the train traveled at an average speed of 48 miles per hour for the first 2 hours and at 60 miles an hour for the next hours. What was the train's average speed for the 6-hour trip? ( Average speed equals total miles divided by total time.)

Answer:

x = 4 ± [tex]\sqrt{19}[/tex]

Step-by-step explanation:

Given

x² - 8x = 3

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 4)x + 16 = 3 + 16

(x - 4)² = 19 ( take the square root of both sides )

x - 4 = ± [tex]\sqrt{19}[/tex] ( add 4 to both sides )

x = 4 ± [tex]\sqrt{19}[/tex]

Final answer:

To solve the equation x^2 - 8x = 3 by completing the square, we first rearrange the equation, add 16 to both sides to form a perfect square, and then take the square root of both sides resulting in the solution set {4 + √19, 4 - √19}.

Explanation:

Completing the Square Method

To solve the equation x2 − 8x = 3 by completing the square, follow these steps:

The solution set for the equation is {4 + √19, 4 − √19}.

Answer:

A.22

Step-by-step explanation:

Answer:

d. 19

Step-by-step explanation:

A matrix is an array of rectangular shape which consists of numbers, symbols, or expressions, arranged in rows and columns.

[tex]\begin{bmatrix}28&21&19\\17&24&15\\22&29&17\end{bmatrix}[/tex]

[tex]w_{1,3}[/tex] means element in first row third column. First row means Frank and third column means August.

So, the number of lawns mowed by Frank in August is

[tex]w_{1,3}=19[/tex]

Answer:

4/21

Step-by-step explanation:

⇒This question is on probability

⇒Number of boys=3

⇒Number of girls=4

⇒P(S)= 4+3=7

Probability for a girl to win is= 4/7

We have 3 awards a free movie ticket, a collectible poster, or a free popcorn

P(S)= 3

Probability of being awarded a free popcorn = 1/3

The probability that a girl will win free popcorn =

[tex]\frac{4}{7} * \frac{1}{3} = \frac{4}{21}[/tex]

Answer:

4/21

Step-by-step explanation:

Answer:

f(x) = (x + 2)(x - 5)(x - 6)

Step-by-step explanation:

given the zeros of f(x) are x = a, x= b and x = c, then the factors are

(x - a), (x - b) and (x - c)

The function is then the product of the factors

f(x) = (x - a)(x - b)(x - c)

Here zeros are x = - 2, x = 5 and x = 6, thus the factors are

(x + 2), (x - 5) and (x - 6), so

f(x) = (x + 2)(x - 5)(x - 6) ← in factored form

Final answer:

To create a polynomial with zeros at -2, 5, and 6, the factored form is (x + 2)(x - 5)(x - 6).

Explanation:

To write a polynomial function in factored form with zeros at −2, 5, and 6, we start by creating factors based on these zeros. Each zero corresponds to a factor of the polynomial where the variable x is set equal to the zero value. Therefore, the factors would be (x + 2), (x - 5), and (x - 6). We then multiply these factors together to get the polynomial.

The factored form of the polynomial is then (x + 2)(x - 5)(x - 6). If you wanted to write this polynomial in standard form, you would expand the factors to get x³ - 9x² + 4x + 60.

Answer:

∛x^4

Step-by-step explanation:

x^(4/3) = ∛x^4

Last option is the answer

For this case according to the order PEMDAS we have:

P: Perform the parenthesis calculations

E: Simplify exponential expressions

MD: Multiplications and divisions from left to right

AS: Addition and subtraction from left to right.

We have:

23 + 5 * 10÷2-33 + (11-8) =

23 + 5 * 10÷2-33 + 3 =

23 + 50÷2-33 + 3 =

23 + 25-33 + 3 =

48-33 + 3 =

15 + 3 =

18

Thus, the value of the expression is 18

ANswer:

18

This statement is true.

When you buy a share in a company, you are investing your money, and you may earn more money if the share’s value rises, or you may lose money if the share’s value falls.

Investing in a company by buying shares makes you a shareholder, with potential income from dividends and stock appreciation. However, it carries risk as there is no guarantee for profits. Diversification is a key strategy when investing in stocks to mitigate risks.

Buying shares in a company is a common method of investment, wherein you become a shareholder and own a part of the company's equity. As a shareholder, you have a claim to the company's assets and profits proportional to the amount of stock you own. There are two primary ways that shareholders can earn money from their investments. One way is through dividends, which are payments distributed from the company's profit to shareholders. The other way is through appreciation in the stock's value, as the company grows and becomes more profitable; this increases the stock's market price, and you can sell your shares for a profit. It's important to understand that purchasing stock does involve risk, as there is no guarantee of dividends or stock appreciation. However, for many, owning stock is preferred over other investments like bonds because of the potential for higher returns. Lastly, when buying stock, especially that of your employer, it's advisable to follow general rules of portfolio investing, such as diversification, not to expose yourself to undue risk.

-3+m/9=10

Add 3 to both sides:

m/9 = 13

Multiply both sides by 9:

m = 13 * 9

m = 117

Answer:

The proportional relationship between the number of pages (p) and the number of hours (h) is represented by the equation  

. Write the equation in standard form with a constant of proportionality greater than 1.

Step-by-step explanation:

The first blank is "division" and the second blank is "multiplying"

12 / (3) = 4

5 x 3 = 15

15 + 4 = 19

The student's equation 12 _ (7 - 4) + 5 _ 3 = 19 is solved by inserting addition after 12 and subtraction after 5, resulting in 12 + (7 - 4) + 5 - 3. Following correct order of operations, we get the desired result of 19.

The student has presented a mathematical equation with missing operations that needs to be solved to equal 19. To find the correct operations, we can see that 12 with an addition operation followed by 5 minus 3 gives us 14. Adding this to the original 12 gives us the desired result of 19. Hence, the missing operations are addition after the 12 and subtraction after the 5.

The equation now looks like 12 + (7 - 4) + 5 - 3 = 19. Here, we first perform the operation inside the parentheses, which is 7 - 4 = 3. Then, we substitute this result into the expression and proceed with the operations: 12 + 3 + 5 - 3. Next, we add the numbers together, which gives us 12 + 3 + 5 = 20, and finally deduct 3 to get 20 - 3 = 19.

This kind of problem teaches us the significance of operation placement within equations, as seen in different examples provided. Understanding the properties of arithmetic operations and the correct application of the order of operations (parentheses, exponents, multiplication and division, addition and subtraction) is crucial for solving such mathematical puzzles.

Answer:

All answers in the pic attached

Answer:

see explanation

Step-by-step explanation:

Given

[tex]\frac{x}{4}[/tex] > - 16 ( multiply both sides by 4 )

x > - 64

To show the solution on a number line

Place an open circle ( indicating x ≠ - 64 ) at - 64

greater than - 64 is to the right of - 64 , hence the direction of the shaded line points to the right of - 64

Tell me if you have troubles understanding something!

Answer:

- 160 I think

Step-by-step explanation

I think i'm right but there are

200 blocks and there are 40 left out so then i did 40 - 200 = -160

Answer:

C) The discriminant is 0.

Step-by-step explanation:

Since the graph of the quadratic equation has only one x-intercept, we can conclude that the quadratic has only one real root.

If a quadratic equation has only one real root, then the discriminant is 0

Check the picture below.

Answer:

See picture below.

Answer:

Graph??

Step-by-step explanation:

I can't really graph, but the answer to this is...

[tex]3x+2y=12\\\\2y=3x+12\\\\y=\frac{3}{2} x+6[/tex]

I divided all by 2 to get y

[tex]y=\frac{3}{2} +6\\\\(2,9) -- (x,y)[/tex]

ANSWER

P'(6,-1)

EXPLANATION

The mapping for a reflection in the line y=x is

The line y=x is the mirror line for a function and it's inverse.

[tex](x,y)\to (y,x)[/tex]

The x and y coordinates swap position.

The reflection of point P(−1, 6) across the line y = x is

P'(6,-1)

Answer:

It is answer C

Step-by-step explanation:

Answer:

C.) y = x^2 -5

Step-by-step explanation:

The table pair (x, y) = (0, -5) tells you that the constant will be -5. Only answer choice C has that value for the constant.

___

You can check other (x, y) values in the rule to see that they work.

Answer:

[tex]\large\boxed{B.\ \dfrac{7}{8}}[/tex]

Step-by-step explanation:

[tex]\text{Put the values}\ x=\dfrac{15}{8}\ \text{and}\ y=-3\ \text{to the expression}\ \dfrac{3}{8}y^2-\dfrac{4}{3}x:\\\\\dfrac{3}{8}(-3)^2-\dfrac{4}{3\!\!\!\!\diagup_1}}\cdot\dfrac{15\!\!\!\!\!\diagup^5}{8}=\dfrac{(3)(9)}{8}-\dfrac{(4)(5)}{8}=\dfrac{27}{8}-\dfrac{20}{8}=\dfrac{27-20}{8}=\dfrac{7}{8}[/tex]

Answer:

94%

Step-by-step explanation:

Since there are 100 questions, it's like 1% for each question. If she answers 94 questions right, then it is 94%.

Answer:

$482.11 in interest

Step-by-step explanation:

Use the compound amount formula.  Calculate the compound amount and then subtract the principle to find the amount of interest earned.

A = P(1 + r)^t, where r is the interest rate as a decimal fraction

This becomes:

A = $575(1 + 0.07)^9, or A = $1057.11.

Subtracting the principal:  A - P:  $1057.11 - $575 = $402.11

The total interest earned is $482 on a principal of $575 invested at an interest rate of 7% compounded annually for nine years

Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.

We know the formula for compound interest is,

A = P(1 + r/100)ⁿ.

Where, A = amount, P = principle, r = rate, and n = time in years.

Given, P = $575, n = 9 and r = 7%.

∴ A = 575(1 + 7/100)⁹.

A = 575(1.07)⁹.

A = 575(1.84).

A = 1057.

So, Interest earned is (A - P) = (1057 - 575) = $482.

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[tex]\bf \cfrac{\textit{small prism}}{\textit{large prism}}\qquad \qquad \stackrel{~\hfill \textit{yes 1:4}}{\cfrac{18}{72}\implies \boxed{\cfrac{1}{4}}\qquad \cfrac{4}{16}\implies \boxed{\cfrac{1}{4}}\qquad \cfrac{3}{12}\implies \boxed{\cfrac{1}{4}}}[/tex]

The figures are same and the ratio of the adjacent sides of the small rectangular prism to big is 1:4 option first is correct.

It is defined as the six-faced shape, a type of hexahedron in geometry.

It is a three-dimensional shape.

As we can see in the figure two three-dimensional figures are given.

To know whether the two figures are similar or not we first find the ratio of the adjacent sides.

4/16 = 1/4

3/12 = 1/4

18/72 =1/4

The ratios are equal that's why the two figures are same, and the ratio is: 1:4

Thus, the figures are same and the ratio of the adjacent sides of the small rectangular prism to big is 1:4 option first is correct.

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Answer:

Option C.

Step-by-step explanation:

It is given that a box contains red, blue, green, purple, and yellow crayons such that the probability of drawing a purple crayon is 3/7.

We draw two crayons randomly such that both draws are independent.

Let X be a random variable that assigns the number of purple crayons to each outcome.

We need to find the range of X.

If no purple crayon is selected, then X=0

If 1 purple crayon is selected, then X=1

If 2 purple crayons are selected, then X=2

The range of X is {0,1,2}.

Therefore, the correct option is C.

Answer:

$5.15

Step-by-step explanation:

A dog collar usually consists of a base(collar), the embellishments and the bag in which it is packed.

As we are given,

Collar Price = c = $3

Embellishment price = e = $2

and

Bag price = b =$0.15

The cost of one collar will be the cost of all these combined.

So,

Cost of collar = c+e+b

=3+2+0.15

=5.15

So the price of one collar is $5.15 ..

Answer:

5.15

Step-by-step explanation:

[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ x^5\div y^2\times x^3\times y^5\implies \cfrac{x^5}{y^2}\cdot x^3\cdot y^5\implies x^5\cdot y^{-2}\cdot x^3\cdot y^5 \\\\\\ x^{5+3}y^{-2+5}\implies x^8y^3[/tex]

Answer:

x⁸y³

Step-by-step explanation:

x⁵ ÷ y² × x³ × y⁵

It will be easier to solve this problem if you first rearrange the expression to associate like terms.

(x⁵ × x³) × (y⁵ ÷ y²)

Now, you can use the rules of exponents: When multiplying, you add exponents; when dividing, you subtract exponents.

x⁵ × x³ = x⁵⁺³ = x⁸  

y⁵ ÷ y² = y⁵⁻² = y³

Thus,

(x⁵ × x³) × (y⁵ ÷ y²) = x⁸y³

ANSWER

The y-intercept is (0,-11)

The x-intercepts are:

(-1,0) and (11,0)

EXPLANATION

The given function is

[tex]f(x) = {x}^{2} - 10x - 11[/tex]

To find the y-intercept, we put x=0 into the function.

[tex]f(0) = {0}^{2} - 10(0) - 11[/tex]

[tex]f(0) = - 11[/tex]

The y-intercept is (0,-11)

To find the x-intercepts, we put f(x)=0.

[tex]{x}^{2} - 10x - 11 = 0[/tex]

[tex](x + 1)(x - 11) = 0[/tex]

This implies that,

[tex]x = - 1 \: or \: x = 11[/tex]

The x-intercepts are:

(-1,0) and (11,0)

For Future Reference____

-1 & 11 are the X Intercepts

Answer:

392 ft²

Step-by-step explanation:

Break this area into two parts, that is, into two trapezoids.  The first trapezoid, on the left, has length 8 ft and average length (30 ft + 27 ft)/2, so its area is (8 ft)(28.5 ft) = 228 ft ².

The second trapezoid has width 8 ft and average length (19 + 22)/2 ft, or 8 ft by 20.5 ft).  The area of this part is 164 ft².

Thus, the total area is 164 ft² + 228 ft², or 392 ft²

Answer:

B. 7

Step-by-step explanation:

When you solve the series for each term, you get 4 + 2 + 1 = 7

Answer:

A

Step-by-step explanation:

B is the correct choice

We used the quadratic formula (-b ± √(b² - 4ac) / 2a) to solve the quadratic equation x² - 2x - 7 = 0. We identified a, b, and c from the equation, plugged them into the formula, and solved for x to find the roots of the equation.

The subject of your question involves solving the equation

x2 - 2x - 7 = 0

using the

quadratic formula.

This is a task in Algebra, a branch of Mathematics. The quadratic formula is a tool for solving equations of the form

ax² + bx + c = 0

, also known as quadratic equations. If we apply the quadratic formula, which is -b ± √(b² - 4ac) / 2a, to solve for your equation, we start by identifying a = 1, b = -2, and c = -7 from your equation. Substituting these into the formula gives:

x = [2 ± √((-2)² - 4*1*(-7))] / 2*1

After simplifying the above, we will get the solutions for x which are the roots of the quadratic equation.

We used the quadratic formula to solve the algebraic equation x2 - 2x - 7 = 0.

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Answer:

see explanation

Step-by-step explanation:

f(x) × g(x)

= (4x - 2)(5x - 6) ← expand factors

= 20x² - 24x - 10x + 12 ← collect like terms

= 20x² - 34x + 12

This is a polynomial of degree 2 and is defined for all real values of x

domain : x ∈ R

12,  x 1 = 12

12 x 2 =24  

12 x 3 = 36

12 x 4 =48

12 x 5= 60  

12 x 6 =72  

12 x 7 = 84

12 x 8= 96

12 x 9= 108  

12 x 10 = 120  

12 x 11=132

12x 12= 144

hope this helps