which polynomial is the product of (4x-3)(x^2+2x-6)

The value of y from the equation y = 150x when x = 2(1/4) is 337.5.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 - 9 is an equation.

We have,

y varies directly with x.

y ∝ x

y = kx

Now,

y = 75 when x = 1/2

75 = k(1/2)

k = 75 x 2

k = 150

Now,

y = kx

y = 150x

When x = 2(1/4) = 9/4

y = 150 x 9/4

y = 337.5

Thus,

The value of y is 337.5.

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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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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.

Between x=-1 and x=1, the average rate of change is 1.

It represents the average change in the function's per-unit value during that time period. Calculating the average rate of change is very helpful for tracking changes in measurable parameters like average speed or average velocity. As the slope of the straight line that links the two spots, the average rate of change between the two points is determined. Use the formula:

(f(b)-f(a))/(b-a) to get the average rate of change of f(x) between x=a and x=b.

Given line in the figure passes through the points A(4, 0), B(-1, -5)

Let the  equation of the line be:

y=mx+ c

Slope m=(-5-0)/(-1-4)

m=1

Therefore, y=x+ c

It passes through (4, 0)

y+ c=0

c=-4

y=x-4=f(x)

f(-1)= -1-4=-5

f(1)= 1-4=-3

The average rate of change=(f(b)-f(a))/(b-a)

=(f(1)-f(-1))/1-(-1)

= -3-(-5)/(1+1)

=2/2

=1

Therefore, Between x=-1 and x=1, the average rate of change is 1.

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Answer:143

Step-by-step explanation: When subtracting a negative number from a negative number(a minus sign followed by a negative turns the two signs into a positive sign) you are then adding a positive

We are given that [tex]\overline\lambda[/tex] is in the point spectrum and we are to prove that the conjugate is the union of the point and residual spectra of the adjoint.

If [tex]\overline\lambda[/tex] ∈ σp(T∗), then T∗v = [tex]\overline\lambda[/tex]v for some v ∈ D(T∗).

Hence, for all u ∈ D(T) we have -

⟨Tu,v⟩ = ⟨u,T∗v⟩ = ⟨u,[tex]\overline\lambda[/tex]⟩ = λ⟨u,v⟩,

⟨(T−λ)u,v⟩ = 0, for all u ∈ D(T)

If λ ∈ σp(T∗), then T∗v = [tex]\overline\lambda[/tex]v for some v∈D(T∗).

Hence, for all u∈D(T), we have ⟨Tu,v⟩=⟨u,T∗v⟩=⟨u,[tex]\overline\lambda[/tex]v⟩=λ⟨u,v⟩,

and therefore,

⟨(T−λ)u,v⟩=0, for all u∈D(T)

i.e. the range of T−λ is not dense and we will have λ ∈ σr(T) ∪ σp(T).

Hence, proved.

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The test hypothesis is

H₀: p=0.08 (null hypothesis) and

Hₐ: p<0.08 (alternative hypothesis )

Given that,

8% of adults in the country contract the flu at any given time during a flu epidemic. The following are the hypotheses:

0% of people who received the vaccine contracted the flu.

8% or less of people who received the vaccine ended up getting the flu.

In order to reject the null hypothesis, there must be proof that 8% of individuals who received the vaccine did not also get the flu.

If the null hypothesis is not rejected, then there is insufficient data to draw the inference that the proportion of people who receive the flu shot is 8%.

The test hypothesis is H₀: p=0.08 (null hypothesis) and Hₐ: p<0.08 (alternative hypothesis )

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The area of each section is 3/4 square feet. To solve the give question use division operation.

What is mixed fraction?

A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder.

Given that the area of the garden is [tex]5\frac{1}{4}[/tex] square feet.

Now convert the mixed fraction with improper fraction:

[tex]5\frac{1}{4}[/tex] = [(5×4) + 1]/4

[tex]5\frac{1}{4}[/tex] = 21/4

We have to divide the area 7 equal area.

Thus divide 21/4 by 7.

21/4 ÷ 7

To convert the division sign into multiplication sign, take the reciprocal of 7:

21/4 × 1/7

= (21 × 1)/(4 × 7)

Divide the denominator and numerator by 7:

= 3/4

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Answer:

Hi!

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

I hope this helps you :)

Gavin should deposit his money into a savings account that is compounded annually at an interest rate of 9%.

What is compound interest?

The interest earned on savings that is computed using both the original principal and the interest accrued over time is known as compound interest.

Given that the current balance is $800.

There were two types of schemes.

First scheme offer compounded annually at an interest rate of 9%

Second scheme offer compounded quarterly at an interest rate of 9%.

The formula of compound interest annually is

A = P(1+r)^t

P = principal = 800

r = rate of interest = 9% = 0.09

t = time = 3 year

A = 800(1+0.09)³

A = 1036.02.

The formula of compound interest annually is

A = P(1+(r/n))^tn

P = principal = 800

r = rate of interest = 3% = 0.03

t = time = 3 year

n = 4

nt = 4×3 =12

A = 800(1+0.03/4)¹²

A = 875.04

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Since Amy's rent is 60 percent of the budget for Rent, Utilities, and Food, she will have $853 to spend on entertainment each month.

The total budget for rent, utilities, and food for nine months is given as $12,798.

Using the mathematical operation of multiplication, the proportion that belongs to rent alone is $7,678.80, representing 60%.

This rental proportion is divided by 9 to determine the monthly budget for rent, which will then be spent on entertainment.

The total budget for rent, utilities, and food for nine months = $12,798

The percentage of the budget for rent = 60%

The amount for rent for nine months = $7,678.80 ($12,798 x 60%)

The monthly rent amount is $853.20 ($7,678.80/9)

Thus, we can conclude that Amy will spend $853 monthly on entertainment if she saves the rent budget.

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The percentage of the rent to the total rent, utilities, and food budget is 60%.

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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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

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 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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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.

According to the given algebraic expression the missing value is [tex]$18 x^8 y^3+48 x^2 y^5= 6x^2y^3 \left(3 x^6+8 y^2\right)$$[/tex].

An equation that includes constants, variables, and a few algebraic procedures is said to be algebraic. A good example of an algebraic equation is 3x2 2xy + d. So, three different sorts of fundamental building blocks make up an algebraic expression: Correlation (i.e. integers) (i.e. numbers)

The subsequent five categories provide further categorization of various algebraic expression forms. These include the monomial, polynomial, binomial, trinomial, and multinomial.

[tex]$6.3 x^2x^6 y^3+8.6 x^2 y^3y^2[/tex]

[tex]$18 x^8 y^3+48 x^2 y^5= 6x^2y^3 \left(3 x^6+8 y^2\right)$$[/tex]

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The complete question is-

[tex]\\$factor the algebraic expression.\\$$18 x^8 y^3+48 x^2 y^5=x-y-\left(3 x^6+8 y^2\right)\\\\$Enter the missing values below\\\\$18 x^8 y^3+48 x^2 y^5=\square x\square y\square (3 x^6+8 y^2)$$[/tex]

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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As no. of crews and time are inversely proportional 10 workers will finish the job in 10 hours.

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given, A crew of six workers completes a job in 15 hours.

We know more crew will finish the job in less no. of hours so they are inversely proportional.

So, C = k/t.

6 = k/15.

k = 90.

Now, C = 10 hence,

10 = 90/t.

t = 90/10.

t = 10 hours.

So, They can finish in 10 hours.

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Answer:

A and B

Step-by-step explanation:

actually the 180° rotation does the same as the reflection over the x-axis and then the reflection over the y-axis.

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 quadratic formula will give us the coordinates of the points of intersection of a line and a quadratic only when the value of the discriminant b^2 - 4ac is either positive or zero .

Given :

the quadratic formula will give us the coordinates of the points of intersection of a line and a quadratic only when the value of the discriminant, is .

Quadratic equation :

Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax2 + bx + c = 0 where a, b, c, ∈ R and a ≠ 0.

Formula :

= -b ± [tex]\sqrt{b^2 - 4ac / 2a}[/tex]

Discriminant = b^2 - 4ac

if b^2 - 4ac = 0 or positive value then only the formula give us the coordinates of the points of intersection of a line .

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Answer:

X=54

Step-by-step explanation:

equate both the equations since angles of opposite sides are equal

2x+2=3x-52

3x-2x= 52+2

x=54

answer:

x=54

Step-by-step explanation:

2x+2=3x-52

move the 2x to 3x because x can't be negative

and add 52 to 2 so x=54

Answer:

(x+5)^2 - 13

Step-by-step explanation:

If you work out the target expression, you get:

(x+a)^2-b = (x+a)(x+a)-b = x^2 + 2ax + a^2 - b

so 2ax must be 10x, hence a = 5

also a^2 - b must be 12, and with a being 5, this means b = 25-12 = 13

Answer:

[tex](x+5)^2 - 13[/tex]

Step-by-step explanation:

In order to convert the given quadratic [tex]x^2 + 10x + 12[/tex] into the form [tex](x+a)^2 - b[/tex], you need to put the given quadratic into vertex form.

⭐What is vertex form?

⭐How do you rewrite a quadratic in vertex form?

I will demonstrate how to "partially complete the square" with the given quadratic.

Given: [tex]x^2 + 10x + 12 = 0[/tex]

Subtract the constant from the LHS and RHS.

[tex]x^2 + 10x = -12[/tex]

Divide the coefficient of the middle term by 2, square that result, and add it to the LHS and RHS.

[tex](\frac{10}{2})^2\\(5)^2\\= 25[/tex]

[tex]x^2 + 10x + 25 = -12 + 25[/tex]

[tex]x^2 + 10x + 25 = 13[/tex]

Write the LHS into the polynomial identity: [tex](a+b)^2[/tex] by factorising

[tex]x^2 + 5x + 5x + 25 = 13[/tex]

[tex]x(x + 5) + 5(x + 5) = 13[/tex]

[tex](x+5)(x+5) = 13[/tex]

[tex](x+5)^2 = 13[/tex]

Subtract 13 from the LHS and RHS.

[tex](x+5)^2 - 13[/tex]

That's it!

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Answer:

A

Step-by-step explanation:

The answer is option A

Hope this helps :)

The average distance from a point in the ball to its center = [tex]\frac{3}{4}[/tex] A

Given the radius in the question = a

The integration of the total distance before dividing the volume will be =

⇒ [tex]\int_0^{2\pi}\int_0^\pi\int_0^A a\cdot a^2\sin\theta\,da\,d\theta\,d\phi[/tex]

⇒ [tex]\int_0^{2\pi}\int_0^\pi\int_0^A a^3\sin\theta\,da\,d\theta\,d\phi[/tex]

⇒ [tex]\frac{A^{4} }{2}[/tex] [tex]\int_0^{2\pi}\int_0^\pi \sin\theta\,d\theta\,d\phi[/tex]

⇒ [tex]\frac{A^{4} }{2}[/tex] [tex]\int_0^{2\pi}1\,d\phi[/tex]

⇒ [tex]\pi A^{4}[/tex]

Let us divide the average distance by the ball's volume,

⇒ [tex]\frac{\pi a^4}{(4/3)\pi a^3}[/tex]

⇒ [tex]{\frac{3a}4}[/tex]

By the use of the Parcly Taxel's way,

Let the radius of the ball be = A

f(x) = probability density function

Distance = D from the given point to the center.

P( D < a )

[tex]\begin{align}P(D\leq r)&= \frac{ \frac 43 \pi r^3 }{\frac 43 \pi R^3}=\frac {r^3}{R^3}, \ \ \ 0\leq r\leq R. \end{align}[/tex][tex]\frac{\frac{4}{3} \pi a^{3} }{\frac{4}{3} \pi A^{3} } = \frac{a^{3} }{R^{3} }[/tex]. 0 [tex]\leq[/tex] a [tex]\leq[/tex] A

Therefore, The average distance from a point in the ball to its center = [tex]\frac{3}{4}[/tex] A

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The multiplications, applying the associative property, are given as follows:

1. (5 x 2) x 3 = 10 x 3 = 30.

2. 4 x (3 x 3) = 4 x 9 = 36.

3. (6 x 1) x 4 = 6 x 4 = 24.

4. 5 x (2 x 4) = 5 x 8 = 40.

5. (2 x 2) x 8 = 4 x 8 = 32.

6. 3 x (2 x 2) = 3 x 4 = 12.

7. (4 x 2) x 4 = 8 x 4 = 32.

8. 6 x (3 x 3) = 6 x 9 = 54.

The associative property of multiplication defines that the order in which the factors are multuiplied does not change the product.

In this problem, we have to consider that the parenthesis gives the precedence of the factors, meaning that the terms inside the parenthesis are multiplied first, and their result should be placed on the blanks below the parenthesis.

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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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