Pls help! Step by step

Answer:

The area of the new triangle would be A = (1/2) * 30ft * 40ft = (1/2) * 1200ft^2 = 600ft^2

Step-by-step explanation:

To increase the size of a triangle by a scale factor of 10/3, you can multiply each side length of the triangle by 10/3.

The new dimensions of the triangle would be (10/3) * 9ft = 30ft and (10/3) * 12ft = 40ft.

The area of a triangle is given by the formula A = (1/2) * b * h, where b is the length of the base and h is the height of the triangle.

Using the new dimensions of the triangle, the area of the new triangle would be A = (1/2) * 30ft * 40ft = (1/2) * 1200ft^2 = 600ft^2.

Answer:

To compare the two financing offers, we need to calculate the total cost of each offer.

Part A: What is the total cost of offer 1?

To calculate the total cost of offer 1, we need to first calculate the total amount of interest that will be paid over the course of the loan. We can do this using the following formula:

Total interest = (interest rate/12) * loan amount * number of payments

In this case, the loan amount is $2,975, the interest rate is 24.90%, and the number of payments is 36 (3 years * 12 months/year). Plugging these values into the formula, we have:

Total interest = (0.2490/12) * $2,975 * 36

Calculating, we find that the total interest is approximately $1,534.89.

To calculate the total cost of the loan, we need to add the total interest to the original loan amount. In this case, the total cost is $2,975 + $1,534.89 = $4,509.89.

Therefore, the total cost of offer 1 is $4,509.89.

Part B: What is the total cost of offer 2?

To calculate the total cost of offer 2, we need to first calculate the total amount of interest that will be paid over the course of the loan. We can do this using the following formula:

Total interest = (interest rate/12) * loan amount * number of payments

In this case, the loan amount is $2,975, the interest rate is 22.90%, and the number of payments is 36 (3 years * 12 months/year). Plugging these values into the formula, we have:

Total interest = (0.2290/12) * $2,

To continue the calculation of the total cost of offer 2, we need to calculate the total interest using the formula:

Total interest = (interest rate/12) * loan amount * number of payments

In this case, the loan amount is $2,975, the interest rate is 22.90%, and the number of payments is 36 (3 years * 12 months/year). Plugging these values into the formula, we have:

Total interest = (0.2290/12) * $2,975 * 36

Calculating, we find that the total interest is approximately $1,405.70.

To calculate the total cost of the loan, we need to add the total interest to the original loan amount. In this case, the total cost is $2,975 + $1,405.70 = $4,381.70.

Therefore, the total cost of offer 2 is $4,381.70.

Part C: Which financing offer should the new homeowner choose?

Based on the total cost of the two financing offers, it is more cost-effective for the new homeowner to choose offer 2. Offer 2 has a lower total cost ($4,381.70) compared to offer 1 ($4,509.89), so it would be the better choice for the new homeowner.

Step-by-step explanation:

Using the Pythagoras theorem, the value of y is [tex]6\sqrt{7}[/tex], and the value that goes in the green box is 6.

What is Pythagoras Theorem?

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.

Mark the intersections as A, B, C, and D.

It is given that BC=12 and CD=9.

The relationship between the height on the hypotenuse of a right triangle and the two line segments it generates on the hypotenuse is described by the right triangle altitude theorem, also known as the geometric mean theorem. It claims that the altitude is equal to the geometric mean of the two segments.

Apply the geometric mean theorem -

(AC)^2 = BC x CD

(AC)^2 = 12 x 9

(AC)^2 = 108

AC = [tex]\sqrt{108}[/tex]

AC = [tex]6\sqrt{3}[/tex]

Triangle ABC is a right-angled triangle, so apply Pythagoras theorem -

(AB)^2=(BC)^2+(AC)^2

(AB)^2=(12)^2+([tex]6\sqrt{3}[/tex])^2

(AB)^2=144+108

(AB)^2=252

AB=[tex]\sqrt{252}[/tex]

AB=[tex]6\sqrt{7}[/tex]

Therefore, the value of y is obtained as [tex]6\sqrt{7}[/tex].

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Answer:

30 students

Step-by-step explanation:

First, we need to find exactly how many students went to school by car and how many went on the bus.

To do this, we simply multiply the fraction of students that used each transportation method by the total number of students.

[tex]\# \textrm{ of students by car} = \dfrac{3}{8} \times 240 = \dfrac{3 \times 240}{8} = \dfrac{720}{8} = 90 \textrm{ students}[/tex]

So, 90 students went to school by car.

[tex]\# \textrm{ of students on bus} = \dfrac{6}{12} \times 240 = \dfrac{1}{2} \times 240 = \dfrac{240}{2} = 120 \textrm{ students}[/tex]

So, 120 students went to school on the bus.

The number of students that walked to school is the same as the number of students who didn't go in a car or on the bus, so to find the number of students that walked to school, we can subtract the number of students that went by car and on the bus from the total number of students.

[tex]\# \textrm{ of students that walked} = 240 - 90 - 120 = 30 \textrm{ students}[/tex]

a. The exact volume, in cubic inches, of water flowing out of the pipe every second is 32π cubic inches.

b. The height, in inches, of the water in the tank after 5 minutes is 600 feet.

c. It will take 0.132 minutes to fill 75% of the tank

A cylinder is a three-dimensional solid object with two bases that are identically circular and are connected by a curving surface that is located at a specific height from the center.

Examples of cylinders are toilet paper rolls and cold beverage cans.

The volume of a cylinder is πr²h.

Curved surface area = 2πrh.

Total surface area = 2πr(h + r).

Given, Water flows at 2 feet per second through a pipe with a diameter of 8 inches so it is a cylindrical shape.

Therefore, The exact volume, in cubic inches, of water flowing out of the pipe every second is,

= π(4)²×2.

= 32π cubic inches.

The volume of the cylindrical tank is,

= π(7.5)²×6.

= 337.5π cubic inches.

The height, in inches, of the water in the tank after 5 minutes would be

= (32π×300)/π×16).

= 600 feet.

Now, 75% of 337.5π cubic inches is (0.75×337.5π) = 253.125π cubic inches.

Therefore the time required to fill 75% of the tank is,

= [(253.125π/32π)]/60 minutes.

= 7.91/60 minutes.

= 0.132 minutes.

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The distance from the top of the tree of height 30 tall to the end of the shadow is 50.

Distance is the length between two point.

To calculate the distance from the top of the tree to the end of the shadow, we use the formula below.

Note: The tree and the shadow form a right angle.

Formula:

Where:

From the question,

Given:

Susbtitute these values into equation 1

Hence, the distance from the top of the tree to the end of the shadow is 50.

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The density of the material is 1533.3 grams per quarts.

Density is the measurement of how tightly a material is packed together. It is defined as the mass per unit volume.

Given that, the density of a certain material is such that it weighs 6900 grams for every 4.5 quarts of volume.

The formula to find the density is Density=Mass/Volume

Density =6900/4.5

Density= 1533.3 grams per quarts

Therefore, the density of the material is 1533.3 grams per quarts.

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The amounts of goo after each hour are given as follows:

The time that it takes for the goo to return to original size is given as follows:

n hours, for which:

[tex](2)^n(0.25)^n = 1[/tex]

An increasing exponential function is defined as follows:

y = a(1 + r)^x.

For which the parameters are given as follows:

Her sample is of 10 grams, and the amopunt of goo increases by 100%, hence the parameter values' are given as follows:

a = 10, r = 1.

Thus the exponential function is defined as follows:

y = 10(2)^n.

Then the amounts are given as follows:

A decreasing exponential function is given as follows:

y = a(1 - r)^x.

The goo shrinks by 75% every hour, hence:

r = 0.75.

The amount after n hours is of 10(2)^n, hence the shrinking function is given as follows:

[tex]y = 10(2)^n(0.25)^n[/tex]

It returns to the original amount when:

y = 10.

Hence:

[tex]10 = 10(2)^n(0.25)^n[/tex]

[tex](2)^n(0.25)^n = 1[/tex]

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Answer:-4x^2-2x+46.

Step-by-step explanation:

To simplify this expression, you can start by distributing the negative sign to the first set of parentheses:

(-3)(x+4)(x-6)-(x^2+8x-10)

Then, you can distribute the -3 to the terms inside the first set of parentheses:

(-3x-12)(x-6)-(x^2+8x-10)

Then, you can combine like terms:

-3x^2+6x+36-x^2-8x+10

This simplifies to:

-4x^2-2x+46

Therefore, the expression that is equivalent to -3(x+4)(x-6)-(x^2+8x-10) is -4x^2-2x+46.

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The option D is correct.Because this equation holds the vertically opposite angle theorem.

Vertically Opposite Angles are holds when two lines intersect each other then the opposite angles formed due to intersection are called vertical angles or vertically opposite angles. A pair of vertically opposite angles are always equal to each other.

Vertical opposite angles that are opposite each other when two lines cross are also known as vertical angles because the two angles share the same corner. Opposite angles are also congruent angles.The equation of a vertical line is given by x = a or x = -a

Now we find

According to vertical opposite angle

x-8=40-2x

x+2x=40+8

3x=48

x=16

We can find value of x by usng vertical opposite angle.

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The line y = - x has a coordinate value of (4, - 4) passing through the origin.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

Given, A line passes through the origin, (−1, 1) and (4, n).

So, The slope of the line is,

m = (1 - 0)/(- 1 - 0).

m = - 1.

Now,

1 = -1(-1) + b.

b = 0.

y = - x.

At x = 4,

y = - 4.

So, The point (4, n) is (4, - 4).

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Answer:

Step-by-step explanation:

take 9 divided by 5 wich = 1.8

For the given line whose equation is [tex]y=x+3[/tex] :

x   y    (x,y)

0 3     (0,3)

1 4     (1,4)

2 5     (2,5)

3      6      (3,6)

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

A line in slope-intercept form, y = mx + b, where m is the slope of the line and b is the y-intercept .

Given the equation y = x + 3, the slope (m) is 1 and the y-intercept (b) is 3.

So, we can fill the table like this:

For the given line whose equation is [tex]y=x+3[/tex] :

x   y    (x,y)

0 3     (0,3)

1 4     (1,4)

2 5     (2,5)

3      6     (3,6)

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Answer: D

Step-by-step explanation: x is a variable, and so is the number of tractors he sells. he is going to get paid $1000 for sure each month.

So 150x(the number of tractors) + 1000(his pay each month)

Answer:

4|x|y²√(3yz)

She forgot the absolute value sign on x, and she left out the exponent on y.

Step-by-step explanation:

Step 1 is correct.

x may be positive, zero, or negative.

√x is always non-negative. To assure that √x² is non-negative, √x² = |x|.

√16 = 4

√3 = √3

√x² = |x|

√y² × √y² = √y^4 = y²

Since y² is always non-negative, there is no need for absolute value sign.

√y^4 = y²

Answer should be

4|x|y²√(3yz)

Step-by-step explanation:

this means :

f(x) / (x + 2) = (x² - 5x + 8) + 8/(x + 2)

f(x) = (x + 2)(x² - 5x + 8) + 8 =

= x³ - 5x² + 8x + 2x² - 10x + 16 + 8 =

= x³ - 3x² - 2x + 24

Answer:

Since the term "3" contains no variables, "3" IS a constant term. In the expression 2x - 5 the constant term is -5.

Answer:

40 + 5 = 45

45 ÷ 9 = 5

Therefore, he will have 5 boxes of rocks.

To solve this problem, we can set up the following equation:

Torrie + John = Sonia - John

This equation represents the fact that John has the same number of dollars more than Torrie as he has less than Sonia. We can then substitute the given values for Torrie, Sonia, and John to solve for John:

430 + John = 760 - John

Combining like terms, we get:

2 * John = 330

Dividing both sides of the equation by 2, we get:

John = 165

Thus, John has $165.

Therefore , the solution is circle Part 1: The central idea ( -5 , 7 ). 2nd part: Radius is 6 in part 2,3rd part: FALSE and Parts 4. There are 10 miles between A and B.

A circular shape called a circle is created by following a moving point in a plane so that its distance from a particular point remains constant. The Greek word kirkos, which means hoop or ring, distance is the source of the English word circle.

Here,

The common circle equation is,

( x - h )² + ( y - k ) ( y - k )

6² = r²

where the circle's radius is r and the center's coordinates are (h, k).

Part 1.

Using the common circle equation, we obtain,

Circle's circumference's coordinate is ( -5 , 7 )

Consequently, the second choice is the right one.

Part 2.

Using the common circle equation, we obtain,

circle radius is six.

Consequently, the first choice is the right one.

Part 3.

Using the common circle equation, we obtain,

Circle's circumference's coordinate is ( 2 , 3 )

Therefore False.

Part 1.

In comparison to the common circle equation, we obtain,

Circle's center's coordinates are: ( -5 , 7 )

As a result, the second choice is the right one.

Part 2.

In comparison to the common circle equation, we obtain,

circle's diameter is six.

As a result, the first choice is right.

Part 3.

In comparison to the common circle equation, we obtain,

Circle's center's coordinates are: ( 2 , 3 )

So, False.

Part 1.

Giving the distance between two points,

Distance between A(-5, 3) and B (5, 3), expressed as:

=> [tex]\sqrt{(x2-x1)^{2} + (y2-y1)^{2} )}[/tex]

= >  [tex]\sqrt{(-5-5)^{2} + (3-3)^{2} )}[/tex]

=> 10

Thus, 3rd Option is correct.

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After evaluating the given expressions the results could be 245 / 89 , 43/6, 33/4 .

What is expression ?

expression can be defined as with the minimum of two variables or numbers and at least one math operation.

Given that ,

7/ 8  * 14  / (3/8 * 6 ) + 2  1/5

= (7/8 * 14 )/ ((18 / 8) + 11/5)

= (98/ 8 ) / (90 + 88) / 40

= (98/ 8 ) /  (178/ 40)

= (98 * 40) / (8* 78)

= 245/89

Hence the final value could be 245/53.

7/ 8  + (6*7/8 - 4 * 3/16 ) / (3/4 )

(7/8 + (21/4 - 3/4 ) )  / (3/4)

(7/8 + 18/4)  / (3/4)

(43/8) / (3/4)

43/6

Hence the final value could be 43/6.

3  1/7  * (3 1/3 * (2/3 + 1/6 ) - 5/18 ) / 2 (3/7)

11/7 * (10/6 - 5/18) / (17/7)

(11/7 )* (27/ 18) /( 17/7)

(11* 27/18 )/ (17)

33/34.

Hence the final value could be 33/34.

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A function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6 then g(-13) = 20

A relation is a function if it has only One y-value for each x-value.

Given a a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45

and that g(0) = -2 and g(-9) = 6,

x=-20 then g(-20)=-5

x=-19 then g(-19)=-4

x=-18 then g(-18)=-3

x=-17 then g(-17)=-2

x=-16 then g(-16)=-1

x=-15 then g(-15)=0

x=0 then g(0)=-2

x=-9 then g(-9)=6

By observing this we can say that as x values are decreasing the function values are increasing and vice versa

So option D is correct

Hence, a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6 then g(-13) = 20

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The next step in the series is, shown in Option C.

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

There are three steps are shown.

Now, In first step, only one line shown.

In second line the line is left to first line.

And, So on.

Hence, The next step in the series is, shown in Option C.

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On solving the value of provided question we can say that - the value of the slope intercept y = -3.

The point on the y-axis where the slope of the line passes is known as the intersection point in mathematics. the location on a line or curve where the y-axis crosses that point. This is demonstrated by putting y = mx+c as the equation for the straight line, where m denotes the slope and c the y-intercept. In the intercept form of the equation, the slope (m) and y-intercept (b) of the line are highlighted. The slope is m, and the y-intercept is b for equations in the intercept form (y=mx+b). Additionally, certain equations may be recast to seem like slope intercepts. For instance, if y=x is rewritten as y=1x+0, the slope becomes 1 and the y-intercept becomes 0.

as we can see from graph that,

line passes through origin, so x= 0

the, y = -5x - 3

y = -3

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So the person talked for 6 minutes.

The unitary approach involves calculating the value of a single unit, from which we may calculate the values of the necessary number of units.

Two quantities are compared to form a ratio. An equality of two ratios is a percentage. How to format a ratio Analyze the ratio to see whether it is part to part or part to whole. Calculate the whole and the pieces as necessary.

To solve this problem, we can use the following equation:

Cost = (Number of minutes x $0.31) + $0.89 + $1.23

We know that cost is $6.15 and the call lasted 6 hours. Since there are 60 minutes in an hour, we can convert the time in hours to minutes by multiplying 6 hours by 60 minutes/hour

So the number of minutes is 6 hours * 60 minutes/hour = 360 minutes

Now we can substitute the values into the equation:

Cost = (360 minutes x $0.31) + $0.89 + $1.23

Cost = $111.6 + $0.89 + $1.23

Cost = $113.72

The equation does not match the $6.15 cost, which means that the person talked for 6 minutes

So the person talked for 6 minutes.

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Answer:

10

I wish you luck in your assignments.

a) Let x be the number of games played and let y be the total price.

What in mathematics is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

(b)

Pin Lanes: y = 10 + 3x

Strike Lanes: y = 4 + 6x

(c) To find the number of games at which the total price is the same at both places, we can set the two equations equal to each other and solve for x:

10 + 3x = 4 + 6x

6x = 6

x = 1

So the total price would be the same if you played 1 game at both Pin Lanes and Strike Lanes.

(d) Since you want to play 4 games, you can substitute x = 4 into the equation for each place:

Pin Lanes: y = 10 + 3(4) = 22

Strike Lanes: y = 4 + 6(4) = 28

Since 4 games at Pin Lanes costs $22 and 4 games at Strike Lanes costs $28, it would be cheaper to play at Pin Lanes.

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The ordered pair solution to the function f(x) is (6, -9) because f(6) = -9,

An equation is an expression relating numbers and variables.

A function is a rule that defines the relationship between the dependent and independent variable. Dependent variables are variables that depends on others variable while independent variables are variables that does not depends on others variable

A solution to a function is the values of the variable that makes the equation true.

Given the function f(x) have solution of f(6) = -9. The ordered pair is (6, -9)

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Therefore , (1, 3), (2, 5), (3, 7) (4, 9) and (1, 3), (2, 3), (3, 3) (4, 3) are the relations that represent a function.  

According to a function's rule, every x value in the domain has one and only one range of y values. Definition. A one-to-one function exists when there is just one and only one value of x such that f(x) = y.

Here,

The relationship is (1, 3), (2, 5), and (2, 7) (4, 9)

Given that 2 is repeated, the connection is not a function.

The relationship is (1, 3), (2, 5), and (3, 7) (4, 9)

Since there are no repeating numbers, the relation is a function.

The relationship stated is (1, 3), (1, 5), and (1, 7). (4, 9)

The relationship is not a 1 repeated function.

The relationships are (1, 3), (2, 3), and (3, 3). (4, 3)

Since there are no repeating numbers, the relation is a function.

The relationship stated is (1, 2), (2, 5), and (2, 1) (4, 5)

As 2 repeated, the relationship is not a function.

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