In ΔQRS, m∠R = 57°, q = 9, and s = 5. Find the area of ΔQRS.

Step-by-step explanation:

For a RIGHT triangle, you can use Pythagorean Theorem to calculate the length of the hypotenuse:

Hypotenuse^2 = leg1 ^2  + leg2 ^2

Hypotenuse^2  = 3^2 + 16 ^2

Hypotenuse ^2 = 265     sqrt both sides

hypotenuse = 16.3 m

Now the perimeter is just all three sides added together:

     3 + 16 + 16.3 = 35.3 m

Answer:

≈ 35,3 m

Step-by-step explanation:

First we need to find the third side of the right-angled triangle by the Pythagorean theorem:

[tex] {16}^{2} + {3}^{2} = 265[/tex]

[tex]265 > 0[/tex]

[tex]the \: third \: side \: is \: \sqrt{265} [/tex]

And now we can find the perimeter:

P = 16 + 3 + √265 ≈35,3 (m)

Answer:

180

Step-by-step explanation:

3x10= 30

30/5 = 6

30 x 6 = 180

Answer:

infinite number of solutions

Step-by-step explanation:

y = x - 8 → (1)

2x - 2y = 16 → (2)

substitute y = x - 8 into (2)

2x - 2(x - 8) = 16

2x - 2x + 16 = 16 ( subtract 16 from both sides )

0 = 0 ← true statement

this true statement indicates the system has an infinite number of solutions

Therefore, Jamie can make 8 bracelets with 1.04 meters of wire.

Perimeter is a measure of the distance around the edge of a two-dimensional object, such as a polygon, a circle, or a rectangle. It is the total length of all the sides or edges that make up the shape. In simple terms, perimeter is the length of the boundary of a flat object, such as the circumference of a circle, or the sum of the lengths of the sides of a polygon. It is usually measured in units such as meters (m), centimeters (cm), feet (ft), or inches (in).

Here,

Jamie has 1.04 meters of wire, which is equivalent to 104 cm (since 1 meter = 100 cm).

Each bracelet requires 13 cm of wire, so the number of bracelets she can make is:

Number of bracelets = Total length of wire ÷ Length of wire per bracelet

Number of bracelets = 104 cm ÷ 13 cm/bracelet

Number of bracelets = 8

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Answer:

x = 35.8

Step-by-step explanation:

[tex]x = 2 \sqrt{ {14}^{2} - {11.2}^{2} } + 19 [/tex]

[tex]x = 2(8.4) + 19 [/tex]

[tex]x = 16.8 + 19 = 35.8[/tex]

From the ogive, we can see that 10 people paid a rent of less than or equal to $1,000, and 19 people paid a rent of less than or equal to $1,700.The midpoint of class with highest frequency (900-1199) is $1,050.

In mathematics, data can be used to identify patterns, trends, and relationships, and to test hypotheses.

To draw an ogive for the given data, we first need to organize the data into classes and calculate their corresponding frequencies and cumulative frequencies. Based on the range of the data, we can choose the following seven classes:

Class 1: 300-599

Class 2: 600-899

Class 3: 900-1199

Class 4: 1200-1499

Class 5: 1500-1799

Class 6: 1800-2099

Class 7: 2100-2399

Using these classes, we can complete the following table:

Class Limit  Class Boundary   Midpoint        Frequency Cumulative Frequency

300-599                299.5-599.5     449.5               1                         1

600-899 599.5-899.5 749.5 4 5

900-1199 899.5-1199.5 1049.5 5 10

1200-1499 1199.5-1499.5 1349.5 4 14

1500-1799 1499.5-1799.5 1649.5 5 19

1800-2099 1799.5-2099.5 1949.5 1 20

2100-2399 2099.5-2399.5 2249.5 4 24

To draw the ogive, we plot the cumulative frequencies against the upper class boundaries. We start at the first lower class boundary and plot a point with a cumulative frequency of zero. Then we plot the cumulative frequency of each subsequent class at the upper class boundary of that class. We then connect the points with smooth curve.

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There are 210 ways that Janelle can choose 4 colors from 10 available colors for her art project.

Janelle needs to choose 4 colors out of 10 available colors for her art project. The order in which she chooses the colors does not matter. We can use the combination formula to determine the number of ways she can choose 4 colors from 10 available colors:

nCr = n! / r!(n - r)!

where n is the total number of colors available, r is the number of colors Janelle needs to choose, and ! denotes the factorial operation.

In this case, we have:

n = 10 (total number of colors available)

r = 4 (number of colors Janelle needs to choose)

Substituting these values into the formula, we get:

10C4 = 10! / 4!(10 - 4)!

= 10! / 4!6!

= (10 x 9 x 8 x 7) / (4 x 3 x 2 x 1)

= 210

Therefore, for her art assignment, Janelle can select 4 colors from a palette of 10 in 210 different ways.

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Answer:

118m

Step-by-step explanation:

102.25m+15.75m=118m

Answer: 2.86 (2 d.p.)

Step-by-step explanation:

The formula for the circumference of a circle is C = πd = 2πr

Substitute 18 for C in the equation

18 = 2πr

Rarrange for r

r = 18 / 2π = 2.86 (2 d.p.)

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]x-y=8\implies -y=-x+8\implies y=\stackrel{\stackrel{m}{\downarrow }}{1}x-8\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ 1 \implies \cfrac{1}{\underline{1}}} ~\hfill \stackrel{reciprocal}{\cfrac{\underline{1}}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{\underline{1}}{1} \implies \text{\LARGE -1}}}[/tex]

[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$4000\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years\dotfill &25 \end{cases} \\\\\\ A = 4000e^{0.08\cdot 25} \implies A=4000e^2\implies A \approx 29556.22[/tex]

Answer:

the answer is 23 cm

Step-by-step explanation: just a guess

The first five terms of the sequence with a = 3 and r = -2 are: 3, -6, 12, -24, 48.

The general formula for a geometric sequence is given by:

an = a * r^(n-1)

where "a" is the first term, "r" is the common ratio, and "n" is the number of the term we want to find.

In this case, we have:

a = 3

r = -2

So the first term is 3, and the common ratio is -2. We can use the formula above to find the first five terms of the sequence:

a1 = 3

a2 = 3 * (-2)^(2-1) = -6

a3 = 3 * (-2)^(3-1) = 12

a4 = 3 * (-2)^(4-1) = -24

a5 = 3 * (-2)^(5-1) = 48

Therefore, the first five terms of the geometric sequence with a = 3 and r = -2 are: 3, -6, 12, -24, 48.

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Answer: First, we need to calculate the taxable income, which is the gross salary minus the tax-free threshold of $18,200:

Taxable income = Gross salary - Tax-free threshold

Taxable income = $18,700 - $18,200

Taxable income = $500

Since the taxable income falls within the range of $18,201-$37,000, we can use the tax rate of 19c for each $1 over $18,200 to calculate the amount of tax payable:

Tax on income = (Taxable income - $18,200) × 0.19

Tax on income = ($500 - $18,200) × 0.19

Tax on income = -$3,382 × 0.19

Tax on income = -$642.58 (rounded to the nearest cent)

However, the calculated tax is negative, which means that the person is entitled to a tax refund as they have paid more tax than they are required to. This can happen if they have been working for only part of the financial year, or if they have had tax withheld at a higher rate than necessary.

Step-by-step explanation:

After 4 months, Dalia will have the same number of gems as Grace, and after that, she will have more.

We need to find out when the number of gems Dalia has will exceed the number of gems Grace has.

Let's represent the number of months by "t".

After t months, Dalia will have 20t gems.

After t months, Grace will have 120 - 10t gems.

To find when Dalia will have more gems than Grace, we can set up an inequality:

20t > 120 - 10t

Simplifying the inequality, we get:

30t > 120

Dividing both sides by 30, we get:

t > 4

This means that Dalia will have more gems than Grace after 4 months.

To check our answer, we can substitute t = 4 into the expressions we found earlier:

After 4 months, Dalia will have 20t = 20(4) = 80 gems.

After 4 months, Grace will have 120 - 10t = 120 - 10(4) = 80 gems.

So, we can see that after 4 months, Dalia will have the same number of gems as Grace, and after that, she will have more.

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A possible value of a is a > 0 , b = 0 , c < 0

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.

From this diagram we can observe the following:

The diagram opens upwards, which means that the coefficient 'a' is positive. The vertex of the parabola is on the y-axis, which means that the x-coordinate of the vertex is 0. This gives us evidence that the equation of the parabola is f(x) = a(x-0 )²c , which simplifies to f(x) = ax² c. It can also be observed that the y-intercept of the graph is c, which means that the constant term is c. Based on the above observations, we can derive the possible values ​​of a, b and c as follows:

A possible value of a is a > 0 because the graph opens up. A possible value of b is b = 0 because there is no horizontal displacement in the parabola. The possible value of C is c < 0; 0 because the y-intercept is negative. Note that c can be 0, but it cannot be positive because the graph does not intersect the x-axis.

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Rectangle ABCD has diagonals AC and BD that converge at point O and

OA = 5x-7, OD = 4x-5.

A relation is any subset of a Cartesian product.

As an illustration, a subset of is referred to as a "binary connection from A to B," and more specifically, a "relation on A."

A binary relation from A to B is made up of these ordered pairs (a,b), where the first component is from A and the second component is from B.

Every item in a set X is connected to one item in a different set Y through a connection known as a function (possibly the same set).

A function is only represented by a graph, which is a collection of all ordered pairs (x, f (x)).

Every function, as you can see from these definitions, is a relation from X

Hence, Rectangle ABCD has diagonals AC and BD that converge at point O and

OA = 5x-7, OD = 4x-5.

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The weights assigned to attributes seem appropriate based on the personnel manager's ranking according to of importance. The weights reflect the relative importance of each attribute in the decision-making.

For example, COMMITMENT is given the highest weight, indicating that the charity places a lot of value on a candidate's commitment to their work. MANAGEMENT EXP and IDEAS are given the next highest weights, indicating that the charity values a candidate's ability to manage and come up with innovative ideas.

On the other hand, EDUCATION is given the lowest weight, indicating that the charity places less emphasis on formal qualifications than on other attributes such as experience and commitment.

The aggregated score for Candidate A is 50, but we don't have any information about the scale or method used to calculate the scores. Therefore, we cannot comment on whether the score is good or bad or whether Candidate A is the best choice for the job.

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The cοrrect answer is x > 0 and x < (- 3) where x is any number οn the number line.

A number line is a οne dimensiοnal graph (rather an endless straight line) οn which οne can represent every pοssible real number. Usually we have zerο serving as the center οf the number line, with the right hand side serving as the pοsitive part οf the real line and the left hand side as the negative part οf the real line.

A number line is endless which implies there is nο bοund tο a number line.

Any number οn the real line is denοted by a dark spοt οn the real line. Fοr example if οne needs tο denοte 3 οn the real line he/she has tο mark 3 with a spοt.

There are three kind οf intervals that can be represented οn the number line namely clοsed [ ] , οpen ( ) and semi-clοsed οr semi- οpen [ ) οr ( ]. Intervals οn number line are being shοwn by thickening that part οf the real line that are under cοnsideratiοn.

Fοr example: (4 , 5) is representing by thickening the number line between 4 and 5 with οpen ends , i.e. circles οn digit 4 and 5.

[4 , 6]   is represented by thickening the number line between 4 and 6 with clοsed οr black dοt ends.

Similarly semi οpen and semi clοsed intervals are represented by thickening the interval between thοse twο pοints with apprοpriate circles and dοts οn the endpοints.

Accοrding tο the given questiοn we need tο mark all described pοints that are pοsitive. Thus all pοints greater than zerο are tο be thickened (excluding zerο). This is dοne by having an οpen end οn pοint zerο and thickening the whοle οf the right hand side οr the pοsitive side οf the number line.

Similarly tο represent all described pοints οn the number line less than ( -3) (excluding ( - 3)) can be dοne by having an οpen end οn pοint ( - 3) and thickening the whοle οf the negative side tο the left οf ( - 3).

Thus to represent all the required points we can write them in a set A as:

A = { x : x > 0; x < ( - 3) }.

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Answer:

The answer is:  −x² + 3x + 2

Step-by-step explanation:

divide the whole expression by -6x

then you get: −x² + 3x + 2

The score that corresponds to the 85th percentile is 82, since it is greater than or equal to 85% of the scores in the data set.

The formula is: percentile = (number of scores below the percentile / total number of scores) x 100%

We want to find the score that corresponds to the 85th percentile, which means that 85% of the scores in the data set are below this score

percentile = 85%

total number of scores = 20

number of scores below the percentile = (85% / 100%) x 20 = 17

This means that we need to find the score that is greater than or equal to 17 of the 20 scores in the data set.

Next, we need to rank the scores in order from lowest to highest:

55, 56, 57, 58, 59, 60, 60, 61, 63, 65, 69, 71, 78, 78, 79, 79, 82, 82, 83, 83

The score that corresponds to the 85th percentile is 82, since it is greater than or equal to 85% of the scores in the data set.

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Answer:

Necesito puntos, lo siento, no puedo ayudarlo con la pregunta, solo informe esto y elimínelo o lo que sea

Step-by-step explanation:

In this case, 3x plus 12 is 3x plus 12. in this situation, [tex]|3x + 12|[/tex] equals -(3x + 12) for expression.

For the expression:

Two vertical bars serve as the absolute value symbol in mathematics, which is used to represent a number's distance from zero regardless of its sign. In other words, a number's absolute value is never negative.

The number 3x + 12's absolute value is denoted by the expression |3x + 12|. We must take into account two scenarios in order to formulate this expression without the absolute value symbol: the non-negative case for 3x + 12 and the negative situation for 3x + 12.

Example 1: 3x + 12 ≥ 0

Because 3x + 12 is not negative, we may simply remove the absolute value symbols since they are not necessary. In this case, 3x plus 12 is 3x plus 12.

Example 2: 3x + 12 < 0

When 3x + 12 is a negative number, we can multiply it by -1 to get the absolute value. This is so because a negative number's absolute value is the same as its positive equivalent. As a result, in this situation, |3x + 12| equals -(3x + 12).

In light of the aforementioned examples, the phrase |3x + 12| can be expressed as follows:

[tex]|3x + 12| =\\{ 3x + 12 if 3x + 12 ≥ 0\\\\{ -(3x + 12) if 3x + 12 < 0[/tex]

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[tex] \: \: \: \: \: \texttt{34.59 + \boxed{\texttt\red{102.336}}} \\ \texttt{ = 136.926}[/tex]

[tex] \: [/tex]

━━━━━━━━━━━━━━━━━━━━━━━

hope it helps:)

Therefore, the volume of the cone to the nearest cubic meter is approximately 333 cubic meters.

Volume is a measure of the quantum of three- dimensional space enthralled by an object, substance, or region of space. It's frequently measured in boxy units similar as boxy measures, boxy bases, or liters. The volume of an object can be calculated using its confines similar as length, range, and height, or by relegation styles where the volume of the object is determined by the quantum of fluid it displaces when submerged in a liquid. The conception of volume is used in numerous areas of wisdom, engineering, and everyday life, similar as measuring the capacity of holders, determining the quantum of fluid in a force, or calculating the size of a room.

by the question.

To find the volume of a cone, we can use the formula:

[tex]V = (1/3) * π * r^2 * h[/tex]

where V is the volume, r is the radius, and h is the height.

Plugging in the given values, we get:

[tex]V = (1/3) * π * (meters)^2 * (meters)[/tex]

V ≈ 333.33 cubic meters (rounded to the nearest cubic meter)

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Answer:

Step-by-step explanation:

350x2x5=3500

Answer:

Part A.) 0.3 or 30%

Part B.) 0.5 or 50%

She flipped the coin 30 times.

She flipped it 9 times for heads.

She flipped it 21 times for tails.

Part A.)

9/30

When you simplify that you get 3/10.

Which is 0.3 or 30%

Part B.)

So there are only 2 sides of a coin.

Heads or tails, So its a 50 - 50

For One side it is 50/100

Which simplifies to 1/2

Or 0.5 which is 50%

Step-by-step explanation:

The dilation is an enlargement, then k > 1. If the dilation is a reduction, then 0 < k < 1.

The dilation constant, also known as the scale factor, represents the amount by which the original figure is enlarged or reduced in the dilation.

We can find the dilation constant by using the distance formula. Let the coordinates of point P be (x,y) and the coordinates of point A be (a,b). Let the coordinates of point B be (u,v), where u and v are unknown.

The distance from A to P is:

d(AP) = √[(x-a)² + (y-b)²]

The distance from A to B is:

d(AB) = √[(u-a)² + (v-b)²]

Since the dilation is centered at A and maps P onto B, we know that the ratio of the distances is the dilation constant:

d(AP)/d(AB) = k

Substituting the expressions for the distances and simplifying, we get:

√[(x-a)² + (y-b)²] / √[(u-a)² + (v-b)²] = k

Squaring both sides, we get:

[(x-a)² + (y-b)²] / [(u-a)² + (v-b)²] = k²

Since we know the coordinates of P and A, we can substitute these values into the equation and solve for k. Once we have k, we can use it to find the coordinates of B.

Note that if the dilation is an enlargement, then k > 1. If the dilation is a reduction, then 0 < k < 1.

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