Please help with 2 and 3 for maths

Answer:

1. [tex](A,B) = (3,-2)[/tex]

2. The values of t are: -3, -1

Step-by-step explanation:

Given

[tex]\frac{x + 7}{x^2 - x - 2} = \frac{A}{x - 2} + \frac{B}{x + 1}[/tex]

[tex]|t| = 2t + 3[/tex]

Required

Solve for the unknown

Solving [tex]\frac{x + 7}{x^2 - x - 2} = \frac{A}{x - 2} + \frac{B}{x + 1}[/tex]

Take LCM

[tex]\frac{x + 7}{x^2 - x - 2} = \frac{A(x+1) + B(x-2)}{(x - 2)(x-1)}[/tex]

Expand the denominator

[tex]\frac{x + 7}{x^2 - x - 2} = \frac{A(x+1) + B(x-2)}{x^2 - 2x + x -2}[/tex]

[tex]\frac{x + 7}{x^2 - x - 2} = \frac{A(x+1) + B(x-2)}{x^2 - x -2}[/tex]

Both denominators are equal; So, they can cancel out

[tex]x + 7 = A(x+1) + B(x-2)[/tex]

Expand the expression on the right hand side

[tex]x + 7 = Ax + A + Bx - 2B[/tex]

Collect and Group Like Terms

[tex]x + 7 = (Ax + Bx) + (A - 2B)[/tex]

[tex]x + 7 = (A + B)x + (A - 2B)[/tex]

By Direct comparison of the left hand side with the right hand side

[tex](A + B)x = x[/tex]

[tex]A - 2B = 7[/tex]

Divide both sides by x in [tex](A + B)x = x[/tex]

[tex]A + B = 1[/tex]

Make A the subject of formula

[tex]A = 1 - B[/tex]

Substitute 1 - B for A in [tex]A - 2B = 7[/tex]

[tex]1 - B - 2B = 7[/tex]

[tex]1 - 3B = 7[/tex]

Subtract 1 from both sides

[tex]1 - 1 - 3B = 7 - 1[/tex]

[tex]-3B = 6[/tex]

Divide both sides by -3

[tex]B = -2[/tex]

Substitute -2 for B in [tex]A = 1 - B[/tex]

[tex]A = 1 - (-2)[/tex]

[tex]A = 1 + 2[/tex]

[tex]A = 3[/tex]

Hence;

[tex](A,B) = (3,-2)[/tex]

Solving [tex]|t| = 2t + 3[/tex]

Because we're dealing with an absolute function; the possible expressions that can be derived from the above expression are;

[tex]t = 2t + 3[/tex]    and   [tex]-t = 2t + 3[/tex]

Solving [tex]t = 2t + 3[/tex]

Make t the subject of formula

[tex]t - 2t = 3[/tex]

[tex]-t = 3[/tex]

Multiply both sides by -1

[tex]t = -3[/tex]

Solving [tex]-t = 2t + 3[/tex]

Make t the subject of formula

[tex]-t - 2t = 3[/tex]

[tex]-3t = 3[/tex]

Divide both sides by -3

[tex]t = -1[/tex]

Hence, the values of t are: -3, -1

Answer:

3x³ - 10x² + 14x - 12

Step-by-step explanation:

(3x² - 4x + 6) × (x - 2)

3x³ - 4x² + 6x - 6x² + 8x - 12

3x³ - 10x² + 14x - 12

Thus, the product of 3x² - 4x + 6 and x - 2 in standard form is 3x³ - 10x² + 14x - 12

Answer:

C

Step-by-step explanation:

C is the only situation in which there is a clear constant of proportionality and no offset (no initial value).  Claires rate is ($4.50 + $0.30)/book, or $4.80/book.

Answer:

[tex]y = 3x-4[/tex]

Step-by-step explanation:

We know that if we were to write an equation with the slope of 3, it would be [tex]y=kx[/tex], where k is the constant (in this case 3.)

So right now, we have [tex]y=3x[/tex].

However, this will not pass through the point (2,2). To do this, we need to add a y-intercept in which (2,2) will be crossed through.

If we have a y-intercept of -4, the points will be:

(0, -4)

(1, -1)

(2, 2)

So our final equation is [tex]y = 3x-4[/tex].

Hope this helped!

Answer: 3x-1y=4 in Ax+By=C form

Step-by-step explanation:

the intercept form is y=3x-4

subracting 3x from both sides would get  -3x+y=-4

distributing -(-3x+y=-4) would get 3x-y=4.

Answer:

x = - 20, h = 34

Step-by-step explanation:

i can't tell ypou what the class period is, but for -x = 20, multiply each side by -1, then you get x = -20

-32 = 2-h

+32 .  +32

0=34-h

+h .   +h

34=h

flip

h=34

Answer:

[tex]\sqrt[5]{y^3}[/tex]

Step-by-step explanation:

[tex]y^{3/5}[/tex] is simply [tex]\sqrt[5]{y^3}[/tex]

Answer:

Step-by-step explanation:

1.

[tex]3 :7 \\Acute \: angle = 90\°\\7+3 = 10\\\frac{7}{10} \times 90\\\\= \frac{630}{10}\\ = 63 \°\\[/tex]

2.

[tex]Let \:the\: other\:acute \:angle\: be \:x\\According\:to \:the \:question ; \\ \:\\(2x-30)+x =90\\2x - 30 +x =90\\2x +x = 90+30\\3x = 120\\\frac{3x}{3} =\frac{120}{3} \\x = 40 \\\\(2x -30)\\2(40) -30\\80 - 30 = 50\\\\\\Angle \:1 = 50\°\\Angle \: 2 = 40\°\\[/tex]

They do. the initial point is same in both lines.

formally,

[tex] \vec{r_1}=(2\hat i+3 \hat j+\hat k)+s(4\hat i-\hat k)[/tex]

$\vec{r_2}=(2\hat i +3 \hat j +\hat k)+t(2\hat i+2\hat j +\hat k)$

if they intersect then $\begin{vmatrix} 4 & 0 & -1 \\ 2 & 2 & 1 \\ (2-2) & (3-3) & (1-1) \end{vmatrix}=0$

(which obviously is zero)

Answer:

infinite solutions

Step-by-step explanation:

4x = 2x + 2x + 5(x-x)

Simplify

4x = 2x + 2x + 5*0

4x = 2x + 2x

4x = 4x

Divide by x

4 =4

This is always true so this has infinite solutions

Answer:

[tex]\huge\boxed{0}[/tex]

Step-by-step explanation:

First we have to do the operation of multiplication

=> (12+6-15)*(4+1-7+2)

Now, Solving the terms inside the brackets

=> (18-15)*(5-7+2)

=> (3)*(-2+2)

=> (3)*(0)

=> 0

Answer:

[tex]\Huge \boxed{{0}}[/tex]

Step-by-step explanation:

[tex](12+6-5*3)*(2*2+1-7+2)[/tex]

Solve brackets.

[tex](12+6-15)*(4+1-7+2)[/tex]

[tex](3)*(0)[/tex]

Multiply both numbers.

[tex]3 \times 0 = 0[/tex]

Answer:C

Step-by-step explanation:

Answer:

29

Step-by-step explanation:

The amounts greater than 40 cents can be formed.

After dividing one number by another, the modulo operation yields the remainder or signed remainder of the division.

Given:

According to the situation the equation can be

C = 5x + 11y, where x and y are non negative integers.

Now, We will fix y-values first, because there are fewer indices modulo 5:

y = 0 --> 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55,... 5y

y = 1 --> 11, 16, 21, 26, 31, 36, 41, 46, 51, 56,... 5y + 11

y = 2 --> 22, 27, 32, 37, 42, 47, 52, 57, ...5y + 22

y = 3 --> 33, 38, 43, 48, 53, 58, ...5y + 33

y = 4 --> 44, 49, 54, 59, ...5y + 44

Then, 39 may be verified to be the smallest number that is impossible to obtain.

By examining each index (0, 1,..., 4), we may demonstrate this by observing that for y = 1, 6 is the largest positive integer congruent to 1 mod 5 that cannot be made, 17 is the largest positive number congruent to 2 mod 5, etc.

The largest of these improbable numbers is 39.

We could say that since 40, 41, ..., 44 are all obtainable, then we can induct by adding a multiple of 5 (i.e. if k is possible, so is k+5),

Hence, all amounts greater than 40 cents can be formed.

Learn more about Modulo here:

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Answer:

x = 0.8

Step-by-step explanation:

4(4x - 2) = x + 4

4*4x + 4*-2 = x + 4

16x - 8 = x + 4

16x - x = 4 + 8

15x = 12

x = 12/15

x = 0.8

Check:

4(4*0.8 - 2) = 0.8 + 4

4(3.2 - 2) = 4.8

4(1.2) = 4.8

Answer:

0.8 in decimal form

Step-by-step explanation:

Answer:

A. 9%; $440.36 million

Step-by-step explanation:

Using A(1+r)t, we can subtract 1-1.09=.09*100=9%.

That means the projected annual growth is 9%

Now we can calculate the worth of the company by replacing t=8, 2008-2000=8

[tex]w=221(1.09)^8\\=440.356=440.36 million[/tex]

Answer:

(C) 87

Step-by-step explanation:

We can use long division to solve this.

[tex]33\overline{\smash{)}#2871}[/tex]

33 goes into 287 8 times and 33 goes into 231 7 times.

So, 87.

Hope this helped!

Answer: C) 87

Step-by-step explanation:

2,871 ÷ 33 = 87

Answer:

y = 10x + 20

Step-by-step explanation:

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Slope-Intercept Form: y = mx + b

Step 1: Find slope m

m = (20 - 10)/(0 - -1)

m = 10/(0 + 1)

m = 10/1

m = 10

y = 10x + b

Step 2: Find y-intercept

(0, 20) is y-int from graph

Step 3: Plug into form

y = 10x + 20

Answer:

Step-by-step explanation:

find LCM of the denominators= 77

so 66/77 - 63/77

3/77

hope this help you pls mark me as brainliest

working for division is on this question is

6/7 divide 9/11

so 6/7 *11/9

66/63 and then you can find its standard form and it cannot be do not

Answer:

B. 13.7 cm^2

Step-by-step explanation:

To find the height of any parallelogram, you must multiply the base x height.

The base is 1.9 cm. The height is 7.2 cm.

A = bh

A = (1.9)(7.2)

A = 13.68

13.7 is the closest answer we can get if we can round, but it really should be 13.68 cm^2.

Answer:

B. 13.7

Step-by-step explanation:

A = bh

A = 1.9*7.2

A = 13.68

(13.68 rounds up to 13.7)

Answer:

[tex]\huge\boxed{Perimeter = 34\ units}[/tex]

Step-by-step explanation:

DE = 10 units

GF = 10 units

DG = 7 units

EF = 7 units

Perimeter of rectangle = Sum of all sides

P = DE + GF + DG + EF

P = 10 + 10 + 7 + 7

Perimeter = 34 units

Answer:

D) 34 units

Step-by-step explanation:

Coordinates:

D: (-5,4)

E: (5,4)

F: (5, -3)

G: (-5,-3)

Distance between points D and E = Distance between points F and G = 10

Distance between points E and F = Distance between points G and D = 7

Formula for perimeter of your rectangle:

2(x) + 2(y) =

2(10) + 2(7) =

20 + 14 = 34 units

That's your answer!

Hope that helps and maybe earns a brainliest!

Have a terrific day! >   <

                                   U

Answer:

x = 13

RQ = 160°

Step-by-step explanation:

Inscribed angles are half the intercepted arc angle.

5x + 15 = ½ (RQ)

RQ = 10x + 30

Arc angles add up to 360°.

10x + 30 + 9x + 17 + 6x − 12 = 360

25x + 35 = 360

25x = 325

x = 13

Therefore, RQ = 160°.

Answer: A.71

Step-by-step explanation: 1.set up the equation

2. 4n-18+n+9=151-5n

3.combine like terms ->  5n-9=151-5n

4.solve for n

5.10n=160

n=16

now you have to plug 16 in for n in order to get the remote exterior angle.

151-5(16)

151-80

71°

The sum of any two interior angle is equal to the third exterior angle. The value of n will be 16°. Then the correct option is B.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

The triangle having the interior angle x and y, and z is the exterior angle of triangle.

m∠x = (4n − 18)°, m∠y = (n + 9)°, and m∠z = (151 − 5n)°

Then the value of n will be

We know that the sum of any two interior angle is equal to the third exterior angle. Then we have

∠x + ∠y = ∠z

4n - 18 + n + 9 = 151 - 5n

10n = 160

n = 16°

Then the correct option is B.

More about the triangle link is given below.

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Answer:

1

Step-by-step explanation:

(-3 + 3) + (-2 + 3) =

= 0 + 1

= 1

Answer:

Hey there!

We can write this equation: 2x+4x=180

6x=180

x=30

Hope this helps :)

The two angles are supplementary angles. When added together they equal 180 degrees.

2x + 4x = 180

Combine like terms:

6x = 180

Divide both sides by 6:

X = 180/6

X = 30

Answer:

40%

Step-by-step explanation:

The whole rectangle is split into 5 parts. Two out of 5 parts are shaded.

Set up a fraction:

[tex]\frac{\text{Shaded}}{\text{Whole}}=\frac{2}{5}[/tex]

Convert into a decimal:

[tex]\frac{2}{5}= 0.4[/tex]

Multiply the decimal by 100 to get the percent:

[tex]0.4*100=40[/tex]

So, forty percent of the rectangle is shaded.

Hope this helps.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Required percentage value = a

total value = b

Percentage = a/b x 100

The percentage of the shaded rectangular boxes in the large rectangle is 40%.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Number of rectangular boxes in the large rectangle = 5

Number of shaded rectangular boxes in the large rectangle = 2

The percentage of shaded rectangular boxes.

= 2/5 x 100

= 2 x 20

= 40%

Thus,

The percentage of the shaded rectangular boxes in the large rectangle is 40%.

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Answer:

50%

Step-by-step explanation:

its a 50/50 chance on it landing either heads or tails

Answer:

$900

Step-by-step explanation:

First, find the area of the floor with the equation A = lw

A = lw

A = (20)(20)

A = 400 ft²

Since each tile covers 1 sq ft and the floor's area is 400 sq ft, they will need 400 tiles.

To calculate the total cost, multiply 400 by 2.25

400(2.25) = 900

= $900

Answer:

The expression in the question can, and should, be written clearly as either  205(2)=8  or as  205(2)=2 . Relying on a left-to-right or right-to-left interpretation is not a good idea.

In cases of associative operators, like  a⋅b⋅c , the parenthesis or other grouping can be omitted because any reasonable interpretation will yield the same result. But this isn’t true of division, which is not associative, nor is it true of mixed operators at the “same level” of precedence, like multiplication/division.

The other answers which say the result is  8  may not be wrong, but they are missing the main issue in that this expression should not be used because of the ambiguity

Step-by-step explanation:

Answer:

-7

Step-by-step explanation:

-1.68j+1.24=13

-1.68j=13-1.24

-1.68j=11.76

j=11.76/-1.68

j=-7

Hi there! Hopefully this helps!

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

Answer: j = -7

You can also rewrite the equation(replace "j" with the answer):

-1.68(-7) + 1.24 = 13.

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

How I solved it:

-1.68j + 1.24 = 13.

We subtract 1.24 from both sides.

-1.68j = 13 - 1.24

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

-1.68j = 13 - 1.24

We subtract 1.24 from 13 to get 11.76.

-1.68j = 11.76

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

-1.68j = 11.76

We then divide both sides by -1.68.

j = [tex]\frac{11.76}{-1.68}[/tex]

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

Expand [tex]\frac{11.76}{-1.68}[/tex] ≈ -7 by multiplying both the numerator and the denominator by 100.

j = [tex]\frac{1176}{-168}[/tex]

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

Divide 1176 by -168 to get -7.

Hi there! :)

Answer:

[tex]\huge\boxed{\frac{9cm}{8cm}}[/tex]

We can disregard the units temporarily to create a ratio for 4.5 to 4:

4.5 is not a whole number- we can convert this number in the ratio to a whole number by multiplying both numbers by 2:

2 · (4.5 : 4) = 9 : 8

Express as a fraction:

[tex]9cm : 8cm = \frac{9cm}{8cm}[/tex]

Answer:

  236.9 m

Step-by-step explanation:

Let x and y represent the distances to the near and far cars, respectively. You know from the definition of the tangent of an angle that ...

  tan(angle of depression) = building height/distance to car

  tan(10°39') = 150/x

  x = 150/tan(10°39')

and

  tan(8°15') = 150/y

  y = 150/tan(8°15')

The difference of these two distances is the distance between the cars:

  y - x = 150/tan(8°15') -150/tan(10°39')

__

The minutes of arc can be converted to fractional degrees:

  15' = 15'/(60'/1°) = (15/60)° = 0.25°

  39' = 39'/(60'/1°) = (39/60)° = (13/20)° = 0.65°

So, the distance of interest is ...

  distance between cars = (150 m)(1/tan(8.25°) -1/tan(10.65°)) ≈ 236.86 m

The cars are about 236.9 meters apart.