Line p is parallel to the line x = -2. What is the slope of line p?

a) positive
b) negative
c) undefined
d) 0

Answer: D) 4

Step-by-step explanation:

x⁴ - x³ - 9x² + 7x + 14 = 0

possible rational roots are: ±{1, 2, 7, 14}

Try x = -1

-1  |   1   -1   -9   7   14

   |   ↓  -1     2   7   -14

       1   -2    -7   14   0 ← remainder is 0 so x = -1 is a root

Let's try x = 2 with the factored polynomial

2  |  1   -2   -7   14

   |  ↓    2   0   -14

       1    0   -7    0  ← remainder is 0 so x = 2 is a root

Factored polynomial x² - 7 can be factored to:

(x - √7) (x + √7)

⇒ x = √7   and x = -√7

The roots are x = {-1, 2, √7, -√7) which are all real numbers.

Answer:

1/2 is the slope of the line

Step-by-step explanation:

To find slope, use the following equation

slope (m) = (y₂ - y₁)/(x₂ - x₁)

First, set each coordinate. Let:

(x₁ , y₁) = (8 , -6)

(x₂ , y₂) = (4 , -8)

Plug in the corresponding numbers for the corresponding variables.

m = (y₂ - y₁)/(x₂ - x₁)

m = (-8 - (-6))/(4 - 8)

Simplify. Note that two negative signs would result in a positive sign.

m = (-8 + 6)/(4 - 8)

Combine like terms.

m = -2/-4

Simplify. Divide common factors from both the numerator and denominator.

m = (-2/-4)/(-2/-2) = 1/2

1/2 is the slope of the line

~

Answer:

16%

Step-by-step explanation:

To find this, we have to divide the amount spent on books by the total amount, then multiply by 100:

[tex]\frac{368}{2300}  * 100 = 16[/tex]

So 16% was spent on books!

16% of last semester college costs was spent on books.

To find the percent of last semester college costs spent on books, we need to divide the amount of money spent on books by the total cost of last semester and multiply by 100 to get a percentage.

Amount spent on books: $368

Total cost of last semester: $2300

Percentage spent on books: 368/2300 * 100 = 16%

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The Apex Savings Bank was required to keep a reserve of 4.5% of the deposit. The bank was free to loan out the remaining 95.5% which equaled $12,128.50.

The reserve rate is the percentage of the deposit that the bank must keep, in this case, Apex Savings Bank. To calculate the reserve rate, we divide the reserve by the deposit and multiply by 100%. Therefore, ($571.50 / $12,700) * 100% = 4.5%. This means the bank had a reserve rate of 4.5% at that time.

Moving on towards the second question about how much Apex Savings Bank was free to loan out. Since the bank must keep 4.5% of the deposit, it is free to loan out the rest, which is 100% - 4.5% = 95.5%. By applying this percentage to the deposit, we see that Apex Savings Bank was free to loan out 95.5% of $12,700, or $12,128.50.

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Answer:

b≤15

Step-by-step explanation:

If he only has 15 birdhouses in stock, then he can only sell 15 or less birdhouses. He cant sell more birdhouses, simply because he doesnt have more than 15.

Final answer:

The inequality representing the number of birdhouses Jason can sell, given he has 15, is b≤15 since he cannot sell more than he has.

Explanation:

The inequality that represents the number of birdhouses, b, Jason can sell at a craft fair, given he has 15 birdhouses, is b≤15. This is because the number of birdhouses he can sell cannot exceed the number he has, which is 15. The inequality b≤15 means that Jason can sell no more than 15 birdhouses, he could sell exactly 15, or he could sell less, depending on the demand at the craft fair.

This constraint ensures that Jason operates within the bounds of his available stock, preventing him from overselling. It implies that Jason can sell up to 15 birdhouses, including the possibility of selling exactly 15 or selling fewer, depending on the demand at the craft fair. This inequality serves as a practical guideline for Jason to manage his sales effectively, aligning his offerings with the limitations of his inventory.

Answer:

first answer is -10

second answer is 10

third answer is -2

fourth answer is 2

Step-by-step explanation:

Explanation to get the answers:

you plug in the b c d and a

depending on what your abc and d are will depend on how the equation goes

like for example if the equation is

a x (c) - (-d) + b

and a=5, b=8, c=10, d=15

then you plug 5 where a is

plug in 10 where c is

plug 15 where d is as a negative

and lastly plug 8 where b is

if you have a calculator/graphing calculator i would use it to help answer these equations

a graphing calculator solves it for you without doing all the extra work like you would on a regular calculator

i use the graphing calculator to help solve equations like this specific one and it works very well

i hope my answers and explanation helps you :)

Answer:

Given equation are:

[tex]y = -\frac{1}{4}x+8[/tex]                  ......[1]

[tex]-2x+8y = 4[/tex]                             .....[2]

Now, Equation of a line is in the form of y =mx+b where m is the slope of the line.

Slope[tex](m_1)[/tex] of equation of line in [1] is;

[tex]y = -\frac{1}{4}x+8[/tex]  

then;

[tex]m_1= -\frac{1}{4}[/tex]

Slope[tex](m_2)[/tex] of equation of line in [2];

[tex]-2x+8y = 4[/tex]

Add both sides 2x we get;

-2x + 8y + 2x = 2x + 4

Simplify:

8y = 2x +4

Divide both sides by 8 we get;

[tex]y = \frac{1}{4} x + \frac{1}{2}[/tex]

then;

[tex]m_2 = \frac{1}{4}[/tex]

Therefore, the given two lines are neither parallel nor perpendicular.

Hi there! :)

Answer:

The answer is B) 17/30

Step-by-step explanation:

In order to find your answer you need to subtract 1/3 from 9/10:

9/10 - 1/3 = chocolate left

Since theses fractions do not have the same denominators (bottom number), the key here is to rewrite both of the fractions so that they have the same denominator:

The denominator is going to be a common multiple of "10" and "3". Ideally it's going to be the least common multiple of "10" and "3".

Let's start with the larger of the two denominators, which is "10". You have to go through its multiples and and see when we get to one that's divisible perfectly by 3.

So 10 is not divisible perfectly by 3, neither is 20. 30 on the other hand is divisible perfectly by 3. 30 is three times 10.

So you can rewrite both of these fractions as something over 30.

1/3 = ?/30

To get from 3 to 30, we have to multiply by 10. So if you multiply the denominator by 10, if you don't want to change the value of the fraction, you have to multiply the numerator (top number) by 10 also.

1/3 = 10/30

Same thing with the other fraction:

9/10 = ?/30 → 3 × 10 = 30 / SO, you need to multiply the numerator by three also → 9 × 3 = 27

9/10 = 27/30

Now that your fractions both have the same denominator, you can subtract the numerators together and put the answer on 30.

27/30 - 10/30 = ?

27 - 10 = 17 → 17/30

Since the fraction is simplified, you are now done.

There you go! I really hope this helped, if there's anything just let me know! :)

Answer:

The experimental probability of red is 20%.

Step-by-step explanation:

When calculating out the experimental probability, you ignore the actual probability of the action taking place. In this case, you only look to what actually did take place. In this case it was 2 out of 10 times, so we complete that math.

2/10 = 20%

Answer:

The experimental probability of it landing on red is 2/10 or 1/5

Step-by-step explanation:

engenuity 2020

Answer:

B) -2/√5

Step-by-step explanation:

see attached

Answer:

The population of the town at the end of 2017 was 65,550.

Step-by-step explanation:

The population of the town was 60,000 in the beginning of 2016.

In 2016, the total population is increased by 15%.

[tex]60,000\times\frac{15}{100}=9000[/tex]

Therefore the population is increased by 9000 and the population of the town at the end of 2016 was

[tex]60,000+9000=69,000[/tex]

In 2017, the total population is decreased by 5%.

[tex]69,000\times\frac{5}{100}=3450[/tex]

Therefore the population is decreased by 3450 and the population of the town at the end of 2017 was

[tex]69,000-3450=65,500[/tex]

Therefore the population of the town at the end of 2017 was 65,550.

The point-slope form:

[tex]y-y_1=m(x-x_1)[/tex]

[tex]m[/tex] - slope

[tex](x_1,\ y_1)[/tex] - point

We have the point [tex](3,\ -2)\to x_1=3,\ y_1=-2[/tex] and the slope [tex]m=\dfrac{2}{3}[/tex]

Substitute:

[tex]y-(-2)=\dfrac{2}{3}(x-3)\\\\\boxed{y+2=\dfrac{2}{3}(x-3)}[/tex]

Answer:

B. 315 mi.

Step-by-step explanation:

180 ÷ 4 = 45

45 x 7 = 315

or...

180 ÷ 4 = 45

45 x 3 = 135

135 + 180 = 315

I hope this helps!

Cheers, July.

The train travels option B. 315 miles in 7 hours.

Speed is the unit rate in terms of distance travelled by an object and the time taken to travel the distance.

Speed is a scalar quantity as it only has magnitude and no direction.

Given that,

Distance train travelled = 180 miles

Time taken to travel the distance = 4 hours

Speed = Distance / Time

           = 180 / 4

           = 45 miles per hour

Also, given that train travels at constant speed.

Distance = Speed × Time

Since speed is constant, the distance train travelled in 7 hours will be,

Distance = 45 × 7

               = 315 miles

Hence the distance train travelled in 7 hours is 315 miles.

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Answer:

Value of D=73

D is positive that means  the roots are real and distinct.

Step-by-step explanation:

We have been given a quadratic equation:

[tex]2x^2-3x+8[/tex]

We have to find its dicsriminant which is [tex]D=b^2-4ac[/tex]

Here, a=-2 , b=-3 and c=8 on comparing with the general equation [tex]ax^2+bx+c=0[/tex]

On substituting the values in the formula of discriminant we get:

[tex]D=(-3)^2-4(-2)(8)[/tex]

[tex]\Rightarrow D=9+64=73[/tex]

Value of D=73

If D is positive that means  the roots are real and distinct.

Answer:

x=3

Step-by-step explanation:

Since this is an isosceles trapezoid

The angles at the top have to equal each other

112 = 30x + 11y

The sides also have to equal each other.

12 = 2x+3y

Divide each side by 3

12/3 = 2x/3 + 3y/3

4 = 2/3 x +y

Subtract 2/3 x from each side

4 -2/3 x =y

Substitute this into the first equation

112 = 30x + 11y

112 = 30x +11(4-2/3x)

112 = 30x +44 -22/3 x

Subtract 44 from each side

112-44 = 30x +44-44 -22/3 x

68 = 30x -22/3 x

Get a common denominator on the right of 3

68 = 90/3x -22/3 x

68 = 68/3 x

Multiply each side by 3/68

68 * 3/68 = 68/3 * 3/68 x

3 =x

Answer:

$60

Step-by-step explanation:

$120/2(half) = $60

Answer: The amount given by his grandfather to him = $60.

Step-by-step explanation:

Given : Andrei's grandfather offered to give him a gift at 50% of the amount of money he saved in one year.

The amount saved by Andrei = $ 120

Then, the amount given by his grandfather to him will be

50% of ( amount saved by Andrei )

= (0.50) x ($120) [When we convert a percent into decimal we divide it by 100]

= $60

Therefore , the amount given by his grandfather to him = $60.

Hi there! :)

Answer:

B. hexagon

Step-by-step explanation:

Every hexagon tessellates. Hexagon is a plane figure having six sides.

I hope this helps you!

Have a nice day! :)

:D

-Charlie

Thank you!

Answer: hexagon

Step-by-step explanation:

We know that equilateral triangles, squares and regular hexagons are the only regular polygons that tessellate .

Hexagon is a six sided regular polygon having all its sides equal. It is one of the three regular polygons which tessellates.

Therefore, from all the given choices the correct answer would be "hexagon".

The complete statement :-Every hexagon tessellates.

Answer:

[tex]\frac{13}{20}[/tex] of the group's video games is either at Jeromes house or Marios  house.

Step-by-step explanation:

Given the statement: Jerome has 1/4 of the group's video games at his house.

Also,Mario has 2/5 of the group's video games at his house.

⇒ Jerome has group's video games at his house(J) = [tex]\frac{1}{4}[/tex]

and

Mario has group's video games at his house(M) = [tex]\frac{2}{5}[/tex]

To find the fraction of the group's video games is either at Jerome house or Mario house.

Between two they have = [tex]J+M[/tex] = [tex]\frac{1}{4} + \frac{2}{5} = \frac{5+8}{20} =\frac{13}{20}[/tex] of the group's video games.

Answer:

[tex]\overline{AM}\cong \overline{AM}[/tex]

Step-by-step explanation:

Given that triangle TAM is congruent to the triangle HAM.

We know that corresponding sides of congruent triangles are equal so we can write:

TA = HA

AM = AM

TM = HM

comparing these with given choices we see that, (AM = AM) is the only matching answer.

Hence final answers is the first choice  [tex]\overline{AM}\cong \overline{AM}[/tex].

Answer:

The answer for fraction part is 6/7

If this helps please mark brainliest

An equation is formed of two equal expressions. The number is 4/3.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the unknown number be represented by x.

The given phrase can be written in the form of an expression "The sum of 1/2 and four times a number is equal to 5/6 subtracted from five times the number" as,

Now, we can write the equation by equating the expressions together and then solving it for x,

(1/2) + 4x = 5x - (5/6)

(1/2) + (5/6) = 5x - 4x

x = (1/2) + (5/6)

x = (3/6) + (5/6)

x = 8/6

x = 4/3

Hence, the number is 4/3.

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Answer: ∠ A = ∠B= 48° and ∠ C = 84°

Step-by-step explanation:

Here, m∠ADE: m∠ADB = 2:9

Let m∠ADE = 2x and m∠ADB = 9x

Where x is any value.

By joining the points D and E (construction)

Since, Here DE ║ AB.

⇒ ∠DAB = 2 x

⇒ ∠ A = 4x ( because AD is the angle bisector so, ∠DAB=∠DAE = 2x )

Now,  Let O is the intersection point of angle bisectors AD and BE.

Then, By the property of angle bisctor.

O is the circumcenter of the triangle ABC.

Therefore, OA = OB

⇒ ∠DAB = ∠EBA = 2 x

But BE is the angle bisceor,

Therefore, ∠EBA = ∠EBC=2 x

But, ∠B = ∠EBA + ∠EBC

⇒ ∠B = 4x

Now, since BD is the same transversal on the parallel lines AB and ED,

⇒ ∠B = ∠ EDC

⇒ ∠ EDC = 4x

Since, ∠ADB + ∠ADE + ∠EDC = 180°

⇒ 9x + 2x + 4x = 180°

⇒ 15x = 180°

⇒ x = 12°

Thus, the measures of the angles of ΔABC are,

∠ A = 4x =4×12 = 48°

∠ B = 4x =4×12= 48°

⇒ ∠ C = 180° - 48°- 48°= 84°

The question is about finding the angles of a triangle given certain conditions. We use the Angle Bisector Theorem and other geometric principles related to angle bisectors. We set up an equation based on these principles and solve for the angles.

The given scenario is about triangle ABC, with AD and BE acting as angle bisectors of ∠A and ∠B respectively. Also, provided is the ratio of m∠ADE to m∠ADB, which is 2/9. Given these conditions, we are to find the measures of the angles of ΔABC.

First, we can make use of the Angle Bisector Theorem, which states that an angle bisector of an angle of a triangle divides the opposite side in a ratio equal to the ratio of the other two sides. From this theorem, we see that m∠ADE / m∠ADB = AD / DB.

We know from the given that m∠ADE/m∠ADB = 2/9.

Since DE is parallel to AB, angle ∠ADE is equal to angle ∠BAC and angle ∠ADB is equal to angle ∠ABC by the corresponding angles postulate.

As ∠ADE and ∠ADB are part of a straight angle ∠ADA, then ∠ABC + ∠BAC = 180° - ∠ADB. We can use these relationships to create an equation, solve for the angles, and find the measures of the angles of ΔABC.

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Answer:

Δ ABC is the required triangle.

Step-by-step explanation:

Since the person is standing at the top of tower.

let the height of tower be 'h' and 'b' be the distance from base of tower to the point where keys are dropped.

Consider, ABC be the right angled triangle with AB be the tower and A be the point where person is standing and C denotes the point where keys dropped finally.

Alpha (α) be the angle at which keys is dropped.

BC denotes the distance from foot of tower to the keys.

[tex]a_1=2;\ a_2=-6;\ a_3=18;\ a_4=-54;\ a_5=162;\ ...[/tex]

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

A recursive rule for a geometric sequence:

[tex]a_1\\\\a_n=r\cdot a_{n-1}[/tex]

[tex]r=\dfrac{a_{n+1}}{a_n}\to r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}=...\\\\r=\dfrac{-6}{2}=-3[/tex]

Therefore [tex]\boxed{a_1=2;\qquad a_n=-3a_{n-1}}[/tex]

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

The exciplit rule:

[tex]a_n=a_1r^{n-1}[/tex]

Substitute:

[tex]a_n=2(-3)^{n-1}=2(3)^n(3)^{-1}=2(3)^n\left(\dfrac{1}{3}\right)\\\\\boxed{a_n=\dfrac{2}{3}\left(-3)^n}[/tex]

Answer:

The area of the given rectangle is 51

Step-by-step explanation:

First we have to find the coordinates of the vertices of the rectangle.

Then the length and breadth of it using distance formula.

The distance d between points (x₁ , y₁) and (x₂ , y₂) is given by

[tex]d= \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]

Finally calculate the area of rectangle using the formula,

Area of rectangle = Length * Breadth

From the given graph, we get the coordinates of the rectangle as

A(2,4) , B(-2,3) , C(1,-9) , D(5,-8)

Breadth, AB = [tex]\sqrt{(-2-2)^{2}+(3-4)^{2}} = \sqrt{16+1} = sqrt{17}[/tex]

Length, BC = [tex]\sqrt{(1+2)^{2}+(-9-3)^{2}} = \sqrt{9+144} = 3 sqrt{17}[/tex]

Now, Area of rectangle = Length * Breadth = AB * BC = √17 * 3√17 = 3 *17 = 51

∴ The area of the given rectangle is 51

Answer:

51

Step-by-step explanation:

Answer: C

Step-by-step explanation:

The general form of the equation is: g(x) = a|x - h| + k  ;

4 units left means h = 4

2 units up means k = 2

--> g(x) = |x - 4| + 2

Option: C is the correct answer.

                C.   [tex]g(x)=|x+4|+2[/tex]

The parent function f(x) is given by:

             [tex]f(x)=|x|[/tex]

Now, we know that for any parent function f(x) the transformation of the type:

 f(x) → f(x+k)

is a translation of the function f(x) k units to the right if k<0

and k units to the left if k<0

and the transformation of the type:

           f(x) → f(x)+k

is a translation of a function f(x) k units upward if k>0

and k units downward if k<0

Now here it is given that:

The function f(x) is shifted 4 units left and 2 units up.

Hence, the transformed function g(x) is given by:

[tex]g(x)=f(x+4)+2\\\\i.e.\\\\g(x)=|x+4|+2[/tex]

Jim and John drank a combined total of 7/10 of their water bottles, with Jim drinking 2/5 (converted to 4/10 for the common denominator) and John drinking 3/10.

To determine how much water Jim and John drank from their water bottles, we can add the fractions of the water they each drank. Jim drank 2/5 of his water bottle, while John drank 3/10 of his. To add these fractions, we need a common denominator, which in this case is 10. Convert 2/5 to 4/10 by multiplying the numerator and denominator by 2. Now, we can add 4/10 (Jim's consumption) and 3/10 (John's consumption) together.

The total amount of water drank by both boys is: 4/10 + 3/10 = 7/10

Thus, together, Jim and John drank 7/10 of their water bottles combined.

x = number of messages sent or received

y = total cost per month

Plan A costs $30 per month plus $0.10 per text message. So the cost for plan A is y = 0.10*x + 30. The portion 0.10*x represents just the cost of the 10 cents per message, and then we add on the fixed cost of $30 to get the total cost.

In a similar fashion, plan B's cost is y = 60. There is no cost per message, so we don't have to include x in the picture. The cost is a flat fee, which leads to a flat horizontal line graph (as shown in the attachment below)

Our two equations are: y = 0.10x+30 and y = 60. Let's use substitution to find x

y = 0.10x + 30

60 = 0.10x + 30 ... replace y with 60 (works because y = 60)

60-30 = 0.10x

30 = 0.10x

0.10x = 30

x = 30/0.10

x = 300

If you send or receive 300 messages, then both plans will cost the same. We can see this on the graph below where the two lines cross at (300,60). Note how plugging x = 300 into the first equation simplifies to y = 60.