What GCF can be factored out of the trinomial?



3x^2-27x-303x
2
−27x−30 = ___\left(1x^2-9x-10\right)(1x
2
−9x−10)

Let v be a vector space and f ⊆ v be a finite set. To show that f ∪{u} is a linearly independent set, we need to prove that the only linear combination of its elements that equals the zero vector is the trivial one (i.e., all coefficients are zero).

Suppose that there exist scalars a1, a2, ..., an, b such that:

b*u + a1*v1 + a2*v2 + ... + an*vn = 0
where v1, v2, ..., vn are elements of f.

We want to show that all coefficients are zero.

Since u /∈span f, we know that u cannot be written as a linear combination of elements of f. Therefore, b ≠ 0.

We can rearrange the equation to get:
b*u = -(a1*v1 + a2*v2 + ... + an*vn)

Since f is linearly independent, we know that the only linear combination of its elements that equals the zero vector is the trivial one. Therefore, a1 = a2 = ... = an = 0.

Substituting this into the equation, we get
b*u = 0

Since b ≠ 0, we know that u = 0, which contradicts the fact that u is not in the span of f.

Therefore, our assumption that there exist nontrivial coefficients that satisfy the equation is false, and f ∪{u} is indeed a linearly independent set.

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Answer:

4th answer is correct

Step-by-step explanation:

First, let us make x the subject.

\(\sf \frac{x+4}{4} =\frac{y+7}{7}\)

Use cross multiplication.

\(\sf 7(x+4)=4(y+7)\)

Solve the brackets.

\(\sf 7x+28=4y+28\)

Subtract 28 from both sides.

\(\sf 7x=4y+28-28\\\\\sf7x=4y\)

Divide both sides by 7.

\(\sf x=\frac{4y}{7}\)

Now let us find the value of x/4.

To find that, replace x with (4y/7).

Let us find it now.

\(\sf \frac{x}{4} =\frac{\frac{4y}{7} }{4} \\\\\sf \frac{x}{4} =\frac{4y}{7}*\frac{1}{4} \\\\\sf \frac{x}{4} =\frac{4y}{28}\\\\\sf \frac{x}{4} =\frac{y}{7}\)

Answer:

54

Step-by-step explanation:

The LCM of 18 and 27 is 54

Answer:

The answer is 2

Step-by-step explanation:

I took the k12 test. Hope this helps!

The correct answer is 2

Now ,  taking the data {26,35,27,30,22}

Adding the data

26+35+27+30+22 = 140

Now , Divide 140 by the total number of values in data set is 5

Therefore,  140/5 = 28

The mean is 28

Now substract the mean from the absolute deviation of 30

that is  30-28 = 2

Hence , The absolute deviation of 30 is data set is 2.

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Answer: disagree its backwards

Step-by-step explanation: the x intercept always comes first so its actually (-4,2)

Answer:

Step-by-step explanation:

Now if you look at this wrong, the student would be correct. The student made a common mistake that many make. The mistake they made was they put the X and Y backwards when making the point. All they have to do is make sure they put the X first then the Y. What they should have put is (-4,2). For any other point, you would replace X and Y in the points. (X,Y)

Answer:

p = 22 , x = 57

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

5p is an exterior angle of the triangle , then

5p = 2p + 21 + 45

5p = 2p + 66 ( subtract 2p from both sides )

3p = 66 ( divide both sides by 3 )

p = 22

then

5p = 5 × 22 = 110

5p and (x + 13) are a linear pair and sum to 180° , that is

5p + x + 13 = 180 , so

110 + x + 13 = 180

x + 123 = 180 ( subtract 123 from both sides )

x = 57

Bryan owns a clothing store,  Insurance: F , Internet bill: F , Clothes: V ,Employees' salaries: F

F is for fixed and V is for variable used .

Fixed cost :

Regardless of production output, fixed costs remain constant. Lease and rental payments, insurance, and interest payments are examples of fixed costs. Costs that are not affected by volume are known as fixed costs. Costs that are usually based on time rather than on how many products or services your company sells or produces are known as fixed costs. Rent and lease payments, salaries, utility bills, insurance, and loan repayments are all examples of fixed costs.

Costs that do not change when production or sales volumes increase or decrease are known as fixed costs. This is because they are not directly involved in providing a service or manufacturing a product. Consequently, fixed costs are regarded as indirect costs.

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Answer:

Step-by-step explanation:

Answer:

both angles 1 and 2 measure 135°

Step-by-step explanation:

angle 1 = angle 2 = 135°

Hope this helps

Option- 3 is correct that is both a and b are true.

a. The statement is true that is cosx = \(1 - \frac{sinx}{cscx+cotx}\)

b. The statement is true that is sinx = \(1 - \frac{cosx}{secx+tanx}\)

Given that,

a. We have to prove the statement is true or false.

Statement: cosx = \(1 - \frac{sinx}{cscx+cotx}\)

Now, Take the right hand side

= \(1 - \frac{sinx}{cscx+cotx}\)

= \(1 - \frac{sinx}{\frac{1}{sinx} +\frac{cosx}{sinx} }\)

By using LCM

= \(1 - \frac{sinx}{\frac{1+cosx}{sinx} }\)

= \(1 - \frac{sinx\times sinx}{1+cosx} }\)

= \(1 - \frac{sin^2x}{1+cosx} }\)

= \(\frac{1+cosx - sin^2x}{1+cosx} }\)

We know from trigonometric identities 1 - sin²x = cos²x

= \(\frac{cos^2x+cosx }{1+cosx} }\)

= \(\frac{cosx(1+cosx )}{1+cosx} }\)

= cosx

LHS = RHS

Therefore, The statement is true

b. We have to prove the statement is true or false.

Statement: sinx = \(1 - \frac{cosx}{secx+tanx}\)

Now, Take the right hand side

= \(1 - \frac{cosx}{secx+tanx}\)

= \(1 - \frac{cosx}{\frac{1}{cosx} +\frac{sinx}{cosx} }\)

By using LCM

= \(1 - \frac{cosx}{\frac{1+sinx}{cosx} }\)

= \(1 - \frac{cosx\times cosx}{1+sinx} }\)

= \(1 - \frac{cos^2x}{1+sinx} }\)

= \(\frac{1+sinx - cos^2x}{1+sinx} }\)

We know from trigonometric identities 1 - cos²x = sin²x

= \(\frac{sin^2x+sinx }{1+sinx} }\)

= \(\frac{cosx(1+sinx )}{1+sinx} }\)

= sinx

LHS = RHS

Therefore, The statement is true

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One way to determine the number is to multiply 2 and 9, this is because the resulting number will be divisible by them perfectly. Let's try:

So our candidate is 18, we need to test if it's divisible by 2 and 9 perfectly:

It is, therefore the number is 18.

Answer:

x = 6

Step-by-step explanation:

2 + 7x = 5x + 14

7x - 5x = 14 - 2

2x = 12

x = 12 : 2

x = 6

Good luck !

96th term of the arithmetic sequence 1, -12, -25, ...1,−12,−25  is -1234

arithmetic sequence 1, -12, -25, .. .1,−12,−25

an arithmetic sequence can be written as

a , a + d , a + 2d , a + 3d , . . . . . a + (n-1)d

nth tern of an arithmetic sequence is

aₙ= a+ (n-1)d

a= first term of an arithmetic sequence

d = common difference of an arithmetic sequence

n = number of terms in an arithmetic sequence

So in the above arithmetic sequence

a= 1

d= -13

n= 96

a₉₆= 1+ (96-1)(-13)

    =  1- (95)13

    =  1- 1235

    = -1234

96th term of the arithmetic sequence 1, -12, -25, ...1,−12,−25  is -1234

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According to the information, the approximation and exact values are V = 65.45 cubic cm (approximation to the nearest hundredth), Exact value: V = (4/3)π(2.5)^3 = 65.44984695 cubic cm (exact).

The formula for the volume of a sphere is:

V = (4/3)πr^3

Since the diameter of the sphere is given as 5 cm, the radius is half of that, which is:

Substituting this value into the formula, we get:

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Answer:

The area of the new triangle is 180 m²

Step-by-step explanation:

let the height of the triangle = h

let the base of the triangle = b

The area of right triangle is given by;

A =  ¹/₂bh

20 = ¹/₂bh

If we multiple each side of the triangle by 3, the new area of the triangle will be as follows;

A= ¹/₂(3b)(3h)

A = ¹/₂(9) (bh)

A = 9(¹/₂bh)

A = 9(20)

A = 180 m²

Therefore, the area of the new triangle is 180 m²

Answer: D

Step-by-step explanation:

The GCF of these numbers. 2^5 · 5· 11 and 2^3· 5^2 · 7 is D. 2³.5

The greatest common factor is the largest number that can divide evenly into two or more other numbers (GCF). The highest common factor is another name for this (HCF). A factor is a smaller number that could divide into a larger one evenly.

Before determining the greatest common factor, enumerate the prime factors of each integer. The greatest common factor of two or more integers is the biggest integer that is a factor of each.

In this case, 2 appears three times as the most frequent factor and 5 only once as the most frequent factor among the numbers.

Hence 2³.5 is the GCF of the given number.

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By using trigonometry,

we have shown that tan(15°) = 2 - √3.

One of the most significant areas of mathematics, trigonometry has a wide range of applications. T

he study of the relationship between the sides and angles of the right-angle triangle is essentially the focus of the field of mathematics known as "trigonometry."

Hence, employing trigonometric formulas, functions, or trigonometric identities can be helpful in determining the missing or unknown angles or sides of a right triangle.

Angles in trigonometry can be expressed as either degrees or radians. 0°, 30°, 45°, 60°, and 90° are some of the trigonometric angles that are most frequently employed in computations.

We can use the half-angle formula for tangent to show that:

tan(15°) = tan(30°/2) = (1 - cos(30°)) / sin(30°)

We know that cos(30°) = √3/2 and sin(30°) = 1/2, so we can substitute those values in:

tan(15°) = (1 - √3/2) / 1/2

Simplifying the denominator and multiplying by the reciprocal:

tan(15°) = 2(1 - √3/2)

Simplifying the expression:

tan(15°) = 2 - √3

Therefore, we have shown that tan(15°) = 2 - √3.

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This distribution shows that there is a 35% probability that a randomly selected smartphone owner has the given app (X = 1), and a 65% probability that they do not have the app (X = 0).

Based on the information provided, the population distribution for the random variable X can be defined as follows:

X = 1 with probability p = 0.35 (smartphone owners who have the given app)

X = 0 with probability 1 - p = 1 - 0.35 = 0.65 (smartphone owners who do not have the given app)

Therefore, the population distribution of X is as follows:

X | Probability

--------------

1 | 0.35

0 | 0.65

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The coordinate matrix TB,B of a linear transformation T with respect to bases B and C is found to be [2 5 4; 1 1 2; -1 -1 -1].

To find the coordinate matrix TB,B of T with respect to B, we can use the formula:

TB,B = Ic,B * Tc,c * Ib,c

where Ib,c is the change of basis matrix from basis B to basis C.

To find Ib,c, we can use the inverse of Ic,B:

Ib,c = (Ic,B)^(-1)

We can use a calculator to find the inverse of Ic,B:

Ib,c = [1/4 1/4 -1/4]

[ 0 1 1 ]

[-1/4 -3/4 3/4]

Now, we need to calculate Ic,B * Tc,c:

Ic,B * Tc,c = [ 1 -3 -1 ] [-2 -2 -27 ] [ 1/4 1/4 -1/4 ] = [ 23 29 68 ]

[-1 2 -1 ] [-1 -3 -1 ] [ 0 1 1 ] [-15 -23 -48]

[-1 -3 -2 ] [ 2 0 -1 ] [-1/4 -3/4 3/4 ] [ 3 11 25]

Finally, we can calculate TB,B:

TB,B = (Ic,B * Tc,c * Ib,c)^(-1)

We can use a calculator to find the inverse of Ic,B * Tc,c * Ib,c:

TB,B = [ 2 5 4 ]

[ 1 1 2 ]

[-1 -1 -1 ]

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The equation of the tangent to the curve at the point corresponding to t=1 is y = x - 2.

To find the equation of the tangent to the curve at the point corresponding to t=1:

We first need to find the corresponding values of x and y. Substituting t=1 into the given equations, we get:

\(x = 1^4 + 3 = 4\)
\(y = 1^3 + 1(1) = 2\)

So the point on the curve corresponding to t=1 is (4,2).

To find the equation of the tangent at this point,

we need to find the slope of the curve at this point. We can do this by taking the derivative of y(x) with respect to x:

\(dy/dx = (dy/dt)/(dx/dt) = (3t^2+t)/(4t^3)\)

Substituting t=1, we get:

dy/dx = (3+1)/(4) = 1

So the slope of the curve at the point (4,2) is 1.

Now we can use the point-slope form of the equation of a line to find the equation of the tangent:

y - 2 = 1(x - 4)

Simplifying, we get:

y = x - 2

So the equation of the tangent to the curve at the point corresponding to t=1 is y = x - 2.

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Answer: $755.9

Explanation:

The total cost of all repairs is the sum of the timing belt kit cost, the brake pads cost, and the labor cost.

Since they require 4.6 hours for the timing belt kit and 1.8 hours for the brake pads. the total labor cost is:

$95 * (4.6 hours + 1.8 hours )

$95 * (6.4 hours)

$608

Because the labor rate is $95/hour

Therefore, the total cost of repair is:

$89.95 + $57.95 + $608 = $755.9

So, the answer is $755.9

If all of the ratios of the variables are equal, then there is a proportional link between the two variables.

One variable is usually a constant value multiplied by the other in proportional interactions. The proportionality constant is the name given to the constant value.

A set of equal ratios connected to one another by a constant of proportionality make up a proportional relationship between two quantities. Different, related representations of proportional connections include tables, equations, graphs, and written descriptions.

We'll now look at a real-world illustration of a proportionate relationship: There is a correlation between the quantity of fuel we put in our car's tank and the price we will have to pay when we fill it up. In other words, we will pay more money the more gas we put in.

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(a)The sign of the bias depends on the relationship between the measurement error and the true value of B.

(b)The regressor poses a more serious problem as it bias, distort the estimated relationship, and undermine the validity of statistical inference.

The OLS estimator of the slope, B, is asymptotically biased,  that it does not converge to the true value of B as the sample size increases.

The regression model

y₁ = a + Bx² + ui

With measurement error the observed model becomes

Yi = y₁ + Wi

Ii = x² + Wi

To estimate the slope, B, using OLS,  minimize the sum of squared residuals

∑ (Yi - ²a - ²B × Ii)²

Taking expectations,

E[(Yi - ²a - ²B × Ii)²] = E[(y₁ + Wi - ²a - ²B× (x² + Wi))²]

Expanding and rearranging terms,

E[(y₁ - ²a - ²B × x²)²] + E[(Wi - ²B × Wi)²] + 2E[(y₁ - ²a - ²B × x²)(Wi - ²B × Wi)]

The first term on the right-hand side represents the bias in estimating B due to the measurement error independent of x, the expectation of this term will be nonzero, indicating bias.

Attenuation bias: Measurement error in the regressor tends to bias the estimated coefficients towards zero, leading to attenuation bias. This bias reduces the estimated relationship between the regressor and the dependent variable, making it harder to detect and estimate the true effect.

Magnification of measurement error: Measurement error in the regressor can get magnified in the estimated coefficients, especially if the measurement error is large compared to the true value of the regressor. This can result in misleading and inaccurate estimates of the coefficients, making it difficult to interpret the relationship between the regressor and the dependent variable correctly.

Impact on inference: Measurement error in the regressor can affect hypothesis testing and confidence interval estimation. It can lead to incorrect conclusions about the statistical significance of the regressor, as well as wider confidence intervals that fail to capture the true parameter values.

Limited ability to correct: While measurement error in the dependent variable adjusted for using instrumental variables or other methods, measurement error in the regressor is more challenging to address. It requires additional information or assumptions about the measurement error process, which may not always be available or accurate.

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Answer:

5

Step-by-step explanation:

Answer:

I believe it’s just 5.

Step-by-step explanation:

You need to substitute the number for the letters so minus 5 times -1 to the power of 3.

The standard form of the quadratic inequality represented by the description is; y <  -2x² + 160x - 2400

An inequality with a quadratic expression is referred to as a quadratic inequality.

It is of the form y = ax² + bx + c (or substitute <,≥ or ≤ for > ) represents a region of the plane that a parabola encircles.

Let's assume that the equation is y = a(x - h)² + k

Where (h, k) is the coordinate of the vertex. Thus;

y = a(x - 40)² + 800

Put the point (60, 0) in the equation

0 = a(60 - 40)² + 800

0 = a(20)² + 800

-800 = 400a

a = -800/400

a = -2

Thus, the equation is;

y = -2(x - 40)² + 800

The inequality is a dashed line and shaded below the parabola and is;

y <  -2(x - 40)² + 800

= y <  -2(x² - 80x + 1600) + 800

y <  -2x² + 160x - 3200 + 800

y <  -2x² + 160x - 2400

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Based on the random sample results, the prediction statements for the entire machine of 200 gumballs is completed below;

Total gumballs in the gumball machine= 200 gumballs

Result from the random sample= 25 gumballs

From the random sample selected:

10 gumballs are red

8 gumballs are blue

5 gumballs are green

2 gumballs are white

There are 10 red gumballs in the machine.

There are 3 more green gumballs than white gumballs in the machine.

= Green gumballs - red gumballs

= 5 - 2

= 3 gumballs

There are 13 gumballs that are either blue or green in the machine.

= Blue gumballs + green gumballs

= 8 + 5

= 13 gumballs

Ultimately, the prediction statement is completed using 10, 3 and 13 respectively.

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Answer:Look at the digit in tens place. If it is 5 or greater, round the digit in hundreds place to the next higher digit. If the digit in tens place is less than 5, leave the digit in hundreds place as it is. Change all the numbers to the right of the hundreds place to zeros.

261 rounded to the nearest hundred is 300.

Step-by-step explanation:

Answer

I dont know what you meant by bears but to the nearest hundred 300.

Step-by-step explanation:

Answer:

3x2 – 5x + 2 = ( 3x-2)( x-1)

Step-by-step explanation:

I hope this helps you!

Have a nice dayyy <3

Answer:

\((3x-2)(x-1)\)

Step-by-step explanation:

Answer:

540°

Step-by-step explanation:

When you have a polygon (shape with 3+ sides), you can split the shape into the lowest number of triangles and use that to calculate the interior angles of the shape. Thus works because triangles have angles that always add up to 180°

A Pentagon can be split into 3 triangles minimum, which means you have 180 + 180 + 180. Or...

180 x 3 = 540