find the missing term of each pair of equivalent ratio 95:15= ____:42 show steps please
and

98:112=63_____

Answer:

k=6

Step-by-step explanation:

We are given a graph of the function f(x) and g(x) such that both the graphs are parabola and the graph of g(x) is a shift of graph of f(x) some units to the left.

The vertex of the graph of f(x) is at x=4

whereas the vertex of the graph of the function g(x) is at x= -2.

This means that the graph of g(x) is a shift of the graph of f(x) 6 units to the left.

This means that:

g(x)=f(x+6)

( Since the translation of a function f(x) k units either to the left or to the right is denoted by:

f(x+k)

when k>0 the shift is to the left and if k<0 the shift is to the right.)

This means that the value of k is 6

Let's call the first unknown integer x and the second one y.

"Four times an unknown integer"

"Multiplied by three times the unknown integer plus a different unknown integer"

"Equals 100."

And so the answer is C: 12x²+4xy-100=0

12x²+4xy-100=0. The equation that represents the statement of the problem is 12x²+4xy-100=0.

The equation is represents by  "Four times an unknown integer, multiplied by three times the unknown integer plus a different unknown integer, equals 100."

First, we have the statement "four times an unknown integer", this is:

4x

Then, multiplied by three times the unknown integer plus a different unknown integer, that is:

4x(3x+y)

And finally, the equation above is equals to 100.

4x(3x+y)=100

Operating

(4x)(3x)+(4x)(y)=100

12x²+4xy=100

Then,  subtracting 100 on both sides of the equation.

12x²+4xy-100=100-100

Obtaining

12x²+4xy-100=0

Answer:

Step-by-step explanation:

600 minus 399 is 201

The trip will take at least two days given the car's mileage limit per tank and the daily driving limit.

To determine how long a journey will take with the given constraints, we first need to understand the limitations. The car can run for 399 miles on one tank of gas, and the maximum you can drive in one day is fixed at 600 miles. Since the daily maximum driving distance is greater than the mileage per tank, the limiting factor is the gas tank range.

Assuming you start with a full tank, you would need to refill once you've driven 399 miles. If there is no wait time for refilling and the efficiency of the car does not change, you could potentially drive for another 399 miles after refilling. However, due to the 600 miles per day limit, you would need to stop before exhausting your second tank. To find out the total driving time, divide the total distance by the daily driving limit (if the total distance is larger than what can be covered in one day).

For example, if the total trip is 700 miles, it would take at least two days because you can cover 600 miles on the first day and the remaining 100 miles on the second day. However, this does not account for any potential stops, breaks, or other delays.

The equations that have the same solution set are equations 1, 3, 5, and 6.

To determine which equations have the same solution set without solving them, we can analyze the equations and identify any properties that indicate equivalent solutions. Let's examine each equation:

1. WIN + 1 = 6x

2. 4 - 6x + 1 = 3

3. 6x - x = 6x

4. 4 - x + 1 = 6x

5. x = 6x

6. 5 = 30x

7. 5 = 42x

Equations with the same solution set:

- Equations 1 and 3 both have the term "6x" on one side and a different expression on the other side. They indicate that the solution for x is the same.

- Equations 5 and 6 both have the same equation "x = 6x", which implies the solution for x is the same.

Therefore, the equations that have the same solution set are equations 1, 3, 5, and 6.

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Answer:

The correct answers are

Step-by-step explanation:

1 2 6

Answer:

q

Step-by-step explanation:

The equation of a line in the form

y = mx ( m is the slope ) passes through the origin

y = 2x is in this form

The only graph to pass through the origin is q

This problem can be solved using probability, the equation of the probability of an event A is P(A)= favorable outcomes/possible outcomes. The interception of two probable events is P(A∩B)= P(A)P(B).

There are 12 black marbels, 10 red marbles, and 18 white marbels, all the same size. If two marbles are drawn from the jar without being replaced.

The total of the marbles is 40.

If two marbles are drawn from the jar without being replaced, what would the probability be:

1. of drawing two black marbles?

The probability of drawing one black marble is (12/40). Then, the probability of drawing another black marble after that is (11/39) due we drawing one marble before.

P(Black∩Black) = (12/40)(11/39) = 132/1560, simplifying the fraction:

P(Black∩Black) = 11/130

2. of drawing a white, then a black marble?

The probability of drawing one white marble is (18/40). Then, the probability of drawing then a black marble after that is (12/39) due we drawed one marble before.

P(White∩Black) = (18/40)(12/39) = 216/1560, simplifying the fraction:

P(White∩Black) = 9/65

3. of drawing two white marbles?

The probability of drawing one white marble is (18/40). Then, the probability of drawing another white marble after that is (17/39) due we drawed one marble before.

P(White∩White) = (18/40)(17/39) = 306/1560, simplifying the fraction:

P(White∩White) = 51/260

4. of drawing a black marble, then a red marble?

The probability of drawing one black marble is (12/40). Then, the probability of drawing then a red marble after that is (10/39) due we drawed one marble before.

P(Black∩Red) = (12/40)(10/39) = 120/1560, simplifying the fraction:

P(Black∩Red) = 1/13

Answer:

The range of the function is [0 , ∞) ⇒ answer B

Step-by-step explanation:

* lets revise the meaning of the domain and the range

- The domain is the values of x

- The domain is all the values of x which make the function is defined

- If there are some values of x make the function undefined, we

 exclude these values from the domain

- The range is the values of f(x) which corresponding to the value of x

* Now lets look to the figure

∵ f(x) = √x

- We can not use the negative values for x because there is no

 square root for negative numbers

∴ All real negative numbers make the function undefined

- We must exclude them from the domain

∴ The domain is all real numbers greater than or equal zero

∴ x ≥ 0

- To find the range use the first value of the domain

∵ the first value of x = 0

∴ f(0) = √0 = 0

∵ x can not be negative

∵ f(x) = √x

∴ f(x) can not be negative

∴ the range is all real numbers greater than or equal zero

∴ f(x) ≥ 0

OR

f(x) = [0 , ∞)

* The range of the function is [0 , ∞)

The answer is:

The correct option is the second option:

[tex]\frac{5}{2},\frac{-1}{2}[/tex]

We are given the following expression:

[tex]\frac{2+-\sqrt{9}}{2}[/tex]

Now, solving we have:

First solution:

[tex]\frac{2+\sqrt{9}}{2}=\frac{2+3}{3}=\frac{5}{2}[/tex]

Second solution:

[tex]\frac{2-\sqrt{9}}{2}=\frac{2-3}{3}=\frac{-1}{2}[/tex]

Hence, we have that the correct option is the second option:

[tex]\frac{5}{2},\frac{-1}{2}[/tex]

Have a nice day!

Answer:

The correct answer is second option

5/2, -1/2

Step-by-step explanation:

From the attached figure we can see that,

(2 ± √9 )/2

To find the simplified form of (2 ± √9 )/2

(2 ± √9 )/2 = (2 + √9 )/2 or (2 - √9 )/2

(2 + √9 )/2 = (2 + 3)/2 = 5/2

(2 - √9 )/2 =  (2 - 3)/2 = -1/2

Therefore simplified form of (2 ± √9 )/2 are

5/2 and -1/2

The correct answer is option 2

Answer:

(5,6)

Step-by-step explanation:

First, count how many units are between b and c, that is 10, half of that is 5 units because they want the mid point so we divided by 2 but now you are going to count 5 units from point b so the y value isn't isn't 5. So from b, count 5 units upwards which lands at 6 so that is the y value. Now you move from their to the right to touch the line (if you understand what i mean) and that would fall at the value of 5. so x is equal 5. Coordinate: (x,y)=(5,6). Hopefully that helped.

The midpoint of the line BC is (5,6).

The midpoint of a line segment is the point equidistant from its endpoints. It is calculated as the average of the x-coordinates and y-coordinates of the endpoints.

Midpoints are crucial in geometry for construction, line segment division, and coordinate geometry. They play roles in physics, engineering, and bisection problems, contributing to spatial reasoning and problem-solving.

The midpoint M of a line segment with endpoints B(x₁, y₁) and C(x₂, y₂) is calculated as:

M = (x₁ + x₂)/2, (y₁ + y₂)/2.

So, for points B(2, 1) and C(8, 11) the midpoint is:

M(2 + 8)2, (1 + 11)/2

= 10/2, 12/2

= (5, 6).

The midpoint of the line BC is (5,6).

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Answer:

Common difference = 5.

Step-by-step explanation:

General term of an arithmetic sequence is a1 + (n - 1)d where a1 = first term and d = common difference.

So here the first term is  8 + (1-1)d = 8 and the 10th term = 8 + (10-1)d = 53

giving 8 + 9d = 53

9d = 45

d = 5.

To calculate the common difference in an arithmetic sequence, subtract the first term from the tenth term and divide by 9 (the number of terms subtracted by one). In this case, (53-8)/9 gives the common difference as 5.

The student's question regards finding the common difference in an arithmetic sequence. In an arithmetic sequence, the difference between any two consecutive terms is constant. This is called the 'common difference'.

To find the common difference, you subtract the first term from the tenth term and divide by the number of terms subtracted by one. In this case, the tenth term is 53 and the first term is 8. So, you subtract 8 from 53, giving you 45. Then you divide 45 by (10-1), which is 9, giving a common difference of 5. Therefore, the common difference for this arithmetic sequence is 5.

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The correct answer is B.

Distance = speed + 90

The equation relates the distance she traveled to her speed is Speed x 90 = distance.

The speed a person travels is the total distance driven per the total time it took to travel.

Speed = total distance / total time

The time it took to drive is 90 minutes:  Speed = distance / 90

In order to determine the equation that relates distance to speed, make distance the subject of the formula. In order to do this, multiply both sides of the equation by 90: Speed x 90 = distance.

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Answer:

The numbers are 49 and 55

Step-by-step explanation:

The sum of two numbers 104

x+y = 104

their difference 6

x-y = 6

Add the two equations together to eliminate y

x+y = 104

x-y = 6

------------------

2x = 110

Divide by 2

2x/2 =110/2

x = 55

x+y = 104

55+y =104

Subtract 55 from each side

55-55+y = 104-55

y =49

Final answer:

To find the two numbers that add up to 104 and have a difference of 6, we solve a system of equations and discover that the numbers are 55 and 49.

Explanation:

The question asks us to find two numbers whose sum is 104 and whose difference is 6. To find the numbers, we can set up a system of equations. Let the two numbers be x and y.

x + y = 104 (sum of the numbers)

x - y = 6 (difference of the numbers)

We solve these equations simultaneously. Adding both equations, we get:

2x = 110

x = 55

Substitute x = 55 in the first equation to find y:

55 + y = 104

y = 104 - 55

y = 49

So, the two numbers are 55 and 49.

Answer:

1/6 (1 gallon of orange juice for every 6 gallons of apple juice)

Step-by-step explanation:

4/24=24/4x1/36

This is because you reverse the division (or fraction) into a easier to solve equation, and the 1/36 is there to balance out that change.

21x is 21x im glad that I can help you

for the first part:

Let's solve for x.

−x+3y=14

Step 1: Add -3y to both sides.

−x+3y+−3y=14+−3y

−x=−3y+14

Step 2: Divide both sides by -1.

−x/−1  =  −3y+14/−1

x=3y−14

Answer:

x=3y−14

Second part:Let's solve for x.

3x−3y=−6

Step 1: Add 3y to both sides.

3x−3y+3y=−6+3y

3x=3y−6

Step 2: Divide both sides by 3.

3x/3= 3y−6/3x=y−2

Answer:

x=y−2

Answer:

54 minutes

Step-by-step explanation:

We can write a proportion to solve this problem.  Put the number of pages over the minutes

27 pages           324 pages

--------------    = ---------------

4.5 minutes         x minutes

Using cross products

27 * x = 324 * 4.5

27x = 1458

Divide each side by 27

27x/27 = 1458/27

x =54

Answer: A) movies for less cost $5 more

Step-by-step explanation:

10 × 3 =30

15 × 2= 30+10=40 movie plus

15 × 3= 45 movies for less

Answer:

A)Movies For Less costs $5 more.

Step-by-step explanation:

Movies Plus charges its customers a $10 monthly service fee plus $2 for each movie the customer rents.

So, 15 movies from this provider will cost = [tex]10+2(15)[/tex]

=> [tex]10+30=40[/tex] dollars.

Movies For Less charges $3 for each movie but does not have a monthly service fee.

So, 15 movies from this provider will cost = [tex]15\times3=45[/tex] dollars.

Comparing both providers, we can see that Movies For Less charges $5 more than Movies Plus.

Therefore, option A is correct.

Answer:

The slope of a line is the change in y divided by the change in x.

( y1 - y2 ) / ( x1 - x2 )

It does not matter which point you choose as (x1, y1) and (x2,y2)

( 7 - 1 ) / ( 1 - 10 )

( 6 ) / ( -9 ) This will simplify to -2/3.

[tex]

f(x)=x^3-2x^2 \\

f(i)=i^3-2i^2=\boxed{-i+2}

[/tex]

Hope this helps.

r3t40

The constant p is determined by the half-life of 1600 years, and since after one half-life, the amount of the element is half of its initial value, we find that x=1/2 and y=1/1600, as e^p can be expressed as (1/2)^(1/1600). Therefore, option (a) is the correct answer.

The equation Q(t) = Q(0)e^pt describes an exponential decay process, such as the decay of a chemical element over time. Given that the half-life of the chemical element is 1600 years, after this period the quantity of the element will be half of its original amount. According to the properties of exponential decay, we know that after one half-life, Q(t) = Q(0)/2.

Substituting t = 1600 into the equation and knowing that Q(1600) = Q(0)/2, we get Q(0)/2 = Q(0)e^(1600p). Simplify by dividing both sides by Q(0), resulting in 1/2 = e^(1600p). To find p, take the natural logarithm of both sides, yielding ln(1/2) = 1600p ln(e), and since ln(e) = 1, we have p = ln(1/2)/1600.

Now, to express e^p as x^y, with both x and y being rational numbers, we look for a rational base x that can represent e^ln(1/2), which simplifies to (1/2). So, x would be 1/2, and because the half-life is 1600 years, y will be proportional to the fraction of that time. Hence, y = t/1600, where t is time in years. From this, you can infer that the base x equals 1/2 and y is 1/1600 for each year surpassing the half-life. Therefore, the correct answer is (a) x = sqrt(1/2), y = 1/1600.

so parallel is just numbers with the same slope but different x value

and perdicular is the One with different signs and oppisite reciprocals

a) perpendicular because -2 is the oppisite sign and reciprocal of 1/2

b)neither

c) niether

and B)

a) 3x-2

b)y=5/2 +4

i think

Answer:

113 beats per minute.

Step-by-step explanation:

904 / 8 = 113

The pulse rate in Salvador is 113 beats per minute.

calculation:

    ⇒number pf heartbeat count = 904

    ⇒time of count= 8 minutes

    ⇒pulse rate= 904/8

                  =113 beats per minute.

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Answer:

Infinitely many solutions.

Step-by-step explanation:

In the equation −2y + 2y + 3 = 3  we see only one variable, and that variable is of the first power.  Ordinarily, we'd say that this equation will have 1 solution.  However, if we combine like terms, we get 0 + 3 = 3, or 0 = 0, which is true for any and all y values.  Infinitely many solutions.

Answer:

Infinitely

Step-by-step explanation:

we have

[tex]-2y+2y+3=3[/tex]

Group terms that contain the same variable

[tex]-2y+2y=3-3[/tex]

Combine like terms

[tex]0=0[/tex] ----> the equation is true for any value of y

therefore

The equation has infinite solutions

Answer:

it has both line and rotational symmetry

Answer:

youre answer is it has both line and rotational symmetry

Step-by-step explanation:

Answer is B. -4,-2,1,3

A quadratic function is graphically represented by a parabola with a vertex located at the origin, below the x-axis, or above the x-axis. .

The points at which the graph crosses or touches the x-axis, give the real roots of the function(or zeros of the function) represented by the graph.

If the graph touches the x-axis and turns back, then it would be a double root at that point. Roots are also called x-intercepts or zeros.

The roots of the graph are Option B -4, -2, 1, and 3.

The standard form of a quadratic is y = ax^2 + bx + c, where a, b, and c are numbers and a cannot be 0. Examples of quadratic equations include all of these: y = x^2 + 3x + 1. y = x^2.

The quadratic equation in its standard form is ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term. The first condition for an equation to be a quadratic equation is the coefficient of x2 is a non-zero term(a ≠0)

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90% out of 105% which would be 0.85

Answer: 0.85

Step-by-step explanation:

Let A be the event that the customer orders a pizza and B be the event that the customer orders a salad.

Then , we have [tex]P(A)=80\%=0.80[/tex]

[tex]P(B)=15\%=0.15[/tex]

[tex]P(A\cap B)=10\%=0.10[/tex]

Now, the probability that he or she  orders either a pizza or a salad is given by :-

[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)\\\\\Rightarrow\ P(A\cup B)=0.80+0.15-0.10=0.85[/tex]

Hence, the required probability = 0.85

Answer:

y = -1/2x +2

Step-by-step explanation:

The linear and quadratic function rules we usually study in algebra come in several forms.

For linear function rules (equations of a line), there are more than half a dozen different forms, each with its own use. A few that often come in handy are the 2-point form, the slope-intercept form, the point-slope form, and the intercept form. Here, the 2-point form can be useful, since you have several points on the line to choose from.

The 2-point form of the equation of a line is ...

y = (y2 -y1)/(x2 -x1)·(x -x1) + y1

point (x1, y1) and point (x2, y2) can be any pair of the given points, in any order. Let's use the first two for points 1 and 2.

y = (0 -1)/(4 -2)·(x -2) +1

y = -1/2(x -2) +1 . . . . . . . . this is a suitable function rule. In this simplified form, it is in point-slope form, where -1/2 is the slope and (2, 1) is the point.

If you want to simplify this a bit, you can put it into slope-intercept form by eliminating the parentheses and combining the constant terms:

y = -1/2x +2

Answer:

notice that every time x increases by 2, y decreases by 1. So, a first guess would be

y = -1/2 x

But, -1/2 (2) = -1, and y(2) = 1, so we need to add 2 at the start. So,

y = 2 - 1/2 x

Answer:

2nd statement is true

Step-by-step explanation:

Please use " ^ " to denote exponentation:   f(x) = 4x^2 + 20x + 25.

Take a look at the second statement.  If you'll substitute -2.5 for x, to find f(-2.5), you'll find that the result is 0;  Thus, this second statement is true.

Answer:

The graph touches the x-axis at (–2.5, 0).

Step-by-step explanation:

Given  : f(x) = 4x² + 20x + 25.

To find : Which statement describes the graph .

Solution : We have given

f(x) = 4x² + 20x + 25.

On factoring

4x² + 10x + 10x+ 25 = 0

On taking  common 2x from first two terms and 5 from last two terms.

2x ( 2x + 5 ) +5 (2x + 5 ) = 0

On grouping

(2x +5) (2x +5)  = 0

For 2x +5 = 0

On subtracting 5 both side

2x = -5

On dividing by 2

x = [tex]\frac{-5}{2}[/tex] = - 2.5

x = - 2.5 .

Points (-2.5 , 0)

Therefore, The graph touches the x-axis at (–2.5, 0).

Answer: a) x=37,

              b)no solutions

              c)x=0

Step-by-step explanation:

In then the problem, you will need to isolate the x, use the inverse operation, and solve. For example, if I had the problem x-6=64, i would have to use the inverse operation  of  6 to isolate the x. You would add 6 on both sides.(addition is the inverse of subtraction). THat would be x=58.

Answer:

D) GE = 10 and GI = 12

Step-by-step explanation:

Given: KI = 4 and GH = 5

K is the centroid of EFG

So

KI = 1/3 (GI)

GI = 3 (KI) = 3(4) = 12

Because K is the centroid of EFG so GH = HE = 5

GE = GH + HE

GE = 5 + 5

GE = 10

Answer

GE = 10 and GI = 12

Answer:

D. GE = 10; GI = 12

Step-by-step explanation:

Given that K is the centroid of EFG, then GH = HE = 5, so GE = GH + HE = 5 + 5 = 10

The 2/3 rule states that the centroid is 2/3 of the way from the vertex to the opposite midpoint. This means that GK is doubled than KI, then GK = 2*4 = 8, and GI = GK + KI = 8 + 4 = 12