Solve each system of equations using a matrix equation. Check your answers. [9y+2z= 14 3x+2y+z= 5 x-y= -1]

Answer: 12

Step-by-step explanation:

5 * 12 + 36 = 96

10 * 12 = 120

12 with the exponent of 2 = 144

Add them all and it is 360

To find the point on the surface 6x = y^2 + z^2 where its tangent plane is parallel to a given plane, we need to find a point on the surface and determine the normal vector of the surface at that point.

Then, we can compare the normal vector of the surface to the normal vector of the given plane to check if they are parallel.

Let's first find a point on the surface by substituting a value for either y or z and solving for x. Let's choose y = 0:

6x = 0^2 + z^2

6x = z^2

x = z^2/6

So, one point on the surface is (z^2/6, 0, z).

To find the normal vector of the surface at this point, we can calculate the partial derivatives with respect to x, y, and z:

∂/∂x (6x) = 6

∂/∂y (y^2 + z^2) = 0

∂/∂z (y^2 + z^2) = 2z

The normal vector is then N = (6, 0, 2z) = (6, 0, 2z) / ||(6, 0, 2z)||, where ||N|| represents the magnitude of N.

To determine if the tangent plane is parallel to a given plane, we compare the normal vector of the surface to the normal vector of the given plane. If they are parallel, their direction vectors should be proportional.

If the given plane is parallel to the xy-plane and has a normal vector N_1 = (0, 0, 1), we can compare it to the normal vector of the surface. In this case, we see that the z-component of N (2z) is not proportional to the z-component of N_1 (1). Therefore, the tangent plane of the surface at the chosen point is not parallel to the given plane.

To find a point on the surface where its tangent plane is parallel to the given plane, we would need to choose a different point on the surface such that the normal vector of the surface at that point is parallel to the given plane's normal vector.

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∠g and ∠h are complementary angles and ∠g and ∠h are acute angles are true statements from the given information

Two angles are given.

∠g = (2x-90)°

∠h = (180-2x)°

We have to find the statement which is true about the angles g and h.

If both angles are greater than zero.

Complementary angles add up to 90 degrees

i.e., ∠g and ∠h are complementary if ∠g + ∠h = 90°.

Substituting the given values:

∠g + ∠h

= (2x-90)° + (180-2x)° = 90°

Thus, ∠g and ∠h are complementary angles.

and both the angles are less than 90 degrees so we can tell that angles ∠g and ∠h  are acute.

So the statement ∠g and ∠h are acute angles is also true

Hence, ∠g and ∠h are complementary angles and ∠g and ∠h are acute angles are true statements

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Answer:

1 = 8 and 50

2= 50 and a

Step-by-step explanation:

Answer:

The last option

Step-by-step explanation:

The last option

Answer:

C

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

The middle 2 numbers are 6 and 8. Add them both up and divide them by 2. Gets you 7.

Answer:

----- (a)

Step-by-step explanation:

The relationship between 7's in 771,568 is :--

700,000 is 10 times more than 70,000

Explanation:

The expression -2(x+5) becomes -2*x - 2*5 which then simplifies to -2x-10

We multiply that outer -2 by each term inside through the use of the distributive property.

The probability that 115 or fewer of the 250 homes were partially financed by the seller is approximately 0.9733.

This problem can be solved using the binomial distribution, where

n = 250 is the total number of home sales in the sample.

p = 0.4 is the probability that any given home sale is partially financed by the seller.

X is the number of home sales in the sample that are partially financed by the seller, which we are interested in.

The probability of X successes in n independent Bernoulli trials, each with success probability p, is given by the probability mass function of the binomial distribution

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items out of n without regard to order.

To solve this problem, we need to calculate the cumulative probability of 115 or fewer home sales being partially financed by the seller

P(X ≤ 115) = P(X = 0) + P(X = 1) + ... + P(X = 115)

We can use a statistical software or calculator to calculate this probability directly, or we can use the normal approximation to the binomial distribution, which is valid when n is large and p is not too close to 0 or 1.

The mean of the binomial distribution is μ = np = 250 * 0.4 = 100, and the standard deviation is σ = sqrt(np(1-p)) = sqrt(60) ≈ 7.746.

To use the normal approximation, we standardize the random variable X as follows

Z = (X - μ) / σ

Then, we can use the standard normal distribution to calculate the probability

P(X ≤ 115) ≈ P(Z ≤ (115 - μ) / σ)

P(Z ≤ (115 - μ) / σ) = P(Z ≤ (115 - 100) / 7.746) ≈ P(Z ≤ 1.934)

Using a standard normal table or calculator, we find that P(Z ≤ 1.934) ≈ 0.9733.

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Answer:

  52°

Step-by-step explanation:

The sum of an angle and its complement is 90°.

__

The sum of 38° and its complement, x, is 90°:

  38 +x = 90 . . . . . an equation to find the complement of 38°

  x = 90 -38 . . . . subtract 38 from both sides

  x = 52 . . . . degrees

The measure of x is 52°.

The top 1 percent of all scores are in range 0.1587 > x > 114.2.

The z score, also referred to as the standard score, serves to calculate how far each data point place is from its mean. In other words, it calculates x's (data point's) deviation in terms of standard deviations.

Given:

IQ scores follow a normal distribution, with a mean of 100 as well as a standard deviation = 14.2.

A z score is determined as follows:

z = (x - μ)/σ

μ = mean of the distribution

σ = standard distribution of the sampling.

1  = (X - 100)/14.2

X  = 114.2

P (x > 114.2) = 1 - P(x < 114.2)

                   =  1 - P(z < 1.0)

                    = 1 - 0.8413

P (x > 114.2) = 0.1587

Therefore, the top 1 percent of all scores are in range 0.1587 > x > 114.2.

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The value of the two required angles of the quadrilateral are:

∠B = 45°

∠A = 135°

Interior consecutive angles of a quadrilateral are supplementary angles, which means that they add up to 180°. This can be proved by the consecutive interior angles theorem which states that "If a transversal intersects two parallel lines, then it means that each pair of interior consecutive angles are supplementary (their sum is 180°).

Now, we are told that the relationship between two consecutive angles of the quadrilateral is:

∠A = 3∠B

Thus, we can say that:

3∠B + ∠B = 180

4∠B = 180

∠B = 45°

Thus;

∠A = 3 * 45° = 135°

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Based on the given data, the process is out of control.

To determine if the process is still in control, we need to compare the new sample measurements to the control limits established in the X-bar and R control charts.

For the X-bar chart:

The UCL (Upper Control Limit) is calculated as the grand average (X-Double Bar) plus A2 times R-Bar:

UCL = 25 + (0.483 * 5) = 27.415

The LCL (Lower Control Limit) is calculated as the grand average (X-Double Bar) minus A2 times R-Bar:

LCL = 25 - (0.483 * 5) = 22.585

For the R chart:

The UCL (Upper Control Limit) for the R chart is calculated as D4 times R-Bar:

UCL = 2.004 * 5 = 10.020

The LCL (Lower Control Limit) for the R chart is 0.

Given the new sample measurements: 33, 37, 25, 35, 34, and 32, we can determine if any of the measurements fall outside the control limits. If any data point falls outside the control limits, it indicates that the process is out of control.

Upon comparing the new sample measurements to the control limits, we find that the measurement 37 exceeds the UCL of the X-bar chart. Therefore, the process is considered out of control.

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Answer:

Step-by-step explanation:

hello : given z =  (-6-10i)/(4+7i)

the complex conjugate of the denominator is : 4-7i

1. Multiply the numerator and the denominator by the complex conjugate of the denominator:  z =  (-6-10i)(4-7i)/(4+7i)(4-7i)

use identity : (a + b)(a - b) = a² - b² calculate the product : (4+7i)(4-7i)

(4+7i)(4-7i) = 4² -(7i)² =16 -49i² =16+49 = 65..... ( i² = -1)

2) Simplify the results calculate the numerator :  (-6-10i)(4-7i)

(-6-10i)(4-7i)  = -24+42i -40i+70i²   = -24+42i -40i-70 .....( i² = -1)

(-6-10i)(4-7i) = -94+2i

now :  z =  (-94+2i )/65  = (-94/65) +(2/65) i

   the real part is :   ( -94/65) and the imaginary part is : 2/65

The area of the shape with parallel sides is 28 unit².

A trapezoid is a quadrilateral (has four sides and four angles) with two pairs of parallel sides. The area is given by:

A = (1/2) * (a + b)h

Where a, b is the length of the parallel sides and h is the height of the trapezoid.

Given that a = 8, b = 6 and h = 4, hence:

A = (1/2) * (8 + 6) * 4 = 28 unit²

The area of the shape with parallel sides is 28 unit².

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Answer:

28

Step-by-step explanation:

khan

Strategy

Area tells us the amount of space enclosed by the figure.

There are many ways we could split up the space into simpler shapes. Let's split the figure into two triangles.

We can find the area of each triangle, then add them to find the total area.

Hint #22 / 5

Area of the triangle on the left

The triangles have the same height.

\begin{aligned} \text{Area}_\text{triangle} &= \dfrac{1}{2} \cdot \text{base} \cdot \text{height}\\\\ &= \dfrac{1}{2} \cdot 6 \cdot 4\\\\ &= 12 \end{aligned}

Area

triangle

​

​

=

2

1

​

⋅base⋅height

=

2

1

​

⋅6⋅4

=12

​

The triangle on the left has an area of \blueE{12}12start color #0c7f99, 12, end color #0c7f99 square units.

Hint #33 / 5

Area of the triangle on the right

\begin{aligned} \text{Area}_\text{triangle} &= \dfrac{1}{2} \cdot \text{base} \cdot \text{height}\\\\ &= \dfrac{1}{2} \cdot 8 \cdot 4\\\\ &= 16 \end{aligned}

Area

triangle

​

​

=

2

1

​

⋅base⋅height

=

2

1

​

⋅8⋅4

=16

​

The triangle on the right has an area of \maroonD{16}16start color #ca337c, 16, end color #ca337c square units.

Hint #44 / 5

Total area

To find the total area of the shape, we can add the two partial areas.

\blueE{12}+\maroonD{16}=\purpleD{28}12+16=28start color #0c7f99, 12, end color #0c7f99, plus, start color #ca337c, 16, end color #ca337c, equals, start color #7854ab, 28, end color #7854ab

Hint #55 / 5

The area of the shape is 28 \text{ units}^228 units

2

28, start text, space, u, n, i, t, s, end text, squared.

Related content

Answer:

19x²

Step-by-step explanation:

sorryy hehe not sure dfhjjsdcbjhrsszzchjjhdssdghhjgesss

Answer:

Step-by-step explanation:

2x + 6x - 27=

8x - 27 (In this step, we add the like terms 2x+6x.)

Is this the kind of answer you needed?

Answer:

d = 4.5

Step-by-step explanation:

d = \(\sqrt{\s(x2-x1)^{2} +(y2-y1)^{2}}\)

d = \(\sqrt{(-4+6)^2+(1-5)^2}\)

d = 4.5

The probability that the cycle time exceeds 60 minutes given that it exceeds 55 minutes is 2/1 or simply 1, which means it is certain that the cycle time exceeds 60 minutes if it exceeds 55 minutes.

Given that the cycle time for trucks hauling concrete to a highway construction site is uniformly distributed over the interval 50 to 70 minutes, we know that the probability density function is:

f(x) = 1 / (70 - 50) = 1/20, for 50 <= x <= 70

To find the probability that the cycle time exceeds 60 minutes given that it exceeds 55 minutes, we need to use conditional probability:

P(X > 60 | X > 55) = P(X > 60 and X > 55) / P(X > 55)

We can simplify this by noticing that if X is greater than 55, then it must be between 55 and 70, and therefore:

P(X > 55) = P(55 <= X <= 70) = (70 - 55) / (70 - 50) = 1/4

Similarly, we can rewrite the numerator as:

P(X > 60 and X > 55) = P(X > 60)

since if X is greater than 60, it is also greater than 55.

Now, to find P(X > 60), we integrate the density function from 60 to 70:

P(X > 60) = ∫60^70 (1/20) dx = (1/20) × (70 - 60) = 1/2

Putting it all together:

P(X > 60 | X > 55) = P(X > 60 and X > 55) / P(X > 55)

= P(X > 60) / P(X > 55)

= (1/2) / (1/4)

= 2

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When sampling from a normal population, such as SAT scores, the distribution of sample means will indeed have a normal distribution with the same mean as the population mean.

However, the variability in sample means will not necessarily be less than the variability in individuals. In fact, the variability in sample means is related to the sample size and the variability of the population.

To clarify, the mean of the sampling distribution of the sample mean is indeed equal to the population mean. This property is known as the expected value or the unbiasedness of the sample mean as an estimator of the population mean.

The standard deviation of the sampling distribution of the sample mean, also called the standard error of the mean, is determined by the population standard deviation (σ) and the sample size (n). The formula for the standard error of the mean is:

Standard Error of the Mean = (Population Standard Deviation) / sqrt(Sample Size)

In the case of SAT scores, if we know the population standard deviation and we take samples of a specific size, we can use the above formula to calculate the standard error of the mean. This standard error represents the average variability or dispersion of sample means around the population mean.

It's important to note that as the sample size increases, the standard error of the mean decreases, indicating that the sample means become more precise estimators of the population mean. This reduction in variability occurs due to the effect of sample size on reducing sampling error.

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Answer:

Step-by-step explanation:

If the tip varies directly with the number of guests, it means that an increase in the amount of tip would be as a result of an increase in the number of guests and a decrease in the amount of tip would be as a result of an decrease in the number of guests.

If we introduce a constant of proportionality, k , the relationship would be

t = kg

Given that

When t = 18, g = 10, then

18 = k × 10

k = 18/10 = 1.8

Therefore, the equation representing the relationship is

t = 1.8g

Answer:

answer is a

Step-by-step explanation:

Answer:

Maggie is 6 years old.

Maggie's brother is 15 years old

Step-by-step explanation:

Take Maggie's age as 'x'

Her brother's age = 3x - 3

Sum of their ages = 21

Hence,

Maggie's age + brother's age = 21

(x) + ( 3x-3 ) = 21

x + 3x - 3 = 21

4x = 21 + 3

4x = 24

x = \(\frac{24}{4}\)

x=  6

Maggie's age = x = 6

Her brother's age = 3x - 3

                              = 3(6) -3

                              = 18 - 3

                               = 15 years

Hope this helps.

The equivalent equation for 3x - 6 is 3(x - 2).

Equation: A statement that two variable or integer expressions are equal. In essence, equations are questions, and the motivation for the development of mathematics has been the systematic search for the answers to these questions.

Given equation:

3x - 6

Take 3 as common from both the term,

= 3(x - 2)

Therefore, the equivalent equation for 3x - 6 is 3(x - 2).

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If the functions be f(x) = 4x + 13 and g(x) = 10x − 2 then the expression (f + g)(x) be 4x + 11.

A function from a set X to a set Y in mathematics assigns each element of X exactly one element of Y. The set X is known as the function's domain, while the set Y is known as the function's codomain. Initially, functions were just an idealized representation of the relationship between two changing quantities.

Given f(x) = 4x + 13 and g(x) = 10x − 2

We must add both functions to reflect the amount of time it takes to travel east and west in order to calculate the round-trip time.

Let the equation be (f + g)(x) = f(x) + g(x)

substitute the values in the above equation, we get

= (4x + 13) + (10x − 2)

simplifying the above equation, we get

= 4x + 13 + 10x − 2

= 4x + 10x − 2 + 13

= 4x + 11

Therefore, the expression (f + g)(x) be 4x + 11.

The completed question is:

The function f(x) represents the time it takes an airplane to travel east. The function g(x) represents the time it takes an airplane to travel west. Given f(x) = 4x + 13 and g(x) = 10x − 2, solve for (f + g)(x) to determine the total roundtrip time.

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The probability that the policyholder is a home renter, given that a renter still has a policy one year after purchase, is approximately 0.260 or 26.0%.

Let H denote the event that the policyholder is a home renter, and A denote the event that the policyholder is an apartment renter. We are given that P(H) = 0.4 and P(A) = 0.6.

Let T denote the time from policy purchase until policy cancellation. We are also given that T | H ~ Exp(1/4), and T | A ~ Exp(1/2).

We want to calculate P(H | T > 1), the probability that the policyholder is a home renter, given that a renter still has a policy one year after purchase:

P(H | T > 1) = P(H and T > 1) / P(T > 1)

Using Bayes' theorem and the law of total probability, we have:

P(H | T > 1) = P(T > 1 | H) * P(H) / [P(T > 1 | H) * P(H) + P(T > 1 | A) * P(A)]

To find the probabilities in the numerator and denominator, we use the cumulative distribution function (CDF) of the exponential distribution:

P(T > 1 | H) = e^(-1/4 * 1) = e^(-1/4)

P(T > 1 | A) = e^(-1/2 * 1) = e^(-1/2)

P(T > 1) = P(T > 1 | H) * P(H) + P(T > 1 | A) * P(A)

= e^(-1/4) * 0.4 + e^(-1/2) * 0.6

Putting it all together, we get:

P(H | T > 1) = e^(-1/4) * 0.4 / [e^(-1/4) * 0.4 + e^(-1/2) * 0.6]

≈ 0.260

Therefore, the probability that the policyholder is a home renter, given that a renter still has a policy one year after purchase, is approximately 0.260 or 26.0%.

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Answer:

4x x 22< x

Step-by-step explanation:

No explanation. Straight answer

Based on the given parameters, we can calculate the maximum values of the construction site. The gross floor area is 9,800m², with 1,800m² allocated for lift lobby and corridor, and 200m² for lift machine room and water tank. The construction cost is $8,000/m².

The design and tendering period is 6 months, and the construction period is 16 months. The expected usage is rental at $200/m² per month, with a letting void of 2 months. The interest rate for short-term finance is 12% per annum, and the initial yield is 5%.

To calculate the maximum values of the construction site, we need to consider various factors. The gross floor area, floor area allocation, and construction cost determine the overall cost of construction. The design and tendering period and construction period provide information on the timeline of the project.

The expected usage and rental rate help estimate the potential income from renting out the space. The letting void represents the period when the space may remain unoccupied, impacting the potential income.

The interest rate for short-term finance is relevant for determining the financing costs associated with the construction project. The initial yield indicates the expected return on investment based on the rental income.

To obtain the maximum values, a comprehensive analysis considering all these factors is required. This analysis would involve calculating the total construction cost, estimating the potential rental income, factoring in the letting void and financing costs, and assessing the initial yield.

Without specific values or formulas provided, it is not possible to provide the exact maximum values based on the given parameters. A detailed financial analysis would be necessary to determine the precise figures.

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Answer:

\(y = \frac{1}{2} x+\frac{3}{2}\)

Step-by-step explanation:

\(\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}\)

Actually Welcome to the Concept of the AP.

1.) For the first Sequence, d= 4

so we get as, an = a + (n-1) d

an = 9/2 + (n-1) 4

an = 9/2 +4n -4

=> an = 1/2 + 4n

2.) d = 3

=> an = 10/3 + (n-1) 3

so, => an = 10/3 +3n -3

=> an = 1/3 +3n

3.) d = -0.2

=> an = 1/2 +(n-1) (-0.2)

=> an = 1/2 -0.2n +0.2

=> an= 0.7 -0.2n

To convert 45 minutes to military time, we first need to determine how many hours 45 minutes represents. 60 minutes are in 1 hour, so 45 minutes represents 45/60 = 0.75 hours.

45 minutes in military time is represented as 0045.

In military time, hours are represented by a 4-digit number, with the first two digits representing the hour and the last two representing the minutes.

To express 0.75 hours in military time, we simply convert the 0.75 hours to minutes (0.75 hours x 60 minutes = 45 minutes) and then express it in military time format.

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