Don’t mind my college name, I’m really in 8th grade and I’m really frustrated in this one.

Answer:

The total length of the road after the crew has worked 31 days is 183 miles.

Step-by-step explanation:

As given

A construction crew is lengthening a road.

The road started with a length of 59 miles, and the crew is adding 4 miles to the road each day.

let L represent the total length of the road (in miles).

let D represent the number of days the crew has worked.

Than the equation becomes

L = 59 + 4D

Now find out the total length of the road after the crew has worked 31 days.

D = 31 days

Put in the equation

L = 59 + 4 × 31

  = 59 + 124

L  = 183 miles

Therefore the total length of the road after the crew has worked 31 days is 183 miles.

Answer:

Option C is correct.

The value of x nearest to tenth is, 21.4 units

Step-by-step explanation:

In a given right angle triangle;

by definition of tangent ratio i,e   [tex]\tan \theta = \frac{opposite side}{Adjacent side}[/tex]

[tex]\tan 25^{\circ} = \frac{10}{x}[/tex]

[tex]0.46630765815 = \frac{10}{x}[/tex]

or

[tex]x = \frac{10}{0.46630765815} = 21.4450692[/tex] units

Therefore, the value of x nearest to tenth is, 21.4 units

Answer:

-2

Step-by-step explanation:

3.3÷(0.8−3)−0.5

First think of PEMDAS

So first do parenthese

(0.8-3)=-2.2

3.3÷-2.2-0.5

Now do division

3.3/-2.2=-1.5

and now subtraction

-1.5-0.5=-2

Cos(y-z) = Cos(z-24)

You have two equations in three unknowns, so no solution for the unknowns is possible.

The tangent equation tells you ...

... tan(z -24) = tan(y -z)

... z -24 = y -z . . . . . . take the arctangent

... cos(y -z) = cos(z -24) . . . . take the cosine

Answer:

18 cm

Step-by-step explanation:

The length of the median is the average of the two base lengths:

... (24 cm + 12 cm)/2 = 18 cm

Answer:

D

Step-by-step explanation:

a) correct is 3/4.5=4/6; b) correct is 3.2/2.4=4/3; c) correct is 4/3.2=3/2.4; d) this is correct answer.

Answer:

19 yards

Step-by-step explanation:

A square has 4 equal sides, thus its area is given by the formula below.

[tex]\boxed{\text{Area of square}=\text{side}^2}[/tex]

Substitute the area of the square into the formula:

361= side²

Square root both sides:

Length of each side

= [tex]\sqrt{361}[/tex]

= 19 yards

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Answer:

See below

Step-by-step explanation:

The values in the table change by $3.80 from one line to the next. Since each change from line to line changes in number of photos by 20, the average cost per photo is $3.80/20 = $0.19. There is apparently a $5.80 -3.80 = $2.00 shipping charge for numbers of photos in the range shown in the table.

Thus, the piecewise function has 3 pieces:

for x < 100: $2.00 + 0.19x

for x < 200: $4.50 + 0.17x

for x ≥ 200: $0.15x

This could be written as ...

[tex]C(x)=\left\{\begin{array}{rcl}\$2.00+0.19x&\text{for}&0\le x<100\\\$4.50+0.17x&\text{for}&100\le x<200\\\$0.15x&\text{for}&x\ge 200\end{array}\right.[/tex]

A point belongs to the x axis if its y coordinate equals zero.

The points on a graph are in the form [tex] (x,f(x)) [/tex], so these points are on the x axis if and only if [tex] f(x)=0 [/tex]

In this case, we have

[tex] f(x) = 0 \iff x^2+14x+49=0 [/tex]

You can observe that your expression is actually a squared binomial: using

[tex] (a+b)^2 = a^2+2ab+b^2 [/tex]

you can notice that

[tex] (x+7)^2 = x^2+14x+49 [/tex]

So, you have

[tex] x^2+14x+49=0 \iff (x-7)^2 = 0 \iff x=7 [/tex]

Now, how we decide if this function "touches" or "passes through" the x-axis at x=7? Well, since our function is a square, it is never negative. So, this graph can't cross the x-axis, but rater touch it from above. The parabola has a U shape, and the point of minimum lies on the x axis.

So, the graph touches the x axis at x=7.

The graph of the function f(x)=x^2+14x+49 is a parabola that touches the x-axis at -7, it does not pass through it because the root of the equation -7 is of multiplicity 2.

The function f(x)=x^2+14x+49 is a quadratic function, which when factorized becomes f(x) = (x+7)^2. This means that the graph of the function touches the x-axis at -7, but does not pass through it because the root of this equation -7 is of multiplicity 2. Hence, the correct answer is B: The graph touches the x-axis at -7.

To visualize this, remember that a quadratic function like this one forms a parabola. The point where the parabola intersects or touches the x-axis corresponds to the solution(s) of the equation. In this case, because there's only one solution (x=-7), the parabola just touches the x-axis at this point, but doesn't cross it.

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Answer:

2x³y

Step-by-step explanation:

Put the coefficient first; combine the exponents of repeated variables; write the expression with the variables in alphabetical order (not essential, but it lends consistency).

= 2·x^(1+2)·y

= 2x^3·y

To write the expression xycdot 2x² as a monomial, multiply the coefficients and add the exponents of like terms, resulting in 2x³y.

When writing the expression xy cdot 2x²as a monomial in standard form, you should apply the associative property of multiplication and combine like terms. To do this, multiply the coefficients together and add the exponents of the like bases.

Firstly, the coefficients 1 (implied for xy) and 2 should be multiplied, giving us 1 cdot 2 = 2. Then, combine the variables by adding the exponents: x¹cdot x² (since x is equivalent to x¹) becomes x⁽¹⁺²⁾, which simplifies to x³. As there is only one instance of y in the expression, its exponent remains 1. Therefore, the final expression in standard form is 2x³y.

the simplified expressions are:

1. [tex](2/3) * x^2 * (1/y) * (1/z^7)[/tex]

2. [tex](3/2) * x^2 * (1/2) * y^2 * (1/2) * z^4[/tex]

3. [tex](2/3) * (x^2 / y) * (1/z^7)[/tex]

4. [tex](2/3x^2) * yz[/tex]

5. [tex](2x^4 * y) / (3z)[/tex]

Let's simplify each of the given expressions using properties of exponents:

1. [tex](2x^4 * y^-4 * z^-3) / (3x^2 * y^-3 * z^4)[/tex]

To simplify this expression, you can use the properties of exponents that state when you divide two terms with the same base, you subtract the exponents:

[tex](2x^4 / 3x^2) * (y^-4 / y^-3) * (z^-3 / z^4)[/tex]

Now, simplify each term separately:

[tex](2/3) * (x^(4-2)) * (y^(-4-(-3))) * (z^(-3-4))[/tex]

[tex](2/3) * x^2 * y^(-1) * z^(-7)[/tex]

The simplified expression is

[tex](2/3) * x^2 * (1/y) * (1/z^7)[/tex]

2. [tex](3x^2 * y^2 * z^4) / 2[/tex]

To simplify this expression, simply divide each term by 2:

[tex](3x^2 / 2) * (y^2 / 2) * (z^4 / 2)[/tex]

The simplified expression is:

[tex](3/2) * x^2 * (1/2) * y^2 * (1/2) * z^4[/tex]

3. [tex](2x^2) / (3y * z^7)[/tex]

To simplify this expression, divide each term in the numerator by 3y and each term in the denominator by 3y:

[tex](2x^2) / (3y * z^7) = (2x^2 / 3y) * (1 / z^7)[/tex]

The simplified expression is:

[tex](2/3) * (x^2 / y) * (1/z^7)[/tex]

4. [tex](2yz) / (3x^2)[/tex]

To simplify this expression, divide each term in the numerator by 3x^2:

[tex](2yz) / (3x^2) = (2 / 3x^2) * yz[/tex]

The simplified expression is:

[tex](2/3x^2) * yz[/tex]

5. [tex](2x^4 * y) / (3z)[/tex]

This expression is already in a relatively simple form, and there are no common factors to further simplify it.

So, the simplified expressions are:

1. [tex](2/3) * x^2 * (1/y) * (1/z^7)\\[/tex]

2. [tex](3/2) * x^2 * (1/2) * y^2 * (1/2) * z^4[/tex]

3.[tex](2/3) * (x^2 / y) * (1/z^7)[/tex]

4. [tex](2/3x^2) * yz[/tex]

5. [tex](2x^4 * y) / (3z)[/tex]

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Use the definition of conditional probability:

[tex]P(\text{sports}\mid\text{senior})=\dfrac{P(\text{sports AND senior})}{P(\text{senior})}[/tex]

We know that 0.10 of students belong to both categories, and that 0.25 of students are seniors, so

[tex]P(\text{sports}\mid\text{senior})=\dfrac{0.10}{0.25}=0.40[/tex]

Answer:

0.40

Step-by-step explanation:

Answer:

9 days.

Step-by-step explanation:

If the company produced 20 more items than 40 items each day, then it must have produced 60 items each day.

Though you're probably expected to write an equation, it's easiest to solve this through educated guess and check.

If there were 120 items to be produced, the company would be required to do it in 3 days (120 items, 40 items/day) but completed it in 2 days (120 items, 60 items/day). In this case, they finished their order 1 day early. But the problem states that they finished 3 days early. So we guess 3 times 120 items, or 360 items. Checking this, they should have finished their order in 9 days (360 items, 40 items/day) but they finished in 6 days (360 items, 60 items/day). 6 is three less than 9, so our guess of 360 items was correct. We have shown that the company should have finished the order in 9 days.

If you had to use an equation:

Let the desired number of days be x. Then, the company finished its order in x - 3 days. Since number of items produced is the number of days times items per day, and it doesn't change:

number of items = 40 items/day * x days = 60 items/day * (x - 3) days

40x = 60(x - 3) = 60x - 180

180 = 20x

x = 9

9 days is the desired answer.

Answer:

9

Step-by-step explanation:

Answer:

D. x = 3 1/8

Step-by-step explanation:

x + 7/8 = 4

The first step is to subtract 7/8 from each side

x + 7/8 - 7/8 = 4 - 7/8

x = 4 - 7/8

We need to borrow from the 4. It become 3 8/8

x = 3 8/8 - 7/8

x = 3 1/8

Answer:

I believe the answer would be D.

Step-by-step explanation:

The answer, I believe, is an Equilateral triangle.

In geometry, an equilateral triangle is a triangle in which all three sides are equal. In the familiar Euclidean geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each other and are each 60°.

Answer:

f(x) = 60 + 15n

Step-by-step explanation:

if the start off amount is 60, so we can simply start it with 60 + ...

If she gets 15 for each customer, and the amount of customers is equal to n, then this can be written by 15n ( 12 * n )

Simply put these two parts together:

60 + 15n

So in a function:

f(x) = 60 + 15n

Answer:

C none of the above

Step-by-step explanation:

-7 / -f

We know that a negative divided by a negative is a positive

-1/-1  * 7/f

1* 7/f

7/f

D. an = 14 - 1.5n

Selection D is the only one that works to give a1 = 12.5.

The explicit rule for the given sequence is option D, an = 14 - 1.5n, which indicates starting from 14, subtract 1.5 times the position of the term (n).

To determine the explicit rule for the given sequence 12.5, 11, 9.5, 8, 6.5, 5, we can observe that the sequence is decreasing by 1.5 each time. Knowing this, we can try to find a relationship between the position of each term (n) and its value (an).

Let's consider the first term when n=1. We need a starting point (initial value when n=1) that degreases by 1.5 for each subsequent term. We can see that the first term of the sequence (12.5) is 1.5 less than 14, so we subtract 1.5 from 14 to define the first term: 14 - 1.5*1 = 12.5. Thus, for any term n, the value would be 14 - 1.5*n.

Therefore, the correct explicit rule is given by option D: an = 14 - 1.5n.

y = -4.2x +34

The differences between adjacent y-values are -4.2 for all data points given, so the data is best modeled by a linear function with a slope of -4.2. The value for x=0 (the y-intercept) will be 4.2 higher than the value for x=1, so will be 34.

Thus the model can be ...

... y = -4.2x + 34

_____

Comment on the attached graph

The graph shows an attempt to model the data with a quadratic function (the first on your answer list). The result is that the x² coefficient is zero, and the model is the equation of a line (as shown above).

Answer:

Linear

Step-by-step explanation:

I got it from passing a quiz

the tale-tell fellow is the base of the exponent ˣ.

if that number is less than 1, is a decay factor, if it's more than 1, is growth.

1.09 is cleary more than 1, so is growth, at what rate?

[tex]\bf \qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &P\\ r=rate\to r\%\to \frac{r}{100}\dotfill &0.0r\\ t=\textit{elapsed time}\dotfill &t\\ \end{cases} \\\\\\ f(x)=4.7(1.09)^x\implies f(x)=4.7(1+\stackrel{\stackrel{r}{\downarrow }}{0.09})^x \\\\\\ r=0.09\implies \stackrel{\textit{converting it to percentage}}{r=0.09\cdot 100}\implies r=\stackrel{\%}{9}[/tex]

Exponential functions are mostly used to represent growth of population.

The true option is: (d)  Exponential growth function; 9%

The function is given as:

[tex]\mathbf{f(x) = 4.7 \cdot 1.09^x}[/tex]

An exponential function is represented as:

[tex]\mathbf{f(x) = a \cdot b^x}[/tex]

By comparison:

[tex]\mathbf{b = 1.09}[/tex]

When b is greater than 1, then the function is a growth function.

Next, we calculate the constant percentage rate of growth (r)

If b is greater than 1, then:

[tex]\mathbf{b = 1 + r}[/tex]

Substitute 1.09 for b

[tex]\mathbf{1 + r = 1.09}[/tex]

Subtract 1 from both sides

[tex]\mathbf{r = 0.09}[/tex]

Express as percentage

[tex]\mathbf{r = 0.09 \times 100\%}[/tex]

[tex]\mathbf{r = 9\%}[/tex]

Hence, the growth rate is 9%

Hence, the true option is: (d)  Exponential growth function; 9%

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I like to use a little X diagram to work mixture problems like this. The constituent concentrations are on the left; the desired mix is in the middle, and the right legs of the X show the differences along the diagonal. These are the ratio numbers for the constituents. Reducing the ratio 32:8 gives 4:1, which totals 5 "ratio units". We need a total of 100 kg of alloy, so each "ratio unit" stands for 100 kg/5 = 20 kg of constituent.

That is, we need 80 kg of 60% alloy and 20 kg of 20% alloy for the product.

_____

Using an equation

If you want to write an equation for the amount of contributing alloy, it works best to let a variable represent the quantity of the highest-concentration contributor, the 60% alloy. Using x for the quantity of that (in kg), the amount of copper in the final alloy is ...

... 0.60x + 0.20(100 -x) = 0.52·100

... 0.40x = 32 . . . . . . . . . . .collect terms, subtract 20

... x = 32/0.40 = 80 . . . . . kg of 60% alloy

... (100 -80) = 20 . . . . . . . .kg of 20% alloy

Answer:

B. b = 11 3/5

Step-by-step explanation:

-3 2/5 + b = 8 1/5

The first step is to isolate b by adding 3 2/5 to each side

-3 2/5+ 3 2/5 + b = 8 1/5 + 3 2/5

b = 8 1/5 + 3 2/5

b = 8+3  + 1/5+2/5

b = 11  3/5

Answer:

34

Step-by-step explanation:

3 + 4 = 7

34 with reversed digits is 43

43 - 34 = 9

Answer:

y=7

Step-by-step explanation:

If you subtract 5 from each side it would be 2y-5=9. Add a 5 back to each side to be 2y=14. Divide each side by 2 to get y=7.

Answer:

k = -2

Step-by-step explanation:

The graph clearly shows the y-intercept of f(x) as being 4, and that of g(x) as being 2. Thus, g(x) = f(x) -2 = f(x) +k.

Subtracting f(x) from that equation, you get k = -2.

_____

Check

g(x) is displaced 3 units to the right of f(x). The slopes of both f(x) and g(x) are 2/3, so a displacement of 3 units right is equivalent to a displacement of 2 units down. k represents the vertical translation, so is -2.

The value of k is found by examining the vertical distance between the graphs of y=f(x) and y=g(x) at the same x-coordinate. Without the visual graphs or specific points, the exact value of k cannot be provided.

The student is asking about the relationship between two functions, where g(x) is related to f(x) by the addition of a constant k.

To find the value of k, one would typically examine the vertical distance between the two function graphs at any given x-coordinate, since g(x) = f(x) + k. Without the graphical information provided, it is not possible to determine the exact value of k.

However, typically if you have two functions with graphs that are vertically shifted versions of each other, and you know two corresponding points on each graph with integer coordinates, you can subtract the y-values of these points to find k.

x = 4; y = 9; length of a side = 5

Here, you're expected to use the fact that all of the sides of a square are the same length.

The left and right sides both have different expressions only in y, so it is convenient to equate them.

... y -4 = 2y -13

... 0 = y -9 . . . . . subtract the left side

... 9 = y . . . . . . . add 9

This tells us the side of the square (s) is ...

... s = y -4 = 9 -4

... s = 5

And we can use this to find x.

... 5 = 2x -3 . . . . equate the x-expression to the square side length

... 8 = 2x . . . . . . add 3

... 4 = x . . . . . . . . divde by the coefficient of x

x and y are 4 and 9; the square side length is 5.

The values of x and y are not given, so the length of the square cannot be determined.

To find the side lengths of the square, we first need to determine the values of x and y. However, the provided information does not give any equations or context to solve for x and y. Without additional information, it is not possible to find the values of x and y, and therefore, we cannot calculate the length of the square. If you have any additional information or equations, please provide them so that we can assist you further.

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Answer:

A. 1⁄2 < 3⁄4

Step-by-step explanation:

1/2   vs 3/4

Get a common denominator of 4

1/2 *2/2   vs 3/4

2/4   vs 3/4

2 is less than 3

2/4 < 3/4

1/2 < 3/4

Answer: The answer is c)5

Answer:

c) 5

Step-by-step explanation: