The probability of guessing on four true and false questions and getting all four questions correct

Answer :

Explaination :

Here we are given with two equations,

So in order to calculate the number of hours (h). We would simply substitute the value of f in first equation. (i.e., keeping them equal)

>> 7h + 20 = 10h + 5

>> 10h - 7h = 20 - 5

>> 3h = 15

>> h = 15 / 3

>> h = 5

The solutions to the equations are (1.702,4.7) and (-4.7,-1.7).

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

The two given equations ( x + 3 ) and ( 13 ( x+5)(x-1) intersects at the ponits (1.702,4.7) and (-4.7,-1.7).

The graph of the above equations is attached with an answer.

Therefore the solutions to the equations are (1.702,4.7) and (-4.7,-1.7).

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Answer:

1) As it is the coeficient of x² is 1, we need to find two numbers whose Sum S(x)=3 and the same numbers whose product is 2, P(x)= 2

S(x) = (  ) + (  ) =3

P(x) = (   )  *  (   ) =2

S(x) = ( 2 ) + ( 1 ) =3

P(x) = (  2 )  *  ( 1  ) =2

These numbers in bold will be coeficients of x.

Rewrite the Trinomial x²+ 3x +2 as x² +2x+1x+2

So x²+3x+2 =x²+2x+1x+2

x² +2x+x+2   Put the x in evidence

x(x+2)+1(x+2)  Find the Maximum Common Divider

(x+1)(x+2)

2) x²+x-6=0

Applying the same procedure. Which two integer number whose sum is 1 and whose Product is -6?

S(x) = ( 3  ) + ( -2  ) =1

P(x) = ( 3  )  * ( -2  ) =-6

Rewrite

x²+x-6

x²+3x-2x-6      Group them

x(x+3)-2(x+3)   Common Term

(x+3)(x-2)

3) Since the a coeficient is ≠ 1, a little adjustment must be made on our algorithm for -2x²+4x+30=0

Firstly multiply a*c, in this case -2 * 30 = -60

Which two numbers multiplied by themselves will turn out to be -60 and whose sum is -60? Since we're working with integers factoring out may be very helpful.

P(x)=  ( 10  )  *   ( - 6 )  = -60

S(x) = (  10 )  +  (  -6 )  = 4

Rewriting

-2x²+10x-6x+30   Group them

2x(x+5) -6(x+5)

(2x-6)(x+5)   Inserting the -1 to finally adjust

-1(2x-6)(x+5)

4) Explanation is the same principle as a≠1

3x²+4x-4=0

P(x) = ( 6  )  *  (-2  ) = -12

S(x) = (  6 ) +  ( -2  )  = 4

3x²+4x-4 = 3x²+6x-2x-4

3x²+6x -2x+4

3x(x+2)-2(x-2)

(3x-2)(x+2)

The other ones are just applications of these, above.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

the circumference (C) of a circle is calculated as

C = 2πr = πd ( d is the diameter and d = 2r ) , then

C = πd = 3.14 × 26 = 81.64 in

Answer:

56.31 degrees

Step-by-step explanation:

6 = opposite and 4 = adjacent

Tan = opposite over adjacent

Tan(theta)=6/4

=56.30993247

Answer: (a) 8 : 15 (b) 8 : 7

Step-by-step explanation: all marbles is 8+7 = 15

ratio of blue marbles to ALL marbles

8 : 15

ratio of blue marbles to red

8 : 7

Answer: 3 hours

Step-by-step explanation:

Bottle = 3.6 liters / 3600 milliliters

Rate = 20 ml a minute

3600 / 20 = 180 minutes

60 minutes = 1 hour

180 / 60 = 3 hours

The area of the training field to the nearest whole number is 8719 msq. meter

The given field is made up of a rectangle and 2 semi circles. The formula for calculating the area of the field is:

Area of the field = area of circle + area of rectangle

Area of field = 3.14(32)² + (86)(64)
Area of field = 3215.36 + 5504

Area of the field = 8719 msq. meter

Hence the area of the training field to the nearest whole number is 8719 msq. meter

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Answer:

Ok hello my name is Christopher and I have already done this and the answer is (6,-7)

Step-by-step explanation:

Two polygonal regions are similar with scale factor 7, if the area of the smaller region is 490 cm² then the area of the larger region would be 3430 cm²

An equation is an expression that shows the relationship between two or more numbers and variables.

Dilation is the increase or decrease in the size of a figure by a scale factor.

Two polygonal regions are similar with scale factor 7. The area of the smaller region is 490 cm², hence:

Area of larger region = 7 * 490 cm² = 3430 cm²

Two polygonal regions are similar with scale factor 7, if the area of the smaller region is 490 cm² then the area of the larger region would be 3430 cm²

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Answer:

Step-by-step explanation:

x + 3 = -x - 1

2x + 3 = -1

2x = -4

x = -2

y = -2 + 3

y = 1

(-2, 1)

answer is A

[tex]y=f(x)= \dfrac x 3 \\\\\text{Replace x with y and then solve for y,}\\\\~~~~x = \dfrac y 3\\\\\implies y = 3x \\\\\implies f^{-1}(x) =3x[/tex]

Answer:

Parameter

Step-by-step explanation:

A statistic is a piece of data we derive from analyzing the data from a sample, a subset of a larger population. A parameter is derived from analyzing that population. Here, we would call the mean of the sample - 4 - a statistic, and the mean of the population - 4.3 - a parameter.

Answer:

Because -4 is 4 units away from 0.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer: -17/4

Step-by-step explanation:

Answer:

V = 2143.57

Step-by-step explanation:

To find the volume of a sphere you need to use this formula:

[tex]V = \frac{4}{3}\pi r^{3}[/tex]

r = radius

Solve:

You need the radius from the diameter. Divide 16/2 which is

8.

[tex]V = \frac{4}{3}(3.14) 8^{3}[/tex]

V = 2143.57

answer: 15

steps:

i means √-1

but in this problem treat

i like x

(7-i) + (5 + 3i) - (-3 + 2i) =

(7-i) + (5 + 3i) +3 - 2i

7-i + 5 + 3i +3 - 2i =

7-i + 5 + 3i +3 - 2i

7+5+3-i+3i-2i

7+5+3+2i-2i

7+5+3 =

15

Answer:

y=x-7

Step-by-step explanation:

Rise over run

-6-(-7)

---------- = 0

-4-(-4)

Point Slope form

y+7=0(x+4)

Y=MX + B

y=x-7

The equation of the line passing through the points (−4,−7) and (−4,−6) in the form of a will be a + 4 = 0.

Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).

Then the equation of the line is given as,

[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]

The equation of the line passing through the points (−4,−7) and (−4,−6) will be

y + 6 = [(−6 + 7) / (−4 + 4)] (x + 4)

y + 6 = (1/0)(x + 4)

x + 4 = 0

Put x = a, then the equation will be

x + 4 = 0

a + 4 = 0

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The midpoint approximation of the area under the curve f(x) = 2x(x-4)(x-8) over the interval [0, 4] with 4 subintervals is 132.

The value of f(1/2) will be:

= 2(1/2)(1/2 - 4)(1/2 - 8)

= 105/4

The value of f(3/2) will be:

= 2(3/2)(3/2 - 4)(3/2 - 8)

= 195/4

The value of f(5/2) will be:

= 2(5/2)(5/2 - 4)(5/2 - 8)

= 165/4

The value of f(7/2) will be:

= 2(7/2)(7/2 - 4(7/2 - 8)

= 63/4

Therefore, the midpoint approximation will be:

= 1/4(105 + 195 + 165 + 63)

= 132

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Step-by-step explanation:

that kind of wording is always misleading.

please give my regards and comments to your teacher.

a square root has ALWAYS 2 solutions : a positive AND a negative one.

in that sense the negative solution to a square root is NOT an extraneous solution.

only any value of x < -10 (to make the argument of the square root negative) as solution would be extraneous.

so, if your teacher wants to say that only the positive solutions of a square root are allowed, it has to be said as an extra definition or by applying the "+" sign to the square root.

so,

x + 4 = sqrt(x + 10)

since the 2 solutions are already given to us, we only need to use them in the equation and see what happens.

x = -1

-1 + 4 = sqrt(-1 + 10)

3 = sqrt(9) = 3 (actually, it is ±3)

so, x = -1 is a real solution.

x = -6

-6 + 4 = sqrt(-6 + 10)

-2 = sqrt(4) = 2 (actually, it is ±2)

so, based on your teacher's expectation of only positive results of the square root (even though it was not stated),

x = -6 is an extraneous solution.

therefore, the third answer (c) is the "correct" answer.

but actually, formally, the second answer (b) is the truly correct answer.

Volume of a Rectangular Prism = length x width x height

Length = 4

Width = 2

Height = a

Volume = 7.2

7.2 = 4 x 2 x a

7.2 = 8 x a

a = 0.9

Answer: a = 0.9

Hope this helps!

Answer:

a = 0.9 cm

Step-by-step explanation:

Volume of a rectangular prism: L*W*H

Substitute the values above into the formula:

V = L*W*H

7.2 = 4*2*a

7.2 = 8a

/8     /8

0.9 = a

Therefore, the value of a is 0.9 cm.

Hope this helps!

Answer:

( 4u + a ) + ( y + 6 )

Step-by-step explanation:

4u(y+6) + a(y+6) ...

The answer is ( 4u + a ) + ( y + 6 )

Answer:

1.5 gallons

Step-by-step explanation:

(3/4) × (2 gallons) = 1.5 gallons

HOPE THIS HELPS AND HAVE A NICE DAY <3

Using a system of equations, it is found that they expect to sell 175 adult tickets and 350 student tickets.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

They expect that twice as many students as adults will attend, hence:

s = 2a.

Their goal is to earn $1,500 from ticket sales, hence:

10a + 5s = 1500.

10a + 5(2a) = 1500.

20a = 1500.

a = 1500/20.

a = 175.

s = 2a = 2 x 175 = 350.

They expect to sell 175 adult tickets and 350 student tickets.

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Answer:

D.

Step-by-step explanation:

it should be the sales tax because you pay a little bit more.

Answer:

  33°

Step-by-step explanation:

Where a transversal crosses parallel lines at right angles, all of the angles at their points of intersection are right angles.

__

Angles at U are right angles, congruent to ∠UXZ. So, acute angle UXW in right triangle UXW is the complement of acute angle UWX:

  ∠UXW = 90° -57° = 33°

Answer:

2 cups

Step-by-step explanation:

Formula: divide the volume value by 16

so its 32 divided by 16

Answer:

Geary street :D

they intersect here

click on the photo. it's not a link it's a screenshot of where they intersect