The sum of three numbers is 11. Two times the smallest is 1 less than the largest, while the sum of the largest and smallest is 7.Use a linear system in three variables to find the three numbers.

The length of the base and the height of the triangle are 7.7 feet and 15.7 feet

From the question, we have the following parameters that can be used in our computation:

Base = 8 feet more than twice the height

Area = 60

This means that

b = 8 + h

A = 60

The area of a triangle is

A = 0.5bh

So, we have

0.5(8 + h)h = 60

This gives

4h + 0.5h² = 60

Rewrite as

0.5h² + 4h - 60 = 0

Using a calculator, we have

h = 7.7

Recall that

b = 8 + h

So, we have

b = 8 + 7.7

Evaluate

b = 15.7

Hence, the base is 15.7 feet

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Part 1

'x more than 7' written as an algebraic expression is:

= 7 + x

Part 2

Let the number be n

Therefore, 'a number less 35' written as an algebraic expression:

=n - 35

Part 3

Let the number be y

'5 times a number' written as an algebraic expression:

=5 x y = 5y

Part 4

Let the number be x.

Part 5

Answer: b

Step-by-step explanation:

Answer: 5

Step-by-step explanation:

you have to divide it so 7 1/2 ÷ 1 1/2

15/2 × 3/2 then you swap the 3/2 to 2/3 so it will be 15/2 × 2/3 you don't have to cross multiplication so you just multiply across so it would be 15×3=30 and then 2×3=6 so it would be 30/6 but that's not the final answer because it and improper fractions so you divide 30÷6=5 and that's how you get 5

Answer:

The answer is 12.

Step-by-step explanation:

First you need to draw a right triangle. Then the shortest side of the triangle is 5 and the longest is 13 so you would have to do a^2 + b^2 = c^2. So the problem would look like this 5^2 + b^2 = 13^2. 5 x 5= 25 and 13 x 13= 169. Now the problem looks like this 25 + b^2 = 169, since you can't do 25 + b you would have to bring it to the other side. Afterwards the problem should look like this b^2 = 144. Now you would have to square the b and 144 so the answer is 12. Sorry for spelling and grammar mistakes. Hoped this helped!

Answer:

15

Step-by-step explanation

The simplest form of the given equation [9(-7t + 4t — 10) — 9t] is [-36t - 90].

If a fraction's top and bottom have only one other common factor, it is said to be in its simplest form.

In other words, the top and bottom cannot be divided further and remain whole numbers.

The simplest form is sometimes referred to as "lowest terms."

So, the simplest form of the equation:

9(-7t + 4t — 10) — 9t

Now, calculate to simplest terms as follows:

9(-7t + 4t — 10) — 9t

-63t + 36t - 90 - 9t

-63t + 27t - 90

-36t - 90

Therefore, the simplest form of the given equation [9(-7t + 4t — 10) — 9t] is [-36t - 90].

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1) Coordinates are (2,-6) and (1,-1)

2) Points are (1,2) and (2,8).

You do the reverse to determine a point's coordinates in a coordinate system. Start at the point, then move up or down a vertical line until you reach the x-axis. Your x-coordinate is shown there. To get the y-coordinate, repeat the previous step while adhering to a horizontal line.

A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.

Given,

Function:

1) f(x) = -x² - 2x + 2

Let x be 1

y = -(1)² - 2(1) +2

y = -1 -2 + 2

y = -1

Points are (1, -1)

Let x be 2

y = -(2)² - 2(2) + 2

y = -4 -4 + 2

y = -6

Points are (2,-6)

2) f(x) = -2x²

Let x be 1

y = 2(1)²

y = 2

Let x be 2

y = 2(2)²

y = 8

So,

Coordinates are (1,2) and (2,8)

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Given the line in point slope form:

y + 1 = 3(x - 2)

Let's rewrite the equation in slope intercept form.

Using the point slope form:

y - y1 = m(x - x1)

Thus, we have the following:

x1 = -2

y1 = 1

slope, m = 3

To write in slope intercept form, all you have to do is to isolate the y.

Thus,

y + 1 = 3(x - 2)

Expand the parenthesis:

y + 1 = 3x - 6

Subtract 1 from both sides:

y + 1 - 1 = 3x - 6 - 1

y = 3x - 6 - 1

y = 3x - 7

Therefore, the equation in slope intercept form is:

y = 3x - 7

ANSWER:

y = 3x - 7

Answer:

Step-by-step explanation:

1 Divide both sides by -3−3.

-\frac{y+1}{3}=x-2

−

3

y+1

​

=x−2

2 Add 22 to both sides.

-\frac{y+1}{3}+2=x

−

3

y+1

​

+2=x

3 Regroup terms.

2-\frac{y+1}{3}=x

2−

3

y+1

​

=x

4 Switch sides.

x=2-\frac{y+1}{3}

x=2−

3

y+1

​

Answer:

3

Step-by-step explanation:

I hope it helps and have a wonderful rest of your day!!!! :)

BRAINIEST is appreciated it would really help me!!!!

The display that would represent the data in the best way that lower quartile, median, and upper quartile would be highlighted would be box ploy. That is option B.

Box plot which is also called box and whisker plot is a type of graphical representation that is used to represent the five number summary of a data set that include the following:

Therefore, among the listed displays, the graphical representation method that can best be used is the box plot.

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Answer:

B - Box Plot

Step-by-step explanation:

I took the test :)

Answer:

w = 4

Step-by-step explanation:

[tex]\frac{w}{2}[/tex] + 3 = 5 ( subtract 3 from both sides )

[tex]\frac{w}{2}[/tex] = 2 ( multiply both sides by 2 to clear the fraction )

w = 4

Answer:

Stratified

Explanation:

In Stratified Sampling, members of the population are divided into subgroups before a random sample of each group is taken.

Therefore in the case of the clinical trial presented, the sampling method used is stratified.

The midsegment determines a smaller triangle that is similar to the larger triangle. If two triangles are similar, then their side lengths are at the same ratio, so that:

From this expression, you can determine the value of x:

-First. multiply both sides by 45:

-Second, divide both sides by 5 to determine the value of x:

The value of x is equal to 5

1) You have the following expressions for angles ∠1 and ∠3

m∠1 = 15x - 5

m∠3 = 10x + 35

In order to find the value of x, you consider that angle ∠1 and ∠3 are congruent, that is, they are equal. Then, you equal the algebraic expressions and solve for x, just as follow:

15x - 5 = 10x + 35 subtract 10x bith sides, add 5 both sides

15x - 10x = 35 + 5 simplify similar terms

5x = 40 divide between 5 both sides

x = 40/5

x = 8

Hence, x = 8, and the values of the angles are:

m∠1 = 15x - 5 = 15(8) - 5 = 115

m∠3 = 10x + 35 = 10(8) + 35 = 115

2) To find the measure of the angle ∠2 you consider that the sum of angles ∠1 and ∠2 is equal to 180°. Thus, you obtain:

m∠1 + m∠2 = 180°

m∠2 = 180 - m∠1 = 180 - 115 = 65

Hence, the measure of angle m∠2 = 65°

Answer:

Cone

100.6in^2

Step-by-step explanation:

Plato answer.

The approximate surface area of the shell is 75π square inches.

Find the area that its outer surfaces possess. Sum of all those surfaces' area is the surface area of the considered object. Right circular cone is the cone in which the line joining peak of the cone to the center of the base of the circle is perpendicular to the surface of its base.

We are given that;

Diameter= 5in

Height=10in

Now,

Substituting these values in the formula for surface area of a cone, we get:

Surface area of a cone = π(5)(5 + 10)

Simplifying, we get:

Surface area of a cone = 75π in²

Therefore, the surface area will be 75π square inches.

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The vertex form of a quadratic function is:

The standard form of a quadratic function is:

We can do the following steps to solve the exercise.

Step 1: We replace the values of h,k, x, and y into the vertex form of a quadratic equation, and we solve for a.

Step 2: We replace the values of a,h, and k into the vertex form of a quadratic equation.

Step 3: We expand the expression inside the parentheses and combine like terms to convert the function into its standard form.

The equation of the graph in standard form is:

Answer:

a)4080 trees

b)104 trees

Step-by-step explanation:

1st - 24 trees

last (40th) - 180 trees

If differences between any row (except 40th) and next row are equal then

2nd - 24 trees+X

3rd - (2nd+X) or 24 trees + 2X

coefficient of X is number of row minus 1, therefore 40th row has 24 trees + 39X, and it is equal to 180. We can make an equation from this:

24tr+39X=180tr

39X=156tr

X=4tr

By this we can find how many trees are there in the 21st, 21st row has 24 trees+20X=24 trees+80 trees=104 trees

To find how many trees are there in the whole orchard, we add them all:

1st - 24 trees, 2nd - 24 trees + X, 3rd - 24 trees + 2X,

easily, it is just 24 trees x 40 + 39X x 20 = 4080 trees

Answer:

(a) 4,080 trees

(b) 104 trees

Step-by-step explanation:

If the first row has 24 trees and the fortieth row has 180 trees, how many additional trees are in each succeeding row?

[tex](40-1)x=180-24[/tex]

[tex]39x=156[/tex]

[tex]x=4[/tex]

That means that each row has 4 more trees than the preceding row. For example, the second row has 28 trees, the third row has 32 trees, and so on. We can write a formula to tell us how many trees are in any given row:

[tex]n=4(r-1)+24[/tex]

where [tex]r[/tex] is the row number between 1 and 40.

(a) 24 + 28 + 32 + 36 + 40 + 44 + 48 + 52 + 56 + 60 + 64 + 68 + 72 + 76 + 80 + 84 + 88 + 92 + 96 + 100 + 104 + 108 + 112 + 116 + 120 + 124 + 128 + 132 + 136 + 140 + 144 + 148 + 152 + 156 + 160 + 164 + 168 + 172 + 176 + 180 = 4,080

(b) Using our formula above:

[tex]n=4(21-1)+24[/tex]

[tex]n=4(20)+24[/tex]

[tex]n=80+24[/tex]

[tex]n=104[/tex]

y = (5/3)^x

For x= 0 , y = 1

For x=1,. y= 5/3

For x=2. y = 25/9= 2 + 7/9

For x= 3. y= (25/9)•5/3 = 10/3 + 35/27

For x= 4. y= (10/3 + 35/27)•5/3= 50/9 + 175/81= 625/81

For x= 5 y = (625/81)•5/3= 3125/243

For x=6. y= 15625/243 = 64 + 73/243

For x=7. y=78125/729 = 107+ 122/729

For x=8. y= 390625/2187= 178+ 1339/2187

NOW Part 2 Drawing it

Answer:

third expression

Step-by-step explanation:

the surface area (SA) is the area of the 6 faces.

Note that opposite faces are congruent.

the surface area is the the area of each face multiplied by 2 , since they are congruent.

SA = 2(front area ) + 2(side area ) + 2(area of base)

   = 2(5 × 7 ) + 2(4 × 7 ) + 2(4 × 5 ) ← third option

  = 2(35) + 2(28) + 2(20)

 = 70 + 56 + 40

= 166 cm²

If a system has at least one solution, it is said to be consistent .

For system to be independent,

If a consistent system has exactly one solution, it is independent .

For system to be dependent,

If a consistent system has an infinite number of solutions, it is dependent .

The graph is given in the question tab which has exactly one solution.

So the given system is consistent and independent.

Using inequality, we know that the maximum number of students that can visit the amusement park is 30.

So, inequality represents the maximum number of students who can go to the amusement park:

Rounding off: x ≤ 30

Therefore, using inequality, we know that the maximum number of students that can visit the amusement park is 30.

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A Voronoi diagram is a division of a plane into areas near each of a given set of objects in mathematics. These things are just infinitely many points in the plane in the simplest scenario (called seeds, sites, or generators). There is a region, known as a Voronoi cell, for each seed that is made up of all points in the plane that are closer to that seed than to any other point. A set of points' Voronoi diagram and Delaunay triangulation are identical.

We are aware that any intersection of half-planes results in a convex region bordered by a collection of linked line segments. Voronoi edges are the line segments that define the limits of Voronoi regions. These edges' termini are known as Voronoi vertices.

Voronoi diagram:

A Voronoi diagram in mathematics is a division of a plane into areas near to each of a given set of objects. These things are simply infinitely many plane points in the most basic scenario (called seeds, sites, or generators).

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Answer:

1a the scatter plot models the heart

Answer:

1. 250x12= 3000. So she earned $3000 in that 12 weeks, if you include the 500 then it would be 3500 dollars if not then it would be 3000 dollars.

2. Divide 75 and 12 and you get 6.25 if you want to estimate. Then the answer would be, all of the fields will be harvested in just 6 days.

3. Divide 54 and 3 and you get 18. 18 weeks if they frame the sanem number each week.

4. If you divide 8,000 and 450 you get 17.7777777778. If you want to estimate then the it would be 18. So it would take about 18 days to fill up the 8,000 gallons of water.

5. This graph is y=20x

6. Don't really know, if the 0 is 360 then 10 and 300 are pretty easy because 10=30. so 0, 10, 20 is 360, 300,240 likes the graph and I would think you can solve this

Answer:

  c = 0

Step-by-step explanation:

You want the value of c such that point (c, 4) is on the line with slope 1 through point (-7, -3).

The point-slope equation of a line with slope m through point (h, k) is ...

  y -k = m(x -h)

The line with slope 1 through point (-7, -3) has equation ...

  y +3 = 1(x +7)

  y = x +4 . . . . . . . subtract 3 and simplify

The value of x when y=4 can be found using this equation.

  4 = x +4

  0 = x . . . . . . . subtract 4

The value of c is 0.

Answer:

Step-by-step explanation:

<DCE≅<BCA

BC≅CE

AC≅CD

BA≅DE

Answer:

50÷6=8 R2

Step-by-step explanation:

                       8  

              6  ⟌50        R2

                     - 0    

                 -------------  

                       50  

                      -48  

                 --------------  

                          2  

So, Miranda will have $8 left to buy.

A linear equation for the trend line in this scatter plot is y = 4x/3 - 5/3.

In order to determine a linear equation for the trend line (line of best fit) that models the data points contained in the scatter plot, we would have to determine its slope by using the points that trend line passes through.

Mathematically, the slope of a straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided in the scatter plot, the trend line passes through the following points:

Substituting the given points into the formula, we have;

Slope, m = (9 - 5)/(8 - 5)

Slope, m = 4/3

At point (5, 5), a linear equation for the line can be calculated by using the point-slope form:

y - y₁ = m(x - x₁)

Where:

Substituting the given points into the formula, we have;

y - y₁ = m(x - x₁)

y - 5 = 4/3(x - 5)

y - 5 = 4x/3 - 20/3

y = 4x/3 - 20/3 + 5

y = 4x/3 - 5/3

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Answer: 19t + 100

Explanation:

From the information given,

she earns $19 per hour

Last week, she worked t hours. This means that the amount earned in t hours is

t * 19 = 19t

If her friend paid her $100 for photoshoot, the expression to represent the total amount April earned last week is

19t + 100

Answer:

11.50 per hour

Step-by-step explanation:

Y = 92

8 = Mx

Y = mx

92 = m(8)

m = 11.50 per hour

So the original amount of money in the bank account is given by a negative number: -$21. If you deposit $6 per day during four days then the total amount of money deposited by the fourth day is:

The total amount of money in the account is given by adding the deposited money to the original amount:

Then the answer is $3.