the lewis family drove 45.6 miles to the river. It took them 1.2 hours to get there. How fast did they drive? Round to the nearest whole number

Using the polynomial expression, the non-real solutions are x = (2 + i√26)/3 and  x = (2 - i√26)/3

Polynomial expressions are mathematical statements that are represented by variables, coefficients and operators

The equation of the polynomial expression is given as:

3x^3 + 14x^2 - 14x + 60 = 0

From the question, we have

Real solution = -6

Rewrite the above equation as

x = -6

Add 6 to both sides of the equation

So, we have

x + 6 = 0

The next step is to divide the polynomial equation 3x^3 + 14x^2 - 14x + 60 = 0 by x + 6 = 0

This is represented as

3x^3 + 14x^2 - 14x + 60/x + 6

Using a graphing calculator, we have

3x^3 + 14x^2 - 14x + 60/x + 6 = 3x^2 - 4x + 10

Next, we determine the solution of the quadratic expression 3x^2 - 4x + 10 using a quadratic formula

So, we have

x = (-b ± √(b² - 4ac))/2a

This gives

x = (4 ± √((-4)² - 4 * 3 * 10))/2 * 3

So, we have

x = (4 ± √-104)/6

This gives

x = (4 ± 2√-26)/6

Divide

x = (2 ± √-26)/3

Rewrite as

x = (2 ± i√26)/3

Split

x = (2 + i√26)/3 and  x = (2 - i√26)/3

Hence, the non-real solutions of the polynomial expression are x = (2 + i√26)/3 and  x = (2 - i√26)/3

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The number of posters Jill had on Monday are 18.

The equation is p + 8 - 4 = 22.

Given that:-

Number of posters bought by Jill on Tuesday = 8

Number of posters left on Thursday = 22

We can write,

Number of posters destroyed on Wednesday = (1/2)*8 = 4

Let the number of posters Jill had on Monday be p.

Hence, the equation for the posters is given by:-

Posters on Monday + Posters bought on Tuesday - Posters destroyed on Wednesday = Total posters on Thursday

It can be written as:-

p + 8 - 4 = 22

Solving the equation, we get

p + 4 = 22

p = 22 - 4

p = 18

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Answer:

(x+3) (x+5)

Step-by-step explanation:

1) When factorising a quadratic like this the first step is to put x in front of two brackets:

(x ) (x )

2) Next check if all numbers in your question is positive (+). In this case it is so we put + after both x in bracket.

(x+ ) (x+ )

3) now the last number in your question is 15 so we find all factors of 15:

1 and 15

3 and 5

4) to know which pair of factors to use we look at owr second number in the question which is 8x. The factors that add up to 8 is 3 and 5.

Voilà

Answer:

take the LCM of the three numbers. Since 2 is a multiple of 4, you can ignore the two and just take the LCM of 4 and 3.5. Since 3.5 is a decimal, the LCM is just 3.5*4 which is 14. That is how many minutes after 8:00 they will flash together again.

Step-by-step explanation:

The time that it will take for it to fall 48 feet will be ✓3 seconds.

From the information, the distance s that an object falls varies directly with the square of the time, t , of the fall and an object falls 16 feet in one second.

This will be:

s = kt²

s = distance

k = constant

t = time

s = kt²

16 = 1²k

k = 16

Therefore, the time that it will take for it to fall 48 feet will be:

s = kt²

48 = 16t²

t² = 48 / 16

t² = 3

t = ✓3

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A rational number is a number that can be written in the form:

Where p and q are coprimes. We are asked for finite sets, we can rule out options 3 and 4. In the set in option 2 the first element is:

This number cannot be written a ratio. We can rule out option 2.

All the elements in the set from option 1 can be written in the form p/q.Thus, the answer is the first option.

If you select four socks at random, the probability that at most three are blue is 42.9%.

Probability is the likelihood of an expected outcome occurring when many possible events can happen.

Probability is represented in percentages, fractions, and decimals to show that it describes what is likely from many outcomes.

The total number of socks in the drawer = 14

The number of blue socks = 8

The number of black socks = 6

The probability of getting a blue sock = 8/14

The probability of getting 3 out of 4 = 3/4

The combined probability = 8/14 x 3/4

= 42.86%

= 42.9%

Thus, when you randomly select four socks, you can probably get blue socks 42.9% of the time.

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The answer closest to the number of cubic inches of rain that the barrel can hold is 30,000. Option A

It is important to note that the formula for determining the volume of a cylinder is expressed as;

Volume = πr²h

Where;

Also note that the formula for diameter is given as;

Diameter = 2 radius

Now, substitute the value of diameter

30 = 2r

Make 'r' the subject of formula

r = 15in

Substitute the values into the formula

Volume = 3. 14(15)²(42)

expand the bracket

Volume = 29, 673 cubic inches

Volume = 30, 000 cubic inches

Hence, the value is 30, 000 cubic inches

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The polynomial area of the framed picture is (27 + 2x) * (15 + 2x) and the value is 693 square units

The area of a shape is the amount of space on the shape

For most regular quadrilaterals, you multiply the side lengths to determine the area

The given parameters are

Width = 15

Length = 27

Also, we have

Length of the frame = x

This means that the area of the framed picture is

Area = (Length + 2 * Length of the frame) * (Width + 2 * Length of the frame)

Substitute the known values in the above equation

Area = (27 + 2x) * (15 + 2x)

In (a), we have

Area = (27 + 2x) * (15 + 2x)

When x = 3, we have

Area = (27 + 2 x 3) * (15 + 2 x 3)

Evaluate

Area = 693

Hence, the area is 693 square units

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Solution:

iven the figure below:

Where

Using the secant-secant theorem expressed as

Given that th e satellite signal reaches Bora-Bora at 38,000 km and Greenland which is an additional 20,000km, this implies that

If the distance from the satellite to Rapa Nui is 45,000 km, this implies that

The total distance from the satelite to St. Helen is expressed as

From equation 1,

Substituting the values, we have

divide both sides by 45000,

Hence, the signal will travel a distance of 48977.77777 km from the satellite to St. Helen.

The water pressure on the submerged object is given by d = P ÷ 64

Pressure is the force applied perpendicularly to an object's surface in relation to the area across which it is applied (symbol: p or P).  

a. The given formula is is P=64d

or , d = P ÷ 64

b. at a pressure of 672

d = 672  ÷ 64

or, d = 10.5 feet

Hence the pressure is 672 pounds per square foot at a depth of 10.5 feet.

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Answer:

C

Step-by-step explanation:

Beacuse part to whole means describing a specific part of a group to the whole group, in our case students wearing green : students

Answer:

It would be A because they ordered 81 cans and in each can there 18 ounces so if you multiply it you can get the Total amount.

A) The intersection of subsets A and B is; A ∩ B = {E3, E7, E9}

B)  The union of subsets A and B is; A ∪ B = {E1, E2, E3, E7, E9}

C) No, the union of A & B is not collectively exhaustive

We are given;

Sample space;

S = [E1, E2, E3, E4, E5, E6, E7, E8, E9, E10]

A = [E1, E3, E7, E9]

B = [E2. E3, E, E9]

A) Now, the intersection of subsets A and B would be the values that are common to both sets. This gives us;

A ∩ B = {E3, E7, E9}

B) The union of the subsets A and B with be the combination of all terms in both subsets and this gives us;

A ∪ B = {E1, E2, E3, E7, E9}

C) The union of A & B is not collectively exhaustive because it does not contain all the data available in the sample space.

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Answer:

29

Step-by-step explanation:

Add 28 + 16=44

Subtract 44 - 15=29

Answer:24 bags

Step-by-step explanation:

Using the given information, the number of bags created with  random seed packets is 16 complete bags of seeds and a remainder of 5 seed packets

The number of bags created achieved by division. This is a basic mathematical operator used in sharing items

Given information

Seed Type                                 Number of Packets

Aster                                                       95

Daisy                                                       160

Pansy                                                      70

Sunflower                                                 -

Wildflower                                                -

Adding the number of packets available gives

95 + 160 + 70 = 325 seed packets

Sharing them in a bag containing 20 seed packets each we divider the total number of seed packets by 20

= 325 seed packets / 20

= 16.25

Therefore 16 bags will be created and 5 will be remaining

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To graph an inequality, treat the <, ≤, >, or ≥ sign as an = sign, and graph the equation.

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Recall that:

Therefore:

Simplifying the above result, we get:

The y-axis it's a vertical line, so is represented by x=0.

Then, a parallel line to this one has to be vertical too, and if it passes thorugh (-2, 3). The equation of the parallel line would be x=-2.

Let me explain with a graph:

Integer represents the total change in the time when you use 5 clues with the condition of using 3 free clues is equal to 10 minutes.

As given in the question,

Number of free clues =3

Total number of clues used to escape from a room = 5clues

Out of these 5 clues, 3 clues are free to use. Hence these 3 clues do not result in any time change.

Hence total time elapsed after usage of 3 clues = 0

Each removes 5 minutes from your remaining time

Integer represents the total change in the time for the usage of 4th and 5th clue = 10 minutes

So overall change in timeline after consuming 5 clues = 10 minutes since each of the 4th and 5th clue results in decrease of 5 minutes each; thus effecting 10 minutes total time change (reduction)

Therefore, integer represents the total change in the time when you use 5 clues with the condition of using 3 free clues is equal to 10 minutes.

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Answer:

B

Step-by-step explanation:

the surface area is the sum of all individual side areas.

a prism (like a cube that is a special prism) has 6 sides.

top-bottom

left-right

front-back

in our case top and bottom are 5×5 squares.

and the other 4 sides are equal 5×20 rectangles.

so, we get

top-bottom : 2× 5×5 = 50 cm²

left-right : 2× 20×5 = 200 cm²

front-back : 2× 20×5 = 200 cm²

in total we have

200 + 200 + 50 = 450 cm²

Answer:

Domain:

{−4,1,6,7}

Range:

{5,3,8,−4}

Step-by-step explanation:

The product of the numbers 758 and 93 is 70494

The numbers are given as

758 x 93

By using the standard algorithm i.e. the partial product method, we have the following equation

758 x 93 = 758 x (90 + 3)

Open the bracket

So, we have the following equation

758 x 93 = 758 x 90 + 758 x 3

Evaluate the products

758 x 93 = 68220 + 2274

Next, we evaluate the sum

758 x 93 = 70494

This means that the final product is 70494

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Answer: 4x + 42 < 50

Step-by-step explanation: $42 is the flat price so that is our constant; $4 per gigabyte is our variable. If she wants to keep her bill UNDER $50 dollars a month you would put a less than symbol.

Answer:

Step-by-step explanation:

i did the work and i got 4x + 42 < 50

The coordinates of vertices U(1 , -3) , V(4 , -3) , T(1 , -4) , W(4 , -4) becomes

U' (1, 3) , V'(4 , 3) , T'(1 , 4) , W'(5 , 4) after the reflection across x-axis occurs.

In the question given 4 coordinates,

U(1 , -3)

V(4 , -3)

T(1 , -4)

W(5 , -4)

the reflection across x-axis

U(1 , -3) →U' (1, 3)

V(4 , -3) → V'(4 , 3)

T(1 , -4) → T'(1 , 4)

W(5 , -4) → W'(5 , 4)

so  after the reflection across the x axis the coordinates of the vertices becomes ,

U' (1, 3) , V'(4 , 3) , T'(1 , 4) , W'(5 , 4)

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Accordig to the given line, City P is above sea level, and City R is below sea level because they are above and below zero, respectively.

There are 90 apples in the pile and the row has 4 fewer apples than the row below.

An arithmetic sequence is defined as an arrangement of numbers that is in a particular order.

The sum of an arithmetic sequence is the sum of the first n terms of the sequence as

Sₙ = n/2(2a+(n−1)d)

In arithmetic, here a₁ is the first term and sequence d represents the common difference.

Sum of the apples = 25 + 21 + 17 + 14 + 13 + 9

This series is in AP where a = 25 , d = - 4 and n = 6

As per the given data, the sum of apples would be as:

S₆ = 6/2(2×25+(6-1)×-4)

S₆ = 3(50 + 5×-4)

S₆ = 3(50 - 20)

S₆ = 3(30)

S₆ = 90

Therefore, there are 90 apples in the pile.

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Answer:

Four.

Step-by-step explanation:

6 divided by 1.5 is 4. We do that because if it takes 1.5 mins to make a full rotation and it takes 6 minutes to do blank rotations, the answer is 4 bc we either ti.es 1.5 by 4 to get 6, or do 6 divided by 1.5 to get 4. Sorry if that was confusing.

The first 3 pair of opposite integers are (-1,1),(-2,2) and (-3,3).

Given that,

We have to find the first 3 pairs of opposite integers.

Opposite integers means the "counting numbers" (sometimes known as integers), as well as zero, are integers. The pairs of integers known as opposite integers share the same absolute value, or, to put it another way, are equally spaced from zero. The numbers 10 and -10 are the opposites. The numbers 43 and -43 are the opposites.

So,

Keep in mind that our whole numbers are our integers. The negative and positive iterations of a number together are called a pair of opposite integers.

We get, the first 3 pair of opposite integers are (-1,1),(-2,2) and (-3,3).

Therefore, the first 3 pair of opposite integers are (-1,1),(-2,2) and (-3,3).

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If  he increased his average speed to 300 m/min and finish the race on minute faster than he had during training. The distance of the race is:  1500 meters.

Slower speed :

rate = 250 m/min

time = x minutes

distance = r×t = 250x meters

Faster speed :

rate = 300 m/min

time = x - 1 minutes

distance = 300x - 300 meters

Equate

distance  = distance

250x = 300x - 300

Collect like terms

50x = 300

Divide both side by 50x

x = 300/50

x = 6 minutes

Hence,

Race distance = 250x where x =6

Race distance = 250×6

Race distance= 1500 meters

Therefore we can conclude that the distance is 1500 meters.

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