Instructions: Given the following image of two parallel lines cut by a transversal, find
the value of a
P Flag
question
Recovery
etry Summer 2020
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jes
7x-6
mpetencies
A
des
5x + 10
Durse Overview and
troduction
Unit 1: The Foundations
of Geometry
Jangles (type the type of angle in
Unit 2. Logic, Reasoning,
and Proof
First, these angles are alternate exterior
the box)
Next, set each angle equal to each other.
Unit 3: Parallel and
Perpendicular Lines
Next, solve for a
Home

Answer:

None of the options are correct, the correct answers are: x = 0.967 and -2.067

Step-by-step explanation:

[tex]x^2 + 1.1x - 2 = 0[/tex]

Comparing this equation with [tex]ax^2 + bx + c = 0[/tex]

a = 1, b = 1.1, c = -2

Using the almighty formula for solving quadratic equation:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a} \\x = \frac{-1.1 \pm \sqrt{1.1^2 - 4(1)(-2)} }{2(1)} \\x = \frac{-1.1 \pm \sqrt{1.1^2 - 4(1)(-2)} }{2(1)} \\x = \frac{-1.1 \pm 3.035 }{2}\\x_1 = \frac{-1.1 + 3.035 }{2} = 0.967\\x_2 = -\frac{-1.1 - 3.035 }{2} = -2.067[/tex]

Answer:

A on edge 2021. Just took practice quiz.

Step-by-step explanation:

x = 1.7 and x = -29.2

Answer:

a) 294

b) 180

c) 75

d) 168

e) 105

Step-by-step explanation:

Given the numbers 0, 1, 2, 3, 4, 5 and 6.

Part A)

How many 3 digit numbers can be formed ?

Solution:

Here we have 3 spaces for the digits.

Unit's place, ten's place and hundred's place.

For unit's place, any of the numbers can be used i.e. 7 options.

For ten's place, any of the numbers can be used i.e. 7 options.

For hundred's place, 0 can not be used (because if 0 is used here, the number will become 2 digit) i.e. 6 options.

Total number of ways = [tex]7 \times 7 \times 6[/tex] = 294

Part B:

How many 3 digit numbers can be formed if repetition not allowed?

Solution:

Here we have 3 spaces for the digits.

Unit's place, ten's place and hundred's place.

For hundred's place, 0 can not be used (because if 0 is used here, the number will become 2 digit) i.e. 6 options.

Now, one digit used, So For unit's place, any of the numbers can be used i.e. 6 options.

Now, 2 digits used, so For ten's place, any of the numbers can be used i.e. 5 options.

Total number of ways = [tex]6 \times 6 \times 5[/tex] = 180

Part C)

How many odd numbers if each digit used only once ?

Solution:

For a number to be odd, the last digit must be odd i.e. unit's place can have only one of the digits from 1, 3 and 5.

Number of options for unit's place = 3

Now, one digit used and 0 can not be at hundred's place So For hundred's place, any of the numbers can be used i.e. 5 options.

Now, 2 digits used, so For ten's place, any of the numbers can be used i.e. 5 options.

Total number of ways = [tex]3 \times 5 \times 5[/tex] = 75

Part d)

How many numbers greater than 330 ?

Case 1: 4, 5 or 6 at hundred's place

Number of options for hundred's place = 3

Number of options for ten's place = 7

Number of options for unit's place = 7

Total number of ways = [tex]3 \times 7 \times 7[/tex] = 147

Case 2: 3 at hundred's place

Number of options for hundred's place = 1

Number of options for ten's place = 3 (4, 5, 6)

Number of options for unit's place = 7

Total number of ways = [tex]1 \times 3 \times 7[/tex] = 21

Total number of required ways = 147 + 21 = 168

Part e)

Case 1: 4, 5 or 6 at hundred's place

Number of options for hundred's place = 3

Number of options for ten's place = 6

Number of options for unit's place = 5

Total number of ways = [tex]3 \times 6 \times 5[/tex] = 90

Case 2: 3 at hundred's place

Number of options for hundred's place = 1

Number of options for ten's place = 3 (4, 5, 6)

Number of options for unit's place = 5

Total number of ways = [tex]1 \times 3 \times 5[/tex] = 15

Total number of required ways = 90 + 15 = 105

(4, 7) lies on the graph of [tex]y=3f(2x)+1[/tex], so plugging in [tex]x=4[/tex] gives [tex]y=7[/tex]:

[tex]7=3f(2\cdot4)+1\implies f(8)=2[/tex]

i.e. if [tex]x=8[/tex], then [tex]y=2[/tex], so the point (8, 2) lies on the graph of [tex]y=f(x)[/tex]. The sum of this point's coordinates is 8 + 2 = 10.

Answer:

3, 5, 7

Step-by-step explanation:

As per triangle inequality theorem:

Assume the sides are equal to 3 smallest odd numbers: 1,3 and 5

The next triple is: 3, 5 and 7

So 3, 5, 7 is the combination of smallest odd numbers to make sides of a triangle

Answer:

f(n + 1) = f(n) + 20

Step-by-step explanation:

Let f(x) equals their pay at every hour of X

Where x is the number of hours, then if we go with the trend where f(1)=110, f(2)=130 f(3)=150 f(4)=170 then would see that as they are working every hour they have their pay increased by $20, from f(1)=110+ $20 gives us f(2)=130 and that is after an hour then we can say

1 hour work=$20

Then additional 1hour+ n= $20 + n

Hence,f(n+1)=f(n)+20

Answer:

the trig sign to use is sine

sin(73)=x/15

multiply each side by 15 giving you:

sin(73)15=x

x=14.3

Answer:

The value of cot theta is undefined for all the options

Step-by-step explanation:

I think the best way to go about this is by the use of a calculator.

All that needs to be done is to input the individual values to see where we have an answer that is out of it.

Now, moving away from the calculators, we know quite well that cot is a derivative of tan.

By knowing the values at which we have tan as undefined, we can appropriately see values where cot too would be undefined.

On a normal scientific calculator, there is no cot functionality.

The way around this is to express

Cot theta as 1/tan theta

Thus cot 90 = 1/cot(90) = calculation error

Cot 180 = 1/tan (180) = calculation error

Cot 270 = 1/tan 270 = calculation error

Cot 450 = 1/tan (450) = calculation error

This shows that the value of cot is undefined for all of these options

Answer:

180

Step-by-step explanation:

Answer:

Amount= $2933.2

Step-by-step explanation:

The interest of $2,500 principal earning with rate of 4%, compounded quarterly, after 4 years

A= p(1+r/n)^(nt)

P= $2500

r= 4/100= 0.04

t= 4

n = 4*4= 16

A= 2500(1+0.04/16)^(16*4)

A= 2500(1+0.0025)^(64)

A= 2500(1.0025)^64

A= 2500(1.17328)

A= 2933.2

Amount= $2933.2

Answer:

Option C is the correct option

Step-by-step explanation:

Given

Point = ( -7 , - 9 )

Slope = - 4

Equation of line ( Point slope form )

[tex]y - y1 = m(x - x1)[/tex]

when point = ( -7 , - 9 )

Hope I helped...

Best regards!!

The equation of the line is 4x + y = -37 then option C is correct.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

The given point is ( -7, - 9 ) and the slope is - 4.

The equation of the line is calculated by,

y - y₁ = m ( x - x₁ )

y - 9 = -4 ( x + 7 )

y = -4x -28 - 9

y = -4x -37

4x + y = -37

Therefore, the equation of the line is 4x + y = -37 then option C is correct.

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here is an example of a fraction that equals a whole number

2/2 would equal a whole number. The bottom number is 2. This means the whole is cut into two equal pieces (halves).

The top number is 2, so we are counting two-halves.

After shading two-halves, you see that the whole circle is shaded. Two-halves is equivalent to 1.

You would plot 2/2 at the same location as the whole number 1.

Answer:

x<-14

Step-by-step explanation:

Hello,

If we multiply by positive numbers it does not change the inequality, right?

So let's multiply by 10 both sides, it comes

[tex]2(4x+1)+10<5(x-6) \\ \\\text{*** develop ***} \\ \\8x+2+10=8x+12 < 5x-30 \\ \\\text{*** subtract 5x ***} \\\\8x+12-5x=3x + 12 < -30 \\ \\\text{*** subtract 12 ***}\\ \\3x+12-12=3x<-30-12 \\ \\3x < -42 \\ \\\text{*** divide by 3, it does not change the inequality ***}\\ \\ x < -42/3=-14[/tex]

I did not find a good way to show you here the number line. You need to basically take all numbers which are at the left of -14 on that line.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

[tex]x < - 14[/tex]

[tex] \frac{1}{5} (4x + 1) + 1 < \frac{1}{2} (x - 6)[/tex]

[tex] \frac{4}{5} x + \frac{1}{5} < \frac{1}{2} x - 3 [/tex]

[tex]8x + 2 + 10 < 5x - 30[/tex]

[tex]8x + 12 < + 5x - 30[/tex]

[tex]8x - 5x < - 30 - 12[/tex]

[tex]3x < - 42[/tex]

[tex] \frac{3}{3} x < \frac{ - 42}{3} [/tex]

[tex]x < - 14[/tex]

Answer:

Step-by-step explanation:

Solution,

Use the BODMAS Rule:

B = Bracket

O = Of

D = Division

M= Multiplication

A = Addition

S = Subtraction

Now,

Let's solve,

[tex]2 + 8 \div 2 \times 3[/tex]

First we have to divide 8 by 2

[tex] = 2 + 4 \times 3[/tex]

Calculate the product

[tex] = 2 + 12[/tex]

Calculate the sum

[tex] = 14[/tex]

Hope this helps...

Good luck on your assignment..

Answer:

14

Step-by-step explanation:

2 + 8 ÷ 2 x 3 =

There is an addition, a division, and a multiplication. According to the correct order of operations, we do first the multiplications and divisions in the order they appear from left to right.

= 2 + 4 x 3

= 2 + 12

Now we do the addition.

= 14

Answer: D) 7 to the 3 power.

Step-by-step explanation:

Answer:

D. 7 to the 3 power

Step-by-step explanation:

I know I'm very late but dont judge :V

This is also seven t the power of three

Answer:

last option

Step-by-step explanation:

It will take 200 / 5 = 40 months for Sara's phone to lose all its value, therefore, the domain is 0 ≤ t ≤ 40 because you can't have negative months. Since negative money is not a thing, the range has to be 0 ≤ V(t) ≤ 200 because it stops at 0 and starts at 200.

Answer:

144 codes are possible

Step-by-step explanation:

Okay for the first digit, we shall be selecting one out of 3,4,5,6.

Meaning we are selecting one out of four choices

The number of ways this can be done is 4C1 ways = 4 ways

For the second digit, we have 5,6,7 or 8, we are still selecting 1 out of 4 selections and the number of ways we can do this is also 4 ways

And lastly , we can choose any digit for the last number expect 5 , so from 0 to 9, we are removing 1 which means we are left with 9 choices

So the number of different area codes possible are ; 9 * 4 * 4 = 144 codes

Answer:  The estimated value is:  " 2.1 " .

__________________________________

Step-by-step explanation:

__________________________________

We are asked to "estimate" :

 5 2/11  -  3/ 2/18 ;

 Note:  Consider:  " 5 2/11 " ;  

 Note that:  "2/11" is close to:  "2/10" ; which can be expressed as a decimal value:  "0.2 " ;

So, consider this value:  "5 2/11 ";  as estimated:  " 5.2 " .

Now, consider:  " 3  2/18 " ;

Note that :  "2/18" can easily be reduced to:  "1/9 ";

               Since:  "(2/18)" = "(2÷2) / (18÷2) " =  "1/9 " ;

Note that "1/9" is close to "1/10" ; which can be expressed as a decimal value:  "0.1 ".

 So, consider:  "3 2/18 " ; as estimated:  " 3.1 " .

__________________________________

So:  To estimate:  " 5 2/11  -  3 2/18 " ;

__________________________________

Use the following:  "5.2  - 3.1 " ;

__________________________________

    5.2

 -  3. 1

__________________________________

  " 2.1 "

___________________________________

The estimated value is:  " 2.1 " .

___________________________________

Hope this is helpful to you!

___________________________________

Answer:

5 pounds.

Step-by-step explanation:

You can start by subtracting 28.60 from 70 which equals 41.4.

Now you just need to divide 41.4 by 8.28 which equals 5.

So, Salma bought 5 pounds of coffee.

Hope this helps! <3

Answer:

D.0

Step-by-step explanation:

Our system of equations is

then we can conclude that

This is a quadratic equation so we will use the dicriminant method:

Let Δ be our dicriminant

The dicriminant is negative so this equation has no real solutions

the the system has no real solutions

Greetings from Brasil...

If we have a translation for left/right, we have to use the expression:

F(X ± C)

if F(X + C), so the function shifted C units to the left

if F(X - C), so the function shifted C units to the right

Bringing to our problem

G(X) = F(X + C)

F(X) = 2X - 1

G(X) = F(X + 7) = 2.(X + 7) - 1

G(X) = F(X + 7) = 2X + 14 - 1

G(X) = F(X + 7) = 2X + 13

Answer:

a) $1520

b) [tex]S_7 =[/tex] $209195

Step-by-step explanation:

The range of salaries forms an arithmetic sequence with the first term as 25325 and its 7th term as 34445:

a) The raise the person can get each year is the common difference of the progression, d.

The nth term of an arithmetic progression is given generally as:

[tex]a_n = a + (n - 1)d[/tex]

where a = first term = 25325

d = common difference

Therefore, the 7th term (34445) will be:

34445 = 25325 + (7 - 1)d

34445 = 25325 + 6d

=> 6d = 34445 - 25325 = 9120

d = 9120 / 6 = $1520

Therefore, the raise the person gets each year (common difference) is $1520.

b) The total amount the person will earn after 7 years is the sum of the salaries of all 7 yeas.

The sum of an arithmetic progression up to the nth term is given as:

[tex]S_n = \frac{n}{2}(2a + (n - 1)d)\\ \\[/tex]

Therefore, the sum of the person's salary for the 7 years is:

[tex]S_7 = \frac{7}{2}(2 * 25325 + (7 - 1)1520)\\ \\S_7 = 3.5 (50650 + 6(1520))\\\\S_7 = 3.5 (50650 + 9120)\\\\S_7 = 3.5 * 59770\\[/tex]

[tex]S_7 =[/tex] $209195

That is the total amount of salary after 7 years

Answer:

Whats the formula for the area of a rectangle?

L x W.  48 x 36 =  1728 sq inches.

Then divide by (12 x12 ) = 144 to find square feet

Step-by-step explanation:

Answer:

The dots plotted on the scatterplot closely follow a graph of exponential decline. The large number-- around 350 texts per day-- by 18-22year-olds, seems to decline exponentially as age increases. With a little work, it may be possible to plot the curve and write an equation to model the decline.

Step-by-step explanation:

Answer:

C (-3,2)

Step-by-step explanation:

Well point Q on the parabola is located on point (1,2),

The corresponding point means the point located all the way to the left of Q which is (-3,2).

Thus,

the point that is corresponding to point Q is C. (-3,2).

Hope this helps :)

Answer:

+When the graph is below the x-axis, the barnacle is underwater.

+The graph dips below the x-axis three times between x = 0 and x = 20, so the barnacle goes underwater three times.

+Every time the barnacle goes underwater, the boat travels pi meters (one half the circumference of the wheel) before the barnacle comes back up, so the barnacle covers 3pi  meters underwater between x = 0 and x = 20

Step-by-step explanation:

To determine the number of times that the times the barnacle went beneath the water level, it can be illustrated when the graph is below the x-axis.

It should be noted that the graph dips below the x-axis three times between x = 0 and x = 20, therefore the barnacle goes underwater three times.

Also, every time the barnacle goes underwater, the boat travels pi meters before the barnacle comes back up.

Learn more about graph on:

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Answer:

Step-by-step explanation:

The question is incomplete. Here is the complete question.

Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length using the Pythagorean theorem and then find the value of the indicated trigonometric function of the given angle. Rationalize the denominator if applicable. Find tan B when a = 96 and c = 100.

Pythagoras theorem states that the square of the hypotenuse side of a right angled triangle is equal to the sum of the square of its other two sides. Mathematically c² = a²+b² where c is the hypotenuse and a,b are the other two sides.

From the question, we are given a = 96 and c = 100, to get the unknown side 'b', we will substitute the given values into the formula above;

c² = a²+b²

100²  = 96² +b²

b²  = 100²  - 96²

b²  = 10,000 - 9216

b²  = 784

b = √784

b = 28

Hence, the unknown length is 28.

To get tanB, we will use the SOH, CAH, TOA trigonometry identity

According to TOA, tan B = opposite/adjacent

tan B = b/a (note that side b is the opposite in this case since the angle we are considering is B)

Given b = 28 and a = 96

tan B = 28/96

tan B = 4*7/4*24

tan B = 7/24

Answer:

Got u 8382 for

Step-by-step explanation:

The one is the one for owing me owning this world haha 8282

Answer:

14°

Step-by-step explanation:

Calculate the common side ZX to both right triangles.

Using the tangent ratio in the upper right triangle.

tan70° = [tex]\frac{opposite}{asjacent}[/tex] = [tex]\frac{ZX}{3}[/tex] ( multiply both sides by 3 )

3 × tan70° = ZX , thus

ZX ≈ 8.24

Using the cosine ratio in the lower right triangle.

cos ZXY = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{XY}{ZX}[/tex] = [tex]\frac{8}{8.24}[/tex] , thus

∠ ZXY = [tex]cos^{-1}[/tex] ([tex]\frac{8}{8.24}[/tex] ) ≈ 14° ( to the nearest degree )

Answer:

5 cm

Step-by-step explanation:

As we can see in the attached figure that G is the point at which the three medians of the triangle meet  i.e we called the centroid

And, according to the property of the centroid, it divides the medians in ratio i.e 2:1

DG: CG = 2 : 1

Since the DG is 10 cm

So, the CG would be half of DG i.e 5 cm

Hence, the CG is 5 cm

Therefore the first option is correct

Answer:

the answer is 5 cm

Step-by-step explanation:

Answer:

50.27

Step-by-step explanation:

First, we have to find the volume of the cone using the formula V=πr^2h/3, where pi is 3.14. After plugging everything in, we get V = 75.4. Then, we have to find 2/3 of that. Rounding to the nearest hundredth, we get 2/3 x 75.4 = 50.27.

Answer:

see file attached

Step-by-step explanation: