1. The circle x² + y² = 45 is shown graphed along with the point (6, 3).
(a) Determine graphically the slope of the line segment connecting the origin to the point (6,3).

(b) Carefully draw in the tangent line to the circle at (6,3) using the negative reciprocal slope of the one you found in (a).

(c) What is the y-intercept of the tangent line?
​

Answer:

[tex]\large\boxed{\tt x^{\circ}= 90^{\circ}}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to find the value of x.}[/tex]

[tex]\textsf{The value of x is an angle for this triangle.}[/tex]

[tex]\textsf{Note that we are given 2 other angles, we can use what is given to us to solve for x.}[/tex]

[tex]\large\underline{\textsf{What is a Triangle?}}[/tex]

[tex]\textsf{A Triangle is a shape with 3 sides, and 3 angles. Sometimes these can be congruent,}[/tex]

[tex]\textsf{other times, and most of the time they're not. These are called Equilateral}[/tex]

[tex]\textsf{Triangles. Every Triangle consists of 3 angles that add up to 180}^{\circ}. \ \textsf{If the angles}[/tex]

[tex]\textsf{don't add up to 180}^{\circ}, \ \textsf{then the shape is not a triangle.}[/tex]

[tex]\textsf{Now that we know a Triangle has 3 angles that add up to 180}^{\circ}, \ \textsf{we can create an}[/tex]

[tex]\textsf{equation where x is the \underline{subject}.}[/tex]

[tex]\large\underline{\textsf{Solving;}}[/tex]

[tex]\textsf{All 3 angles add up to 180}^{\circ}, \ \textsf{let's create an equation.}[/tex]

[tex]\tt 180^{\circ} = 37^{\circ} + 53^{\circ} + x^{\circ}[/tex]

[tex]\textsf{To make x the subject, move x to the other side of the equation by subtracting x.}[/tex]

[tex]\tt 180^{\circ} - x^{\circ}= 37^{\circ} + 53^{\circ} + x^{\circ} - x^{\circ}[/tex]

[tex]\textsf{We should also move 180}^{\circ} \ \textsf{to the other side of the equation as well.}[/tex]

[tex]\tt 180^{\circ} - 180^{\circ} - x^{\circ}= 37^{\circ} + 53^{\circ} -180^{\circ}[/tex]

[tex]\underline{\textsf{We should have;}}[/tex]

[tex]\tt- x^{\circ}= -180^{\circ} + 37^{\circ} + 53^{\circ}[/tex]

[tex]\textsf{We should remove the negative for x by dividing the whole equation by -1.}[/tex]

[tex]\frac{\tt- x^{\circ}= -180^{\circ} + 37^{\circ} + 53^{\circ}}{-1} \rightarrow \tt x^{\circ}= 180^{\circ} - 37^{\circ} - 53^{\circ}[/tex]

[tex]\underline{\textsf{Simplify the right side of the equation;}}[/tex]

[tex]\large\boxed{\tt x^{\circ}= 90^{\circ}}[/tex]

Answer:

[tex]a_4=19[/tex]

Step-by-step explanation:

Given:

[tex]\implies a_2=a_{1}+4=7+4=11[/tex]

[tex]\implies a_3=a_{2}+4=11+4=15[/tex]

[tex]\implies a_4=a_{3}+4=15+4=19[/tex]

Put values get answer

A bran with the dimensions shown is to be painted. One gallon of pain covers 400 square feet. 23 gallons of  pain is need for the one coat of the barn. Option B is correct.

Given that,

A bran with the dimensions shown is to be painted.

One gallon of pain covers 400 square feet.

We have to find how much gallon of paint for one coat on the entire external of the bran, including the roof.

So,

We can see in the picture

1 side of the barn is rectangle with length and breath that is 24 feet and 60 feet.

1 side of the barn is square with side 40 feet.

The front upper side has a triangle with height 21 feet.

Now, We find the area of the rectangle.

Area of rectangle is length × breath

=24feet×60 feet  

=1440 square feet

1440 square feet divided by 400 square feet

1440/400=3.6

So, the bran has 2 rectangular sides so 3.6+3.6=7.2

Now, we find the area of square.

Area of square is side × side

=40 feet ×40 feet

=1600 square feet

1600 square feet divided by 400 square feet.

1600/400=4

So, the barn has 2 square side so 4+4=8

Now, we find the area of triangle.

Area of triangle is 1/2×breath ×height.

=1/2×40 feet×21 feet

=1/2×840 square feet

=420 square feet

420 square feet divided by 400 square feet.

420/400=1.05

So, the barn has 2 triangles back and front so 1.05+1.05=2.1

Now, we find the area of roof

Roof is in rectangle with breath 60 feet and height 21 feet

Area of rectangle is length × breath

=60 feet ×21 feet

=1260 square feet

1260 square feet divided by 400 square feet.

1260/400=3.15

So, the barn has 2 rectangle roof so 3.15+3.15=6.3

Now, Adding all the areas we get

=7.2+8+2.1+6.3

=23.6

Therefore, approximately 23 gallons of  pain is need for the one coat of the barn. Option B is correct.

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Answer: 23 gallons

Step-by-step explanation: ANSWER ON EDMENTUM

Answer:

Minimum: 189

Maximum: 786

Median: 572

Lower quartile: 275

Upper quartile: 653

Step-by-step explanation:

Listing the numbers in order from least to greatest, we have: 189, 274, 276, 403, 572, 649, 652, 654, 786.

From this, we can see that the smallest (minimum) value is 189, and the largest (maximum) value is 786.

We can find the the median by taking off a number from each side of the number set one by one. When done, we can see that the number in the middle is 572, so that is our median.

To find the upper and lower quartiles, split the number set in half where the median lies and find the median of those two sections.

Q1: 189, 274, 276, 403

274 + 276 = 550

550 ÷ 2 = 275

--------------------------

Q3: 649, 652, 654, 786

652 + 654 = 1306

1306 ÷ 2 = 653

So, the lower quartile range is 275, and the upper quartile range is 653.

hope this helps!

The mean of the set is less than the median. Option B is correct.

Given that,
Norberto received the following scores on his last five spelling tests 93, 66, 78, 85, and 98.

The mean of the values is the ratio of the total sum of values to the number of values.

Here,
Marks scored by Norberto in 5 spelling tests are 93, 66, 78, 85, and 98.
Mean of marks score = total marks scored / total spelling test
Mean of marks score = (93 + 66 + 78 + 85 + 98) / 5
Mean of marks score = 420 / 5 = 84

Now,
In order to get the median,
Arrange the marks in ascending order,
66, 78, 85, 93, 98
n = 5
median = (n + 1) / 2th term  
             = (5 + 1) / 2th term
             =  6 / 2 = 3 th term
Median = 85
Here, 85 > 84 implies the median is more than the mean.

Thus, the mean of the set is less than the median. Option B is correct.

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Answer:

64

Step-by-step explanation:

Answer:

7.722[tex]cm^2[/tex]

Step-by-step explanation:

Work out the area of the circle

By the length of the square, you know the diameter of the circle is 12 cm so the radius is 6cm. Then you can calculate the area of the circle by doing

[tex]6^{2}[/tex]π =36π [tex]cm^{2}[/tex]

Work out the area of the square

12 x 12 = 144 [tex]cm^{2}[/tex]

So the bit not occupied by the circle will be 144- 36π = 30.888 [tex]cm^2[/tex]

However, the shaded area is just 1/4 of this bit so 30.888 / 4 = 7.722 [tex]cm^2[/tex]

Answer:

the letter d does not have symmetry

Step-by-step explanation:

Answer:

180° = pi radians

Step-by-step explanation:

360° = 2pi radians

90° = pi/2 radians

see image

180° is pi radians.

pi radians is equivalent to 180 degrees, option B is correct.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

The radian equivalent of 180° is pi radians.

This is because a full circle is 360°, which is equivalent to 2 pi radians. Therefore, half of a circle or an angle of 180° is equivalent to half of 2 pi radians, which is pi radians.

Hence,  pi radians is equivalent to 180 degrees, option B is correct.

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Answer:

To find the surface area of a cube, use the formula: surface area = 6s^2, where s is the length of one of the sides. If you don't know the length of the sides, you can find the surface area using volume. Just find the cube root of the volume, which is equal to the length of one side of the cube.

Step-by-step explanation:

Answer:

0.00604

Step-by-step explanation:

the exponent - 3 means move the decimal point 3 places to the left

A positive exponent + 3 means move the decimal point 3 places to the right.

6.04 × [tex]10^{-3}[/tex] = 0.00604

Polynomial is an expression that consists of indeterminates(variable) and coefficient. The polynomial f(x) is x³-12x²+256=0.

Polynomial is an expression that consists of indeterminates(variable) and coefficient, it involves mathematical operations such as addition, subtraction, multiplication, etc, and non-negative integer exponentials.

As the zeros of the polynomial are 8(multiplicity 2), -4. Therefore, the factors of the polynomial can be written as,

[tex]x = 8\\x-8=0[/tex]

[tex]x =-4\\x+4=0[/tex]

Now, the polynomial f(x) which is a third-degree polynomial can be written as,

[tex](x-8)(x-8)(x+4)=0\\\\(x-8)^2(x+4)=0\\\\(x^2-16x+64)(x+4)=0\\\\x^3-16x^2+64x+4x^2-64x+256 = 0\\\\x^3-12x^2+256=0[/tex]

Hence, the polynomial f(x) is x³-12x²+256=0.

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Answer:

10

Step-by-step explanation:

10

Answer:

10

Step-by-step explanation:

1) -9 on both sides

2) m/5=2

3) multiply both sides by 5

4) m=10

Answer:

f^−1(x)=x7

Step-by-step explanation:

To find the inverse , inerchange the variable and slove for Y

Answer:

$900

Step-by-step explanation:

60/4 = 15

60 x 15 = 900

Answer:

900

Step-by-step explanation:

900 it's not that hard 60/4 15x60

Answer:

It should be

likes dislikes

teens 96% 4%

adults 21% 79%

senior 18% 82%

citizens

Step-by-step explanation:

100 people

100%

so 1 person = 1%

i guess

Answer:

The answer is x= 6.2 and y= 5.7

Step-by-step explanation:

Let the two numbers be x and y.

1st condition:

x+y= 11.9 --- (1)

2nd condition:

x-y=0.5--- (2)

Solving 1 and 2

x+y= 11.9 --- (1)

x-y=0.5--- (2)                           (here +y and -y  will get cancelled)

_____________

2x= 12.4

x= 12.4/2 = 6.2

∴x= 6.2

Now, put x= 6.2 in equation (1)           ( u can put in eqn 2 also)

6.2+y= 11.9

y= 11.9-6.2= 5.7

∴y= 5.7

To recheck you can put the value of x and y in any of the eqns.  

The LHS will be equal to RHS if the values we got are correct.

Hope it helps.

Answer: I think It's 38

Step-by-step explanation:

you can multiply or add all of them together

Answer: Andrew ate 22 grapes on Monday.

Step-by-step explanation:

From Monday to Friday it is 4 days. since he ate 2 more grapes every day. You multiply 2 by 4. To get 8 and subtract 30 by 8 to get 28.

Answer:

x = -52

Step-by-step explanation:

[tex]\frac{1}{3}x-\frac{2}{3}=-18[/tex]

Let us solve for x.

[tex]\frac{1}{3}x=-18+\frac{2}{3}[/tex]

[tex]\frac{1}{3}x=-\frac{18*3}{1*3} +\frac{2}{3}[/tex]

[tex]\frac{1}{3}x=-\frac{54}{3} +\frac{2}{3}[/tex]

[tex]\frac{1}{3}x=\frac{-54+2}{3}[/tex]

[tex]\frac{1}{3}x=\frac{-52}{3}[/tex]

Use cross multiplication to find the value of x.

[tex]\frac{1x}{3}=\frac{-52}{3}[/tex]

[tex]3*1x=3*-52[/tex]

[tex]3x=-156[/tex]

Divide both sides by 3.

x = - 52

Answer:

C

Hope This Helps! :)

Answer:

36

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

Divide 72 by 2, and you get 36

Answer:

21.5

Step-by-step explanation:

19+24=43

43/2=21.5

hope it really helps......!!!!!!

By working with fractions, we will see that the amount that Rollie borrowed from his sister is $31.50.

Let's say that Rollie borrowed a quantity x.

The first month, Rollie returns one third of x + $3, so now he owes:

x - x/3 - 3 = (2/3)*x - 3

the second month returns another third of what he owes plus $3, so now he returns:

(1/3)*((2/3)*x - 3) + 3 = (2/9)*x + 2

So no he owes:

(2/3)*x - 3 - (2/9)*x - 2 = (4/9)*x - 5

Finally, on the third month he returns:

(1/3)*((4/9)*x - 5) + 3 = (4/27)*x - 5/3 + 3 = (4/27)*x + 4/3

Now he owes:

(4/9)*x - 5 -  (4/27)*x - 4/3 = (8/27)*x - 19/3

And that is equal to $3, what he owes at the end of the third month, so we need to solve:

(8/27)*x - 19/3 = 3

(8/27)*x = 3 + 19/3 = 28/3

Solving for x, we get:

x = (27/8)*(28/3) = 31.5

So Rollie borrowed $31.5 from his sister.

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Answer:

You have to share number too

Answer:

135 degrees.

Step-by-step explanation:

Circumference of the circle

= 8pi inches.

8pi equals 360 degrees

So 3pi = (3pi / 8pi) * 360

= 3/8 * 360

= 135 degrees.

Answer:

x + 1

Step-by-step explanation:

[tex]3x - (2x+4)+5[/tex]

[tex]3x-2x-4+5[/tex]

[tex]3x-2x+1[/tex]

[tex]x+1[/tex]

The equation that can be used to find the coordinates of B given the coordinates of A and the length of the line segment AB is given by: Option B: 3 =√[(x-4)² + (y-2)²]  

The shortest distance(length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:

[tex]D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units.[/tex]

For this case, we're specified that:

The coordinates of A are (4,2)

The distance from A to B = 3

Let the coordinates of B be (x,y), and (p,q) = (4,2), then we get;

[tex]D = \sqrt{(x-p)^2 + (y-q)^2}\\\\or\\\\3 = \sqrt{(x-4)^2 + (y-2)^2}\\[/tex]

Thus, the equation that can be used to find the coordinates of B given the coordinates of A and the length of the line segment AB is given by: Option B: 3 =√[(x-4)² + (y-2)²]  

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