Solve for x..
12x + 7 < -11 OR
5x – 8 > 40

Answer:  a) add n+1 to the previous term

               b) add the previous two terms

               d) subtract n+1 from the previous term

               e) multiply the previous term by 3

               f) subtract 2 from previous term then add 5 to the next term

Step-by-step explanation:

a) 1, 3, 6, 10

    ∨  ∨  ∨

  +2 +3 +4           The next term is 10 +5 = 15

b) 1, 2, 3, 5

    ∨  ∨  ∨

  =3 =5 =8        The next term is 5 + 8 = 13

d)  8, 7, 5, 2

      ∨  ∨  ∨

     -1  -2  -3             zThe next term is 2 - 4 = -2

e) 1, 3, 9, 27

     ∨  ∨  ∨

    ×3 ×3 ×3         The next term is 27 × 3 = 81

f) 49, 47, 52, 50, 55

      ∨    ∨    ∨    ∨

     -2   +5   -2   +5      The next term is 55 - 2 = 53

                                    The following term is 53 + 5 = 58

a. Add the next consecutive natural number to the previous term.

b. Divide the previous term by 2.

c. Multiply the previous term by 3.

d. Subtract the next consecutive natural number from the previous term.

e. Alternate between subtracting 2 and adding 5.

a. 1, 3, 6, 10, __, __

Pattern Description: This sequence is created by adding consecutive natural numbers to the previous term.

The next term is (10 + 5 = 15).

The term after that is (15 + 6 = 21).

So the pattern is: Add the next consecutive natural number to the previous term.

Next two terms: 15, 21

b. 1, 1/2, 1/4, 1/8, __, __

Pattern Description: This sequence is created by dividing the previous term by 2.

The next term is (1/8 / 2 = 1/16).

The term after that is (1/16 / 2 = 1/32).

So the pattern is: Divide the previous term by 2.

Next two terms: 1/16, 1/32

c. 1, 3, 9, 27, _, __

Pattern Description: This sequence is created by multiplying the previous term by 3.

The next term is (27 × 3 = 81).

The term after that is (81 × 3 = 243).

So the pattern is: Multiply the previous term by 3.

Next two terms: 81, 243

d. 8, 7, 5, 2, _, __

Pattern Description: This sequence is created by subtracting consecutive natural numbers starting from 1.

The next term is (2 - 4 = -2).

The term after that is (-2 - 5 = -7).

So the pattern is: Subtract the next consecutive natural number from the previous term.

Next two terms: -2, -7

e. 49, 47, 52, 50, 55, _, __

Pattern Description: This sequence alternates between subtracting 2 and adding 5.

The next term is (55 - 2 = 53).

The term after that is (53 + 5 = 58).

So the pattern is: Alternate between subtracting 2 and adding 5.

Next two terms: 53, 58

Complete question:

Copy and complete each sequence below. Using words, not numbers, describe how the patterns work. (For example, write, “Double the previous number.”)

a. 1, 3, 6, 10,__, __

b. 1, 1/2 1/4 1/8 , __ , __

c. 1, 3, 9, 27,__, __

d. 8, 7, 5, 2,___, __

e. 49, 47, 52, 50, 55, __, __

Answer:

X²+4x+3=0

Step-by-step explanation:

y = X² + 4x + 3

y = 0

Solution:

x = -3, x² = -1

Steps:

X² + 4x + 3 = 0

write 4x as a sum

X²+ 3x + x + 3 = 0

Factor out x from expression

X (x + 3) + x + 3 = 0

Factor out x + 3 from expression

(x + 3) x (x + 1) = 0

When the product of factors equals 0, at least one factor is 0

x + 3 = 0

x + 1 = 0

solve for x

x = -3

x + 1 = 0

solve for x

x = -3

x = -1

The final solutions are

X = -3, X² = -1

Answer:

Option A.

Step-by-step explanation:

The vertex form of a parabola is

[tex]y=a(x-h)^2+k[/tex]

where, (h,k) is vertex and a is a constant.

The vertex of the parabola is (-2,-1).

Substitute h=-2 and k=-1 in the above equation.

[tex]y=a(x-(-2))^2+(-1)[/tex]

[tex]y=a(x+2)^2-1[/tex]     .... (1)

The parabola passes through the point (0,3). So, it must be satisfy by the point (0,3).

[tex]3=a(0+2)^2-1[/tex]

[tex]3+1=4a[/tex]

[tex]a=1[/tex]

Substiturte a=1 in equation (1).

[tex]y=1(x+2)^2-1[/tex]

On simplification we get

[tex]y=x^2+4x+4-1[/tex]

[tex]y=x^2+4x+3[/tex]

It means the equation [tex]x^2+4x+3=0[/tex] could be solved using the given graph.

Therefore, the correct option is A.

Answer:

Dave should stop at Springfield.

Step-by-step explanation:

As shown, Gilmore is 26 miles away.

And Dave is driving to Gilmore but he wants to stop for lunch when he is about halfway there.

That means he wants to stop around [tex]\frac{26}{2}=13[/tex] miles.

And Springfield is 15 miles away that is nearest to 13 miles.

Hence, Dave should stop at Springfield.

Answer:

Area of the rug will be 6912 square inches.

Step-by-step explanation:

Rob has purchased a rug having measurement 72 inches by 98 inches for his apartment.

Since the rug will be in the shape of a rectangle, area will be represented by the formula,

Area = Length × width

        = 72 × 96

        = 6912 square inches.

Therefore, area of the rug will be 6912 square inches.

To calculate the area of Rob's rug, multiply the length of 96 inches by the width of 72 inches, resulting in an area of 6,912 square inches. Thus, the area of the rug is 6,912 square inches.

To find the area of Rob's rug, you need to multiply the length and the width of the rug.

The formula for area is:

Area = Length × Width

Using the given dimensions:

Area = 96 inches × 72 inches = 6,912 square inches

Therefore, the area of the rug is 6,912 square inches.

Answer:

2 Scoops

Step-by-step explanation:

1/3 plus 1/3 equals 2/3, so he would need two 1/3 scoops.

Answer:

The answer is 2/3 okay? Pls thx me!

Answer:

if you're asking what 21 divided by 40 is then it's 0.525

Step-by-step explanation:

Answer:

1  5/6

Step-by-step explanation:

ab = (-2 3/4) * (-4/6)

     = ( -11/4) * ( -4/6)

     = (11 * 4) / (4 * 6 )

      = 11/6

       = 1  5/6

The third number to the left of the decimal is the hundreds, so you have 200.

The 2nd number to the left of  the decimal is the tens, so you have 30.

The first number to the left of the decimal is the ones, and you have 0 ones, so you have 0.

The first number to the right of the decimal is the tenths place, which is 0 so it is 0.0

The second number to the right is the hundredths place, which is 0.07

The third number is the thousandths place, which is 0.001

The expanded form becomes:

200 + 30 + 0 + 0.0 + 0.07 + 0.001

Answer:

230.071 = 200 + 30 + 0.07 + 0.001

Step-by-step explanation:

First, make the following table.  

Hundreds:      2

Tens:               3

Ones:              0

Decimal:          .  

Tenths:           0

Hundredths:   7  

Thousandths: 1

With the help of this table, now it is easy to write the expanded form as follows

230.071 = 200 + 30 + 0.07 + 0.001

Answer:

127.3

Step-by-step explanation:

The area of the room = (40 x 24) - (20 x 12)

Area = 960 - 240 = 720 square feet

Divide square feet by width of a strip:

720 / 12 = 60 linear feet.

The answer is D.

Answer : The correct option is, (D) 60

Step-by-step explanation :

First we have to calculate the area of room.

Area of room = Area of big rectangle + Area of small rectangle

Area of rectangle = Length × Width

Area of room = (40 × 12) + (20 × 12)

Area of room = 720 square feet

Now we have to calculate the number of linear feet will he need to buy.

Number of linear feet = [tex]\frac{\text{Area of room}}{\text{Width of carpet strips}}[/tex]

Number of linear feet = [tex]\frac{720}{12}=60[/tex]

Thus, the number of linear feet will he need to buy is, 60

Answer:

173,482-5.5=173,476.5

Answer:

$9,541.51

Step-by-step explanation:

Final answer:

To create a 35% saline solution by mixing a 50% and a 30% solution, the nurse needs to use 6000cc of the 30% solution.

Explanation:

The question asks how much of a 30% saline solution a nurse needs to mix with 60cc of a 50% saline solution to achieve a final solution concentration of 35%. To solve this problem, let's denote the volume of the 30% solution needed as x cc. Using the concept of weighted averages for concentrations, we can set up the following equation:

(60cc × 50%) + (x cc × 30%) = (60cc + x cc) × 35%

Solving this equation, we get:

3000 + 0.3x = 0.35(60 + x)

3000 + 0.3x = 21 + 0.35x

Subtracting 0.3x from both sides:

3000 = 21 + 0.05x

Subtracting 21 from both sides and dividing by 0.05:

x = 6000 cc

Therefore, the nurse should use 6000cc of the 30% saline solution to achieve the desired concentration.

Answer:

GCF(15,20) = 5

Step-by-step explanation:

Prime Factorization of 15

Prime factors of 15 are 3, 5. Prime factorization of 15 in exponential form is:

15 = 31 × 51

Prime Factorization of 20

Prime factors of 20 are 2, 5. Prime factorization of 20 in exponential form is:

20 = 22 × 51

Factors of 15

List of positive integer factors of 15 that divides 15 without a remainder.

1, 3, 5

Factors of 20

List of positive integer factors of 20 that divides 15 without a remainder.

1, 2, 4, 5, 10

Greatest Common Factor

We found the factors and prime factorization of 15 and 20. The biggest common factor number is the GCF number.

So the greatest common factor 15 and 20 is 5.

Answer:

x^(1/12).

Step-by-step explanation:

By the laws of indices:

(x ^ 1/2)^1/6)

= x ^(1/2*1/6)

= x^(1/12).

Answer:

Y = 30

Step-by-step explanation:

hope this helps u out :)

Answer:

3t-2

Step-by-step explanation:

so we have three points, A, B and C, if indeed AC is the diameter of the circle, then half the distance of AC is its radius, and the midpoint of AC is the center of the circle, morever, since B is also on the circle, the distance from B to the center must be the same radius distance.

in short, half the distance of AC must be equals to the distance of B to the midpoint of AC, if indeed AC is the diameter.

[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{7}~,~\stackrel{y_1}{4})\qquad C(\stackrel{x_2}{12}~,~\stackrel{y_2}{3}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{12+7}{2}~~,~~\cfrac{3+4}{2} \right)\implies \left( \cfrac{19}{2}~~,~~\cfrac{7}{2} \right)=M\impliedby \textit{center of the circle}[/tex]

now, let's check the distance from say A to the center, and check the distance of B to the center, if it's indeed the center, they'll be the same and thus AC its diameter.

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{7}~,~\stackrel{y_1}{4})\qquad M(\stackrel{x_2}{\frac{19}{2}}~,~\stackrel{y_2}{\frac{7}{2}})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AM=\sqrt{\left( \frac{19}{2}-7 \right)^2+\left( \frac{7}{2}-4 \right)^2} \\\\\\ AM=\sqrt{\left( \frac{5}{2}\right)^2+\left( -\frac{1}{2} \right)^2}\implies \boxed{AM\approx 2.549509756796392} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ B(\stackrel{x_1}{10}~,~\stackrel{y_1}{6})\qquad M(\stackrel{x_2}{\frac{19}{2}}~,~\stackrel{y_2}{\frac{7}{2}}) \\\\\\ BM=\sqrt{\left( \frac{19}{2}-10 \right)^2+\left( \frac{7}{2}-6 \right)^2} \\\\\\ BM=\sqrt{\left( -\frac{1}{2}\right)^2+\left( -\frac{5}{2} \right)^2}\implies \boxed{BM\approx 2.549509756796392}[/tex]

AC must be the diameter of the circle.

What is Circle?

A circle is a closed two dimensional figure in which the set of all the points in the plane is equidistance from a center.

Given that;

A circle passes through points A(7, 4), B(10, 6), C(12, 3).

Now,

If AC is diameter of the circle then half the distance of AC is its radius and midpoint of AC is the center of the circle.

Since, B is also on the circle , then distance from B to the center must be same radius distance.

Midpoint of AC is calculated as;

= (7 + 12 / 2 , 4 + 3/2)

= (19/2 , 7/2)

= (9.5 , 3.5)

Now, Distance from A to the center and check the distance of B to the center as;

AM = √(9.5 - 7)² + (3.5 - 4)²

AM = 2.5495

And,

BM = √(9.5 - 7)² + (3.5 - 6)²

BM = 2.5495

So,  Distance from A to the center and the distance of B to the center is same.

Thus, AC must be the diameter of the circle.

Learn more about the circle visit:

https://brainly.com/question/25927269

#SPJ2

Answer:

7.

Step-by-step explanation:

Let the number be n, then

7 + √5 = n + √5

As the 2 sides are equal in value, n must be 7.

Paulo's time in standard notation is 15,600 seconds. Miguel ran the marathon in a shorter time of 15,360 seconds. For the given equations, A) and B) each have one solution (x=3 and x=10, respectively), while C) has an infinite number of solutions.

To convert Paulo's time from scientific to standard notation, we multiply 1.56 by 10 to the power of 4. This equals 15,600 seconds. Next, we need to convert Miguel's time to seconds to directly compare the two durations. Miguel ran for 4 hours and 16 minutes, which is equal to (4 × 3600) + (16 × 60) = 14,400 + 960 = 15,360 seconds. Therefore, Miguel ran the race in a shorter amount of time by 240 seconds.

For question 2, we solve the following equations:

For equation A) 2x + 4(x - 1) = 2 + 4x, after simplifying we get 2x + 4x - 4 = 2 + 4x. The 4x terms cancel out and we are left with 2x - 4 = 2. Solving for x gives x = 3. This equation has one solution.

For equation B) 25 - x = 15 - (3x + 10), simplifying gives 25 - x = 5 - 3x. Solving for x yields x = 10, so this equation also has one solution.

For equation C) 4x = 2x + 2x + 5(x - x), simplifying results in 4x = 4x, which is true for all values of x. Therefore, this equation has an infinite number of solutions.

As question 3 involves an image that we cannot see here, this part of the student's question has been left unanswered.

Answer:

6

Step-by-step explanation:

5*6=30

7*6=42

Hey!

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

Solution:

30 / 5 = 6

42 / 7 = 6

5 x 6 = 30

7 x 6 = 42

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

Answer:

Multiplier is 6!

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

Hope This Helped! Good Luck!

Answer:

16

Step-by-step explanation:

because eight is 50% of 16

Answer: She will be 16

Step-by-step explanation:

Answer:

When there is not a constant rate of change

Step-by-step explanation:

A linear model shows a continuous response variable as a function of one or more predictor variables.

A linear model is a good fit for a set of data when the plotted points show a constant rate of change.

When a plot of values form a scatter plot, it is difficult to identify a linear model because the points will not appear to follow a trend.

To come up with a linear function in this case will require you to identify the line of best fit then extending the line to y-axis intercept so as to be able to find the slope.

Fraction Decimal Percentage

30/1000 0.03 3%

29/1000 0.029 2.9%

28/1000 0.028 2.8%

29/997 0.02909 2.909%

Answer:

0.029

Step-by-step explanation:

Answer:

Step-by-step explanation:

f(x)= x-4/√x

f  exist for : x  >  0

so the domain is : D= ]0 ; + ∞[

Answer:

5x10⁸

Step-by-step explanation:

Cell = 200 cubic micrometers.

Te question is, how many 200 cubic micrometers are there in a cubic centimeter. 1st, we have to convert 200 cubic centimeter into cubic centimeter:

1cm = 1x10⁴micro, which is the same to:

1x10⁻⁴ cm = 1micro

Now, we have to cube both sides, to "equal the volumes"

(1x10⁻⁴cm)³ = (1micro)³

1x10⁻¹²cm = 1micro³

Multiple both sides by 200:

200 x 1x10⁻¹²cm = 1micro³ x 200

2x10⁻¹⁰cm³ = 200micro³

Finally, 1 cubic cm / 2x10⁻¹⁰cm³ = 5x10⁸

Final answer:

Explaining the number of cells in a cubic centimeter based on the volume of a 10 μm cell.

Explanation:

For a 10 μm cell:

Calculate the volume: V = (4/3)πr³

Convert diameter to radius: r = 5 μm

Substitute and calculate volume: V = (4/3)π(5)³ = 524 μm³

Convert to cubic centimeters: 1 μm³ = 10^-9 cm³, so 524 μm³ = 5.24 x 10^-7 cm³

Calculate the number of cells in 1 cm³: 1 cm³ / 5.24 x 10^-7 cm³ = 1.91 x 10^6 cells

If two coins are tossed simultaneously, you will have one of the possible results

[tex]HH,\ HT,\ TH,\ TT[/tex]

with probability 1/4 each.

So, you'll have at least one head if you have HH, HT or TH, i.e. with probability 3/4.

Similarly, you have at most one tail if you get HH, HT or TH, so the probability will be the same.

In fact, both claims (at least one head and at most one tail) are verified by the same set of outputs HH, TH, HT, since they're not satisfied only by the output HH.

So, if those claims are not satisfied with probability 1/4, they're satisfied with probability 3/4.

Final answer:

The probability of getting at least one head when tossing two coins is 0.75.

When two coins are tossed simultaneously, the sample space consists of the following possible outcomes: {HH, HT, TH, TT}. To find the probability of getting at least one head, we can count the favorable outcomes which include at least one head: these are HH, HT, and TH. Thus, there are 3 favorable outcomes.

The total number of possible outcomes is 4. Therefore, the probability is 3 out of 4, or
0.75.

To find the probability of getting at most one tail, we consider the favorable outcomes: these are HH, HT, and TH. Again, we can see there are 3 favorable outcomes.

Since the total number of outcomes is the same, the probability remains
0.75.

Answer:

18,21,36

Step-by-step explanation:

Answer:

Step-by-step explanation:

Start train 1 at 6 pm an train 2 at 9pm

Answer:

No solution

Step-by-step explanation:

Subtract 5k from both sides

Simplify

No solution