The length of one of the legs of a right triangle is 13. The lengths of the other two sides are consecutive integers. Use the Pythagorean theorem to solve for the the larger of the two missing sides (the hypotenuse).

Answer:

The answer is:  −x² + 3x + 2

Step-by-step explanation:

divide the whole expression by -6x

then you get: −x² + 3x + 2

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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Answer: the right one is d

Step-by-step explanation:

Answer:

Table 4

Step-by-step explanation:

The first table is a linear function, with the points of (-240), (-72), (0), (2), and (6).

The second table is also a linear function, with the points of (-768), (-16), (0), (48), and (384)

The third table is a linear function, with the points of (-48), (-6), (0), (6), and (48)

The fourth table is the only one that is a linear function because the first four points are (0) and the last one is (-12)

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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Answer:

(x - 4)(x+8)

(Hopefully this helps, and if you can please give me brainliest)

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: 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.)

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:

Answer:

Step-by-step explanation:

350x2x5=3500

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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Here is a vector of observations representing the number of defects in 25 1-square-yard specimens of a particular type of woven fabric. This data is provided to facilitate its entry into R.

The data provided is the number of defects in 25 1-square-yard specimens of woven fabric of a particular type. This data can be used to analyze the quality of the fabric and identify any potential issues with the manufacturing process.

It is important to copy this data into R as a vector so that it can be easily analyzed using various statistical techniques. In R, vectors are used to store multiple values of the same type, and they can be used to perform mathematical operations and statistical analyses. Once the data is in R, various descriptive statistics, such as the mean, median, and standard deviation, can be calculated to gain insights into the quality of the fabric and identify any potential trends or patterns in the data.

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

[tex] \: [/tex]

━━━━━━━━━━━━━━━━━━━━━━━

hope it helps:)

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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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]

Step-by-step explanation:

8 ( 3 + 4 - 2)  =   8 x 3   + 8 x 4    -   8x 2       <  ===== distributive property

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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By first method, he volume of the rectangular prism is (9/32) cubic feet.

By second method, the volume of the rectangular prism is (27/64) cubic feet, which agrees with the volume calculated using the first method.

Volume is a measurement of the amount of space that an object occupies. It is the three-dimensional space occupied by an object. Volume is typically measured in cubic units such as cubic meters, cubic centimeters, cubic feet, and so on.

We can determine the volume of the rectangular prism in two different ways using the formula:

Volume = Length x Width x Height

First Method:

In the first method, we simply substitute the given dimensions of the rectangular prism into the formula and calculate the volume:

Volume = (3/4) ft x (3/8) ft x (3/4) ft

Volume = (9/32) ft³

Second Method:

In the second method, we can use the fact that the rectangular prism can be divided into 4 smaller rectangular prisms, each with dimensions (3/4) ft x (3/8) ft x (3/16) ft. We can calculate the volume of one of these smaller prisms and then multiply by 4 to get the total volume:

Volume of one smaller prism = (3/4) ft x (3/8) ft x (3/16) ft

Volume of one smaller prism = (27/256) ft³

Total volume = 4 x Volume of one smaller prism

Total volume = 4 x (27/256) ft³

Total volume = (27/64) ft³

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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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Answer:

118m

Step-by-step explanation:

102.25m+15.75m=118m

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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solution-

Actual measure= 6m wide ie.600cm wide

her model is =12cm wide

so scale factor =600/12= 50

so length will be =800/50 =16cm

hence gher model will be 16cm long

Answer:

  40°

Step-by-step explanation:

You want the measure of ∠LNO, marked as y°, given the two vertical angle pairs {100°, (x -y)°} and {y°, 2/7x°}.

Vertical angles have the same measure, so we can write the equations ...

We want the value of y, so it makes sense to solve these equations using a method that eliminates x. Rewriting the second equation to solve for x, we have ...

  x° = 7/2y°

Substituting this into the first equation gives ...

  100° + (7/2y -y)°

  100° = 5/2y°

  2/5(100) = y° = 40°

The measure of ∠LNO is 40°.

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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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]

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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Answer:

the answer is 23 cm

Step-by-step explanation: just a guess

Step-by-step explanation:

the area of a rectangle is

length × width

the perimeter of a rectangle is

2×length + 2×width

so,

length×width = 48 cm²

2×length + 2×width = 28 cm

length + width = 14 cm

length = 14 - width

we use this in the first equation :

(14 - width) × width = 48

14×width - width² = 48

-width² + 14×width - 48 = 0

a quadratic equation

ax² + bx + c = 0

has the general solution

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = width

a = -1

b = 14

c = -48

width = (-14 ± sqrt(14² - 4×-1×-48))/(2×-1) =

= (-14 ± sqrt(196 - 192))/-2 =

= (-14 ± sqrt(4))/-2 =

= (-14 ± 2)/-2 =

= 7 ± 1

width1 = 7 + 1 = 8 cm

width2 = 7 - 1 = 6 cm

length1 = 14 - width1 = 14 - 8 = 6 cm

length2 = 14 - width2 = 14 - 6 = 8 cm

so, we see, one of them must be 8 cm, and the other 6 cm.

let's length be the longer side, so

length = 8 cm

width = 6 cm