A (vector, reflection) is a congruence transformation.

Answer:

4.92 ft

Step-by-step explanation:

The ladder is the hypotenuse of a right triangle

adjacent  leg / hypotenuse =  cos 75

cos 75 = adjacent leg / 19

19 cos 75 ° = adjacent leg = 4.92 ft

When the thermometer reads 6 degrees the temperature drops 15 degrees overnight, the temperature at 9:00pm will be 16°.

From the information, the thermometer reads 6 degrees the temperature drops 15 degrees overnight the it rises 25 degrees at 9:00am.

Therefore, the temperature at 9:00pm will be:

=6° - 15° + 25°

= 16°

Therefore, the temperature at 9:00pm will be 16°.

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Answer:

The midpoint of the line segment AB

is at (−1, 0).

Step-by-step explanation:

In a general sense the midpoint formula for a line segment whose endpoints are

[tex] \sf ( x_1 + x_2) (y_1 + y_2)[/tex]

would be the mean of the abscissa and the ordinate as seen in the formula below:

[tex] \sf \: (x_m, \: y_m) = ( \frac{x_1 + x_2}{2} , \frac{y_1 + y_2}{2} )[/tex]

When the line segment lies on one axis, then the there would be only one non-zero value in the ordered pair.

Assuming that the line segment AB

is in the x-axis, then the coordinates of the points would be:

[tex] \sf \: A(−2, 0)B(0,0)[/tex]

To get the midpoint, substitute the points above in the formula for the midpoint:

[tex] \sf \: (x_m, \: y_m) = ( \frac{x_1 + x_2}{2} , \frac{y_1 + y_2}{2} ) \\ \sf \: = ( \frac{ - 2 + 0}{2} ),0 \\ \sf \: = ( \frac{ - 2}{2} ), 0 \: \: \: \: \: \: \: \: \\ \sf \: ( - 1, 0)[/tex]

The midpoint of the line segment AB

is at (−1, 0).

After a translation 4 units left, a reflection across the x-axis, and a translation 2 units down, the coordinates of the image are (-1, 2).

In mathematics, a translation is the movement of a shape to the left or right, and/or up or down. The translated shapes appear to be the same size as the original shape, implying that the shapes are congruent.

They have simply been moved in one or more directions. There is no change in the shape because it is simply moving from one location to another.

According to transformation rule in graph, when moving it to the right, you add the x value And when moving to the left, you subtract the x value,

Value of x = 3

Here the reflection of x has translated 4 units left, which implies

3 - 4 = -1

And, when moving up you add to the y value and when moving down you  subtract to the y value,

Value of y = 4

Here the reflection of y has translated 2 units down, which implies

4 - 2 = 2

Thus, the coordinates of the image formed by the reflection are (-1, 2)

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 A parabola having vertex at the origin and focus at (2,0) is expressed by the following equation:

x = y²/8

  A parabolic function is one that has a quadratic variable, its shape is defined by the intersection of an inclined plane whose angle of inclination with respect to the axis of revolution of the cone is equal to that presented by its generatrix.

Since the vertex and the focal axis are on the same axis, we analyze that:

(y - 0)² = 4p(x - 0)

Focus

0 + p = 2

p = 0 + 2

p= 2

(y - 0)² = 4*2(x - 0)

(Y)² = 8(X)

x = y²/8

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The slope-intercept form is y = 1/2x - 4 for line perpendicular to 4 x+2 y=7 through (4,-2) ,

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

In an equation, perpendicular lines have the opposite reciprocal slope. In other words, if a line's slope is a positive fraction, its reciprocal slope is negative.

Here given that  4 x+2 y=7

can also be written as

y = -2x + 7/2

Here -2 is the slope and 7/2 is the y-intercept

To find a perpendicular line to the following equation, use the opposite reciprocal slope and point, then solve using the point-slope formula.

y - y₁ = m(x - x₁)

We have, m = 1/2, x₁ = 4and y₁ = -2

y - (-2)= 1/2(x - 4)

y + 2= 1/2x - 2

y = 1/2x - 4

We have the slope-intercept form y = 1/2x - 4 of a line  perpendicular to  4 x+2 y=7 through (4,-2)

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Answer:

at least two solution so c

Answer:

[tex]{ \tt{area = \pi {r}^{2} }} \\ \\ { \tt{ = 3.14 \times {6}^{2} }} \\ \\ = 113.04 \: mm {}^{2} [/tex]

Answer:

A = 113.1 mm²

Step-by-step explanation:

Area of circle = πr²

A = 22/7(6mm)²

A = 22/7(36mm²)

A = 792mm²/7

A = 113.1 mm²

Therefore the area of the circle is 113.1mm².

A constant is a value or number that is consistently the same regardless of how it is expressed.

In the mathematical expression 3x + 5y + 3 the constant is 3.

Therefore, in the mathematical expression 3x + 5y + 3 the constant is 3.

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Answer:

1 5/6 or 11/6

Step-by-step explanation:

2/3+3/4+5/12 = 11/6

Answer:

22/12

Step-by-step explanation:

Add all 2/3 + 3/4 +5/12

=take LCM of 3 , 4, 12

=

12/8 +9 + 5

= 22/12

Answer:

Step-by-step explanation:

8-3k-6 = 2-3k   (distribute -3 to (k+2))

-3k+2 = 2-3k  (8-6 is 2)

2 = 2   (subtract 3k from both sides)

2 = 2 means all real numbers

Answer:

0

Step-by-step explanation:

Distribute

8-3(k+2)=2-3k

8-3k+2=2-3k

subtract

8-6=2

2-3k+2=3k

rearrange

-3k+2=3k

I dont feel like typing the rest, watch khan academy

(ill take your email if you want to review on the weekend)

On simplifying the expression 13.8+ (-11.5) , we get 2.3 . And additions

13.8 + (-11.5) and (-13.8) +  11.5 are numbers will same value and opposite sign.

For adding a negative and a positive number, use the sign of the larger number and subtract.

For example: (–8) + 2 = -6

Given that we have to solve 13.8 + (-11.5) = 13.8-11.5 (we subtract smaller no from larger and will use the sign of lager number that is + here)

13.8+(-11.5) = 13.8-11.5 =2.3

13.8+(-11.5) simply means that 13.8 -11.5 which is subtraction of 11.5 from 13.8

but (-13.8) +  11.5 = -13.8 +11.5  =  -( 13.8 -11.5) [taking -1  common from the expression]

Therefore , -13.8 + 11.5 has same value as 13.8- 11.5 but opposite  in sign.

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Answer:

-20

Step-by-step explanation:

Answer: C. 7/9

Step-by-step explanation:

If we find the decimal values of 1/9,2/9 and so on then we will get 1/9=0.11,2/9=0.22,3/9=0.33,4/9=0.44,5/9=0.55,6/9=0.66,7/9=0.77,

8/9=0.88,9/9=1.

Given some values in which the denominator is 12 and we are required to find the values of numbers whose denominator is 9.

Decimal expansion is basically representation of a non-negative real number r is its expression as a sequence of symbols consisting of decimal digits traditionally written with a single separator.

1/9=0.11

2/9=0.22

3/9=0.33

4/9=0.44

5/9=0.55

6/9=0.66

7/9=0.77

8/9=0.88

9/9=1

Hence if we find the values of 1/9,2/9 and so on then we will get decimals of 1/9=0.11,2/9=0.22,3/9=0.33, 4/9=0.44,5/9=0.55,6/9=0.66, 7/9=0.77, 8/9=0.88,9/9=1.

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The first number (a) is - 5 and the second number (b) is 4.

let the first number be a

let the second number be b

given,

On adding 3 times the first number and 4 times the second number we get 1

=> 3 a + 4 b = 1                -      eq 1

On adding 2 times the first number and 3 times the second number we get 2

=> 2 a + 3 b = 2              -      eq 2

To solve the obtained equations using elimination method

Multiplying eq 1 with 3 and eq 2 with 4, we get

9 a + 12 b = 3                 -    eq 3

8 a + 12 b = 8                -     eq 4

Subtract eq 4 from eq 3

=> a = - 5

On Substituting the value of a in either eq 1 or eq 2, we get

b = 16

Therefore, using the elimination method, we get the first number as - 5 and the second number as 4.

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Answer:

Positive Irrational Number

Step-by-step explanation:

The whole numbers are the numbers without fractions and it is a collection of positive integers and zero. Integers are the numbers that can be positive, negative or zero, but cannot be a fraction. All rational numbers can be expressed as a fraction whose denominator is non-zero. Whereas, pi cannot be expressed in the fraction of two integers and has no accurate decimal value, so pi is an irrational number.

Answer:

i had this question before and the correct answer was "subtract 12r from both sides of the equation" im sorry if im wrong that was my correct answer when i had this question

Step-by-step explanation:

Answer:

m∠B = 26°

Step-by-step explanation:

∠A and ∠B being complementary means  m∠A + m∠B = 90°

4x + 24 + 3x - 4 = 90

7x + 20 = 90

 7x = 70

  x = 10

m∠B = (3•10 - 4)° = 26°

Answer:

m∠A = 46°

Step-by-step explanation:

For the given situation, we can clearly say that the change in one quantity will also cause a change in the second quantity.

Correlation is a relationship between the values ​​of two variables. A scatter plot is a useful tool for displaying data about two variables as a series of points in the x and y plane and determining whether there is a correlation between the variables.

Causality means that one event causes another. Well-designed experiments can only determine causality. In such experiments, similar groups receive different treatments, and the results of each group are examined.

The collected data on the number of miles driven and fuel expenses. we found that number of miles driven tended to be lower when fuel expenses were high, and the number of miles driven tended to be higher when fuel expenses sales were high.

We do not conclude that more fuel expenses mean fewer miles driven. Likely, an Increased in fuel expenses and the number of miles driven may be caused by a third factor, car mileage. So, the present case is a case of negative correlation.

Negative correlation: y decreases as x increases.

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The expression to represent the number of cousins that Anna has is c + 5.

We are given a statement that says:

Number of cousins that Simon has is equal to = c

Now, it is also given that Anna has 5 more cousins than Simon.

So, we have to write an expression to show the number of cousins that Anna has.

An expression is a combination of constants and variables to express something or a statement.

So, the expression will be made by adding 5 to c

So, we get the expression as:

The number of cousins that Anna has = c + 5

Therefore, we get that, the expression to represent the number of cousins that Anna has is c + 5.

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Answer:

2) (1/3)x + 15 = 45

Step-by-step explanation:

Given that,

→ Katelynn's commute takes 15 minutes more than 1/3 as many min as Petra's.

→ It takes Katelynn 45 minutes.

Then the equation will be,

→ (1/3) times + 15 = 45

→ (1/3)x + 15 = 45

Hence, option (2) is correct.

Based on the calculation below, we have:

The tuition per year is $36,000; and

The amount of increase in the tuition each year is $1,000.

The tuition per year and the amount of increase in the tuition each year can be calculated as follows:

Number of semesters in a year = 2

Tuition per semester = $18,000

Amount of increase in the tuition each semester = $500

Therefore, we have:

Tuition per year = Number of semesters in a year * Tuition per semester = 2 * $18,000 = $36,000

Amount of increase in the tuition each year =  Number of semesters in a year * Amount of increase in the tuition each semester = 2 * $500 = $1,000

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By substitution, the solution of the system of equations, r + s = -12 and 4r - 6s = 12, is (-6 , -6).

A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.

There are three methods that can be used to solve system of linear equations.

1. Elimination

2. Substitution

3. Graphing

Using substitution method, given two linear equations in r and s,

r + s = -12     (equation 1)

4r - 6s = 12     (equation 2)

Using the first equation, find the value of one variable, lets say r, in terms of the other.

r + s = -12     (equation 1)

r = -12 - s

Substitute the value of r to the second equation.

4r - 6s = 12     (equation 2)

4(-12 - s) - 6s = 12

-48 - 4s - 6s = 12

Combining all terms containing the variable s on one side and the constants on the other side of the equality, and solving for s.

-48 - 4s - 6s = 12

-4s - 6s = 12 + 48

-10s = 60

s = -6

Substitute the value of s in the equation of r and solve for r.

r = -12 - s

r = -12 - (-6)

r = -12 + 6

r = -6

Hence, the solution of the given system of equations is (-6 , -6).

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Answer:

No, they must sum up to give 360 degrees so it's not possible for them to be equal, if they are equal like 180 degrees each, there won't be a polygon formed!

Answer: y - 6 = -(1/2)(x+1)

Step-by-step explanation:

1. First step is to remember point slope form (a common way of expressing the equation for a line).

y - y1 = m(x - x1)

2. Next fill in the data we are given.

y - 6 = m(x -(-1)) ----> y - 6 = m(x + 1)

3. Next step is to find the value of the slope (m) using slope formula.

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

4. Fill in the data

m = (5 - 6) / (1 +1) = - 1 /2

5. Add the calculated slope to the point slope form.

y - 6 = -(1/2)(x+1)

Answer:

Not 100% sure. Hope it helps you

For equation (1), we get the Slope as 3 / 4 and y intercept as - 9 and for equation (2), we get the Slope as 3 / 4 and y intercept as - 4.

We are given 2 equations:

y = 3 / 4 x - 9 ...(1)

and y = 3 / 4 x - 4 ... (2)

Slope for equation (1) will be

slope = m1 = 3 / 4

Slope for equation (2) will be

Slope = m2 = 3 / 4

Y intercept for equation (1) will be:

= - 9

Y intercept for equation (2) will be:

= - 4

Also, since the Slope of equation are equal, so, it has no solutions as they are parallel to each other.

Therefore, for equation (1), we get the Slope as 3 / 4 and y intercept as - 9 and for equation (2), we get the Slope as 3 / 4 and y intercept as - 4.

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The required slope of the line through the points (0, 15), (9, 0)

is -5 / 3.

Given that,
To determine the slope of the line passing through the pair of points (0, 15), (9, 0).

The slope of the line is a tangent angle made by line with horizontal. i.e. m = tanx where x in degrees.

Here,
Slope of line ( m ) = [ y₂ - y₁ ]  /   [x₂ - x₁]
We have points (0, 15), (9, 0).
y₂ = 0  y₁ = 15  x₂ = 9  x₁ = 9
now,
m = 0 - 15 / 9 - 0
m = -15 / 9
m = -5 / 3

Thus, the required slope of the line is -5 / 3.

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