If both cars in Exercise 62 are on one side of the plane and if the angle of depression to one car is 38∘ and that to the other car is 52∘, how far apart are the cars?

Answer: False.

Step-by-step explanation: An equilateral triangle is always an acute triangle because all of its angles are congruent (equal) to 60 degrees. An acute triangle is a triangle with all its angles are less than 90 degrees, so an equilateral triangle with all angles of 60 degrees is an acute triangle. An acute triangle doesn't necessarily have to be an equilateral triangle.

answer : the answer is false

Answer: The distance is 8.

1. steps to find the value of x

The first step is to equalize the form of the equation.

y = 6x-11 = -6x+y= -11

-2x-3y = -7

thus becoming:

-6x+y= -11

-2x-3y = -7

Then eliminate y:

-6x+y= -11 | times -3| becomes 18x-3y=33

18x-3y=33

-2x-3y = -7

y in the equation can be eliminated to become:

20x=40

x=40/20

x=2

steps to find the value of y:

The first step is to equalize the form of the equation.

y = 6x-11 = -6x+y= -11

-2x-3y = -7

thus becoming:

-6x+y= -11

-2x-3y = -7

Then eliminate x:

-2x-3y = -7 | multiplied by 3| becomes -6x-9y=-21

-6x+y= -11

-6x-9y=-21

x in the equation can be eliminated to become:

10y=10

y=-10/10

y=1

2.

1. steps to find the value of x

The first step is to equalize the form of the equation.

2x-3y = -1

y = x-1 becomes -x+y=-1

thus becoming:

-2x-3y = -1

-x+y=-1

Then eliminate y:

-x+y=-1| times -3| to 3x-3y=3

-2x-3y = -1

3x-3y=3

y in the equation can be eliminated to become:

-5x=-4

x=4/5

Steps to find the value of y:

The first step is to equalize the form of the equation.

2x-3y = -1

y = x-1 becomes -x+y=-1

thus becoming:

-2x-3y = -1

-x+y=-1

Then eliminate x:

-x+y=-1| multiplied by 2| becomes -2x+2y=-2

-2x-3y = -1

-2x+2y=-2

x in the equation can be eliminated to become:

-5y=1

y=-1/5

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Answer:

Step-by-step explanation:

the way to determine if two atoms are of elements in the same group in the periodic table is to look at the number of valence electrons in the outermost energy level of the atom. Elements in the same group have the same number of valence electrons. For example, elements in Group 1 have 1 valence electron, elements in Group 2 have 2 valence electrons, and so on.

It's worth mentioning that the group in the periodic table is also known as family or column.

Answer: 56

Step-by-step explanation:

-5(2-14)-2^2

REMEMBER PEMDAS

-5(2-14)-> -10+70-2^2

-10+70-4=56

The statement which best describes the triangle or triangles, if any, that can be formed with the sides measuring 60 centimeters, 100 centimeters, and 40 centimeters include the following: A. No triangle.

In Mathematics, the Triangle Inequality Theorem is represented by this mathematical expression:

b - c < a < b + c

Where:

a, b, and c represent the side lengths of this triangle.

By applying the Triangle Inequality Theorem to the side lengths of this triangle, the number of triangles that can be formed would be determined as follows:

60 + 40 > 100 (False and no triangle).

In conclusion, we can logically deduce that the two (2) short side lengths does not exceed the long side lengths and as such no triangle can be formed with the sides measuring 60 centimeters, 100 centimeters, and 40 centimeter.

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Complete Question:

Which best describes the triangle or triangles, if any, that can be formed with the sides measuring 60 centimeters, 100 centimeters and 40 centimeter?

A. No triangle

B. One unique scalene triangle

C. infinitely small similar scalene triangles

D. Two unique scalene triangles.

Answer:

25√x^21

Step-by-step explanation:

x 21/25

180

since it's a rectangle it wil have 4 sides hence to find breadth we need to make it a square so all 4 sides will be equal hence 54 minus 3 times 2 and the length of the rectangle is 3 cm longer than the breadth of the rectangle making the perimeter into 48 after the equation 48 divide by 4 equal 12 . so now we know that the breadth of the rectangle is 12 we can add 3 to 12 to find the length of the rectangle and use 12 times 15 to find the area of the rectangle

Answer:

6(x+2y) + 3 + 4y + 5

6x+12y+3+4y+5

Simplified: 6x+16y+8

Step-by-step explanation:

Therefore , solving the provided question we cans say that

quadratic equation - x^2-5x-4 = 0 and x = 1 , 3

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

Here,

Given :

we have

quadratic equation -

x^2-5x-4 = 0

x(x-1) -3(x-3) =

(x-1)(x-3) = 0

x = 1 , 3

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the equation 10-2x is plotted below.

What is equation straight line?

Y = mx + c is the general equation for a straight line, where m denotes the line's slope and c the y-intercept. It is the version of the equation for a straight line that is used most frequently in geometry. There are numerous ways to express the equation of a straight line, including point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a geometric object with two dimensions and infinite lengths at both ends. The formulas for the equation of a straight line that are most frequently employed are y = mx + c and axe + by = c. Other versions include point-slope, slope-intercept, standard, general, and others.

The equation of the line y=10−2x

m=-2

intercept = 10

Hence the equation 10-2x is plotted below.

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A aggregate of 360 residers left Planet X in the once three times.

What's Linear Equation?

A direct equation is an algebraic equation of the form y = mx b, where m is the pitch and b is the y- intercept, and only a constant and a first- order( direct) term are included. The variables in the antedating equation are y and x, and it's sometimes appertained to as a" direct equation of two variables."

The point- pitch form, standard form, and pitch- intercept form are the three main types of direct equations.

At a pace of 120 occupants every time, they've been departing earthX.

So, by the formuls;

- 120x 3 = 360

thus, A aggregate of 360 residers left Planet X in the once three times.

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An ordered pair is a set of two values, (x,y), that represents a point on a coordinate plane. The x-coordinate represents the horizontal position and the y-coordinate represents the vertical position. The formula for an ordered pair is (x,y). where x and y are the coordinates.

Answer:

29/50

Step-by-step explanation:

Answer: Depends on how much a cupcake costs

Step-by-step explanation: If Albert has $30 and spends it on two $8 pies, he has $14 left. If cupcakes are $1 each, then he can get 14 cupcakes. If cupcakes are $0.50 each, then he can get 28 cupcakes. If cupcakes are $0.25 each, then he can get 56 cupcakes.

Answer:

6x^3 + x^2 - 12x^2 - 18x - 6x - 6 = 6x^3 - 18x^2 - 12x - 6.

Step-by-step explanation:

simplify the expression (2x+3)(3x^2-6x+2)
First, we'll use the distributive property to expand the product of the two binomials:

(2x+3)(3x^2-6x+2) = 2x(3x^2-6x+2) + 3(3x^2-6x+2)

Next, we'll expand the product of each term in the first binomial with each term in the second binomial, using the distributive property again:

= 2x3x^2 + 2x(-6x) + 2x2 + 33x^2 + 3*(-6x) + 3*2

We can now simplify the resulting terms by combining like terms and combining the coefficients:

= 6x^3 -12x^2 + 4x + 9x^2 -18x + 6

we will combine the like terms

= 6x^3 - 18x^2 + 4x + 6

This is our final expression in standard form

Answer:

900

Step-by-step explanation:

[tex]I=Prt=(9000)(0.02)(5)=900[/tex]

Therefore , the solution of the given problem of expression comes out to  be the first number plus twice the second number, or the summation of the numbers c and d.

An algebraic expression must be checked by replacing each variable with a number and performing arithmetic operations. In the example above, the answer variable is identical to 6, since 7 + 8 = 15. If we know the values of the variables, we can replace them with those values and evaluate the expression.

Here,

Assuming that:

The formula is as follows:

= c + 2d

Here, the real numbers are c and d.

c should be the first number.

The following number is d.

A digit is a mental construct that can be employed in the counting, measuring, and naming of objects. The numbers include 1, 2, 56, etc. as an example.

the two-fold sum between the first and second numbers.

In term of c and d, or

the product of c and d divided by two

The first number plus twice the second number, or the summation of the numbers c and d, is what the mathematical equation c + 2d means in verbal form.

Therefore , the solution of the given problem of expression comes out to  be the first number plus twice the second number, or the summation of the numbers c and d.

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Percentage of questions attempt by Desmond's in his math's exam is given by :

a) In his first attempt percentage of question answered by Desmond is 67.74%.

b) In his second attempt percentage of question answered by Desmond is 93.55%.

c) Improvement in the percentage of question answered by Desmond is 25.81%.

As given in the question,

Total number of questions attempted by Desmond = 31

Number of questions fully right in first attempt of Desmond = 21

a ) Correct percentage of questions in the first attempt

= ( 21 / 31 ) × 100

= 67.74%

b) Number of questions fully right in second attempt of Desmond = 29

Correct percentage of questions in the second attempt

= ( 29 / 31 ) × 100

= 93.55%

c ) Improvement in the percentage comparing both the attempts

= ( 93.55 - 67.74 ) %

= 25.81%

Therefore, the percentage of questions attempt by Desmond is given as follow :

a) In his first attempt percentage of question answered by Desmond is 67.74%.

b) In his second attempt percentage of question answered by Desmond is 93.55%.

c) Improvement in the percentage of question answered by Desmond is 25.81%.

The above question is incomplete , the complete question is :

Desmond's GCSE math's exam is next week. As part of his revision he attempted 31 questions on his least favorite topic of percentages. He got 21 questions fully right on the first attempt. Two days later he tried all 31 questions again and this time got 29 correct.

a) What percentage of question did he get correct on his first attempt?

b) What percentage of question did he get correct on his second attempt?

c) What is the percentage improvement in Desmond's results?

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Answer:

D

The parallelogram proves that D is correct

The equation of the perpendicular bisector of the segment with endpoints G (-2,0) and H(8,-6) would be, y = -(3/4)x + (9/2)

What is Perpendicular bisector of the segment?

A perpendicular bisector is a line that cuts another line segment through the junction point at a straight angle. As a result, a perpendicular bisector always cuts a line segment through its midway. The term bisect means to divide equally or uniformly.

The midpoint of the segment GH is the point (3,-3).

The slope of the line perpendicular to GH is the negative reciprocal of the slope of GH, which is -6/8 = -3/4

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

The point-slope form of the equation of the line is y - y1 = m(x - x1)

So we have

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

y + 3 = (-3/4)x + (9/2)

We can find the equation of the perpendicular bisector of the segment G(x1, y1) and H(x2, y2) by using the midpoint of the segment, (x1 + x2)/2, and (y1 + y2)/2, and the slope of the segment, (y2 - y1)/(x2 - x1)

so our final equation is y = -(3/4)x + (9/2)

Therefore, equation of the perpendicular bisector of the segment with endpoints G (-2,0) and H(8,-6) would be, y = -(3/4)x + (9/2)

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The pairs which cannot be written or expressed in the notation of (a,b) and do not follow a specific order are not ordered pairs .

What are Ordered Pairs ?

The Ordered Pair is defined as a pair of elements that have specific importance for order of their placements. Ordered pairs are used in coordinate geometry to represent a point on a coordinate plane.

So , the numbers that do not follow the specific order of placements cannot be called as Ordered Pairs .

Two Ordered Pairs [tex](a_{1} ,b_{1} )[/tex] and [tex](a_{2} ,b_{2} )[/tex] can be considered as equal if and only if [tex]a_{1} =a_{2}[/tex] and [tex]b_{1} =b_{2}[/tex] .

Every point on Coordinate Plane is represented by ordered pair (x, y) where "first element x" is called x coordinate and "second element y" is called y-coordinate.

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Answer:

F=4

Step-by-step explanation:

1+3(4f-7)=28

3×4f= 12f

3×-7= -21

ADD THE LIKE TERMS

1+-21= -20

now you have 12f-20=28

at 20 to both sides

12f=48

divide 12 from both sides

48/12=4

F=4

On solving the question, The value of x in Right Angle Triangle is  .The value of x is .[tex]16\sqrt{2}[/tex]

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or previously rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.

A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

In the triangle 2 angles are  respectively.

The third angle is  = 45

The triangle is issosceles triangle

So the side which is not x is 16.

Now by using pythagorus Theorem

The value of x is .[tex]16\sqrt{2}[/tex]

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On solving the provided question, we can say that percentage of the days was she late = 14/250 * 100 = 5.6%

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.

Karrie was late to work = 14 times last year.

she worked = 250 days last year

percentage of the days was she late = 14/250 * 100 = 5.6%

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Answer:

The simple interest is calculated by multiplying the principal amount by the interest rate and the number of years.

Simple Interest = Principal x Interest Rate x Time

The simple interest on Boden's account is:

800 x 3.2% x 4 = 800 x 0.032 x 4 = $256

To find the total amount in the account after 4 years, we add the interest to the principal:

800 + 256 = $1056

So, Boden's account will have $1056 after 4 years.

A graph of the line with slope -3 passing through the point (4, -1) has been plotted in the image attached below.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

From the information provided above, we have the following slope and data points on the line:

At point (4, -1), a linear equation of this line can be calculated in point-slope form as follows:

y - y₁ = m(x - x₁)

y - (-1) = -3(x - 4)

y + 1 = -3x + 12

y = -3x + 12 - 1

y = -3x + 11

Next, we would use an online graphing calculator to plot the above linear equation in slope-intercept form as shown in the graph attached below.

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....................

Answer:

12.73%

Step-by-step explanation:

24 + 32 = 56(veggie sandwich)

112 + 150 = 262

262 + 64 = 326

326 + 58 = 384

384 + 56(veg sand) = 440

440 = total number of students

Divide 100 by 440 and you get 0.23

Multiply that by 56 and you get 12.73%

:)