Which of the following is a solution for the equation 7x + 21 = 105?

105
15
84
12

Answer:

a is the answer because when x⁴ will go up it will be x-4

Answer:

704 cubic units

Step-by-step explanation:

First let's calculate the volume of the cube. The formula to calculate the volume of a cube is V = a^3, a being the edge length of the cube. So we need to cube the value of a, which is 8. 8 cubed is 512 cubic units.

Now we need to calculate the volume of the triangular prism. The formula to calculate the volume of a cube is V = 1/2b * a * h, a being the side edge length of the prism, b being the height of the triangular side, and h being the base edge length of the triangular side, if that makes any sense (easier to explain visually). h and a are equal to the given a, which is 8 in this case. And b in the formula is equal to b in the given problem. So we substitute the values into the formula: V = (1/2*6) * 8 * 8 = 3 * 64 = 192 cubic units.

Now we take the sum of both of the figures:

512 + 192 = 704 cubic units.

Answer:

NT and MT

Step-by-step explanation:

Sorry I'm late lol.

The two segments form a right angle where they intersect, which is a common indication of perpendicular lines.

We are given that the surface lies within the cylinder x2 y2 = 64.

Since z = xy, we need to find the bounds for x and y such that the xy surface lies within the cylinder x2 y2 = 64.

The cylinder has a radius of 8 since x2 + y2 = 64 has a solution of (8, 0).

So, we need to find the bounds for x and y within the circle x2 + y2 = 8.

We can use polar coordinates to do this.

Let x = r cosθ and y = r sinθ.

Then the surface equation becomes: z = r cosθ ⋅ r sinθ = r2 cosθ sinθ

And the cylinder equation becomes:

r2 cos2θ sin2θ = 64r2 sin2θ cos2θ = 64r2 sin2θ = 64/cos2θr = 8/(cosθ sinθ) = 8/(1/2 sin2θ) = 16/sin2θ

And we have the bounds for r, which is between 0 and 16/sin2θ.

Now we integrate with respect to θ:

∫02π ∫016/sin2θ r2 cosθ sinθ dr dθ

We can solve the inner integral by substituting u = r2 and du = 2r dr:∫016/sin2θ r2 cosθ sinθ dr = ∫0(16/sin2θ)2 cosθ sinθ (1/2) du= (1/2) ∫0(16/sin2θ)2 cosθ sinθ du= (1/2) [u sinθ]016/sin2θ= (1/2) (16/sin2θ) sinθ = 8/sinθ

So the integral becomes: ∫02π (8/sinθ) dθ

We can split it into two parts:

∫02π 8 cotθ dθ = 8 [ln|sinθ|]02π= 0

So the area of the surface z = xy that lies within the cylinder x2 y2 = 64 is 0.

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You must identify the equation that defines the graph in order to assess the graph's expression. This equation will be a mathematical expression that explains the connection between the graph's variables.

A graph is a visual representation of the relationship between two or more variables. It is a way of showing how the variables change in relation to each other. A graph typically consists of a set of points plotted on a coordinate plane, with each point representing a specific set of values for the variables. The shape of the graph can reveal patterns and trends in the data, and it can be used to make predictions and draw conclusions about the relationship between the variables.

You can use the coordinates of points on a graph, the slope and y-intercept of the graph (if it's a linear function), or the properties of the graph to get its equation (such as the shape of the curve or the presence of asymptotes).

Once you have the equation for the graph, you may simplify it and substitute the variable values there to evaluate the expression.

Take the graph of the function y = x2 - 2x + 1, for instance. You can substitute the value of x into the equation and simplify to determine the value of this function for a specific value of x. For instance, the function's value in the case of an x of 3 is y = 32 - 2(3) + 1 = 9 - 6 + 1 = 4.

A graph itself can be used to assess the expression of a graph. To determine the equation of the graph, you may, for instance, read the coordinates of the graph's points or examine the curve's shape and any asymptotes' locations.

Keep in mind that you need a mechanism to represent both the graph and the equation that describes it in order to evaluate the expression of a graph. This could entail manually creating the graph, using software or a graphing calculator, or representing the graph as a table of values.

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Answer:

a < -12

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

-11 > 1 + a

Step 2: Solve for a

Here we see that any value a smaller than -12 would work as a solution to the inequality.

Answer:

a < -12

Step-by-step explanation:

Answer:

4/3

Step-by-step explanation:

Lets begin by moving the negative 1 to the right. We are now at 4x = 3y + 6. If we move the 3y to the left and 4x to the right, we then get to -3y = -4x +6. We now need to divide by -3. This simplifies to y = 4/3x + 6. Therefore, the slope would be 4/3.

Rolling a pair of dice, the theoretical probability of rolling each sum can be determined by dividing the number of possible outcomes for each sum by the total number of possible outcomes (36).  

Empirical probability, which is based on actual results from an experiment, can differ from theoretical probability, which is the expected probability based on mathematical calculations. In the case of rolling a pair of dice, the theoretical probability of rolling each sum can be determined by dividing the number of possible outcomes for each sum by the total number of possible outcomes (36). For example, the theoretical probability of rolling a sum of 7 is 6/36 or 1/6.

However, the empirical probability of rolling each sum may differ from the theoretical probability due to the random nature of the experiment. In other words, the actual results may not perfectly match the expected results due to chance variations. Additionally, factors such as the condition of the dice and the manner in which they are rolled can also affect the outcomes.

To compare the empirical and theoretical probabilities of rolling a pair of dice, we can calculate the range, mean, median, and mode of the results from the experiment. The range is the difference between the highest and lowest values observed, the mean is the average of all the results, the median is the middle value in the set, and the mode is the most frequently observed value.

Overall, the empirical probabilities may vary from the theoretical probabilities due to chance variations and other factors, but by analyzing the central tendency of the results, we can gain a better understanding of the overall outcomes of the experiment.

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Step-by-step explanation:

x² - 9

1. There is no common factor other than 1.

2. √x² = x; √9 = 3

3. a = x; b = 3

4. x² - 9 = (x - 3)(x + 3)

Answer:

K.E = 100 J

Step-by-step explanation:

Here, we are interested in calculating the kinetic energy of the body.

Mathematically;

Kinetic energy K.E = 1/2 * m * v^2

From the question, m = 50kg and v = 2 ms^-1

Substituting these values into the equation, we have;

K.E = 1/2 * 50 * 2^2 = 200/2 = 100 J

Answer:

59

Step-by-step explanation:

We know that all the angles must add up to 180

so we have

38+2b-20+b-15=180

solve for b

3b+3=180

3b=177

b=59

Answer:

b=59

Step-by-step explanation:

angles in the triangle add up to 180

this would mean that

38 +2b-20 + b-15 = 180

if we simplify this then it would be

3+3b= 180

rearrange

3b = 177

b = 59

The depreciated value of the tractor after 6 years is $116,800. This means that after 6 years, the tractor has lost $37,200 in value from its initial purchase price of $154,000.

a) The given linear model for the depreciated value V of the tractor after t years is V = -6,200t + 154,000. This equation represents a linear relationship between the time (in years) since the tractor was purchased (t) and its depreciated value (V). The coefficient of t, -6,200, represents the rate at which the value decreases per year, and the constant term, 154,000, represents the initial value of the tractor when it was purchased.

b) To find the depreciated value of the tractor after 6 years, we substitute t = 6 into the linear model:

V = -6,200(6) + 154,000

V = -37,200 + 154,000

V = 116,800

Therefore, the depreciated value of the tractor after 6 years is $116,800. This means that after 6 years, the tractor has lost $37,200 in value from its initial purchase price of $154,000.

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The Mystery PROCEDURE's behaviour is best described by the statement Return whether or not word is in list.

When control is sent back to the caller function, the running of a function is complete. Following the call, the calling function immediately continues operation. The invoking function might get a value via a return statement. Visit Return type to find out more.

The script or function that called the function will receive a value once the function has completed its task. Return values can be of any of the four variable types: handle, integer, object, or string. The task your function completes has a significant impact on the outcome it produces. A return, often known as a financial return, is the amount that an investment makes or loses over time.

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The complete question is,

PROCEDURE Mystery (word, list)

{

FOR EACH item IN list

{

IF (item = word)

{

RETURN (true)

}

}

RETURN (false)

}

Which of the following best describes the behavior of the Mystery PROCEDURE?

The equivalent fractions for 2/3 is (3×2)/(3×3) = 6/9 and for  5/12 is (4×5)/(4×12) = 20/48.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

The equivalent fraction for 2/3 is (3×2)/(3×3) = 6/9.

The equivalent fraction for 5/12 is (4×5)/(4×12) = 20/48.

We have to multiply the same number to both the numerator and denominator to get equivalent fractions.

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Answer:

3 batches

Step-by-step explanation:

First simplify 1/2 into 3/6

which into 1/6 makes three which means Mark can make 3 batches of cookies.

(If Mark had a full pound he could make 6 batches of cookies)*

Have a good day. :)

Hope this helps!

(brainliest would be appreciated)

Answer:

3 batches

Step-by-step explanation:

Answer:

Obviously B

Step-by-step explanation:

Given that Jackson digs a hole at a rate of 3/5 feet every 10 minutes, and he dug for 40 minutes. Thus, the total depth of the hole dug by him is given by:

3/5 x 4 = 12/5

= 2.4 feet (Depth of the hole dug by Jackson)

After he placed the plant in the hole, the depth of the plant is 9/10 feet.

So, the total depth of the hole that is filled after he placed the plant is:

2.4 + 9/10= 12/5 + 9/10

               = 24/10 + 9/10

               = 33/10 feet

Now, if we consider ground level as zero, then the elevation of the hole is 33/10 feet above the ground level.

Therefore, the relative elevation of the hole after placing the plant in the hole is 33/10 feet above ground level.

Jackson digs a hole at a rate of 3/5 feet every 10 minutes. After digging for 40 minutes, Jackson places a plant in the hole that fills exactly 9/10 feet of the hole. The problem is based on the concept of fraction addition and subtraction along with conversion of mixed fractions into improper fractions. Here, we need to calculate the elevation of the hole after the plant is placed. It is given that Jackson digs a hole at a rate of 3/5 feet every 10 minutes. After digging for 40 minutes, the total depth of the hole dug by Jackson is 2.4 feet. Now, when he places the plant in the hole that fills exactly 9/10 feet of the hole, the depth of the hole that is filled becomes 33/10 feet. Therefore, the relative elevation of the hole after placing the plant in the hole is 33/10 feet above ground level.

Relative elevation of the hole after placing the plant in the hole is 33/10 feet above ground level.

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Answer:

-2

(0, 1)

Step-by-step explanation:

Giveb the function :

F(x) = 3^x + 1 – 2

To obtain the asymptote, take the limit of f(x) as x as tends to ∞

3^(∞+1) - 2 = 0 - 2

Hence,

y = 0 - 2.

y = - 2

The y intercept, this is the value of y when x = 0

Hence, put x = 0

F(0) = 3^(0 + 1) – 2

f(0) = 3^1 - 2

f(0) = 3 - 2

f(0) = 1

Y - intercept = (0, 1)

Answer:

hope this helps you out

it's 21 a or b

you can choose witch one you want to use

Step-by-step explanation:

there is 2 possible answers

Answer:

O {(-2,-5).(-3,5),(4,-5), (5,5)}

Step-by-step explanation:

brainest plz

Answer:

m= - 3

b= 3

Step-by-step explanation:

Answer:

20%

Step-by-step explanation:

25 divided by 5 is 5 and in fractions 1/5 is 20 therefore 20% for every 5 pounds so if you lose 5 pounds you lost 20% of her weight.

Answer:

ana totta

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.

C is the correct answer since it can be expressed as a fraction which equals to 7/9.

Hope it helps:)

Answer:

A

Step-by-step explanation:

Pi is an irrational number so it can't be B.

√(5) is an irrational number so it can't be D.

It could be either A or C... Hm, go with A. Let me know if it works.

We can express the equation of the regression line as y = a + bx, where a is the intercept and b is the slope obtained from the coefficients.

The least squares regression line through the given points can be found using matrix operations. By representing the points as a matrix and applying a series of calculations, the line that minimizes the sum of squared errors can be determined.

To find the least squares regression line, we first represent the given points as a matrix X, where each row corresponds to a point and the first column is filled with 1s. We also create a column vector y containing the y-values of the points. Next, we calculate the transpose of X and multiply it with X to obtain the matrix X^T * X. Then, we compute the inverse of X^T * X, which we multiply by the transpose of X and y to get the coefficients of the regression line. Finally, we can express the equation of the regression line as y = a + bx, where a is the intercept and b is the slope obtained from the coefficients.

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Based on the ratios given of 0.3 : 4 = 9 : y, the value of y can be found to be 120

From the given ratios of 0.3 : 4 = 9 : y, we can infer that these are equivalent ratios.

This means that y is to 9, what 4 is to 0.3.

The value of y can therefore be found by direct proportion:

0.3 : 4

9 : y

Cross multiplying gives:

0.3 y = 36

y = 36 / 0.3

y = 120

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John will clean the house for 5/2 = 2.5 hours.

What is quadratic equation?

The polynomial equation whose highest degree is two is called a quadratic equation or sometimes just quadratics. It is expressed in the form of:

ax² + bx + c = 0

where x is the unknown variable and a, b and c are the constant terms.

Given, that John cleans the house 2 hours more than Jane.

Let x be the time taken by the Jane and x +2 be the time taken by John.

Total they work for 2 hours 24 minutes

first we will convert minutes into hours, 24/60

= 2.4 hours

Let time taken by John = 1/x+2

time taken by Jane = x

1/x + 1/(x+2) = 2.4

Taking lcm,

x+x+2 = 2.4(x)(x+2)

2x +2 = 2.4\(x^{2}\) +4.8x

2.4x\(x^{2}\)+2.8x -2 = 0

On solving it,

x = \(\frac{b-\sqrt{b^{2-4ac} } }{2a}\)

x = 1/2 and x = -5/3

only x = 1/2 is possible value.

Time taken by John = 1+1/2

=5/2

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Paula's song took 4.565 minutes to download. It's likely that they both equation downloaded their tracks using the same web technique.

In mathematics, an equation is a statement which defines the equivalence of two expressions. An equation is made up of two sides linked by the algebraic symbol (=). The argument "2x + 3 = 9," for example, states that the sentence "2x + 3" equals the value "9." The goal of solving equations is to find the value or values of the variable(s) that enable the equation to be valid. Equations can be simple or complex, linear or nonlinear, and contain one or more parts. In the equation "\(x2\) + 2x - 3 = 0," the variable x is raised to the second power. Lines are used in many areas of mathematics, including algebra, calculus, and geometry.

Based on the statistics provided Paula's song took 4.565 minutes to download, while Amanda's song took 4.575 minutes. They most likely downloaded their tunes utilizing exactly the same online approach.

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Answer:

(2x-5)feet

Step-by-step explanation:

The area of the rectangular garden A = Length × Width

Given the area A(x) = 2x² - 21x + 40

And the width =x-8 feet

To get the length, we will simply factorise the area function as shown;

You will just factorise the area

Factorizing 2x² - 21x+40

2x² − 21x + 40

2x² -16x - 5x + 40

2x(x - 8) -5(x - 8)

=(2x−5)(x−8)

Hence the length of the garden is

(2x-5)feet