Type the correct answer in each box. Use numerals instead of words.
Consider this system of linear equations.
4x - 3y = -8
3x + 2y = -6

The solution to this system is ( , )

Answer:

[tex]sin(theta) = \frac{5}{13} [/tex]

Answer:

66 because 10 percent of 60 is 6 so add 60 and 6

The option that interchanges the hypothesis with the conclusion is the Converse.

In logic and mathematics, the Converse of an if-then statement switches the positions of the hypothesis (the "if" part) and the conclusion (the "then" part).

It is formed by flipping the original statement.

For example, let's consider the statement: "If it is raining, then the ground is wet."

The hypothesis is "it is raining," and the conclusion is "the ground is wet."

The Converse of this statement would be: "If the ground is wet, then it is raining."

Here, the positions of the hypothesis and the conclusion are interchanged.

It's important to note that the Converse is not always true.

In some cases, the original statement and its converse may have different truth values.

A statement and its converse can be both true, both false, or one true while the other false.

The Converse is a distinct logical operation from other concepts such as the Biconditional and the Inverse.

The Biconditional establishes a two-way relationship between two statements, while the Inverse negates both the hypothesis and the conclusion of the original statement.

Therefore, the option that interchanges the hypothesis with the conclusion is the Converse.

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Answer: Converse

Step-by-step explanation: Took the exam answer above correct

The height of the triangle is 6 inches and the base of the triangle is 30 inches.

Let's denote the height of the triangle as h inches. According to the given information, the base of the triangle is 6 inches more than 4 times the height, which can be expressed as 4h + 6 inches.

The formula for the area of a triangle is given by the formula A = (1/2) * base * height. Substituting the given values, we have:

90 = (1/2) * (4h + 6) * h

To solve for h, we can first multiply both sides of the equation by 2 to eliminate the fraction:

180 = (4h + 6) * h

Next, we can distribute the h on the right-hand side:

[tex]180 = 4h^2 + 6h[/tex]

Rearranging the equation to form a quadratic equation in standard form:

[tex]4h^2 + 6h - 180 = 0[/tex]

Now, we can solve this quadratic equation for h using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:

The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:

[tex]x = (-b ± \sqrt{(b^2 - 4ac)) / (2a)}[/tex]

In our equation, a = 4, b = 6, and c = -180. Plugging in these values, we get:

[tex]h = (-6 ± \sqrt{(6^2 - 4 * 4 * -180)} ) / (2 * 4)[/tex]

Simplifying further:

[tex]h = (-6 ± \sqrt{(36 + 2880)} ) / 8h = (-6 ± \sqrt{(2916)} ) / 8[/tex]

h = (-6 ± 54) / 8

Now we can find the two possible values for h:

h1 = (-6 + 54) / 8 = 48 / 8 = 6

h2 = (-6 - 54) / 8 = -60 / 8 = -7.5

Since height cannot be negative in this context, we discard the solution h2 = -7.5.

So, the height of the triangle is 6 inches.

Now, we can use this value of h to find the base of the triangle:

Base = 4h + 6 = 4 * 6 + 6 = 24 + 6 = 30 inches.

So, the height of the triangle is 6 inches and the base of the triangle is 30 inches.

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The slope from the table is greater than the slope from the graph hence the table shows a greater rate.

The slope of a graph is the measure of how steep a line is. It is the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. Mathematically, slope is represented as:

Slope (m) = (change in y)/(change in x)

The slope from the table is;

y2 - y1/x2 - x1

m = 42 - 30/7 - 5

= 6

The slope from the graph is;

8 - 0/1.5 - 0

m = 5.33

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The left-hand side simplifies to 14, and the right-hand side is also 14. Therefore, the equation is true when m = 4.

"LHS = RHS" stands for "left-hand side equals right-hand side". It is a notation commonly used in mathematics to show that two expressions are equal to each other.

In mathematics, to substitute means to replace a variable or expression in an equation or function with a specific value or expression.

To substitute the value 4 for m in the given equation, we replace every occurrence of m:

m + 2(m + 1) = 14

4 + 2(4 + 1) = 14

4 + 2(5) = 14

4 + 10 = 14

14 = 14

14 is the result of simplifying the left and right sides, respectively. Consequently, when m = 4, the equation is accurate.

So, the value 4 is a solution to the given equation.

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There are 100 cookies.

To find the number of cookies, we can set up a proportion using the given ratio of cookies to glasses of milk, which is 4:1. Let x be the number of cookies:

4/1 = x/25

Now, cross-multiply and solve for x:

1 * x = 4 * 25

x = 100

(10) The value that will make the equation a perfect square is 25.

(11) The value that will make the equation a perfect square is 64.

(12) The value that will make the equation a perfect square is 400.

(13) The value that will make the equation a perfect square is 6.25.

To make a perfect square trinomial of the form x² + bx + c, we need to add (b/2)² to both sides.

the perfect square is calculated as;

x² + 10x + __

b = 10,

(b/2)² = 25

the perfect square is calculated as;

x² - 16x + __

b = -16

(b/2)² = 64

the perfect square is calculated as;

x² + 40x + __

b = 40

(b/2)² = 400

the perfect square is calculated as;

x² + 5x + __

b = 5

(b/2)² = 6.25

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The cube root function represented by the graph is h(x) = ∛(x + 3) - 2.

The parent cube root function is f(x) = ∛x

If we translate the parent cube root function 3 units to the left, this means that we replace x with (x + 3) in the function.

This results in the new function g(x) = ∛(x + 3). So, for any input value of x, the output value of g(x) is the cube root of (x + 3).

Similarly, if we translate the parent cube root function 2 units down, this means that we subtract 2 from the function.

So, the new function h(x) = ∛(x + 3) - 2.

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The condensed form of the expression abc x abc x abc is (abc)^3

When we have the same base raised to different exponents that are being multiplied together, we can simplify or condense the expression by adding the exponents.

In this case, we have the same base "abc" being raised to the exponent of 1 three times, so we can write it as:

abc x abc x abc

To condense this expression, we add the exponents 1+1+1=3, and write it as:

(abc)^3

So, the condensed form of the expression "abc x abc x abc" is "(abc)^3".

This is an example of the exponent rule for multiplying powers with the same base.

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Therefore, Janelle would need 1872 square inches of plywood to make the chest.

A square inch (sometimes known as an in2 or sq. in.) is a unit of area measurement. A square with sides that are one inch long has an area of one square inch: Two lengths are used to measure a square area.

The areas of all the sides must be added up in order to determine the surface area of the chest. For instance, if we use 1/2 inch plywood and the chest is 24 inches by 12 inches by 18 inches, the surface area of the chest would be:

Top and bottom: 2 * (24 inches * 12 inches) = 576 square inches

Front and back: 2 * (18 inches * 12 inches) = 432 square inches

Sides: 2 * (24 inches * 18 inches) = 864 square inches

Total surface area = 576 + 432 + 864 = 1872 square inches

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The balance in the account after the given period is [tex]\$6,872.74[/tex]  

we know that

The compound interest formula is equal to  

[tex]\text{A}=\text{P}(1+\frac{\text{r}}{\text{n}})^{\text{nt}}[/tex]

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]\text{t}= 8 \ \text{years}[/tex]

[tex]\text{P}=\$4,000[/tex]

[tex]\text{r}=0.07[/tex]

[tex]\text{n}=1[/tex]

substitute in the formula above

[tex]\text{A}=\$4,000(1+\frac{0.07}{1})^{1\times8}=\$6,872.74[/tex]  

The function with y-intercept as 1 is h(x) = 0.5(2)ˣ + 0.5.

The y-intercept is the point where the graph intersects the y-axis. In other words, the y-intercept of a function is the value of y when x = 0.

Therefore, let's find the function with y-intercept as 1.

Hence,

h(x) = 0.5(2)ˣ + 0.5

Let's make x = 0 to check if the value of y = 1

Therefore,

h(x) = 0.5(2)ˣ + 0.5

h(0) = 0.5(2)⁰ + 0.5

h(0) = 0.5(1) + 0.5

h(x) = 0.5 + 0.5

h(x) = 1

Therefore, the function with y-intercept as 1 is h(x) = 0.5(2)ˣ + 0.5

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Answer:

To solve this problem, we can use the concept of direct variation, which states that two quantities vary directly with each other if they can be expressed as y = kx, where y is the dependent variable, x is the independent variable, and k is a constant of variation.

In this case, the distance traveled is the dependent variable and the speed is the independent variable. We are given that the distance traveled is 17.5 miles when the time (or speed) is 15 minutes.

So, we can set up the proportion:

distance / time = constant

17.5 miles / 15 minutes = k

Solving for k, we get:

k = 17.5 / 15

k = 1.16667 (rounded to 5 decimal places)

Now that we have the constant of variation k, we can use it to find the distance traveled in 2 hours (which is equivalent to 2 hours * 60 minutes/hour = 120 minutes).

distance = k * time

distance = 1.16667 * 120

distance = 139.99964 miles (rounded to 5 decimal places)

So, the correct answer is C) 140 miles, as it is the closest rounded value to the calculated distance of 139.99964 miles.

The interval(s) for which the function is decreasing are (3, 1) and (4, ∝)

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

The graph

The interval(s) for which the function is decreasing is when

As x increases, the function values decreases

Using the above as a guide and examining the graph, we have the following:

The function is decreasing at (3, 1) and (4, ∝)

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The probability that the science teacher trips over the cords for the first time during the 4th period of the day is 0.0279.

A discrete probability distribution has countable alternative values for the random variable and a stated probability for each one. Since the potential values are 0, 1, or 2, and the probability of each conceivable value can be determined, the probability distribution of the number of heads acquired after two coin flips is an example of a discrete probability distribution.

In contrast, a continuous probability distribution has a continuous range of possible values for the random variable and a probability of zero for any given value.

Given that, the probability of tripping is given as: 0.35.

Now, the probability of tripping on the 4th period is given by:

[tex]P(X=k) = (1-p)^{(k-1)} * p[/tex]

Now, for k = 4 and p = 0.35 we have:

[tex]P(X=4) = (1-0.35)^{(4-1)} * 0.35[/tex]

P(X=4) = 0.0279

Hence, the probability that the science teacher trips over the cords for the first time during the 4th period of the day is 0.0279.

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2nd and 3rd scatterplot do not suggest a linear relationship between x and y.

What is scatterplot?

A scatter plot is a particular type of plot or mathematical diagram by using Cartesian coordinates to display values for typically two variables for a set of values. It represents the correlation between two sets of data which may be linear or non linear sometimes strongly positive linear sometimes it may be curvilinear sometimes it may be null.

In the first plot it visibly showing a graph for straight line that is strong positive linear scatter plot. Same for the last but there is a little difference that it is negative linear scatter plot.

For the second one there is a null scatter plot. So there is no correlation.

For the 3rd graph there is a curvilinear relation in the scatterplot.

Hence, 2nd and 3rd scatterplot do not suggest a linear relationship between x and y.

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Answer:

Step-by-step explanation:

125 pounds decreased by 4%  it would be 120 because 4% of 125 is 5, so you subtract 5 from 125 and then you get 120.

Answer:

Your late fee is $13.13 (15% of $87.50).

Your past due balance plus the late fee equals $100.63 ($87.50 + $13.13).

Adding the new charges of $75.00 to $100.63, your new total is $175.63.

Therefore, your new total is $175.63.

Answer:

1 pound of jelly beans cost $1.75 , 1 pound of trail mix cost $3.75

Step-by-step explanation:

let j represent 1 pound of jelly beans and t represent 1 pound of trail mix , then

5j + 3t = 20 → (1)

7j + 9t = 46 → (2)

multiplying (1) by - 3 and adding to (2) will eliminate t

- 15j - 9t = - 60 → (3)

add (2) and (3) term by term to eliminate t

(7j - 15j) + (9t - 9t) = 46 - 60

- 8j + 0 = - 14

- 8j = - 14 ( divide both sides by - 8 )

j = [tex]\frac{-14}{-8}[/tex] = 1.75

substitute j = 1.75 into either of the 2 equations and solve for t

substituting into (1)

5(1.75) + 3t = 20

8.75 + 3t = 20 ( subtract 8.75 from both sides )

3t = 11.25 ( divide both sides by 3 )

t = 3.75

then

cost of 1 pound of jelly beans = $1.75

cost of 1 pound of trail mix = $3.75

Answer:

Cost for each pound of jelly beans:  $1.75

Cost for each pound of trail mix:  $3.75

Step-by-step explanation:

Define the variables:

Using the given information and defined variables, create a system of equations:

[tex]\begin{cases}5J+3T=20\\7J+9T=46\end{cases}[/tex]

To solve the system of equations, multiply the first equation by 3 to create a third equation:

[tex]5J \cdot 3+3T \cdot 3=20\cdot 3[/tex]

[tex]15J+9T=60[/tex]

Subtract the second equation from the third equation to eliminate the term in T:

[tex]\begin{array}{crcrcl}&15J & + & 9T & = & 60\\\vphantom{\dfrac12}- & (7J & + & 9T & = & 46)\\\cline{2-6}\vphantom{\dfrac12} &8J&&&=&14\end{array}[/tex]

Solve the equation for J by dividing both sides by 8:

[tex]\dfrac{8J}{8}=\dfrac{14}{8}[/tex]

[tex]J=1.75[/tex]

Therefore, the cost of each pound of jelly beans is $1.75.

To find the cost of one pound of trail mix, substitute the found value of J into one of the original equations and solve for T.

Using the second equation:

[tex]7(1.75)+9T=46[/tex]

[tex]12.25+9T=46[/tex]

[tex]12.25+9T-12.25=46-12.25[/tex]

[tex]9T=33.75[/tex]

[tex]\dfrac{9T}{9}=\dfrac{33.75}{9}[/tex]

[tex]T=3.75[/tex]

Therefore, the cost of each pound of jelly beans is $3.75.

Total stored energy = (1/625) ∞

Voltage, also known as electric potential difference, is the measure of the electric potential energy per unit of charge in an electric circuit. It is the force that drives the electric charge in a circuit, similar to how pressure drives water through a pipe. Voltage is measured in volts (V) and is usually represented by the symbol "V". Voltage can be either positive or negative, depending on the direction of current flow and the orientation of the voltage source.

A. The voltage across an inductor is proportional to the time derivative of the current through it, according to Faraday's law of electromagnetic induction. This can be expressed mathematically as:

v(t) = L di/dt

where v(t) is the voltage across the inductor, L is the inductance in henries, and di/dt is the time derivative of the current through the inductor.

In this case, we have [tex]v(t) = 8e^{(-4t)[/tex] V and L = 250 H. Integrating both sides of the above equation with respect to time gives:

∫v(t) dt = L ∫di/dt dt

∫[tex]8e^{(-4t)} dt = 250[/tex] ∫di/dt dt

[tex]-2e^{(-4t)[/tex]= 250i(t) + C

where C is the constant of integration. We can assume that the initial current is zero, so at t = 0, i(0) = 0. This means that C = -2. Substituting this into the equation above, we get:

[tex]-2e^{(-4t)[/tex]= 250i(t) - 2

Solving for i(t), we get:

i(t) = (2/250) [tex]- (2/250)e^{(4t)[/tex]

B. The power absorbed by an inductor is given by:

P = i² R

where P is the power, i is the current, and R is the resistance of the circuit. In an ideal inductor, the resistance is zero, so the power absorbed is also zero.

However, the energy stored in an inductor can be calculated using the following formula:

E = 1/2 L i²

where E is the energy stored, L is the inductance, and i is the current.

In this case, we have L = 250 H and i(t) = (2/250) [tex]- (2/250)e^{(4t)[/tex]Substituting these values into the above equation, we get:

E = 1/2 (250) [(2/250) [tex]- (2/250)e^{(4t)]^2[/tex]

Simplifying this expression, we get:

E = (1/625) [tex]- (2/625)e^{(4t)[/tex]+ (2/625)e^(8t)

To determine the total stored energy, we need to integrate this expression over the interval 0 to infinity, since the voltage and current are given for all values of t. This gives:

Total stored energy = ∫E dt from 0 to infinity

Total stored energy = (1/625) ∫1 dt from 0 to infinity[tex]- (2/625) ∫e^{(4t)[/tex]dt from 0 to infinity + (2/625) ∫e^(8t) dt from 0 to infinity

Total stored energy = (1/625) ∞ [tex]- (2/625) [1/4 e^{(4t)][/tex]from 0 to infinity + (2/625) [1/8 e^(8t)] from 0 to infinity

Since the integrals involving exponential functions go to infinity as t goes to infinity, these terms become zero. Therefore, we are left with:

Total stored energy = (1/625) ∞

which is an infinite value. This is because the energy stored in an inductor is not finite, but rather is dependent on the magnetic field generated by the inductor, which can extend infinitely far.

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Step-by-step explanation:

when we are supposed to find each degrees of a certain angle on an equilateral triangle all we have to know is that a triangle is equal to 180° there for each angle or each line is equal to 180° / 3

Answer:

b. parallelogram

Step-by-step explanation:

The figure cannot be square because a square has four congruent sides and four right angles, and this figure does not have either of those properties.

The figure cannot be a triangle because a triangle has only three vertices, and this figure has four vertices.

The figure cannot be a trapezoid because a trapezoid has at least one pair of parallel sides, and it is not clear from the given information whether any of the sides are parallel.

The figure could be a parallelogram, which is a quadrilateral with opposite sides parallel. To determine whether this is the case, we can check whether the slopes of opposite sides are equal. Here are the slopes of the sides:

AB: (4-1)/(1-(-4)) = 3/5

BC: (-1-4)/(6-1) = -5/5 = -1

CD: (-4-(-1))/(1-6) = 3/5

DA: (1-(-4))/(-4-1) = -5/5 = -1

We can see that the slopes of opposite sides AB and CD are equal, and the slopes of opposite sides BC and DA are equal. Therefore, the figure is a parallelogram.

The figure cannot be a kite because a kite is a quadrilateral with two pairs of adjacent congruent sides, and this figure does not have that property.

So the answer is: b. parallelogram.

The three statements that are true about the function and its graph are:

The graph of the function is a parabola.

The graph opens downwards, since the coefficient of x² is positive.

The graph contains the point (0, 12), which can be obtained by substituting x=0 in the function.

To check the other statements:

To find f(-10), we substitute x=-10 in the function:

f(-10) = 1/5*(-10)² - 5*(-10) + 12 = 82. So the statement "The value of f(–10) = 82" is true.

To check if the graph contains the point (20,-8), we substitute x=20 in the function:

f(20) = 1/5*(20)² - 5*(20) + 12 = -68. This means the point (20,-8) does not lie on the graph of the function.

To check if the graph contains the point (0,0), we substitute x=0 in the function:

f(0) = 1/5*(0)² - 5*(0) + 12 = 12. This means the point (0,0) does not lie on the graph of the function.

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Answer:

Okay, based on your previous question and the analysis, the 3 statements that are true about the function f(x) = x2 – 5x + 12 and its graph are:

   The graph of the function is a parabola.

   The graph contains the point (0, 0).

So the options you should select are:

2) The graph of the function is a parabola.

   The graph contains the point (0, 0).

Let me know if selecting options 2 and 5 makes sense! I can provide any additional details or clarification if needed.

Please let me know if you have any other questions! I'm happy to help explain any other concepts related to this quadratic function and its graph.

Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 .The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).

Okay, just to reiterate, based on the previous analysis, the 3 statements that are TRUE about the quadratic function f(x) = x2 – 5x + 12 and its graph are:

   The graph of the function is a parabola. (true)

   The graph contains the point (0, 0). (true)

   The graph of the function opens down. (false, unknown without seeing graph)

   The value of f(–10) = 82 (false)

   The graph contains the point (20, –8). (false)

So you should select options:

2) The graph of the function is a parabola.

   The graph contains the point (0, 0).

Please let me know if selecting these 3 options makes sense and matches the analysis. I can re-explain anything if needed.

Your selected options should be:

2) The graph of the function is a parabola.

   The graph contains the point (0, 0).

   The graph of the function opens down.

Let me know if these look correct or if you have any other questions! I'm happy to help explain further or go over any part of the analysis.

Please select options 2, 5 and 3 as the statements that are true about the quadratic function and its graph.

Step-by-step explanation:

Answer:

inflationary expenditure gap of $500

Step-by-step explanation:

At AE2 there is an inflationary expenditure gap of $500 (assuming full-employment output is $2000). The fiscal authority could increase taxes or decrease expenditures, which will shift the aggregate expenditures schedule down to AE0.

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Answer:

the required answer is √5-√6