2(2x-5y)(3x+4y)-6(2x-5y)(x-y) factorise by taking out the common factors

[tex](3x^2 - 4x + 1) + (-x^2 + x - 9)=\\3x^2-4x+1-x^2+x-9=\\2x^2-3x-8[/tex]

Answer:

b y=2.4x -1.8

Step-by-step explanation:

the equation y=2.4x -1.8 represents 2.4 from it

Answer:

2

Step-by-step explanation:

3x^2

The coefficient is 3

The variable is x

The exponent is 2

Answer:

  tan(α) = 1/tan(90°-α)

Step-by-step explanation:

The tangent of one is the reciprocal of the tangent of the other.

__

In a right triangle, ...

  tan = opposite/adjacent

For the two complementary acute angles in such a triangle, opposite and adjacent are swapped. That is the tangent of one is the inverse of the tangent of the other. (That inverse is also known as the cotangent.)

  tan(α) = cot(90°-α) = 1/tan(90°-α)

Mistake found

3x-2(2x-4)=2

3x - 4x - 8 = 2 instead of 3x - 4x + 8 = 2

Correct answer

x= -13 y= -30

Answer:

See below.

Step-by-step explanation:

So we have the system of equations:

[tex]3x-2y=21 \text{ and } y=2x-4[/tex]

The student took the following steps:

[tex]3x-2(2x-4)=21\\3x-4x-8=21\\-x-8=21\\-x=29\\x=-29\\y=2(-29)-4=-58-4=-62[/tex]

The student's mistake is in step 2. He/she distributed incorrectly. You are supposed to distribute the -2 to both terms, so it should be -4x plus 8, since -2 times -4 is positive 8. Fixing that mistake, we will have:

[tex]3x-2(2x-4)=21\\3x-4x+8=21 \\-x+8=21\\-x=13\\x=-13\\y=2(-13)-4=-26-4=-30[/tex]

Thus, the final answers should be (-13, -30).

Answer:

72°

Step-by-step explanation:

From the figure given, angle D intercepts arc ABC. According to the Inscribed Angle Theorem:

m < D = ½(ABC) = ½(AB + BC)

Thus,

[tex] 56 = \frac{1}{2}(AB + 40) [/tex]

Solve for AB

[tex] 56 = \frac{AB + 40}{2} [/tex]

Multiply both sides by 2

[tex] 56*2 = \frac{AB + 40}{2}*2 [/tex]

[tex] 112 = AB + 40 [/tex]

Subtract both sides by 40

[tex] 112 - 40 = AB + 40 - 40 [/tex]

[tex] 72 = AB [/tex]

Arc AB = 72°

Answer:

B) $73

Step-by-step explanation:

add all of your values and divide by the amount of values

52+55+55+55+59+64+66+68+72+73+73+73+73+75+81+81+83+84+84+86+87=

1,499

1,499 divided by 21 = 71.3809523...

which rounds to 73

HOPE THIS HELPS!!! :)

The median is of $48 in the stem leaf plot and option B is correct.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

The median of a data-set is the value that separates the bottom 50% from the upper 50% of values.

The graph has 16 values, already ordered.

It is an even number, hence the median is the mean of the 8th and the 9th values, which considering the key are both 48,

Hence, the median is of $48 and option B is correct.

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Stem-and-Leaf Plot shows the amount of money each student spends

on travel per day in dollars. What is the median for the data in this graph?

Stem Leaf

A) $35

B) $48

C) $53

D) $54

Answer:

Solution :  (− 3, 5, 6)

Step-by-step explanation:

We have the following system of equations that we have to solve for,

[tex]\begin{bmatrix}x+3y-z=6\\ 4x-2y+2z=-10\\ 6x+z=-12\end{bmatrix}[/tex]

To solve this problem we can start by writing the matrix with their respective coefficients --- (1)

[tex]\begin{bmatrix}1&3&-1&|&6\\ 4&-2&2&|&-10\\ 6&0&1&|&-12\end{bmatrix}[/tex]

Now we can reduce this to row echelon form, receiving our solution --- (2)

[tex]\begin{pmatrix}1&3&-1&6\\ 4&-2&2&-10\\ 6&0&1&-12\end{pmatrix}[/tex] Swap row 1 and 3,

[tex]\begin{pmatrix}6&0&1&-12\\ 4&-2&2&-10\\ 1&3&-1&6\end{pmatrix}[/tex] Cancel leading coefficient in row 3,

[tex]\begin{pmatrix}6&0&1&-12\\ 0&-2&\frac{4}{3}&-2\\ 0&3&-\frac{7}{6}&8\end{pmatrix}[/tex] Swap row 2 and 3

[tex]\begin{pmatrix}6&0&1&-12\\ 0&3&-\frac{7}{6}&8\\ 0&-2&\frac{4}{3}&-2\end{pmatrix}[/tex] Cancel leading coefficient in row 3

[tex]\begin{pmatrix}6&0&1&-12\\ 0&3&-\frac{7}{6}&8\\ 0&0&\frac{5}{9}&\frac{10}{3}\end{pmatrix}[/tex]

At this point you can see that we have to cancel the leading coefficient in each row, to row echelon form. Continuing this pattern we have the following matrix,

[tex]\begin{bmatrix}1&0&0&|&-3\\ 0&1&0&|&5\\ 0&0&1&|&6\end{bmatrix}[/tex]

As you can see, x = - 3, y = 5, and z = 6, giving us a solution of (− 3, 5, 6). This is the fourth option.

Answer:

Lets start with the top row.

First, add the two values.

5+14=19

Now, divide each value by the total.

5/19=0.26315789473

Round the decimal to the nearest hundredth.

5/19=0.26

14/19=0.73684210526

Round it to the nearest hundredth.

14/19=0.74

Now, The second row.

Add the two values.

16+7=23

Divide the first value by the total.

16/23=0.69565217391

Round it to the nearest hundredth.

16/23=0.70

Divide the second value by the total.

7/23=0.30434782608

Round to the nearest hundredth.

7/23=0.30

Done!

Answer:

Row 1: 0.26 0.74

Row 2: 0.70 0.30

Step-by-step explanation:

Khan

Answer:

Area of quadrilateral ABCD = 29.79 units² (Approx)

Step-by-step explanation:

Area of triangle ABD

s = (3.48+8.66+8.6) / 2

s = 10.37

Area of triangle ABD = √10.37(10.37-8.66)(10.37-8.6)(10.37-3.48)

Area of triangle ABD = √212.4616

Area of triangle ABD = 14.5760625 unit²

Area of triangle ACD

s = (3.54+8.84+8.6) / 2

s = 10.49

Area of triangle ACD = √10.49(10.49-8.6)(10.49-8.84)(10.49-3.54)

Area of triangle ACD = √227.3558

Area of triangle ACD = 15.0783222 unit²

Area of quadrilateral ABCD = Area of triangle ABD + Area of triangle ACD

Area of quadrilateral ABCD = 14.5760625 unit² + 15.0783222 unit²

Area of quadrilateral ABCD = 29.6542units²

Area of quadrilateral ABCD = 29.79 units² (Approx)

Answer:

tan(<G) = [tex] \frac{HI}{GI} [/tex]

Step-by-step explanation:

Given:

Right triangle ∆GHI,

Required:

Equivalent of tan(<G)

SOLUTION:

Recall the acronym for trigonometric ratios of angles in a right triangle: SOHCAHTOA.

Thus, the TOA in the acronym above stands for:

Tan(θ) = side opposite to θ ÷ side adjacent to θ

Where,

θ is the angle of interest = <G

Opposite side = HI

Adjacent side = GI

The equivalent of tan(<G) = [tex] \frac{HI}{GI} [/tex]

Answer:

9). h² - 7h + 11

10). 2a² + 14a + 16

11). 3

12). 2h + 4x - 3

Step-by-step explanation:

9). If j(x) = x² + x - 1

  j(h - 4) = (h - 4)² +(h - 4) - 1

             = h² - 8h + 16 + h - 4 - 1

             = h² - 7h + 11

10). If f(x) = 2x² + 2x - 8

     f(a + 3) = 2(a + 3)² + 2(a + 3) - 8

                 = 2(a² + 6a + 9) + 2a + 6 - 8

                 = 2a² + 12a + 18 + 2a - 2

                 = 2a² + 14a + 16

11). If f(x) = 3x - 1

   [tex]\frac{f(x+h)-f(x)}{h}=\frac{3(x+h)-1-(3x-1)}{h}[/tex]

                     [tex]=\frac{3x+3h-1-3x+1}{h}[/tex]

                     = 3

12). If, f(t) = 2t² - 3t + 7

     [tex]\frac{f(x+h)-f(x)}{h}=\frac{2(x+h)^{2}-3(x+h)+7-(2x^2-3x+7)}{h}[/tex]

                        [tex]=\frac{2(x^2+h^2+2hx)-3x-3h+7-2x^2+3x-7}{h}[/tex]

                        [tex]=\frac{2x^2+2h^2+4hx-3x-3h+7-2x^2+3x-7}{h}[/tex]

                        [tex]=\frac{2h^2+4hx-3h}{h}[/tex]

                        = 2h + 4x - 3

Answer:

Step-by-step explanation:

[tex] \mathsf{3(2 \frac{1}{2} - 1) + \frac{3}{10} }[/tex]

Convert mixed number to improper fraction

[tex] \mathrm{3( \frac{5}{2} - 1) + \frac{3}{10} }[/tex]

Calculate the difference

⇒[tex] \mathrm{3( \frac{5 \times 1}{2 \times 1} - \frac{1 \times 2}{1 \times 2} }) + \frac{3}{10} [/tex]

⇒[tex] \mathrm{ 3 \times( \frac{5}{2} - \frac{2}{2}) } + \frac{3}{10} [/tex]

⇒[tex] \mathrm{3 \times ( \frac{5 - 2}{2} ) + \frac{3}{10} }[/tex]

⇒[tex] \mathrm{3 \times \frac{3}{2} + \frac{3}{10} }[/tex]

Calculate the product

⇒[tex] \mathrm{ \frac{3 \times 3}{1 \times 2} + \frac{3}{10} }[/tex]

⇒[tex] \mathrm{ \frac{9}{2} + \frac{3}{10}} [/tex]

Add the fractions

⇒[tex] \mathsf{ \frac{9 \times 5}{2 \times 5} + \frac{3 \times 1}{10 \times 1} }[/tex]

⇒[tex] \mathrm{ \frac{45}{10} + \frac{3}{10} }[/tex]

⇒[tex] \mathrm{ \frac{45 + 3}{10 } }[/tex]

⇒[tex] \mathrm{ \frac{48}{10} }[/tex]

Reduce the numerator and denominator by 2

⇒[tex] \mathrm{ \frac{24}{5} }[/tex]

Further more explanation:

Addition and Subtraction of like fractions

While performing the addition and subtraction of like fractions, you just have to add or subtract the numerator respectively in which the denominator is retained same.

For example :

Add : [tex] \mathsf{ \frac{1}{5} + \frac{3}{5} = \frac{1 + 3}{5} } = \frac{4}{5} [/tex]

Subtract : [tex] \mathsf{ \frac{5}{7} - \frac{4}{7} = \frac{5 - 4}{7} = \frac{3}{7} }[/tex]

So, sum of like fractions : [tex] \mathsf{ = \frac{sum \: of \: their \: number}{common \: denominator} }[/tex]

Difference of like fractions : [tex] \mathsf{ \frac{difference \: of \: their \: numerator}{common \: denominator} }[/tex]

Addition and subtraction of unlike fractions

While performing the addition and subtraction of unlike fractions, you have to express the given fractions into equivalent fractions of common denominator and add or subtract as we do with like fractions. Thus, obtained fractions should be reduced into lowest terms if there are any common on numerator and denominator.

For example:

[tex] \mathsf{add \: \frac{1}{2} \: and \: \frac{1}{3} }[/tex]

L.C.M of 2 and 3 = 6

So, ⇒[tex] \mathsf{ \frac{1 \times 3}{2 \times 3} + \frac{1 \times 2}{3 \times 2} }[/tex]

⇒[tex] \mathsf{ \frac{3}{6} + \frac{2}{6} }[/tex]

⇒[tex] \frac{5}{6} [/tex]

Multiplication of fractions

To multiply one fraction by another, multiply the numerators for the numerator and multiply the denominators for its denominator and reduce the fraction obtained after multiplication into lowest term.

When any number or fraction is divided by a fraction, we multiply the dividend by reciprocal of the divisor. Let's consider a multiplication of a whole number by a fraction:

[tex] \mathsf{4 \times \frac{3}{2} = \frac{4 \times 3}{2} = \frac{12}{2} = 6}[/tex]

Multiplication for [tex] \mathsf{ \frac{6}{5} \: and \: \frac{25}{3} }[/tex] is done by the similar process

[tex] \mathsf{ = \frac{6}{5} \times \frac{25}{3} = 2 \times 5 \times 10}[/tex]

Hope I helped!

Best regards!

Answer:

Step-by-step explanation:

m

Answer:

x = ±4

Step-by-step explanation:

4x^2 = 64

Divide each by 4

4x^2 /4= 64/4

x^2 = 16

Take the square root of each side

sqrt(x^2) = ±sqrt(16)

x = ±4

Answer:

[tex]\boxed{\boxed{x=\pm 4}}[/tex]

Step-by-step explanation:

[tex]4x^2 = 64[/tex]

Divide both sides by 4.

[tex](4x^2)/4 = 64/4[/tex]

Simplify.

[tex]x^2 =16[/tex]

Take the square root on both sides.

[tex]\sqrt{x^2 } =\pm \sqrt{16}[/tex]

Simplify.

[tex]x=\pm 4[/tex]

Answer:

You just answered my question so you can ask yours, what a sped. Now i'm doing the same thing.

Step-by-step explanation:

Answer:

[tex](x + 6)^2 = 49[/tex]

[tex]x = 1[/tex]    or [tex]x = -13[/tex]

Step-by-step explanation:

Given

[tex]12x = 13 - x^2[/tex]

Using Completing the Square

[tex]12x = 13 - x^2[/tex] ---- Add [tex]x^2[/tex] to both sides

[tex]x^2 + 12x = 13 - x^2 + x^2[/tex]

[tex]x^2 + 12x = 13[/tex]

Divide the coefficient of x by 2; then add the square to both sides

[tex]x^2 + 12x + 6^2 = 13 + 6^2[/tex]

[tex]x^2 + 12x + 36 = 13 + 36[/tex]

[tex]x^2 + 12x + 36 = 49[/tex]

Factorize

[tex]x^2 + 6x + 6x + 36 = 49[/tex]

[tex]x(x + 6) + 6(x + 6) = 49[/tex]

[tex](x + 6)(x + 6) = 49[/tex]

[tex](x + 6)^2 = 49[/tex]

Hence, the equation is [tex](x + 6)^2 = 49[/tex]

Solving further

Take square root of both sides

[tex](x + 6) = \sqrt{49}[/tex]

[tex]x + 6 = \±7[/tex]

[tex]x = \±7- 6[/tex]

This implies that

[tex]x = 7 - 6[/tex]     or [tex]x = -7 -6[/tex]

[tex]x = 1[/tex]    or [tex]x = -13[/tex]

HEnce, the solutions are [tex]x = 1[/tex]    or [tex]x = -13[/tex]

Answer:

(x+6)^2=49 and  x=−6±7

Step-by-step explanation:

Answer: 1880 pounds

Step-by-step explanation: when you take the average adult weight, around 160 lbs. you multiply that by eight. you get 1280. then you estimate that each of the children weigh around 100 lbs, then you add 600 to 1280 and get 1,880 lbs

Answer:

c=13.42

Step-by-step explanation:

[tex]A^2+B^2=C^2\\6^2+14^2=C^2\\C^2=144+36\\C^2=180\\\sqrt{c^2}=\sqrt{180} \\c=13.42[/tex]

Divide total feet by feet in a mile:

63,756/5280 = 12.075 miles

Divide 70 minutes by 60 minutes per hour:

70/60 = 1.166666 hours( round to 1.17)

Miles per hour = total miles/ total hours:

12.075/1.17 = 10.32 miles per hour

Answer:

A & C

Step-by-step explanation:

-9 is a whole number is rational

Answer:

D

Step-by-step explanation:

The exterior angles are out of the triangle at all times and it adds up to make 180 with anyone of the inside angle of the triangle.

The pair also rests on the same flat/straight line and that makes a pair.

Therefore we can say that it is formed by a linear pair/group with one of the interior/inside angles of the triangle.

So, the correct answer would be D.

The true statement about an exterior angle of a triangle is C; It forms a linear pair with one of the interiior angles of the triangle .

An exterior angle of a triangle is equal to the sum of the opposite interior angles.

We know that the exterior angles are out of the triangle at all times and it adds up to make 180 with anyone of the inside angle of the triangle.

The pair also rests on the same straight line and that makes a pairs.

Therefore we can say that it is formed by a linear pair with one of the interior angles of the triangle.

So, the correct answer would be C.

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Step-by-step explanation:

Since it's a direct variation

y = kx

where k is the constant of proportionality

To find the value of y when x = –0.5 we must first find the relationship between the variables

When

x = 3

y = 2

2 = 3k

Divide both sides by 3

[tex]k = \frac{3}{2} [/tex]

So the formula for the variation is

When x = - 0.5 or - 1/2

[tex]y = \frac{3}{2} ( - \frac{1}{2} )[/tex]

We have the final answer as

Hope this helps you

Answer:

3, 10, 1080

Step-by-step explanation:

A coefficient, is the number that is multiplying a variable, such as x. A constant is any other number, not multiplying a variable.

For part one, the number multiplying the variable x is 3, so 3 is the coefficient.

For part two, the only number not multiplying a variable is the 10, so that is the constant.

To find how many miles she drove, we first need to subtract the first 30 dollars from the final payment.

300-30=270

We than need to divide 270 by .25, because that is how much it costed per mile.

270/.25=1080

Answer:

In the first question shown, the answer is 3

In the second question shown, the answer is 10

In the third question shown, the answer is 1080 miles

Step-by-step explanation:

First question - 3 is the number before x, making it the coefficient

Second question - 10 is the only number without a variable, making it a constant

Third question - .25 * 1080 = 270. 270 + 30 = 300.

Answer:

A 0.6 0.9 1.2 1.5 1.8

B 3/8 5/8 7/8 9/8 11/8

C -7 -5 -3 -2 -1

D 1, 1 1/3, 1 2/3, 2, 2 1/3

E 0.61 0.72 0.83 0.94 1.05

Step-by-step explanation:

Answer:

A.  x  x   1.2  1.5  1.8

B.  3/8   x   x  x  1 2/8

C.  x  x  -3  -2  -1

D.   0  x  x  x  5 1/3

E.   x  x   0.83  0.94  1.05

Step-by-step explanation:

hope it helped

Answer:

The correct option are;

1) D. A quadratic equation of this form can always be solved using the square root property

2) B. Isolate the quantity being squared

3) C. The square root property requires a quantity squared by itself on one side of the equation. The only quantity squared is X so divide both sides by 2 before applying the square root property

Step-by-step explanation:

Where the quadratic equation is of the form x² = b, the square root property method can be used to solve the equation. Due to the nature of square roots, putting a plus-minus before the square root of the constant on the right hand side of the equation after taking the square roots of both sides of the equation, two answers are produced.

It is however to first isolate the term with the squared variable, after which the square root of both sides of the equation is taken.

Answer:

The correct statements are b, c and e.

Step-by-step explanation:

Consider the dot plot for Noah and Jada's score in the trivia game.

From the dot plot it is quite clear that the data form a bell-shaped curved or a normal curve.

For the normal distribution:

Mean = Median = Mode

Noah's mean score = 5

Jada's mean score = 3

The standard deviation of a data set is the measure of dispersion of the observations of that data set from their mean.

On closely studying the graphs we can see that the Noah and Jada's scores are almost at a same distance from the mean, i.e. the spread of Noah's score is same as the spread of Jada's score.

So, the correct statements are:

b. The standard deviation of Noah's scores is equal to the standard deviation of Jada's scores.

c. The mean of Noah's scores is greater than the mean of Jada's scores.

e. Using only Noah's scores, the mean is equal to the median

Answer:

30x+160

simple all you had to do is 10*3x and 8x2=16 and 10*16 and you will get 30x+160

Step-by-step explanation:

Answer:

30x + 80x^2

Step-by-step explanation:

10 (3x + 8x^2)

10 * 3x + 10 * 8x^2

30x + 80x^2

Hi there! :)

Answer:

[tex]\huge\boxed{V = 359.01 mm^{3} }[/tex]

Use the formula V = 1/3(bh) to solve for the volume of the cone where b = πr² where π ≈ 3.14:

Find the area of the base:

b = π(7)²

b = 49π

b = 153.86 mm²

Find the volume:

V = 1/3(153.86 · 7)

V = 1/3(1077.02)

V = 359.006 ≈ 359.01 mm³.