Lock 4 (screen will be blank until you crack the code for lock #3) Awe-sum! You have reached the last lock. Use your equation solving skills to find the value of each variable. Use the values you calculate to help you move along in the puzzle and find all of the missing variables. When you have found all of the variables Imove to the next screen.

Problems:
4a +2= -10
a(2+ b) = -12
-5c+b= 22
7(c+d) = 14
d-c-e= 17

Answers:
a=
b=
c=
d=
e=​

[tex]\displaystyle\\Answer:\ y=\frac{7}{16}x^2 -\frac{7}{4}x-\frac{5}{4}[/tex]

Step-by-step explanation:

The vertex is also the symmetry point of the parabola. The formula for finding the x-coordinate of the parabola: x = -b/2a  (2,-3)

Hence,

[tex]\displaystyle\\2=\frac{-b}{2a} \\[/tex]

Multiply both parts of the equation by -2a:

[tex]\displaystyle\\-4a=b\ \ \ \ \ (1)[/tex]

[tex]y=ax^2+bx+c\ \ \ \ \ -\ \ \ \ \ the\ quadratic\ equation\\\\Thus,[/tex]

You can make a system of equations on two points belonging to the quadratic equation:

[tex]-3=a(2)^2+b(2)+c\\4=a(6)^2+b(6)+c\\\\-3=4a+2b+c\ \ \ \ (2)\\4=36a+6b+c\ \ \ \ (3)\\\\[/tex]

Substitute (1) into equations (2) and (3):

[tex]-3=4a+2(-4a)+c\\4=36a+6(-4a)+c\\\\-3=4a-8a+c\\4=36a-24a+c\\\\-3=-4a+c\ \ \ \ (4)\\4=12a+c \ \ \ \ (5)\\\\\\[/tex]

Subtract equation (4) from equation (5):

[tex]7=16a[/tex]

Divide both parts of the equation by 16:

[tex]\displaystyle\\\frac{7}{16} =a\ \ \ \ (6)[/tex]

Substitute (6) into equations (1):

[tex]\displaystyle\\-4(\frac{7}{16} )=b\\\\-\frac{4*7}{4*4}=b\\\\-\frac{7}{4}=b[/tex]

Substitute values a and b into equation (2):

[tex]\displaystyle-3=4(\frac{7}{16})+2(-\frac{7}{4})+c\\\\ -3=\frac{7}{4} -\frac{14}{4}+c\\\\ -3=-\frac{7}{4}+c \\\\-3+\frac{7}{4}=-\frac{7}{4}+c+\frac{7}{4} \\\\ \frac{-3*4+7}{4} =c\\\\\frac{-12+7}{4}=c\\\\ -\frac{5}{4}=c[/tex]

Thus,

[tex]\displaystyle\\y=\frac{7}{16}x^2 -\frac{7}{4}x-\frac{5}{4}[/tex]

Answer: 16+d>20

d>4

Step-by-step explanation:

d=digs

16+d>20

16-16+d>20-16

d>4

The time at which the truck will pass the car is 2.5 hours and the distance at which the car and truck meet is 200km.

Velocity is defined as the ratio of the distance moved by the object at a particular time. The velocity is a vector quantity so it needs both the magnitude and the direction.

Given that at 2 p.m., a car is 100 km east of Toronto, driving eastward at 80 km/h. A truck leaves Toronto at 2 p.m. and is driving eastward at 120 km/h.

The time will be calculated as:-

Relative velocity = Distance / Time

Time = Distance /  Relative velocity

Time = 100 / 120 - 80

Time = 2.5 Hours

Distance of car = Speed x time = 80 x 2.5

Distance of car = 80 x 2.5

Distance of car = 200 Km

Therefore, the time at which the truck will pass the car is 2.5 hours and the distance at which the car and truck meet is 200km.

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The new balance in Jackie's account after 2 days will be -$27.50.

It should be noted that for each day that her checking account balance falls below zero, she is charged by the bank a fee of $7.50 per day.

Since her current balance in the account is –$12.50, the new balance after 2 days will be:

= -12.50 + (-7.50 × 2)

= -12.50 + -15

= -27.50

The balance is -27.50

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Answer:

5/4 Quotient[24/5] and 6

Step-by-step explanation:

5/4 Quotient[24/5]

Simplify the following:

(4 + 4/5)/(4/5)

Multiply the numerator of (4 + 4/5)/(4/5) by the reciprocal of the denominator. (4 + 4/5)/(4/5) = ((4 + 4/5)×5)/4:

((4 + 4/5)×5)/4

Put 4 + 4/5 over the common denominator 5. 4 + 4/5 = (5×4)/5 + 4/5:

(((5×4)/5 + 4/5) 5)/4

5×4 = 20:

((20/5 + 4/5)×5)/4

20/5 + 4/5 = (20 + 4)/5:

(((20 + 4)/5)×5)/4

20 + 4 = 24:

(24/5×5)/4

24/5×5 = (24×5)/5:

((24×5)/5)/4

((24×5)/5)/4 = (24×5)/(5×4):

(24×5)/(5×4)

(24×5)/(5×4) = 5/5×24/4 = 24/4:

24/4

The gcd of 24 and 4 is 4, so 24/4 = (4×6)/(4×1) = 4/4×6 = 6:

Answer: 6

Answer:

a) y = 6

b) y = 3x + 3

Step-by-step explanation:

a.)

plug 1 into x in the equation:

[tex]-12+4y=12[/tex]

add 12 to both sides to isolate 4y:

[tex]4y=24[/tex]

divide both sides by 4 to simplify x:

[tex]y=6[/tex]     [24/4=6]

b.)

add 12x to both sides to isolate 4y:
[tex]4y=12x+12[/tex]

divide both sides by 4x to simplify x:

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

Point R' is located at (28, -20)

=========================================================

Reason:

The translation rule is [tex](\text{x},\text{y})\to (\text{x}+4,\text{y}-7)[/tex]

It says to add 4 to the x coordinate, and subtract 7 from the y coordinate.

If we apply the rule to point R(24, -13), then we have...

[tex](\text{x},\text{y})\to (\text{x}+4,\text{y}-7)\\\\(24,-13)\to (24+4,-13-7)\\\\(24,-13)\to (28,-20)\\\\[/tex]

This rule shifts the point 4 units to the right and 7 units down.

Step-by-step explanation:

we are calculating miles.

when we have speed, which is mph or miles/hour. what do we have to multiply it with to get miles ? hours !

miles/hour × hour = miles

so, in the function D(x) the speed 60 mph has to be multiplied by the hours spent driving to get the driven miles.

x = hours spent driving

the domain is the interval or set of all valid x (input) values. the range is the interval or set of all valid y (function result) values.

so what are valid x (number of driving hours) values ?

it starts with 0, if course (before actually driving). and it goes up to 4 (after 4 hours the 240 miles are "done").

the domain is

0 <= x <= 4

and the range ? that is all the function result values for the valid x values.

for x = 0 this starts at 240.

and goes down for x = 4 to 0.

the range is

0 <= y (= D(x)) <= 240

The slope between (4, 30) and (12, 90) and between (4, 30) and (10, 75) is the same.

Slope is the 'steepness' of the line, also commonly known as rise over run. slope is dividing the change in the y-value between two points over the change in the x-value.

given co-ordinates:

(4, 30), (10, 75), (12, 90), (22, 165)

Now, the slope between (4, 30) and (12, 90)

m= ( 90-30)/ (12-4)

m= 60 / 8

m = 7.5

and, the slope between (4, 30) and (10, 75)

m= ( 75-30)/ (10-4)

m=45 / 6

m= 7.5

Hence, The slope between (4, 30) and (12, 90) and between (4, 30) and (10, 75) is the same.

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Answer:

Step-by-step explanation:

You want to find f(6) and f(a) when f(x) = 15/(x -3).

To evaluate a function, put the argument where the variable is and simplify as needed.

Put 6 where x is:

  f(6) = 15/(6 -3) = 15/3

  f(6) = 5

Put 'a' where x is:

  f(a) = 15/(a -3) . . . . . . cannot be simplified

Answer:

$100.25 total

100.25-15-20= $65.25 total for three days

For three Dayan three hours so 3*3 = 9 hrs total

65.25/9=7.25

Hence per hour $7.25

Step-by-step explanation:

Selena is right. This relation represents a function.

The set of points given is {(2,-4),(3,-4),(4,-4),(5,-4),(6,-4)}.

We can consider 2, 3, 4, 5, 6 as x-values and -4 as the y-value.

Here, the values 2, 3, 4, 5, 6 are related to -4.

This relation represents a function.

Because no two same x-values are related to different y-values. In other words, different x-values can be mapped to same y-value. But two same x-values should not be related to different y-values for the map to be a function.

So here all the x-values are related to the y-value -4. So this is a many-to-one function.

Function is a relation which maps a particular set of points(Domain) to another set of values(Codomain) through which one domain value has exactly one image in the co-domain.

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Answer:

3/5

Step-by-step explanation:

500 is the money she started with if you put that over the money she spent on vegetables it would be 300/500 when simplified it's 3/5

Reason:

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

The two negatives cancel to form a positive.

Here's how to visualize what's going on: Draw a number line. Plot a marker at -4. Then move 10 units to the right and you should arrive at 6. This visually indicates -4+10 = 6

Another way to visualize: Imagine you are on basement level 4 of a tall building. If you move up 10 floors, then you'll arrive at the 6th floor. We treat the ground floor as floor 0. It might help to draw a vertical number line.

Answer:

Following is the answer for your question your question can be done in this manner.

The correct form of the partial fraction decomposition for given expression 7x+18/x^2+9x is A/x + B/(x + 9)

The correct answer is an option(B)

In this question, we have been given an expression x² + 9x = x (x + 9),

We need to write the correct form of the partial fraction decomposition for given expression.

Suppose, (7x + 18) / (x² + 9x) = A/x + B/(x + 9)

where A and B are some constants.

To find them, multiply both sides by x² + 9x :

7x + 18 = A (x + 9) + Bx

and then we solve for A and B.

Therefore, the correct form of the partial fraction decomposition for given expression 7x+18/x^2+9x is A/x + B/(x + 9)

The correct answer is an option(B)

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Answer:

The correct answer is option B

Step-by-step explanation:

Answer:

x = 10

Step-by-step explanation:

We are given the following equation:

[tex]8x + 5(2x+3) = 195[/tex],

and told to find [tex]x[/tex].

In order to calculate the value of [tex]x[/tex], we have to rearrange the equation to make [tex]x[/tex] the subject:

[tex]8x + 5(2x+3) = 195[/tex]

⇒ [tex]8x + (5 \times 2x) + (5 \times 3) = 195[/tex]       [Distributing 5 into the brackets]

⇒ [tex]8x + 10x + 15 = 195[/tex]

⇒ [tex]18x + 15 = 195[/tex]

⇒ [tex]18x + 15 - 15 = 195 - 15[/tex]       [Subtracting 15 from both sides of equation]

⇒ [tex]18x = 180[/tex]

⇒ [tex]\frac{18}{18}x = \frac{180}{18}[/tex]                  [Dividing both sides of equation by 18]

⇒ [tex]x = \bf 10[/tex]

Therefore, the value of x is 10.

Statistical power is influenced by all of the following except observed test value.

If there is a real effect present to detect, the statistical power of a hypothesis test is the likelihood of finding it. When an experiment is complete, power may be calculated and presented to make comments about how confident one could be in the conclusions taken from the study's results. It may also be employed as a tool to calculate the sample size or the number of observations needed to detect an effect in an experiment. You will learn the significance of a hypothesis test's statistical power in this lesson, and you'll learn how to compute power analyses and power curves as part of an experimental design.

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By using the concept of linear equations, amount of driving when two of these plans cost the same will be at x = 100.

The cost when two plans cost the same is $67.

The linear equation in one variable is written as ax + b = 0, where a and b are two integers and x is a variable. This equation has only one solution.

Given data:

First plan has it in initial fee of $55 and cost an additional $0.12 per mile.

Second plan has an initial fee of $50 in cost an additional $0.17 per mile.

Linear Equation for first plan: f(x) = 55+0.12x

Linear Equation for second plan: s(x) = 50+0.17x

Here, x is a variable.

To find out the distance when the two plans cost the same, we'll need to solve:

55 + 0.12x = 50 + 0.17x

55 - 50 = 0.17x- 0.12x

5 = 0.05x

x = 5/0.05

x = 100

The cost when the two plans cost the same :

f(100) = 55 + 0.12(100)

f(100) = $67

s(100) = 50 + 0.17(100)

s(100) = $67

Hence, two of the plans will cost the same at x=100 and cost will be $67.

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The probability that it was an HH coin is [tex]\frac{1}{50}[/tex]

Conditional Probability P(B/A) is defined as probability of occurrence of B given that A has already occurred  .

Baye's Theorem describes the probability of an event based on conditions that might be related to event .

P(A/B)={P(B/A)*P(A)}/P(B)

Total number of coins =100

Total number of HH coins = 1

P(HH) =Probability of getting HH=1/100

P(H/HH)=Probability of H knowing that HH has already occurred=1

Next to find Probability Of H

We need to find two thing

(i) Probability H appears and is a fair coin= [tex]\frac{1}{2} *\frac{98}{100} =\frac{98}{200}[/tex]

(ii)Probability H appears and is a HH coin = [tex]\frac{1}{100}[/tex]

P(H)= (i)+(ii) =100/200=1/2

BY Baye's Theorem

P(HH|H)={P(H|HH)∗P(HH)}/P(H)

[tex]=\frac{1*\frac{1}{100} }{\frac{100}{200} }[/tex]

[tex]=\frac{2}{100}[/tex]

[tex]=\frac{1}{50}[/tex]

Therefore , The probability that it was an HH coin is [tex]\frac{1}{50}[/tex]

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The solutions associated with each case are listed below:

According to the statement, we find that the two functions are f(x) = x + 2 and g(x) = 2 · x and we are asked to perform on the functions to obtain all resulting expressions and, if possible, to evaluate on each case:

Case 1

(f + g) (x) = f (x) + g (x) = (x + 2) + 2 · x = 3 · x + 2

Case 2

(f - g) (x) = f (x) - g (x) = (x + 2) - 2 · x = 2 - x

Case 3

(f · g) (x) = f (x) · g (x) = (x + 2) · (2 · x) = 2 · x² + 4 · x

Case 4

(f / g) (x) = f (x) / g (x) = (x + 2) / (2 · x) = 1 / 2 + 1 / x

Case 5

(f ° g) (x) = f [g (x)] = 2 · x + 2

Case 6

(g ° f) (x) = g [f (x)] = 2 · (x + 2) = 2 · x + 4

Case 7

(f ° f) (x) = f [f (x)] = (x + 2) + 2 = x + 4

Case 8

(g ° g) (x) = g [g (x)] = 2 · (2 · x) = 4 · x

Case 9

(g ° g) (- 2) = 4 · (- 2) = - 8

Case 10

(f ° f) (- 2) = - 2 + 4 = 2

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We know that an arc is a part of the entire perimeter of a circle.

Radian is defined as a unit of plane angular measurement that is equal to the angle subtended by the circle at the center by an arc that is of the length equal to the radius

We also know that the circle as a whole contains 2π radians

we know that s=rΘ

S=rθ represents the central angle in radians and r is the length of the radius.

Thus we can say that radian measure of an angle theta is the length of the arc.

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The total number of students in Ridgewood Junior High School is 2500 students

It is given that all students in Ridgewood Junior High School either get lunch in the school cafeteria or brought it from home on Tuesday.

No. of students who brought their lunch on Tuesday= 2% = 50 students

Let x be the total number of students in the Ridgewood Junior High School, therefore formulating the equation we get:

2% of x = 50

2/100*x = 50

x = 2500

Total number of students in the school = 2500

Hence, the total number of students in Ridgewood Junior High School is 2500 students

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The correct interpretation regarding the solution of the compound inequality is given as follows:

Drivers located below mile marker 47 or at mile marker 70 or above never get pulled over.

To solve a compound inequality involving the or operation, we solve each inequality, then apply the union operation to their solutions.

In this problem, the following inequalities help us find the miles x in which the drivers are never pulled over.

The solutions are found as follows:

2x - 18 ≥ 122

2x ≥ 140

x ≥ 140/2

x ≥ 70.

5x + 15 < 250.

5x < 235

x < 235/5

x < 47.

Hence the correct option is given by:

Drivers located below mile marker 47 or at mile marker 70 or above never get pulled over.

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Answer:

2/3

Step-by-step explanation:

6 divided by 3 is 2, so you have to divided 4 by 2, which is 2.

Answer:

⅔

Step-by-step explanation:

4 divide by 2 = 2

6 3

therefor 2/3 is equvelet too 4/6.

Hope this helped

The mass of 3 mangoes and 5 oranges together is 5x kg.

Let the mass of mangoes be 'x'

Given the total mass that pawpaw has = a total mass of 8 mangoes

                                                       = 8x

mass of an orange = 2/5 the mass of a mango

                               = 2/5 * x

Now, the mass of 3 mangoes and 5 oranges together as

= 3 * mass of mangoes + 5 * mass of orange

= 3 * x + 5 * 2/5 * x

= 3x + 2x

= 5x kg

The mass of 3 mangoes and 5 oranges together is 5x kg.

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Answer: 10

Step-by-step explanation: 1 1 1 1 1+ 1 1 1 1 1= 1 1 1 1 1 1 1 1 1 1 or 10

Answer:

12 dogs

Step-by-step explanation:

Ratios are scaleable, so let's look at all of the equivalent ratios of 3:2. However it needs to add up to 20 (the sum will be in parenthesis)

3:2 (Sum of 5)

6:4 (Sum of 10)

9:6 (Sum of 15)

12:8 (Sum of 20) ----> Correct Answer