Lily helped Mr Cruz cross the road earlier today. After a short introduction of themselves, Lily found out that she is 50 years younger than Mr Cruz. Given that Mr Cruz will be 6 times as old as Lily in 4 years, how old is Mr Cruz now?

Answer:

log base(6) [tex]\frac{z^{2}y^{3} }{w^{10} }[/tex]

Step-by-step explanation:

log base(6) [tex]\frac{z^{2}y^{3} }{w^{10} }[/tex]

Answer:

d= 4[tex]\sqrt{2}[/tex] or 5.66

Step-by-step explanation:

(-2,7) and (2,3)

d = [tex]\sqrt{(x2-x1)^{2} + (y2-y1)^{2} }[/tex]

d= [tex]\sqrt{(2-(-2))^{2} + (3-7)^{2} }[/tex]

d = [tex]\sqrt{16 + 16}[/tex]

d= 4[tex]\sqrt{2}[/tex] or 5.66

Answer: (1, 2)

Step-by-step explanation:

y = -x² + x + 2

y = -x + 3

1. Set the two equations equal to each other:

-x² + x + 2 = -x + 3

2. move one of the equations to the other side:

-x² + 2x - 1

3. Factor out a -1:

-1 (-x² + 2x - 1) = 0

x² - 2x + 1

4. Factor:

(x - 1)(x - 1)

x = 1

5. Plug in 1 to one of the equations:

y = -x + 3

y = -(1) + 3

y = 2

6. Write as coordinates:

(1, 2)

The correct answers: tan 120= -√3.

The correct answer is (E)

Angles are the angles between  bisecting lines or surfaces at or near their meeting point.

Given : [tex]\theta\\[/tex] = 2π/3

               = 2*180/3= 120

So, First and the fourth statement is not correct.

and, cos 120= -1/2

sin 120= √3/2

So, B and D statement is also wrong

tan 120= -√3.

Hence, the only correct statement is tan 120= -√3.

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Answer:

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

Step-by-step explanation:

We were given to points on the line we are trying to find, hence we are able to determine the slope/gradient.

[tex]( - 1, \: 1) \: and \: (1, \: 7) \\ slope = \frac{ {y}^{2} - {y}^{1} }{ {x}^{2} - {x}^{1} } \\ \\ s = \frac{7 - 1}{1 - ( - 1)} \\ s = \frac{6}{2} [/tex]

Slope is equal to 3.

Since we have the value for the slope, we can now use one of the points on the line to determine the equation of the line.

note that the coefficient of x is the slope. In this case the A from the standard form (Ax + By= C) is the slope.

[tex] \\ let \: us \: use \: the \: point \: ( - 1, \: 1) \\ a = 3 \: \: \: \: y = 1 \: \: \: x = - 1\\ ax + by = c \\ 3( - 1) + 1 = c \\ - 3 + 1 = c [/tex]

[tex] - 2 = c \\ therefore \: the \: equation \: of \: the \\ \: line \: is \\ ax + by = c \\ 3x + y = - 4[/tex]

Answer:

y=1/2x+1= A

y=-2x-4= C

x-2= E

y=-3= F

y=1/2x+3.5=B

I hope this helps

Step-by-step explanation:

Answer:

-102.1

Step-by-step explanation:

When adding negative numbers, act as if you are subtracting that same number, but in its positive form.

So in reality, you could rewrite the equation as: (-7.8) - 12 - 82.3 = -102.1

22.5 = 1.5x

x = 22.5/1.5

x = 15

hope it helps...!!!

Answer:

x = 15

Step-by-step explanation:

1.5x = 22.5

x = 22.5/1.5

assuming your finding x

Answer:

A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on the ordered pair 3, 8.

Step-by-step explanation:

Finding the solution of these 2 equations

Equating them :

Substitute in a equation to find y :

The solution is (3, 8).

The 1st explanation is the correct one.

Answer:

d =5

Step-by-step explanation:

d = [tex]\sqrt{(x2-x1)^2 + (y2-y1)^2}[/tex]

at (1,5), (5,2)

d= [tex]\sqrt{(5-1)^2 +(2-5)^2}[/tex]

[tex]d = \sqrt{16 + 9} \\d=\sqrt{25}\\ d =5[/tex]

Therefore 5 is the distance.

Answer:

C

Step-by-step explanation:

calculate the distance d using the distance formula

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

with (x₁, y₁ ) = (1, 5 ) and (x₂, y₂ ) = (5, 2 )

d = [tex]\sqrt{(5-1)^2+(2-5)^2}[/tex]

   = [tex]\sqrt{4^2+(-3)^2}[/tex]

    = [tex]\sqrt{16+9}[/tex]

    = [tex]\sqrt{25}[/tex]

    = 5

Answer:

Step-by-step explanation:

3y-9x=9

3y-9x+9x=9+9x

3y=9x+9

y=3x+3

If a line is perpendicular to an equation, the slope is flipped.

So, 3x would equal to -3x.

The final equation is y=-3x+3

Answer:

(a) The number of accidents was reduced by 0.67 per month for every additional 100 drivers in the program.

Step-by-step explanation:

We are given the options,

(a) The number of accidents was reduced by 0.67 per month for every additional 100 drivers in the program.

(b) The number of accidents was reduced by 0.67 per month every month.

(c) The number of accidents increased by 0.67 per month for every additional 100 drivers in the program.

(d) There were 0.67 accidents per month.

We can eliminate option 'c' because the accidents are obviously not increasing, but rather, decreasing. We can also eliminate option 'd' (which to a certain extent is rather vague) because there is a trend in the data. If there were only 0.67 accidents per month (which is impossible anyway), then the graph would be that of [tex]y=0.67[/tex] which is indeed a straight line. Finally, we can eliminate option 'b' because the x-axis isn't in terms of months, but drivers in the program. This leaves 'a' as the only logical answer, which we can see is true because the graph trends downward (hence the negative slope) by about 0.67 per 100 drivers. With a bit of understanding about the problem, we can eliminate the illogical answers to find the correct one!

Note: you may be wondering why the slope isn't just -0.67, but that is because then it would go down by 0.67 for each driver in the program. Therefore, the slope was divided by 100 to yield us a slope of -0.0067 which makes it go down 0.67 per 100 drivers instead of only 1 driver.

Answer:

24.49 units

Step-by-step explanation:

It si NOT a right triangle, so you'll have to use law of sines

angle C = 180 - 45-75 = 60 degrees

30 / sin60 =  AC / sin 45

AC = 30 * sin 45 / sin 60 = 24.49 units

Answer:

f(2)=x

Step-by-step explanation:

Number one you did not give enough information for me to solve the question but from what you did provide I got the answer which is provided above

Answer:

5 dimes and 10 nickels

Step-by-step explanation:

0.1d + 0.05n = 1

d + n = 15

d + 0.5n = 10

d + n = 15

0.5n = 5

n = 10

d + n = 15

d + 10 = 15

d = 5

Answer: 5 dimes and 10 nickels

Answer:

Step-by-step explanation:

Step-by-step explanation:

Firstly find the area if the parallelogram which is

=length of the base × vertical height

=

[tex]12m \times 5m[/tex]

=

[tex]60 {m}^{2} [/tex]

Now solve for the area of the circle

=

[tex]\pi {r}^{2} [/tex]

RADIUS = DIAMETER ÷2

[tex] \frac{4m}{2} [/tex]

=

[tex]2m[/tex]

so the area of the circle

=

[tex] \frac{22}{7} \times 2m \times 2m[/tex]

[tex] \frac{22}{7} \times 4 {m}^{2} [/tex]

[tex]12.57 {m}^{2} [/tex]

subtract the area of the circle from the parallelogram

=

[tex]60 {m }^{2} - 12.57 {m}^{2} [/tex]

=

[tex]47.43 {m}^{2} [/tex]

Done

⇒ open circle at (-2, 5) with a line to the left

⇒ closed circle at (-2, 3) with a line segment to an open circle at (0, 3)

⇒ closed circle at (0, 0) with a line segment to an open circle at (2, 0)

⇒ closed circle at (2, -3) with a line to the right

Answer:

5

___    

y+5

Step-by-step explanation:

first

---->         3y                    2(y+5)

       ---------------------- +   ----------

         (y+2)(y+5)              (y+2)(y+5)  

then

---->   3y+2(y+5)

          ------------

          (y+2)(y+5)

then

---->  3y+2y+10

       ----------

        (y+2)(y+5)

then

-----> 5(y+2)

        ---------

        (y+2)(y+5)

then

-----> 5

     -------

       y+5

Answer:

2664.3

Step-by-step explanation:

The volume of a sphere is

V = 4/3 πr³

Multiply the radius (which is the diameter divided by 2), 8.6 by itself 3 times, and them multiply it by pi and 4/3 to achieve a volume of 2664.31 or aproximatley 2664.3.

Answer:

v=59 m3 i think if it helps please mark brainliest

(i) 47 * 1 = 47

Why? This is because the Multiplication Identity Property states that any number w multiplied by 1 is equal to w

(ii) 135 * 0 = 0

Why? The Zero Property of Multiplication states that 0 multiplied by any number is 0.

(iii) 3 * 5 = 5 * 3

Why? The order numbers are multiplied in does not impact the answer's value according to the Commutative Property of Multiplication

(iv) 7 + 0 = 7

Why? The Zero Property of Addition states that 0 added to any number x is equal to x

(v) 125 * 315 - 125 * 215 = 125 * (315 - 215) = 12500

Why? The Distributive Property states that a * c - a * b = a * (c - b).

Answer:

B. 11

Step-by-step explanation:

Hope this helps! ;-)

Answer:

11

Step-by-step explanation:

15-12/3

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction

15-4 = 11

Answer:

x = 30º

Step-by-step explanation:

Let's call the midpoint of OP, R.

The triangle of OQR would be an equilateral triangle since OQ = OR as they are both radii and is OQR and ORQ are 60º, ROQ is also 60º, making the triangle equilateral. Because tangents meet a circle at 90º, the angle RQP would be 30º and since angles on a straight line add to 180º, the angle QRP would be 180-ORQ which is 120º. Now we know the 2 angles in triangle of QRP so we can work out the final angle since angles in a triangle add to 180º. So:

180 - 120 - 30 = 30º.

x = 30º

This would also prove that QR and RP are the same since base angles in an isosceles triangle are equal.

Answer:

B and C are both in slope-intercept-form.

Step-by-step explanation:

Slope Intercept Form is --> y = mx + b, where m is the slope, and b is the y-intercept.

Both B and C have a slope (-6/4 for B, -3/2 for C) and both have a y-intercept (8/4 or 2).

I hope this helps. Please mark me brainliest!

Answer:

the dimensions of the rectangle are 34cm and 15cm

Step-by-step explanation:

proof:

p= (2 × 34) + (2 × 15)

=68 + 30

= 98

hope this helps!!

Answer: 34x15

Step-by-step explanation:

A rectangle

Knowing the properties of a rectangle, the opposite sides are equal and parallel.

Determine formula

Since both sides are equal, our formula is [tex]((2(3x-1))*2)+((2x+3)*2)=98[/tex]

Solve for X

Side 1:

[tex]((2(3x-1))*2)[/tex]

[tex]((6x-2)*2)[/tex]

[tex](12x-4)[/tex] simplified

Side 2:

[tex]((2x+3)*2)[/tex]

[tex](4x+6)[/tex] simplified

Solve:

[tex](12x-4) + (4x+6) = 98[/tex]

[tex]16x+2=98[/tex]

[tex]16x=96[/tex]

[tex]\frac{16x}{16} = \frac{96}{16}[/tex]

[tex]x = 6[/tex]

Substitute x

[tex]2(3(6)-1) = 34[/tex]

[tex](2(6)+3) = 15[/tex]

The dimensions of this rectangle are 34x15.

The expression that represents the volume of the cone is one-third pi r squared h = one-third (4) squared (8).

A cylinder is a three-dimensional object. It is a prism with a circular base. A cone is a three-dimensional object made up of a circular base and a vertex.

volume of a cylinder = πr²h

= pi x r² x 7

volume of a cone = 1/3  πr²

= 1/3 pi x 4² x8

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Answer:

A is Correct

Step-by-step explanation:

Answer:

h(x) = x³ + 4x² - 49x - 196

Step-by-step explanation:

h(x) = (x² - 49)(x + 4) <== distribute

h(x) = x²(x) - 49(x) + x²(4) - 49(4)

h(x) = x³ - 49x + 4x² - 196 <== rewrite in standard form (descending degrees)

h(x) = x³ + 4x² - 49x - 196

Hope this helps!

Answer:

7x²a(x + a)

Step-by-step explanation:

7x³a = 7 * x * x * x * a

7x²a² = 7 *x * x * a *a

Common factor = 7x²a

So we have to take the common factor from the two terms

7x³a + 7x²a² = 7x²a ( x + a)