation formula (x,y) -> (x-6,y+8) to the location (-4, 1), the pre-image would be (-4+6, 1-8) = (2,-7).

So the appropriate response is: (-2, -7).

Shifts and scaling are two common transformations used in geometry to create new shapes from figures in a plane. Images are the new (modified) shapes, and preimages are the original, unmodified shapes.

The preimage is the body of the object as it was originally, and the transformed shape of the object is termed the image.

The word "preimage" is plural (mathematics) The collection of all domain elements mapped onto a specific subset of the function's arguments.

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An infinite amount

When you are only given angles, then that means that the sides could be anything. 1, 2, 3, 1298371823, they are all possible.

Answer:

only 1

Step-by-step explanation:

Because I'm smart

Sry for the bad explanation but the answer is correct.

The wingspan of the real aeroplane is equal to 68.25 cm.

In Geometry, a scale factor is the ratio of two corresponding side lengths or diameter in two similar geometric figures such as aeroplanes, which can be used to either horizontally or vertically enlarge (increase) or reduce (decrease or compress) a function that represents their size.

Mathematically, the scale factor of a geometric figure can be calculated by dividing the dimension of the image by the dimension of the pre-image (original figure):

Scale factor = 13/4

Scale factor = 3.25

For the wingspan of the real aeroplane, we have:

Real Wingspan = 3.25 × 21

Real Wingspan = 68.25 cm.

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Based on the given bar chart, the modal mark of the pupils test score is 6.

A bar chart is the graphical representation of data using rectangles also referred to as bars.

A mode is a statistical measure which shows the data with the most reoccurring value. Simply put, the mode is the value which occurs most in a frequency distribution.

Number of pupils Marks scored

1. 1

2. 2

3. 3

3. 4

4. 5

5. 6

3. 7

2. 8

1. 9

1. 10

Therefore, 5 pupils scored 6 marks which is the Model mark because it has the highest number of pupils to the test scores.

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This inequality can be expanded to x - 214 ≤ -23, which means that any value of x that is less than or equal to -23 satisfies the inequality.

1. x + 191 ≥ 214

2. x - 214 ≤ -23

1. To solve this inequality, we add 23 to both sides of the equation: x - 23 = 191.

x + 191 ≥ 214

2. To solve this inequality, we subtract 191 from both sides of the equation: x - 23 = 191.

x - 214 ≤ -23

1. x + 191 ≥ 214

This inequality can be expanded to x + 191 ≥ 214, which means that any value of x that is greater than or equal to 214 satisfies the inequality.

2. x - 214 ≤ -23

This inequality can be expanded to x - 214 ≤ -23, which means that any value of x that is less than or equal to -23 satisfies the inequality.

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Let x be the price per pound of apples and y be the price per pound of potatoes.

For Ethan, the total cost for apples was $25.50 - 5y and the total cost for potatoes was $25.50 - 8x.

So, we have the following two equations:

8x + 5y = 25.5

3x + 10y = 18.5

Solving this system of linear equations, we get:

x = 1.71 and y = 2.36.

So, the ordered pair (x,y) = (1.71, 2.36) represents the price per pound of apples and potatoes.

the equation for the line will be y = -5x +11 .

What is equation straight line?

Y = mx + c is the general equation for a straight line, where m denotes the line's slope and c the y-intercept. It is the version of the equation for a straight line that is used most frequently in geometry. There are numerous ways to express the equation of a straight line, including point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a geometric object with two dimensions and infinite lengths at both ends. The formulas for the equation of a straight line that are most frequently employed are y = mx + c and axe + by = c. Other versions include point-slope, slope-intercept, standard, general, and others.

The given line is y = x/5 +3

the slope is m = 1/5

So the slope of the perpendicular line will be -5

So the equation of line will be y-3 = m1(x-1)+3

y-3 = -5x+5+3

y = -5x +11

Hence the equation for the line will be y = -5x +11 .

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When a point T(- 1, 2) is rotated 180° clockwise about the origin, the coordinates of the new point T' may be obtained using coordinate plane rotation rules would be (1, -2).

The x-coordinate changes its sign with a 180° clockwise rotation, as does the y-coordinate.

As a result, the coordinates of T' following a 180° clockwise revolution around the origin are:

T'(x', y') = ( -(-1), -(2)) = (1, -2)

So, point T' is located at (1, -2).

It's worth noting that rotations about the origin keep the distance between the source and the point being rotated constantly.

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Answer:

No, it is not legal to drive at 80 mph, even if everyone else is driving at that speed, if the posted speed limit is 65 mph. The posted speed limit is the maximum legal speed that drivers are allowed to travel on a particular road, and it is a law that must be followed.

Step-by-step explanation:

Answer:

3149

Step-by-step explanation:

800(4)-{3(5)•5(2)-7(27)}-y

800(4)-{3(5)•5(2)-7(27)} - 90

3200 -{15•10-189} - 90

3200 -{150-189} - 90

3200  -{-39} - 90

3200 + 39 - 90

3149

Answer: 3.28

Step-by-step explanation: so on monday it snowed 3.02 plus 0.26 on tuesday, now add 3.02 + 0.26 = 3.28

hope it helps !!!

The length of side MN is approximately 4.43 for the right triangle MNO.

In a right triangle MNO, with side NO equivalent to 4 and MO equivalent to 1.9, and with points MNO equivalent to 25 degrees and MON equivalent to 90 degrees, the length of side MN can be tracked down utilizing the Pythagorean hypothesis.

The Pythagorean hypothesis expresses that in a right triangle, the square of the length of the hypotenuse (the longest side) is equivalent to the number of squares of the other different sides. Thus, for this situation:

MN² = NO² + MO²

MN² = 4² + 1.9²

MN² = 16 + 3.61

MN² = 19.61

Taking the square root of both sides:

MN = √(19.61)

MN = 4.43

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The question is -

Consider the right triangle MNO below. Which expressions represent the length of the side MN?

Answer:

a)3⋅37/2⋅5

​ =11 1/10

​=11.1

b) -1.1

Step-by-step explanation:

0.5(-77.8 - 11)/-4 =

= 0.5(-88.8)/-4 = 0.5(22.2) = 11.1

as you can see, when just doing it step by step, this can be done just in the head without the need of a calculator.

remember the priorities for mathematical operations :

1. brackets

2. exponents

3. multiplications and divisions

4. additions and subtractions

and also

+×+ = +

-×- = +

-×+ = -

+×- = -

therefore, -88.8/-4 = 22.2

and

0.5 = 1/2

so, 22.2×0.5 = 22.2/2 = 11.1

regarding average :

the average of a set of data is always the sum of all the data divided by the number of data points.

so, we see here 5 data points.

their sum is

-32.6 + 24.7 - 8.3 + 19.1 - 8.4 = -5.5

the average is then

-5.5/5 = -1.1 m sea level

Addition of more points change the pattern on the plot

There is another linear association on the scatterplot

From the question, we have the following parameters that can be used in our computation:

The scatterplot

When more points are added to the plot, the points may tend to change the relation on the scatterplot

Yes, there is.

This is represented by the set of points that form the negative linear relation

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Answer:

B, C, F

Step-by-step explanation:

To see if the point (4, -5) is on the graph of each equation or not, we have to put the number in and test it.

A.  3(4)+2(-5) = 4

12 - 10 = 4

2 = 4

So, it is not in graph A

B. 2(4) + 3(-5) = -7

8 - 15 = -7

-7 = -7

So, it is in graph B

C.  -5 = 4(4) -21

-5 = 16 - 21

-5 = -5

So, it is in graph C

D. y=6x-15

-5 = 6(4) - 15

-5 = 24 - 15

-5 = 9

So, it is not in graph D

E. 1/5y = 7 -5/2x

1/5(-5) = 7 -5/2(4)

-1 = 7 - 10

-1 = -3

So, is not in graph E

F. 3/4x + 2/10y = 2

3/4(4) + 2/10(-5) = 2

3 - 1 = 2

2 = 2

So, it is in graph F

So, point (4,-5) is on graphs B, C, F

The expression that will be a perfect square binomial is

x² + 2bx + b² = (x+b)²

What is meant by a perfect square trinomial?

By multiplying a binomial by another binomial, perfect square trinomials—algebraic equations with three terms—are created. A number can be multiplied by itself to produce a perfect square. Algebraic expressions known as binomials are made up of simply two words, each of which is separated by either a positive (+) or a negative (-) sign. Similarly, trinomials are three-term algebraic expressions.

For example, if we take a binomial (x + 3)

The perfect square trinomial is (x + 3)² = x² + 6x + 9

Given equation is x² + 2bx - b

The general equation is ax² + bx +c

Comparing the expressions we get,

 a = 1

b = 2b

c = -b

A trinomial is a perfect square if and only if it satisfies the condition

b² = 4ac

Substituting the above values,

(2b)² = 4 * 1 * -b

4b² = - 4b

The value of b² can never be a negative number. So the above relation is not true for the given expression.

For the expression to become a perfect square binomial, the last term should be b².

Therefore the expression that will be a perfect square binomial is

x² + 2bx + b² = (x+b)²

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Answer:

(3x+3) cm

Step-by-step explanation:

x+(x+4)+(x-1)=x+x+4+x-1

=x+x+x+4-1

=(3x+3) cm

The sum in degrees of Angle A and Angle B is 28 degrees

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

3x + 2 = x + 10

This means that

2x = 8

Divide by 2

x = 4

S, we have

Sum = 3x + 2 + x+ 10

Evaluate

Sum = 3 * 4 + 2 + 4 + 10

Sum = 28

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Answer:

3/4 or 0.75

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

Given expression

Find its value using logarithm rules:

The rules used above:

Answer:

y = - 8x + 20

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 8x - 5 ← is in slope- intercept form

with slope m = - 8

• Parallel lines have equal slopes , then

y = - 8x + c ← is the partial equation of the parallel line

to find c substitute (3, - 4 ) into the partial equation

- 4 = - 8(3) + c = - 24 + c ( add 24 to both sides )

20 = c

y = - 8x + 20 ← equation of parallel line

If the probability of Dan winning is 'p', then the probability that he does not win is ' 1-p' .

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. The probability of a event happening and the same event not happening is 1 or 100%.

Let Dan winning in a raffle is Event A.

Let Dan not winning in a raffle is Event B.

Probability of Dan winning + Probability of not winning = 1

   p + P(B) = 1

P(B) = 1 - p

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