Which equation could be represented by the number line?

It will take 4.9 days for 21 locust to eat 420 grams of grass

From the question, we have the following parameters:

Given that the amount of grass is constant at 420 grams

The given parameters can be represented using the following ratio

Ratio = Locust : Days

So, we have

Locust : Days = 30 : 7

When there are a total number of 21 locust eating the grass, then we have

21 : Days = 30 : 7

Express as fraction

Days/21 = 7/30

This gives

Days = 21 * 7/30

Evaluate

Days = 4.9

Hence, the number of days is 4.9 days

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1. Using the order of mathematical operations, the values in brackets are added and multiplied to a product of $4.50 as the total tax.

2. Using the distributive property to expand the expression, 0.05(50 + 40) is  0.05 x 50 +  0.05 x40.

3. The total tax using the expanded expression is $4.50, the same product as when evaluating the original mathematical expression.

4. The original expression involves finding the total cost first before calculating the tax on the total.

The following is the order of mathematical operations:

1) The original expression, 0.05(50 + 40):

= 0.05 x 90

= 4.5

= $4.50

2) The expanded expression, 0.05(50 + 40)

=  0.05 x 50 +  0.05 x40

= 2.5 + 2.0

= 4.5

= $4.50

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Yes, the numbers will be similar.

it will be true if the numbers were -3, 5, -16 and -10

Explanation:

The first list: -3, 5, 16 and -10

Arranging from least to greatest:

-10, -3, 5, 16

Arranging the same numbers from closest to zero to farthest to zero:

Let's use zero as our reference. Then start arranging towards the left and right side of it.

-10, -3, 0, 5, 16

Looking at the above: when we remove 0, we would have same answer as the arrangement from least to greatest:

-10, -3, 5, 16

The second list:

-3, 5, -16, -10

Arranging from least to greatest:

-16, -10, -3, 5

Arranging the same numbers from closest to zero to farthest to zero:

Let's use zero as our reference. Then start arranging towards the left and right side of it.

-16, -10, -3, 0, 5

Looking at the above: when we remove 0, we would have same answer as the arrangement from least to greatest:

-16, -10, -3, 5

Hence, fromt the above: if we arrange the same numbers from least to greatest and from closest to zero to farthest to zero, we would arrive at the same result.

The value of the functions are;

(f. g)(x) =  9x² + 5  

(g . f)(x) = 3x² + 15

A function can be defined as a law, rule or expression showing the elaborate relationship between two variables in an expression or equation.

The variables are;

Given the functions;

To determine  (f .g)(x), we substitute the value of g(x) as x  in the function, we have;

(g)(x) = (3x)² + 5

expand the bracket

(g)(x)  = 9x² + 5

To determine (g . f )(x), substitute the value of x as fx)

(g . f)(x) = 3(x² + 5)

expand the bracket

(g . f)(x)= 3x² + 15

Hence, the functions are  9x² + 5 and  3x² + 15

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Answer:

[tex](x-1)^2+(y-9)^2=3^2[/tex]

Step-by-step explanation:

The standard form of the equation of a circle is:

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

Where a and b are the x and y, coordinates, and r is the radius.

So, you can just substitute the a and b values for the x and y values of the center to find the equation of the circle.

The secant function is the reciprocal of the cosine function.

We can evaluate trigonometric functions of angles outside the first quadrant using reference angles as we have already done with the sine and cosine functions. The procedure is the same:

Find the reference angle formed by the terminal side of the given angle with the horizontal axis. The trigonometric function values for the original angle will be the same as those for the reference angle, except for the positive or negative sign, which is determined by x– and y-values in the original quadrant. (Figure) shows which functions are positive in which quadrant.

An even function is one in which f(-x) = f(x)

An even function is one in which f(-x) = - f(x)

Cosine and secant are even:

Therefore from the drop down the correct answer : secant function is EVEN

The employee's paycheck after FICA and SDI deductions as well as

withholding tax deductions is $1158.65.

FICA is a federal payroll tax in the US. It is taken out of every paycheck and stands for the Federal Insurance Contributions Act. Your nine-digit number enables Social Security to precisely record your self-employment or insured wages. You accrue credits for Social Security benefits as you work and pay FICA taxes.

The final monthly paycheck of the employee after deducting all taxes is $1158.65.

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Answer:

≈0.694 or rounded to 0.7

Step-by-step explanation:

4.06/5.85≈0.694

In this type of question, we will use the exponential equation

Where:

a is the initial amount

b is the factor of growth or decay

Since it is a half-life, then

b = 1/2 = 0.5

Since it is now 50 grams, then

a = 50

Since x is the number of years, then

x = 700

Substitute them in the rule above

It will be representing 0 grams after 700 years

The answer is A

Answer:

x = 3

Step-by-step explanation:

When twenty is reduced by one-third of a number, the result is 19. Find the number.

20 - 1/3x = 19

subtract 20 to both sides:

20 - 1/3x - 20 = 19 - 20

-1/3x = -1

multiply both sides by -3:

-3(-1/3x) = -1(-3)

x = 3

Answer:

B. the amount spent on grapes compared with the weight of the purchase

Answer:

She ended up with fewer apples by buying the bigger bags.

Explanation:

The total weight of 2 bags of apples weighing 314 pounds each is equal to:

2 x 314 = 628 pounds

At the same way, the total weight of 3 bags weighing 223 pounds each is:

3 x 225 = 675 pounds

Since 628 pounds is less than 675 pounds, Marlene ended up with fewer apples by buying the bigger bags

We will find it as follows:

The volume of such a sphere is given by the expression found.

***

When we have a binomial at the power of a number, of the form:

We use Pascal's triangle to determine the expansion. Pascal's triangle is the following:

Each row can be used to calculate a specific power, in our case the binomial is at the power of three, and we will use the 4rth row to expand, that is:

As you can see, the numbers that accompany a & b are the ones found in the 4th row of Pascal's triangle. We also see that the "degree" o the expansion always sums 3, that is a^3 has an overall degree of 3, a^2b has an overall degree of 3, ab^2 has an overall degree of 3 & b^3 has an overall degree of 3.

***

If we, for example, wanted to expand (a + b)^4, we then would have the following:

*We would use the 5th row and get:

[Pascal's triangle expands to infinity. So, you in theory can manually expand any binomial at any power, but for big numbers, it will take a long time]

***

In our case, the binomial was:

And, its respective expansion is:

Recall that:

Therefore as sin x approaches 0 and cos x approaches 1, the value of cot x approaches infinity.

Answer: True.

For k=2 for infinite solutions.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

4(4x + 1) = k(8x + 2)

Now, the equation should have infinite solutions

In consider the situation then we must put value of k such that LHS part become Equal to RHS.

Now, take k=2

4(4x + 1) = k(8x + 2)

LHS: 4(4x+1)= 16x+ 4

RHS: 2(8x+ 2)= 16x+ 4

Hence, k=2 for infinite solutions.

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We are given the following series

-6, -2, 2, 6

Common difference = last term - first term

For the first two terms

The common difference is calculated as

Last term - first term

Last term = -2

First term = -6

Common difference = -2 - (-6)

= -2 + 6

common difference = 4

Common difference = 2 - (-2)

common difference = 2 + 2

Common difference = 4

Last two terms

common difference = 6 - 2

Common difference = 4

The common difference for this sequence is 4

The sequence is arithmetic.

The scatterplot that do not show a clear relationship and would not have a trend line is: graph B.

A trend line is also referred to as a line of best fit and it can be defined as a statistical or analytical tool that is commonly used in conjunction with a scatter plot, in order to determine whether or not there's any association (correlation) between data points.

In Mathematics, there are different types of trend line and these include the following:

By critically observing the scatter plot (see attachment) which models the data in the given table, we can reasonably and logically deduce that the data points in graph B are scattered around and as such, it does not illustrate a clear relationship (pattern).

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Given:

The number is 60.

Aim is to find the result when 60 is increased by 40%.

First calculate 40% of 60,

Now, add the amount 24 in 60.

Answer: 84 is a 40% increase of 60.

Answer: 41

so he has 49 books and he sold 15 so its 49-15= 34 so he bought 7 more books so its 34+7=41

Step-by-step explanation:

Have great day

Given:

3.7284

The given number should be read as "three point seven two eight four.

Option D is the correct answer.

Answer:

y= -2x -7

Step-by-step explanation:

The equation of a line in slope-intercept form is given by y= mx +c.

Given that the slope is -2, we can substitute m= -2 into the equation.

y= -2x +c

The value of c can be found by substituting a point in which the line passes through into the equation. In this case, the point is (-4, 1).

y= -2x +c

When x= -4, y= 1,

1= -2(-4) +c

1= 8 +c

Subtract 8 on both sides:

c= 1 -8

c= -7

Substituting c= -7 into the equation:

y= -2x -7

Optional step:

To check our answer, we can substitute one coordinate and see if the other coordinate is the same as the given coordinate. For example, let's substitute the x-coordinate of -4 into the equation.

y= -2(-4) -7

y= 8 -7

y= 1

Since the y-coordinate is indeed 1, the equation above is correct.

Additional reading:

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The lcm of the rational algebraic equation 6/x+x-3/4=2 be (24 -3x - 4x²) / 4x = 0.

The least common multiple is defined as the set of numbers with the least common multiple. The lowest positive integer with more than one factor in the set is HCF.

The given equation below as:

⇒ 6/x + x - 3/4 = 2

We must find the lcm of the rational algebraic equation.

⇒ 6/x + x - 3/4 = 2

Rearrange the term of 2 in the equation,

⇒ 6/x + x - 3/4 - 2 = 0

Take LCM in the above equation,

⇒ [tex]\dfrac{6\times4+x\times4x-3\times x -2 \times 4x}{4\times x}[/tex]

⇒ (24 + 4x² -3x - 8x²) / 4x = 0

Combine the likewise terms in the numerator,

⇒ (24 -3x - 4x²) / 4x = 0

Therefore, the required answer would be (24 -3x - 4x²) / 4x = 0.

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let j be justin, e for Eva and m for Emma. We get

so we get that, replacing all the variables

so we get that Eva has $20. therefore Justin has $27.5 and Emma has $15.5

Check the picture below.

[tex]cos(\theta )=\cfrac{x}{10}\implies \stackrel{chain~rule}{-sin(\theta )\cdot \cfrac{d\theta }{dt}}=\cfrac{1}{10}\cdot \cfrac{dx}{dt} -sin(\theta )\cdot \cfrac{d\theta }{dt}=\cfrac{1}{10}(0.7)[/tex]

[tex]\cfrac{d\theta }{dt}=\cfrac{0.07}{-sin(\theta )}~\hfill \stackrel{\textit{when the ladder's bottom is 8ft, x = 8}}{sin(\theta )=\cfrac{8}{10}\implies sin(\theta )=\cfrac{4}{5}} \\\\\\ \cfrac{d\theta }{dt}=-\cfrac{0.07}{~~ \frac{4 }{5 } ~~}\implies \implies \cfrac{d\theta }{dt}=-0.07\cdot \cfrac{5}{4}\implies {\Large \begin{array}{llll} \cfrac{d\theta }{dt}=-0.0875~\frac{rad}{s} \end{array}}[/tex]

the rate is negative because the angle is decreasing as the ladder slides outwards.

AA (or AAA) or Angle-Angle Similarity

If any two angles of a triangle are equal to any two angles of another triangle, then the two triangles are similar to each other.

We do not have 3 angles.

SAS or Side-Angle-Side Similarity

If the two sides of a triangle are in the same proportion of the two sides of another triangle, and the angle inscribed by the two sides in both the triangle are equal, then two triangles are said to be similar.

We have two sides and 1 angle. But, two sides of a triangle are not in the same proportion of the two sides of another triangle

SSS or Side-Side-Side Similarity

If all the three sides of a triangle are in proportion to the three sides of another triangle, then the two triangles are similar.

Letter D

The last term using factorization method to make the perfect square is 3 and the final expression is (x + 3)².

What is factorization method?

The factorization method is used for the quadratic based equation whose highest degree is either two or more than two. Depending upon the degree of the variable, the number of factors are calculated. And by substituting the calculated value to check whether the answer is correct or not.

According to the question, the given quadratic equation can be solved by performing factorization as well as by adding the half of the coefficient of the x-term to the given equation.

Therefore, the expression can be written as:

x² + 6x + 3² = 0

⇒(x + 3)² = 0

Hence, the last term by using factorization method to make the perfect square is 3 and the final expression is (x + 3)².

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The argument of the polar coordinate is -45 degrees, which can be converted as,

Thus, the required point is D.

The best estimate for the product 9/10 x 5/11 is 1/2.

Product in Mathematics simply means a number that you get when you multiply. It is used to illustrate tye concept of multiplication

In this case, the estimate for 9/10 is 1 and the estimate of 5/11 is 1/2. Therefore, the product will be:

= 1 × 1/2

= 1/2

This shows the estimation.

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