There are two cameras that take pictures of a traffic intersection. Camera A starts taking pictures at 6 AM and takes a picture every 11 minutes. Camera B starts taking pictures at 7 AM and takes pictures every 7 minutes. Camera A and Camera B take a picture at the same time at four different times before noon. When Camera A and Camera B take their last picture together, how many minutes before noon is it?

Answer:

(6x + 9y)(6x - 9y)

Step-by-step explanation:

We can use the difference of squares which states that a² - b² = (a + b)(a - b), in this case, a = 6x and b = 9y so the answer is (6x + 9y)(6x - 9y).

Answer:

The original number could be 85.

Step-by-step explanation:

Let the 2 digits be x and y.

Let the number be xy then, assuming that x is the larger digit:

x - y = 3.

x = y + 3

Also

10y + x + 10x + y = 143

Substituting for x:

10y + y + 3 + 10(y + 3) + y = 143

22y + 33 = 143

22y = 110

y = 5.

So x = y + 3 = 8.

Answer:

➥ 10(x + 3) + x + 10x + x + 3 = 143

➥ 10x + 30 + 12x + 3 = 143

➥ 22x + 33 = 143

➥ 22x = 143 - 33

➥ 22x = 110

➥ x = 110/22

➥ x = 5

The unit digit number = x = 5

The tens digit number = x + 3 = 5 + 3 = 8

The original number = 10(x + 3) + x

The original number = 10(5 + 3) + 5

The original number = 50 + 30 + 5

The original number = 85

Hence,the original number is 85.

Answer:

60 miles per hour.

Step-by-step explanation:

420 miles in 7 hours is the same thing as (420 / 7) = 60 miles per hour.

Hope this helps!

Answer:

60 miles / hour

Step-by-step explanation:

The unit rate will be the number of miles in 1 hour. Therefore, we must divide the miles by the hours.

miles/hours

We know it is 420 miles in 7 hours.

420 miles / 7 hours

Divide 420 by 7

420/7=60

60 miles/ hour

The unit rate is 60 miles per hour.

Answer:

62

Step-by-step explanation:

hope that helps! if it is an answer

The Phrase is: "The resulting number is 62."

We have the expression as

52 + 2x

Now, To evaluate the expression 52 + 2x when x = 5,

we substitute the value of x into the expression and simplify:

=52 + 2(5)

= 52 + 10

= 62.

Thus, The resulting number is 62.

Learn more about Expression here:

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Answer:

360

Step-by-step explanation:

Answer:

[tex]\large \boxed{{x=-3}}[/tex]

Step-by-step explanation:

[tex]{\mathrm{view \ attachment}}[/tex]

Answer:

Difference : 4th option

Step-by-step explanation:

The first thing we want to do here is to factor the expression x² + 3x + 2. This will help us if it is similar to the factored expression " ( x + 2 )( x + 1 ). " The denominators will be the same, and hence we can combine the fractions.

x² + 3x + 2 - Break the expression into groups,

( x² + x ) + ( 2x + 2 ) - Factor x from x² + x and 2 from 2x + 2,

x( x + 1 ) + 2( x + 2 ) - Group,

( x + 2 )( x + 1 )

This is the same as the denominator of the other fraction, and therefore we can combine the fractions.

x - 1 / ( x + 2 )( x + 1 )

As you can see this is not any of the options present, as we have not expanded ( x + 2 )( x + 1 ). Remember previously that ( x + 2 )( x + 1 ) = x² + 3x + 2. Hence our solution is x - 1 / x² + 3x + 2, or option d.

Answer:

3x3÷2= 4.5cm^2

The formula is 1/2×base×slanted height

Step-by-step explanation:

Answer:

Step-by-step explanation:

V = ¹/₃•(¹/₂•10•9)•10 = ¹/₃•45•10 = 15•10 = 150 in²

Answer:

Hi, there!!

Hope you mean the answers in the solution.

Hope it helps...

Answer:

Step-by-step explanation:

7)

JKLM is a isosceles trapezium.

KL // JM

∠K + ∠J =  180   {Co interior angles}

50 +∠J = 180

      ∠J = 180 - 50

      ∠J = 130

As it is isosceles, non parallel sides KJ = LM &  

∠L = ∠K

∠L = 50

∠M = ∠J

∠M = 130

8)JKLM is a isosceles trapezium.

KL // JM

∠K + ∠J =  180   {Co interior angles}

100 +∠J = 180

      ∠J = 180 - 100

      ∠J = 80

As it is isosceles, non parallel sides KJ = LM &  

∠L = ∠K

∠L = 100

∠M = ∠J

∠M = 80

Answer: [tex]y=\dfrac12x-\dfrac{3}{4}[/tex]

Step-by-step explanation:

Given, The equation of line WX is 2x + y = −5.

It can be written as [tex]y=-2x-5[/tex] comparing it with slope-intercept form y=mx+c, where m is slope and c is y-intercept, we have

slope of WX = -2

Product of slopes of two perpendicular lines is -1.

So, (slope of WX) × (slope of perpendicular to WX)=-1

[tex]-2\times\text{slope of WX}=-1\\\\\Rightarrow\ \text{slope of WX}=\dfrac{1}{2}[/tex]

Equation of a line passes through (a,b) and has slope m:

[tex]y-b=m(x-a)[/tex]

Equation of a line perpendicular to WX contains point (−1, −2) and has slope [tex]=\dfrac12[/tex]

[tex]y-(-2)=\dfrac{1}{2}(x-(-1))\\\\\Rightarrow\ y+2=\dfrac12(x+1)\\\\\Rightarrow\ y+2=\dfrac12x+\dfrac12\\\\\Rightarrow\ y=\dfrac12x+\dfrac12-2\\\\\Rightarrow\ y=\dfrac12x-\dfrac{3}{4}[/tex]

Equation of a line perpendicular to line WX in slope-intercept form that contains point (−1, −2) [tex]:y=\dfrac12x-\dfrac{3}{4}[/tex]

Step-by-step explanation: Ants are one of the most abundant insects on our planet and the reasons are their eusocial, complex societal behaviors and their ability to survive in many and various ecosystems. Like most other animal societies, reproduction is one of the core reasons why ants are so prevalent.

Acrobat Ant

Reproduction for ants is a complex phenomenon that involves finding, selecting and successfully fertilizing females to ensure that the eggs laid are able to survive and molt through the successive stages of the ant’s life cycle – larvae, pupae and adults.

Answer:

81

Step-by-step explanation:

Start: 50

After 1 day: 50 * 1.1

After 2 days: 50 * 1.1 * 1.1 = 50 * 1.1^2

After 3 days: 50 * 1.1^2 * 1.1 = 50 * 1.1^3

...

After 5 days: 50 * 1.1^5 = 80.53

Answer: 81

Answer:

Step-by-step explanation:

Volume of the can is expressed as Length *Breadth* Height.

If the area of the can base is Length * Breadth

Volume of the can = area of the base of the can * Height

Given parameters

Volume of the can V = 3416.32cm³

Height of the can h = 17cm

Required

Area of the base of the can

Substituting the given parameters into the formula we have;

V = Ah

A = V//h

A = 3416.32/17

A = 200.96cm²

Hence, the area of the base of the can is 200.96cm²

Answer:

Length of diagonal = 6

Step-by-step explanation:

Given that

Diagonal of a rectangle makes an angle of [tex]30^\circ[/tex] with the longer side.

Kindly refer to the attached diagram of the rectangle ABCD such that diagonal BD makes angles of [tex]30^\circ[/tex] with the longer side CD and BA.

[tex]\angle CDB =\angle DBA =30^\circ[/tex]

Side AD = BC = 3 units

To find:

Length of diagonal BD = ?

Solution:

We can use the trigonometric ratio to find the diagonal in the [tex]\triangle BCD[/tex] because [tex]\angle C =90^\circ[/tex]

Using the sine :

[tex]sin\theta = \dfrac{Perpendicular }{Hypotenuse }[/tex]

[tex]sin\angle CDB = \dfrac{BC}{BD}\\\Rightarrow sin30^\circ = \dfrac{3}{BD}\\\Rightarrow \dfrac{1}2 = \dfrac{3}{BD}\\\Rightarrow BD =2 \times 3 \\\Rightarrow BD = \bold{6 }[/tex]

So, the answer is:

Length of diagonal = 6

6:40 or 6 hour 40 minutes,

if you go back(subtract) 1 hour and 40 minutes

i.e. 6hours 40 minutes- 1 hour 40 minutes

subtract minutes from minutes and hours from hours,

5:00

note that here the minutes value is not negative so it was not a problem, what If it was 6:40-1:50?

Answer:answer=A

Step-by-step explanation: 3×3×3×2×2=72

Answer:

YUP THEY RIGHT

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hello, when you try to find the intersection point(s) you need to solve a system like this one

[tex]\begin{cases} y&= m * x + p }\\ y &= a*x^2 +b*x+c }\end{cases}[/tex]

So, you come up with a polynomial equation like.

[tex]ax^2+bx+c=mx+p\\\\ax^2+(b-m)x+c-p=0[/tex]

And then, we can estimate the discriminant.

[tex]\Delta=(b-m)^2-4*a*(c-p)[/tex]

If [tex]\Delta<0[/tex] there is no real solution, no intersection point.

If [tex]\Delta=0[/tex] there is one intersection point.

If [tex]\Delta>0[/tex] there are two real solutions, so two intersection points.

Hope this helps.

Answer:

3, 10, 1080

Step-by-step explanation:

A coefficient, is the number that is multiplying a variable, such as x. A constant is any other number, not multiplying a variable.

For part one, the number multiplying the variable x is 3, so 3 is the coefficient.

For part two, the only number not multiplying a variable is the 10, so that is the constant.

To find how many miles she drove, we first need to subtract the first 30 dollars from the final payment.

300-30=270

We than need to divide 270 by .25, because that is how much it costed per mile.

270/.25=1080

Answer:

In the first question shown, the answer is 3

In the second question shown, the answer is 10

In the third question shown, the answer is 1080 miles

Step-by-step explanation:

First question - 3 is the number before x, making it the coefficient

Second question - 10 is the only number without a variable, making it a constant

Third question - .25 * 1080 = 270. 270 + 30 = 300.

Answer:

vertex(-3,27)

Step-by-step explanation:

f(x)= x^2+ 6x + 36 ( a=1,b=6,c=36)

V(h,k)

h=-b/2a=-6/2=-3

k=f(-3)=3²+6(-3)+36

f(-3)=9-18+36=27

vertex(-3,27)

Answer:

f(1) = 11

Step-by-step explanation:

f(x) = 3x + 8

Let x=1

f(1) = 3(1) +8

    = 3+8

   = 11

Answer:

See below.

Step-by-step explanation:

There is an infinite n umber of systems of equations that has (1, 4) as its solution. Are you given choices? Try x = 1 and y = 4 in each equation of the choices. The set of two equations that are true when those values of x and y are used is the answer.

Answer:

96 possible outcomes

Step-by-step explanation:

2 x 6 x 8 = 96

Answer:

Step-by-step explanation:

Since the sequence is a geometric sequence

For an nth term in a geometric sequence

[tex]A (n) = a ({r})^{n - 1} [/tex]

where

a is the first term

r is the common ratio

n is the number of terms

To find the eighth term we must first find the first term

4th term = 108

common ratio = 3

That's

[tex]A(4) = a ({r})^{4 - 1} [/tex]

[tex]108 = a ({3})^{3} [/tex]

[tex]27a = 108[/tex]

Divide both sides by 27

For the eighth term

[tex]A(8) = 4 ({3})^{8 - 1} [/tex]

[tex]A(8) = 4({3})^{7} [/tex]

The final answer is

Hope this helps you

Answer:

$2.

Step-by-step explanation:

This is because the base price is $12, which means the constant is 12. The toppings are the only things you can add to the pizza, so the price of each additional topping is the slope of the pizza's cost. The slope is 2 dollars.

Hope this helps!

Answer:

2

Step-by-step explanation:

If we were to write a linear equation in slope-intercept form (y = mx + b where m = slope and b = y-intercept) of this situation, it would be y = 2x + 12 where y is the price and x is the number of toppings. This is because the price for every topping is 2x but the base price doesn't change, therefore it's a constant so it would be + 12. In this case, since m = slope, the slope is 2.

Answer:

Clyde is 49.74 away from the harbor

Step-by-step explanation:

Here in this question, we are interested in knowing the distance of Clyde from the harbor.

The key to answering this question is having a correct diagrammatic representation. Please check attachment for this.

We can see we have the formation of a right angled triangle with the distance between Clyde’s ship and the harbor the hypotenuse.

To calculate the distance between the two, we shall employ the use of Pythagoras’ theorem which states that the square of the hypotenuse is equal the sum of the squares of the two other sides.

Let’s call the distance we want to calculate h.

Mathematically;

h^2 = 25^2 + 43^2

h^2 = 625 + 1849

h^2 = 2474

h = √2474

h = 49.74 miles

The vertical line test helps us see that we have a function. Note how it is not possible to draw a single straight line through more than one point on the curve. Any x input leads to exactly one y output. This graph passes the vertical line test. Therefore it is a function.

The function is not one-to-one because the graph fails the horizontal line test. Here it is possible to draw a single straight horizontal line through more than one point on the curve. The horizontal line through y = 2 is one example of many where the graph fails the horizontal line test, meaning the function is not one-to-one.

The term "one-to-one" means that each y value only pairs up with one x value. Here we have something like y = 2 pair up with multiple x values at the same time. This concept is useful when it comes to determining inverse functions.

Answer: 2

Step-by-step explanation:

Given: Shaquira has made 86  chocolate chip cookies and 42 sugar cookies.

Shaquira wants to create identical packages of cookies to sell, and she must use all of the cookies.

Now, the greatest number of identical packages that Shaquira can make= GCD of 86 and 42

Prime factorization of 86 and 42:

86 = 2 ×43

42 = 2 × 3 × 7

GCD of 86 and 42 = 2   [GCD = greatest common factor]

Hence, the greatest number of identical packages that Shaquira can make =2

Answer:

1) 0.3 ; 0.7

Step-by-step explanation:

Given the following :

Probability that product A launch : P(A) = 0.45

Probability that product B launch : P(B) = 0.60

Probability that both product launch : P(AnB) = 0.35

P(A alone) = p(A) - p(AnB)

P(A alone) = 0.45 - 0.35 = 0.1

P(B alone) = p(B) - p(AnB)

P(B alone) = 0.60 - 0.35 = 0.25

Probability that neither product will launch :

1 - [p(A alone) + p(B alone) + p(AnB)]

1 - [0.1 + 0.25 + 0.35]

1 - 0.7 = 0.3

Probability that at least one product will launch :

P(A alone) + p(B alone) + p(AnB)

0.1 + 0.25 + 0.35 = 0.7

Answer:

[tex]-2 \geq w \geq 2[/tex]

Step-by-step explanation:

Given

[tex]|-w| \geq 2[/tex]

Required

Solve for w

[tex]|-w| \geq 2[/tex]

In absolution functions;

[tex]|-w| = |w|[/tex]

So, the given expression can be rewritten as

[tex]|w| \geq 2[/tex]

Removing the absolute sign, will gibe

[tex]w \geq 2[/tex] or [tex]w \leq -2[/tex]

When the second inequality os rewritten, it gives

[tex]w \geq 2[/tex] or [tex]-2 \geq w[/tex]

Reorder both inequalities

[tex]-2 \geq w[/tex] or [tex]w \geq 2[/tex]

Lastly, both inequalities are combined

[tex]-2 \geq w \geq 2[/tex]

Answer:

362880 ways

Step-by-step explanation:

Given

10 digits

Required

Number of 10 digits that can be formed if no repetition and 2 must always start;

Since digit 2 must always start and no repetition is allowed, then there are 9 digits left

Digit 2 can only take 1 position

9 digits can be arranged without repetition in 9! ways;

Calculating 9!

[tex]9! = 9 * 8 *7 * 6 * 5 * 4 * 3 * 2 * 1[/tex]

[tex]9! = 362880[/tex]

Number of arrangement  = 1 * 362880

Number of arrangement  = 362880 ways