<1 and <2 are vertical angles. If m<4=
(6x + 11)' and m<2= (10x - 91°, find m<1.

Answer:

a. True

b. True

c. False

d. False

e. False

Step-by-step explanation:

a

[tex]x-y-z=1\\x+2y-2z=2\\3x+3y-3=3\\\\\begin{pmatrix} 1 & 1 & -1|&1\\ 2&2&-2|&2\\3&3&-3|&3\end{pmatrix}\\\\\\R_2 \rightarrow R_2-R_1\\R_3 \rightarrow R_3-R_1\\\\\begin{pmatrix} 1 & 1 & -1|&1\\ 0&0&~~0|&0\\0&0&~~0|&0\end{pmatrix}\\\\x+y-z=1[/tex]

thus there is a plane

b. If a system of solution has more than one solution than it can have infinite amount of solutions so there can be any amount of solutions except 2.

c. The solution set of a consistent rank 2 linear system with four unknowns will be a plane in the four dimensional space.

d. Following is an example which proves it wrong  i-e no solution

[tex]\\\\\\\\x_1=1\\x_2+x_3=2\\x_2+x_3+x_4=0\\[/tex]

e.as shown from following example  it has infinite solutions

[tex]\\\\\\\\x_1+x_2=1\\2x_1+2x_2=2\\x_3=1\\x_4=1\\[/tex]

so a system can have  more than one solution

Answer:

  see the attachment

Step-by-step explanation:

We hope this assignment came with an explanation. Otherwise, it's a meaningless image of numbers and circles.

__

We suspect the top circle is supposed to contain the product of the left and right circles, and the bottom circle is supposed to contain their sum.

When you're given only the product and sum, it can work reasonably well to look at the factorization of the product, and the sums of the factor pairs. It usually doesn't take long to find the sum of interest, if the numbers you're looking for are integers. (For the last problem, we had to look at several factor pairs before we found the right one.)

Answer:

[tex]\sin(2u)=-\dfrac{24}{25}[/tex]

[tex]\cos(2u)=\dfrac{7}{25}[/tex]

[tex]\tan(2u)=-\dfrac{24}{7}[/tex]

Step-by-step explanation:

Given sin(u) = -3/5, use the trigonometric identity sin²θ + cos²θ = 1 to find cos(u):

[tex]\begin{aligned}\sin^2(u)+\cos^2(u)&=1\\\\\left(-\dfrac{3}{5}\right)^2+\cos^2(u)&=1\\\\\dfrac{9}{25}+\cos^2(u)&=1\\\\\cos^2(u)&=1-\dfrac{9}{25}\\\\\cos^2(u)&=\dfrac{16}{25}\\\\\cos(u)&=\dfrac{4}{5}\end{aligned}[/tex]

As u is in the interval 3π/2 < u < 2π, the angle is in quadrant IV of the unit circle. In quadrant IV, cos is positive and sin is negative. Therefore:

[tex]\sin(u)=-\dfrac{3}{5} \qquad \cos(u)=\dfrac{4}{5}[/tex]

Calculate tan(u) by using the identity tanθ = sinθ/cosθ:

[tex]\tan(u)=\dfrac{-\frac{3}{5}}{\frac{4}{5}}=-\dfrac{3}{4}[/tex]

[tex]\boxed{\begin{minipage}{5 cm}\underline{Double Angle Identities}\\\\$\sin (2\theta)=2\sin \theta \cos \theta $\\\\$\cos (2\theta)=\cos^2\theta-\sin^2\theta$\\\\$\tan (2\theta)=\dfrac{2\tan\theta}{1 -\tan^2\theta}$\\\end{minipage}}[/tex]

Use the double angle identities to find sin(2u), cos(2u) and tan(2u).

[tex]\hrulefill[/tex]

[tex]\begin{aligned}\sin (2u)&=2\sin u \cos u\\\\&=2\left(-\dfrac{3}{5}\right) \left(\dfrac{4}{5}\right)\\\\&=-\dfrac{24}{25}\end{aligned}[/tex]

[tex]\hrulefill[/tex]

[tex]\begin{aligned}\cos (2u)&=\cos^2u - \sin^2u\\\\&=\left(\dfrac{4}{5}\right)^2-\left(-\dfrac{3}{5}\right)^2\\\\&=\dfrac{16}{25}-\dfrac{9}{25}\\\\&=\dfrac{7}{25}\end{aligned}[/tex]

[tex]\hrulefill[/tex]

[tex]\begin{aligned}\tan (2u)&=\dfrac{2\tan(u)}{1 -\tan^2(u)}\\\\&=\dfrac{2\left(-\frac{3}{4}\right)}{1 -\left(-\frac{3}{4}\right)^2}\\\\&=\dfrac{-\frac{3}{2}}{1 -\frac{9}{16}}\\\\&=\dfrac{-\frac{3}{2}}{\frac{7}{16}}\\\\&=-\dfrac{3}{2} \cdot \dfrac{16}{7}\\\\&=-\dfrac{48}{14}\\\\&=-\dfrac{48\div2}{14\div2}\\\\&=-\dfrac{24}{7}\end{aligned}[/tex]

Answer:

Step-by-step explanation:

Refer to attachment

Let the side of the triangle be a

The line segment x as per Pythagorean is: √(a² - 10²)

Therefore the vertices of the triangle are equidistant from the vertex of the square, so the distance x is same for both vertices

From the triangles we have side of the triangle:

Comparing the two we have:

So the value of a is:

Answer:

10√6 - 10√2

Step-by-step explanation:

The shorter leg of the small triangle created by the square and the equilatoral triangle = x

Other leg = 10

One of the triangles is a 45-45-90 triangle, so the hypotenuse, which also happens to be a side of the equilatoral triangle can be denoted as √2(10-x).

Using pythagoearn theorem, we know that relative to the other 2 of the 15-75-90 triangles, their hypotenueses which also happen to be sides of the equilatoral triangle are √(100+x^2)

So using transitivity, we can create this equation:

√(100+x^2)=√2(10-x)

Solving this using quadratic equations, we get that x= 20+10√3, x=20-10√3

The first equation can't be true since x has to be <10, so that means

x=20-10√3

We has substitute this into another equation to get a side length of the equilatoral triangle.

The answer is 10√6 - 10√2

Answer:

153700

Step-by-step explanation:

Answer:

Newton's law also states that the strength of gravity between any two objects depends on two factors: the masses of the objects and the distance between them. Objects with greater mass have a stronger force of gravity between them.

Step-by-step explanation:

Answer:

ssssss

Step-by-step explanation:

Answer:addidion

Step-by-step explanation:

The value for log₂11 is 3.459.

To find the logarithm of 11 base 2, we need to determine the power to which we must raise 2 to obtain the value 11. In other words, we need to solve the equation 2^x = 11 for x.

Finding the exact value of log₂11 can be challenging since 11 is not a power of 2. Therefore, we can approximate the answer using numerical methods.

One way to approach this is by using the bisection method. We start by considering a lower bound and an upper bound for the value of x. Since 2^3 = 8 and 2^4 = 16, we can choose the interval [3, 4] as a starting point.

Next, we evaluate the midpoint of the interval, x = (3 + 4) / 2 = 3.5, and calculate 2^3.5 ≈ 11.314. Since this is larger than 11, we update our upper bound to 3.5.

We repeat the process by evaluating the midpoint of the new interval [3, 3.5], which gives us x = (3 + 3.5) / 2 = 3.25. Calculating 2^3.25 ≈ 10.63, we see that it is smaller than 11. Thus, we update our lower bound to 3.25.

We continue this iterative process, halving the interval each time, until we reach a satisfactory level of precision. After several iterations, we find that the value of x is approximately 3.459.

Therefore, an approximation for log₂11 is 3.459.

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Answer:

e. a point estimate

Step-by-step explanation:

When an estimate for the unknown population parameter is expressed by a single value it is called a point estimate.

Example : If we wish to find the height of a very large group of students on the basis of a sample and we find it to be 64 inches. 64 inches is the point estimate.

Similarly the value given is the point estimate.

Point estimate of the population parameter provides as an estimate a single value calculated from the sample that is likely to be close in value to the unknown parameter. It is to be noted that a point estimate will not in general be equal to the population parameter as the random sample used is one of the many possible samples which could be chosen from the population.

Answer:

Yes

Step-by-step explanation:

Step 1: Define

f(x) = x - 3

(5, 2) is equal to x = 5, f(x) = 2

Step 2: Substitute and Evaluate

2 = 5 - 3

2 = 2

Answer:

The y-intercept is -2

the slope is 2.5/1 or 2.5

Explantation:

The slope formula is m=y2-y1/x2-x1

we can use the points (1,0.5) and (0,-2)  (i got these points from the graph)

m=-2-0.5/0-1

m=2.5 or 2.5/1

The recursive formula of the linear growth model is Pₙ = Pₙ ₋ ₁ + 5

The explicit formula of the model is P(n) = 7 + 5n

37 cars are sold in the 6th week

From the question, we have the following parameters that can be used in our computation:

P₀ = 7

P₁ = 12

So, the common difference is

d = 12 - 7

Evaluate

d = 5

The recursive formula of the linear growth model is

Pₙ = Pₙ ₋ ₁ + d

So, we have

Pₙ = Pₙ ₋ ₁ + 5

Here, we have

P₀ = 7

d = 5

The explicit formula of the linear growth model is

P(n) = P₀ + nd

So, we have

P(n) = 7 + 5n

This means that

n = 6

So, we have

P(6) = 7 + 5 * 6

Evaluate

P(6) = 37

Hence, 37 cars are sold in the 6th week

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Answer:

divide by 15 y to get x=g/15y

Step-by-step explanation:

Hope this helps

Answer:

(a) 16 students failed for exactly two of the three reasons.

(b) 7 students failed because of poor attendance and not studying but not because of not turning in assignments.

(c) 14 students failed because of exactly one of the three reasons.

(d) 3 students failed because of poor attendance and not turning in assignments but not because of not studying.

Step-by-step explanation:

We are given that one semester in a chemistry class, 14 students failed due to poor attendance, 23 failed due to not studying, 15 failed because they did not turn in assignments, 9 failed because of poor attendance and not studying, 8 failed because of not studying and not turning in assignments, 5 failed because of poor attendance and not turning in assignments, and 2 failed because of all three of these reasons.

As shown in the diagram attached below, a Venn diagram represents the situation given in the question;

In the diagram below, 2 in represents purple color represents the number of students failed because of all three of these reasons.

7 represents the number of students who failed because of poor attendance and not studying but not due to not turning in assignments.

6 represents the number of students who failed because of not studying and not turning in assignments but not due to poor attendance.

3 represents the number of students who failed because of poor attendance and not turning in assignments but not due to not studying.

2 in red color represents the number of students who failed only due to poor attendance.

8 in red color represents the number of students who failed only due to not studying.

4 in red color represents the number of students who failed only due to not turning in assignments.

(a) The number of students who failed because of exactly two of the three reasons = 7 + 6 + 3 = 16 students.

(b) The number of students who failed because of poor attendance and not studying but not because of not turning in assignments = 9 - 2 = 7 students.

(c) The number of students who failed because of exactly one of the three reasons = 2 + 8 + 4 = 14 students.

(d) The number of students who failed because of poor attendance and not turning in assignments but not because of not studying = 5 - 2 = 3 students.

Answer:

1+2

Step-by-step explanation:

Answer:

There are infinity many numbers between 2.23 an 2.24, but if you want the exact middle, it's 2.235

Hope this helped :)

Answer:

1. y = 80°

2. m<1 = 70°

3. y = 92°

Step-by-step explanation:

1. Since lines c and b are parallel lines cut across by transversal a, therefore:

y = 80° (alternate exterior angles are congruent)

2. m<1 is the supplement of m<4, because the angle that forms a linear pair with <1, corresponds with <4.

Therefore: m<1 = 180° - 110° = 70°

3. First, find the value of x.

(x + 1)° + (x - 3)° = 180° (supplementary)

x + 1 + x - 3 = 180°

2x - 2 = 180°

2x = 180 + 2 (addition property of equality)

2x = 182

x = 182/2 (division property of equality)

x = 91

(x + 1)° = y° (alternate interior angles are congruent)

Substitute x = 91

91 + 1 = y

92° = y

Answer:

a:(5x+3)+(3x+7)=180°

linear angle

Answer:

a = 4, b = 0

Also, a = 0 and b = 0 :)

Answer:

20.31

Step-by-step explanation:

2 tens = 20

3 tenths = 0.3

1 thousandths = 0.01

20.31

Answer:

a. P(AUB) = 0.74

b. P(A∩C) = 0.24

c. P(BUC) = 0.71

d. P(Bc) = 0.55

e. P(A∩B∩C) = 0.11

Step-by-step explanation:

n(U) = Total number of elements in the set = number of elements in the universal set = 38

A: (Outcome is an odd number (00 and 0 are considered neither odd nor even)]

An odd number referred to any integer, that is not a fraction, which is not possible to be divided exactly by 2. Therefore, we have:

A: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35

B: 2, 4, 6, 8, 10, 11, 13, 15, 17, 20, 22, 24, 26, 28, 29, 31, 33, 35

C: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18

a. Calculate the probability of AUB

AUB picks not more than one each of the elements in both A and B without repetition. Therefore, we have:

AUB = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 33, 35

n(AUB) = number of elements in AUB = 28

P(AUB) = probability of AUB = n(AUB) / n(U) = 28 / 38 = 0.736842105263158 = 0.74

b. Calculate the probability of A ∩ C  

A∩C picks only the elements that are common to both A and C. Therefore, we have:

A∩C: 1, 3, 5, 7, 9, 11, 13, 15, 17

n(A∩C) = number of elements in A∩C = 9

P(A∩C) = probability of A∩C = n(A∩C) / n(U) = 9 / 38 = 0.236842105263158 = 0.24

c. Calculate the probability of BUC

BUC picks not more than one each of the elements in both B and C without repetition. Therefore, we have:

BUC: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 22, 24, 26, 28, 29, 31, 33, 35

n(BUC) = number of elements in BUC = 27

P(BUC) = probability of A∩C = n(BUC) / n(U) = 27 / 38 = 0.710526315789474 = 0.71

d. Calculate the probability of Bc

Bc indicates B component it represents all the elements in the universal set excluding the elements in B. Therefore, we have:

Bc: 00, 0, 1, 3, 5, 7, 9, 12, 14, 16, 18, 19, 21, 23, 25, 27, 30, 32, 34, 36

n(Bc) = number of elements in Bc = 20

P(Bc) = probability of Bc = n(Bc) / n(U) = 20 / 38 = 0.526315789473684 = 0.55

e. Calculate the probability of A∩B∩C

A∩B∩C picks only the elements that are common to A, B and C. Therefore, we have:

A∩B∩C: 11, 13, 15, 17

n(Bc) = number of elements in A∩B∩C = 4

P(A∩B∩C) = probability of A∩B∩C = n(A∩B∩C) / n(U) = 4 / 38 = 0.105263157894737 = 0.11

Note: All the answers are rounded to 2 decimal places.

Answer:

0

Step-by-step explanation:

Answer:

D as in Drink

Loan S as a Snake

Step-by-step explanation:

The loan that offers the lowest effective interest rate is loan P.

Effective interest rate is the actual interest rate that is paid on a loan. It takes into effect the compounding.

Effective annual rate = (1 + APR / m ) ^m - 1

M = number of compounding

Loan P = (1 + 0.10393/365)^365 - 1 = 10.95%

Loan Q = (1 + 0.10516/52)^52 - 1 = 11.08%

Loan R = (1 + 0.10676 / 12)^12 - 1 = 11.2%

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Answer:

n[tex]\geq[/tex]6

Step-by-step explanation:

Answer:

n ≥ 6

Step-by-step explanation:

[tex]n-9\geq -3\\\\\mathrm{Add\:}9\mathrm{\:to\:both\:sides}\\\\n-9+9\ge \:-3+9\\\\Simplify\\\\n\ge \:6[/tex]

Answer:

10 gumballs

Step-by-step explanation:

Since gumballs are 20 percent of 50 pieces(or 1/5), we divide 50 by 1/5.

We then get ten as our answer.

Answer:

the 3 numbers are 49 56 and 63

Answer:

8 - 10 or -2

Step-by-step explanation:

h(-4) = -2(-4) - 10 = 8 - 10. If you want the answer to the problem, 8 - 10 = -2.