How can x + 3 = −2x + 5 be set up as a system of equations?

Answer:

y=-5/2x-19/2

Step-by-step explanation:

The vertex of the quadratic equation is (-7,8).

Isolate the variable y for the equation 2x-5y=7

You get y = 2/5x-7/5

The slope we have to find is the inverse of the current slope.

So the slope for the final equation is -5/2.

Then use point slope form to get y - 8 = -5/2 * (x+7)

Then convert it into slope intercept form to get y - 8 = -5/2x - 35/2

Then add 8 to each side to get y=-5/2x-19/2

Answer:

option A is the correct choice

Step-by-step explanation:

The trigonometric equation you are using has a general form

y = A* tan w*(x - r)

Where

A is the amplitude of the function

w is the frequency rad/s

r  is the phase shift

In your case

A = 2

B = w = 3

r = pi/2

y = 2* tan 3*(x - pi/2)

A complete probability model provides a framework for calculating the likelihood of events within an experiment or a process. When we talk about a complete probability model, we are referring to a comprehensive description that includes all necessary components to understand and predict outcomes within a probability space.

Let's look at each option and determine which one correctly describes a complete probability model:

A. A list of all possible outcomes in the sample space and their probabilities.
- **This option is correct because a complete probability model does indeed require a list of all possible outcomes (the sample space) and the probability associated with each outcome.** Every outcome must be accounted for, and the sum of the probabilities of all individual outcomes must equal 1. This is because the sample space encompasses every possible outcome that could occur, and their associated probabilities reflect the likelihood of each of these outcomes.

B. The actual outcomes of a trial.
- This option is incorrect because the actual outcomes of a trial are observational results from a single execution of the probability experiment and do not represent a comprehensive model. A complete probability model is theoretical and does not depend on individual trial results, even though it can predict the distribution of those results over many trials.

C. The number of trials conducted.
- This option is incorrect. The number of trials refers to the experimental aspect of probability where an experiment or process is repeated multiple times. It does not provide a model of the entire probability space, only empirical data based on these repetitions.

D. The difference between the theoretical and experimental probabilities of all outcomes.
- This option is incorrect as it refers to the concept of variance between what is expected theoretically and what is observed in practice. While this can be a useful measure for understanding how closely an experiment follows its theoretical predictions, it is not a description of a complete probability model itself.

Given the options, the correct answer is:
A. A list of all possible outcomes in the sample space and their probabilities.

This is the definition of a complete probability model as it provides the necessary information to fully describe the probability of events within a given context.

Answer:

36 and 32

Step-by-step explanation:

So what you do is look at the radius which is 18. The radius is half the distance. So all you have to do is do 18*2=36.

Same with the other one 16*2=32.

Those are your answers.

Answer:

Normally it would be 40 and anything over 80 hours in a two-week time frame would be considered OT

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

its 3

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

We can use the property of exponents  [tex]\frac{a^b}{a^c}=a^{b-c}[/tex]  over here.

Let's use this property to write:

[tex]\frac{a^n}{a^3}\\=a^{n-3}[/tex]

This is equal to a^9, hence, n - 3 = 9. Let's solve for n:

[tex]n-3=9\\n=9+3\\n=12[/tex]

n = 12

Answer:

option C

12

Step-by-step explanation:

Given in the question an expression

[tex]\frac{a^{n} }{a^{3} }=a^{9}[/tex]

To solve for n we will use rules of exponent

cross multiply

[tex]a^{n}=a^{9}a^{3}[/tex]

apply product rule

[tex]a^{n}=a^{9+3}[/tex]

[tex]a^{n}=a^{12}[/tex]

Apply logarithm on both sides of equation

[tex]lna^{n}=lna^{12}[/tex]

apply power rule of logarithm

nln(a) = 12ln(a)

ln(a) will cancel out on each side so we are left with

n= 12

Answer: The real number is 8540

Step-by-step explanation: 85.4  1000

Step-by-step explanation:

Area of a trapezoid is 1/2h(b1+b2)

So let's substitute.

1/2*17*(15+27)

1/2*17*42

Answer is 357 cm squared

Answer:

a. y÷x=5 , b. y=60 because x is increased by 2 times  so y should be increased by 2 times

Step-by-step explanation:

Answer:

[tex]\boxed{\bold{\left(x+7\right)\left(x+1\right)\left(x-1\right)=0}}[/tex]

Step-by-step explanation:

Factor [tex]\bold{x^3+7x^2-x-7}[/tex]

[tex]\bold{\left(x+7\right)\left(x^2-1\right)}[/tex]

Factor [tex]\bold{0}[/tex]

[tex]\bold{0}[/tex]

Rewrite Equation

[tex]\bold{\left(x+7\right)\left(x+1\right)\left(x-1\right)=0}[/tex]

[tex] {x}^{3} + 7 {x}^{2} - x - 7 = 0 \\ \Leftrightarrow {x}^{2} (x + 7) - (x + 7) = 0 \\ \Leftrightarrow ( {x}^{2} - 1)(x + 7) = 0 \\ \Leftrightarrow (x - 1)(x + 1)(x + 7) = 0 \\ \Leftrightarrow x = - 7 \: \vee \: x = - 1 \: \vee \: x = 1[/tex]

Answer:

Equations are composed for many expressions.

Expressions can indicate variables, constants, etc.

Best regards

Answer:

Step-by-step explanation:

Expressions generally contain literals and may be "evaluated" by subbing the given values of the literal into them.  Expressions may be simplified, including being rewritten in alternative forms.

Equations, on the other hand, involve the " = " symbol.  If a literal, such as x or y, is included in the equation, we can usually solve the equation for that literal, thereby creating a function.

Answer:

[tex]\large\boxed{The\ vertex:\ (-5,\ 49)}[/tex]

Step-by-step explanation:

[tex]f(x)=ax^2+bx+c\\\\\text{The vertex}\ (h,\ k),\ \text{where}\ h=\dfrac{-b}{2a}\ \text{and}\ k=f(h).\\\\\text{We have:}\ y=-x^2-10x+24\to f(x)=-x^2-10x+24\\\\a=-1,\ b=-10,\ c=24.\\\\\text{Substitute:}\\\\h=\dfrac{-(-10)}{2(-1)}=\dfrac{10}{-2}=-5\\\\k=f(-5)=-(-5)^2-10(-5)+24=-25+50+24=49[/tex]

Answer:  in 12 years (2017)

               23,000 students enrolled

Step-by-step explanation:

Let x represent the number of years since 2005.

Let y represent the number of students enrolled.

College A: y = 14,000 + 750x

College B: y = 35,000 - 1000x

Solve the system using the Substitution Method:

14,000 + 750x = 35,000 - 1000x

           +1000x               +1000x

14,000  + 1750x = 35,000

-14,000                 -14,000

                1750x = 21,000

                        x = 12

Input x = 12 into one of the equations to solve for y.

y = 35,000 - 1000x

  = 35,000 - 1000(12)

  = 35,000 - 12,000

  = 23,000

Explanation on when two colleges will have the same enrollment and what the enrollment will be at that time.

Step 1: Set up equations for the enrollment at each college over time. Let x be the number of years since 2005:

College A enrollment = 14000 + 750x

College B enrollment = 35000 - 1000x

Step 2: Set the two equations equal to each other:

14000 + 750x = 35000 - 1000x

Step 3: Solve for x to find when the colleges will have the same enrollment:

x = 10 years

Step 4: Substitute x back into the equations to find the enrollment at each college after 10 years:

College A enrollment = 14000 + 750(10) = 21500 students

College B enrollment = 35000 - 1000(10) = 25000 students

Answer:

Which U.S. political parties would likely approve of a plan to help unemployed workers?

Step-by-step explanation:

1. Communists

2. Democrats

3. Libertarians

4. Republicans

5. Socialists

the answer is 5,3,1

Final answer:

The Libertarian Party wants little to no government interference. The Democratic and Republican parties have different stances on helping unemployed workers, taxing businesses for environmental cleanup, and providing cheaper healthcare.

Explanation:

In the United States, the Libertarian Party is a third-party that wants little to no government interference. They advocate for limited government intervention in both social and economic areas. For example, they support lower taxes, less regulation, and individual freedom.

The Democratic and Republican parties would likely approve of a plan to help unemployed workers. The Democrats often propose policies such as extending unemployment benefits and increasing job training programs, while the Republicans tend to support tax cuts and reducing government regulations to stimulate job growth.

The Democratic party is more likely to approve of a tax on businesses to clean up the environment. They generally advocate for stricter environmental regulations and support policies aimed at reducing pollution. The Republican party, on the other hand, often opposes new taxes and regulations on businesses.

The Democratic party and the Progressive wing of the Democratic party would likely approve of a plan to provide cheaper healthcare. They have been pushing for measures such as expanding Medicaid, implementing a public health insurance option, and decreasing prescription drug prices. The Republican party, however, tends to advocate for free-market solutions and reducing government involvement in healthcare.

[tex]7\frac{4}{5} = \frac{28}{5}[/tex]

because 7 x 4 = 28

[tex]4\frac{7}{5} = \frac{28}{5}[/tex]

because 4 x 7 = 28

This means that

[tex]7\frac{4}{5} = [tex]4\frac{7}{5}[/tex]

[tex]6\frac{12}{5} = \frac{72}{5}[/tex]

because 6 x 12 = 72

This means

[tex]7\frac{4}{5} = [tex]6\frac{12}{5}[/tex]

Answer:

8

Step-by-step explanation:

200 divided by 25 is 8

Answer: $654.72

Step-by-step explanation:

11 percent of $704 is $77.44  -  (11*704/100)

You do $704-$77.44 because it is on sale.

Equalling $626.56

4 percent of $704 is $28.16 - (4*704/100)

Add $28.16 to 626.56 because your being taxed.

Equalling $654.72 your answer

The total cost of the $704 tablet computer, after an 11% discount and 4% sales tax, is $651.62.

To find the total cost of the $704 tablet computer, we first need to calculate the sale price after the 11% discount. The discount amount can be found by multiplying the original price by 11% (or 0.11). So, the discount amount is $704 * 0.11 = $77.44. The sale price is then $704 - $77.44 = $626.56.

Next, we need to calculate the sales tax amount. The sales tax rate is 4%, so the tax amount is $626.56 * 0.04 = $25.06.

Finally, to find the total cost, we need to add the sale price and the sales tax amount together. Therefore, the total cost of the $704 tablet computer, including the discount and sales tax, is $626.56 + $25.06 = $651.62.

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Answer:

4 inches long each i think im not completely sure

Step-by-step explanation:

Rectangle has its adjacent sides perpendicular to each other. The lengths of the sides of the considered rectangle are: 5 inches and 12 inches.

Its the sum of length of the sides used to made the given figure.

For a rectangle, as the rectangle has two of its sides equal to its length, and rest two are equal to its width, thus,

perimeter of rectangle = twice of (width + length)

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]  

where |AB| = length of line segment AB.

In a rectangle, its adjacent sides are perpendicular to each other(making 90 degrees with each other), thus, when its diagonal is drawn, we can use Pythagoras theorem to relate its length, width and length of the diagonals (both of diagonals of a rectangle are of same length).

Thus,  using Pythagoras theorem, we get:

[tex](|Diagonal|)^2 = |Length|^2 + |Width|^2[/tex]

Suppose its length and width are L and W, then we get two equations:

Perimeter = 2(L + W) = 34 inches

Diagonal² = 13² = 169 = L² + W²

From the first equation, getting L in terms of W, we get:

[tex]L = 17 - W[/tex]

Putting this value in second equation, we get:

[tex]L^2 + W^2 = 169\\(17-W)^2 + W^2 = 169\\289 + W^2 + W^2 -34W = 169\\2W^2 -34W + 120 = 0\\W^2 - 17W + 60 = 0\\W^2 -12W - 5W + 60 = 0 \\W(W - 12) - 5(W - 12) = 0\\\\(W-5)(W-12) = 0\\W = 5, 12[/tex](in inches)

Thus, we get L= 17-W = 12 or 5,

Thus, dimensions of the considered rectangle are 5 inches and 12 inches.

Learn more about solutions of quadratic equations here:

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Answer:

[tex] 0.25 [/tex]

Step-by-step explanation:

We are given the following verbal expression and we are to first translate it and then evaluate it:

'6- the square root of 25 divided by 4'

[tex] \frac { 6 - \sqrt { 25 } } { 4 } [/tex]

Taking the square root first to get:

[tex] \frac { 6 - 5 } { 4 } [/tex]

[tex] \frac { 1 } { 4 } [/tex]

[tex] 0.25 [/tex]

Answer:

.25

Step-by-step explanation:

Answer:

A=75 cm

Step-by-step explanation:

The formula of the area of a triangle is A=bh/2.

A=(15)(10)/2.

A=150/2

A=75 cm is your answer.

Answer:

A=75 cm

Step-by-step explanation:

A=bh/2 is the formula for the area of a triangle

1) Multiply 15 the base and the height 10 first

A=(15)(10)

A= 150 cm

2) divide 150cm by 2

A=150/2

A=75 cm is your answer.

Hopes this helps My friend!

Answer:

x = 5

Step-by-step explanation:

In this problem, the angles are vertical, which mean that they are congruent.

So we can set them equal to each other and solve.

13x + 19 = 84

Subtract 19 from both sides.

13x = 65

Divide each side by 13

x = 5

ANSWER

[tex]y \leqslant - 2x - 2[/tex]

EXPLANATION

The boundary line passes through (-2,2) and (0,-2).

The slope of this line is

[tex]m = \frac{ - 2 - 2}{0 - - 2} [/tex]

[tex]m = \frac{ - 4}{2} = - 2[/tex]

The y-intercept is , c=-2.

The slope-intercept form of this line is given by;

[tex]y = mx + c[/tex]

We substitute values to obtain;

[tex]y = - 2x - 2[/tex]

Since the lower half-plane is shaded the required inequality is

[tex]y \leqslant - 2x - 2[/tex]

40+20=72-12 is how you rewrite it

To correctly rewrite the equation 4(10+5)=6(12-2) using the distributive property, we apply the property to each term inside the parentheses. The equation can be correctly rewritten as 60=60.

To correctly rewrite the equation 4(10+5)=6(12-2) using the distributive property, we apply the property to each term inside the parentheses. Starting with the left side, we have 4(10+5). Using the distributive property, this becomes 4(10) + 4(5) = 40 + 20 = 60. Now, let's apply the distributive property to the right side of the equation. We have 6(12-2), which becomes 6(12) - 6(2) = 72 - 12 = 60. Therefore, the equation 4(10+5)=6(12-2) can be correctly rewritten as 60=60 using the distributive property.

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Answer:

48.4512

product means the answer so just multiply.

Answer:

it is 48.4512

Step-by-step explanation:

so what i like to do is first step: dont worry about the decimals at the moment so the equation would be 824 x 588. then it is 484,512. Third step is count how many numbers is behind the decimals. There are 4 so move 4 spaces to the left which we get 48.4512. Hope this helps!

Answer:

y=1/5

Step-by-step explanation:

6x-5y=5

3x+5y=4

we are now going to multiply the second equation by -6

6x-5y=5

-2(3x+5y=4)

so it becomes

6x-5y=5

-6x-10y=-8

the 6 can cancels out so it becomes  -15y=-3

divide both sides by -15

y=1/5

The X coordinate is X = 1

See the image

Answer:

b

Step-by-step explanation:

The true statement is B. A rhombus is a parallelogram. This is true because rhombuses have parallel opposite sides, defining them as parallelograms. The other statements are false due to specific conditions not met by all parallelograms, rhombuses, or trapezoids.

The true statement among the options provided is B. A rhombus is a parallelogram. This is because all rhombuses have opposite sides that are parallel to each other, which is a defining property of parallelograms. Not all parallelograms are squares because a square is a special type of parallelogram where all sides are equal in length and all angles are right angles - a condition not required for a general parallelogram.

Similarly, not all rhombuses are squares since rhombuses do not require all angles to be right angles. Lastly, a trapezoid typically has only one pair of parallel sides, not two, which differentiates it from parallelograms.

To illustrate why a rhombus is a parallelogram, we can consider A1 Constructibility of parallelograms: Given any three points P, Q, and R, there exists a point S such that quadrilateral PQRS is a parallelogram. In a rhombus, all four sides are of equal length - satisfying the conditions of a parallelogram, which requires only that opposite sides be parallel and of equal length.

When it comes to the diagonals of a rhombus being perpendicular, we use the concept of the scalar or dot product of vectors. The diagonals bisect each other at right angles because the dot product of the vectors representing the diagonals equals zero, indicating that they are perpendicular to each other. This fact further underscores the relationship between rhombuses and parallelograms and their distinct geometric properties.

[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{}{ h},\stackrel{}{ k})\qquad \qquad radius=\stackrel{}{ r} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (x-\stackrel{h}{3})^2+(y-\stackrel{k}{7})^2=9\implies (x-\stackrel{h}{3})^2+(y-\stackrel{k}{7})^2=\stackrel{r}{3^2}~\hfill \begin{cases} center~(3,7)\\ radius=3 \end{cases}[/tex]

Final answer:

The radius of the circle with the equation (x − 3)² + (y − 7)² = 9 is found by taking the square root of 9, which is 3. Therefore, the correct answer is A) 3.

Explanation:

The question asks to find the radius of a circle given its equation. The standard form of the equation of a circle is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. Comparing this with the given equation (x − 3)² + (y − 7)² = 9, we see that the value of r² is 9.

Therefore, the radius r of the circle is the square root of 9, which is 3.

Hence, the correct answer is A) 3.

Answer is A because it’s moved 2 to the right which makes it x-2 and it’s moved 1 down so -1 and it needs to be -x because it’s facing down so the answer is A

Answer:

Option A. f(x) = -(x - 1)² - 1

Step-by-step explanation:

After the transformation of g(x) = x², vertex of the red parabola f(x) is (2, -1).

Therefore, equation of the parabola in the vertex form will be

f(x) = (x - 2)² - 1

Since opening of the parabola is downwards so the function will be

f(x) = - (x - 2)² - 1

This function matches with option A.