Module 5: Directions: Respond to this question to demonstrate your understanding of the topic/content. Be sure to provide adequate and relevant details learned in the module to support your response. Pay close attention to organizing your response so it makes sense and uses correct grammar. Your response should be at least 5-7 sentences at a minimum.


Question: How do you determine whether a system of linear equations has no solution, one solution, or infinitely many solutions? Describe what each type of solutions look like.

Answer:

C=20

Step-by-step explanation:

Answer: D

Step-by-step explanation:

5²-11=14

6^2-11= 25

14>25

as the question asks for something lower than 25 not lower/equal to the answer is D.

The range of values for which f(x) < 25 are -6 < x < 6. The correct answer choice is e).

To find the values of x for which f(x) < 25, we substitute the expression for f(x) into the inequality and solve for x.

Given f(x) = x² - 11, we need to find the values of x that make f(x) less than 25.

x² - 11 < 25

Adding 11 to both sides, we have:

x² < 36

To determine the values of x that satisfy this inequality, we take the square root of both sides. Since the square root of a number can be positive or negative, we consider both positive and negative solutions.

x < √36

x > -√36

Simplifying, we get:

x < 6

x > -6

Therefore, the correct answer choice is e) -6 < x < 6, as it represents the range of values for which f(x) < 25. This means that x can take any value between -6 and 6 (excluding -6 and 6) for the inequality to hold true.

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Answer:

B) 67°C.

Step-by-step explanation:

Newton's Law of Cooling is given by:

[tex]\displaystyle \frac{dT}{dt}=k(T-A)[/tex]

Where T is the temperature of the coffee, A is the room temperature, and k is a positive constant.

We are given that the coffee cools from 100°C to 90°C in one minute at a room temperature A of 25°C.

And we want to find the temperature of the coffee after four minutes.

First, solve the differential equation. Multiply both sides by dt and divide both sides by (T - A). Hence:

[tex]\displaystyle \frac{dT}{T-A}=k\, dt[/tex]

Take the integral of both sides:

[tex]\displaystyle \int \frac{dT}{T-A}=\int k\, dt[/tex]

Integrate:

[tex]\displaystyle \ln\left|T-A\right| = kt+C[/tex]

Raise both sides to e:

[tex]|T-A|=e^{kt+C}=Ce^{kt}[/tex]

The temperature of the coffee T will always be greater than or equal to the room temperature A. Thus, we can remove the absolute value:

[tex]\displaystyle T=Ce^{kt}+A[/tex]

We are given that A = 25. Hence:

[tex]\displaystyle T=Ce^{kt}+25[/tex]

Since the coffee cools from 100°C to 90°C, the initial temperature of the coffee was 100°C. Thus, when t = 0,T = 100:

[tex]100=Ce^{k(0)}+25\Rightarrow C=75[/tex]

Hence:

[tex]T=75e^{kt}+25[/tex]

We are given that the coffee cools from 100°C to 90°C after one minute at a room temperature of 25°C.

So, T = 90 given that t = 1. Substitute:

[tex]90=75e^{k(1)}+25[/tex]

Solve for k:

[tex]\displaystyle e^k=\frac{13}{15}\Rightarrow k=\ln\left(\frac{13}{15}\right)[/tex]

Therefore:

[tex]\displaystyle T=75e^{\ln({}^{13}\! /\!{}_{15})t}+25[/tex]

Then after four minutes, the temperature of the coffee will be:

[tex]\displaystyle \begin{aligned} \displaystyle T&=75e^{\ln({}^{13}\! /\!{}_{15})(4)}+25\\\\&\approx 67^\circ\text{C}\end{aligned}[/tex]

Hence, our answer is B.

Answer:

C

Step-by-step explanation:

its asking for y, on the graph, the line is placed on point 4

Answer:

1

Step-by-step explanation:

x-y+xy=1-1+1*1=0+1=1

Answer:

1

Step-by-step explanation:

X=1

Y=1

here,

x-y+xy=1-1+1×1

or,x-y+xy=0+1=1

Staysafe❤

Given:

There are 35 times as many students at Wow University as teachers.

When all the students and teachers are seated in the 8544 seat auditorium, 12 seats are empty.

To find:

The total number of students.

Solution:

Let x be the number of teachers at Wow University. So, the number of student is :

[tex]35\times x=35x[/tex]

When all the students and teachers are seated in the 8544 seat auditorium, 12 seats are empty.

[tex]x+35x=8544-12[/tex]

[tex]36x=8532[/tex]

[tex]x=\dfrac{8532}{36}[/tex]

[tex]x=237[/tex]

The number of total students is:

[tex]35x=35(237)[/tex]

[tex]35x=8295[/tex]

Therefore, the total number of students is 8295.

Answer:

B

Step-by-step explanation:

t = 20u

r = 5u/2

3rt = 3((20u)(2.5u))

3rt = 3(50u)

3rt = 150u

The value for the expression 3rt is 50u².

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:

We have  t = 20u and r= 5u/2.

We have to find the value of 3rt by putting the value of t and r as

3rt

= 3 (5u/ 2) (20u)

= 5u x 10u

= 50 u x u

= 50 u²

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Answer:

Step-by-step explanation:

eq. of line with slope m and intercept 3 is

y=mx+3

∵ it passes through (10,53)

53=10m+3

10m=53-3=50

m=50/10=5

y=5x+3

so standard form of eq. is

5x-y+3=0

or

5x-y=-3

Answer:

42

Step-by-step explanation:

2*3*2+3*5*2=12+30=42

Answer:

[tex]93[/tex]

Step-by-step explanation:

Given:

If [tex]x=3[/tex] & [tex]y=5[/tex], find [tex]2x^2+3y^2[/tex]

Solution:

Replace 3 with x and 4 with y:

[tex]2(3)^2+3(5)^2[/tex]

[tex]=2(9)+3(25)[/tex]

[tex]=18+75[/tex]

[tex]=93[/tex]

Answer:

A

Step-by-step explanation:

simplify equation A

then you will get same as the expression above

Answer:

-6

(3*2)-12

6-12

-6

Step-by-step explanation:

Answer:

[tex]f(2) = -6[/tex]

Step-by-step explanation:

[tex]f(x) = 3x - 12[/tex]

[tex]f(2) = 3(2) - 12[/tex]

[tex]f(2) = 6 - 12[/tex]

[tex]f(2) = -6[/tex]

Answer:

36 inches = 0.000568182 miles

Answer:

We know that,

Vertically opposite angles are equal,

So, x° = 70°

=> x = 70

Hi there!  

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I believe your answer is:  

(0.286, 5.587)

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Here’s why:  

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Hope this helps you. I apologize if it’s incorrect.  

Answer:

[tex]22^{\circ}[/tex]

Step-by-step explanation:

Line [tex]\overline{PM}[/tex] is a diameter of the circle because it passes through the circle's center O. Therefore, arc [tex]\widehat{PLM}[/tex] must be 180 degrees, as these are 360 degree in a circle.

We can then find the measure of arc [tex]\widehat{LM}[/tex]:

[tex]\widehat{LP}+\widehat{LM}=180^{\circ},\\92^{\circ}+\widehat{LM}=180^{\circ},\\\widehat{LM}=88^{\circ}[/tex]

Arc [tex]\widehat{LM}[/tex] is formed by angle [tex]\angle LPM[/tex]. Define an inscribed angle by an angle with a point on the circle creating an arc on the circumference of the circle. The measure of an inscribed angle is exactly half of the measure of the arc it forms.

Therefore, the measure of [tex]\angle LPM[/tex] must be:

[tex]m\angle LPM=\frac{88}{2}=44^{\circ}[/tex]

Similarly, the measure of [tex]\angle LNP[/tex] must be:

[tex]m\angle LNP=\frac{92}{2}=46^{\circ}[/tex]

Angles [tex]\angle LPM[/tex] and [tex]\angle MPN[/tex] form angle [tex]\angle LPN[/tex], which is one of the three angles in [tex]\triangle LPN[/tex]. Since the sum of the interior angles of a triangle add up to 180 degrees, we have:

[tex](\angle MPN+\angle LPM)+\angl+ PLN+\angle LNP=180^{\circ},\\\angle MPN+44+46+68=180,\\\angle MPN=180-44-46-68,\\\angle MPN=\boxed{22^{\circ}}[/tex]

99 boys and 1 girl makes 99 percent of boys. To make it 98%, 50 boys must leave the theatre, so there are 49 boys and 1 girl, making 98% of boys.

We have l = 20 * 20 * 20 = 8000 cm3

One cube will have l = 5 * 5 * 5 = 125 cm3

-> The maximum number of cubes that need to use to fill the container with water is 8000 / 125 = 64

Given:

The limit problem is:

[tex]lim_{x\to -5}\dfrac{\dfrac{1}{5}+\dfrac{1}{x}}{10+2x}[/tex]

To find:

The value of the given limit problem.

Solution:

We have,

[tex]lim_{x\to -5}\dfrac{\dfrac{1}{5}+\dfrac{1}{x}}{10+2x}[/tex]

It can be written as:

[tex]=lim_{x\to -5}\dfrac{\dfrac{x+5}{5x}}{2(5+x)}[/tex]

[tex]=lim_{x\to -5}\dfrac{x+5}{5x}\times \dfrac{1}{2(5+x)}[/tex]

[tex]=lim_{x\to -5}\dfrac{1}{5x\times 2}[/tex]

[tex]=lim_{x\to -5}\dfrac{1}{10x}[/tex]

Applying limit, we get

[tex]lim_{x\to -5}\dfrac{1}{10x}=\dfrac{1}{10(-5)}[/tex]

[tex]lim_{x\to -5}\dfrac{1}{10x}=\dfrac{1}{-50}[/tex]

Therefore, the value of given limit problem is [tex]-\dfrac{1}{50}[/tex].

the answer is in the picture

Answer:

It should be B,  180 cm

Step-by-step explanation:

x = circumference of  circle D

18/360 = 9/x

9*360 = 18x

9*360/18 = x

x = 180

Answer:

[tex] \rm Numbers = 4 \ and \ -3.[/tex]

Step-by-step explanation:

Given :-

The sum of two numbers is 1 .

The product of the nos . is 12 .

And we need to find out the numbers. So let us take ,

First number be x

Second number be 1-x .

According to first condition :-

[tex]\rm\implies 1st \ number * 2nd \ number= -12\\\\\rm\implies x(1-x)=-12\\\\\rm\implies x - x^2=-12\\\\\rm\implies x^2-x-12=0\\\\\rm\implies x^2-4x+3x-12=0\\\\\rm\implies x(x-4)+3(x-4)=0\\\\\rm\implies (x-4)(x+3)=0\\\\\rm\implies\boxed{\red{\rm x = 4 , -3 }}[/tex]

Hence the numbers are 4 and -3

Answer:

Step-by-step explanation:

If the product of 2 integers is -12, then that equation looks like this:

xy = -12

If the sum of those same 2 integers in 1, then that equation looks like this:

x + y = 1

Let's solve the second equation for x and plug it into the first equation. Solving the second equation for x gives us

x = 1 - y and plug that into the first equation in place of x to get:

(1 - y)y = -12 and

[tex]y-y^2=-12[/tex] Now move everything over to one side and factor to find y:

[tex]-y^2+y+12=0[/tex] and the 2 values for y are

y = -3 and y = 4. Let's see what happens when we solve for x.

If xy = -12 and y is -3:

x(-3) = -12 so

x = 4

If xy = -12 and y is4:

x(4) = -12 so

x = -3

So it looks like the 2 integers are -3 and 4

Answer:

La norma de los signos es para el producto de números reales, y la norma es la siguiente.

(+)*(+) = (+)

(+)*(-) = (-)

(-)*(+) = (-)

(-)*(-) = (+)

Es decir, el producto de dos números de mismo signo es siempre positivo

El producto de dos números de distinto signo es siempre negativo.

Particularmente, para la suma esta norma no funciona (pues no está definida para la suma)

Pero en casos como:

5 - (-4)  

(esto sería: "la diferencia entre cinco y menos cuatro")

notar que podemos reescribir esto como:

5 + (-1)*(-4)

Ahora podemos aplicar la norma de los signos:

5 + 4 = 9

Donde aplicamos la norma de los signos,  

Podemos concluir que, si bien es una regla que aplica al producto, siempre la tenemos que tener en cuenta en cualquier operación que hagamos.

Por lo podemos concluir que la respuesta correcta es verdadero.

Answer:

≈ 14%

Step-by-step explanation:

percent increase is calculated as

[tex]\frac{increase}{original}[/tex] × 100%

Increase = 16489 - 14523 = 1966 , then

percent increase = [tex]\frac{1966}{14523}[/tex] × 100% = [tex]\frac{1966(100)}{14523}[/tex] ≈ 14% ( to nearest percent )

Answer:

14% :)

Step-by-step explanation:

Hello,

f(x+5)=f(x)

Periode is 5

Answer:

It's 4 on acellus, not 5 :)

Step-by-step explanation:

Answer:

8.9m/s

Step-by-step explanation:

Time= 28s

Displacement= 250m

Velocity=?

Velocity (v) = displacement (d)/ Time (t)

V= 250/28

V=8.9m/s

OR YOU CAN APPROXIMATE IT

V=8.928

YOU CAN APPROXIMATE IT TO

V=8.93m/s

Answer:

Step-by-step explanation:

Slope = m = 3

(x₁ , y₁) = (-1 , 2)

Point slope form: y - y₁ = m(x - x₁)

y - 2 = 3(x - [-1] )

y - 2 = 3(x + 1)

y - 2 = 3*x + 3*1

y - 2 = 3x + 3

    y = 3x + 3 + 2

    y = 3x + 5

Answer:

Step-by-step explanation:

[tex]5) 5\frac{11}{12}+3\frac{5}{6}=5+\frac{11}{12}+3+\frac{5}{6}\\\\ =8 +\frac{11}{12}+\frac{5*2}{6*2}\\\\= 8 +\frac{11}{12}+\frac{10}{12}\\\\=8 +\frac{11+10}{12}\\\\= 8+\frac{21}{12}\\\\=8+ 1\frac{9}{12}\\\\= 9\frac{9}{12}[/tex]

the answer is in the picture