Show that the rational numbers -15/35 and 4/(-6) are not equal?

Answer:

x = 0

Step-by-step explanation:

Since the points are collinear , then

AB + BC = AC , that is

11 + 2x + 10 = x + 21

2x + 21 = x + 21 ( subtract x from both sides )

x + 21 = 21 ( subtract 21 from both sides )

x = 0

Answer:

ΔABC ~ ΔQPR by the Angle-Angle (AA) similarity theorem of two triangles

Step-by-step explanation:

The coordinates of the vertices are given as follows;

A = (1, 2), B =(9, 8), C = (1, 8)

P= (5, -3), Q = (-7, 6), R = (-7, -3)

The given dimensions of AB and PQ are 10, and 15 respectively

The, l lengths of the sides of triangles are found as follows;

[tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]

For segment BC, we have;

B =(9, 8), C = (1, 8)

(x₁, y₁) = (9, 8), (x₂, y₂) = (1, 8), substituting gives;

Length BC = 8

For length CA, C = (1, 8) A = (1, 2)

(x₁, y₁) = (1, 8)

(x₂, y₂) = (1, 2)

The length found by substituting the values for (x₁, y₁), (x₂, y₂) in the length equation gives; Length CA = 6

Given that length  CA² + BC² = 8² + 6² = 64 + 36 = 100 = BA², we have by Pythagoras theorem, we have ΔABC is a right triangle

Similarly, for ΔQPR, we have;

Length QR, Q = (-7, 6), R = (-7, -3) = 9

Length PR, P= (5, -3), R = (-7, -3) = 12

QR² + PR² = 9² + 12² = 225 = 15² = PQ²

∴ ΔQPR is a right triangle

By comparing the ratio of the sides, we have;

cos(θ) = PR/PQ = 12/15 = 4/5, θ = cos⁻¹(4/5) = 36.9°

∠RPQ = 36.9°

sin(θ) = QR/PQ = 9/15 = 3/5

Similarly in triangle ΔABC, we have;

cos(θ) = BC/AB = 8/10 = 4/5

∠CBA = 36.9°

Therefore, ∠CBA ≅ ∠RPQ = 36.9°

Also ∠PRQ ≅ ∠BCA = 90° (Angle opposite hypotenuse side of right triangle

Therefore, ΔABC and ΔQPR are similar triangles by the Angle-Angle (AA) similarity theorem of two triangles.

Answer:

B. [tex] \frac{HI}{GI} [/tex]

Step-by-step explanation:

The trigonometric ratio formula for tangent of any angle in a right triangle is given as:

tan(θ) = [tex] \frac{opposite}{adjacent} [/tex]

Note: it is the length of the side opposite to the θ, and the length of the side adjacent to θ.

Thus, in the right triangle given, ∆GHI,

θ = <G

The length of side the opposite <G = HI

The length of the side adjacent to <G = GI

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

Answer:

136^3 cm

Step-by-step explanation:

Big square:

5 × 4 × 6 = 20 × 6 = 120

Small rectangle:

7 - 5 = 2

2 × 2 × 4  = 4 × 4 = 16

Both:

120 + 16 = 136

The volume of this figure is 136 cm^3.

Hope this helped.

Answer:

Below

Step-by-step explanation:

First you can find the front area and just multiply it by the length

Find the area of the small square

A = lw

   = (2)(2)

   = 4 cm^2

Find the area of the large square

A = lw

   = (6)(5)

   = 30 cm^2

Now just multiply the area of the two by the length

34 x 4 = 136 cm^3

Hope this helps!

Answer: False. This expression is a monomial!

Answer:

false

Step-by-step explanation:

it is molonomial

Answer:

Below

Step-by-step explanation:

Notice that x is between 10 and -10 but takes only the values that are integers.

The inequalities:

● we can write an inequality that includes all these values.

● -10 《 x 《 10

This is a possible inequality

Multiply both sides by 2 and you will get a new one:

● -20 《 2x 《 20

You can multiply it by any number to generate a new inequality.

Or you can add or substract any number.

Answer:

75 pounds

Step-by-step explanation:

(x) + (x) + (x+20) = 185

3x + 20 = 185

3x = 165

x = 55

Large dog = 55 + 20 = 75

Answer:

12 inches

Step-by-step explanation:

A=1/2bh

30=1/2b5

(30*2)/5=b

B=12

Answer:

The correct option is;

45°

Step-by-step explanation:

By angle sum theorem, we have that the sum of angles in a triangle = 180°

Therefore, we have;

When the interior angles of the triangle are constructed to be 60° and 75°, we have by the angle sum theorem;

The third angle + 60° + 75° = 180°

Which gives;

The third angle  = 180°- 60° - 75° = 180°- 135° = 45°

The measurement of the third angle by the angle sum theorem will be 45°

The correct option is ∠third angle = 45°.

Answer:

Step-by-step explanation:

j    -  total number of cars she installed axles on

2    - number of axles she installed on one car

2·j   - total number of axles she installed on

46   - total number of axles she installed on

2·j = 46              {divide both sides by 2}

Answer:

x^2 -10x+2

Step-by-step explanation:

(3x^2 - 11x - 4) – (x – 2) (2x + 3)

FOIL

(3x^2 - 11x - 4) – (2x^2-4x+3x-6)

Combine like terms

(3x^2 - 11x - 4) – (2x^2 -x-6)

Distribute the minus sign

3x^2 - 11x - 4 – 2x^2 +x+6

Combine like terms

x^2 -10x+2

Answer:

b^12

Step-by-step explanation:

(b^4)^3

We know that x^y^z = x^(y*z)

b^4^3 = b^*4*3) = b^12

Answer:

Step-by-step explanation:

Let the price of the item = Rs x

13% of x = 390

[tex]\frac{13}{100}*x=390\\\\\\x = 390*\frac{100}{13}\\\\\\[/tex]

x = Rs. 3000

Answer:

19 of 95% grades

Step-by-step explanation:

90= (0+95(x-1))/x

90x=0+95(x-1)

90x=95(x-1)

90x=95x-95

90x-95x=-95

-5x=-95

x=-95/-5

x=19

Answer:

The answer is A f(x) = -2x + 40

Step-by-step explanation:

it has a negative 2 because the dumps are decreasing by 2 every week and x is the amount of weeks and + 40 because that is the amount you started with.

Answer:

D

Step-by-step explanation:

The midpoint is the average of the 2 endpoints, that is

midpoint = [tex]\frac{-7+12}{2}[/tex] = [tex]\frac{5}{2}[/tex] = 2.5 → D

Answer:

Step-by-step explanation:

To model the equation for the cost of Each Arrangement.

We need to itemize all parameters needed.

An arrangement consists of

1. one vase

2. twelve roses

Given that 1 vase cost $2 and

The cost of one rose is r

Let the total cost of the arrangement be C

Hence C is the  cost of the vase plus the cost of 12 roses combined, this is given as

[tex]C = 12r + 2[/tex]

Answer:  B) 5 inches

======================================================

Explanation:

1 ft = 12 in

9 ft = 108 in ... multiply both sides by 9

9 ft, 9.5 in = 108 in + 9.5 in = 117.5 in

The board's length of 9 ft, 9.5 inches is the same as 117.5 inches.

It's cut into sections of 11.25 inches, so we have (117.5)/(11.25) = 10.44 approximately which rounds down to 10.

Having 10 sections of length 11.25 inches each, takes up 10*11.25 = 112.5 inches so far. That leaves 117.5 - 112.5 = 5 inches as the remaining piece of the board.

Answer:

Step-by-step explanation:

Draw a line through the data points with about half of the points on one side of the line and the other half on the other side.  You'll see that there is a slight positive rise in the graph as we move from left to right, but the correlation is weak.  Thus, 0.4 is the correct correlation coefficient in this case.

The correlation coefficient that would best describe the data give in the table is 0.4 which is a weak positive correlation.

The statistical concept of correlation describes how closely two variables move in tandem with one another.

As the graph is scattered in such a way that,if we draw a line from the centre, we can observe that as 'x' increases 'y' also increases so the relation is positive correlation.

But it is seen in the graph that these points are scattered, so this relation is weak. For positive weak correlation the value should be less than 0.5.

Therefore, the given graph shows positive weak correlation with value 0.4.

To know more about statistics, here

https://brainly.com/question/23724696

#SPJ2

Answer:

d = 55.5  

x = 1

c = 11

m = [tex]\frac{1}{122}[/tex]

k = [tex]\frac{a}{(c + 5)}[/tex]

Step-by-step explanation:

Sorry, the formatting is slightly hard to understand, but I think this is what you meant.

Q1.

[tex]\frac{1}{6}[/tex]d - 8 = [tex]\frac{5}{8}[/tex] x 2

Step 1. Simplify.

[tex]\frac{5}{8}[/tex] x 2 = [tex]\frac{5}{8}[/tex] x [tex]\frac{2}{1}[/tex] = [tex]\frac{10}{8}[/tex]

Step 2. Cancel out the negative 8.

[tex]\frac{1}{6}[/tex]d - 8 = [tex]\frac{10}{8}[/tex]

+ 8 to both sides (do the opposite: [tex]\frac{1}{6}[/tex]d is subtracting 8 right now, but to cancel that out, we will do the opposite of subtraction, i.e. addition)

[tex]\frac{1}{6}[/tex]d = [tex]\frac{10}{8}[/tex] + 8

Step 3. Simplify.

[tex]\frac{10}{8}[/tex] + 8 = [tex]\frac{10}{8}[/tex] + [tex]\frac{8}{1}[/tex] = [tex]\frac{10}{8}[/tex] + [tex]\frac{64}{8}[/tex] = [tex]\frac{74}{8}[/tex] = [tex]\frac{37}{4}[/tex]

Step 4. Cancel out the [tex]\frac{1}{6}[/tex].

[tex]\frac{1}{6}[/tex]d = [tex]\frac{37}{4}[/tex]

÷ [tex]\frac{1}{6}[/tex] from both sides (do the opposite: d is multiplied by [tex]\frac{1}{6}[/tex] right now, but to cancel that out, we will do the opposite of multiplication, i.e. division)

÷ [tex]\frac{1}{6}[/tex] = x 6

So....

x 6 to both sides

d = [tex]\frac{37}{4}[/tex] x  6 = [tex]\frac{37}{4}[/tex] x [tex]\frac{6}{1}[/tex] = [tex]\frac{222}{4}[/tex] = [tex]\frac{111}{2}[/tex] = 55.5

Step 5. Write down your answer.

d = 55.5

Q2.

3x - 4 + 5x = 10 - 2x × 3

Step 1. Simplify

3x - 4 + 5x = 3x + 5x - 4 = 8x - 4

10 - 2x × 3 = 10 - (2x × 3) = 10 - 6x

Step 2. Cancel out the negative 6x

8x - 4 = 10 - 6x

+ 6x to both sides (do the opposite - you're probably tired of reading this now - right now it's 10 subtract 6x, but the opposite of subtraction is addition)

14x - 4 = 10

Step 3. Cancel out the negative 4

14x - 4 = 10

+ 4 to both sides (right now it's 14x subtract 4, but the opposite of subtraction is addition)

14x = 14

Step 4. Divide by 14

14x = 14

÷ 14 from both sides (out of the [14 × x] we only want the [x], so we cancel out the [× 14])

x = 1

Step 5. Write down your answer.

x = 1

Q3.

7(c - 3) = 14 × 4

Step 1. Expand the brackets

7(c - 3) = (7 x c) - (7 x 3) = 7c - 21

Step 2. Simplify

14 x 4 = 56

Step 3. Cancel out the negative 21

7c - 21 = 56

+ 21

7c = 56 + 21

7c = 77

Step 4. Cancel out the ×7

7c = 77

÷ 7

c = 77 ÷ 7

c = 11

Step 5. Write down your answer.

c = 11

Q4.

11([tex]\frac{m}{22}[/tex] + [tex]\frac{3}{44}[/tex]) = 87m + m × 5

Step 1. Expand the brackets

11([tex]\frac{m}{22}[/tex] + [tex]\frac{3}{44}[/tex]) = (11 x [tex]\frac{m}{22}[/tex]) + (11 x [tex]\frac{3}{44}[/tex]) = ([tex]\frac{11}{1}[/tex] x [tex]\frac{m}{22}[/tex]) + ([tex]\frac{11}{1}[/tex] x [tex]\frac{3}{44}[/tex]) = [tex]\frac{11m}{22}[/tex] + [tex]\frac{33}{44}[/tex] = [tex]\frac{m}{2}[/tex] + [tex]\frac{3}{4}[/tex]

Step 2. Simplify.

87m + m x 5 = 87m + 5m = 92m

Step 3. Cancel out the add [tex]\frac{3}{4}[/tex]

[tex]\frac{m}{2}[/tex] + [tex]\frac{3}{4}[/tex] = 92m

- [tex]\frac{3}{4}[/tex]

[tex]\frac{m}{2}[/tex] = 92m - [tex]\frac{3}{4}[/tex]

[tex]\frac{m}{2}[/tex] = [tex]\frac{92m}{1}[/tex] - [tex]\frac{3}{4}[/tex]

[tex]\frac{m}{2}[/tex] = [tex]\frac{368m}{4}[/tex] - [tex]\frac{3}{4}[/tex]

[tex]\frac{m}{2}[/tex] = [tex]\frac{368m - 3}{4}[/tex]

Step 4. Cancel out the ÷ 4

[tex]\frac{m}{2}[/tex] = [tex]\frac{368m - 3}{4}[/tex]

x 4

2m = 368m - 3

Step 5. Cancel out the 368m

2m = 368m - 3

- 368m

-366m = - 3

Step 6. Cancel out the × -366

-366m = -3

÷ -366

m = [tex]\frac{-3}{-366}[/tex]

m = [tex]\frac{1}{122}[/tex]

Step 7. Write down your answer.

m = [tex]\frac{1}{122}[/tex]

Q5.

ck + 5k = a

Step 1. Factorise

ck + 5k = (c × k) + (5 × k) = (c + 5) x k = k(c + 5)

Step 2. Cancel out the × (c + 5)

k(c + 5) = a

÷ (c + 5)

k = a ÷ (c + 5)

k = [tex]\frac{a}{(c + 5)}[/tex]

Answer:

1) 11[tex]\sqrt{3}[/tex]

2) 2[tex]\sqrt{2}[/tex]

3) [tex]20\sqrt{3} + 15\sqrt{2}[/tex]

4) [tex]53 + 12\sqrt{10}[/tex]

5) -2

6) [tex]7\sqrt{2} - 5\sqrt{3}[/tex]

Step-by-step explanation:

1) 2[tex]\sqrt{12}[/tex] + 3[tex]\sqrt{48}[/tex] - [tex]\sqrt{75}[/tex]

=(2 × 2[tex]\sqrt{3}[/tex] )+ (3 × 4[tex]\sqrt{3}[/tex]) - 5[tex]\sqrt{3}[/tex]

= 4[tex]\sqrt{3}[/tex] + 12[tex]\sqrt{3}[/tex] - 5[tex]\sqrt{3}[/tex]

= 11[tex]\sqrt{3}[/tex]

2) 4[tex]\sqrt{8}[/tex] -2[tex]\sqrt{98}[/tex] + [tex]\sqrt{128}[/tex]

= (4 × 2[tex]\sqrt{2}[/tex]) - (2 × 7[tex]\sqrt{2}[/tex]) + 8[tex]\sqrt{2}[/tex]

= 8[tex]\sqrt{2}[/tex] - 14[tex]\sqrt{2}[/tex] +8[tex]\sqrt{2}[/tex]

= 2[tex]\sqrt{2}[/tex]

3) 5[tex]\sqrt{12\\}[/tex] - 3[tex]\sqrt{18} + 4 \sqrt{72} +2\sqrt{75}[/tex]

= 5× [tex]2\sqrt{3}[/tex] - 3×[tex]3\sqrt{2}[/tex] + 4×[tex]6\sqrt{2}[/tex] + 2×[tex]5\sqrt{3}[/tex]

= [tex]10\sqrt{3} - 9\sqrt{2} +24\sqrt{2} +10\sqrt{3}[/tex]

= [tex]20\sqrt{3} + 15\sqrt{2}[/tex]

4) [tex](2\sqrt{2} + 3\sqrt{5} )^{2}[/tex]

= [tex]8 + 12\sqrt{10} + 45[/tex]

= [tex]53 + 12\sqrt{10}[/tex]

5) [tex](1+\sqrt{3} ) (1-\sqrt{3} )[/tex]

= [tex]1 - 3[/tex]

= -2

6) [tex](2\sqrt{6} -1) (\sqrt{3} -\sqrt{2} )[/tex]

= [tex]2\sqrt{18}-2\sqrt{12} -\sqrt{3} +\sqrt{2}[/tex]

= 2×[tex]3\sqrt{2}[/tex] - 2×[tex]2\sqrt{3}[/tex] - [tex]\sqrt{3} + \sqrt{2}[/tex]

= [tex]6\sqrt{2} - 4\sqrt{3} -\sqrt{3} +\sqrt{2}[/tex]

= [tex]7\sqrt{2} - 5\sqrt{3}[/tex]

Hope the working out is clear and will help you. :)

Step-by-step explanation:

please I solved the question in the diagram above

This is the same as writing  v = sqrt(ar)

===========================================

Work Shown:

[tex]a = \frac{v^2}{r}\\\\ar = v^2\\\\v^2 = ar\\\\v = \sqrt{ar}\\\\[/tex]

I multiplied both sides by r to isolate the v^2 term, then I applied the square root to fully isolate v.

Answer:

Step-by-step explanation:

Our interval is 180 to 270 so that's quadrant III. In quadrant 3, both x and y are negative. If we set up our right triangle in this quadrant and label it accordingly with the values given for tangent theta, we find that the missing length is the hypotenuse. Solve for that using Pythagorean's Theorem. Doing that gives us that the hypotenuse is [tex]\sqrt{61}[/tex].  Now we can solve for your other identities. First,

[tex]cos(2\theta)=2cos^2\theta-1[/tex] (There are 3 identities for cos(2θ) and regardless of which one you pick, the answer will be the same every time...promise!)

Filling in now:

[tex]cos(2\theta)=2(\frac{-5}{\sqrt{61} })^2-1[/tex] and simplified a bit:

[tex]cos(2\theta)=2(\frac{25}{61})-1[/tex] and a bit more:

[tex]cos(2\theta)=\frac{50}{61}-\frac{61}{61}[/tex] giving us, finally:

[tex]cos(2\theta)=-\frac{11}{61}[/tex]

Now for b. We have an identity for the half angle of sin:

[tex]sin(\frac{\theta}{2})=[/tex] ±[tex]\sqrt{\frac{1-cos\theta}{2} }[/tex]  and filling in:

[tex]sin(\frac{\theta}{2})=[/tex] ±[tex]\sqrt{\frac{1-(-\frac{5}{\sqrt{61} } )}{2} }[/tex] which simplifies a bit to:

[tex]sin(\frac{\theta}{2})=[/tex] ±[tex]\sqrt{\frac{1+\frac{5}{\sqrt{61} } }{2} }[/tex] and a bit more to:

[tex]sin(\frac{\theta}{2})=[/tex] ±[tex]\sqrt{\frac{\sqrt{61}+5 }{2\sqrt{61} } }[/tex]  I'm not sure if this is the form you need it in, but this is the answer, as convoluted and crazy as it may look.

As for the cosine half-angle, the identity is the same, except there's a + sign in the numerator of the identity instead of a -, giving us the solution:

[tex]cos(\frac{\theta}{2})=[/tex] ±[tex]\sqrt{\frac{\sqrt{61}-5 }{2\sqrt{61} } }[/tex]

Answer:The first issue one most notice is the words “at least” We are trying to find the probability of at least 2 girls.

The five possible outcomes for girls are 0,1,2,3,4. The odds of 1 girl out of 4 is .25 and the odds of 1 boy out of 4 is .25 (same as the odds of 3 out of 4 girls). Therefore the odds of 1 OR 3 girls must be .5 because 1 girl and 3 girls each has a .25 probability. If the probability of (1 OR 3 girls) equals .5, then the probability of 2 girls must be a different number.

The probability of 2 or more girls, is the sum of the probability of 4 girls (.06125)(—-.5 to the 4th power—— ), plus the probability of 3 girls (.25)——(the same as the probability of 1 boy)—- plus the probability of 2 girls. Since we know the probability of zero boys is .0625 (again, .5 to the 4th power) and the probability of 1 boy is .25 (the same as the probability of 3 girls )———then the probability of 2 girls is ((1 minus (the sum of the probability of 0 OR 1 boys) plus the (sum of the probability of 3 or 4 girls)), or 1-((.0625+.25)+(.0625+.25)), or .375. We had to derive the probability of two from the other known probabilities. Therefore .375+.25+.0625=.6875 is the probability of both AT LEAST 2 girls and also NO MORE than 2 boys. Notice this adds up to 1.375 because the probability of the central number 2 (i.e., .375) appears on both sides.

First subtract the amount the bow takes from the total:

70 - 32 = 38 inches

The width is 14 on top and bottom so subtract 14 x 2 = 28 from 38:

38-28 = 10

Divide 10 by the 2 sides:

10/2 = 5

The height is 5 inches.

Answer:

Step-by-step explanation:

Given,

Principal ( P ) = N 250

Time ( T ) = 4 years

Amount ( A ) =N 330

Rate ( R ) = ?

First, finding the Interest :

According to definition of Amount ,

Amount = Principal + Interest

plug the values

⇒[tex] \sf{330 = 250 + I}[/tex]

Move i to left hand side and change it's sign

⇒[tex] \sf{ - I = 250 - 330}[/tex]

Calculate

⇒[tex] \sf{ - I = - 80}[/tex]

Change the signs of the both equation

⇒[tex] \sf{I = 80 }[/tex]

Interest = 80

Finding the rate :

Simple Interest = [tex] \sf{ \frac{PTR}{100} }[/tex]

plug the values

⇒[tex] \sf{80 = \frac{250 \times 4 \times R}{100} }[/tex]

Multiply the numbers

⇒[tex] \sf{80 = \: \frac{1000 \: R}{100} }[/tex]

Apply cross product property

⇒[tex] \sf{1000R = 100 \times 80}[/tex]

Multiply the numbers

⇒[tex] \sf{1000R = 8000}[/tex]

Divide both sides of the equation by 1000

⇒[tex] \sf{ \frac{1000R}{1000} = \frac{8000}{1000} }[/tex]

Calculate

⇒[tex] \sf{R = 8 \: \% \: }[/tex]

Thus, Rate = 8 %

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

Let's learn about Principal , Interest , Time , Rate and Amount :

Hope I helped!

Best regards!!

Answer:

1.

(a) The Domain is the set of inputs of the function.

Considering that the function takes a period of 3 weeks (21 days), the domain is [0, 21], once we can't evaluate what happens after the 21st day.

[tex]\text{Domain is } [0, 21][/tex]

Otherwise, it could be [tex][0, \infty)[/tex]

Note: We include 0 and 21.

Once the greatest balance was $400, it will not exceed $400, either it doesn't show negative values.

[tex]\text{Range is } [0, 400][/tex]    

Note: We include 0 and 400.

(b)

Once the greatest balance was $400, when x=0, it seems that the y-value is half of $400, therefore, approximately $200. It also represents the initial value, the amount of money when she opened the account.

(c)

[tex]f(x)=B(d)[/tex]

[tex]B(12)=0[/tex]

(d)

It is in segment 4.

The balance equal to zero means that the y-value of the graph is zero, therefore in the x-axis.

Answer:

(3,0) lie between quadrants I and II. (-9, -3) lie in quadrant III

Answer:

7.9 * 10 ^-6

Step-by-step explanation:

Move the decimal 6 places to the left so there is one number before the decimal

0.0000079

7.9

The exponent is -6  ( negative because we moved it to the left)

7.9 * 10 ^-6

Answer:

Hey there!

7.9 × 10-6 is your answer.

Hope this helps :)