Write the standard form of the equation of the circle with radius 7 and center (5,−7).

Answer:

The third circle on the bottom

Step-by-step explanation:

looking at it tells you that none of the other answers were correct.

Step-by-step explanation:

If x=10

\(\tt{ x^2-2(x+5) }\) ⠀

\(\tt{ (10)^2-2×(10+5) }\) ⠀

\(\tt{100-2×15 }\) ⠀

\(\tt{ 100-30 }\) ⠀

\(\bold{ 70 }\) ⠀

The area of a rectangle with a width of 5.1 cm and a height of 11.2 cm is 57.12 cm².

To find the area of a rectangle, we multiply its length by its width. In this case, the width is given as 5.1 cm and the height (or length) is given as 11.2 cm.

Area = length × width

Area = 11.2 cm × 5.1 cm

Calculating the product, we get:

Area = 57.12 cm²

Therefore, the area of the rectangle is 57.12 cm².

The correct answer is: 57.12 cm².

It is important to note that when calculating the area of a rectangle, we should always include the appropriate unit of measurement (in this case, cm²) to indicate that we are dealing with a two-dimensional measurement. The area represents the amount of space covered by the rectangle's surface.

So, the area of a rectangle with a width of 5.1 cm and a height of 11.2 cm is 57.12 cm².

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The linear inequality represented by the graph is defined as follows:

y ≥ -2x + 1.

The ordered pairs that are solutions to the inequality x < -3 are given as follows:

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

For which the coefficients are given as follows:

The function in this problem crosses the y-axis at y = 1, hence the intercept b is given as follows:

b = 1.

When x increases by one, y decays by two, hence the slope m is given as follows:

m = -2.

The shaded region, considering the solid line, is given by the values to the right of the line, hence the inequality is defined as follows:

y ≥ -2x + 1.

The inequality for this problem is defined as follows:

x < -3.

The ordered pairs have the following format:

(x,y).

Hence all the ordered pairs that have x < -3, no matter the coordinate of y, are solutions to the inequality.

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Using the formula of combination and the provided condition that any child can get any number of books, The answer is 637.

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. We use permutation to determine how many possible ways we have to arrange items from a collection system.

The required formula is:

\(C(n,r) = \frac{n!}{r!(n-r)!}\)

where, n= total number of objects in the set.

r= number of choosing objects from the set.

from the given data, total number of books = n= 5

number of children we need to distribute, r= 10

total possible ways of distribution= C(10,1)+C(10,2)+C(10,3)+C(10,4)+C(10,5)

=10+45+120+210+252

=637

hence, we have total 637 possible ways to distribute.

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Answer:

Step-by-step explanation:

let the original price be x

discount is 25%, .25x

discounted price x-.25x=.75x

112.50=.75x

x=150 was the membership selling before the discount

All vectors of the form(a, b, a - 2b) is a subspace of R³. So, the correct option is option(D).

If W is a set of one or more vectors from a vector space V, then W is a subspace of V if and only if

Now, check the options and find out the option which satisfy the subspace conditions.

A) All the vectors are of form (0, a,a²)

let (0,1,1) = u and v=(0,2,4) and both are belongs to { 0, a,a² : a∈R }, (0,0,0)∈ {0, a,a² : a∈R }.

u + v = (0,1,1) + (0,2,4) = (0,3, 5) not belongs to

{ 0, a,a² : a∈R }. So, this is not correct option.

B) Here, (0,0,0) does not belongs to

{0, a, a+2 : a∈R } because if a= 0 then a+2 =/ 0 .

So, it is also not subspace.

C) All vectors of the form (a, b, 2)

The third tuple is 2 which never be equal to zero. Hence, (0,0,0) does not belongs to (a, b, 2) and it is not form subspace.

D) All vectors of the form (a, b, a - 2b)

When a = 0 , b = 0 => (0,0,0) ∈(a, b, a - 2b)

let u = ( a1, b1 , a1- 2b1) and v = ( a₂, b₂ , a₂ - 2b₂)

and α∈R

u + v = ( a₁, b₁ , a₁- 2b₁ ) + ( a₂, b₂ , a₂ - 2b₂)

= ( a₁ +a₂ , b₁+b₂ , a₁+a₂ -2(b₁ - b₂)) €(a, b, a - 2b)

αu = α(a₁ , b₁ , a₁- 2b₁)

=( αa₁ , αb₁ , α(a₁ - 2b₁))∈(a, b, a - 2b)

both the conditions are satisfied, so it is Subspace of R³.

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Answer:

what is the sum.

Step-by-step explanation:

Take the sum - 11 =x

Answer:

( -1 , -3 ) , ( 4 , -3 ) , (4 , -1 )

The volume of the solid is equal to the integral of the area of the semi-circular cross sections multiplied by the length of the interval. The area of the semi-circular cross sections is equal to πr²/2, where r is the diameter running from y. Therefore, the volume is equal to π/2∫0,9r²dy.

Step 1: Substitute the expression for the area of the semi-circular cross section into the equation for the volume of the solid:

V = π/2∫0,9r²dy

Step 2: Integrate the equation to find the volume of the solid:

V = π/2[y³/3]|0,9

Step 3: Evaluate the integral:

V = π/2(9³/3 - 0³/3)

step 4: Solve for the volume of the solid:

V = 7π/2

The volume of the solid is equal to the integral of the area of the semi-circular cross sections multiplied by the length of the interval. The area of the semi-circular cross sections is equal to πr²/2, where r is the diameter running from y. Therefore, the volume is equal to π/2∫0,9r²dy. To calculate the volume, we must first substitute the expression for the area of the semi-circular cross sections into the equation for the volume of the solid: V = π/2∫0,9r²dy. Then, we must integrate the equation to find the volume of the solid: V = π/2[y³/3]|0,9. After that, we must evaluate the integral: V = π/2(9³/3 - 0³/3). Finally, we must solve for the volume of the solid: V = 7π/2. The answer is the volume of the solid is 7π/2.

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Answer:

ITS OPTION 3

Step-by-step explanation:

The inputs 4 and 8 have more than one out, the relation is not a function.

A relation is said to be a function if one input is mapped to one output.

that is, each x-value can only have one y-value.

From the table;

Input, output

4 ----- 1

8 ----- 3

4 ------5

8 ----- 4

4  is an input, it has an output of 1.

4 appeared again as input but this time has an output of 5.

This means one input has more than one output.

Also, 8 is an input, it has an output of 3.

8 appeared again as input but this time has an output of 4.

Which also means one input has more than one output.

Therefore, the relation is not a function.

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Answer:

2,3,7,2,5

Step-by-step explanation:

When you factorize a number you divide them until the outcome numbers are prime. 420 is equal to 42 and 10.

42 is equal to 6 and 7 and 6 is 2 times 3

2,3,7 is prime

10 is 2 times 5

2 and 5 is prime

Answer:

420 = 2² × 3 × 5 × 7

Step-by-step explanation:

The first few prime numbers are:  2, 3, 5, 7, 11, 13, 17, ...

To find which prime numbers multiply together to make 420, start by dividing 420 by the first prime number, 2:

⇒ 420 ÷ 2 = 210

As 210 is not a prime number, we need to divide again.  Let's try dividing by 2 again:

⇒ 210 ÷ 2 = 105

As 105 is not a prime number, we need to divide again.  105 is not divisible by 2, so let's try dividing it by the next prime number, 3:

⇒ 105 ÷ 3 = 35

As 35 is not a prime number, we need to divide again.  35 is not divisible by 2 or 3, so let's try dividing it by the next prime number, 5:

⇒ 35 ÷ 5 = 7

As 7 is a prime number, we can stop.

Therefore, 420 is the product of all the prime numbers we found together with the final one:

⇒ 420 = 2 × 2 × 3 × 5 × 7

As 2 appears twice, we can write this using exponents:

⇒ 420 = 2² × 3 × 5 × 7

Answer:

220 adults and 250 children

Step-by-step explanation:

we require to set up 2 equations and solve simultaneously.

let a be the number of adults and c the number of children , then

a + c = 470 → (1) based on number of people

3a + c = 910 → (2) based on ticket sales

subtract (1) from (2) term by term to eliminate c

(3a - a) + (c - c) = 910 - 470

2a + 0 = 440

2a = 440 ( divide both sides by 2 )

a = 220

substitute a = 220 into (1) and solve for c

220 + c = 470 ( subtract 220 from both sides )

c = 250

that is 220 adults and 250 children attended

Two years ago, an investment of R1 500000 has increased to R1 700000 and has delivered R40 000 worth of dividends over the two years. Then the return on investment would be 16%.

We can use the following formula to calculate ROI:

ROI = (gain from investment - cost of investment) / cost of investment

where, gain from investment is the total value of the investment (including dividends), and cost of investment is the initial investment.

Using the values given in the question, we can calculate the ROI as:

ROI = ((R1,700,000 + R40,000) - R1,500,000) / R1,500,000 = R240,000 / R1,500,000

ROI = 0.16 or 16%

Therefore, the return on the investment is 16%.

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The characteristic polynomial  x³ - 7x² + 16x - 12  The characteristic polynomial of a square matrix in linear algebra is a polynomial that is invariant under matrix similarity and has the eigenvalues as roots.

Its coefficients include the determinant and the trace of the matrix.

Characteristic polynomial of a 3×3 matrix A is given by ; x³ - trace(A)x² + (A​​​​​​11 + A​​​​​​22 + A​​​​​​33 )x - determinant(A)

Where A​​​​​​ii is the determinant of the matrix obtained by deleting i​​​​​​ th row and i th column.

Here trace(A) = sum of the diagonals = 12 - 7 + 2 = 7

A​​​​​​11 = -7 × 2 = -14

A​​​​​​22 = 2 × 12 = 24

A​​​​​​33 = ( 12×-7) - (-10×9) = 6

Determinant(A) = 12(-7×2 - 0) + 10(2×9 - 0) = 12

Substituting these values in above equation , we obtain;

x³ - 7x² + (-14 + 24 + 6)x - 12 = x³ - 7x² + 16x - 12.

Hence x³ - 7x² + 16x - 12 is the characteristic polynomial of A.

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Answer: 5

Step-by-step explanation:

First order from least to gratest: 3, 4, 5, 5, 5, 6, 6, 7, 8, 8, 9, 11

Then find median (center): 6

Next find the lower quartile also known as the first quartile: 5

Your answer is 5

If you need additional help you can go to khan academy it is a great site with math for pre-k -SAT. Using khan academy I have become an A student.

I hope this helps and may God bless you. Have a nice day, bye!

Answer:

54.6cm

Step-by-step explanation:

Arc length = radius * central angle

= 18.2*3

=54.6

Answer:

9 squares

Step-by-step explanation:

Anne bought a piece of ribbon = 7 over 9 m long = 63 m²

she used = 3 over 18 m = 54 m²

left = 9 m²

maximum number of squares she could form of 1 m = 9

Answer:

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

Simplify the equation by distribution, then substitute the value of d and solve for c:

Answer:

x = 11.75

Step-by-step explanation:

Rounding to two decimal places, the Z-score corresponding to the youngest senator of age 39 is -1.40.

To find the Z-score corresponding to a particular value in a normal distribution, we use the formula:

Z = (x - μ) / σ

where x is the value of interest, μ is the mean, and σ is the standard deviation.

Part 1 of 2: For the oldest senator of age 85:

Z = (x - μ) / σ = (85 - 56.5) / 12.5 ≈ 2.28

Rounding to two decimal places, the Z-score corresponding to the oldest senator of age 85 is 2.28.

Part 2 of 2: For the youngest senator of age 39:

Z = (x - μ) / σ = (39 - 56.5) / 12.5 ≈ -1.4

Rounding to two decimal places, the Z-score corresponding to the youngest senator of age 39 is -1.40.

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Standard Deviation for given set of data is 0.25634797778466.

What is standard deviation?

Given that,

Sample size :12.3,11.9,12.5,12.1,12.6,11.9,12.2,12.1

Count, N: 8

Sum, submission x: 97.6

Mean, x: 12.2

Variance, s2:  0.065714285714286

s^2 = Σ(xi - x)^2/N - 1

= (12.3 - 12.2)2 + ... + (12.1 - 12.2)^2/8 - 1

= 0.46/7

=  0.065714285714286

s =  √0.065714285714286

=  0.25634797778466

Standard Deviation for given set of data is 0.25634797778466.

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[Hello, blueface1728]

Answer:

[D] −6 < x < 9

Step-by-step explanation:

So, if a < u <b then a < u and u <b

-7 < x - 1 and x -1 < 8

Solving

-7 < x - 1  = x > -6

x - 1 < 8 = x < 9

Combine the intervals

-6 < x < 9

Now looking at the answer choice :

6 < x < 9

−6 > x > 9

6 > x > −9

−6 < x < 9

Thus, the answer is [D] −6 < x < 9

Kavinsky

The true options regarding the triangle diagram are;

m∠5 + m∠6 = 180°

m∠2+ m∠3 = m∠6

m∠2 + m∠3 + m∠5 = 180°

We see the attached image showing ΔABC with Exterior angles as;

∠ 1 , ∠ 4 ,and ∠ 6

Now, the exterior angle property of triangles states that; An exterior angle of a triangle is equal to the sum of the opposite interior angles.

For Exterior ∠1 we have;

∠1 = ∠5 + ∠3 (Exterior angle Property of Triangle)

Similarly,

For Exterior ∠ 4 we have;

∠4 = ∠5 + ∠2   (Exterior angle Property of Triangle)

For Exterior ∠6 we have;

∠6 = ∠2 + ∠3   (Exterior angle Property of Triangle)

From Triangle Sum Property, we know that the sum of the measures of angles in a triangle is equal to 180°. Thus;

m∠2 + m∠3 + m∠5 = 180° (Triangle Sum Property)

Linear Pair of angles states that the measure of a straight angle is 180° and as such a linear pair of angles must add up to 180°. Thus;

m∠5 + m∠6 = 180°  (Linear Pair)

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Answer:

x + 5 + 5x + 10 + 2y = 6x + 2y + 15

Step-by-step explanation:

Group like terms

= x + 5x + 2y + 5 + 10  

Add the number 5 + 10 = 15  

= x + 5x + 2y + 15

Add similar elements x + 5x = 6x  

= 6x + 2y + 15

Have a good day :)