The sum of -4 and 5 times a number is multiplied by 3. The result is 212 less than 7 times the number. What is the number?

Answer:

The answer is about 1.732, the exact form being [tex]\sqrt{3}[/tex].

Step-by-step explanation:

The square root of 12 is 3.4641. You then divide this by 2 and you get approximately 1.732. This in the exact form is [tex]\sqrt{3}[/tex].

Answer:Look below

Step-by-step explanation:

f(x) = x^3

g(x) = f(x-4) which shifts f(x) 4 units to the right

g(x) = (x-4)^3

h(x) = g(x) + 6 shift g(x) 6 units up

h(x) = (x-4)^3 + 6

The turning point of f(x) is at (0,0),  then shift  4 units to the right and 6 units up, I got (4,6)

Probability of choosing pink balloon is  [tex]\frac{2}{5}[/tex].

Step-by-step explanation:

Given,

Number of green balloons = 5

Number of yellow balloons = 3

Number of red balloons = 4

Number of pink balloons = 8

Total number of balloons = 5+3+4+8 = 20

To find the probability of pink balloon.

Formula

Probability of an even = number of outcomes ÷ total number of outcomes

So,

Probability of choosing pink balloon = [tex]\frac{8}{20}[/tex] = [tex]\frac{2}{5}[/tex]

Answer:

s = -18

b is correct option

Step-by-step explanation:

[tex]\frac{4}{s} =\frac{-2}{9}[/tex]

By cross multiplication

4×9 = -2×s

0r

-2×s = 4×9

s = 36 ÷ -2

s = -18

Answer:

g = 3

Step-by-step explanation:

If you distribute (x+7)(x-4) you get:

x²+3x-28

Compare it to the question:

x²+gx-28

and it becomes obvious that g = 3

The solution is, the value of g makes the equation true is, g = 3.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

from the given information we get,

If you distribute (x+7)(x-4) you get:

x²+3x-28

Compare it to the question:

x²+gx-28

and it becomes obvious that g = 3

Hence, The solution is, the value of g makes the equation true is, g = 3.

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Answer:

25 + 6 = 31

Step-by-step explanation:

Answer:

2 times 8 is 16. 16 minus 4 is 12 plus 5 is 17. answer is 17.

Step-by-step explanation:

since h=8

The steps of the value of the expression:

2(8)-4+5

16-4+5

12+5

17

Answer:

1. 130/6

2. 65/3

3. 260/12

Step-by-step explanation:

The first thing is to calculate the weight of 10 quarts of milk, like this:

(13 pounds / 6 quarts) * 10 quarts = 130/6 pounds

The three fractions could be:

1. 130/6 pounds weigh 10 quarts of milk.

2. 65/3 pounds weigh 10 quarts of milk.

3. 260/12 pounds weigh 10 quarts of milk.

Answer:

a

Step-by-step explanation:

Final answer:

Number sense enhances a student's understanding of multiplication and helps them choose the most efficient written method. For example, 0.5 can be easily multiplied mentally, and this knowledge can be applied to written methods for multiplying decimals.

Explanation:

In mathematics, number sense refers to a person's understanding of numbers and their relationships. It involves the ability to perform mental calculations and estimate the magnitude of numbers. On the other hand, written methods such as partial products or area models are specific algorithms or procedures used to solve mathematical problems, including multiplying decimal numbers.

The relationship between number sense and written methods for multiplying decimal numbers is that number sense enhances a student's understanding of the concept of multiplication and helps them make connections between different strategies or methods. By developing number sense, students can choose the most efficient written method based on their understanding of the numbers involved and their relationships.

For example, if a student has a strong number sense, they may recognize the relationship between a decimal that can be easily multiplied mentally, such as 0.5, and other decimal numbers. They can then use this knowledge to apply a written method like area models or partial products to solve problems that involve multiplying decimals.

Answer:

It is C. Just look at the farthest points, and those are the numbers in your inequality.

To analyze a function's graph, identify the domain and range, find the intercepts, assess whether the function is increasing or decreasing, and locate the extrema points.

Without the graph, I can't provide a specific analysis. However, I can guide you on how to analyze a function graph. A function graph can give specific details such as the function's domain and range, its intercepts, whether it's increasing or decreasing, and any extrema points (maxima or minima).

To find the domain, you need to identify which 'x' values are included on the graph. The range refers to the 'y' values covered by the graph. The intercepts are points where the graph crosses the 'x' axis (x-intercepts) and 'y' axis (y-intercepts).

By checking if the function is rising (increasing) or falling (decreasing), and spotting the highest and lowest points (maxima and minima), you can explore the behavior of the function.

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Answer:

The residual value is the farthest from the line of best fit is 0.7.

Step-by-step explanation:

A simple linear regression line is given by,

[tex]\hat y = \alpha + \beta X + \hat e[/tex]

Here,

α = constant,

β = slope

e = residual.

The difference amid the observed value of the dependent variable (Y) and the predicted value (y) is known as the residual (e).  

The formula to compute the residual is,

[tex]\hat e=y-\hat y[/tex]

The information provided is:

x           y           e

1          2.0       -0.4

2         3.5         0.7

3         5.0        -0.2

4         6.1         -0.6

5         8.0         0.0

The residuals are the difference between the actual value and the predicted value.

They can also be defined as the distance between the line of best fit and the actual value of the dependent variable.

The data point that is the farthest from the line of best fit is, y = 3.5.

The residual value of y = 3.5 is 0.7.

In terms of units distance, this value of y is the farthest from the line of bet fit.

Thus, the residual value is the farthest from the line of best fit is 0.7.

Answer:

Yes I agree, because 32 times 8 plus 48 times 8 equals 8x(32+48)

Step-by-step explanation:

Final answer:

The binomials that are a difference of squares are [tex]9x^2 - 16[/tex] and [tex]m^6 - 25[/tex], as both can be factored into the form (a + b)(a - b).

Explanation:

The question asks which binomials are a difference of squares. A difference of squares is a binomial in the form [tex]a^2 - b^2[/tex], which can be factored into (a + b)(a - b). Analyzing the given options:

[tex]y^4 + 9[/tex]: This is not a difference, it's a sum.

[tex]9x^2 - 16[/tex]: This is a difference of squares because [tex]9x^2 = (3x)^2[/tex] and 16 = [tex]4^2[/tex].

[tex]m^6 - 25[/tex]: This is a difference of squares because [tex]m^6 = (m3)^2[/tex] and [tex]25 = 5^2[/tex].

[tex]p^7 - 1[/tex]: This is not a difference of perfect squares; [tex]p^7[/tex] is not a perfect square.

Therefore, the binomials that are a difference of squares are [tex]9x^2 - 16[/tex] and [tex]m^6 - 25[/tex].

Answer:

x² - 9

Step-by-step explanation:

A difference of squares has the form

a² - b²

Thus

x² - 9

= x² - 3² ← is a difference of squares

Answer:

+180

Step-by-step explanation:

When we graph the function, it has a vertex of (3, 16).

The maximum of the graph is the highest "x" value on the graph which is 3.

Since the maximum is 3, it will take 3 seconds for the ball to reach its maximum height.

A graph will be shown below showing the function and vertex.

Best of Luck!

Answer:

3 seconds

Step-by-step explanation:

We need to find where the maximum i.  The maximum or minimum  is at the vertex.  We know where the zero are because the equation is written in the zero form

We know the vertex is 1/2 way between the zeros

h(x)=-(x+1)(x-7)

Using the zero product property

x+1 = 0  x-7 =0

The zeros are at -1 and 7

Adding the two together and dividing by 2

(-1+7)/2 = 6/2 =3

The maximum is at 3.  We know it is the maximum because the equation is pointing down because of the negative out front.

Answer:y=-2x+3

Step-by-step explanation:

the 3 is the y coordinate

the slope is -2

April has a total of 6 pieces of paper, with each piece being 4 inches long after she cuts the 2-foot paper into halves and then into thirds.

To solve this problem, we need to perform two cuts. The initial length of the paper is 2 feet. When April cuts the length of paper into halves, she now has two pieces each of 1 foot in length. Then, she cuts each of these halves into thirds. To find out how many pieces she has in total, we multiply 2 halves by 3, resulting in 6 pieces of paper in total.

To determine the length of each piece in inches, we start with the original measurement in feet. Since 1 foot is equivalent to 12 inches, we convert the 1-foot pieces to inches by multiplying by 12. Then, we divide by 3 to represent the three cuts that April makes:

1 foot = 12 inches

Each cut piece = 12 inches / 3

Each piece is 4 inches long.

Answer: 165 bags

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

English translation:

An employee receives a commission  equivalent to 5% of your salary, X. What

expression represents the total money that  will receive the employee?

Solution:

We have to find the expression that gives us the total money of the employee. His total money is what he gets, the salary, PLUS the commissions.

His salary is "x"

and his commissions is 5% of his salary.

5% = 5/100 = 0.05

So,

Commissions = 0.05x

Total Money = Salary + Commission = x + 0.05x = 1.05x

Correct answer is B

Answer:

I believe the answer is A

Answer:

907.46cm

Step-by-step explanation:

Area of Cirlce = πr^2

R= 17

R^2= 289

289 x 3.14 = 907.46

907.46cm

Answer:

Area of the circle = [tex]907.46\;cm^2[/tex]

Step-by-step explanation:

Diameter of the DVD = [tex]34\;cm[/tex]

[tex]Radius=\dfrac{34}{2}=17\;cm[/tex]

Area of the circle= [tex]\pi \times r^2[/tex]

      As,

         [tex]\pi =\dfrac{22}{7}=3.14[/tex]

Area is:

      [tex]=3.14\times 17\times 17\\\\=3.14\times 289\\\\=907.46\;cm^2[/tex]

Area of the circle is: [tex]907.46\;cm^2[/tex]

Answer: 6,3

Step-by-step explanation: 3/3 and then 9/3=3 • 0+12=12, 12/2=6,

Please give brainliest

The system of inequalities consists of x > 6 and x < 3, which have no overlapping solution. No number can satisfy both conditions simultaneously; hence, there is no solution to the system.

To solve the given system of inequalities, let's solve each inequality separately:

For the first inequality 2x - 12 > 0, we add 12 to both sides to get:

2x > 12

Now, we divide both sides by 2:

x > 6

This inequality means that x must be greater than 6.

For the second inequality 3x < 9, we divide both sides by 3:

x < 3

This tells us that x must be less than 3.

If we look at both solutions, x > 6 and x < 3, there is no overlap between these two sets of numbers.

Therefore, there is no solution to the system, since no number can be both greater than 6 and less than 3 at the same time.

Answer:

  a) 8.7 km

  b) 187.6°

Step-by-step explanation:

Given

Travel vectors (distance)∠(direction) ...

Find

(Rounded to the nearest tenth ...)

  a) |d₂|

  b) ∠d₂

Solution

In order for the sum of the three travel vectors to represent a round trip, their sum must be zero. That is, the value of d₂ must be the opposite of the sum of the other two vectors. A vector calculator can find the desired value easily. Here, we will show the calculation using the law of cosines and the law of sines.

__

a) A diagram can be helpful. Since we want to find the opposite of the sum of the given vectors, we can start by drawing their sum. In our diagram, d₁ is segment AB, and d₃ is segment BC. Their sum is the segment AC.

The internal angle ABC is the supplement of the difference of the angles for d₁ and d₃, so is 180° -(47° -3°) = 136°. Then the law of cosines gives length AC as ...

  AC² = AB² +BC² -2AB·BC·cos(B)

  AC² = 8² +1² -2·8·1·cos(136°) = 65 -16cos(136°) ≈ 76.5094

  AC ≈ √76.5094 ≈ 8.747

The distance traveled on day 2 is about 8.7 km.

__

b) Given the side lengths of a triangle and one angle, the law of sines can be used to find the other angles. Here, it is convenient to find the internal angle at A. The law of sines tells us ...

  sin(A)/BC = sin(B)/AC

  sin(A) = BC/AC·sin(B)

  A = arcsin(BC/AC·sin(B)) = arcsin(1/8.747·sin(136°)) ≈ 4.555°

The direction angle from C to A will be the sum of the 3° direction angle of AB and the internal triangle angle A we just found, added to 180°. That sum is ...

  ∠CA = 180° +3° +4.6° = 187.6°

  ∠d₂ = 187.6°

Answer:

Distance traveled 8.6 kilometers on day two

Daniela traveled in a direcrion of 234degrees on day two

Step-by-step explanation:

I had the same exact question and found the answers after having it incorrect

Answer:

y = 6/5x -5

Step-by-step explanation:

Using the slope formula,

you can find the slope

or just divide the amount of units up by

the amount of units right.

Then find the y intercept which is (0,5)

Answer:

y = [tex]\frac{6}{5}[/tex]x -5

Step-by-step explanation:

Whenever we have a line such as this one, (A linear or straight line) we can write an equation with the form y = mx + b

m is the slope

b is the y-intercept

To calculate slope or "m" we see how many times the point goes up, and how many times it goes to the right, and then put it in a fraction.

(Units it goes up) / (Units it goes to the right)

The y-intercept is what number the line intersects on the y-axis.

On this line it intersects at the -5 point.

So the equation when you put in the values is y = [tex]\frac{6}{5}[/tex]x -5

Check out the diagram below. Note how for the left triangle, the side ZW is not between the marked angles V and W. So we do not use ASA and instead go with AAS. The order matters. If for instance, we knew that VW = WY, then we would go with ASA.

Answer:

area of a circle = 1808.64meters²

Step-by-step explanation:

given that ,

π = 3.14

circumference = 150.72meters

calculate the area of the circle.

to calculate the circumference of a circle

recall,

circumference of a circle = 2πr

circumference of a circle = 2 x 3.14 x r

circumference of a circle =  6.28r

150.72meteras = 6.28r

divide both sides by 6.26

150.72meters/6.28 = 6.28r/6.28

24meters = radius

radius = 24 meters

now to calculate the area of the circle

recall the formulae for finding the area of a circle is given to be = πr²

area of a circle = πr²

area of a circle = 3.14 x ( 24)²

area of a circle = 3.14 x 576meters²

area of a circle = 1808.64meters²