In ΔABC, ∠C measures 46° and the values of a and c are 10 and 9, respectively. Find the remaining measurements of the triangle, and round your answers to the nearest tenth. ∠A = 82.2°, ∠B = 62.8°, b = 17.1 ∠A = 53.1°, ∠B = 80.9°, b = 12.4 ∠A = 53.1°, ∠B = 80.9°, b = 17.1 ∠A = 82.2°, ∠B = 62.8°, b = 12.4

Answer: 21

Step-by-step explanation:

9  + 10 = 21

The expression simplifies to 81 over 16 by applying the exponent rules, particularly recognizing that any number to the power of 0 is 1 and when raising a power to a power, we multiply the exponents.

The student's question is asking to simplify the expression 3 to the power of 2 multiplied by 5 to the power of 0 whole over 4, the whole squared. To simplify this expression, we should apply the exponent rules.

Let's simplify step-by-step:

First, recognize that any number raised to the power of 0 is 1.

The expression now  simplifies to square of three, since anything multiplied by 1 remains unchanged.

Now, take the entire expression over 4 and square it as indicated.

Thus, the correct answer is 3 to the power of 4 multiplied by 1 squared over 4 squared equals 81 over 16.

Options A, B, and D each have exactly one solution. Option C has no solution because it simplifies to a contradiction.

To determine which of the given equations have exactly one solution, we will analyze each equation to see if it can be simplified or rearranged to form an identity (true for all values of [tex]\( x \))[/tex] or a contradiction (false for all values of [tex]\( x \))[/tex], or if it remains a valid equation with a unique solution for [tex]\( x \).[/tex]

An equation has exactly one solution if it can be simplified to the form [tex]\( ax = b \)[/tex] where [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are constants, and [tex]\( a \)[/tex] is not zero.

Let's analyze each option step by step:

Option A: [tex]\( -5x + 12 = -12x - 12 \)[/tex]

1. Add [tex]\( 12x \)[/tex] to both sides: [tex]\( -5x + 12x + 12 = -12 + 12x \).[/tex]

2. This simplifies to [tex]\( 7x + 12 = -12 \).[/tex]

3. Subtract [tex]\( 12 \)[/tex] from both sides: [tex]\( 7x = -24 \).[/tex]

4. Divide by

  This equation has exactly one solution, [tex]\( x = -\frac{24}{7} \).[/tex]

Option B: [tex]\( -5x + 12 = 5x + 12 \)[/tex]

1. Add [tex]\( 5x \)[/tex] to both sides: [tex]\( -5x + 5x + 12 = 5x + 5x + 12 \).[/tex]

2. This simplifies to [tex]\( 12 = 10x + 12 \).[/tex]

3. Subtract \( 12 \) from both sides: [tex]\( 0 = 10x \).[/tex]

4. Divide by [tex]\( 10 \)[/tex]: [tex]\( x = 0 \).[/tex]

  This equation has exactly one solution, [tex]\( x = 0 \).[/tex]

Option C: [tex]\( -5x + 12 = -5x - 12 \)[/tex]

1. Subtract \( -5x \) from both sides: [tex]\( 12 = -12 \).[/tex]

  This simplifies to a contradiction since [tex]\( 12 \)[/tex] does not equal [tex]\( -12 \).[/tex]

  Therefore, this equation has no solution.

Option D: [tex]\( -5x + 12 = 5x - 5 \)[/tex]

1. Add \( 5x \) to both sides: [tex]\( -5x + 5x + 12 = 5x + 5x - 5 \)[/tex].

2. This simplifies to [tex]\( 12 = 10x - 5 \)[/tex].

3. Add [tex]\( 5 \)[/tex] to both sides: [tex]\( 17 = 10x \).[/tex]

4. Divide by [tex]\( 10 \)[/tex]: [tex]\( x = \frac{17}{10} \)[/tex].

  This equation has exactly one solution, [tex]\( x = \frac{17}{10} \)[/tex].

Based on this analysis, Options A, B, and D each have exactly one solution. Option C has no solution because it simplifies to a contradiction.

Answer:

Step-by-step explanation:its not a improper fraction

Answer:

1 and 2/9

Step-by-step explanation:

7 goes into 9 1 time and there are 2 left over so that 2 would be 2/9 so it's 1 whole and 2/9

Answer:

$20,001

Step-by-step explanation:

Let $x be the amount of dollars Lincoln needs to make in sales to earn more than $1500.

His boss pays him $500 for the week, plus a 5% commission on each vehicle he sells.

5% of $x is $0.05x, the Lincoln earns

[tex]\$(500+0.05x)[/tex] in total.

Hence,

[tex]500+0.05x>1,500[/tex]

Solve this inequality:

[tex]0.05x>1,500-500\\ \\0.05x>1,000\\ \\5x>100,000\\ \\x>20,000[/tex]

Lincoln needs to make in sales more than $20,000, so the minimum amount of dollars Lincoln needs to make in sales is $20,001

Answer:

x + 2 = 0 and y - 3 = 0

Step-by-step explanation:

We have to find the solution of the system of equations  

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

⇒ 12x + 4y = - 12 .......... (2) and  

3x - 4y = - 18 ........... (3)

Now, solving equations (2) and (3) we get,

15x = - 30

⇒ x = - 2

Hence, from equation (1) we get, 2y = - 6 - 6x = - 6 - 6(- 2) = 6

⇒ y = 3

Therefore, the solution of the given system of equations is (-2,3).

Now, x + 2 = 0 and y - 3 = 0 are another system of equations that have the same solutions. (Answer)

Good evening ,

Answer:

(x - 6 + i)(x - 6 - i) = x² - 12x + 37

Step-by-step explanation:

(x - 6 + i)(x - 6 - i) = [(x - 6) + i]×[(x - 6) - i] = (x-6)² - i² = (x-6)² + 1 = x² - 12x + 37 .

:)

Answer:

-5a - 4 is the expression equivalent

Following are the calculation to the given expression:

Given:

[tex]\bold{7a-8-12a+4}[/tex]

To find:

solve the expression=?

Solution:

[tex]\to \bold{7a-8-12a+4}\\\\\to \bold{-5a-4}\\\\[/tex]

Therefore, the final answer is "[tex]\bold{-5a-4}[/tex]".

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Answer:

∠A= 112.5°, ∠B=67.5°, ∠C is 67.5° and ∠D 112.5°.

Step-by-step explanation:

Consider the provided information.

The sum of all interior angle of a polygon is: [tex](n-2)180[/tex]

Substitute n = 8.

[tex](8-2)180=1080[/tex]

Thus, the measure of each angle is: [tex]\frac{1080}{8}=135[/tex]

∠B and ∠C are congruent and their sum is 135°

∠B+∠C=135°

∠B=67.5°

Hence, the m angle B and m angle C is 67.5°.

The sum of all angles of a quadrilateral is 360°.

∠A+∠D+∠B+∠C=360°

∠A+∠D=360°-135°

∠A+∠D=225°

∠A and ∠D are congruent and their sum is 225°

∠A+∠D=225°

∠A=∠D=112.5°

Hence, the m angle A and m angle D is 112.5°.

The focus must be the point (0, 4), because it is equidistant from the vertex (0, 2) as the focus is from the directrix, y = 0, which indicates that the focus is twice the distance from the vertex to the directrix or (0, 4)

The evaluation that shows the reasons the focus must be the point (0, 4) are as follows;

The location of the vertex of the parabola at the point (0, 2), and the location of the directrix on the x-axis, we get;

The location of the focus is on the line passing through the vertex, which is the line x = 0

The definition of a parabola is the path of a point that moves such that the distance from the focus and the directrix are the same

The equation of the directrix is; y = 0

The shortest distance of the vertex from the directrix is 2 - 0 = 2 units

The distance from the focus to the vertex is therefore 2 units

Whereby the focus is 2 units above the x-axis, the focus, which is 2 units from the vertex on the remote side of the directrix is 2 + 2 = 4 units above the x-axis and the coordinates of the vertex must be (0, 4)

The definition of a parabola indicates that the location of the focus should be 2 units from the

The complete question found through search can be presented as follows;

A parabola is shown graphed on the grid below. Its directrix is the x-axis

(a) Explain why the focus must be the point (0, 4)

The coordinates of  the vertex of the parabola is (0, 2)

The coordinates of other points on the parabola are (-8, 8), (8, 8)

Answer:

The graph of y + 1 = −3/5 (x − 4) would be a straight line. The graph figure is attached below.

Step-by-step explanation:

As the linear equation y + 1 = −3/5 (x − 4) is given.

Since y-y₁ = m (x - x₁) is the Point-slope form is the general form y-y₁=m(x-x₁) for linear equations.

Hence, from the linear equation we can determine the slop which is m = -3/5

Also, when we put x = 0 in the linear equation, we determine the y-intercept as follows:

                            y + 1 = −3/5 (x − 4)

                            y + 1 = -3/5(-4)      ∵x = 0

                            y = 12/5 - 1

                            y = 7/5

y-intercept: 7/5

Hence,

Table for some points can be made for x and values as:

0           7/5

1            4/5

The graph of y + 1 = −3/5 (x − 4) would be a straight line. The graph figure is attached below.

Keywords: graph, straight line

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Answer:

7000

Step-by-step explanation:

nhi batunga

Answer:

Step-by-step explanation:

A = L * W

A = 99

L = 2w + 7

now we sub

99 = (2w + 7)(w)

99 = 2w^2 + 7w

2w^2 + 7w - 99 = 0

(2w - 11)(w + 9) = 0

2w - 11 = 0

2w = 11

w = 11/2

w = 5 1/2 ft (or 5.5 ft) <==== width is 5 1/2 ft)

L = 2w + 7

L = 2(5.5) + 7

L = 11 + 7

L = 18 ft <====== length is 18 ft

Answer:

82q

Step-by-step explanation:

-2(-5)q+(-72)(-q)

10q+72q

82q

Hey there! :)

-2(-5)q + (-72)(-q)

Simplify!

10q + (72q)

Since both terms contain "q," we know that we can add them together.

Simply look at it this way: 10+72 , then add the q at the end of your answer.

10 + 72 = 82 --> add the q! Therefore, your final answer is 82q.

~Hope I helped! :)

Answer:

C

Step-by-step explanation:

They're solid lines and overlap at that point

Answer:

(0,3) (3,0)

Step-by-step explanation:

if your asking for y=-x+3

or y=x+3 is (0,3) (0,-3

Answer:

40 min

Step-by-step explanation:

1 x 48 + .20 .48

(1.20) (48)=  40 min

To find kilometers per hour, we need to multiply 2 1/6 by 3, because it took Linley 1/3 hour to ride that far.

2 1/6 * 3 = 6 1/2

So, her average speed in kilometers per hour is 6 1/2 kph

Answer:

Step-by-step explanation:

The domain on all x-squared parabolas is all real numbers.  

The range of an x-squared parabola is always found at the y coordinate of its vertex, and then is determined by whether it opens upwards or downwards. Our vertex has a y coordinate of -1 and opens downwards, so the range is all real numbers less than or equal to -1.

There are no x-intercepts (aka places on the graph that go through the x-axis), but the y-intercept is also the vertex, which is (0, -1).

Because this is an upside down parabola, it has a max point, again at the vertex.  It has no min point.

It increases from negative infinity to its max point and is notated as follows: (-∞, 0]

and decreases from its max point to negative infinity: [0, -∞)

The situation that can be represented by the inequality x < 3 is that the backpack is heavier than 3 kg.

The situation that can be represented by the inequality x < 3 is: The backpack is heavier than 3 kg.

This means that if the weight of the backpack is represented by 'x', then 'x' is less than 3 kg.

For example, if the weight of the backpack is 2 kg, then 2 is less than 3, which satisfies the inequality x < 3.

The situation that can be represented by the inequality x<3 is "The ceiling is lower than 3 m." This inequality shows that the value of x is less than 3. In real-world terms, it could mean the height of a ceiling, length of an object, or the age of a child, among other things. However, in the given options, it corresponds to a ceiling's height being less than 3 meters.

Let's explore a couple of examples to understand inequalities better with metric measurements:

Answer:

B) y=1/2x-3/2

Step-by-step explanation:

y=2x+3

x=2y+3

2y=x-3

y=1/2x-3/2

Answer:

B

Step-by-step explanation:

EDGE 2020

Answer:

I could do 1 and 3

1) 2x-3y=-2 ....1

-

2x+y=14......2

=-4y=-16

y=4

Substitute (y=4) into equation 1

2x-3 (4)=-2

2x-12=-2

2x=-2+12

2x=10

×=5

3) 5x+5y=20....1

-

-3x+5y=4......2

=8x=16

x=2

Substitute (x=2) into equation 1

5 (2)+5y=20

10+5y=20

5y=20-10

5y=10

y=2

Answer: (1) x = 5 , y = 4

(2) x = -3 and y = 0

(3) x = 2 and y = 2

Step-by-step explanation:

(1) 2x - 3y = -2  ................... equation 1

   2x + y = 14 ................ equation 2

solving the system of linear equation by elimination method. We need to decide the variable to eliminate first , in this case , since the coefficient of x are the same  and they have the same signs (+), we can eliminate the variable x first by subtracting equation 1 from equation 2, so we have

2x - 2x + y - (-3y ) = 14 - ( - 2)

4y = 16

divide through by 4

y = 4

substitute y = 4 into equation 1 , we have

2x - 3 (4) = -2

2x - 12 = -2

2x = -2 + 12

2x = 10

x = 5

Therefore :

x = 5 and y = 4

(2) x = -6y - 3 ....................... equation 1

    8x + 8y = -24 ....................... equation 2

Solving the system of linear equation by substitution method , substitute x = -6y - 3 into equation 2 , equation 2 becomes

8(-6y - 3 ) + 8y = -24

expanding , we have

-48y - 24 + 8y = -24

-40y - 24 = -24

Add 24 to both sides , we have

- 40y = -24 + 24

-40y = 0

divide through by -40

y = 0/-40

y = 0

substitute y = 0 into equation 1 , equation 1 then becomes

x = -6(0) - 3

x = -3

Therefore : x = -3 and y = 0

(3)  5x + 5y = 20 ........................ equation 1

    -3x + 5y = 4  ............................ equation 2

solving the system of linear equation by elimination method , we have to decide the variable to eliminate first , since the coefficient of y are the same and are both positive, we will eliminate y by subtracting equation 2 from equation 1 , we have

5x - (-3x) + 5y - 5y = 20 - 4

5x + 3x + 0 = 16

8x = 16

x = 2

substitute x = 2 into equation 1 , equation becomes

5(2) + 5y = 20

10 + 5y = 20

5y = 20 - 10

5y = 10

y = 2

Therefore : x = 2 and y = 2

Answer:

2 units

Question:

Calculate the distance between (3 + i) and (3 − i).

Step-by-step explanation:

This problem is equivalent to the problem:

"Calculate the distance between the points (3,1) and (3,-1)."

Since the [tex]x[/tex]-coordinates are the same, this is a vertical distance.

A vertical distance be be found by computing the positive difference of the [tex]y[/tex]-coordinates. In other words, we need only the find the distance between the numbers [tex]y=1[/tex] and [tex]y=-1[/tex] on a number line.

This distance is 1-(-1)=1+1=2 units.

Answer:

The value of [tex]a_{4}=15[/tex]

Step-by-step explanation:

Given that [tex]a_{1}=6[/tex] and [tex]a_{n}=a_{n-1}+3[/tex]

Given sequence is of the form arithmetic sequence

For arithmetic sequence the sequence is [tex]a_{1},a_{2},a_{3},...[/tex]

The nth term is of the form  [tex]a_{n}=a_{n-1}+d[/tex]

Here  [tex]a_{1}=6[/tex] and [tex]a_{n}=a_{n-1}+3[/tex]

from this the common differnce is 3.

Therefore d=3

To find  [tex]a_{2}[/tex], [tex]a_{3}[/tex] , [tex]a_{4}[/tex]

[tex]a_{n}=a_{n-1}+d[/tex]

put n=2 and d=3 we get

[tex]a_{2}=a_{2-1}+3[/tex]

[tex]a_{2}=a_{1}+3[/tex]

[tex]a_{2}=6+3[/tex]   (here  [tex]a_{1}=6[/tex] )

Therefore [tex]a_{2}=9[/tex]

[tex]a_{n}=a_{n-1}+d[/tex]

put n=3 and d=3 we get

[tex]a_{3}=a_{3-1}+3[/tex]

[tex]a_{3}=a_{2}+3[/tex]

[tex]a_{3}=9+3[/tex]   (here  [tex]a_{2}=9[/tex] )

Therefore [tex]a_{3}=12[/tex]

[tex]a_{n}=a_{n-1}+d[/tex]

put n=4 and d=3 we get

[tex]a_{4}=a_{4-1}+3[/tex]

[tex]a_{4}=a_{3}+3[/tex]

[tex]a_{4}=12+3[/tex]   (here  [tex]a_{3}=12[/tex] )

Therefore [tex]a_{4}=15[/tex]

Therefore the sequence is 6,9,12,15,...

Therefore the value of [tex]a_{4}=15[/tex]

Answer:

y=1/2x+5

Step-by-step explanation:

y=mx+b

The equation of the line that passes through the point (6,8) and has a slope of 1/2 will be y=1/2x+10.

A straight line is a combination of endless points joined on both sides of the point. A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

It is given that the equation of the line that passes through the point (6,8) and has a slope of 1/2,

The standard equation of the line passes through the points (x₁,y₁) having slope m is,

y-y₁=m(x-x₁)

Substitute the given value as

y-8=-1/2(x-6)

2(y-8)=-1(x-6)

2y-16=x-6

2y=x-6+16

2y=x+10

y=1/2x+10

Thus, the equation of the line that passes through the point (6,8) and has a slope of 1/2 will be y=1/2x+10.

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Answer:

Step-by-step explanation:

39 cars every 3 hrs.......that means (39/3) = 13 cars every hr

and if its 13 cars every hr....in 7 hrs, there will be (7 * 13) = 91 cars <==

you can either do it that way....the unit rate way...OR

you can set it up as a proportion...

39 cars to 3 hrs = x cars to 7 hrs...

39 / 3 = x / 7....cross multiply

(3)(x)= (39)(7)

3x = 273

x = 273/3

x = 91 <====

either way, u get the correct answer

Answer:

y = -2x + 3

Step-by-step explanation:

4x + 2y - 6 = 0

2y - 6 = -4x

2y = -4x + 6

y = -2x + 3

Answer:

The slope-intercept form is,

y = -2x + 3

Step-by-step explanation:

The given equation of the line is,

4x + 2y  - 6 = 0

Subtracting "(4x- 6)" from both sides of the above equation, we get

   4x + 2y - 6 - (4x - 6) = 0 - (4x - 6)

⇒ 4x + 2y - 6 - 4x + 6 = 0 - 4x + 6

⇒ 2y = -4x + 6

Now, dividing both sides by '2' of the above equation, we get

 2y ÷ 2 = (-4x + 6) ÷ 2

⇒y = -2x + 3

This is the required slope-intercept form of the given line.

13.23  miles

Step-by-step explanation:

The vector creates an inverted right-angled triangle. The westbound car will have covered 20 miles while the southbound car will ahve covered 15 miles in 30 mins;

40 miles /hr * ½ hr = 20 miles

30 miles/ hr * ½ hr = 15 miles

To find the hypotenuse (distance between the two cars), we shall use the formulae;

a² + b² = c²

20² + 15² = c²

c² = 20² – 15²

c² =  175

c = 13.23

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Final answer:

To find the total distance driven to and from work over 3 days, multiply the daily round-trip distance of 4310 miles by 3, resulting in 12,930 miles.

Explanation:

The question asks how many miles you would drive to and from work in 3 days if your round-trip to work is 4310 miles. To calculate this, you just need to multiply the daily round-trip distance by the number of days you travel. In this case, you travel to and from work for 3 days.

Determine the daily round-trip distance. (Already provided as 4310 miles)

Multiply the daily round-trip distance by the number of days traveled: 4310 miles × 3 days.

The calculation would be 4310 miles × 3 which equals 12,930 miles. This is the total distance driven to and from work over the 3 day period.

Answer

Step-by-step explanation:

From the attached diagram below,

< ADC + <D = 180° (sum of linear angle) ------------(1)

<B + <C + <D = 180° (sum of interior angle in a triangle)---------(2)

Since the two equations are equal to 180°, We equate the two equation

i.e

(1) = (2)

< ADC + <D = <B + <C + <D

<D from the left hand side will cancel <D on the right hand side

We are now left with

<ADC = <B + <C

The Exterior Angle Theorem is proven by using the Triangle Sum Theorem, the Linear Pair Postulate, and the Subtraction Property of Equality to show that the sum of the interior opposite angles of a triangle equals the exterior angle.

To complete the proof of the Exterior Angle Theorem using the fact that angle ACD is an exterior angle of triangle BCD and prove that angle B + angle C = angle ACD, follow the steps below: