What are the factors of x ^ 2 + 4x + 3

The greatest number of snack bags is 10.

The largest of all the common factors between two or more numbers is known as the Highest Common Factor (HCF). It is also known as the Greatest Common Element (GCF).

HCF is a fundamental method that allows you to equally distribute items throughout a group or set.

We can use the idea of HCF to determine the same when you are organizing a party and want to make sure that nothing is wasted or you require a proper calculation.

Here we have

Number of carrots = 75

Number of celery sticks = 40

Here we are making snack bags such that each bag contains the same combination of carrot and celery sticks.

To find the greatest number of snack bags we need to find HCF of 70 and 40 as given below

Write given numbers as the product of prime numbers

=> 70 = 2 × 5 × 7

=> 40 = 2 × 2 × 2 × 5  

List out the common factors

=> 2 × 5  

=> HCF (70, 40) = 10

Therefore,

The greatest number of snack bags is 10.

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The slope and y intercept of the equation are -6 and 75 respectively.

The slope of a line is a number that describes both the direction and the steepness of the line.

Given that, the equation of a line is y = 75 - 6x

Comparing to the standard equation of the line, y = mx+c

m = slope and c is the y intercept.

In the equation, we can see,

The slope (m) = -6

The y intercept (put x = 0) = y = 75 - 6x0

y = 75

Hence, the slope is -6 and y intercept is 75.

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Answer:

  (d)  The other solution to function f is -3 + 5i

Step-by-step explanation:

Given a solution to quadratic function f is -3-5i, you want to know the other solution.

The complex solutions to quadratic equations come in conjugate pairs. That is, if one solution is -3-5i, the other solution will be the same thing with the sign of the imaginary part reversed:

  The other solution is -3+5i.

__

Additional comment

This is true only if the quadratic has real coefficients. (We typically don't study any other kind.)

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The statement "Return on equity will not change if the firm increases its use of debt" is false.

Return on equity (ROE) is a financial ratio that shows how well a company is managing the capital that shareholders have invested in it. To calculate ROE, one would divide net income by shareholder equity.

Given is a statement, "Return on equity will not change if the firm increases its use of debt".

As we know that, The equity equals the assets minus total debt, a company decreases its equity by increasing the debt, or we can say, when debt increases, the equity decreases and since equity is ROE's denominator, ROE in turns gets a boost.

Hence, the statement "Return on equity will not change if the firm increases its use of debt" is false.

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The quantity of the hardener added to 18 containers of resin will be 990 ml.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that the formula for glue says to add 55ml of hardener to each container of resin.

The quantity of hardener for 18 containers will be calculated as,

Q = 18 x 55

Q = 990 ml

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Answer:

Factored form is (x - 5) (x² + 5x + 25)

Step-by-step explanation:

You can get the factors directly by using the formula for a³ - b³.

After using trigonometric function the value of to the nearest tenth digit is 11.11

What is Trigonometric function ?

Trigonometric functions are mathematical functions that are used to describe relationships between certain angles and lengths in a triangle. They are based on the ratios of the sides of a right triangle and are used in a variety of applications including surveying, navigation, engineering, and physics. Trigonometric functions are commonly referred to as sine, cosine, tangent, cotangent, secant, and cosecant. Each of these functions can be used to calculate the angle of a triangle, the length of the sides, or the area of the triangle.

Function of Sine

The ratio of the opposing side's length to the hypotenuse is known as an angle's sine function.
Sin a =Opp/Hypot = CB/CA

Cos Function
The cosine of an angle is the ratio of the neighbouring side's length to the hypotenuse's length.
Adjacent/Hypotenuse = AB/CA is the cosine of.

Functional Tan
The ratio of the lengths of the adjacent and opposing sides is known as the tangent function. It should be noted that the ratio of sine and cosine to the tan may also be used to express the tan.
Tan a = Opposite/Adjacent = CB/BA
In terms of sine and cos, tan is also equivalent to:
Tan = cos a/sin a
Sin 46° = 8/x
x = 8/Sin 46°
x= 8/0.72
x=11.11

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The average speed of the winning car is  79.38 miles per hour.

Given : Distance covered by rally car race course = 515.97 miles

Time taken to complete the course by winning car = 6.5 hours

The average speed of the winning car = ( Distance covered by rally car race course) ÷  (Time taken to complete the course by winning car)

= (515.97)÷ (6.5) miles per hour

= 79.38 miles per hour

Hence, the average speed of the winning car =  79.38 miles per hour.

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The growth of the mass of the sample of a bacteria is represented by the exponential model m(x) = 5 · 1.02ˣ.

In this problem we find the case of mass of a sample of a bacteria (m(x)), in miligrams growing in time (x), in days. This growth is done exponentially, the exponential model is shown below:

m(x) = m' · (1 + r / 100)ˣ

Where:

We have that the mass of the sample was initially 5 miligrams and grows at a rate of 2 % during 10 days. If we know that m' = 5 mg and r = 2, then the exponential model for the sample is:

m(x) = 5 · 1.02ˣ

The exponential model for the sample of a bacteria is equal to m(x) = 5 · 1.02ˣ.

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The triangles are congruent by SAS rule, according to the question.

What do you mean by congruency means?

When two geometrical figures are completely same, they are said to be congruent. Congruent refers to objects that are the same size and shape. The concept of congruence can be applied to figures, angles, and line segments. Any two line segments are deemed to be congruent if their lengths are the same. If the measure of two angles is the same, they are said to be congruent. The sides and angles of two triangles are said to be equal if they are congruent. Congruent refers to objects that are precisely similar in size and shape. The forms stay equal no matter how they are rotated, flipped, or turned. For instance, create two circles with the same radius, cut them out, and stack them.

According to the given question,

We have the given information:

AC║EC

BC║DC

Now, we need to show the congruency in the given triangles,

We already have two sides of the triangles are parallel.

The angles are also same, when two lines are bisects each other.

∠ACB≈∠ACD

Therefore, the given triangles are congruent by SAS rule.

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Answer:

Hi!

If you're trying to solve for z, the answer would be -34.

I hope this helps you :)

Answer:

The original price of the tie was 20 dollars

Step-by-step explanation:

The price of the t-shirt was originally 24, but because he bought it on sale, he would have payed 12 because 24x.5=12.  This means we can subtract the value payed for the shirt from the total money payed. 22(total)-12(shirt)=.  10 (tie). However, 10 is the price he payed for the tie, not its original value. We can find this by multiplying 10x2, which gives us our answer.

Answer:

20 dollars is the original price

Answer:

(7,-1)

Step-by-step explanation:

x + 7y = 0

x = -7y  Substitute -7y for x

2x -8y = 22

2(-7y) - 8y = 22

-14y - 8y = 22

-22y = 22  Divide both sides by -1

y = -1

Solve for x:

x - -7y

x = -7(-1)

x = 7

(7,-1)

a) The probability that Cathy passes the CPA on the first try is of: 0.56 = 56%.

b) The probability that Cathy passes the CPA exam on the second or third try is of: 0.3548 = 35.48%.

A probability is the division of the number of desired outcomes by the number of total outcomes.

56% of students who graduated pass the CPA exam, hence the probability of passing on each test, including the first, is of:

0.56 = 56%.

Then the probabilities for the second or the third test are given as follows:

Then the probability that Cathy passes the CPA exam on the second or third try is calculated as follows:

p = 0.44 x 0.56 + 0.44² x 0.56 = 0.3548 = 35.48%.

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Answer:

The correct answer to this expression is 9x + 7y. To find this answer, you need to combine like terms. This means that you need to add together any terms that have the same variable and coefficient. In this case, the expression has two terms with the variable x and two terms with the variable y. The coefficients of the x terms are 2 and 7, and the coefficients of the y terms are 3 and 4. To combine these terms, you need to add the coefficients of the x terms together to get 9, and add the coefficients of the y terms together to get 7. Therefore, the combined expression is 9x + 7y.

Answer:

[tex]x = -2[/tex]

Step-by-step explanation:

[tex]\textsf {Square both sides:}\\\\(\sqrt{3x+12} )^2 = 3x + 12\\\\(\sqrt{x+8} )^2 = x + 8[/tex]

(The square of the square root of a value is the value itself

[tex](\sqrt{x} )^2 \;is\;x[/tex])

The original identity then becomes
[tex]3x + 12 = x + 8\\\\3x - x = 8 - 12\\\\2x = -4\\\\x = -4/2\\\\x = -2[/tex]

The equation in the form Ax+ By=C is 4x-3y=27 if the line passes through the point (-6, 1) and slope is 4/3.

A mathematical formula that connects two expressions with the equals sign (=) expresses the equality of the two expressions. The word equation and its translations in several languages might have slightly different meanings. For instance, in French, an equation is defined as including one or more variables, whereas in English, an equation is defined as any properly expressed formula that consists of two expressions joined by the equals sign.

The values of the variables that must fulfill the equality to make up the solution are referred to as the unknowns, together with the variables for which the equation must be solved.

Given point is (-6, 1)

Slope m=4/3

The equation of the line is:

y-y₁=m(x-x₁)

y-1=(4/3)(x+6)

3y-3=4x+24

4x-3y=27

Therefore, the equation in the form Ax+ By=C is 4x-3y=27

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The correct statement regarding the spread of the data from the frequency table is given as follows:

The data has an outlier in the 13 to 15 range and shows that a large group purchased tickets to the game.

To classify the spread of the data, we need to understand the frequency table, which shows that number of people who purchased each range of tickets.

The frequencies mean that:

The person purchasing between 13 and 15 tickets represents an outlier, as the interval 13-15 is far from the other observations in the data-set.

This means that the first option gives the correct description of the spread of the data-set.

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Answer:

A

Step-by-step explanation:

The answer is option A

Hope this helps :)

The value of the Test statistic =z=-1.67

We have the value of sigma = 6, n = 260

In a hypothesis test, a test statistic—a random variable—is computed from sample data. To decide whether to reject the null hypothesis, you can utilize test statistics. Your results are compared to what would be anticipated under the null hypothesis by the test statistic. The p-value is computed using the test statistic.

Now using the formula of Test static

Test statistic will be:  [tex]\mathrm{z}=\frac{\overline{\mathrm{x}}-\mu}{\frac{\sigma}{\sqrt{\mathrm{n}}}}\\[/tex]

Where, n = total number of sample = 100

[tex]\bar x[/tex] = mean of the given data

[tex]\mu[/tex] = total number of hours taken to receive a basic driving licence.

So, putting the value given in the question,

We will get the value of test static as:

[tex]=\frac{99-100}{\frac{6}{\sqrt{260}}}=-1.67[/tex]

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The exponential formula that shows population is y = y₀ (1.031)ˣ.

An exponential function is a function which can be defined as y = y₀ aˣ, Where 'x' is a variable and 'a' is a constant.

Given that,

The growth of population is exponential.

Also,

The initial population y₀ = 3190.

And after 4 year the population y = 3605.

Use exponential formula

y = y₀ aˣ     (1)

Where x = time

Substitute the values in the formula,

3605 = 3190 a⁴

3605/3190 = a⁴

1.13009  = a⁴

a = 1.031

Substitute the value of a in equation (1),

y = y₀ (1.031)ˣ

The required formula is y = y₀ (1.031)ˣ.

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Using the binomial probability formula the value of P ( X  = 4 ) = 23.04 %.

Given :

Biologists estimate that a baby elk has a 44% chance of surviving to adulthood. Assume this estimate is correct. Suppose researchers choose 7 baby elk at random to monitor. Let X = the number who survive to adulthood. Use the binomial probability formula to find P ( X = 4 ).

here ,

p = 0.44

q = 0.56

Number of trials n = 7

P ( X = 4 ) = C ( n , r ) * p^r * q^n - r

= C ( 7 , 4 ) * 0.44^4 * 0.56^7 - 4

= 35 * 0.44^4 * 0.56^3

= 0.23037

≈ 0.2304

= 0.2304 * 100%

= 23.04 %

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The ice cream that the machine produces during the 2nd minute will be 0.8 cups of ice cream.

Rate demonstrates how many times one number can fit into another number. They contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

Typically, a rate is defined as the ratio of two quantities expressed in different units. The first quantity is typically written as the numerator of a fraction, and the second quantity is written as the denominator. By condensing them into the simplest form possible, we can calculate the rate.

A rate is a ratio that contrasts two distinct quantities represented by various units. A comparison of two numbers with various quantities or units is called a rate. A ratio or a rate out of 100 is what is known as a percentage.

Here, landon's ice cream machine produced 1.2 cups of ice cream in 3 minutes. If it produced the same amount each minute, the ice cream that the machine produces during the 2nd minute will be:

= (1.2 / 3) × 2

= 0.4 × 2

= 0.8 cups.

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Answer:

4

Step-by-step explanation:

let n be the integer , then n tripled is 3n, so

[tex]\frac{3}{4}[/tex] n + 9 = 3n ( multiply through by 4 to clear the fraction )

3n + 36 = 12n ( subtract 3n from both sides )

36 = 9n ( divide both sides by 9 )

4 = n

the required integer is 4

If Liana is indifferent between the bundles (2,6) and (6,2), then it means that she values these two bundles equally. This means that Liana does not have a preference for one bundle over the other.

If Liana's indifference curves are bowed inward, it means that she is willing to give up more units of one good in order to get more units of the other good, as she moves along the indifference curve. This implies that Liana has a diminishing marginal rate of substitution (MRS) between the two goods.

Therefore, if Liana is indifferent between (2,6) and (6,2), it does not necessarily follow that she prefers (4,4) to (6,2). It is possible that Liana may also be indifferent between (4,4) and (6,2), or she may prefer (6,2) to (4,4). This would depend on the specific shape and location of Liana's indifference curves.

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Answer:

Below

Step-by-step explanation:

.94 % is .0094 in decimal

   this exponential growth is like a bank account compounded yearly

         factor =  ( 1+.0094)^30  = 1.3240  

                   which would represent 32.40% growth

Answer:

  B.  False

Step-by-step explanation:

You want to know if it is true that a tessellation can be created from circles.

A tessellation is the covering of a plane, using one or more geometric shapes with no overlaps and no gaps.

As the attachment shows, it is not possible to cover a plane with circles, leaving no gaps.

A tessellation cannot be created using circles. The proposition is False.