Tony gets paid $5 per hour to babysit his cousin. This weekend, he babysat on
both Saturday and Sunday. He made a total of $55. Tony babysat for 6 hours on
Sunday. For how many hours did he babysit on Saturday?
Let x = hours spent babysitting on Saturday. Choose the equation and
solution steps that correctly represent this problem.

Answer:

x = -8

I hope this helps!

Answer:

m∠C = 102°

Step-by-step explanation:

This diagram is a Quadrilateral inscribed in a circle

The first step is to determine what m∠B

is

The sum of opposite angles in an inscribed quadrilateral is equal to 180°

m∠D + m∠B = 180°

m∠B = 180° - m∠D

m∠B = 180° - 80°

m∠B = 100°

Second step is we proceed to determine the exterior angles of the circle

m∠ADC = 2 × m∠B

m∠ADC = 2 × 100°

m∠ADC = 200°

m∠ADC = m∠CD + m∠AD

m∠AD = m∠ADC - m∠CD

m∠AD = 200° - 116°

m∠AD = 84°

The third step is to determine m∠BAD

m∠BAD = m∠AD + m∠AB

m∠BAD = 84° + 120°

m∠BAD = 204°

The final step Is to determine what m∠C is

It is important to note that:

m∠BAD is Opposite m∠C

Hence

m∠C = 1/2 × m∠BAD

m∠C = 1/2 × 204

m∠C = 102°

Answer:

164

Step-by-step explanation:

B for brackets

O for of

D for division

M for multiplication

A for addition

S for subtraction

You first start with the brackets (20) and multiply with 4 which is equal to 80 and then add it to 84 which makes 164

I hope this helps

Answer:Yes, because all integers have decimals. No, because integers do not have decimals. No, because integers cannot be negative. Jeremy says that 5.676677666777... is a rational number because it is a decimal that goes on forever with a pattern.

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

Required

State if the product of rational numbers and integer is an integer

The statement is false and the proof is as follows

Literally, rational numbers are decimal numbers that can be represented as a fraction of two integers;

Take for instance: 0.2, 0.5, 2.25, etc.

When any of these numbers is multiplied by an integer, the resulting number can take any of two forms;

1. It can result to an integer:

For instance;

[tex]0.2 * 5 = 1[/tex]

[tex]0.5 * 4 = 2[/tex]

[tex]2.25 * 8 = 18[/tex]

2. It can result in a decimal number

For instance;

[tex]0.2 * 3 = 0.6[/tex]

[tex]0.5 * 5 = 2.5[/tex]

[tex]2.25 * 7 = 15.75[/tex]

From (1) above, we understand that the product can result in an integer.

Hence, the statement is false

Answer: plot a point at (-8, -5)

The y coordinate flips from positive to negative, or vice versa, when we reflect over the horizontal x axis. The x coordinate stays the same.

The rule can be written as [tex](x,y) \to (x,-y)[/tex]

Answer:

x = 150 feets

Step-by-step explanation:

Given that,

The height of a building model is 2% of its actual height.

The building model is 3 feet tall, h = 3 feet

We need to find the height of the actual building. Let it is x.

According to question,

h = 2% of x

We have, h = 3 feet

So,

[tex]x=\dfrac{h}{2\%}\\\\x=\dfrac{3}{2/100}\\\\x=150\ \text{feet}[/tex]

So, the actual height of the building is 150 feets.

Answer:

[tex]\frac{(^3_1)*(^{37}_4)}{(^{40}_5)}[/tex]

Step-by-step explanation:

The total number of ways in which 5 specimens can be selected from the  dish at random is given as C(40, 5).

Since only one of the five specimens would have the trait, the number of ways of selecting the one specimen out of the 3 specimens with the trait is C(3, 1).

3 specimens have the trait therefore 37 specimens (40 - 3) do not have the trait. The number of ways in which the remaining 4 specimens out of the 5 spemimens that do not have the trait is C(37, 4).

Therefore, the probability that only 1 of the 5 specimens selected will have the trait = [tex]\frac{C(3,1)*C(37,4)}{C(40,5)} =\frac{(^3_1)*(^{37}_4)}{(^{40}_5)}[/tex]

Answer:

Step-by-step explanation: Multiply

70000000000*50000000000000=3.5e+24

Answer:

[tex]\large \boxed{1296}[/tex]

Step-by-step explanation:

6 raised to 4 indicates that the base 6 has an exponent or power of 4.

[tex]6^4[/tex]

6 is multiplied by itself 4 times.

[tex]6 \times 6 \times 6 \times 6[/tex]

[tex]=1296[/tex]

[tex](-3+5,10-7)=(2,3)[/tex]

Answer:

u should put this also in English then type it in so it will translate

Answer:

  x ≥ -4/5

Step-by-step explanation:

Maybe you want to solve ...

  4x+4 ≤ 9x +8

  0 ≤ 5x +4 . . . . . subtract 4x+4

  0 ≤ x +4/5 . . . . . divide by 5

  -4/5 ≤ x . . . . . . . subtract 4/5

Answer:

x ≥−4/5

Step-by-step explanation:

Answer:

11 adults and 16 children

Step-by-step explanation:

a + c = 27 and 4a + c = 60

3a = 60 - 27 = 33

a= 11  

so c = 16

Answer:

The equation for the circle 12 seconds after the anchor is dropped is x^2 + y^2 = 360,000

Step-by-step explanation:

To find the equation for the circle 12 seconds when the radius of the ripple increases at a rate of 50 cm/s, the circle radius will be;

50 * 12 = 600 cm

Then place the equation inform of Pythagoras equation which is;

x^2 + y^2 = r^2

Where r is the radius

x^2 + y^2 = 600^2

x^2 + y^2 = 360,000

Then, the equation for the circle 12 seconds after the anchor is dropped is x^2 + y^2 = 360,000

Answer:

When radius is doubled:

Circumference becomes double.

Area becomes four times.

When diameter is doubled:

Circumference becomes double.

Area becomes four times.

Step-by-step explanation:

Given that

Radius of a circle is doubled.

Diameter of circle is doubled.

To study:

The effect on circumference and area on doubling the radius and diameter.

Solution/explanation:

Let us discuss about the formula for circumference and area.

Formula for Circumference of a circle in form of radius:

[tex]C =2\pi r[/tex]

It is a linear equation in 'r'. So by doubling the radius will double the circumference.

Formula for Area of a circle in form of radius:

[tex]A =\pi r^2[/tex]

It is a quadratic equation in 'r'. So by doubling the radius will make the area as four times the earlier area.

Testing using example:

Let the initial radius of a circle = 7 cm

Initial circumference = [tex]2 \times \frac{22}{7} \times 7 = 44 cm[/tex]

Initial area = [tex]\frac{22}{7} \times 7 \times 7 =154 cm^2[/tex]

After doubling:

Radius = 14 cm

circumference = [tex]2 \times \frac{22}{7} \times 14 = 88 cm[/tex]   (Twice the initial circumference)

area = [tex]\frac{22}{7} \times 14 \times 14 =616 cm^2[/tex] (4 times the initial area)

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

Formula for Circumference of a circle in form of Diameter:

[tex]C =\pi D[/tex]

It is a linear equation in 'D'. So by doubling the diameter will double the circumference.

Formula for Area of a circle in form of diameter:

[tex]A =\dfrac{1}{4}\pi D^2[/tex]

It is a quadratic equation in 'D'. So by doubling the Diameter will make the area as four times the earlier area.

Testing using example:

Let the initial diameter of a circle = 28 cm

Initial circumference = [tex]\frac{22}{7} \times 28 = 88 cm[/tex]

Initial area = [tex]\frac{1}{4}\times \frac{22}{7} \times 28 \times 28 =616cm^2[/tex]

After doubling:

Diameter = 56 cm

circumference = [tex]\frac{22}{7} \times 56= 176 cm[/tex]   (Twice the initial circumference)

area = [tex]\frac{1}{4}\times \frac{22}{7} \times 56 \times 56 =2464cm^2[/tex] (4 times the initial area)

So, the answer is justified:

When radius is doubled:

Circumference becomes double.

Area becomes four times.

When diameter is doubled:

Circumference becomes double.

Area becomes four times.

Answer:

Hey there!

X+Y=0.

For example, two numbers that are equally far from the 0 on a number line are -2 and 2.

-2+2=0

Hope this helps :)

Answer:

x + y = 0

Step-by-step explanation:

Since the two values are the same distance from zero on the number line (i.e., they are equivalent in distance) and one is in the negative direction, and the other is in the positive direction, then the sum of both will be zero.

Since they are the same distance, just opposite in direction, it requires the same amount of "hops" for both values to reach zero, hence they will cancel each other out when added together.

Consider, -1 and 1.  Both are the same distance from 0; however, if you add them together (-1 + 1) you'll get the sum to be 0.

Cheers.

Answer:

Step-by-step explanation:

Given the expression 4sinB = 3sin(2A+B), we are to show that the expression 7cot(A+B) = cotA

Starting with the expression

4sinB= 3sin(2A+B)

Let us re write angle B = (A + B) - A

and 2A + B = (A + B) + A

Substituting the derived expression back into the original expression ww will have;

4Sin{(A + B) - A } = 3Sin{(A + B)+ A}

From trigonometry identity;

Sin(D+E) = SinDcosE + CosDSinE

Sin(D-E) = SinDcosE - CosDSinE

Applying this in the expression above;

4{Sin(A+B)CosA - Cos(A+B)SinA} = 3{Sin(A+B)CosA + Cos(A+B)sinA}

Open the bracket

4Sin(A+B)CosA - 4Cos(A+B)SinA = 3Sin(A+B)CosA + 3Cos(A+B)sinA

Collecting like terms

4Sin(A+B)CosA - 3Sin(A+B)cosA = 3Cos(A+B)sinA + 4Cos(A+B)sinA

Sin(A+B)CosA = 7Cos(A+B)sinA

Divide both sides by sinA

Sin(A+B)CosA/sinA= 7Cos(A+B)sinA/sinA

Since cosA/sinA = cotA, the expression becomes;

Sin(A+B)cotA = 7Cos(A+B)

Finally, divide both sides of the resulting equation by sin(A+B)

Sin(A+B)cotA/sin(A+B) = 7Cos(A+B)/sin(A+B)

CotA = 7cot(A+B) Proved!

Answer:

m = 0, P(3)/2, P(4)/6, P(5)/12 ..........

Step-by-step explanation:

For non zero polynomial, that is all real x as follows:

x = 1, 2, 3, 4 ............

Using, P(1 + x) = P(1 - x)

For x = 1: P(2) = P(0) = 1

For x = 2: P(3) = P(-1) = 2

Hence, P(x)/m(x - 1) can be solved as follows:

When = 1

P(2)/0 = 1

∴ m = 0

When x = 2

P(3)/m = 2

∴ m = P(3)/2

When x = 3

P(4)/2m = 3

∴ m = P(4)/6

When x = 4

P(5)/3m =  4

∴ m = P(5)/12

Hence, m = 0, P(3)/2, P(4)/6, P(5)/12......

The correct answer is D. ​No because the permutations rule would be used to determine the total number of combinations.

Explanation:

The difference between a combination and a permutation is that in permutations the order is considered. This applies to the numbers in a lock because these need to be in order. Therefore, to analyze the permutations in a lock, the rule for permutations should be used. This includes the general formula P (n,r) =[tex]\frac{n!}{(n-r) !}[/tex]; in this, n is the number of objects and r refers to the objects used in a permutation. Thus, the term "combination" is inappropriate because this is a permutation, and the permutation rule should be used.

Answer:

£23.96

Step-by-step explanation:

Area to be painted:

3.6 m * 8.3 m = 29.88 m^2

The area to be painted is 29.88 m^2.

A tin of paint covers 8 m^2. We divide to find the number of tins needed.

29.88/8 = 3.735

Since full tins must be bought, the smallest number of tins needed is 4.

Now we find the price of 4 tins. 1 tin costs £5.99, so 4 tins cost:

4 * £5.99 = £23.96

A.

[tex]|\Omega|=6\\|A|=3\\\\P(A)=\dfrac{3}{6}=\dfrac{1}{2}[/tex]

B.

[tex]|\Omega|=8\\|A|=3\\\\P(A)=\dfrac{3}{8}[/tex]

C.

[tex]|\Omega|=4\\|A|=1\\\\P(A)=\dfrac{1}{4}[/tex]

D.

[tex]|\Omega|=24\\|A|=5\\\\P(A)=\dfrac{5}{24}[/tex]

E.

[tex]|\Omega|=10\\|A|=10\\\\P(A)=\dfrac{10}{10}=1[/tex]

F.

[tex]|\Omega|=10\\|A|=0\\\\P(A)=\dfrac{0}{10}=0[/tex]

Answer:

2.6 miles

Step-by-step explanation:

1 hour 26 minutes= 86 minutes

86-34=52 total walk time

52 minutes= 5*1/2 miles

=2.5 miles walked

and 2 minutes.

so we need to find 1/5 of 1/2

(1/2)/5=0.1 mile

2.5+0.1=2.6 miles

Answer:

Step-by-step explanation:

When you draw out that picture (and very good description, btw!) basically what you have is a right triangle that has a base of 32 and a hypotenuse of 45. The right angle is one of the base angles and x is the vertex angle. We need to find the vertex angle before we can find the angle of depression from the second bird to the watcher. The side of length 32 is opposite the angle x, and 45 is the hypotenuse, so the trig ratio we need is the only one that directly relates side opposite to hypotenuse, which is the sin ratio:

[tex]sin(x)=\frac{32}{45}[/tex] and

sin(x) = .711111111

Go to your calculator and hit the 2nd button then the sin button and on your screen you will see:

[tex]sin^{-1}([/tex]  

and after that open parenthesis enter in your decimal .711111111 and hit equals. You should get an angle of 45.325. That's angle x. But that's not the angle of depression. The angle of depression is the one complementary to angle x.

Angle of depression = 90 - angle x and

Angle of depression = 90 - 45.325 so

Angle of depression = 44.67 or 44.7 degrees.

Answer:

Its 45.3!!!

Step-by-step explanation:

Answer:

k=0

Step-by-step explanation:

[tex]k+(2-5k)(6)=k+12\\k-30k+12=k+12\\12-12=29k+k\\0=30k\\k=0[/tex]

Answer:

k=0

Step-by-step explanation:

Answer:

(-2, 4, 2)

Where x = -2, y = 4, and z = 2.

Step-by-step explanation:

We are given the system of three equations:

[tex]\displaystyle \left\{ \begin{array}{l} 4x -y -2z = -8 \\ -2x + 4z = -4 \\ x + 2y = 6 \end{array}[/tex]

And we want to find the value of each variable.

Note that both the second and third equations have an x.

Therefore, we can isolate the variables for the second and third equation and then substitute them into the first equation to make the first equation all one variable.

Solve the second equation for z:

[tex]\displaystyle \begin{aligned} -2x+4z&=-4 \\ x - 2 &= 2z \\ z&= \frac{x-2}{2}\end{aligned}[/tex]

Likewise, solve the third equation for y:

[tex]\displaystyle \begin{aligned} x+2y &= 6\\ 2y &= 6-x \\ y &= \frac{6-x}{2} \end{aligned}[/tex]

Substitute the above equations into the first:

[tex]\displaystyle 4x - \left(\frac{6-x}{2}\right) - 2\left(\frac{x-2}{2}\right)=-8[/tex]

And solve for x:

[tex]\displaystyle \begin{aligned} 4x+\left(\frac{x-6}{2}\right)+(2-x) &= -8 \\ \\ 8x +(x-6) +(4-2x) &= -16 \\ \\ 7x-2 &= -16 \\ \\ 7x &= -14 \\ \\ x &= -2\end{aligned}[/tex]

Hence, x = -2.

Find z and y using their respective equations:

Second equation:

[tex]\displaystyle \begin{aligned} z&=\frac{x-2}{2} \\ &= \frac{(-2)-2}{2} \\ &= \frac{-4}{2} \\ &= -2\end{aligned}[/tex]

Third equation:

[tex]\displaystyle \begin{aligned} y &= \frac{6-x}{2}\\ &= \frac{6-(-2)}{2}\\ &= \frac{8}{2}\\ &=4\end{aligned}[/tex]

In conclusion, the solution is (-2, 4, -2)

Answer:

x = -2

y =4

z=-2

Step-by-step explanation:

4x−y−2z=−8

−2x+4z=−4

x+2y=6

Solve the second equation for x

x = 6 -2y

Substitute into the first two equations

4x−y−2z=−8

4(6-2y) -y -2 = 8  

24 -8y-y -2z = 8

-9y -2z = -32

−2(6-2y)+4z=−4

-12 +4y +4z = -4

4y+4z = 8

Divide by 4

y+z = 2

z =2-y

Substitute this into -9y -2z = -32

-9y -2(2-y) = -32

-9y -4 +2y = -32

-7y -4 = -32

-7y =-28

y =4

Now find z

z = 2-y

z = 2-4

z = -2

Now find x

x = 6 -2y

x = 6 -2(4)

x =6-8

x = -2

Answer:

7 8 9

Step-by-step explanation:

The dilation rule (x,y) --> (1.5x, 1.5y) says to multiply each coordinate by the scale factor 1.5

Point A in blue is located at (5,5). After dilation, it will move to A ' (7.5, 7.5)

Point B is located at (0,2) and it moves to B ' (0,3)

Point C is located at (1,-1) and it moves to C ' (1.5, -1.5)

This all matches with what is shown below, so the answer is choice B

Answer:

6

Step-by-step explanation:

To calculate x+10, we first need to find x. To do this, we can use the first equation.

We are given the equation:

[tex]x^2-8x=48[/tex]

To solve for x, turn one side of the equation into 0 and solve. Therefore:

[tex]x^2-8x=48\\x^2-8x-48=0\\(x-12)(x+4)=0\\x=-4, 12[/tex]

So, the possible values for x are -4 and 12.

However, we are also told that x<0. In other words, x must be negative. Thus, we can remove 12. That leaves us with: x=-4.

So:

[tex]x+10\\(-4)+10\\=6[/tex]