Solve the equation by factoring: x^2-8x+15=0

Answer:

a. Had at least one of these features = 290

b. Had all three features = 95

c. Did not have any of these features = 10

d. Had exactly two of these features = 125

Step-by-step explanation:

Given that;

Total parks = 300

15 had only camping

20 had only hiking trails

35 had only picnicking

-> 185 had camping

15 + a + d + c = 185 ------lets say equation 1

->  140 had camping and hiking trails

a + d = 140 ------------- lets say equation 2

now lets substitute equation 2 in 1

15 + 140 + c = 185

c = 30

->  125 had camping and picnicking

c + d = 125 lets say equation 3

substitute  c = 30 into equation 3

30 + d = 125

d = 95

Also substitute d = 95 in equation 2

a + 95 = 140

a = 45

->  210 had hiking trails

a  + b + d + 20 = 210

45 + b + 95 + 20 = 210

b = 50

Now e ( which is dont have any features)

= Total - (15 + 20 + 35 + a  + b + c + d)

= 300 - (15 + 20 + 35 + 30  + 50 + 45 + 95)

= 300 - 290

e = 10

so

a) Had at least one of these features :

Total - e

300 - 10 = 290

b) Had all three features :

Had all three features is d

d = 95

c) Did not have any of these features;

Did not have any of these features is e

e = 10

d) Had exactly two of these features;    

a + b + c

30 + 50 + 45

= 125

Answer:

The probability that each player will receive three picture cards = 0.0324

Step-by-step explanation:

As given,

A deck of 52 cards contains 12 picture cards

Remaining card = 52 - 12 = 40

So,

Total number of ways in which 12 picture card is distributed = \(\frac{12!}{3! 3! 3! 3!}\)

Now,

The Total number of ways in which Remaining cards are distributed = \(\frac{40!}{10! 10! 10! 10!}\)

So,

Total number of ways of getting 3 picture card and remaining card = \(\frac{12!}{3! 3! 3! 3!}\)× \(\frac{40!}{10! 10! 10! 10!}\)

= \(\frac{12! 40!}{(3!)^{4} (10!)^{4} }\)

Now,

Total number of ways to distribute 52 cards so that each people get 13 card = \(\frac{52!}{13! 13! 13! 13!} = \frac{52!}{ (13!)^{4} }\)

∴ The probability = \(\frac{\frac{12! 40!}{(3!)^{4} (10!)^{4} }}{\frac{52!}{(13!)^{4} }}\)

                            = \(\frac{12! 40!}{(3!)^{4} (10!)^{4} }\)×\(\frac{(13!)^{4} }{ 52! }\)

                           = \(\frac{12! 40!}{(3!)^{4} (10!)^{4} }\)×\(\frac{(13.12.11.10!)^{4} }{ 52.51.50.49.48.47.46.45.44.43.42.41.40! }\)

                           = \(\frac{12!}{(3!)^{4} }\)×\(\frac{(13.12.11)^{4} }{ 52.51.50.49.48.47.46.45.44.43.42.41}\)

                           = \(\frac{479,001,600}{(6)^{4} }\)×\(\frac{(1716)^{4} }{ 52.51.50.49.48.47.46.45.44.43.42.41}\)

                           = 0.0324

∴ we get

The probability that each player will receive three picture cards = 0.0324

The sinusoidal function that rises from a minimum point at (3,-2) to a maximum point at (7, 8) is y = 5 sin(π/2(x - 3)) + 3

We are given that;

Minimum point= (3,-2)

Maximum point= (7, 8)

Now,

To construct a sinusoidal function that rises from a minimum point at (3,-2) to a maximum point at (7, 8), we can use the following steps:

Find the amplitude A. The amplitude is the distance from the midline of the function to the maximum or minimum point. The midline is the average of the maximum and minimum values, which is (8 + (-2))/2 = 3. The distance from 3 to 8 or -2 is 5, so A = 5.

Find the period P. The period is the length of one cycle of the function, or the horizontal distance between two consecutive maximum or minimum points. In this case, the period is 7 - 3 = 4. The constant B is related to the period by the formula B = 2π/P, so B = 2π/4 = π/2.

Find the horizontal shift C. The horizontal shift is the amount that the function is shifted left or right from its standard position. In this case, we want the function to have a minimum point at x = 3, so we need to shift it right by 3 units. This means that C = 3.

Find the vertical shift D. The vertical shift is the amount that the function is shifted up or down from its standard position. In this case, we want the function to have a midline at y = 3, so we need to shift it up by 3 units. This means that D = 3.

Putting it all together, we get:

y = 5 sin(π/2(x - 3)) + 3

Therefore, by the function the answer will be y = 5 sin(π/2(x - 3)) + 3.

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Answer:

x² + y² = 6

Circle Center at the origin; r = square root 6

(x - 0)² + (y - 0)² = (✓6)²

x² + y² = 6

Answer: $200,000

Step-by-step explanation:

The price of her home is $200,000.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

The closing costs run from 2% to 7% of the purchase price.

Approximate closing costs would range from $4,000 to $12,000.

Price of her home = x

This means,

2% of x =  4000

(2/100)x = 4000

(1/50)x = 4000

x = 4000 x 50

x = 200,000 ____(1)

7% of x = 12,000

(7/100)x = 12,000

x = (12,000 x 100)/7

x = 171428.57

x = 171429 _____(2)

Now,

From (1) and (2) we can say that,

x = $200,000

Thus,

$200,000 is the price of her home.

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The complete question:

The closing costs run from 2% to 7% of the purchase price.

Becky was told that based on the price of her home, her approximate closing costs would range from $4,000 to $12,000. How much was the price of her home?

Answer:

13 ft

Step-by-step explanation:

8(13.3) + 2(23.8) + 12.3 = 166.3

179.3 - 166.3 = 13

Answer:

The dot product of vectors is the method used to "multiply" vecotrs since vectors aren't directly multiplieable

Step-by-step explanation:

Answer:

To find the absolute value of an negative number, just take away the negative sign

The absolute value of a number can NEVER be negative

Step-by-step explanation:

For example, to find the absolute value of -22, it would be 22, since it is 22 points away from zero. To find the absolute value of -99.9, it would be 99.9.

A negative number is NOT always the absolute value of a number.

For example, the absolute value of 34 is, 34. If you plot it on a number line, it is 34 points away from zero, therefore proving a negative number is NOT always the absolute value of a number.

The absolute value of a number can NEVER be negative.

Answer:

The absolute value of a number is always POSITIVE! To find the absolute value, all you need to do is take away the negative sign!

Have a great day!

Answer:

B. principal

Step-by-step explanation:

Now

Answer:

4 km

Step-by-step explanation:

How far can a person run in 15 minutes if he or she runs at an average speed of 16 km/h?

1 hours = 60 minutes

\(\implies \sf 16 km/h = \dfrac{16\:km/h}{60\:min}=\dfrac{4}{15} km/min\)

If the person runs for 15 minutes, then:

\(\implies \sf total\:distance\:run=\dfrac{4}{15}\:km/min \times 15\:min=4\:km\)

The statement, yes, they are independent because P(student) = 0.8 and P(student | logo A) = 0.8.

To determine if being a student and preferring logo A are independent events, we need to compare the probabilities of these events occurring.

The probability of being a student, denoted as P(student), is given as 0.8. This means that out of the total population (125), 80% are students.

The probability of a student preferring logo A, denoted as P(student | logo A), is given as 0.8.

This means that out of the students (100), 80% prefer logo A.

If the events of being a student and preferring logo A are independent, then the probability of a student preferring logo A (P(student | logo A)) should be the same as the probability of being a student (P(student)).

However, in the given options, both options A and D state that P(student | logo A) = 0.8, which is the same as P(student).

This suggests that being a student and preferring logo A are independent events.

Hence, Yes, they are independent because P(student) = 0.8 and P(student | logo A) = 0.8.

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The two similar triangles in this problem are given by:

C. QRS and TUV

Similar triangles share these two features:

Hence, the similar triangles are QRS and TUV, as the side lengths proportions are given as follows:

3/6 = 2.4/4.8 = 1.8/3.6.

Hence option C is correct.

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By using the concept of internal angles of a triangle, the solution of the system of linear equations related to the geometrical system is (x, y) = (40, 40).

In this system we have a geometrical system formed by two right triangles with a common hypotenuse. Right triangles are triangles where one of its internal angles are right angles and the sum of the measures of the internal angles within a triangle equals 180°. Then, this geometrical system can be modelled by using the following linear equations:

(x + 20) + 90 + 30 = 180         (1)

20 + 90 + (y + 30) = 180         (2)

By using the concept of internal angles of a triangle, the solution of the system of linear equations related to the geometrical system is (x, y) = (40, 40).

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Answer:

h=46

Step-by-step explanation:

Add 18 to both sides

Answer: 78

Step-by-step explanation:

a) The distance of the stone above ground level at time t :

d(t)= -4.9t² + 950

b) It takes 13.92 seconds the stone to reach the ground

c)  With 136.42 m/s velocity the stone strikes the ground.

d) If the stone is thrown downward with a speed of 8 m/s, it will take 13.13 seconds to reach the ground

Here, a  stone is dropped from the upper observation deck of a tower, 950 m above the ground.

(a)  the distance of the stone above ground level at time t would be,

d(t)  = 0.5 (-9.8) t² + v(0) t + d(0)

      = (-4.9)t² + 0t + 950

      = -4.9t² + 950

(b) Now we find the time the stone takes to reach the ground.

i.e., the value of 't' when d = 0

Substituting d(t) = 0 in the above equation.

-4.9t² + 950 = 0

t² = (-950) / (-4.9)

t² = 193.88

t = 13.92 seconds

(c) We need to find the velocity the stone takes to strike the ground

i.e., the velocity when t  = 13.92 seconds

v(t) = v(0) + gt      

v(13.92) = 0 + (9.8)(13.92)

v = 136.42 m/s

(d) here, v(0) = -8 m/s  

Velocity is negative because stone is being thrown downward.

d(t) = 0

(-4.9)t² + v(0) t + d(0) = 0

(-4.9)t² -8t + 950 = 0

Using the quadratic formula we solve above equation for,

t = -14.76, 13.13

We can disregard the negative solution

So, we get t = 13.13 seconds.

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Answer:

There are 39 different choices

Step-by-step explanation:

Add the the flavors of ice cream the cones and the scoops.

31+2=33

1+2+3=6

33+6=39

Hope this helps

Answer:

see below

Step-by-step explanation:

ASA congruence theorem: If two angles and the side between two angles of one triangle are congruent to the corresponding angles and side of another triangle, then the two triangles are congruent.

△ABG and △IBG has same side BG, ∠ABG congruent with ∠IBG, ∠AGB congruent with ∠IGB

Therefore △ABG is congruent with △IBG

then IG is congruent with AG

Answer:

In ΔABG and ΔIBG

∡AGB=∡IGB given

BG=BG reflexive property

∡ABG=∡IBG given

AB=BC given

ΔABG ≅ ΔIBG by ASA (Angle-Side-Angle) axiom.

Since,

The corresponding side of the congruent triangle theorem states that if two triangles are congruent, then all of their corresponding sides are also congruent.

IG=AG being corresponding side of congruent triangle.

Hence Proved.

The form of association that would be found in the variables would be:

As the number of hours spent playing a video game increases, the player is likely to reach higher levels within the game. So positive association.

The number of letters in a person's name and the last digit of their phone number are likely to be unrelated and randomly distributed. There is no association.

As the temperature of the drink decreases, the number of ice cubes in the drink is likely to increase, and vice versa. This is therefore negative association.

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The dimensions of your mowing plot if x = 13 meters is;

Length = 31 meters

Width = 36 meters

We are told that Your plot has a length which is five more than two times x and the width is three less than three times x

This means that, the length given as words is "5 more than 2 times x" and the width given as words is "3 times x minus 3"

The expression for length would be  2x + 5

The expression for width would be 3x - 3

Now, if x = 13 meters, then we see that;

Length = 2(13) + 5 = 31 meters

Width = 3(13) - 3 = 36 meters

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Answer:

An acute angle

Step-by-step explanation:

An acute angle is smaller than an obtuse ad right angle.

hope this helps and hope it was right 'cause I really don't know what you meant. :)

Answer:

how are we supposed to now if u didnt give the ratio

Step-by-step explanation:

The potential energy of the bowling ball relative to the rack when it is on the floor must be Zero.

Potential Energy:

Potential energy is the energy possessed by an object due to its position relative to other objects, its own tension, electrical charge, or other factors.

Common types of potential energy are the gravitational potential energy of a body, the elastic potential energy of an extended spring, and the electrical potential energy of an electric charge in an electric field. The unit of energy in the International System of Units (SI) is the joule, whose symbol is J.

However, the term potential energy was introduced by the Scottish engineer and physicist William Rankin in the 19th century. It ties in with the concept of potentiality of the Greek philosopher Aristotle. Potential energy is associated with the forces acting on an object, and the total work these forces exert on the object depends only on the initial and final positions of the object in space. These forces, called conservative forces, can be represented at any point in space by a vector represented as the gradient of a particular scalar function called the potential.

Forces that can be derived from a potential are also called conservative forces. The work done by the conservative force is

                          W = - ΔU

where ΔU is the force. A negative sign provides the rule that work done on the force field increases the potential energy and work done by the force field decreases the potential energy. Common notations for potential energy are PE, U, V, and Ep.

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Answer:

$90

Step-by-step explanation:

To find out how much money he can save by paying the total amount at the time of purchase, first you have to determine the total amount that Jackson would pay if he can agree to pay $250 down and $130 a month for 18 months:

$250+(130*18)=$2590

Then, you need to find the difference:

$2590-$2500=$90

According to this, the answer is that you will save $90 by paying the total amount at the time of purchase.

This question is based on the simply math calculation. Therefore, the money can he save is $90 by paying the total amount at the time of purchase.

Given:

Jackson wants to purchase a home theater system that sells for $2500. Either he can pay the total amount at the time of purchase or he can agree to pay $250 down and $130 a month for 18 months.

We need to determined money can he save by paying the total amount at the time of purchase.

According to the question,

To find out,  money he can save by paying the total amount at the time of purchase, first you have to determine the total amount that Jackson would pay if he can agree to pay $250 down and $130 a month for 18 months:

⇒ $250+(130 \(\times\) 18)=$2590

Now, calculating the difference:

⇒ $2590 - $2500 = $90

Therefore, the money can he save is $90 by paying the total amount at the time of purchase.

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There are 51 trees, 41 weeds, and 16 grasses that are significant pollen producers.

In the context of beekeeping, the phrase "pollen source" refers to flowering plants that provide pollen to bees and other insects. Bees gather pollen to use as a source of protein for their young.

G, W, and T should stand for the number of grasses, weeds, and trees that serve as significant pollen sources.

According to information provided, state A is home to 80 significant sources of pollen. This data can be represented as follows in an equation:

G + W + T = 108......(1)

According to what is said, there are 7 times as many weeds as there are grasses. This data can be represented as follows in an equation:

W = 3G - 7......(2)

We are also informed that there are three times as many trees as there are grasses. This data can be represented as follows in an equation:

T = 3G + 3

We are also informed that there are three times as many trees as there are grasses. This data can be represented as follows in an equation:

G + W + T = 108

G + 3G - 7 + 3G + 3 = 108

7G - 4 = 108

7G = 112

G= 112/7

G = 16

Therefore, there are 16 grasses that are major pollen sources.

Number of weeds that are major pollen sources:

W = 3G - 7  = 3(16) - 7  = 48 - 7 = 41

Therefore, there are 41 weeds that are major pollen sources.

Number of trees that are major pollen sources:

T = 3G + 3  = 3(16) + 3  = 48 + 3  = 51

Therefore, there are 51 trees that are major pollen sources.

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Answer:

\(\sum_{i=0}^{15} (3i-1)\)

Step-by-step explanation:

for i=0 you have the first term, 3*0-1 = -1

for i=1 you have the second term, 3*1-1 = 2

...

for i=15 you have the last term, 3*15-1 = 44

Answer:  

Scale distance on map representation = 2.4 cm

Step-by-step explanation:

Given:

Scale factor [6 cm - 15 Km]

Actual distance = 6 km

Find:

Scale distance on map representation

Computation:

Scale distance on map representation = Actual distance[6cm / 15km]

Scale distance on map representation = 6km [6cm / 15km]

Scale distance on map representation = 36 / 15

Scale distance on map representation = 2.4 cm

The graph of the function is attached, and the y-intercept of the graph is 64

The table of values is given as

x 2 3 4 5

f(x) 16 8 4 2

In the above table of values, we can see that

As x increases by 1, the value of y changes by a factor of 1/2

This means that the table of values is an exponential function

An exponential function is represented as

y = ab^x

In this case,

b = the change in the factor of y

So, we have

b = 1/2

The equation becomes

y = a(1/2)^x

Using one of the values on the table, we hace

16 = a(1/2)^2

Evaluate

16 = a * 1/4

This gives

a = 64

So, the equation of the function is

y = 64(1/2)^x

Next, we plot the graph of the function

See attachment for the graph of the function that represents the table of values

On the graph, we can see  that

y = 64 when x = 0

This means that the y-intercept of the graph is 64

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Answer:

64.

Step-by-step explanation:

Answer and Step-by-step explanation:

It ensures that you don't accidently skip a step or get confused by which numbers are being used. By writing it down, it allows you to look back and see if you answer was correct or incorrect.

For example:

On a test, you need to do a complicated math problem that you know you can do in your head. It would still be a good idea to write down the process, so that you can see in front of you the numbers you get and results. If it is incorrect when checking over you answers, then you can go through the steps you made to see where you made a mistake.

#teamtrees #PAW (Plant And Water)

Answer:

Because when you need to use this information in the future it will be in your notebook/binder. When you study each lesson you will have the answers in your notes for when you do a Test or quiz. When doing math in your head it is called mental math but it is only used when needed.

Step-by-step explanation:

- chicken box