There is a jar of green and red marbles. If there are 21 marbles total and the ratio of green to red is 3:4, how many red marbles are there?

Answer:

Step-by-step explanation:

Parallel lines have same slope

19) y = x - 4

m = 1 ;   (2, 3 )

Equation: y - y₁ = m(x- x₁)

             y - 3 = 1(x - 2)

              y - 3 = x -2

                   y = x - 2 + 3

y = x + 1

20) 2x + 3y = 3

We have to write in y = mx + b  form

3y =  - 2x - 3

[tex]y=\frac{-2}{3}x-\frac{3}{3}\\\\y=\frac{-2}{3}x-1\\\\m=\frac{-2}{3}[/tex]; (-6, -1)

[tex]y-[-1]=\frac{-2}{3}(x-[-6])\\\\y+1=\frac{-2}{3}(x+6)\\\\y+1=\frac{-2}{3}x+\frac{-2}{3}*6\\\\y+1=\frac{-2}{3}x-4\\\\y=\frac{-2}{3}x-4-1\\\\y=\frac{-2}{3}x-5[/tex]

for perpendicular lines, m2 = -1/m1

21) y = 2x+ 5

m1 = 2

[tex]m_{2}=\frac{-1}{2}[/tex];     (-2,8)

[tex]y-8=\frac{-1}{2}(x-[-2])\\\\y-8=\frac{-1}{2}(x+2)\\\\y-8=\frac{-1}{2}x+2*\frac{-1}{2}\\\\y-8=\frac{-1}{2}x-1\\\\y=\frac{-1}{2}x-1+8\\\\y=\frac{-1}{2}x+7[/tex]

22) x+ 4y = 8

           4y = -x + 8

             [tex]y=\frac{-1}{4}x+\frac{8}{4}\\\\y=\frac{-1}{4}x+2\\\\m_1=\frac{-1}{4}\\\\m_{2}=4\\\\[/tex]

m2 = 4;  (-2,-11)

y - [-11] = 4(x -[-2])

y + 11 = 4 (x + 2)

y + 11 = 4x + 8

      y = 4x + 8 - 11

      y = 4x - 3

Answers:

16. sin(A) = a/12

17. tan(A) = a/9

18. sin(B) = 3/4    (reduced from 9/12)

19. cos(B) = a/12

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

Explanation:

The sine of an angle is equal to the ratio of the opposite side over the hypotenuse. For reference angle A, the opposite side is BC = a. The hypotenuse is always the longest side. The hypotenuse is AB = 12.

sin(angle) = opposite/hypotenuse

sin(A) = BC/AB

sin(A) = a/12

Similarly,

sin(B) = opposite/hypotenuse = AC/AB = 9/12 = 3/4.

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

Tangent is the ratio of opposite over adjacent

tan(angle) = opposite/adjacent

tan(A) = BC/AC

tan(A) = a/9

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

Cosine is the ratio of adjacent over hypotenuse

cos(angle) = adjacent/hypotenuse

cos(B) = BC/AB

cos(B) = a/12

we see that this is the same result as sin(A). It turns out that sin(A) = cos(B) if and only if A+B = 90. In other words, the sin(A) = cos(B) when A and B are the acute angles of a right triangle.

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

Side note: you could use the Pythagorean theorem to solve for the value of 'a'. All of this assumes that triangle ACB is a right triangle.

Answer:

1) negative

2) positive

3) the quotient is 0 which is neither +ve or -ve

4) negative

Step-by-step explanation:

To find the sign of the quotient, you first check the sign of the two numbers..

If the sign of ONE of the numbers is negative and one is positive, then the sign of the quotient will be negative too.

If the sign of BOTH the numbers is negative, it'll also be negative and visa versa

Hope it helps

Answer:

r = 8

Step-by-step explanation:

15 = 1.5r+3

Subtract both sides of the equation by 3.

15-3 = 1.5r+3-3

12 = 1.5r

Divide both sides of the equation by 1.5.

12/1.5=1.5r/1.5

8 = r

r = 8

Answer:

[tex]8[/tex]

[tex]1.5r + 3 = 15 \\ 1.5r = 15 - 3 \\ 1.5r = 12 \\ r = \frac{12}{1.5} \\ r = \frac{120}{15} \\ r = 8[/tex]

Answer:

conclusion

Step-by-step explanation:

Statement (B) "There are no even prime numbers" can be proved wrong using a counterexample.

So, as we all know that all multiples of 4 are also multiples of 2.

But the statement (B) is wrong as there are prime even numbers.

For example: 2

The factor of 2 has only 1 and the number itself which is 2 (Even) and no other number.

Therefore, statement (B) "There are no even prime numbers" can be proved wrong using a counterexample.

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The correct question is given below;

3. Which statement could be proven false using a counterexample?

A) All multiples of 4 are also multiples of 2.

B) There are no prime even numbers.

Answer:

The area is π= 3.14 approx

Hope it helps!

Step-by-step explanation:

Area of circle = πr^2

Radius= r = 1 unit

So area,

= 3.14*(r)^2

= 3.14*(1)^2

= 3.14*1

= 3.14 or π if you want the specific answer

Answer:

Area of circle = πr^r

Area = 22/7*(1)^2

Area= 22/7 or 3.14 unit

Answer:

Option C

Step-by-step explanation:

I am going to assume that one doesn't know what an inconsistent or consistent system of equations is, let alone what a dependent and independent system of equation is. Well an inconsistent system is one that have no solutions, while a consistent system of equations has solutions. A consistent dependent system has infinite solutions, while a consistent independent system has 1 solution.

_______________________________________________________

This system of equations has one solution, as the slopes are not the same nor a multiple of one another ( no solution ) , and the equations are not the same either, nor a multiple of one another ( infinite solutions ). Thus, the system of equations is consistent, independent - Option C

I hope that clarified any questions that you had, as the answer was not Option D!

Answer:

16x + 8y -3/2

Step-by-step explanation:

The expression can be represented mathematically as follows.

-2(-8x - 4y + 3/4) = - 10x - 8y - 1 1/4

-2(-8x - 4y + 3/4) = - 10x - 8y - 5/4

The first way to solve this expression is by opening the bracket by multiplying the outside values by the inner values.

-2(-8x - 4y + 3/4)

Multiply -2 by all the values in the brackets

-2 × - 8x = 16x not - 10x

-2 × - 4y = 8y not -8y

-2 × 3/4 = -6/4 = - 3/2  not -5/4

Bringing the value together the expected answer will be 16x + 8y -3/2 and not  - 10x - 8y - 5/4.

Answer

A, B, and C

Step-by-step explanation:

Hope this helps!

Answer:

[tex]5n^2[/tex]

Step-by-step explanation:

This is a quadratic sequence.

The nth term must have [tex]n^2[/tex].

The sequence has a factor of [tex]5[/tex].

[tex]5n^2[/tex]

[tex]5(1)^2=5\\5(2)^2=20\\5(3)^2=45\\5(4)^2=80\\5(5)^2=125[/tex]

Few terms to this sequence are:

5, 20, 45, 80, 125, 180, 245, 320, 405, 500, 605, 720, 845, 980, 1125, 1280, 1445, 1620, 1805, 2000, 2205, 2420, 2645, 2880, 3125, 3380, 3645, 3920, 4205, 4500, 4805, 5120, 5445, 5780, ...

Answer:

the answer is 6 just check it

Answer:

ED = 4 units

Step-by-step explanation:

Observing the figure given to us, we can deduce the following:

=>CE = EA (because point E is the midpoint of CA)

Therefore, if CE = EA = x unit, CA = 2x

=>Also, CD = DB (because point D is the midpoint of CB)

Therefore, if CD = DB = y, CB = 2y

Thus, CA/CE = CB/CD = 2 (2x/x = 2y/y)

Going by the above ration we got comparing the ratio of the corresponding sides of ∆CAB and ∆CED (2:1), we can conclude that ∆CAB ~ ∆CED

Using the ratio of the corresponding sides of ∆CAB to ∆CED = (2:1), measure of segment ED is calculated below:

AB/ED = 2/1

8/ED = 2/1

Cross multiply

8 × 1 = 2 × ED

Divide both sides by 2

8/2 = ED

ED = 4 units

Answer:

A, C, D and K

Step-by-step explanation:

Inequalities:

y ≤ −2x + 10  and  y >1/2x-2

Finding zeros for the first inequality:

Space to the left of this line (as y≤ ) is the solution for this inequality, any points on this line are inclusive.

Finding zeros for the second inequality:

Space above this line (as y > sign) is the solution for this inequality, any points on this line are not inclusive.

Now we have the space of intersection of the above inequalities.

So the points in same section are the solution.

They are:

See attached for explanation

Answer:

-3.48

Step-by-step explanation:

7.008 + (-3.6) + (-6.888) =

Subtract 3.6 from 7.008 = 3.408

3.408 -6.888

Subtract 6.888 from 3.408

6.888 - 3.408  and take the negative sign

-3.48

Answer:

7.008+(-3.6)+(-6.888) So. + and - is always -.We get this:

=7.008−3.6−6.888      (7.008-3.6=3.408)

=3.408−6.888

=−3.48

I hope this help you :)

Step-by-step explanation:

Answer:

∠JKL = 38°

Step-by-step explanation:

PQRS, JQK and LRK are straight lines

Let's take the straight lines in the diagrams one after the other to find what they consist.

The related diagram can be found at brainly (question ID: 18713345)

Find attached the diagram used for solving the question.

For straight line PQRS,

2x°+y°+x°+2y° = 180°

(Sum of angles on a Straight line = 180°)

Collect like terms

3x° + 3y° = 180°

Also straight line PQRS = straight line PQR + straight line SRQ

For straight line PQR,

2y + x + ∠RQM = 180° ....equation 1

For straight line SRQ,

2x + y + ∠MRQ = 180° ....equation 2

Straight line PQRS = addition of equation 1 and 2

By collecting like times

3x +3y + ∠RQM + ∠MRQ = 360°....equation 3

Given ∠QMR = 33°

∠RQM + ∠MRQ + ∠QMR = 180° (sum of angles in a triangle)

∠RQM + ∠MRQ + 33° = 180°

∠RQM + ∠MRQ = 180-33

∠RQM + ∠MRQ = 147° ...equation 4

Insert equation 4 in 3

3x° +3y° + 147° = 360°

3x +3y = 360 - 147

3x +3y = 213

3(x+y) = 3(71)

x+y = 71°

∠JQP = ∠RQK = 2y° (vertical angles are equal)

∠LRS = ∠QRK = 2x° (vertical angles are equal)

∠QRK + ∠RQK + ∠QKR = 180° (sum of angles in a triangle)

2x+2y + ∠QKR = 180

2(x+y) + ∠QKR = 180

2(71) + ∠QKR = 180

142 + ∠QKR = 180

∠QKR = 180 - 142

∠QKR = 38°

∠JKL = ∠QKR = 38°

Answer:

∠JKL = 38°

Step-by-step explanation:

I did the question in class today!

Answer:

6, 30

Step-by-step explanation:

Let the numbers be p and q

p = 2 × 3 × a

a = 1

p = 6

q = 2 × 3 × b

b = 5

q = 30

6 = 2 × 3

30 = 2 × 3 × 5

HCF = 2 × 3 = 6

LCM = 2 × 3 × 5 = 30

30/15 = 2

Answer: 6, 30

Answer:

-10

Step-by-step explanation:

Variable k is denoted as vertical movement. In this case, the -10 is k. Therefore, the graph is moving 10 units down from the parent graph.

Answer:

c = 730 cm

Step-by-step explanation:

To solve this question we just need to use the law of sines:

The ratio between a side in the triangle and its opposite angle is always the same.

So we have that:

[tex]a / sin(A) = c / sin(C)[/tex]

[tex]714 / sin(78) = c / sin(90)[/tex]

sin(78) is equal 0.9781 and sin(90) is equal 1, so we have:

[tex]714 / 0.9781 = c / 1[/tex]

[tex]c = 714 / 0.9781 = 730\ cm[/tex]

Answer:

x=12

Step-by-step explanation:

The isosceles triangle consist of two right angle triangle of the same dimensions.

Let the unknown side of the right angle triangle=y

x=y+y

x=2y

Right angle triangle

c^2=a^2+b^2

c=10

a=8

b=y

c^2-a^2=b^2

10^2-8^2=y^2

100-64=y^2

36=y^2

y=√36

=6

y=6

Recall

x=2y

Substitute the value of y into the equation

x=2(6)

=12

Therefore,

x=12

Answer:

x=12

Step-by-step explanation:

The isosceles triangle is made up of 222 congruent right triangles.

The base of each right triangle is \dfrac12

2

1

​

start fraction, 1, divided by, 2, end fraction the base of the isosceles triangle.

Hint #22 / 6

When we have a right triangle we can use the Pythagorean Theorem to solve for a missing side.

The equation for the Pythagorean Theorem is

a^2 + b^2 = c^2a

2

+b

2

=c

2

a, squared, plus, b, squared, equals, c, squared

where aaa and bbb are the lengths of the two legs of the triangle, and ccc is the length of the hypotenuse.

[How can I tell which side is the hypotenuse?]

Hint #33 / 6

First we can find the missing length for one of the right triangles. Let's label the drawing with aaa, bbb, and ccc:

Note that aaa and bbb could be switched because they are legs.

Hint #44 / 6

Let's use the Pythagorean Theorem to solve for xxx.

\begin{aligned} \blueD a^2 + \greenD b^2 &= \goldD c^2 ~~~~~~~~~\small\gray{\text{The Pythagorean Theorem}}\\\\ \blueD{a}^2 + \greenD{ 8}^2 &= \goldD{10}^2 ~~~~~~~\small\gray{\text{Plug in the side lengths}}\\\\ a^2 +64 &= 100 ~~~~~~\small\gray{\text{Evaluate } 8^2 \text{ and } 10^2}\\\\ a^2 &= 36~~~~~~~~\small\gray{\text{Subtract 64 from each side}}\\\\ a &= 6 ~~~~~~~~~~\small\gray{\text{Take the square root of each side}}\\\\ \\\end{aligned}

a

2

+b

2

a

2

+8

2

a

2

+64

a

2

a

​

=c

2

         The Pythagorean Theorem

=10

2

       Plug in the side lengths

=100      Evaluate 8

2

 and 10

2

=36        Subtract 64 from each side

=6          Take the square root of each side

​

Hint #55 / 6

Since a=6a=6a, equals, 6 and aaa is half the length of xxx, we can multiply to find xxx.

x x x=a⋅2=6⋅2=12

Hint #66 / 6

x = 12x=12

Answer:

5n and -5n cancel so we're left with -mp + pn which can be factored to p(-m + n).

Answer:

[tex]\frac{6}{5x^{10}}[/tex]

Step-by-step explanation:

Step 1: Simplify square roots

√72 = 6√2

√50 = 5√2

So, [tex]\frac{x^86\sqrt{2} }{x^{18}5\sqrt{2} }[/tex]

Step 2: Cancel like terms

[tex]\frac{6}{x^{10}(5)}[/tex]

Step 3: Rewrite

And we should get our answer!

Answer:

.4

Step-by-step explanation:

Of means multiply

20% * 2

Change to decimal form

.20 * 2

.4

Answer:

c, 106

Step-by-step explanation:

Answer:

106

Step-by-step explanation:

pls mark as brainliest

Answer:

D

Step-by-step explanation:

[tex]\dfrac{\sqrt{4}}{\sqrt{25}}= \\\\\\\dfrac{2}{5}= \\\\\\0.4[/tex]

Hope this helps!

Answer:

17ft/min

Step-by-step explanation:

1865-1525 =  340

multiply the rest by 20 and see which gets 340 ft. so the only correct one is 17ft/min

Answer:

A) All real numbers

B) All real numbers except y = 0

C) All real numbers except x = -7

D) All real numbers except b = 10

Step-by-step explanation:

An expression is defined at all those points at which it does not give the value equal to [tex]\infty[/tex] or does not give the zero by zero form.

i.e. [tex]\frac{0}{0}[/tex] Numerator and Denominator both having zeroes.

Now, let us have a look at the given expressions:

A) 5y+2

Here, Denominator is 1. So, there is no constraint on the value of y.

Hence, at all Real Numbers, the expression is defined.

[tex]B)\ \dfrac{8}{y}[/tex]

Here, denominator is y,

At [tex]y = 0[/tex], the value of expression will approach towards [tex]\infty[/tex]

Hence, this expression is defined at All Real numbers except y = 0

[tex]C)\ \dfrac{1}{x+7}[/tex]

Here, zero by zero form is not possible.

Let us check the value of x where the denominator can be 0 and as a result the expression tends to reach value [tex]\infty[/tex].

x+7=0

At x = -7, the denominator will be 0 and as a result the expression tends to reach value [tex]\infty[/tex].

Hence, the expression is defined at All real number except x = -7

[tex]D) \dfrac{2b}{10-b}[/tex]

Here zero by zero form is not possible.

Let us check the value of b where the denominator can be 0 and as a result the expression tends to reach value [tex]\infty[/tex].

10-b=0

At b = 10, the denominator will be 0 and as a result the expression tends to reach value [tex]\infty[/tex].

Hence, the expression is defined at All real number except b = 10

Answer:

14.97

Step-by-step explanation:

c^2 - a^2 = b^2

18^2 - 10^2 = x^2

324 - 100 = x^2

x^2 = 224

x = 14.97

Answer:

141

Step-by-step explanation:

Given the array of numbers: 1 2 3 4 5 6 7 8 9 10 11 12 ...

These are the set of positive integers.

The number directly above 140 is the next consecutive whole number after 140. This is "the number" 141.

Therefore, 141 is the number that is directly above 140 in this array of numbers.

Answer:

[tex]\frac{1}{7^1}[/tex] or 1/7

Step-by-step explanation:

When you divide exponents (with the same base), you simply just subtract the exponents. Therefore, 14 minus 15 is -1, so you'll get [tex]7^{-1}[/tex]. That simplifies to [tex]\frac{1}{7^1}[/tex] or 1/7.

The people are under thirty years old is 692.

It is required to find the people are under thirty years old.

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

Given:

There are 2076 people at a concert.

One third of the people at the concert are under thirty years old.

According to given question we have,

Total number of people at a concert= 2076

Multiply 2076 by 1/3 we get,

= 1/3*2076

= 692 people were under 30 years old

Therefore, the people are under thirty years old is 692.

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Answer:

The angle at vertex D is acute

Triangle DEF is a right triangle

Step-by-step explanation:

Acute means that the angle is smaller that 90degrees

Correct statement are,

The angle at vertex D is acute.

And, Triangle DEF is a right triangle,

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

We have to given that;

Triangle DEF has a 90° angle at vertex E.

Since, In triangle DEF,

vertex E has 90 degree.

So, Possible value of angle E and F are less than 90 degree

Hence, The angle at vertex D is acute.

And, Triangle DEF is a right triangle,

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