Solve the following absolute value inequality graphically: |x|-3>1.

Answer:

1. s = 19

2. 17

3. R

4. Angle bisector

5. 53°

Step-by-step explanation:

1. If VY is a midsegment of triangle WXZ, then by midsegment theorem,

[tex]VY=\dfrac{1}{2}WX.[/tex]

Since [tex]WX=s+55[/tex] and [tex]VY=s+18,[/tex] then

[tex]s+18=\dfrac{1}{2}(s+55)\\ \\2(s+18)=s+55\\ \\2s+36=s+55\\ \\2s-s=55-36\\ \\s=19[/tex]

2. A triangle has two sodes of length 18 and 2 units.

Let c units be the length of the third side. Then

[tex]18+c>2\\ \\2+c>18\\ \\2+18>c[/tex]

So,

[tex]c>-16\\ \\c>16\\ \\c<20[/tex]

Hence, [tex]16<c<20,[/tex] and the smallest possible whole-number length for the third side is 17 units.

3. In triangle QSR, the smallest angle is opposite to the smallest side. The smallest side is the side with length of 49 m, then the smallest angle is angle R.

4. Given ∠VYW≅∠WYX.

Definition of angle bisector: An angle bisector in a triangle is a line segment that bisects one of the vertex angles of a triangle.

Thus, YW is angle Y bisector.

5. Consider two right triangles ACD and ABC. In these triangles,

Then, by HL postulate, triangles ACD and ABC are congruent. Congruent triangles have congruent corresponding sides, then

∠ACD ≅ ∠ACB

and

m∠ACB = m∠ACD = 53°

Percent increase in attendance is 42.85% (Approx.)

Given that;

Number of people in first season = 840

Number of people in last season = 1200

Find:

Percent increase in attendance

Computation:

Percent increase in attendance = [(1200 - 840)/840]100

Percent increase in attendance = [360/840]100

Percent increase in attendance = [0.4285]100

Percent increase in attendance = 42.85% (Approx.)

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Final answer:

To find the percent increase in attendance from the first to the last basketball game, the number of people at the beginning is subtracted from the number at the end, the result is divided by the initial number, and then multiplied by 100 to get the percentage, which in this case is approximately 43%.

Explanation:

To calculate the percent increase in attendance from the first to the last basketball game, you subtract the initial number of attendees from the final number of attendees, divide the result by the initial number and then multiply by 100 to get it in percentage form.

The formula for percent increase is:
Percent Increase = ((Final Value - Initial Value) / Initial Value) * 100

Using the provided numbers:

Initial attendance = 840

Final attendance = 1,200

Subtract the initial attendance from the final attendance: 1,200 - 840 = 360

Divide the change in attendance by the initial attendance: 360 / 840 = 0.4286 (approximately)

Multiply by 100 to find the percent: 0.4286 * 100 = 42.86%

Round to the nearest percent: 43% increase.

Therefore, the percent increase in attendance was 43%.

Answer:

Part 1) The length of the apothem is 13.32'

Part 2) The perimeter of the decagon is 86.5'

Step-by-step explanation:

we know that        

A regular decagon has 10 equal sides and 10 equal interior angles

A regular decagon can be divided into 10 congruent isosceles triangle

(they are isosceles since their two sides are the radii of the polygon and the unknown side is the side of the polygon)  

 The vertex angle of each isosceles triangle is equal to

[tex]\frac{360^o}{10}=36^o[/tex]

To find out the side length of the decagon, we can use the law of cosines

so

[tex]c^2=a^2+b^2-2(a)(b)cos(C)[/tex]

where

c is the length side of decagon

a and b are the radii

we have

[tex]a=14'\\b=14'\\C=36^o[/tex]

substitute the values

[tex]c^2=14^2+14^2-2(14)(14)cos(36^o)[/tex]

[tex]c^2=392-(392)cos(36^o)[/tex]

[tex]c^2=392-(392)cos(36^o)[/tex]

[tex]c=8.65'[/tex]

To fin out the perimeter of decagon multiply the length side by 10

so

[tex]P=8.65(10)=86.5'[/tex]

To find out the apothem we can apply the Pythagorean Theorem in one isosceles triangle

see the attached figure to better understand the problem

[tex]r^2=a^2+(c/2)^2[/tex]

substitute the given values

[tex]14^2=a^2+(8.65/2)^2[/tex]

solve for a

[tex]a^2=14^2-(8.65/2)^2[/tex]

[tex]a=13.32'[/tex]

Answer:

Step-by-step explanation:

If the sides are all equal to each other, the figure is a regular octagon. one is given to you below.

Answer:

The value of x is 5.

Step-by-step explanation:

Label the diagram such as

Given:

AD= x

DB= x +5

AE = x - 2

EC = x + 1

DE || BC

To Find:

x = ?

Solution:

Basic Proportionality Theorem:

"If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio".

DE || BC

∴ [tex]\dfrac{AD}{DB}= \dfrac{AE}{EC}[/tex] ...Basic Proportionality Theorem

Substituting the values in it we get

[tex]\dfrac{x}{x+5}= \dfrac{x-2}{x+1}\\x(x+1)=(x+5)(x-2)\\\\x^{2}+x= x^{2}+3x-10\\  -2x=-10\\\\x=\dfrac{10}{2}=5\\ \\\therefore x =5[/tex]

The value of x is 5.

Answer:

1/4

Step-by-step explanation:

The probability of pulling a blue marble is 5/10 = 1/2

The probability of pulling a blue marble twice is 1/2 * 1/2 = 1/4

Answer:

1. Inverse of matrix A exist  If and Only If

c. the determinate does not equal zero

2. The inverse of matrix A

a.does not exist

Step-by-step explanation:

Given:

Consider matrix A.  2 by 2

A=[tex]\left[\begin{array}{cc}1&1\\1&1\end{array}\right][/tex]

To Find:

Does the inverse of matrix A exist?

Solution:

1. Inverse of matrix A exist  If and Only If

c. the determinate does not equal zero

For the Given Matrix A We have

Det |A| = 1×1 -1×1

Det |A| = 0

2. The inverse of matrix A

a.does not exist

Answer:

The determinate does not equal zero and does not exist

Step-by-step explanation:

Answer:

756

Step-by-step explanation:

8(90 +6)-4b

Plug in known values

8(90 + 6) - 4(3)

Solve

720 + 48 - 12

768 - 12

756

Hope this helps :)

Answer:

x = 142º

Step-by-step explanation:

The measurements of all of the angles in a triangle always equal 180º.

We can use this formula: x + y = 180º

Now, substitute in the known value(s) into the formula.

x + 38º = 180º

Solve

x = 180º - 38º =  142º

x = 142º

Hope this helps :)

Answer:

$104.12

Step-By-Step Explanation:

First divide $416.48 by 4 ↓

                                         $416.48÷4= $104.12

Callie will have $104.12 less than what she earned each month once you take away the money she is paying for car repairs.

Callie will have $104.12 less than what she earned each month once you take away the money she is paying for car repairs.

Problem-solving is the act of defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.

Problem-solving starts with identifying the issue. As an example, a trainer may need to parent out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.

Learn more about Problem-solving here: brainly.com/question/13818690

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Answer:

[tex]\displaystyle y = -2\frac{1}{2}x + 20\frac{1}{2}[/tex]

Step-by-step explanation:

First, find the rate of change [slope]:

[tex]\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \\ \frac{-8 + 3}{-5 + 7} = -\frac{5}{2} = -2\frac{1}{2}[/tex]

Then plug these coordinates into the Slope-Intercept Formula instead of the Point-Slope Formula since you get it done swiftly that way. It does not matter which ordered pair you choose:

3 = −2½[7] + b

−17½

[tex]\displaystyle 20\frac{1}{2} = b \\ \\ y = -2\frac{1}{2}x + 20\frac{1}{2}[/tex]

_______________________________________________

8 = −2½[5] + b

−12½

[tex]\displaystyle 20\frac{1}{2} = b \\ \\ y = -2\frac{1}{2}x + 20\frac{1}{2}[/tex]

** You see? I told you it did not matter which ordered pair you choose because you will always get the exact same result.

I am joyous to assist you anytime.

Answer:

The correct answer is A. Debit Revenue and Credit Income Summary

Step-by-step explanation:

Let's recall that at the end of the accounting year, closing entries transfer the balances from the temporary accounts to a permanent account with the purpose that those temporary accounts will begin the next accounting year with zero balances.

However, an intermediate account called Income summary is created and used in the closing stage of the accounting year to register all income and expense balances and determine the net result for the period (income or loss).

Upon saying that, usually revenue accounts have a credit balance.  To make it zero we want to decrease the balance.  We will debit the revenue account and credit the Income Summary account.  This credit to income summary should be exactly the total revenue from the income statement.

The correct answer is A. Debit Revenue and Credit Income Summary

Answer:

Step-by-step explanation:

During the closing process, which of the following would likely occur?

Question options:

Debit Revenue and Credit Income Summary

Answer:

See below

Step-by-step explanation:

Parent function is:

Transformations are:

shifts f(x) 4 units down

stretches f(x) by a factor of 4 away from the x-axis

shifts f(x) 4 units right

compresses f(x) by a factor of toward the y-axis (must be 4)

Answer:

Step-by-step explanation:

20-pack of Dr. Pepper cost $5.50 . As per this deal

  Cost of one pack = 5.5/20 = $ 0.275

a 6-pack cost $1.50.As per this deal

  Cost of one pack = 1.50/6 = $ 0.25

A 6-pack cost $1.50 is the better deal.

Answer:

4 cuts

Step-by-step explanation:

you first do a vertical cut

then a horizontal cut

then two diagonal cuts

Answer:

4 cuts

Step-by-step explanation:

Answer:

The net effect of amount in John account after 5 months is  $A - $200

Step-by-step explanation:

Given as :

The amount of money withdraws by John each month from his account = $40

Let The total amount of  money did John had in his account = $A

Let the amount left in John account after 5 months of withdraw = $x

So, According to question

∵ Each month the money withdraw from account = $40

∴ In 5 months , the money withdraw = $40 × 5

I.e In 5 months , the money withdraw = $200

So, The left money in account after withdraw in 5 months = $A - The amount withdraw in 5 months

I.e x = $A - $200

So, The balance in account after 5 months = x =  $A - $200

Hence, The net effect of amount in John account after 5 months is             $A - $200  Answer

Answer:

X < -2

Step-by-step explanation:

5x/5 < -10/5. Divide each side by 5

Answer:

13

Step-by-step explanation:

w^2=(-2)(-2)=4

4-(-8)+1=4+8+1=12+1=13

Answer:

Sample Response: George did not put parentheses around the total snack amount to be subtracted from his $15. He needed to total the purchases and then subtract that amount from $15.

Step-by-step explanation:

Answer: if a=9, b=3, and c=1/3 then...

a^2 ÷ 3 = 9^2÷3

= 27

a^2 + 30 - 18 = 9^2+30-18

= 93

4b^2 · 3 = 4×3^2×3

= 108

ac ÷ (2b) = 9×1/3÷ (2×3)

= 1/2

3c ÷ (2b^2) = 3×1/3 ÷ (2×3^2)

= 1/18

Step-by-step explanation:

With a^2 ÷ 3, you would replace any letters with the number it says to replace it with. so, "a" would be replaced with 9, since it says that a=9. So, once your done with all of that, the equation would become, 9^2÷3.

With a^2 + 30 - 18, you would also, replace any letters with the number it says to replace it with. So, "a" would be replaced with 9, since it says that a=9. So, then after you do all of that, the equation would be, 9^2+30-18.

With 4b^2 · 3, you would do the same thing, you would replace any letters  with the number it tells you to replace it with. So, "b" would be replaced with the number, 3. And if you don't already know... when "b" turns into 3, the number doesn't become 43. When "b", gets changed to 3, it becomes 4×3. So, after all that is done, then the equation would turn into, 4×3^2×3.

With ac ÷ (2b), you would do the same thing that was done above. Start by replacing any letters with the numbers that, it says to replace it with. Which you would replace "a" with 9, "c" with 1/3, and "b" with 3. And like I said above if the letters change to a number the numbers don't just stay as numbers, they get multiplied by each other. like when you change "a" to 9 and "c" to 1/3... it becomes 9×1/3. Same thing with b, when "b" gets changed to 3... since the number 2 is right next to it... it becomes, 2×3. So, after all that is done, the equation turns out to be, 9×1/3 ÷ (2×3).

And last but not least, to solve 3c ÷ (2b^2)... To solve 3c ÷ (2b^2), you would change any letters with the numbers that it says to replace it with. Like changing "c" to 1/3, and "b" to 3. And when changing "c" to 1/3, you'd notice that since 3 is right next to "c", you would multiply them together, 3×1/3. Same thing when changing "b" to 3, you would multiply it by the number it is next to. So, it would be 2×3. So, after all of that is done the equation turns into, 3×1/3 ÷ (2×3^2).

Final answer:

Using the given values (a=9, b=3, c=1/3), the expressions evaluate to 27, 93, 108, 0.5, and 1/18 respectively, after calculation.

Explanation:

To evaluate each expression with the given values a=9, b=3, and c=1/3, we substitute these values into each expression and perform the appropriate arithmetic operations:

[tex]a^2[/tex] ÷ 3 = 92 ÷ 3 = 81 ÷ 3 = 27

[tex]a^2[/tex] + 30 - 18 = 92 + 30 - 18 = 81 + 30 - 18 = 93

[tex]4b^2[/tex] · 3 = [tex]4(3)^2[/tex] · 3 = 4(9) · 3 = 36 · 3 = 108

ac ÷ (2b) = (9)(1/3) ÷ (2(3)) = 3 / 6 = 1/2= 0.5

3c ÷ (2b2) = (3)(1/3) ÷ (2(3)2) = 1 / (2(9)) = 1 / 18 = 0.0556

[tex]y = 1.3x + 3[/tex]

Answer:

6:24

12:48

Step-by-step explanation:

3 : 12  

 x2

6:24

 x2

12:48

:)

Answer: 1 : 4 and 2 : 8

Step-by-step explanation: To find 2 different ratios that are equal to the ratio 3:12, we first rewrite the ratio 3:12 as the fraction 3/12. Notice that we can find 1 of our equal ratios by simply writing this fraction in lowest terms. if we divide both the numerator and denominator of 3/12 by their greatest common factor of 3, we get the equal ratio 1/4.

Now we can use 1/4 to find another equal ratio. If we multiply both the numerator and denominator of 1/4 by 2, we get the equal ratio 2/8.

Finally, remember to write these ratios using the same form as the original problem. 1 : 4 and 2 : 8.

Answer:

369/10

Step-by-step explanation:

10 1/4=41/4

3 3/5=18/5

----------------

(41/4)(18/5)=738/20

simplify

369/10

Answer:

36 9/10

How to Solve:

First you must convert 10 1/4 into an improper fraction. To do that you must multiply ten by four and add one. The total of that will become the new numerator and the denominator will stay the same.

10 1/4 → 41/4

Next you should also convert 3 3/5 into an improper fraction. To do that you must multiply three by five and add three. The total of the will become the new numerator and the denominator will stay the same.

3 3/5 → 18/5

Now multiply the numerators.

41 × 18= 738

Now multiply the denominators.

4 × 5 = 20

Apply the new numerator and denominator into a fraction.

738/20

Now you simplify the fraction by dividing both the numerator and denominator by two.

738/20 ÷ 2/2 = 369/10

Finally, the improper fraction must be converted into a mixed fraction.

369/10 → 36 9/10

Therefore, 10 1/4 times 3 3/5 equals 36 9/10

Answer:

The “blank” is 4

Step-by-step explanation:

4 1/4= 16/x+ 1/4

We want to get rid of the 1/4. So we subtract it from both sides and get

4= 16/x

We know that if we put 16 divided by 4, you get 4.

This gives you 4= 16/4.

This is your final answer.

Answer:

y = [tex]\frac{1}{4}[/tex] x + 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 4, 0) and (x₂, y₂ ) = (0, 1)

m = [tex]\frac{1-0}{0+4}[/tex] = [tex]\frac{1}{4}[/tex]

Note the line crosses the y- axis at (0, 1) ⇒ c = 1

y = [tex]\frac{1}{4}[/tex] x + 1 ← equation of line

Answer for the question No.17

Answer:

[tex]x=28.11\ degree[/tex]

[tex]m\angle\ ABC=28.11\ degree[/tex]

Step-by-step explanation:

Answer for the question No.17

Given:-

[tex]\angle\ BAD=(5x+10)\ degree[/tex]

[tex]\angle\ ADC=(87)\ degree[/tex]

[tex]\angle\ DCB=(3x+10)\ degree[/tex]

Let,[tex]m\angle\ ABC=x[/tex]

In quadrilateral ABCD,

[tex]\angle\ BAD+\angle\ ABC+\angle\ DCB +\angle\ ADC =360\ degree[/tex] ---(sum of angle of quadrilateral is 360 degree)

[tex]\therefore\ (5x+10)+x+(3x+10)+87=360[/tex]

[tex]9x+107=360[/tex]

[tex]9x=360-107[/tex]

[tex]9x=253[/tex]

[tex]x=\frac{253}{9}[/tex]

[tex]\therefore\ x=28.11\ degree[/tex]

SInce x=[tex]m\angle ABC[/tex]

[tex]\therefore\ m\angle\ ABC=28.11\ degree[/tex]

Answer:

9p

Explanation:

4p + 5p are like terms since they have the same variable p

All you have to do is add the numbers

(4+5)p = 9p

Answer:

Co-ordinates of endpoint is  (-24,-17)

Step-by-step explanation:

The question should be given as :

Find the coordinates of the other endpoint of the segment, given its midpoint (-19,-18) and one endpoint (-14,-19).

Step-by-step explanation:

Given point:

Endpoint (-14,-19)

Mid-point of segment  (-19,-18)

Let endpoint have co-ordinates [tex](x_2,y_2)[/tex]

Using midpoint formula:

[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

Where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are co-ordinates of the endpoint of the segment.

Plugging in values to find the midpoint of segment.

[tex]M=(\frac{-14+x_2}{2},\frac{-19+y_2}{2})[/tex]

We know [tex]M(-19,-18)[/tex]

So, we have

[tex](-19,-18)=(\frac{-14+x_2}{2},\frac{-19+y_2}{2})[/tex]

Solving for [tex]x_2[/tex]  

[tex]\frac{-14+x_2}{2}=-19[/tex]

Multiplying both sides by 2.

[tex]\frac{-14+x_2}{2}\times 2=-19\times 2[/tex]

[tex]-14+x_2=-38[/tex]

Adding both sides by 14.

[tex]-14+x_2+14=-38+14[/tex]

∴ [tex]x_2=-24[/tex]

Solving for [tex]y_2[/tex]  

[tex]\frac{-19+y_2}{2}=-18[/tex]

Multiplying both sides by 2.

[tex]\frac{-19+y_2}{2}\times 2=-18\times 2[/tex]

[tex]-19+y_2=-36[/tex]

Adding both sides by 19.

[tex]-19+y_2+19=-36+19[/tex]

∴ [tex]y_2=-17[/tex]

Thus co-ordinates of point N is (-24,-17)