3. Factor each of the following polynomials using GCF and/or 2 binomials. Show your work. 4 points
A.5x^2 – 2x =
B.x^2 – 12x – 45 =
C.2x^2-x-15
D.9x^2-16​

Answer:

5 × x + 8

Would be the equation you are looking for.

Answer:

Michael bought 8 shirts

Step-by-step explanation:

Let the number of shirts to be buy be x

The number of ties too will also be x

The number of pants will be x/4 since he will be buying four times the number of pants for shirts

Amount spent on shirt is 35 * x = $35x

Amount spent on ties = 25 * x = $25x

Amount spent on pants = 40 * x/4 = $10x

Adding all together;

35x + 25x + 10x = 560

70x = 560

x = 560/70

x = 8

To efficiently divide the tasks, you can focus on the task that takes the longest for your roommate and vice versa. Your roommate should handle the dishes in 40 minutes, you should handle vacuuming in 15 minutes.

Since you have an hour before your parents' arrival, it is essential to allocate the tasks efficiently. Your roommate takes 40 minutes to do the dishes and 60 minutes to vacuum, while you take 30 minutes to do the dishes and 15 minutes to vacuum. To optimize the time, your roommate should handle the task that takes them the longest, which is doing the dishes in 40 minutes. Meanwhile, you should focus on vacuuming, which you can complete in just 15 minutes.

By dividing the tasks in this way, your roommate will finish washing the dishes within 40 minutes, while you will complete vacuuming in 15 minutes. This ensures that both tasks are done by the time your parents arrive, utilizing the time efficiently and meeting the deadline.

Therefore, by assigning the dishes to your roommate and vacuuming to yourself, both tasks can be completed within the hour before your parents' arrival, allowing you to have a clean dorm before their visit.

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The domain of f is the set of all real numbers f(x,y) as (x,y) varies throughout the domain D with three variables.

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

The functions of a point (or vector) in R2 or R3 that have real values will now be looked at. These functions will typically be defined on sets of points in R2, but there will be occasions when we utilise points in R3 and when it is more convenient to think of the points as vectors (or terminal points of vectors).

Each point f(x,y) in D is given a real number f(x,y) according to a real-valued function f defined on a subset D of R2. The domain of f is the set of all real numbers f(x,y) as (x,y) varies throughout the domain D, and the range of f is the greatest set D in R2 on which f is defined.

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Answer:

12000

Step-by-step explanation:

sqrt144*1000000= sqrt144*sqrt10^6= 12*10^3=12000

Answer: its number two

The Correct change to make the Equation correct is Change (x+5) to (x−5).

The Correct option is (C).

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:

12(2x+6)+4(x+5)=5x−17

28x + 72= 5x-17

23x = 109

x= 4.73

First, change (2x+6) to 12(2x−6).

12 (2x - 6) + 4(x+5) = 5x- 17

24x - 72 +4x +20 = 5x- 17

28x -52 = 5x- 17

23x = 35

x= 1.52

Now, Change (x+5) to (x−5).

12 (2x + 6) + 4(x-5)  = 5x- 17

24x + 72 +4x -20  = 5x- 17

28x + 52  = 5x- 17

23x = 69

x=3

Hence, Change (x+ 5) to (x-5).

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The value of a=-9 using the remainder theorem.

Remainder Theorem is a method for dividing polynomials according to Euclidean geometry. This theorem states that when a polynomial P(x) is divided by a factor (x - a), which isn't really an element of the polynomial, a smaller polynomial is produced along with a remainder.

The remainder theorem means just what it says on the tin: The remainder is obtained by r=a when a polynomial a(x) is divided by a linear polynomial b(x) whose zero is x equal to k.

Put x=a in the first expression to find the remainder.

\(4(a)^2+3a+9\)

Put x=a/2 in the second expression to find the remainder.

\(4(a/2)^2+3(a/2)+9\)

Now it is given that the first remainder is four times the second remainder.

\(4(a)^2+3a+9=4(4(a/2)^2+3(a/2)+9)\\4(a)^2+3a+9=4(a)^2+6a+36\\3a=-27\\a=-9\)

So, the value of a=-9 using the remainder theorem.

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Answer:

有两个，是23 和29

所以是 A

Finding the sum of two complex numbers, z₁ and z₂, geometrically on the complex plane, one can follow these steps:

1. Construct z₁ and z₂ as vectors on the complex plane. Treat the complex plane as a Cartesian coordinate system, where the real part of a complex number represents the x-axis and the imaginary part represents the y-axis.

2. Draw a vector from the origin (0,0) to z₁. This vector represents z₁.

3. Draw a vector from the origin to z₂. This vector represents z₂.

4. To find z₁ + z₂, place the tail of the second vector (representing z₂) at the head of the first vector (representing z₁). The resulting vector, starting from the origin and ending at the head of the second vector, represents the sum z₁ + z₂.

5. Measure the length of the resulting vector, which represents the magnitude of z₁ + z₂. You can also find the angle between this vector and the positive real axis, which represents the argument (phase) of z₁ + z₂.

To find z₁ - z₂ geometrically, one can as well follow a similar procedure:

1. Plot z₁ and z₂ as vectors on the complex plane.

2. Draw a vector from the origin to z₁. This vector represents z₁.

3. Draw a vector from the origin to z₂. This vector represents z₂.

4. To find z₁ - z₂, place the tail of the second vector (representing z₂) at the head of the first vector (representing z₁), but in the opposite direction. The resulting vector, starting from the origin and ending at the head of the second vector, represents z₁ - z₂.

5. Measure the length of the resulting vector, which represents the magnitude of z₁ - z₂. You can also find the angle between this vector and the positive real axis, which represents the argument (phase) of z₁ - z₂.

Do not forget to consider both the magnitude and the angle when determining the geometric representation of complex number addition and subtraction on the complex plane.

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Answer:

D

Step-by-step explanation:

9 is the constant of proportionality

Have a great day

The period of the given trigonometric function is: 20.

The distance between the repetition of any function is called the period of the function. For a trigonometric function, the length of one complete cycle is called a period.

Sine and cosine functions start repeating the same pattern of y-axis values after every 2(pi). The period is defined as just the distance on the x-axis before the pattern repeats.

Now, looking at the trigonometric graph, we see that the x-interval for which the graph repeats itself is 20

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The ring R is said to consist of all functions f(x) that have an expression of the form f(x).

The given ring of trigonometric polynomials, R, consists of all the functions that have an expression of the form f(x). The expression f(x) is defined as below:f(x) = a0 + a1cos(x) + b1sin(x) + a2cos(2x) + b2sin(2x) + a3cos(3x) + b3sin(3x) + … + ansin(n*x) + bnsin(n*x)where n is a non-negative integer, and the coefficients a0, a1, b1, a2, b2, a3, b3, an, and bn are real numbers.In this way, every element of R is expressed as a trigonometric polynomial, and every trigonometric polynomial belongs to R. So, the ring R is said to consist of all functions f(x) that have an expression of the form f(x).Hence, this is the required proof.

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After 15 years (t), Trevon earned an annual simple interest rate of 13.17 percent (r).

Divide the investment by the lending rates, the duration of time, and certain other factors to arrive at simple interest. Simple revenue = principal + interest + hours is the marketing formula. This method makes it easiest to calculate interest. The most conventional technique to figure out interest is by subtracting a portion of the principal sum. He will only pay his share of the 100% interest, for example, if he borrows $100 from either a friend and commits to pay it back with 5% interest. $100 (0.05) = $5. When you borrow more money, you must pay interest, and when you give it out, you must charge interest. Interest is often determined as an extra component of the loan total. The interest rate on the loan is this percentage.

given

I = Prt

r = l/(Pt)

r = $3,653.75/($1850  x  15)

r = .1316666 = 13.17%

After 15 years (t), Trevon earned an annual simple interest rate of 13.17 percent (r).

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In the polygon ABCD, the production of point A' and point D' is (-2,-2)  and (4,-2) respectively.

In coordinate planes, the rule of transformation involves interchanging the x and y values on the plane such that:

\(\mathbf{(x,y) \to (k_x, k_y)}\)

where;

From the given information:

Now, using the coordinate vertices:

The corresponding coordinate of the image vertices is as follows:

A(-1,-1) → A'(2 × (-1), 2 × (-1))

A' = (-2,-2)

D(2,-1) → A'(2 × (2), 2 × (-1))

D' = (4,-2)

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The angle (in radians) between vectors u and v is approximately 1.66 radians, rounded to two decimal places.

To find the angle between two vectors, we can use the dot product formula and the magnitudes of the vectors. Let's calculate the angle between vectors u and v:

Given:

u = 4i - 6j

v = 5i + 4j

Step 1: Calculate the dot product of u and v.

The dot product of two vectors u and v is given by:

u · v = |u| |v| cosθ

where |u| and |v| are the magnitudes of vectors u and v, respectively, and θ is the angle between them.

To calculate the dot product, we multiply the corresponding components of u and v and sum them:

u · v = (4 * 5) + (-6 * 4) = 20 - 24 = -4

Step 2: Calculate the magnitudes of vectors u and v.

The magnitude of a vector is given by:

|u| = √(u₁² + u₂²)

For vector u:

|u| = √((4)² + (-6)²) = √(16 + 36) = √52 ≈ 7.21

For vector v:

|v| = √((5)² + (4)²) = √(25 + 16) = √41 ≈ 6.40

Step 3: Calculate the angle θ.

Using the dot product formula mentioned earlier, we have:

-4 = (7.21)(6.40)cosθ

Solving for cosθ:

cosθ = -4 / (7.21 * 6.40) ≈ -0.086

To find θ, we can take the inverse cosine (arccos) of cosθ:

θ ≈ arccos(-0.086) ≈ 1.66 radians

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The probability that there is a continuous stripe encircling the cube is 3/16.

A single, thin stripe is painted from the center of one edge to the center of the other edge on each face of a cube. Each face's edge pairing is selected independently and at random.

For each of the cube's six faces, there are two possible stripe orientations, resulting in a total of 2 x 6 = 64 possible stripe permutations. Since there are three sets of parallel faces, the stripe orientation for the remaining faces is determined uniquely by the pair of faces that does not contribute to the encircling stripe. Additionally, there are two possible orientations for the stripe on each face that is non-contributing.

A continuous stripe surrounds the cube as a consequence of a total of

3 * 2 * 2 = 12 stripe variations.

The necessary probability is 12/64, which equals 3/16.

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The annual premium of Susie's insurance company apply as a result of accident is $255 for an year. This is because the monthly insurance payment has been increased by $21.25.

What is Health insurance?

Health insurance or the medical insurance is an insurance which covers the whole or a part of the risk of a person which is incurring the medical expenses. Depending upon the health insurance plan, the risk is shared among many individuals.

Main body:

The increase in monthly insurance payment = $21.25

So, the annual increase in the premium amount paid by Susie will be:

Monthly increase in insurance payment × 12

(As there are 12 months in an year)

Annual increase in premium amount = $21.25 × 12

Annual increase in premium amount = $255

Therefore, the annual increase in the amount of premium paid by Susie for health insurance is $225.

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The circumference of the parachute is  100.48 feet whose radius is 16 feet.

The circumference of a circle can be found using the formula:

circumference = 2πr

where r is the radius of the circle and π (pi) is a constant approximately equal to 3.14159.

The radius of the parachute is given as 16 feet.

Therefore, we can find the circumference of the parachute by plugging in r = 16 into the formula:

circumference = 2π(16)

= 32π

= 32 × 3.14

=100.48

Therefore, the circumference of the parachute is closest to 100.48 feet.

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Answer:

a. 2.25 km

Step-by-step explanation:

the scale on a map means how many units in the mapp corresponds to how many units in reality.

in this case

1 cm on the map = 75000 cm in reality =

= 75000/100 m = 750 m =

= 750/1000 km = 0.75 km

3 cm = 3×1 cm = 3 × 0.75 km = 2.25 km

The shaded area is 239.4 ft²

Answer: 70

Step-by-step explanation:

you would do 8C4

If there are 8 pieces to choose from, there are 1,680 different ways distinct displays are possible.

\(^mP_k = k! \times ^mC_k = k! \times \dfrac{m!}{k! \times (m-k)!} = \dfrac{m!}{ (m-k)!}\\\\^mP_k = \dfrac{m!}{ (m-k)!}\)

This is called permutation of k items chosen out of m items (all distinct).

To find the Ways can 8 pieces of art in the front window be arranged in the display window.

Let us use permutation to find the number of ways can 8 pieces of art in the front window be arranged in the display window.

here we have

n= 8

r= 4

substituting the values,

\(^nC_r = \dfrac{n!}{ (n-r)!}\\\\^8C_4 = \dfrac{8!}{ (8-4)!}\\\\^8C_4 = \dfrac{8!}{ (4)!}\\\\^8C_4 = 8 \times 7 \times 6\times 5\\\\^8C_4 =1680\)

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Answer:

y = 2

Step-by-step explanation:

Given

\(\frac{2y-1}{15}\) = \(\frac{y}{10}\) ( cross- multiply )

10(2y - 1) = 15y ← distribute left side

20y - 10 = 15y ( subtract 15y from both sides )

5y - 10 = 0 ( add 10 to both sides )

5y = 10 ( divide both sides by 5 )

y = 2

Answer:

6 Meters

Step-by-step explanation:

If the car is driving at a constant velocity of 36 m/s and accelerates at -6.0 m/s ^2 to a stop, then the distance of the car decelerates to a stop in 6 seconds.

a=v/t ->>> 6= 36/t

Answer:

Înălțimea bazinului este de 20 m

Step-by-step explanation:

Raza de bază a bazinului cilindric = lățimea peretelui dreptunghiular = 15 m

Suprafața peretelui dreptunghiular = lungime × lățime = 300 m²

300 m² = lungime × 15 m

lungime = 300 m² / 15m

lungime = 20 m

Lungimea peretelui dreptunghiular = înălțimea bazinului cilindric = 20 m

Prin urmare, înălțimea bazinului = 20 m.

The assumption necessary to apply a goodness-of-fit test is that the data are measured with a nominal or ordinal scale.

Goodness-of-fit tests are used to determine whether an observed frequency distribution of categorical data fits an expected theoretical distribution. They compare the observed frequencies with the expected frequencies based on a specified distribution. The data being analyzed using a goodness-of-fit test are typically categorical, such as counts or proportions in different categories or groups.

Therefore, the correct answer is: The data are measured with a nominal or ordinal scale.

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Answer:

Step-by-step explanation:

The implied utilization of the resources in the process can be calculated by dividing the demand rate by the total capacity of the resources. In this case, the total capacity is 1.1 + 0.93 = 2.03 clients per hour. Therefore, the implied utilization is 0.75 / 2.03 = 0.369 (or 36.9%).

The implied utilization represents the proportion of the available capacity that is being utilized to meet the demand. In this scenario, approximately 36.9% of the total capacity is being utilized to serve the clients. This indicates that there is still some unused capacity available in the process.

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The feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

To determine whether the feasible set for each system of constraints is convex, we need to analyze the constraints individually and examine their intersection.

a) (x1)² + (x2)² > 9

This constraint represents points outside the circle with a radius of √9 = 3. The feasible set includes all points outside this circle.

b) x1 + x2 ≤ 10

This constraint represents points that lie on or below the line x1 + x2 = 10. The feasible set includes all points on or below this line.

c) x1, x2 > 0

This constraint represents points in the positive quadrant, where both x1 and x2 are greater than zero.

Now, let's analyze the intersection of these constraints:

Considering the first two constraints (a and b), we can see that the feasible set consists of all points outside the circle (constraint a) and below or on the line x1 + x2 = 10 (constraint b).

To determine whether the feasible set is convex, we need to check if any two points within the set create a line segment that lies entirely within the set.

If we consider the points (5, 5) and (3, 7), both points satisfy the individual constraints (a) and (b). However, the line segment connecting these two points, which is the line segment between (5, 5) and (3, 7), exits the feasible set since it passes through the circle (constraint a) and above the line x1 + x2 = 10 (constraint b).

Therefore, the feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

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