10. A circular Harkness table is placed in a comer of a room so that it touches both walls. A mark is made on the
edge of the table, exactly 18 inches from one wall and 25 inches from the other wall. What is the radius of the
table?

[tex] \huge\mathbb{ \underline{SOLUTION :}}[/tex]

[tex]\\[/tex]

The [tex]\mathrm{distributive \: property}[/tex] states that an expression that is given in the form of [tex]\small\sf{ A(B + C)}[/tex] can be solved as [tex]\small\sf{A \times (B + C) = AB + AC}[/tex] . So:

[tex]\small\longrightarrow\sf{-24-18-2+4}[/tex]

[tex]\small\longrightarrow\sf{-42+2}[/tex]

▪ [tex]\large\tt{All \: \: options \: \: are \: \: wrong}[/tex]

[tex]\\[/tex]

[tex]\huge \mathbb{ \underline{ANSWER:}}[/tex]

[tex]\small\longrightarrow\sf{−6 (2^2+3) − 2 (1^2 - 2) = \underline{-6(4+3)}}[/tex]

Answer:

30%

Step-by-step explanation:

1) Based on the given conditions, formulate:

30 meters/100 meters

2) Calculate 30 meters/100 meters:

3/10

3) Convert to percentage:

- 3/10 x 10/10

- 3x10/10x10

30/100

30/100 = 30%

You’re done!

Also, if you could label this brainliest that would be a great help!

Thanks xx

-Dante

Answer: 88°

Step-by-step explanation:

We know that the ratio of ∠DCB : ∠ACD is 3:1. In other words, ∠DCB is [tex]\frac{3}{3+1}[/tex], or [tex]\frac{3}{4}[/tex] of the whole angle (i.e., ∠ACB), while ∠ACD is [tex]\frac{1}{4}[/tex] of the whole angle.

To easily find ∠ACB, which is the sum of both angles, we can add up all the angles of [tex]\triangle ABC[/tex] and set it equal to 180°.

[tex]m\angle A + m\angle B + m\angle ACB = 180\\75+53+m\angle ACB=180\\128+m\angle ACB=180\\m\angle ACB=52[/tex]

From here, we can calculate ∠BCD by multiplying the value of ∠ACB by three-fourths.

[tex]m\angle BCD = \frac{3}{4}(m\angle ACB)\\m\angle BCD = \frac{3}{4}(52)\\m\angle BCD = 39[/tex]

Similar to what we did to get the measure of ∠ACB, we can add up all the angles measures of [tex]\triangle DBC[/tex] to get the measure of ∠BDC.

[tex]m\angle B + m\angle BDC + m\angle BCD = 180\\53+m\angle BDC + 39= 180\\92+ m\angle BDC=180\\m\angle BDC = 88[/tex]

The measure of ∠BDC is 88°.

The quadratic equation use to determine the thickness of the frame, x is 4x² + 10x - 1 = 0.

The correct option is D.

A quadratic equation is an algebraic equation of the second degree in x.. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.

Total area  = 7 square feet

and,

Total area = Length x Width

So,

7 = (2x + 3)(2x + 2)

7 = 4x2 + 4x + 6x + 6

7 = 4x2 + 10x + 6

4x2 + 10x + 6 - 7 = 0

4x2 + 10x - 1 = 0

Hence,

The quadratic equation use to determine the thickness of the frame, x is 4x² + 10x - 1 = 0.

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I understand that the question you are looking for is:

Mary wants to hang a mirror in her room. the mirror and frame must have an area of 7 square feet. The mirror is 2 feet wide and 3 feet long.  Square with an inner frame with height of 2 ft on the left frame and width of 3 ft on the top. Arrow on the bottom frame with an x and an arrow on the right frame with an x. Which quadratic equation can be used to determine the thickness of the frame, x?

A. x² + 14x - 2 = 0

B. 2x² + 10x - 7 = 0

C. 3x² + 12x - 7 = 0

D. 4x² + 10x - 1 = 0

Answer:

6pi

Step-by-step explanation:

First, find the circumference of the circle with radius 9. The formula is C = 2*pi*r, so C = 2*pi*9 = 18pi. Since arc is intercepted by the 120 degree central angle, the arc length is essentially 120/360 = 1/3 of the circumference. So, the arc length is 18pi*1/3 = 6pi, or approximately 18.850.

Answer:

$9600 saving / year

Step-by-step explanation:

1/5 of $21000 = 21000 / 5 = $4200 / month on rent

3/7 of $21000 = (21000 / 7) x 3 = $9000 / month on food (shocking right :) food is expensive)

1/3 of $21000 = 21000 / 3 = $7000 on other expenses / month

total savings/month = salary/month - rent/month - food/month - other expenses/month

total savings/month = 21000 - 4200 - 9000 - 7000

total savings/month = $800

BUT the question asks for savings per year. therefore, we must multiply the savings per month by total months per year (12)

800 x 12 = $9600

the person's total savings per year, with a salary of $21000 per month, is equal to $9600 per year

The function  which represents the modified design of the roller coaster is Y = 2f(0.15x²-10x+C).

What  define a function?

A technical definition of a function is: a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Here, the function: Y = 2f(0.3x - 1) + 10

Therefore, to transform the function

We have to compare with a general function and integrate.

g(x) = f(bx + c).

We now integrate to transform the function which gives us

Y = (2f) integral {0.3x - 1} + 10

Y = 2f { 0.15x² - x } + 10x + c

Y = 2f(0.15x²-10x+C)

Modified design of roller coaster is

Y = 2f(0.15x²-10x+C)

Thus, the function  which represents the modified design of the roller coaster is Y = 2f(0.15x²-10x+C).

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Answer:

A graph 1

Step-by-step explanation:

Given the length of the two diagonals of the kite, the area of kite ABDC is 33 squared centimeters.

Formular for the area of a kite is expressed as;

A = pq/2

Where p and q are the two diagonals of the kite.

Given the data in the question;

From the diagram, we can determine line AM and line MD using Pythagoras theorem.

c² = a² + b²

First, we find line AM

c² = a² + b²

5² = 3² + b²

25 = 9 + b²

b² = 25 - 9

b² = 16

b = √16

b = 4

Line AM = 4

Next, we determine Line MD

c² = a² + b²

(√58)² = 3² + b²

58 = 9 = b²

b² = 58 - 9

b² = 49

b = √49

b = 7

Line MD = 7

Now, we can find the area of the kite.

Diagonal p = BC = 6

Diagonal q = AD = AM + MD = 4 + 7 = 11

Area = pq/2

Area = [ 6 × 11 ]/2

Area = 66 / 2

Area = 33cm²

Given the length of the two diagonals of the kite, the area of kite ABDC is 33 squared centimeters.

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The solution is,  U={ keys on a keyboard}, could describe U .

A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.

Here, we have,

S is a subset of U,

so all of the elements of S must be also elements of U

If U was {letters}, 4, 9, ? would not belong there

If U was {numbers }, x, y, ? would not belong to U

If U was {punctuation marks }, 4, 9, x, y would not be in U

all the elements of S are in U={ keys on a keyboard}

Answer:  U={ keys on a keyboard}, could describe U.

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Answer:

rotate 180° about origin

The preimage and image of the figure are given below. The transformation rule that is applied is (x, y) → (-x, y).

Given a triangle with vertices A(—3, 2), B(—l, —l), and C(—4, —2), which is preimage. Further, an image is created of this triangle that has vertices at A'(3, 2), B'(l, —l), and C'(4, —2). As shown in the given figure.

Now, as per the image and preimage in the given graph. The image is the reflection of the preimage about the y-axis. This can be verified as when the image and preimage are reflected about the y-axis the vertices change as:

(x, y) → (-x, y)

A(-3, 2) → A'(3,2)

B(-1, -1) → B'(1, -1)

C(-4, -2) → C'(4,-2)

Hence, the transformation rule is (x, y) → (-x, y).

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Answer: No this is not a linear function as the y values have different first differences.

Step-by-step explanation:

First we look at the x values. We start off and look at the second x value and subtract the first x value from it (That would be 1-0) and that equals to 1. Then we look at the third x value and subtract the second x value from it (2-1) and that equals to 1. Then we look at the fourth x value and subtract the third x value from it (That would be 3-2) and that is 1. Next we look at the fifth x value and subtract the fourth x value from it (That would be 4-3) and that is 1.

Now we look at the y values and do the same thing as with the x values. We start off and look at the second y value and subtract the first y value from it (That would be 1-0) and that equals to 1. Then we look at the third y value and subtract the second y value from it (4-1) and that equals to 3. Then we look at the fourth y value and subtract the third y value from it (That would be 9-4) and that is 5. Next we look at the fifth y value and subtract the fourth y value from it (That would be 16-9) and that is 7.

Even though the x values all have the same first differences, the y values do not and so this cannot be a linear function.

I hope this helps. Tell me if something doesn't make sense.

Answer:

No, it is a quadratic relation.

Step-by-step explanation:

Work out the first differences between the given y-values:

[tex]0 \underset{+1}{\longrightarrow} 1 \underset{+3}{\longrightarrow} 4 \underset{+5}{\longrightarrow} 9 \underset{+7}{\longrightarrow} 16[/tex]

As the first differences are not the same, this is not a linear relation.

Work out the second differences:

[tex]1 \underset{+2}{\longrightarrow} 3\underset{+2}{\longrightarrow}5\underset{+2}{\longrightarrow}7[/tex]

As the second differences are the same, the relation is quadratic and will contain an x² term. The coefficient of x² is always half of the second difference.  As the second difference is 2, the coefficient of x² is one.

[tex]\begin{array}{|c|c|c|c|c|c|}\cline{1-6}x & 0 & 1 & 2 & 3 & 4\\\cline{1-6}x^2 & 0 & 1 & 4 & 9 & 16\\\cline{1-6}\end{array}[/tex]

Comparing x² with the given y-values, we can see that no further operation is needed.  Therefore, the relation is quadratic and the equation is [tex]y=x^2[/tex].

There are 30240 ways in which we can select five people from a group of ten if the order of selection is important.

Given that there are 10 total number of people.

We are required to find the number of ways in which 5 people can be selected from 10 people.

Permutations is basically the number of arrangements that can be possible with the number of things , people, etc. It is denoted as [tex]nP_{r}[/tex]=n!/(n-r)!.

We have 10 people and we have to select 5 people from them then the number of ways can be find out by [tex]10P_{5}[/tex].

We have to expand this permutation.

=10!/(10-5)!

=10!/5!

=10*9*8*7*6*5!/5!

=10*9*8*7*6

=30240 ways

Hence there are 30240 ways in which we can select five people from a group of ten if the order of selection is important.

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Solving a system of equations we will see that there are 150 blue marbles in the bag

We know that initially, the ratio of red to blue marbles is 3:5

This means that if there are 8*n marbles in the bag, there are:

Now, when he adds 10 red marbles, the new ratio is 2:3, this means that if now there are 5*m marbles, we have:

Where we will have two relations, so we have a system of equations:

3*n + 10 = 2*m

8*n + 10 = 5*m

With these two we can find the value of n and m.

To do that, we isolate m in the first equation:

m = (3*n + 10)/2

Now we can replace that in the other equation to get:

8*n + 10 = 5* (3*n + 10)/2

Now we can solve this for n:

2*(8*n + 10) = 5*(3n + 10)

16n + 20 = 15n + 50

n = 50 - 20 = 30

n = 30

And the number of blue marbles is:

5*n = 5*30 = 150

There are 150 blue marbles.

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Answer:

Here is the full list of equivalent fractions to 32.  3/2, 6/4, 96, 12/8, 15/10, 18/12, 21/14, 24/16, 27/18, 30/20, 33/22, 36/24, 39/26, 42/28, 45/30, 48/32, 51/34, 54/36, 57/38, 60/40

Step-by-step explanation:

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The equation represents a population of 370 animals that increases at an annual rate of 11% is .

It is defined as the function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a^x

where a is a constant and a>1.

Given that,

A population of 370 animals that increases at an annual rate of 11%

a = 370, r = 11%

[tex]p=a(1+r)^{t}[/tex]

  = [tex]370(1+0.11)^{t}[/tex]

p  =  [tex]370(1.11)^{t}[/tex]

Hence, The equation represents a population of 370 animals that increases at an annual rate of 11% is .

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Answer:

A, C, D

Step-by-step explanation:

The sum of the length of the overall pattern in the given cartesian coordinate is calculated as; 44

We are told that The final line on the plan is parallel to the y-axis and passes through x = -10

Now, looking at the pattern, the lengths of each side are as follows;

1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6, 6.5

Thus, the sum of the length of the overall pattern is calculated as;

1.5 + 2 + 2.5 + 3 + 3.5 + 4 + 4.5 + 5 + 5.5 + 6 + 6.5 = 44

Therefore we can conclude from all the deductions and calculations above that the sum of the length of the overall pattern in the given cartesian coordinate is calculated to be; 44

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Answer:

Step-by-step explanation:

Just multiply how much she waxes in 3/5 hour by 5/3.  Answer is 100/3 or 33.33 sq. meters per hour

Answer:

y = 1/5x -3

Step-by-step explanation:

Use y = mx +b as your model.  We plug in our slope for me and our y-intercept for b.

First you have to figure out the side length of the triangle.

sin(60)= X/8

Let's call x the side length.

8 sin(60)=X

X=6.93

The multiply it by 4

The area is 27.72

The function can be solved as follows:

(h - g)(2.1) = 3.51

g(x) = 2x² + 3x - 9

h(x) = x² + 2x - 6

(h - g)(x) = h(x) - g(x)

(h - g)(x) = 2x² + 3x - 9 - ( x² + 2x - 6)

(h - g)(x) =  2x² + 3x - 9 - x² - 2x + 6

(h - g)(x) = 2x² - x² + 3x - 2x - 9 + 6

(h - g)(x) = x² + x - 3

Therefore,

(h - g)(2.1) = (2.1)² + (2.1) - 3

(h - g)(2.1) = 4.41 + 2.1 - 3

(h - g)(2.1) = 6.51 - 3

(h - g)(2.1) = 3.51

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Answer:

96 and 192

Step-by-step explanation:

This is a geometric sequence with a common ratio of 2 :

3 × 2 = 6

6 × 2 = 12

12 × 2 = 24

24 × 2 = 48

48 × 2 = 96

96 × 2 = 192

Therefore our final answers are 96 and 192

Hope this helped and have a good day

Answer:

50 days

Step-by-step explanation:

40×300=1200

1200-700

500

so 1 day is 10 . 50 days is 500

The number of days he was absent from work will be 50 days

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that a man gets Rs. 40 for every day he works, but is fined Rs. 10 for every day he is absent If he got Rs. 700 at the end of 30 days.

The number of days he was absent from work will be calculated as below:-

40×300 = 1200

             = 1200-700

             = 500

1 day is 10 then 50 days is 500. Therefore, the number of days he was absent from work will be 50 days

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The function that best models the position of the weight is s(t) = 6cos (pi/2*t).

From the information, we know that the spring is going to have a sin or a cos equation.

We have that the maximum distance of the spring is 6 inches and it is achieved at t=0. We have that the function is of the form 6sin(at+B).

We have that the period is 4 minutes and therefore that the time component in the equation needs to make a period (2pi) in 4 minutes.

In general, a=2pi/T where a is this coefficient, T is the period. Finally, for B, since sin(pi/2)=1, we have that B=pi/2 because when t=0, we have that 6sin(B)=6.

Substituting, we have s(t) = 6cos (pi/2*t).

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Answer:

question no c 0•08

Step-by-step explanation:

at first

1/4+1/3-1/2

0•25+0.33-0.50

0.58-0.50

0.08 answer

Answer: y=-3m+13

Step-by-step explanation:

y=mx+c

m is the gradient

y=-3x+c

We know one point

-2=3(-5)+c

Solve for c

-2=-15+c

13=c

y=-3m+13

[tex]f(x)=-\frac{3}{4}x-3[/tex]

A graph is a diagram that depicts the connections between two or more objects. A pie chart is a type of graph. 5. A mathematical function or equation is shown by a curve or line, usually represented using a Cartesian coordinate system.

The equation for f (x):

[tex]y=f(x)=mx+b[/tex]

The slope of the line is m.

The point of intersection of the line with the y-axis is b.

To find the slope first by the following formula:

[tex]=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]

Two points of the line: [tex](x_{1} ,y_{1})=(x_{2},y_{2} )[/tex]

[tex](x_{1} ,y_{1})=(-4,0)[/tex]

[tex](x_{2} ,y_{2})=(0,-3)[/tex]

Substituting:

[tex]m=\frac{-3-0}{0-(-4)}[/tex]

[tex]m=-\frac{3}{4}[/tex]

Find the y-intercept Looking at the graph, we find the line intercepts the y-axis at y=-3.

Therefore, b=-3.

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After finding the intercept form of the graph of the given straight line, it can be obtained that [tex]f(x)=-\frac{4}{5}x-3[/tex].

If the graph of a straight line cuts the x-axis at the point [tex](a,0)[/tex] and the y-axis at the point [tex](0,b)[/tex], then the equation of the straight line in intercept form will be [tex]\frac{x}{a}+\frac{y}{b}=1[/tex].

Here, in the given figure, we can see that the graph of [tex]y=f(x)[/tex] is a straight line.

From the graph, we can see that the straight line cuts the x-axis at the point [tex](-3\frac{3}{4},0)=(-\frac{15}{4},0)[/tex] and cuts the y-axis at the point [tex](0,-3)[/tex].

So, here, [tex]a=-\frac{15}{4}[/tex] and [tex]b=-3[/tex].

Hence, the equation of the straight line in intercept form is

[tex]\frac{x}{a}+\frac{y}{b}=1\\\frac{x}{-\frac{15}{4}}+\frac{y}{-3}=1\\\frac{y}{-3}=1+\frac{4x}{15}\\y=-\frac{4}{5}x-3[/tex]

Therefore, finding the intercept form of the given straight line, we obtain that [tex]f(x)=-\frac{4}{5}x-3[/tex].

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The area of the polygon is 25.5 square units

From the figure, we have the following coordinates

A = (-2, 1)

B = (3, 2)

C = (5, -3)

D = (-1, -3)

The area of the polygon is then calculated as:

A = 0.5 * |(x1y2 - x2y1) + (x2y3 - x3y2) + (x3y4 - x4y3) + (x4y1 - x1y4)|

Substitute the known values in the above equation

Area = 0.5 * |(-2 * 2 - 3 * 1) + (3 * -3  - 5 * 2) + (5 * -3  + 1 * -3) + (-1 * 1 + 2 * -3)|

Evaluate the sum of products

Area = 0.5 * |-51|

Remove the absolute bracket

Area = 0.5 * 51

Evaluate the product

Area = 25.5

Hence, the area of the polygon is 25.5 square units

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The property best describes the Function f IP 4- to- 1 Correspondance.

f is Nat Bijective since Not one-one.

x1= 010101 = 010111

then 2 and 7 2 maps to 0101

So f is mat one-one.

fip Mat 2 - to- 1 correspondance

Since

2 , = 0101 vo , 212 = 0101 01 , 23 = 010 / 1 1

One point 0101

go,

f is Not 2 - to- 1 correspondance.

7 12) is the storing a with the last two

bits mold so we have only $ possibility

of 4 strings going to a single storing.

f can not be 16 - to - 1 correspondance.

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