One bulldozer clears land twice as fast as another. Together they clear a large tract in 1.5 hours. How long would the larger bulldozer take?

Answer:

113

Step-by-step explanation:

Finding a remainder seems like you should be dividing. Remember everything is a shortcut for something else in math. So first you learn Long Division, but that's too much writing, so then you learn Synthetic Division, but there's an even shorter shortcut. It is called Remainder Theorem. If you just substitute 3 (because x-3 in the question) into the function, and you calculate it, you get the remainder.

f(x) = 4x^3 + 5

f(3) = 4(3)^3 + 5

f(3) = 4(27) + 5

= 108 + 5

= 113

See image.

The answer is 237.55

Define Percentage

A ratio or figure stated as a fraction of 100 is called a percentage. Although the abbreviations "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.

Given expression is,

125.8% of £188.83

Rewrite it as,

⇒ 125.8 / 100 * 188.83

⇒ 1.258 * 188.83

⇒ 237.54814

⇒ 237.55 (rounded to 2 Decimal places)

Hence, the answer is 237.55

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Answer: The answer is C: No solution

Step-by-step explanation:

By squaring the other side (to therefor remove the square off X) you get [tex]x-3=x+6\sqrt{x} +9[/tex]

You then cancel out the equal terms, in this case x, to reach the equation:

[tex]-3=6\sqrt{x} +9[/tex]

This equation, has no solution, as the left side is always negative, and the right side will always be positive, making any statement for x false.

Answer:

see explanation

Step-by-step explanation:

(a)

given y is inversely proportional to x² then the equation relating them is

y = [tex]\frac{k}{x^2}[/tex] ← k is the constant of variation

to find k use any ordered pair from the table

using (2, 4 ) , then

4 = [tex]\frac{k}{2^2}[/tex] = [tex]\frac{k}{4}[/tex] ( multiply both sides by 4 )

16 = k

y = [tex]\frac{16}{x^2}[/tex] ← equation of variation

(b)

when y = 25 , that is

25 = [tex]\frac{16}{x^2}[/tex] ( multiply both sides by x² )

25x² = 16 ( divide both sides by 25 )

x² = [tex]\frac{16}{25}[/tex] ( take square root of both sides )

x = ± [tex]\sqrt{\frac{16}{25} }[/tex] = ± [tex]\frac{4}{5}[/tex]

the positive value of x is then [tex]\frac{4}{5}[/tex]

The value of x is 4 for the isosceles triangle has a base that measures x+2 with legs that measure 4x-3 and 2x+5.

Therefore, an isosceles triangle has two equal sides as well as two equal angles. An equilateral triangle is one in which all of its sides are equal, and a scalene triangle is one in which none of its sides are equal. The characteristics of an isosceles triangle are as follows: There is agreement between two sides. The base of an isosceles triangle refers to the third side of the triangle, which is unequal to the other two sides. The two angles that are opposite the equal sides line up perfectly.

Here,

Since the adjacent sides of isosceles triangles are equal,

4x-3=2x+5

4x-2x=5+3

2x=8

x=4

The isosceles triangle has a base that measures x+2 and legs that measure 4x-3 and 2x+5, so x is equal to 4.

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Answer:

Step-by-step explanation:

The slope of the line y = -5x-4 is -5 or -5/1 so the slope of the perpendicular line is +1/5 eg…

y = x/5 + c

To find c we substitute x=15, y=-2

-2 = 15/5 + c

-2 = 3 + c

C = -5

So the equation is

Y = x/5 - 5

The length AB of rectangle in terms of x is (4 + x) and values of a and b are 10 and 4.

The side AB measures (4 + x). Hence, the length of AB in terms of x is (4 + x).

The area of rectangle is calculated by the formula-

Area = length × breadth

Keep the values in formula -

28 = (4 + x) (6 + x)

Performing multiplication of both brackets with each other

28 = 24 + 4x + 6x + x²

Solving and rewriting the equation

x² + 10x = 4

Equation in question - x² + ax = b

Comparing both the equations, we get a = 10 and b = 4.

Thus, length of AB is (4 + x) and value fo a is 10 and b is 4.

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Answer:

Step-by-step explanation:

36×(35)-1000=1260-1000=260

Answer: The general form for an equation that models a wave is this: (+/-) a (sin/cos) (2π(x-p)/T), where a is your amplitude, p is your phase shift, and T is your period. The (+/-) becomes + if the graph is to start in the positive direction, and - if it is to start in the negative direction. The (sin/cos) becomes sine if the graph is to start at 0 before being shifted, while it becomes cosine if the graph is to start at the amplitude.

In this case, our graph starts out negative, and at the amplitude with no phase shift, so the (+/-) becomes -, (sin/cos) becomes cos, and p is zero. Substituting in the values given in the problem, a = 9 and T = 7, we find this equation: d = -9cos(2πt/7).

Step-by-step explanation:

Answer:

550.4 square units.

Step-by-step explanation:

This problem is easier than it seems.

To find the area of the parallelogram, multiply 11 and 32 to get 352 sq. units

The two semicircles must be equal because the sides of a parallelogram must be equal.

So if you add the semicircles together, you get a circle.

So we're really finding parallelogram+circle.

The area of a circle is [tex]\pi[/tex]x[tex]r^{2}[/tex], and the circle's radius is 8 because the radius is half of the diameter.

[tex]\pi[/tex]≈3.1 because you're rounding to the nearest tenth.

3.1x64=198.4 sq. units

198.4+352=550.4 square units.

The probability of drawing two yellow marbles if the first one is placed back in the bag before the second draw is 0.022

Since the formula we refer to in calculating probability is

P = no of possible outcomes/ total number of outcomes

Since we were provided with 10 marbles out of which 2 are yellow, 3  are pink and  5 are blue

So the total outcomes are = 1,The total number of yellow marble is  2

The probability that  the first ball drawn is yellow :

P₊= 2/10= 1/5

the probability of drawing the second ball to be yellow is:

P₂= 1/9

the total probability of  drawing two yellow marbles if the first one is placed back in the bag before the second draw is :

P= 1/5 *  1/9

= 1/45

= 0.022

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What is the probability of drawing two yellow marbles if the first one is NOT placed back into the bag before the second draw? There are 10 marbles total, 2 yellow, 3 pink, and 5 blue

The measure of angle EAC IS 50°

The angle bisector in geometry is the ray, line, or segment which divides a given angle into two equal parts. For example, an angle bisector of a 60-degree angle will divide it into two angles of 30 degrees each. In other words, it divides an angle into two smaller congruent angles. Given below is an image of an angle bisector of ∠AOB.

∠BAE = x + 30, ∠EAC = 3x - 10

If AE is a line that bisects BAC,

then ∠BAE = ∠EAC

which becomes,

x + 30 = 3x - 10

collecting like terms,

x - 3x = -10 - 30

-2x = -40

x = -40/-2

x = 20°

But m ∠EAC = 3x - 10

substituting x = 20°

we have ∠EAC = 3(20) - 10

                          = 60 - 10

    ∠EAC       = 50°

In conclusion, the value of  ∠EAC  = 50°

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Lily's time is spent in biology class on lesson is 1 hour or 60 minutes.

Time of one class = 1 hour and fifteen minutes

As we know, 1 hour = 60 minutes

So, time of a class = 60 + 15

Performing addition

Time of a class = 75 minutes

Time spent in talking in biology class = 5 minutes

Time spent in reviewing old homework = 10 minutes

Total time spent = 15 minutes

Remaining time = 75 - 15

Performing subtraction

Remaining time = 60 minutes

Hence, 60 minutes or 1 hour is spent on the lesson.

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The amount of energy that the ball will have at 10 m/s is; 600 J

From the given table, we see that when the velocity is 2 m/s, then the energy is 20 J.

If we take the square of the velocity, we get 2² = 4.

Thus, we need to multiply 4 by 6 to get the energy that is equal to 24 as 4 * 6 = 24.

Similarly;

For velocity equal to 3 m/s, the energy is given as:

E = 6 * 3²

E = 54 J

Thus, the general formula to find the energy is given as:

E = 6 * v²

where;

E is the energy

v is the velocity

Now, for velocity equal to 10 m/s, energy is given as;

E = 6 * 10

E = 60 J

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Answer:

156°

Step-by-step explanation:

m5 = m7 (vertical angles)
m4 + m5 = 180 (supplementary)
m5 = 180 - 124 = 156

So measure of both angle 5 and 7 is 156

The number of pack of cards sold at the state of Arkansas is 8100.

For the values given in question.

The tax on playing card in state of Arkansas = 6 cents per pack.

Total revenue generated =  $48600.

Divide total revenue by one pack price to get the number of packs.

Number of pack = Total revenue/price of each pack

Number of pack =  $48600/6

$48600.Number of pack = 8100

Thus, the number of pack of cards sold at the state of Arkansas is 8100.

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Answer:

your answer is 16

Step-by-step explanation:

So, to solve (1 + 3)²

first add 1 and 3

then you will get 4

and your equation would be (4)²

then you just square 4.

(4)² > 4x4 = 16

hope this helps (can you mark as brainiest pls)

The table for the linear equation is summarized below:

d                         t

3                        13

4                        18

5                        23

6                        28

In this problem we have a two-column table associated to a linear function, the first column of the table represent a set of values of the domain (d) of the function and the second column of the table is for the set of values of the range (t) of the same. We need to fill the second column of the table with the values associated with the range:

d = 3

t = 5 · 3 - 2

t = 15 - 2

t = 13

d = 4

t = 5 · 4 - 2

t = 20 - 2

t = 18

d = 5

t = 5 · 5 - 2

t = 25 - 2

t = 23

d = 6

t = 5 · 6 - 2

t = 30 - 2

t = 28

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The predicted fuel efficiency for a speed of 30 mph will be 26.50 mpg when the least-squares regression line is given.

If the data demonstrates a stronger link between two variables, the line that best matches this linear relationship is known as a least-squares regression line, and it minimizes the vertical distance between the data points and the regression line. A regression line is a straight line that illustrates how a response variable y varies when an explanatory variable x changes. The line is a mathematical model that predicts the value of y given a value of x. A regression line predicts the value of y for a given value of x. A regression line is discovered through regression analysis. When the explanatory variable changes, the regression line shows how much and in which direction the response variable changes.

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The corresponding measure of each angle is 80, 80, 80, 100 and 100 degrees

Given: m<7=100 degrees

To find <6, <8, <2, <5 and <11

In the <7 is vertically opposite <5. Since vertically opposite angles are equal.

Thus, <5 =  <7 =   100 degrees

Also,  <5 and <6 are angles on a straight, and the sum of angles on a straight line is 180 degrees. Thus:

<5 + <6 = 180

100 + <6 = 180

<6 = 180 -100 = 80 degrees

Also, <6  and <8 are vertically opposite.

Thus, <8 = <6 = 80 degrees

<2 and <6 are corresponding angles, and corresponding angles are equal. Thus, <2 = <6 = 80 degrees

Likewise, <11 and <7 are corresponding angles

Thus, <11 = <7 = 100 degrees

Therefore, the measure of angle <6, <8, <2, <5 and <11 are 80, 80, 80, 100 and 100 degrees respectively

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Answer:

i think it might be c

Step-by-step explanation:

As RS=TU and ST=UR by distance formula, The given quadrilateral RSTU is rectangle and The diagonals RT=US so they are equal and bisect each other at right angle.

A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason. Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel. An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposite sides. A rectangle has two dimensions—length and width—because it is a two-dimensional shape. The rectangle's longer side is its length, and its shorter side is its width.

Here,

Calculate the length of sides by distance formula.

RS=√(y2-y1)²+(x2-x1)²

=√(2-4)²+(-2-2)²

=√4+8

=√(12

=2√3 units

ST=√(y2-y1)²+(x2-x1)²

=√(0-2)²+(-1-(-2))²

=√(4+1)

=√5 units

TU=√(y2-y1)²+(x2-x1)²

=√(2-0)²+(3-(-1))²

=√(4+8)

=√12

=2√3 units

UR=√(y2-y1)²+(x2-x1)²

=√(4-2)²+(3-2)²

=√(4+1)

=√5 units

RT=√(y2-y1)²+(x2-x1)²

=√(0-4)²+(-1-2)²

=√(16+9)

=√25

=5 units

US=√(y2-y1)²+(x2-x1)²

=√(2-2)²+(-2-3)²

=√(0+25)

=√25

=5 units

Because the given quadrilaterals, RS=TU and ST=UR, are rectangles and the diagonals, RT=US, are equal and at right angles to one another, according to the distance formula.

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The number of minutes in total that the three swimmers spent in completing the race is; 4.12795 minutes

We are given;

Time taken by Martin to finish swimming = 78.934 seconds

Time taken by Abby to finish swimming = 83.978 seconds

Time taken by the last teammate to finish the race = 84.765 seconds

Thus;

Total time taken by the three swimmers to finish the race = 78.934 + 83.978 + 84.765 = 247.677 seconds

Now, we want to know the total time they spent in minutes and we know that the unit of conversion is;

60 seconds = 1 minute

Thus;

247.677 seconds = (247.677 * 1)/60 = 4.12795 minutes

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a) 88 unique special dinners are there if there are 8 appetizers and 11 entrees.

b) 84 unique special dinners are there if there are 12 appetizers and 7 entrees.

Given that,

In a typical Chinese restaurant, the Special Dinner is frequently offered, allowing the customer to select one appetizer and one entrée.

We have to find

a) How many unique special dinners are there if there are 8 appetizers and 11 entrees.

b) How many unique special dinners are there if there are 12 appetizers and 7 entrees.

We solve

a) We just multiply

8×11=88

b) 12×7=84

Therefore, a) 88 unique special dinners are there if there are 8 appetizers and 11 entrees.

b) 84 unique special dinners are there if there are 12 appetizers and 7 entrees.

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The equation of linear equation is y = -5x +3.

What is equation of linear equation?

A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line. This is the reason why it is named as a 'linear equation'.

The standard form or the general form of linear equations in one variable is written as, Ax + B = 0; where A and B are real numbers, and x is the single variable. The standard form of linear equations in two variables is expressed as, Ax + By = C; where A, B and C are any real numbers, and x and y are the variables.

The slope intercept form of linear equation is

y = mx + b

where m is the slope.

Given,

The slope = -5

and the points are (4, -17)

y = -17, x = 4, m = -5

-17 = -5(4) + b

-17 = -20 + b

-17 + 20 = b

b =3

The equation of linear equation is y = -5x + b

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Answer:

Theres nothing to see?

Step-by-step explanation:

Answer:

First is one value of x

Second is no values of x

Third is all values of x

Step-by-step explanation:

Please give brainliest!