The outdoor temperature, in degrees Fahrenheit, is recorded at noon for ten consecutive school days. The measurements were as follows:37°, 42°, 38°, 26°, 35°, 25°, 38°, 34°, 28°, 23°

Answer:

Option B is correct

Step-by-step explanation:

Doug is x years old, so Byron is x+3 years old. The product of their ages would then be x times x+3:

x(x+3) = 40

x2 + 3x = 40

x2 + 3x + 40 = 0

Now, factor the equation:

(x+8)(x-5) = 0

Then, solve for both values of x:

x+8 = 0

x = -8

x-5 = 0

x = 5

As no one can have a negative age, we simply disregard x=-8 as invalid. Therefore, Doug is 5 years old & Byron must be 5+3 - or 8 years old.

Answer:

Doug is 10 years old; option A

Step-by-step explanation:

set up expressions using the information you already know:

B (byron)

D (doug)

B = D + 3

B * D = 40

you can now solve by plugging in an expression for the variable B in the second equation.  

D + 3 * D = 40

D + 3D = 40

(combine like terms)

4D = 40

(divide by 4 on both sides to isolate the variable and balance the equation)

4D/4 = 40/4

D = 10

So, the answer is A; Doug is 10 years old

Answer:

221

Step-by-step explanation:

Substitute x = 7 and y = 8 into the expression

5(7)² - 3(8)

= 5(49) - 24

= 245 - 24

= 221

Answer:

C

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

it the only one that make sense

Answer:

-2/5

Step-by-step explanation:

( -8/ 125) ^ 1/3

We know (a/b) ^ 1/3 = a^ 1/3  / b^1/3

( -8) ^ 1/3  / ( 125) ^ 1/3

Rewriting

( -2^3) ^ 1/3  / ( 5^3) ^ 1/3

We know that a^b^c = a^(b*c)

-2^(3* 1/3)  / 5^(3 * 1/3)

-2 / 5

Answer:

-2/5

Step-by-step explanation:

Step-by-step explanation:

Let the increase in the size of the length and breath be 'x'.

The area of the rectangle = 12in × 8in

=96 in²

From the question,

(12+x)(8+x)=96×2 in²

or, 96+12x+8x+x²= 192

or, x²+20x+96-192=0

or, x²+20x-96=0

or, x²+24x-4x-96=0

or, x(x+24)-4(x+24)=0

or, (x-4)(x+24)=0

Either, Or,

x-4=0 x+24=0

Therefore, or, x= –24 (Which is impossible)

x=4

So the new dimensions are 12+4=16 inch and 8+4=12 inch.

Answer:

[tex]gradient = - 3 \\ y = mx + c \\ 2 = ( - 3 \times 0) + c \\ c = 2 \\ \therefore \: y = - 3x + 2 \\ y = 2 - 3x[/tex]

Answer:

8

Step-by-step explanation:

Answer:

Hi, there your answer is 4

Step-by-step explanation:

Answer:

$600

Step-by-step explanation:

I = 2000(.15)(2)

I = 600

Answer:

C. [tex] 2 y^2 [/tex]

Step-by-step explanation:

[tex]( {3} \degree {y}^{2} ) \times \: 2(xy) \degree \\={3} \degree {y}^{2} \times \: 2\times x \degree\times y \degree \\=1 {y}^{2} \times \: 2\times 1\times 1 \\ = {y}^{2} \times 2 \\ = 2 {y}^{2} [/tex]

Answer:

7√3

Step-by-step explanation:

tan 60° = x/7

√3 = x/7

x = 7√3

Answer:

x = 20.

Step-by-step explanation:

First, you should remember the relation:

Distance = Speed*Time.

First, we know that a man travels a distance of 20km at a speed of x km/h, in a time T.

We can write this as:

20km = (x km/h)*T

We know that the time is shortened by 12 minutes if the speed is increased by 5km/h

Rewriting these 12 minutes in hours (remember that 60min = 1 hour)

12 min = (12/60) hours = 0.2 hours

Then from this, he can travel the same distance of 20km in a time T minus 0.2 hours if the speed is increased by 5 km/h

We can write this as:

20km = (x + 5 km/h)*(T - 0.2 h)

Then we have a system of two equations, and we want to find the value of x:

20km = (x km/h)*T

20km = (x + 5 km/h)*(T - 0.2 h)

First, we should isolate the variable T in one of the equations, if we isolate it in the first one, we will get:

20km/(x km/h) = T

Replacing that in the other equation we get:

20km = (x + 5 km/h)*(T - 0.2 h)

20km = (x + 5 km/h)*( 20km/(x km/h) - 0.2 h)

Now we can solve this for x.

Removing the units (that we know that are correct) so the math is easier to read, we get:

20 = (x + 5)*(20/x - 0.2)

We only want to solve this for x.

20 = x*20/x - x*0.2 + 5*20/x - 5*0.2

20 = 20 - 0.2*x + 100/x - 1

subtracting 20 in both sides we get:

20 - 20 = 20 - 0.2*x + 100/x - 1 - 20

0 = -0.2*x + 100/x - 1

If we multiply both sides by x we get:

0 = -0.2*x^2 + 100 - x

-0.2*x^2 - x + 100 = 0

This is just a quadratic equation, we can solve it using the Bhaskara's equation, the solutions are:

[tex]x = \frac{-(-1) \pm \sqrt{(-1)^2 - 4*(-0.2)*100} }{2*-0.2} = \frac{1 \pm 9 }{-0.4}[/tex]

Then the two solutions are:

x = (1 + 9)/-0.4 = -25

x = (1 - 9)/-0.4 = 20

As x is used to represent a speed, the negative solution does not make sense, so we should use the positive one.

x = 20

then the average speed initially is 20 km/h

Answer:

7.1 in

Step-by-step explanation:

A triangle adds up to 180 degrees, and we know angle S is 90 degrees, so angle U is 180-90-42=48 degrees.

Using the law of Sines, we can say that

sin(90)/9.5 = sin(48)/ side ST

Thus, side ST = sin(48) * 9.5/sin(90) = 7.1 in

Answer:

infinitely many solutions

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

It is a 30, 60, 90 triangle

if the leg on the same side as the 90 degree angle is [tex]14\sqrt{3}[/tex], then:

The base is 14, and the hypotenuse is 28

In this type of triangle:

the base [tex]\sqrt{3}[/tex] is the other leg

and 2 times the base is the hypotenuse

so x=14, and y=28

Answer D

Answer:

$1.50

Step-by-step explanation:

25% of 6 is basically just 6/4, which is 1.5.

This is money we're talking about, so the answer is $1.50

Answer:

second option : the side length was multiplied by 5.

Step-by-step explanation:

a = side length of the original square

A² = a×a

(a+5)×(a+5) = a² + 10a + 25

and that should be equal to a²×25

a² + 10a + 25 = 25a² ?

10a + 25 = 24a²

no, that is not true for all a

a×5 × a×5 = a²×25 = 25A²

this is the correct solution, as it is true for all a.

For the area to be  25a², the side length was increased by 5.

Let a be the side length of the original square, hence:

A = a²

Increasing the length by 5 will give:

(a+5)×(a+5) = a² + 10a + 25

Factorizing the result

a² + 10a + 25 = (a+5)²

a² + 10a + 25 = 25a²

This shows that for the area to be  25a², the side length was increased by 5.

Learn more on area of square here: https://brainly.com/question/25092270

Answer:

let kiran's age be x

kiran's father's age is 65

acc.to ques

kiran's father is 8 years older than 3 times kiran's age ....which gives us the equation as follows

8+3x =65

therefore

3x =65-8

3x =57

x =57/3

x= 19 ans

so kiran's age is 19 years.

Answer:

kiran is 19 years old.

Step-by-step explanation:

kiran's father age = 65

let kiran's age be x

kiran's father is 8 years older than three times kiran's age means 8 + 3x

so according to the question equation is

65 =  8 + 3x

65 - 8 = 3x

57/3 = x

19 = x

therefore kiran's age is 19 years.

Answer:

Step-by-step explanation:

tan x = 5.6/9.7

tan x = 0.57732

x = 29.9 to nearest tenth

I hope I'm correct if not I tried my best

bye :-)

Answer:

37 1/2 miles

Step-by-step explanation:

1. 3 3/4 + 2 1/2 = 6 1/4

2. 6 1/4 x 6 = 37 1/2

Answer:

(3 , 0 )

Step-by-step explanation:

At x-axis, y-co ordinate is 0

So, (3,0)

Answer: (3, 0)

Step-by-step explanation: The x-intercept is a point where a line crosses the x-axis and it's important to understand that all x-intercepts have a y-coordinate of zero. So the point (3, 0)  is the x-axis.

In the picture below, I have plotted a few points including the point

in this problem to show you that all x-intercepts have a y-coordinate of zero.

Answer:

f/9

Step-by-step explanation:

n + 5/5 = f + 9/9

do cross multiplication

5(f+9)=9(n+5)

5f+45=9n+45

5f=9n+45-45

5f=9n+0

f/9 = n/5

Answer:

I think its C

Step-by-step explanation:

Answer:

b =  2

Step-by-step explanation:

hope it works

Answer

IS 2/4

Step-by-step explanation:

1/3 = 4/12  1/4 = 3/12  4/12+3/12= 6/12 = 2/4

Answer:

{x,y}={5,-3}

Step-by-step explanation: