Laci and Leon are saving money to go to an amusement park. Laci has $1 more than 4 times the amount of money Leon has. Together, they have $76. Write an equation to determine how much money they have together

By combining the like terms, the simplified form of the expression 6r+3s+2s+4r is 10r+5s

Given,

The expression = 6r+3s+2s+4r

Rearrange the terms

6r+4r+3s+2s

Combine the like terms

6r+4r+3s+2s=(6+4)r+(3+2)s

=10r+5s

Hence, By combining the like terms, the simplified form of the expression 6r+3s+2s+4r is 10r+5s.

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Answer:

The next two terms is 144 and 169

Answer:0-ounce package of cashews costs $8.11 is better then a 16-ounce package of cashews costs $12 , because cost per ounce for the 10-ounce package of cashews = $ is greater then cost per ounce for the 16-ounce package of cashews = $

Step-by-step explanation:

Answer: x=-20/3

Step-by-step explanation:

6(x + 1) = 3x - 14

6x+6 = 3x - 14

6x-3x+6 = 3x-3x - 14

3x+6 = -14

3x+6-6=-6-14

3x=-20

x=-20/3

The coordinate of C=(4,0).

The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h.

Given:

ΔABC with

A(3, 0), B(7, 3)

let the coordinate of c(x, y)

Also, Perimeter of triangle = 2 * Area of triangle

Area of triangle=1/2 * b * h

Area=1/2 * 4 * 3

Area=1/2 * 12

Area=6 units

Perimeter= AB + BC + CA

Now,

Now, using distance formula

AB = √(7-3)² + (3-0)²

AB = √16+9

AB= 5 units

Perimeter of triangle=5+4+3

Perimeter =12

So, the coordinate of C=(0+4,0)

C=(4, 3-3)

C=(4,0)

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Answer: the number would be 6

Step-by-step explanation:

6 x 2 = 12, 12 - 5 = 7, so the number is 6

Answer:

7.5 hours

Step-by-step explanation:

Answer:

7.5 hours

Step-by-step explanation:

A car is traveling at 100 km/hr. How many hours will it take to cover a distance of 750 km? 750km ÷ 100km/hr = 7.5 hrs.

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Given that the two angles form a linear pair, the measure of each angle is 40° and 140°.

The sum of angles of a linear pair is always equal to 180°.

Given the data the data in the question;

Let x represent the measure of the first angle.

Since the sum of angles of a linear pair is always equal to 180°.

m∠1 + m∠2 = 180

x + 3.5x = 180

Solve for x

4.5 = 180

x = 180/4.5

x = 40

Hence,

Measure of angle 1 = x = 40°

Measure of angle 2 = 3.5x = 3.5(40) = 140°

Given that the two angles form a linear pair, the measure of each angle is 40° and 140°.

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The expression that is a difference between two terms is:

5y - 7

An algebraic expression should have at least one variable, and here we know that we should find a difference (remember that a difference is a subtraction).

And it must have two terms, then the expression is something like:

A - B

Such that A or B depend on the variable.

With this in mind, we can see that the correct option (the only subtraction with two terms) is the first one:

5y - 7

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2 and -2 both are the solution of the equation x/2 = 2/x.

According to the given question.

We have an equation 2/x = x/2.

As we know that, as we know that, an equation is a condition on a variable such that two expressions in the variable should have equal value.

Therefore, the solution of the equation 2/x = x/2 is given by

2/x = x/2

⇒ 2  = (x/2)x    (multiplying both the sides by x)

⇒ 2 = x^2/2

⇒ 2(2) = x^2  (multiplying by 2 both the sides by 2)

⇒ 4 = x^2

⇒ x^2 = 4

⇒ x = √4

⇒ x = ±2

⇒ x = 2 or -2

Now we will check 2 is the solution of the given equation or not.

Therefore,

LHS = 2/2 = 1

RHS = 2/2 = 1

Here, LHS = RHS. Therefore, 2 is the solution of the given equation.

Similarly, for -2

LHS = 2/-2 = -1

RHS = -2/2 = -1

Here. RHS = LHS. Therefore, -2 is also the solution of the given equation.

Hence, 2 and -2 both are the solution of the equation x/2 = 2/x.

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Answer: 2:3, 6:1, 4:1, 6:1

Step-by-step explanation:

The first step is by finding the GCF. For 24:36 the GCF is 12. Once you divide you get 2:3. For 12:2 the GFC is 2. For 16:4 it is 4 and you get 4:1 and finally 18:3 the GCF is 3 and you get 6:1.

Step-by-step explanation:

In order to get answer of this question, we should use the distance formula. So, what is that formula? let us see the formula and simplify to get the answer :)

[tex]{ \red{ \tt{given}}}[/tex]

[tex]{ \orange{ \tt{(1, - 1)}}} = { \green{ \tt{(x1,y1)}}}[/tex]

[tex]{ \orange{ \tt{(7,8)}}} = { \green{ \tt{(x2,y2)}}}[/tex]

[tex]{ \blue{ \tt{d}}} = { \green{ \tt{ \sqrt{ {(x1 - x2)}^{2} + ( {y1 - y2)}^{2}}}}}[/tex]

[tex]{ \blue{ \tt{d}}} = { \green{ \tt \sqrt{ {(1 - 7)}^{2} + { (- 1 - 8)}^{2}}}}[/tex]

[tex]{ \blue{ \tt{d}}} = { \green{ \tt{ \sqrt{ {(6)}^{2} + {( - 9)}^{2}}}}} [/tex]

[tex]{ \blue{ \tt{d}}} = { \green{ \tt{ \sqrt{36 + 81}}}}[/tex]

[tex]{ \blue{ \tt{d}}} = { \green{ \tt{ \sqrt{117}}}} [/tex]units.

Answer:

Not possible without knowing what the spinners are

Answer: C

Step-by-step explanation:

6 planes

Answer: C, 6)

Step-by-step explanation: Area of square = a2 Square units, where a is the side length of square.

Area of rectangle = l × b Square units, where l is the length, b is the breadth.

Area of circle = π × r2 Square units, where r is the radius of a circle.

Answer:

I hope it's helpful.........

In order to get standard deviation of 15. Subtract 68 from everybody's score, then divide these values by 15.

The square root of the variance is used to determine the standard deviation. An alternative method of calculating it is to identify the mean of a data set, compare each data point to the mean, square the differences, add them all together, divide by the number of points in the data set minus 1, and then compute the square root.

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Mr. Olsen uses an unusual grading system in his class. After each test, he transforms the scores to have a mean of 0 and a standard deviation of 1. Mr. Olsen then assigns a grade to each student based on the transformed score. On his most recent test, the class's scores had a mean of 68 and a standard deviation of 15. What transformations should he apply to each test score? Explain.

The slope of the line that contains the given points E(6,3) and, F(-6,3) is 0.

It is given in the question that the line contains the points E(6,3) and F(-6,3).

We know that:-

The formula to find the slope of a line that contains points (a,b) and (c,d) is given by:-

m = (d-b)/(c-a)

Here, we have

m = slope of the line

(a,b) = (6,3)

(c,d) = (-6,3)

Hence, putting the values of (a,b) and (c,d) , we get

Slope of the line that contains the given points E(6,3) and, F(-6,3) is given by:-

(3-3)/(-6-6) = 0/-12= 0

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Step-by-step explanation:

35×35 may be ?? ..........

Answer:

x = 0

Step-by-step explanation:

Vertical asymptotes are vertical lines which correspond to the zeroes of the denominator of a rational function

For f(x) set the denominator = 0 and solve for x

For [tex]\frac{1}{x^2}[/tex]

set x² = 0

x = √0  = 0 which is the vertical asymptote

Answer:

x = 0

Step-by-step explanation:

The Vertical asymptotes are vertical lines which correspond to zeroes of denominators.

For f(x) set the denominator = 0 and solve for x

For \fract {1}{x^2}

you set x² = 0

x = √0 = 0 which is the vertical asymptote

The recursive formula for the arithmetic sequence [tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + d

A recursive formula is a sequence in which terms are defined using one or more previous terms which are given. If we know the nth term of an arithmetic sequence and you know a common difference, d, we can find the (n+1)th term using the recursive formula.

[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + d

The sequence -2, 7, 16, 25,.... is in arithmetic sequence and its common difference is 7 - (-2) = (16-7)= 9 .

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The pilot's distance is increasing.

In the graph, we can see distance on y axis and time on x axis. It is clearly visible that at 2 minutes, the distance covered is 0.4 miles. Further, at 4 minutes, the distance covered increases to 0.8 miles. At 6 minutes, the distance covered again increases by 0.4 miles and is 1.2 miles. At 8 minutes, the distance covered in 1.6 miles, which again increases by 0.4.

Now, it is evident that distance is increasing.

We can further calculate the speed using given information -

Speed = distance/time

Total distance = 1.6 - 0.0

Total distance = 1.6 miles

Total time = 8 - 0

Total time = 8 minutes

Speed = 1.6/8

Speed = 0.2 miles per minute.

Hence, the distance of pilot is increasing at constant rate or speed of 0.2 miles per minute.

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The complete question and figure is attached -

The graph below represents the distance a pilot is from the home airport during a period of time. A 2-column table with 5 rows titled Time and Distance Ran by Myra. The first column is labeled Time (minutes) with entries 0, 2, 4, 6, 8. The second column is labeled Distance (miles) with entries 0.0, 0.4, 0.8, 1.2, 1.6. Which describes the pilot’s distance in section I? zero constant decreasing increasing

The equation of the line in point-slope form, which passes through the pair of points located at (0 , 0) and (-4 , -5), is y + 5 = 5/4(x + 4).

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).

Getting the slope of the two points: (0 , 0) and (-4 , -5)

m = (y2 - y1)/(x2 - x1)

m = (-5 - 0)/(-4 - 0)

m = -5/-4

m = 5/4

Using the point slope form, plug in the values of the slope and Point A to set up the equation.

(y - y1) = m(x - x1)

where m = 5/4 and (x1 , y1) = (-4 , -5)

(y - -5) = 5/4(x - -4)

y + 5 = 5/4(x + 4)

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Here we can conjecture that :

The measure of an exterior angle is equal to the sum of measures of its nonadjacent interior angles.

The exterior angle of any polygon is defined as the angle which is at the outside boundaries of that polygon. whereas, the interior angle is defined as the angle which is inside the polygon. In the other words if the polygon has the point within the angle it is in the interior of the angle , but if the point is outside then is it said to be in the exterior of the angle.

Non adjacent angles are those angles which are not adjacent to each other. The non adjacent angles follow one of the  properties which are listed below:

In the given question,

taking a example say a triangle ABC with  ∠A=64,  ∠B = 45 and an external angle x to the side AC.

as sum of angles equal to 180

thus,  ∠A +  ∠B +  ∠C = 180

         64 + 45 +  ∠C = 180

          ∠C = 180-109 = 71

now as x is external to  ∠C,

therefore x = 180 -  ∠C = 180 - 71

                x = 109 =  ∠A +  ∠B

Hence we can make the conjecture that, the measure of an exterior angle is equal to the sum of measures of its nonadjacent interior angles.

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f (0) = 1 is the output for the given input .

What is  linear function ?

f(x)= -4 x+1

Put x = 0    ⇒   - 4 × 0 + 1

                  ⇒   0 + 1

                  ⇒   1

Therefore f (0) = 1

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Answer:

0.0000002702

Step-by-step explanation:

2.702 * 10^-7

The seventh term of the given geometric sequence is: [tex]\frac{4}{625}[/tex].

Given: 100, 20, 4, ....

Here, a₁ = 100, r = [tex]\frac{100}{20}=\frac{20}{4}=\frac{1}{5}[/tex], for the given geometric progression.

In the formula: [tex]a_n=a_1(r^{n-1})[/tex]

For n = 7, a₇ = 100 ([tex](\frac{1}{5})^{7-1}[/tex]

=> a₇ = 100 [tex](\frac{1}{5})^6[/tex]

=> a₇ = 4([tex]\frac{1}{625}[/tex])

Hence, The seventh term of the given geometric sequence is: [tex]\frac{4}{625}[/tex].

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The plane's average speed during the flight is 381.43 miles per hour.

The average speed is the quotient of the total distance covered during the flight divided by the total time used.

The Average Speed is the scalar quantity that shows the rate of change in displacement from one point to another.

The distance for the first miles = 1,295 miles

The time it took the plane to cover the distance = 3 hours 33 minutes

The distance for the last lap = 738 miles

The time it took the plane to cover the last distance = 1 hour 47 minutes

The total distance covered for the journey = 2,033 miles (1,295 + 738)

The total time for the journey = 5 hours 20 minutes or 5.33 hours

Average Speed = 2,033/5.33

= 381.43 miles per hour

Thus, the plane's average speed during the flight is 381.43 miles per hour.

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The probability that the camper is heading in the N to NE direction when a camper lost in the woods points his compass in a random direction is 1/8.

As given,

Compass is divided into 8 sectors N→NE→E→SE→S→SW→W→NW→N

Whole compass represents the circle with area 360 degrees

Area of each sector is equal to 45 degrees

Probability that the camper is heading in the N to NE direction

=45/360

=1/8

Therefore, the probability that the camper is heading in the N to NE direction when a camper lost in the woods points his compass in a random direction is 1/8.

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The function that represents the Transformation of the graph is  F(X+1/2).

Different non-vertical lines have different slopes and/or y-intercepts. They are graphs of various linear functions. If there are two such lines, one can be considered a transformation of the other. There is a group of functions called the family, each function being a transformation of a special function called a parent. Linear functions form a series of functions. All linear functions are transformations of the function y = x. The function y = x is an upper linear function. Each family role is a transformation of a parent's role. The conversion type is translation. A translation moves the graph of the parent function horizontally, vertically, or both without changing shape or orientation. So, the function that represents this transformation is F(X+1/2).

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