If triangle ABC is dilated with scale factor of 2.5, find the length of A’B’ given A( 0,0), B(-4.5, -4.5) and C(-2.5, 2.5) and then find the midpoint of A’B’

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:

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:

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]

Step-by-step explanation:

get a ruler and measure every side of B do the same with A then compare one of the same sides on each shape, figure out what number is multiplied to equal the larger side on A

Answer:

280 pupils

Step-by-step explanation:

27 + 38 + x = 100 Find what percentage is the Year 9 which is 35%

800 x 0.35 = 280 pupils

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:

20 3/4

Step-by-step explanation:

21 4/8 is the same as 21 2/4 or even 21 1/2, but for this equation, it would be easier to put it as 21 2/4.

Then you would just minus 21 4/8 by 3/4 which would then leave you with 20 3/4.

I hope this helped!

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:

a:(5x+3)+(3x+7)=180°

linear angle

Answer:

65 mph

Step-by-step explanation:

195÷3=65. you take your miles total and divide them by your tim total

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 :)

9514 1404 393

Answer:

  1/4

Step-by-step explanation:

Each coordinate of H'J'K' is 1/4 of the value for HJK.

The scale factor is 1/4.

Answer:

1/4 would be right I am 100% sure

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:

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

Step-by-step explanation:

Hope this helps

Answer:

[tex]88<m<-176[/tex]

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:

24/71

Step-by-step explanation:

Probability = favorable outcomes/total outcomes

Answer:

6.2 (Approximated).

Step-by-step explanation:

12x-7 > 67

Add 7 to both sides.

12x > 74

Divide 12 from both sides.

12/12x > 74/12

Final answer

x > 6.2 (approximately)

Answer:

1+2

Step-by-step explanation:

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:

20.31

Step-by-step explanation:

2 tens = 20

3 tenths = 0.3

1 thousandths = 0.01

20.31

Answer: 114

Step-by-step explanation:

-6 x -19= 114

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:

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

Answer:

ssssss

Step-by-step explanation:

Answer:addidion

Step-by-step explanation:

Answer:

$5,700 was invested in the 7% account

Step-by-step explanation:

Let the amount invested in 7% interest account be x while the other account is y

Total amount invested is &12,350

Thus:

x + y = 12,350 ••••(i)

interest on 7% = 7% of x = 7/100 * x = 7x/100

Interest on 6% = 6% of y = 6/100 * y = 6y/100

Since both have same interest;

7x/100 = 6y/100

7x = 6y

y = 7x/6

Put this into equation i

x + 7x/6 = 12,350

Multiply through by 6

6x + 7x = 74,100

13x = 74,100

x = 74,100/13 = $5,700

The amount of drug left in the blood stream at 2pm is: 6.10 mg

The exponential growth function we are given is expressed as:

y = y₀[tex]e^{-0.36t}[/tex]

where:

y is amount of drug in the blood stream

y₀ is amount of drug injected into the blood stream

t is number of hours after the drug was injected.

Thus, we are told that 15 milligrams was injected into the blood stream at 11:30 am. Thus, the amount of drug left in the blood stream at 2pm which is 2.5 hours after is:

y = 15 * [tex]e^{(-0.36 * 2.5)}[/tex]

y = 15 * 0.4066

y = 6.10 mg

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The polar coordinates of the point P are (-6, π/3).

To identify the coordinates of the point in polar form based upon the given conditions, we need to use the polar coordinate system. In this system, a point is represented by an ordered pair (r, θ),

where r is the distance from the origin to the point, and θ is the angle that the line segment connecting the point to the origin makes with the positive x-axis, measured in a counterclockwise direction from the positive x-axis to the line segment.

Let's consider an example to understand this concept better.Suppose we are given the point P with rectangular coordinates (-3, -3√3). We need to find its polar coordinates.

Let's begin by finding the distance r from the origin to the point P. We can use the distance formula for this purpose.

We get:r² = (-3)² + (-3√3)² = 9 + 27 = 36r = ±6

Since P lies in the third quadrant, its distance from the origin must be negative. Therefore, we take r = -6.

Now, we need to find the angle θ that the line segment OP makes with the positive x-axis. We can use the tangent function for this purpose. We get:tan θ = (-3√3)/(-3) = √3θ = π/3 (since P lies in the third quadrant)

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