Find the radius of the circle if the center is at (1,2) and the point (-3,4) lies on the circle

52 divided by 4 then you’ll get 13

Answer:

The answer in the procedure

Step-by-step explanation:

we know that

[tex]sin(A + B) = sin A cos B + cos A sin B[/tex]

In this problem we have

[tex]sin(x + \pi)=sin (x)cos(\pi) + cos(x)sin(\pi)[/tex]

Remember that

[tex]sin(\pi) = 0[/tex]

[tex]cos(\pi) = -1[/tex]

substitute

[tex]sin(x + \pi) = sin(x)(-1) + cos(x)(0)[/tex]

[tex]sin(x + \pi) = -sin(x)[/tex]

Final answer:

To prove that sin (x + π) = -sin x, the trigonometric identity for the sine of a sum is used, and by considering the specific values for cos π and sin π, the identity simplifies to the required expression.

Explanation:

To show that sin (x + π) = -sin x, we can use the trigonometric identity for the sine of a sum:

sin (α + β) = sin α cos β + cos α sin β

Applying this identity to sin (x + π):

sin (x + π) = sin x cos π + cos x sin π

Since cos π = -1 and sin π = 0, we substitute these values:

sin (x + π) = sin x (−1) + cos x (0)

sin (x + π) = −sin x + 0

Hence, sin (x + π) = −sin x, demonstrating the original statement.

Answer:

center:(4,-2)

Radius: 3 units

Step-by-step explanation:

The standard equation of a circle is given as [tex](x-h)^2+(y-k)^2=r^2[/tex], where (h,k) is the center and r is the radius of the circle.

The given equation is [tex](x-4)^2+(y+2)^2=9[/tex].

We compare to the standard equation of the circle to get;

[tex]x-h=x-4[/tex]

[tex]\Rightarrow -h=-4[/tex]

[tex]\Rightarrow h=4[/tex]

and

[tex]y-k=y+2[/tex]

[tex]\Rightarrow -k=2[/tex]

[tex]\Rightarrow k=-2[/tex]

Hence the center of the circle is (4,-2).

Also, we have [tex]r^2=9[/tex]

Therefore [tex]r=\sqrt{9}[/tex]

[tex]r=3[/tex] units.

Answer:

Center at (4,-2); radius: 3

Step-by-step explanation:

Answer:

[tex]4,151.25\ m^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the trapezoidal prism (swimming pool) is equal to

[tex]V=BL[/tex]

where

B is the area of the trapezoidal base

L is the length (distance between the two trapezoidal faces)

Find the area B

[tex]B=\frac{1}{2}(4+8)(30.75)=184.5\ m^{2}[/tex]

[tex]L=22.5\ m[/tex]

Find the volume

[tex]V=184.5(22.5)=4,151.25\ m^{3}[/tex]

Answer:

46x^2 + 73x + 15

Step-by-step explanation:

Expand both equations

Wall = (6x + 7)(8x + 5) = 48x^2 + 56x + 30x + 35 = 48x^2 + 86x + 35

Mural = (x + 4)(2x + 5) = 2x^2 + 5x + 8x + 20 = 2x^2 + 13x + 20

Minus them.

Wall - Mural =

(48x^2 + 86x + 35) - (2x^2 + 13x + 20)

(48x^2 - 2x^2) + (86x - 13x) + (35 - 20)

46x^2 + 73x + 15

Answer:

46x^2 + 73x + 15

Step-by-step explanation:

Expand both equations

Wall = (6x + 7)(8x + 5) = 48x^2 + 56x + 30x + 35 = 48x^2 + 86x + 35

Mural = (x + 4)(2x + 5) = 2x^2 + 5x + 8x + 20 = 2x^2 + 13x + 20

Minus them.

Wall - Mural =

(48x^2 + 86x + 35) - (2x^2 + 13x + 20)

(48x^2 - 2x^2) + (86x - 13x) + (35 - 20)

46x^2 + 73x + 15

48 and 81 basically you just have to multiply

Answer:

144 cubic inches

Step-by-step explanation:

We are given a diagram of a pyramid with length = 8 inches, height = 9 inches and width = 6 inches.

We are to find the volume of this pyramid.

We know that the formula of volume of a pyramid is given by:

[tex] \frac { l \times w \times h } { 3 } [/tex]

Substituting the given values in the above formula to get:

Volume of pyramid = [tex] \frac { 8 \times 6 \times 9 } { 3 } [/tex] [tex]=\frac{432}{3}[/tex] = 144 cubic inches

Answer:

Dividend- The number that is divided is called the dividend

Divisor- a number that divides a integer ( It is the number that is divided by the Dividend)

Quotient- is the result when dividing.

Remainder-  is the amount that is left over after dividing

Step-by-step explanation:

Example

36 ÷ 6 = 6

36 is the Dividend

6 is the Divisor

6 is the Quotient

No remainder

Hopes this helps!

Answer:

17.5 yds because Radius is half of the circumference

Step-by-step explanation:

The radius of the circle with a circumference of 35 π yards is 17.5 yards.

The circumference of a circle is the perimeter of a circle. Therefore,

where

r =radius

Therefore,

circumference = 35πyard

35π = 2πr

divide both sides by 2π

35π / 2π = 2πr / 2π

r = 17.5 yards

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Answer:

The concep of rectilinean line between point A and point B.

Search about euclidean laws.

Besr regards

The line between is point A and point B.

Answer:

I believe the answer would be 4 gift bags.

Step-by-step explanation:

The highest number both numbers can be divided by and get a a whole number is 4. Four is the greatest common factor. So there will be 4 bags with 7 bottles of lotion and 3 candles inn each bag.

Answer:

Step-by-step explanation:

Factoring the number of items

Common factor is 4, so the number of gift bags is 4 the greatest

The number that is in the millions place is 3

The value of each digit in a number is known as the place value. The correct option is C, 3.

The value of each digit in a number is known as the place value. The 5 in 350, for example, represents 5 tens, or 50, whereas the 5 in 5,006 represents 5 thousand, or 5,000. It is critical that children that while a digit can be the same, its value is determined by its position in the number.

Identification of the place value of a digit in a number:

The million in a digit is represented by the sixth digit from the right in a number. Therefore, In the number 3,657,892, the digit that is in the millions of places is 3.

Learn more about the Place Value:

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Answer:

since triangles are similar

4/x = 7x/7

=》 4/x = x

=》x^2 = 4

=》 x = 2

for right triangles a^2 = b^2+c^2

DF^2 = 7^2+2^2 = 53

=》 DF = 7.28

perimeter of DEF = 7 +2+7.28 = 16.28

Answer:

Step-by-step explanation:

$300-$125=$175

Answer:

64 inches

Step-by-step explanation:

12 x 3ft (1yard)=36in

Answer:

JMK = 54

JKH = 126

HLK = 90

HJL = 27

LHK = 63

JLK = 27

Step-by-step explanation:

Just use 180 for total angles in each triangle. Vertical angles mean the opposite to 126 is 126 and the other two that make up the inner vertices are (360- 126*2)/2 = 54

So, 126, `16, 54 , 54 are the inner angles in the circle. Just go from there.

Answer: 13

Step-by-step explanation:

In order to solve this equation you need to replace x with 9.

2/3 x 9 + 7=

6 + 7=

13

Answer:

The first graph.

Step-by-step explanation:

An exponential function has a graph that is a smooth curve; it either increases  at an ever increasing rate or decreases at an ever increasing rate.

The only graph that fits these characteristics is the first one.

Answer:

First graph is the exponential function

Step-by-step explanation:

The x value of exponential function is all real numbers

x can take any value positive or negative numbers

In the first graph , as x value increases the graph goes down

The first graph is an exponential function .

Second graph is the cubic function as the graph goes from left and it goes down on the right .

Third graph is an rational function because we have two graph on both sides of vertical asymptote

The fourth graph is not an exponential function as the domain is not all real numbers.

Lean more : brainly.com/question/15535185

A decameter is the longest, as it has a length equal to 10 meters.

Hope this helps!

Answer:

Decameter

Step-by-step explanation:

A decameter = 10 meter

millimeter = 0.001 meter

meter = meter

centimeter = 0.01 meter

Best regars

Answer:

D

Step-by-step explanation:

An absolute value is measuring how far away the value is from 0.

Since -1/4 is 1/4 away from 0, D is the answer.

Answer:

D) 13

Step-by-step explanation:

3(-4)=-12+1=-11

2(-1)=-2+4=-2

11+2=13

Step-by-step explanation:

(4/5+3/5)+3.5*5

= 7/5+7/2*5

= 7/5+35/2

= 14/10+175/10

= 189/10

= 18.9

Answer:

The value of the expression is 18.9

Step-by-step explanation:

The expression is:

[tex]\bigg( \frac{4}{5}+\frac{3}{5}\bigg)+3.5\times 5[/tex]

The first step is to solve the parenthesis. As both fractions have the same denominator, the numerators must be added:

[tex]\bigg( \frac{4+3}{5}\bigg)+3.5\times 5[/tex]

[tex]\bigg( \frac{7}{5}\bigg)+3.5\times 5[/tex]

The second step is to perform the division between 7 and 5, it is 1.4:

[tex]1.4+3.5\times 5[/tex]

The third step is to perform the multiplication between 3.5 and 5, it is 17.5:

[tex]1.4+17.5[/tex]

The last step is to perform the sum, it is 18.9:

[tex]1.4+17.5=18.9[/tex]

Thus, the value of the expression is 18.9.

Answer:

ON MONDAY:  35 mosquitos.

ON TUESDAY: 6 flies.

Step-by-step explanation:

As you can see in the diagram, the frog eats 3 flies for every 7 mosquitoes (for lunch). Then you can expresed this ratio as following:

3:7 or [tex]\frac{3}{7}[/tex]

Based on the table:

-If the frog eats 15 flies on monday, then the number of mosquitos that it eats can be calculated as following:

[tex]\frac{3}{7}=\frac{15}{mosquitoes}\\\\mosquitoes=\frac{15*7}{3}\\\\mosquitoes=35[/tex]

-If the frog eats 14 mosquitoes on tuesday, then the number of flies that it eats can be calculated as following:

[tex]\frac{3}{7}=\frac{flies}{14}\\\\flies=\frac{14*3}{7}\\\\flies=6[/tex]

To evaluate the expression, we follow the order of operations (PEMDAS). The result of the expression is 31.

To evaluate the expression 24 ÷ 3 + 7 ⋅ 2 – 15 ÷ 5 + 6 ⋅ 2, we need to follow the order of operations, also known as PEMDAS. PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Therefore, the evaluated expression is equal to 31.

1 + x < 5

the sum means addition, so the sum of 1 and x is 1 + x and less than 5 means exactly that, less than 5. The less than sign is represented by <

The statement "the sum of 1 and x is less than 5"written as an inequality is 1 + x < 5.

x < 4

An inequality is a statement that is of two quantities one is specifically less than (or greater than) another.

The sum of 1 and x is less than 5

1 + x < 5

Subtract 1 from both sides

x < 5 - 1

x < 4

Therefore, x is less than 4

Read more on inequality:

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Answer:

To find the answer, you must multiply/divide the amount in cups by calories per cup.

Step-by-step explanation:

Butter only has 0.3 cups, so The calories will only be 30% of what is written down. 30% of 1627= 488.1 calories

Marshmallows is 4.25 times larger then the calories per cup, so now you'll have to multiply.

4.25*159=675.75 calories

Finally, Cereal is 5.5 times larger then the calories per cup, so we will multiply again.

5.5*101=555.5 calories

Finally, add all the number together to find the total amount of calories in the marshmallow treats.

555.5+675.75+488.1=1,719.35  calories

There is a total of 1,719.35 calories in the marshmallow treats.

♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫

➷ There are 6 surfaces:

2 of them have an area of 84 square inches

2 of them have an area of 37 1/3 square inches

2 of them have an area of 1

You add them all together, and you get:

Final answer:

244 2/3 square inches

✽

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

TROLLER

The total surface area for the given prism is 808 square inches.

The question asks to calculate the surface area of a rectangular prism in square inches. The dimensions given are 1 1/2 ft (length), 2/3 ft (width), and 5/6 ft (height). To convert these measurements to inches, we multiply by 12 since there are 12 inches in a foot. Thus, the dimensions in inches are:

To find the surface area, we calculate the area of each face and then sum them:

Now, add up all the areas of the faces to get the total surface area:

Surface Area = 360 + 288 + 160 = 808 square inches.

Answer: C.

Step-by-step explanation:

All we need to do is add all the number together:

Convert to decimals for easier adding:

2.5+2.5+(3.5*5)+4.25+4.25+5.5=36.50km

Now we convert to a fraction: 36.50=36 2/4km

So the answer is 36 2/4km