Question 10
What is the equation of the line shown?

The placement results provided, the student should start with Math 100.

The placement results indicate that the student has placements for Math 111, Math 100, and Math 102+. Math 111 typically corresponds to a higher-level course than Math 100, and Math 102+ implies a placement beyond Math 102.

To progress towards Math 103E, it is essential to follow the recommended course sequence. Usually, Math courses are designed to build upon previously learned concepts and skills. Starting with Math 100 would provide the foundational knowledge necessary to succeed in subsequent courses.

Therefore, the student should first start with Math 100, and upon successful completion, they can proceed to Math 103E. It is important for the student to consult with their academic advisor or the mathematics department at their institution for specific course placement and sequencing information to ensure they are following the appropriate path.

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Answer:

x = 16

Step-by-step explanation:

Opposite sides are equal in a parallelogram

AD = BC

5x - 12 = 3x + 20

5x - 3x = 20 + 12

2x = 32

x = 32/2

x = 16

Answer:

453 adult tickets and 877 student tickets were sold.

Step-by-step explanation:

Given that adult tickets to a basketball game cost $ 5 and student tickets cost $ 1, and a total of $ 3,142 was collected on the sale of 1,330 tickets, to determine how many of each type of ticket were sold the following calculations must be performed:

5 - 1 = 4

1330 x 1 = 1330

3142 - 1330 = 1812

1812/4 = 453

1330 - 453 = 877

877 x 1 + 453 x 5 = X

877 + 2265 = X

3142 = X

Therefore, 453 adult tickets and 877 student tickets were sold.

Answer:

The 1st and second is yes and the last one is no.

Step-by-step explanation:

to find the mid-point you add the two x and divide it by 2 same as y.

For a vector-valued function

\(\mathbf f(\mathbf x)=\mathbf f(x_1,x_2,\ldots,x_n)=(f_1(x_1,x_2,\ldots,x_n),\ldots,f_m(x_1,x_2,\ldots,x_n))\)

the matrix of partial derivatives (a.k.a. the Jacobian) is the \(m\times n\) matrix in which the \((i,j)\)-th entry is the derivative of \(f_i\) with respect to \(x_j\):

\(D\mathbf f(\mathbf x)=\begin{bmatrix}\dfrac{\partial f_1}{\partial x_1}&\dfrac{\partial f_1}{\partial x_2}&\cdots&\dfrac{\partial f_1}{\partial x_n}\\\dfrac{\partial f_2}{\partial x_1}&\dfrac{\partial f_2}{\partial x_2}&\cdots&\dfrac{\partial f_2}{\partial x_n}\\\vdots&\vdots&\ddots&\vdots\\\dfrac{\partial f_m}{\partial x_1}&\dfrac{\partial f_m}{\partial x_2}&\cdots&\dfrac{\partial f_n}{\partial x_n}\end{bmatrix}\)

So we have

(a)

\(D f(x,y)=\begin{bmatrix}\dfrac{\partial(e^x)}{\partial x}&\dfrac{\partial(e^x)}{\partial y}\\\dfrac{\partial(\sin(xy))}{\partial x}&\dfrac{\partial(\sin(xy))}{\partial y}\end{bmatrix}=\begin{bmatrix}e^x&0\\y\cos(xy)&x\cos(xy)\end{bmatrix}\)

(b)

\(D f(x,y,z)=\begin{bmatrix}\dfrac{\partial(x-y)}{\partial x}&\dfrac{\partial(x-y)}{\partial y}&\dfrac{\partial(x-y)}{\partial z}\\\dfrac{\partial(y+z)}{\partial x}&\dfrac{\partial(y+z)}{\partial y}&\dfrac{\partial(y+z)}{\partial z}\end{bmatrix}=\begin{bmatrix}1&-1&0\\0&1&1\end{bmatrix}\)

(c)

\(Df(x,y)=\begin{bmatrix}y&x\\1&-1\\y&x\end{bmatrix}\)

(d)

\(Df(x,y,z)=\begin{bmatrix}1&0&1\\0&1&0\\1&-1&0\end{bmatrix}\)

Answer:

I think :

c is 30 triangle

b is 60 triangle

d is 90 triangle

Answer:

Correct answer is \(C)\ 254\ m^{2}\)

Step-by-step explanation:

As per the given diagram, we know the following details:

Height of the triangular pyramid is 14m.

Side of base = 10m

Height of Triangular base = 8.7m

Formula for surface area of triangular pyramid:

\(\text{Area = Area of Triangular base + 3 }\times\text{Area of side triangle}\)

(Triangular base is shown in the dotted lines in the question figure.

The other 3 triangles are the side triangles.)

We know that,

\(\text{Area of a triangle = }\dfrac{1}{2} \times \text{Base} \times \text{Height}\)

\(\Rightarrow \text{Required Surface Area = } \dfrac{1}{2} \times 8.7 \times 10 + 3 \times \dfrac{1}{2} \times 14 \times 10\\\Rightarrow \dfrac{1}{2}\times (87 + 3 \times 140)\\\Rightarrow \dfrac{1}{2}\times (87 + 420)\\\Rightarrow \dfrac{1}{2} \times 507\\$\approx$ 254 m^{2}\)

Hence correct answer is \(C)\ 254\ m^{2}\).

Answer:

2 /5

Step-by-step explanation:

The three consecutive integers are -121, -120 and -119.

Integers:

Integers are a number with no decimal or fractional part and it includes negative and positive numbers, including zero.

Given,

If the second of three consecutive integers is subtracted from 120, the result is the sum of the first and third.

Here we need to find the integers.

Let x be the first unknown integer.

Then x + 1 is the second unknown integer and x + 2 is the third unknown integer.

Here we know that,

(x+1) - 120 = x + (x +2)

=> x - 119 = 2x + 2

=> 2x - x + 2 + 119

=> x + 121

=> x = -121

Then the other two number are

=> x + 1 => -121 + 1 = -120

=> x + 2 => -121 + 2 = -119

When we verify it,

=> -120 - 120 = -121 - 119

=> -240 = -240

So, the three consecutive integers are -121, -120 and -119.

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The correct order from least to greatest is log₂ 26, log₂ 33, log 26, eln 4, the correct option is D.

We are given that;

The logs log, 26, log, 33 and log3 26

Now,

We can simplify these expressions using the following identities:

eln x = x

log a a = 1

log a (b × c) = log a b + log a c

log a (b / c) = log a b - log a c

Using these identities and the properties of logarithms listed above, we can compare the given expressions as follows:

A. eln 4 = 4; log 26 < log 33; so we have:

4 < log 26 < log 33

B. eln 4 = 4; so we have:

log 33 < 4 < log 26 < log 26

C. eln 4 = 4; so we have

log₂ 26 < log 26 < log 33 < 4

D. eln 4 = 4; so we have:

log₂ 26 < log₂ 33 < log 26 < 4

Therefore, by logarithm the answer will be log₂ 26, log₂ 33, log 26, eln 4.

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Answer:

20. A. 357.8 in³

B. 1231.5 yd³

Step-by-step explanation:

20.

A.

Volume of Pyramid : ⅓*base area * height

here,

Base area = area of rectangle=length*breadth =10*8=80in²

Now

Height can be calculated by using Pythagorous theorem

height =\(\sqrt{(slant\: height)^2-(\frac{breadth}{2})^2}\)

height =\(\sqrt{14^2-(\frac{8}{2})^2}=\sqrt{196-16}=\sqrt{180}=13.42 in\)

height =13.4 in

Now

Volume of pyramid = ⅓*base area *height

Volume of Pyramid=⅓*80*13.42

Volume of Pyramid=357.8 in³

B.

Volume of cone = ⅓*area of base* height

Here

slant height=24 yd

height =?

diameter=14yd

radius =14/2=7 yd

Let's find the height:

By using the Pythagorous theorem,

slight height²=radius²+height²

substituting value

25²=7²+height²

height²=25²-7²

height =\(\sqrt{576}\)=24 yd

Now

Area of Base= πr²=π*7²=153.94 yd²

Now

Volume = ⅓*area of base*height =⅓*153.94*24=1231.5 yd³

So,

Volume of cone is 1231.52 yd³.

To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by -3. The solution to system B will be the same as the solution to system A.

What is Linear equation ?

Linear equation can be defined as the equation in which the highest degree is one.

First equation of system A multiplied by -3:

(-3)(x+6y=5)

(-3)(x)+(-3)(6)=(-3)(5)

-3x-18=-15

Sum of the second equation of system A and the first equation multiplied by -3:

(-3x-18)+(3x-7y)=(-15)+(-35)

-3x-18+3x-7y=-15-35

-25y=-50

System B

x+6y=5

-25y=-50

Hence,  To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by -3. The solution to system B will be the same as the solution to system A.

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Answer:

C. X²-4X+6

MY ANSWER(not sure)

Answer:

In the figure, the ratio of the perimeter of rectangle ABDE to the perimeter of triangle BCD is 1 . The area of polygon ABCDE is 24 square units.

Step-by-step explanation:

This was correct on plato :D

Step-by-step explanation:

have a great day give me a like

Answer:

750

Step-by-step explanation:

A relative value indicating hundredth parts of any quantity. 1.5 is 0.2% of 750.

A relative value indicating hundredth parts of any quantity.

We need to find the number whose 1.5 is 0.2%.(one point five is zero point two percent)

Let x be the number which is 0.2% of a number 1.5.

The percentage value is converted to decimal value by dividing with 100.

0.2/100×x=1.5

zero point two divided by hundred time of x is equal to one point five.

0.002x=1.5

Divide both sides by 0.002

x=1.5/0.002

x equal to one point five by zero point zero zero two.

x=750.

x equal to seven hundred fifty.

Hence 1.5 is 0.2% of 750.

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The volume of ice cream Nathan serves in a single scoop cone is 67.32 in³.

The volume of a cone is calculated using the following formula as shown below;

V = ¹/₃πr²h

where;

The radius = d/2 = 5.5 in / 2 = 2.75 in

The volume of the cone is calculated as follows;

V = ¹/₃ x π x ( 2.75 in )² x 3

V = 23.76 in³

The /volume of the sphere is calculated as follows;

V = ⁴/₃ πr³

Since he added half of the volume of sphere, the new volume becomes;

V = ¹/₂ x ⁴/₃ πr³

V = ²/₃πr³

V = ²/₃π(2.75)³

V = 43.56 in³

The total volume = 23.76 in³ + 43.56 in³ = 67.32 in³

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Answer:

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

Step-by-step explanation:

The line passes through the origin, so its y-intercept is (0,0). Therefore, we can eliminate choices B and C since they have a y-intercept ≠ 0.

Also recall that the rate of change in a linear function is defined by the change in y divided by the change in x, or the rise/run. We see there's a rise of 4 and a run of 7. Therefore, the slope of the line is 4/7, making choice A correct.

Answer:

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

Answer:

A.  80.6

B.  83

Step-by-step explanation:

Average Test Score (Language Arts class) function:

\(f(x)=0.3x+80\)

To determine the test average after completing test 2, substitute x = 2 into the given function:

\(\begin{aligned} \implies f(2)&=0.3(2)+80\\&=0.6+80\\&=80.6\end{aligned}\)

Average Test Score (Social Studies class) table:

\(\begin{array}{|c|c|}\cline{1-2} x&g(x)\\\cline{1-2} 1&85\\\cline{1-2} 2&83\\\cline{1-2} 3&81\\\cline{1-2} \end{array}\)

To determine the test average after completing test 2, find the value of the function from the table when x = 2:

\(\implies g(2)=83\)

Answer:

a

Step-by-step explanation:

Answer:

The first one

Step-by-step explanation:

A

Answer:

the experimental probability of being struck by lightning in this city is approximately 0.56667%.

Step-by-step explanation:

The experimental probability of an event happening is calculated by dividing the number of times the event occurred by the total number of trials or observations. In this case, the event is being struck by lightning, and the trials are the total number of people in the city.

The number of people struck by lightning is given as 85, and the total population of the city is 1.5 million. To find the experimental probability of being struck by lightning in this city, we can divide the number of people struck by lightning by the total population and multiply by 100% to express the answer as a percentage:

Experimental probability = (number of people struck by lightning / total population) * 100%

Experimental probability = (85 / 1,500,000) * 100%

Experimental probability = 0.0056667 * 100%

Experimental probability = 0.56667%

Therefore, the experimental probability of being struck by lightning in this city is approximately 0.56667%.

Answer:

m∠1=(180-110)=70°

m∠2=(180-115)=65°

m∠3= 65° because lines q and m are parallel

m∠4=115° because lines q and m are parallel

m∠5=(70+65)=(180-135)=45°

m∠6=45° because it is an alternate angle of m∠5

m∠7=(70+65)=(180-135)=45°  

Step-by-step explanation:

Answer:

C)  Domain:  all real numbers x except x = ±2

E)  f(x) → ∞ as x → -2⁻ and as x → 2⁺, f(x) → -∞ as x → -2⁺ and as x → 2⁻

Step-by-step explanation:

Given function:

\(f(x)=\dfrac{3x^2}{x^2-4}\)

The domain of a function is the set of all possible input values (x-values).

A rational function is undefined when the denominator is equal to zero.

The denominator of the given function is zero when:

\(\implies x^2-4=0\)

\(\implies x^2=4\)

\(\implies \sqrt{x^2}=\sqrt{4}\)

\(\implies x= \pm 2\)

Therefore the domain of the function is:

The excluded x-values are x = -2 and x = 2.

To find the behaviour of the function near the excluded x-values, input values of x that are very near either side of excluded values:

\(x \rightarrow -2^-: \quad f(-2.001)=\dfrac{3(-2.001)^2}{(-2.001)^2-4}=3002.250...\)

\(x \rightarrow -2^+: \quad f(-1.999)=\dfrac{3(-1.999)^2}{(-1.999)^2-4}=-2997,750...\)

\(x \rightarrow 2^-: \quad f(1.999)=\dfrac{3(1.999)^2}{(1.999)^2-4}=-2997.750...\)

\(x \rightarrow -2^+: \quad f(2.001)=\dfrac{3(2.001)^2}{(2.001)^2-4}=3002.250...\)

Therefore, the behaviour of the function near the excluded x-values:

Answer:

1. Statement: ∠RVS ≅ ∠SVT

2. Statement: m∠RVS + m∠SVT = 180°

3. Statement: m∠RVS + m∠RVS = 180°

4. Statement: m∠RVS = 90°

5. Statement: Line RT ⊥ Line SU

1. Reason: Given

2. Reason: Angles forming a linear pair sum of 180°

3. Reason: Substitution

4. Reason: Algebra

5. Reason: Defintion of perpendicular lines

Step-by-step explanation:

First, write the given (line 1).

Next, use the fact that angles forming a linear pair sum to 180° to show m∠RVS + m∠SVT = 180° (line 2).

Next, substitute m∠RVS for m∠SVT in m∠RVS + m∠SVT=180° (line 3).

Next, use algebra to show m∠RVS = 90° (line 4).

Finally, use the definition of perpendicular lines to prove that Line RT ⊥ Line SU (line 5).

Hope this helps :D

Answer:

1. Statement: ∠RVS ≅ ∠SVT

2. Statement: m∠RVS + m∠SVT = 180°

3. Statement: m∠RVS + m∠RVS = 180°

4. Statement: m∠RVS = 90°

5. Statement: Line RT ⊥ Line SU

1. Reason: Given

2. Reason: Angles forming a linear pair sum of 180°

3. Reason: Substitution

4. Reason: Algebra

5. Reason: Defintion of perpendicular lines

Step-by-step explanation:

the area of a rectangle is

length × width

the perimeter of a rectangle is

2×length + 2×width

so,

length×width = 48 cm²

2×length + 2×width = 28 cm

length + width = 14 cm

length = 14 - width

we use this in the first equation :

(14 - width) × width = 48

14×width - width² = 48

-width² + 14×width - 48 = 0

a quadratic equation

ax² + bx + c = 0

has the general solution

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = width

a = -1

b = 14

c = -48

width = (-14 ± sqrt(14² - 4×-1×-48))/(2×-1) =

= (-14 ± sqrt(196 - 192))/-2 =

= (-14 ± sqrt(4))/-2 =

= (-14 ± 2)/-2 =

= 7 ± 1

width1 = 7 + 1 = 8 cm

width2 = 7 - 1 = 6 cm

length1 = 14 - width1 = 14 - 8 = 6 cm

length2 = 14 - width2 = 14 - 6 = 8 cm

so, we see, one of them must be 8 cm, and the other 6 cm.

let's length be the longer side, so

length = 8 cm

width = 6 cm

According to the 1.5 outlier rule, there are two outliers.

An outlier is a number that is way smaller or way larger than that of other numbers in a data set.

The 1.5 rule for large outliers is :

Q3 - (1.5 x IQR)

Where:

IQR = 13 - 6 = 7

13 + (1.5 x 7) = 23.50

Outliers are numbers that are greater than 23.50. These are 26 and 39.

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Each letter should be matched to its correct term as follows;

1. A ⇔ Efficiency.

2. B ⇔ Impossible.

3. C ⇔ Inefficiency.

In Economics and Mathematics, a production possibilities curve (PPC) can be defined as a type of graph that is typically used for illustrating the maximum and best combinations of two (2) products that can be produced by a producer (manufacturer) in an economy, if they both depend on the following two (2) factors;

Based on the production possibilities curve shown in the image attached above, we can reasonably infer and logically deduce that each of the letters represent the following terminologies;

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x/3 + x/5 = 1 hr

8x/15 = 1 hr

x = 15/8

15/8 times 2 for round trip. 15/4 miles or 3.75 miles total