Which graph below solves the following system of equations correctly?

y = three over four times x squared minus 3
y = negative three over four times x squared plus 3
A) two quadratic graphs opening up. They intersect at 0 and negative 3.

B)one quadratic graph opening up and one quadratic graph facing down. They intersect at 0, 3.

C) quadratic graph opening up and quadratic graph opening down. They intersect at 0, negative 3.

D) two parabolas one facing down with a vertex at 0, 3 and one facing up with a vertex at 0, negative 3

Answer:

(-inf,2]

Step-by-step explanation:

[tex](w \circ r)(x)=w(r(x))[/tex]

[tex]w(2-x^2)[/tex] I replaced r(x) with 2-x^2

[tex](2-x^2)-x[/tex] I replace the x in w(x)=x-2 with 2-x^2

[tex]-x^2-x+2[/tex]

You can graph this to find the range.

But since this is a quadratic (the graph is a parabola), I'm going to find the vertex to help me to determine the range.

The vertex is at x=-b/(2a).  Once I find x, I can find the y that corresponds to it by using y=-x^2-x+2.

Comparing ax^2+bx+c to -x^2-x+2 tells me a=-1, b=-1, and c=2.

So the vertex is at x=1/(2*-1)=-1/2.

To find the y-coordinate that corresponds to that I will not plug in -1/2 in place of x into -x^2-x+2.

This gives me

-(-1/2)^2-(-1/2)+2

-1/4 +  1/2  +2

Find a common denominator which is 4.

-1/4 +  2/4  +8/4

8/4

2.

So the highest y value is 2 ( I know tha parabola is upside down because a=negative number)

That mean then range is 2 or less than 2.

So the answer an interval notation is (-inf,2]

Answer:

12:1

Step-by-step explanation:

12:1Answer:

Step-by-step explanation:

Answer:

y = - x + 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 1, 2) and (x₂, y₂ ) = (4, - 3)

m = [tex]\frac{-3-2}{4+1}[/tex] = [tex]\frac{-5}{5}[/tex] = -1, hence

y = - x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (- 1, 2), then

2 = 1 + c ⇒ c = 2 - 1 = 1

y = - x + 1 ← equation in slope- intercept form

The equation is y = –x + 1.

To find the slope-intercept form of a line passing through two points, calculate the slope using the given points and then use one point to find the y-intercept. The final equation for the line through the points (–1, 2) and (4, –3) is y = –x + 1.

To write an equation in slope-intercept form for the line passing through the points (–1, 2) and (4, –3), we first need to calculate the slope (m) using the formula
m = (y2 - y1) / (x2 - x1). Plugging in our points gives us m = (–3 – 2) / (4 – (–1)) = –5 / 5 = –1. Now that we have the slope, we can use one of the points to find the y-intercept (b). Using the point (–1, 2) and the slope-intercept formula y = mx + b, we plug in the values to get 2 = (–1)×(–1) + b, simplifying to 2 = 1 + b, which yields b = 1. Thus, the equation is y = –x + 1.

Answer:

Step-by-step explanation:

[tex]C(F)=\dfrac{5}{9}(F-32)[/tex]

The function C(F) represents the temperature of F degrees Fahrenheit converted to degrees Celsius.

The function C(F) represents the temperature of F degrees Fahrenheit converted to degrees Celsius. Temperature conversion is the process of converting between different temperature scales, such as Fahrenheit (°F), Celsius (°C), and Kelvin (K).

Each scale measures temperature differently, so conversions are necessary for various applications. The most common conversion formulas are: Celsius to Fahrenheit: °F = (°C × 9/5) + 32, and Celsius to Kelvin: K = °C + 273.15. These conversions are vital for international communication, weather reports, and scientific calculations.

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The event "not rolling 1, 3, 4, or 5" is the same event as "rolling 2 or 6".

Since the possible outcomes of a number cube have the same probability, the probability of rolling 2 or 6 is given by

[tex]\dfrac{\text{\# of good outcomes}}{\text{\# of possible outcomes}}=\dfrac{2}{6}=\dfrac{1}{3}[/tex]

Answer:

The graph in the attached figure

Step-by-step explanation:

we have that

[tex]f(x)=x-4[/tex] ------> For [tex]x < 2[/tex]

[tex]f(x)=-2x+2[/tex] ------> For [tex]x\geq2[/tex]

To graph this piece wise- defined function

In the interval (-∞,2) ----> graph the line [tex]f(x)=x-4[/tex]

In the interval [2,∞) ----> graph the line [tex]f(x)=-2x+2[/tex]

The function is continue -----> the domain is all real numbers

using a graphing tool

see the attached figure

Final answer:

The truth value of the conditional statement ¬q → ¬p, with p being true and q being false, is false.

Explanation:

The question is asking about the truth value of the conditional statement ¬q → ¬p, where p is true and q is false. In a conditional statement of the form 'if q then p', written symbolically as q → p, the statement is false only when q is true and p is false. Otherwise, the statement is true. In this case, ¬q means 'not q' and ¬p means 'not p'. Given that q is false, ¬q is true. Given that p is true, ¬p is false. Thus, the statement ¬q → ¬p is of the form 'true → false', which makes the entire conditional statement false.

Final answer:

The truth value for the conditional statement ¬q → ¬p when p is true and q is false is false. This is because the contrapositive of any conditional statement must have the same truth value as the statement itself, and the given condition does not maintain this logical equivalence.

Explanation:

The truth value for the following conditional statement ¬q → ¬p when p is true and q is false is what we are trying to determine. The proposition ¬q → ¬p is the contrapositive of the conditional p → q. According to logic, a conditional proposition and its contrapositive always have the same truth value. Since we are given that p is true and q is false (¬q is true), using the definitions of the logical operators, we find that the contrapositive of the original conditional should also be true if the original is true.

In this case, the contrapositive is ¬q → ¬p, which, when translated in terms of the given truth values, becomes true → false. This suggests that if ¬q is true, then ¬p is true as well; however, since we know p is true, the situation given (¬q is true, ¬p is false) is not possible because it would not uphold the truth of the original proposition. Thus, the provided sequence of truth values does not maintain the logical equivalence of the contrapositive, making it incorrect. Therefore, the truth value of ¬q → ¬p is false under the given conditions.

Arc length will be equal to the perimeter divided by 4 since we are talking about quarter circle.

[tex]2\pi r/4=\pi r/2=6\pi/2\approx\boxed{9.42}[/tex]

Hope this helps.

r3t40

Answer:

9.42 inches

Step-by-step explanation:

the cercle length is : 2π×r = 2×3.14 ×6=37.68 inches

the arc length of a quarter circle is : 37.68/4 =9.42 inches

Answer:

946

Step-by-step explanation:

To find just the remainder when dividing a polynomial by x-3, you could just plug in 3 into that polynomial.

If you were dividing by x+3, the remainder would just be the polynomial evaluated at x=-3.

Anyways plugging in 3 gives

7(3)^4 + 12(3)^3 + 6(3)^2 - 5(3) + 16

Just put this into your nearest calculator .

It should output 946.

You could use synthetic division or even long.

Synthetic Division.

We put 3 on outside because we are dividing by x-3.

3. | 7. 12. 6. -5. 16

| 21. 99. 315. 930

________________________

7. 33. 105. 310. 946

The remainder is the last number in the last column.

The plugging in and the synthetic division will always work when dividing by a linear expression.

Answer:

Step-by-step explanation:

Start by removing the brackets.

Left Brackets

30(1/2 x - 2)

30*1/2 x - 30*2

15x - 60

Right Bracket

40(3/4 y - 4)

40*3/4 y - 4*40

10*3 y - 160

30y - 160

Now put these 2 results together.

15x - 60 + 30y - 160     Combine the like terms.

15x + 30y - 220            That's one answer Others are possible.

5(3x + 6y - 44)

Answer:

74

Step-by-step explanation:

Answer:

Step-by-step explanation:

We know:

1. Diagonals of a rhombus are perpendicular.

2. Diagonals divide the rhombus on four congruent right triangles.

3. The sum of measures of acute angles in a right triangle is equal 90°.

Therefore we have the equation:

(2x + 3) + (3x + 2) = 90           combine like terms

(2x + 3x) + (3 + 2) = 90

5x + 5 = 90               subtract 5 from both sides

5x = 85             divide both sides by 5

x = 17

The value of x is 17. This means that the angles formed by the diagonals of the rhombus are 37 degrees (2 * 17 + 3) and 53 degrees (3 * 17 + 2), and they indeed form congruent right triangles as required in the properties of a rhombus.

To find the value of x in the given equation, we start by understanding the properties of a rhombus and how its diagonals divide it into four congruent right triangles.

Given information:

Diagonals of a rhombus are perpendicular.

Diagonals divide the rhombus into four congruent right triangles.

Let's proceed with the steps to solve for x:

Step 1: Recognize that the angles formed by the diagonals are 2x + 3 and 3x + 2. Since these angles are congruent right angles, their sum is equal to 90 degrees.

Step 2: Set up the equation:

(2x + 3) + (3x + 2) = 90

Step 3: Combine like terms:

5x + 5 = 90

Step 4: Isolate x by subtracting 5 from both sides of the equation:

5x = 85

Step 5: Solve for x by dividing both sides by 5:

x = 85 / 5

x = 17

Hence, the value of x is 17. This means that the angles formed by the diagonals of the rhombus are 37 degrees (2 * 17 + 3) and 53 degrees (3 * 17 + 2), and they indeed form congruent right triangles as required in the properties of a rhombus.

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Answer:

ship B is going in a straight line north ship A is going diagonal make a straight line where each ship is moving towards and where ever they intersect will be where the ship in distress is located

hope this helped

Answer: 32

Step-by-step explanation: You need to use PEMDAS. First, multiply the two numbers.

3(8) = 24

Then, add 8.

24 + 8 = 32

32 is your answer.

Answer:

178.98 square feet

Step-by-step explanation:

Alright so we need to find two areas here and find the difference to find the area of the path.

The two shapes involved is a smaller circle inside a bigger circle.

Let's look at the smaller circle, the gardening area.

You are given is has a radius of 8 ft.

The area of a circle is [tex]\pi \cdot r^2[/tex] where r is the radius.

So the area of the smaller circle is [tex]\pi \cdot 8^2[/tex].

Now time to look at the bigger area (which will have some overlapping area with the smaller one which will subtract out to find the area of path).

The diameter of the smaller circle was (8+8)=16 feet.

What is the diameter of the bigger one.  The path is 3 ft wide so we have to add a 3 before the diameter of the smaller circle to another 3 after that diameter to get the diameter of the bigger circle.  So the diameter of the bigger circle is (3+16+3)=22 feet.  The radius is half the diameter so the radius is 22/2=11.

The area of the bigger circle is [tex]\pi \cdot 11^2[/tex].

The area of the path=

the area of bigger circle     -      the area of smaller circle=

[tex]\pi \cdot 11^2-\pi \cdot 8^2[/tex]

Type this into your calculator with 3.14 instead of the [tex]\pi[/tex] button.

178.98 square feet

The answer is:

[tex]PathArea=178.98ft^{2}[/tex]

To calculate the are of the path alone, we need to add the width of the path to the radius of the garden in order to know is radius, then, calculate the total  area (using garden radius plus path width) and then, subtract it the area of the circular garden.

We know that the radius of the circular garden is equal to 8 feet, and the circular path has a width of 3 feet, so, the radius of the circular path will be:

[tex]CPath_{radius}=8feet+Path_{width}\\\\Path_{radius}=8feet+3feet=11[/tex]

Now, calculating the areas, we have:

Garden Area:

[tex]CircularGardenArea=\pi *radius^{2}\\\\CircularGardenRadius=\pi *8ft^{2}=3.14*64ft^{2}=200.96ft^{2}[/tex]

Total Area:

[tex]TotalArea=\pi *(8feet+3feet)^{2}=\pi *(11ft)^{2}=3.14*121ft^{2}=379.94ft^{2}[/tex]

Now, calculating the area of the path, we have:

[tex]TotalArea=CircularGardenArea+PathArea\\\\PathArea=TotalArea-CircularGardenArea\\\\PathArea=379.94ft^{2}-200.96ft^{2}=178.98ft^{2}[/tex]

Hence, we have that:

[tex]PathArea=178.98ft^{2}[/tex]

Have a nice day!

Answer:

B,D, and E

Step-by-step explanation:

They all label the vertices in the correct order and do not label sides when naming it.

Answer:

B. [tex]\Delta TAX[/tex],

D. [tex]\Delta AXT[/tex]

E. [tex]\Delta XTA[/tex].

Step-by-step explanation:

We have been given a triangle. We are asked to choose the valid names for our triangle from the given choices.

We know that labels of the vertices of the triangle are used to name a triangle. In naming triangle, we can start from any vertex and we should keep the letters in order as we go around the triangle.

We can see that vertices of our given triangle are labeled as A, T and X, therefore, we can get three names for our triangle as:

[tex]\Delta TAX[/tex], [tex]\Delta AXT[/tex] and [tex]\Delta XTA[/tex].

Therefore, options B, D and C are correct choices.

Answer:

The second polynomial is:

[tex]6d^5-2c^3d^2+5c^2d^3-12cd^4+8[/tex]

Step-by-step explanation:

Given

[tex]Sum\ of\ polynomials=S=8d^5-3c^3d^2+5c^2d^3-4cd^4+9\\Polynomial\ 1=A=2d^5-c^3d^2+8cd^4+1\\Polynomial\ 2=B=?\\S=A+B\\B=S-A\\=8d^5-3c^3d^2+5c^2d^3-4cd^4+9-(2d^5-c^3d^2+8cd^4+1)\\=8d^5-3c^3d^2+5c^2d^3-4cd^4+9-2d^5+c^3d^2-8cd^4-1\\=8d^5-2d^5-3c^3d^2+c^3d^2+5c^2d^3-4cd^4-8cd^4+9-1\\=6d^5-2c^3d^2+5c^2d^3-12cd^4+8[/tex]

[tex]\bf \cfrac{x^8}{x^{14}}\implies x^8x^{-14}\implies x^{8-14}\implies x^{-6}\implies \stackrel{\textit{using the power rule}}{-6x^{-7}\implies \cfrac{-6}{x^7}}[/tex]

Question 1:

We have the following expression:

[tex]4x ^ {-4}[/tex]

By definition of power properties we have to:

[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]

Then, rewriting the expression:

[tex]\frac {4} {x ^ 4}[/tex]

ANswer:

[tex]\frac {4} {x ^ 4}[/tex]

Question 2:

For this case we have the following expression:

[tex]\frac {x ^ 8} {x ^ {14}} =[/tex]

By definition of power properties of the same base we have:

[tex]x ^ n * x ^ m = x ^ {n + m}[/tex]

Then, we can rewrite the denominator of the expression as:

[tex]\frac {x ^ 8} {x ^ 8 * x ^ 6} =[/tex]

Simplifying terms of the numerator and denominator:

[tex]\frac {1} {x ^ 6}[/tex]

ANswer:

[tex]\frac {1} {x ^ 6}[/tex]

Answer:

[tex]Pr=\dfrac{45}{208}\approx 0.216.[/tex]

Step-by-step explanation:

You are given the information about students:

In total, there are 45 + 60 + 82 + 21 = 208 students.

Use the definition of the probability:

[tex]Pr=\dfrac{\text{Number of favorable outcomes}}{\text{Number of all possible outcomes}}[/tex]

Number of favorable outcomes = 45

Nomber of all possible outcomes = 208,

hence,

[tex]Pr=\dfrac{45}{208}\approx 0.216.[/tex]

[tex]\bf \stackrel{\mathbb{P~E~M~D~A~S}}{7+3^2+(12-8)\div 2\times 4}\implies 7+3^2+(\stackrel{\downarrow }{4})\div 2\times 4\implies 7+\stackrel{\downarrow }{9}+(4)\div 2\times 4 \\\\\\ 7+9+\stackrel{\downarrow }{2}\times 4\implies 7+9+\stackrel{\downarrow }{8}\implies \stackrel{\downarrow }{16}+8\implies 24[/tex]

Answer:

78 and 46

Step-by-step explanation:

Substitution (look it up it's hard to explain lol)

Let's solve for x.

−b3+3b2+8−x−5b2−9=5b3+852+17

Step 1: Add b^3 to both sides.

−b3−2b2−x−1+b3=5b3+869+b3

−2b2−x−1=6b3+869

Step 2: Add 2b^2 to both sides.

−2b2−x−1+2b2=6b3+869+2b2

−x−1=6b3+2b2+869

Step 3: Add 1 to both sides.

−x−1+1=6b3+2b2+869+1

−x=6b3+2b2+870

Step 4: Divide both sides by -1.

−x

−1

=

6b3+2b2+870

−1

x=−6b3−2b2−870

Answer:

x=−6b3−2b2−870

Answer:

the answer is the first option -6b^3

Step-by-step explanation:

yup

Answer:

[tex]\large\boxed{h^{-1}(x)=\dfrac{3x+4}{2}}[/tex]

Step-by-step explanation:

[tex]h(x)=\dfrac{2x-4}{3}\to y=\dfrac{2x-4}{3}\\\\\text{Exchange x to y and vice versa}:\\\\x=\dfrac{2y-4}{3}\\\\\text{Solve for y:}\\\\\dfrac{2y-4}{3}=x\qquad\text{multiply both sides by 3}\\\\2y-4=3x\qquad\text{add 4 to both sides}\\\\2y=3x+4\qquad\text{divide both sides by 2}\\\\y=\dfrac{3x+4}{2}[/tex]

Answer:

The graph in the attached figure

Step-by-step explanation:

Let

x -----> time of the first process in minutes

y -----> time of the second process in minutes

we know that

The time of the first process multiplied by 4 (because is repeated 4 times) plus the time of the second process multiplied by 1 (because is repeated only once) must be less than or equal to 3 minutes

so

The inequality that represent this situation is

[tex]4x+y\leq 3[/tex]

The solution of the inequality is the shaded area below the solid line

The equation of the solid line is [tex]4x+y=3[/tex]

The y-intercept of the solid line is the point (0,3)

The x-intercept of the solid line is the point (0.75,0)

The slope of the solid line is negative m=-4

using a graphing tool

The solution is the shaded area

The graph in the attached figure

Remember that the time cannot be a negative number

Answer:

The inequality represents the situation is:

[tex]4x+y\leq 3[/tex]

And the graph is attached in the solution.

Step-by-step explanation:

Given information:

Time of first process in minutes[tex]=x[/tex]

Time of second process in minutes [tex]=y[/tex]

As we know that ,

according to the given information in the question we can write:

the inequality represents the situation is:

[tex]4x+y\leq 3[/tex]

Here, the y-intercept of the solid line is the point (0,3)

And the x-intercept of the solid line is the point (0.75,0)

And the slope is negative [tex]m=-4[/tex]

Now the graph of the above inequality can be formed as attached in the solution:

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Answer:

[tex]f(x) = {2}^{x } \\ f(x) = 8 \\ \\ {2}^{x} = 8 \\ \\ {2}^{x } = {2}^{3} \\ \\ x = 3[/tex]

The value of x when f(x) = 8 is 3 in f(x) = 2^x

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

f(x) = 2^x

To find the value of x when f(x) = 8, we need to solve the equation 2^x = 8.

We can rewrite 8 as 2^3

So, the equation becomes:

2^x = 2^3

Since the bases are the same, we can equate the exponents:

x = 3

Hence, the value of x when f(x) = 8 is 3.

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[tex]\bf \qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ \stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+6}x\stackrel{\stackrel{c}{\downarrow }}{+9}=0 ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{\underline{one real solution}}~~\textit{\Large \checkmark}\\ positive&\textit{two real solutions}\\ negative&\textit{no solution} \end{cases} \\\\\\ 6^2-4(1)(9)\implies 36-36\implies 0[/tex]

Answer:

log3c-log3(9) i.e. [tex]log_{3}c-log_{3}9[/tex]

Step-by-step explanation:

As per logarithmic relation

[tex]log_{base}\frac{A}{B}=log_{base}A-log_{base}B[/tex]

Now, in the given question base value is 3. Therefore

[tex]log_{3}\frac{c}{9}=log_{3}c-log_{3}9[/tex]

Hence the correct answer is third option.

The expression is equivalent to log₃ (c/9) is log₃ (c) - log₃ (9).

The power to which a number must be increased in order to obtain additional values is referred to as a logarithm. The easiest approach to express enormous numbers is this manner. Numerous significant characteristics of a logarithm demonstrate that addition and subtraction logarithms can also be written as multiplication and division of logarithms.

We have,

log₃ (c/9)

We know the from the property of logarithm

logₐ (c/d) = logₐ (c) - logₐ(d)

and, logₐ (cd)= logₐ(c) x logₐ (d)

So, log₃ (c/9)

= log₃ (c) - log₃ (9)

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Answer:

A C D

Step-by-step explanation:

A prime Trinomial is one that cannot be reduced into integer factors. It is easier to define a non prime trinomial first.

x^2 - 4x - 12 can be factored into

(x - 6)(x + 2) -6 and 2 are integers.

So B is not prime.

All of the others are prime. You need to use the quadratic formula to solve them.

B factors into

x^2 - 13x + 42

(x - 7)(x - 6)

Answer:

A.  True.

Step-by-step explanation:

The value increases by the same amount ($5) every year so it is simple interest.

Answer:True

Step-by-step explanation:

Answer:

[tex]\huge \boxed{90}[/tex]

Step-by-step explanation:

First thing you do is subtract.

10-2=8

[tex]\displaystyle \frac{10!}{8!}[/tex]

Then you cancel the factorials.

[tex]\displaystyle \frac{10!}{8}=10\times9[/tex]

Multiply numbers from left to right to find the answer.

[tex]\displaystyle 10\times9=90[/tex]

[tex]\huge \textnormal{90}[/tex], which is our answer.

Hope this helps!

Final answer:

The value of 10!/(10-2)! simplifies to 90 after canceling out the common factorial terms, hence the correct answer is option C (90).

Explanation:

The expression 10!/(10-2)! represents a calculation involving factorials. The factorial of a number n is denoted n! and means the product of all positive integers from 1 up to n.

So, to simplify this expression, we can expand both factorials:

10! means 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1,
and (10-2)! or 8! means 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1.

When we divide 10! by 8!, the terms 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 (which is 8!) cancel out, leaving us with:

10 x 9 = 90.

Therefore, 10!/(10-2)! simplifies to 90, which is option C.

Answer:

77°

Step-by-step explanation:

[tex]\\ T = \frac{1}{2}  (RU - SU)\\ \\ 21 =\frac{1}{2}(119 - SU)\\ \\ 42 = 119 - SU\\ SU=77[/tex]

The measure of mSU from the given diagram is 77 degrees

The half of the difference of the intecepted arc is equal to the measure of the angle at the vertex

Applying this theorem to the given figure, we will havea;

1/2(119 - mSU) = 21

119 - mSU = 2(21)

119 - mSU = 42

Determine the measure of mSU

mSU = 119 -42

mSU = 77degrees

Hence the measure of mSU from the given diagram is 77 degrees

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