Match each system of linear equations with the graph of its solution, represented by the shaded region of the graph.

y ≥ 5x − 1
y ≥ -2x + 3
Graph shows system of inequalities. A line goes through (minus 2, 7), (0, 3), (2, minus 1). Another line goes through (minus 6, minus 1), (0, minus 1), (1, 4). Lines intersect at (0.5, 1.8) in quadrant 1 and region below intersection is shaded.
y ≤ 5x − 1
y ≥ -2x + 3
Graph shows system of inequalities plotted on a coordinate plane. A solid line goes through (0, 3) and (2, minus 1). Another solid line goes through (0, minus 1) and (1, 4). The region below first solid line and above second solid line is shaded.
y ≥ 5x − 1
y ≤ -2x + 3
Graph shows system of inequalities plotted on a coordinate plane. A solid line goes through (0, 3) and (2, minus 1). Another solid line goes through (0, minus 1) and (1, 4). The region above both the solid lines is shaded.
y ≤ 5x − 1
y ≤ -2x + 3

Answer: -1 Is the answer.

Answer:

index of m is -2

Step-by-step explanation:

any number or letter to the negatIve power(index) is the same as 1 divided by that number or letter to the positive index.

for example, 10^-2 = 1/10^2 and X^-4 is the same as 1/X^4.

The product of the rational expressions given is; (7x²-7x)/(x²-4)

The given rational expressions are;

Hence, the product of the two Rational Expressions can be evaluated as follows;

The product of the rational expressions given is therefore; (7x²-7x)/(x²-4)

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√7 + √9 is not equal to √7 + 9 because  different quantities are being added.

The square root of a number is a value that, when multiplied by itself, gives the original number.

From the information given, we have that the expression;

√7 + √9 involves adding the square root of 7 to the square root of 9.

Then, we can simply it as the the square root of 9 is 3

But then, the expression √7 + 9 involves adding the square root of 7 to the number 9.

Therefore, √7 + √9 is not equal to √7 + 9 because you're adding different quantities

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Answer:

Hey

Step-by-step explanation:

Answer:

Gross salary =G

Number of worked hours =x

Dollar per hour =$12

substitute the given data into the gross salary formula and simplify.

Gross salary = (number of worked hours)

G =(x) (12)

G =12x

Therefore, G(x) =12x

Hence the function is G(x) = 12x

Check the picture below.

The relative minimum point is B. Option B is the correct option.

What is the relative minimum?

The function's graph makes it simple to locate relative minima. It is the pivotal point in the function's graph. Relative minima are locations where the function's graph shifts from decreasing to increasing. A point that is lower than the points to its left and right is said to be at its relative minima.

The points of the graph function are A, B, C, D.

The lowest point among the given points on the graph is B.

Thus the relative minimum point is B.

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Set up your equation

4q + q = 315                      Add                                  (q = amount of quarters)

5q = 315                            Divide

q = 63                              

Therefore he has 63 quarters.

To find the amount of nickels, multiply 4 and 63

4 x 63 = 252

Therefore he has 63 quarters and 252 nickels.

I hope this helps! :)

   The line is positive because it is going upwards. The y-intercept is positive 3. It can be found by seeing where the line intercepts the y-axis. The slope of the line is 2 and it can be found by using "rise over run."

(I saw the image on another question you had asked. Have a nice day!)

Using the concept of exponential decay, the predicted number of people is  233,176,000

To predict the number of gas-powered cars on the road in 10 years, we'll apply the given annual decrease rate of 1.9% to the initial count of 286 million.

First, let's calculate the decrease rate per year:

Decrease rate = 1.9% = 1.9/100 = 0.019

Next, we'll calculate the predicted count after 10 years using the formula for exponential decay:

Predicted count = Initial count * (1 - Decrease rate)^Number of years

Substituting the values:

Predicted count = 286 million * (1 - 0.019)^10

Calculating the value:

Predicted count ≈ 286 million * (0.981)^10

Rounding the answer to the nearest whole number:

Predicted count ≈ 286 million * 0.816

Predicted count ≈ 233,176,000

Therefore, the best prediction for the number of people driving gas-powered cars in 10 years, based on the given information, is approximately 233,176,000.

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Any triangle's three interior angles add up to 180 degrees, according to the Triangle Sum Theorem.

Any triangle's three interior angles add up to 180 degrees, according to the Triangle Sum Theorem. m∠1+m∠2+m∠3=180∘.

Here,

According to the triangle sum theorem, a triangle's total angles equal 180°. Therefore, using the Substitution property

=> (3x)° + 90° + (x+10)° = 180°,

=>  m(A,B,C) = 180.

To find x, combine similar terms to get

=> 4x + 100 = 180. Then, using the subtraction condition of equality, convert => 13 1/2 to 80.

=> Finally, divide 80 by  5 ( 13 1/2) to find x.

The substitution property may be used to get the measure of the angle A, yielding mA = 5 ( 13 1/2) °.

When the expression is finally simplified, m < A = 66 2/3.

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The true statement about the function is C. function f and function g are not inverse because f{g(x)} = g{f(x)} .

An inverse function or an anti function, which can reverse into another function.In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by 'f' or 'F', then the inverse function is denoted by f-1 or F-1.

now the given functions are,

f(x) = √(2x + 2) and

g(x) = (x^2 -2)/2

Now,

f{g(x)} = f{(x^2 -2)/2}

         = √(2(x^2 -2)/2 + 2)

         = √ x^2 -2 + 2

f{g(x)} = √ x^2

f{g(x)} =  x

Now,

g{f(x)} = g{ √(2x + 2)}

         = (√(2x + 2)^2 -2)/2

         = (2x + 2) -2 /2

         = 2x/2

f{g(x)} = x

Here we see that ,

f{g(x)} = g{f(x)}

Hence f and g are not inverses.

∴The true statement about the function is C. function f and function g are not inverse because f{g(x)} = g{f(x)} .

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Answer:

(A)48

(B)volume of one of the small cubes is 1/64cm^3

c)3/4x1x1=3/4cm^3

Step-by-step explanation:

Answer:

Step-by-step explanation:

Fourth row is least accurate.

Answer:

125.7

Step-by-step explanation:

To round 125.671 to the nearest tenth consider the hundredths’ value of 125.671, which is 7 and equal or more than 5. Therefore, the tenths value of 125.671 increases by 1 to 7.

125.671 rounded to the nearest tenth = 125.7

The following table contains starting numbers close to 125.671 rounded to the nearest 10th.

Answer:

If a number has a decimal point, then the first digit to the right of the decimal point indicates the number of tenths.

Step-by-step explanation:

in the question, the number 125.671 the decimal is after 5 and before 6. so, the tenth place is 6 and it is greater than 5. we can round it to 125.7

The equation in terms of x that represents the given relationship is 114 = (1 + 3x) * (Width)

Let's break down the information given:

Height of the rectangular box = 7 ft

Length of the rectangular box = 1 ft longer than thrice the width (x)

Volume of the rectangular box = 798 ft³

To write an equation that represents the given relationship, we need to relate the length, width, and height to the volume.

The volume of a rectangular box is given by the formula: Volume = Length * Width * Height.

Given that the height is 7 ft, we can substitute this value into the equation.

Volume = (Length) * (Width) * (7)

Now, let's focus on the length. It is described as 1 ft longer than thrice the width.

Length = 1 + (3x)

Substituting this value into the equation, we have:

Volume = (1 + (3x)) * (Width) * (7)

Since the volume is given as 798 ft³, we can set up the equation as follows:

798 = (1 + (3x)) * (Width) * 7

Simplifying further, we get:

798 = 7 * (1 + 3x) * (Width)

Dividing both sides of the equation by 7, we have:

114 = (1 + 3x) * (Width)

Therefore, the equation in terms of x that represents the given relationship is:

114 = (1 + 3x) * (Width)

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Answer:

3/4

Step-by-step explanation:

tan C = opposite side/ adjacent side = AB / BC = 24 /32 = 3*8/ 4*8 = 3/4

Answer:

(-2,-4)

Step-by-step explanation:

Turning the point 180 degrees causes the point to be reversed, or upside down, therefore the numbers will become negative.

The value of x is equal to 8.

Similar figure are zoomed in or zoomed out (or just no zoom) version of each other. They are scaled version of each other, and by scale, we mean that each of their dimension(like height, width etc linear quantities) are constant multiple of their similar figure.

In the similar triangles, TRS similar to DBC

TS/ SR = DC/ CB

70 / (11x - 4) = 50 / 60

Using cross products

70 (60) = 50 (11x - 4)

Distribute

4200 = 550x - 200

550x = 4200 + 200

550x = 4400

x = 8

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Total cost of work in process Work in process inventory, ending=$1,320,000

The scenario dictates that the computation of the provided data be as follows:-

Buying raw materials will cost $1,800,000.

$20k is the opening stock of raw materials.

Raw material closing stock: $3,140,000.

Purchase of raw materials plus opening stock of raw materials minus closing stock of raw materials equals direct material used.

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\(~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$8.75\\ P=\textit{original amount deposited}\dotfill & \$1000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &\frac{1}{4} \end{cases} \\\\\\ 8.75 = (1000)(\frac{r}{100})(\frac{1}{4})\implies 8.75=\cfrac{10r}{4} \\\\\\ 8.75=\cfrac{5r}{2}\implies 17.5=5r\implies \cfrac{17.5}{5}=r\implies \stackrel{\%}{3.5}=r\)

Answer:

perimwter = 2(4x-6 + 2x+4) = 2 (6x-2) = 12x-4

We can see that the correct equation that can depict the problem is 3(d+17.20) = 782.07. Option D

We have to look at the problem that we have here. In the case of the question that we have been asked, we can see that for the problem that has been given here, it is clear that; Allison went on a business trip and stayed at a hotel for three nights. She paid a total of $782.07 for the room and to park her car.

If it is known that Each night, the hotel charged d dollars and $17.20 for parking. We can say that let the amount that is charged for the lodging be d and we have the equation as; 3(d+17.20) = 782.07.

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Answer:

c. 3^5

Step-by-step explanation:

hope this helps

The number 243 can be expressed in exponent form as 7³.

Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.

A) 243

Factors of 243 are

243 =7×7×7=7³

B) 33

Factors of 33 are

33 =3×11

C) 34

Factors of 34 are

34 =2×17

D) 35

Factors of 35 are

35 =5×7

Therefore, the number 243 can be expressed in exponent form as 7³.

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Answer: Barry's Swimwear sold a greater fraction of the bathing suits in stock as long as the store had fewer than 72 bathing suits in stock.

Step-by-step explanation:

Barry's Swimwear sold 15 out of an unknown number of bathing suits in stock, so we can express this fraction as 15/x, where x is the total number of bathing suits in stock at Barry's Swimwear. Similarly, Philip's Sun Wear sold 5 out of 72 bathing suits in stock, so we can express this fraction as 5/72.

To compare these two fractions, we need to express them with a common denominator. One way to do this is to find the least common multiple of the two denominators, which in this case is 72. To express 15/x with a denominator of 72, we can multiply both the numerator and the denominator by a factor of 72/x. This results in the fraction 15*(72/x)/72 = 15/x. Similarly, we can express 5/72 with a denominator of 72 by multiplying both the numerator and the denominator by a factor of 72/72, which results in the fraction 5*(72/72)/72 = 5/72.

Now that we have both fractions expressed with a common denominator of 72, we can compare them directly. 15/x is greater than 5/72 as long as x is less than 72. This means that Barry's Swimwear sold a greater fraction of the bathing suits in stock as long as the store had fewer than 72 bathing suits in stock.

Answer:

\(x^{4}-17x^{2} +16\) = (x -1)(x + 1)(x - 4)(x + 4)

Step-by-step explanation:

At first, let us find the first two factors of \(x^{4}-17x^{2} +16\)

∵ The sign of the last term is positive

∴ The middle signs of the two factors are the same

∵ The sign of the middle term is negative

∴ The middle signs of the two factors are negative

∵ \(x^{4}\) = x² × x² ⇒ first terms of the two factors

∵ 16 = -1 × -16 ⇒ second terms of the two factors

∵ x²(-1) + x²(-16) = -x² + -16x² = -17x² ⇒ the value of the middle term

∴ (x² - 1) and (x² - 16) are the factors of \(x^{4}-17x^{2} +16\)

Now let us factorize each factor

→ The factors of the binomial a² - b² (difference of two squares) are

   (a - b) and (a + b)

∵ x² - 1 is the difference of two squares

∴ Its factors are (x - 1) and (x + 1)

∵ x² - 16 is the difference of two squares

∴ Its factors are (x - 4) and (x + 4)

∵ (x -1), (x + 1), (x - 4), and (x + 4) are the factors of (x² - 1) and (x² - 16)

∵ (x² - 1) and (x² - 16) are the factors of \(x^{4}-17x^{2} +16\)

∴ (x -1), (x + 1), (x - 4), and (x + 4) are the factors of \(x^{4}-17x^{2} +16\)

∴  \(x^{4}-17x^{2} +16\) = (x -1)(x + 1)(x - 4)(x + 4)

Factoring an expression involves rewriting the expression in simpler forms

The factorized expression is (x - 4)(x + 4)(x - 1)(x + 1)

The expression is given as:

\(\mathbf{x^4 - 17x^2 + 16}\)

Express 17 as 1 + 16

\(\mathbf{x^4 - 17x^2 + 16 = x^4 - x^2 - 16x^2 + 16}\)

Factorize

\(\mathbf{x^4 - 17x^2 + 16 = x^2(x^2 - 1) - 16(x^2 - 1)}\)

Factor out x^2 - 1

\(\mathbf{x^4 - 17x^2 + 16 =(x^2 - 16)(x^2 - 1)}\)

Express 16 as 4^2, and 1 as 1^2

\(\mathbf{x^4 - 17x^2 + 16 =(x^2 - 4^2)(x^2 - 1^2)}\)

Apply difference of two squares

\(\mathbf{x^4 - 17x^2 + 16 =(x - 4)(x + 4)(x - 1)(x + 1)}\)

Hence, the factorized expression is (x - 4)(x + 4)(x - 1)(x + 1)

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Total amount spend by Mr. Josh is,

⇒ $7,978

We have to given that,

Mr. Josh spends $153 every week on gas to get to work.

Since, We know that,

1 year = 52.1429 weeks

Here, Mr. Josh spends $153 every week on gas to get to work.

Hence, Amount Mr. Josh spend annually to go to work is,

⇒ $153 × 52.1429

⇒ $7,978

Therefore, Total amount spend by Mr. Josh is,

⇒ $7,978

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The probability of the flights at the airlines at least 4 of the next 5 are overbooked from the given histogram is equal to 0.446.

Histogram is attached.

As given in the question,

Required histogram is attached.

From the attached histogram,

Histogram is attached.

The probability of 4 overbooked flights for the given airlines 'P (4) =  0.332

The probability of 4 overbooked flights for the given airlines 'P(5)' = 0.114

Required probability of at least 4 for the next 5 flights of the given airlines

= P ( x ≥ 4 ) upto next P(5)

= P(4) + P(5)

= 0.332 + 0.114

= 0.446

Therefore, the probability of at least 4 upto next 5 flights of the given airlines from the given histogram is equal to 0.446.

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Answer: Statement 1 is false.

Step-by-step explanation: 1 is false because all natural numbers, whole numbers, and integers are rationals.