Use properties of logarithms to expand log(r^2 s^11)/t^14

Answer: 2(2x-1)(3x+2)

Step-by-step explanation: Assuming everything else is factored properly, the only thing left needing to be factored is 12x^2 + 2x - 4, which can be factored accordingly to 2(2x-1)(3x+2)

The height of the trapezoid is 13cm.

A trapezoid is a convex quadrilateral with at least one pair of parallel sides.

Area of a trapezoid =   0.5 x (sum of the lengths of the parallel sides) x height

Height = area / (0.5 x sum of lengths)

Sum of lengths = 23 + 17 = 40 cm

= 260 / (0.5 x 40) = 13 cm

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Answer:

THE LAST ONE

Step-by-step explanation:

it doesn't pass the vertical line test

The volume of the cone-shaped hole with a depth of 3 feet and a base circumference of 44 feet is approximately 307.62 cubic feet.

To find the volume of the cone-shaped hole, we will use the formula for the volume of a cone, which is V = (1/3)πr²h. First, we need to find the radius (r) and the height (h) of the cone. We know the height (h) is 3 feet. To find the radius (r), we will use the given circumference of the base, which is 44 feet.

Step 1: Find the radius (r) using the circumference formula C = 2πr.
C = 44 feet, and we will use 22/7 for π.

44 = 2 * (22/7) * r
44 = (44/7) * r

Now, divide both sides by (44/7):
r = 7 feet

Step 2: Calculate the volume (V) using the cone volume formula V = (1/3)πr²h.
V = (1/3) * (22/7) * (7²) * 3

Simplify the expression:
V = (1/3) * (22/7) * 49 * 3

Cancel out the 3s:
V = (22/7) * 49

Multiply the numbers:
V ≈ 307.62 cubic feet

So, the volume of the cone-shaped hole is approximately 307.62 cubic feet.

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Answer:

C). 10.

Step-by-step explanation:

x^2 = 6^2 + 8^2 = 100

x = 10.

Answer:

C 10 Cm yuh yuh yuh yuh yuh

Answer:4.5

Step-by-step explanation:

Answer:

Answer is B

Step-by-step explanation:

Answer:

IT is B

Step-by-step explanation:

Answer:

See attached image.

Step-by-step explanation:

Substitute 1,2,3, or 4 for \(x\). Then calculate using the order described by PEMDAS.

Answer:

2/3r + p

Step-by-step explanation:

2/3r + 4/3p - 1/3p

combine like terms, terms with like coefficients can be combined, terms that do not have like coefficients cannot be combined

coefficient- the variable that a number is multiplied by

2/3r + 4/3p - 1/3p

combine

2/3r + 3/3p

or

2/3r + p

Answer:

the student calculated the marginal relative frequency which is the 20.7/29 =71.4%  the joint relative frequency =20.7

Step-by-step explanation:

Answer:

480

Step-by-step explanation:

6*5*2*8 = 480 different lunches

P.S sorry if this isnt right

Answer: D

Step-by-step explanation:

Just do 7 x 88 LOL

Answer:

1.5° per day

Step-by-step explanation:

Given that :

Total temperature change = drop by 12°

Number of days for the change = 8 days

Rate at which temperature changed is constant

Change in temperature per day :

Total change in temperature / number of days

12° / 8

= 1.5° per day

Answer:

it is 2/5 i think

ANSWER

(c) 3.75x + 9.50 = 28.25

EXPLANATION

Each ride costs $3.75 so x rides will cost 3.75x

Then we know that Jose paid for the admission that costs $9.50 and the rides $28.25. Therefore, the sum of the costs of x rides and the admission is 28.25:

Answer:

dont get it

Step-by-step explanation:

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

After plotting the inequalities, we see that the second set satisfies the graph provided.

How can we graph inequalities?

A linear or quadratic inequality can be graphed in a manner similar to that of an equation. The distinction is that an inequality displays a range of values greater than or less than, thus your graph will display more than just a dot on a number line or a line on a coordinate plane. You can figure out which numbers are part of an inequality solution by utilizing algebra and evaluating the inequality sign.

Let the first inequality be  \(3x+5y\leq 10\).

When we plot the equality, we see that it covers the portion including the origin.

Next inequality is \(-x+y > -5\).

When plotting this one, we again see that it covers the portion including the origin.

The last equality is \(y-6 > -5x\).

While plotting it, we see that this line overlaps the other 2 lines making a common space of the triangle that is shown in the figure.

Hence the second set of inequalities represent the graph.

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After plotting the inequalities, we see that the second set satisfies the graph provided.

How can we graph inequalities?

To graph inequalities, you can use a number line or a coordinate plane. Here's an example of how to graph an inequality on a number line:

First, determine the inequality symbol: >, <, ≥, or ≤.

Next, determine the value of the inequality.

Plot the value on the number line, using an open circle for > or <, and a closed circle for ≥ or ≤.

Shade in the region on one side of the plotted point, according to the inequality symbol. For example, if the inequality is x > 3, then you would shade in the region to the right of 3, since values greater than 3 satisfy the inequality.

Here's an example of how to graph an inequality on a coordinate plane:

First, determine the inequality symbol: >, <, ≥, or ≤.

Next, rewrite the inequality in the form "y > f(x)" or "y < f(x)" by isolating the y term on one side of the inequality.

Plot the function f(x) on the coordinate plane.

Shade in the region above or below the plotted function, depending on the inequality symbol. For example, if the inequality is y > f(x), then you would shade in the region above the plotted function, since values of y greater than f(x) satisfy the inequality.

Let the first inequality be \(3x+5y\leq 10\)

When we plot the equality, we see that it covers the portion including the origin.

Next equality is \(-x+y > -5\)

When plotting this one, we again see that it covers the portion including the origin.

The last equality is \(y-6 > -5x\)

While plotting it, we see that this line overlaps the other 2 lines making a common space of the triangle that is shown in the figure.

Hence the second set of inequalities represent the graph.

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Answer:

General form of a linear equation:  \(y=mx+b\)

(where m is the slope and b is the y-intercept)

A linear equation has a constant rate of change which is represented by the slope (m).  It is the rate at which one quantity is changing with respect to another quantity.

Part (a)

Given equation:  \(y=-9x+55000\)

where:

The rate of change (slope) is -9 and represents that for every 1 mile driven, the value of the car decreases by $9.

The initial value is the y-intercept (b) as this is the value when x = 0.

Therefore, the initial value of car is $55,000.

Part (b)

To find the number of miles at which the car be valued at $35,002, set the equation to $35,002 and solve for x:

\(\implies -9x+55000=35002\)

\(\implies -9x=35002-55000\)

\(\implies -9x=-19998\)

\(\implies x=\dfrac{-19998}{-9}\)

\(\implies x=2222\)

Therefore, the car will be valued at $35,002 after 2,222 miles.

Given equation:  \(y=0.39x+2.55\)

where:

The rate of change (slope) is 0.39 and represents that for every increase of 1 oz of weight in carrots, the price of the carrots increases by $0.39

The initial value is the y-intercept (b) as this is the value when x = 0.

Therefore, the initial cost of the carrots is $2.55.

Part (b)

To find the weight of carrots you can buy for $6.06, set the equation to $6.06 and solve for x:

\(\implies 0.39x+2.55=6.06\)

\(\implies 0.39x=6.06-2.55\)

\(\implies 0.39x=3.51\)

\(\implies x=\dfrac{3.51}{0.39}\)

\(\implies x=9\)

Therefore, you can buy 9 oz of carrots for $6.06

Part (c)

To find out how much it costs to buy 21 oz of carrots, substitute x = 21 into the equation and solve for y:

\(\implies y=0.39(21)+2.55\)

\(\implies y=10.74\)

Therefore, it costs $10.74 to buy 21 oz of carrots.

Answer:

Resultado es dos (2)

Answer:

2

Step-by-step explanation:

Answer:

bean

Step-by-step explanation:

bean

Answer:

TU = 5

Step-by-step explanation:

Since, U is the midpoint of TV.

\(\therefore TV = 2 \times TU \\ 3x - 23 = 2(x - 6) \\ 3x - 23 = 2x - 12 \\ 3x - 2x = 23 - 12 \\ x = 11 \\ \\ TU = x - 6 \\ TU = 11 - 6 \\ \huge \red { \boxed{TU = 5}}\)

Answer:

D.

Step-by-step explanation:

6.52^2 = 42.3 according to the table so 6.5 should be a good estimate.

\((\stackrel{x_1}{1}~,~\stackrel{y_1}{-2})\hspace{10em} \stackrel{slope}{m} ~=~ 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{ 3}(x-\stackrel{x_1}{1}) \implies {\large \begin{array}{llll} y +2 = 3 ( x -1) \end{array}}\)

Similar figures have sides that are proportional and corresponding angles are congruent to each other

Answer:

2(b+6)

Step-by-step explanation:

Answer:

Corresponding angles

Step-by-step explanation:

The name of these angels lying in the same position are called corresponding angle.

These angles are equal. When we talk of parallel lines, they are sets of lines that travel in the same direction but never meet. The third line that cuts through the two sets of parallel lines is referred to as the transversal line.

So the positions of these angles on each of the set of the parallel lines are equal in each of the cases and they are equal and are referred to as being corresponding to each other

When analyzing a consumer's utility function: preferences, marginal utility, optimal consumption, and substitution and income effects.

From a consumer's utility function alone, you may determine the following:

1. Preferences: A consumer's utility function represents their preferences for different goods and services. By analyzing the function, you can determine which items the consumer prefers and how much they value them.

2. Marginal utility: The marginal utility is the additional satisfaction a consumer receives from consuming one more unit of a good or service. It can be derived from the utility function by taking its first derivative with respect to the quantity of the good or service.

3. Optimal consumption: By analyzing a consumer's utility function and taking into account their budget constraint, you can determine the optimal consumption bundle that maximizes their utility.

4. Substitution and income effects: The utility function can also help you analyze how changes in prices or income will affect a consumer's consumption choices, through the substitution and income effects.

Remember to keep these terms in mind when analyzing a consumer's utility function: preferences, marginal utility, optimal consumption, and substitution and income effects.

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Step-by-step explanation:

since it is a quadratic equation, we know it must have 2 solutions.

132 is a bit larger than 10².

so, let's try x = 10 :

10 + 10² = 132

10 + 100 = 132

110 = 132

not correct, but close.

the real solution must be a bit larger than x = 10.

we know, that 12² = 144. that is already too large (as the sum with x must be only 132).

so, let's try x = 11

11 + 11² = 132

11 + 121 = 132

132 = 132

correct !

so, x = 11 is one solution.

for the second solution, it is very often that it has the opposite sign to the first solution, but its absolute value is relatively close to the first solution.

so, when thinking negative values, x² has to go higher than 132, so that x (with its negative value) can bring it back down to 132.

what we just thought about +12 might have some merit for -12.

let's try x = -12 :

-12 + (-12)² = 132

-12 + 144 = 132

132 = 132

correct !

so, x = -12 is the second solution.

summary :

x = 11

x = -12

are the 2 solutions.