ABCD is a rhombus. Solve for the length of AB if the two diagonals lengths are: AC = 12 units, BD = 16 units.

Answer:

nth term = -3-5(n-1)

Step-by-step explanation:

Answer:

Carla needs to make at least 11 two-pointer shots in the surrent game

Step-by-step explanation:

The first thing we can do is to find the difference between the number of points that Carla scored in her first game and her second game.

This will be 46 - 24 = 22 points difference

Carla needs to make a certain number of two-pointers to get at least the same score she had in her previous game.

We can get this number of two-pointers that needed to be made by dividing the difference in scores by 2

i.e number of two-pointer shots = 22/2 =11 shots

Therefore, Carla needs to make at least 11 two-pointer shots to be able to get the same score in her current game.

The possible values of k are -0.56, -3.56, -2 and -1.

We have the equation of the parabola, y = 0.5 (x- 3 ) ( x+ k)

Substituting x=0, we get that i.e. y =0.5 * (-3) * k -1.5k

So, the y-intercept is (0,-1.5k).

Thus, the height of the triangle becomes |-1.5k| = 1.5k

Again, substituting y=0, 0 = 0.5 (x-3) (x+k) i.e. i.e. x0=(x-3) (x+k)=3 and x=-k

So, the x-intercepts are (3,0) and (-k,0).

Thus, the base of the triangle is 3+k if k>-3 or -3-k if k<-3.

As, area of a triangle = 1/2 * (base )* (height )

Substituting the values, we get,

1.5=1/2 *(3+k)*(1.5k)

i.e.3= 4.5 k + 1.5k ²

i.e. k = -0.56 and k = -3.56

or

1.5=1/2* (-3-k )*(1.5k)

i.e.

3 = -4.5 k - 1.5²

i.e. k = -2 and k = -1.

Thus, the possible values of k are -0.56, -3.56, -2 and -1.

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To determine the number of ways that exactly one husband is not dancing with his own wife, we can consider the different possibilities, which comes out to be 108.

First, we need to select one husband who will not dance with his own wife. There are 4 ways to choose this husband.

Once the husband is chosen, there are 3 other wives remaining, and each wife has 3 possible partners (excluding her own husband). Therefore, there are 3 possibilities for each of the 3 wives, giving us a total of 3^3 = 27 ways to assign partners to the remaining couples.

Therefore, the total number of ways that exactly one husband is not dancing with his own wife is 4 * 27 = 108.

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The function which is representing the red graph is x³ - 5. So the correct answer is option D.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

In the graph when plotted on the x and y-axis the function D is  x³ - 5 shows the red graph in the given figure.

The graph i also attached with the answer below.

Therefore the function which is representing the red graph is x³ - 5. So the correct answer is option D.

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Answer:

The answer is C There were no mosques on the African continent.  

Step-by-step explanation:

The area of the polygon is solved to be  1044 squared cm

The area of the composite polygon is solved by dividing the object into two sections. Then adding up the areas

Section 1 has dimensions:

length * width = 46 * 14 = 644

section 2 has dimensions:

length = 46 - 21 = 25

width = 30 - 14 = 16

Area = 25 * 16 = 400

Area of the composite figure

section 1  + section 2

= 644 + 400

= 1044 squared cm

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The orthogonal complement S is the set of all vectors orthogonal to the subspace S in R5 whose third and fourth components are zero. To find S, we need to find vectors such that vu = 0 for all u in S using the dot product. The orthogonal complement S has dimension three and a basis for it is f1, f2, f3, where f1 = (1,-1,0,0,0) f2 = (0,0,1,0,0) f3 = (0,0,0,1,0).

Let's begin by defining the orthogonal complement S⊥, which is the set of all vectors orthogonal to the subspace S in question. The subspace S is defined as the set of all vectors in R5 whose third and fourth components are zero. Let's go through the steps to find S⊥.

Step 1: Determine the dimensions of S The dimension of the subspace S is two. This is because the subspace consists of vectors whose third and fourth components are zero. Therefore, only the first, second, fifth components are nonzero, making up a 3D subspace. Since S is a subspace of R5, the remaining two components can also take any value and thus the dimension of S is 2.

Step 2: Determine a basis for S To determine a basis for S, we can use the fact that the subspace is defined as all vectors whose third and fourth components are zero.

Therefore, a basis for S is given by {e1, e2}, where e1 = (1,0,0,0,0) and e2 = (0,1,0,0,0).

Step 3: Find the orthogonal complement S⊥ To find S⊥, we need to find all vectors orthogonal to S. This means we need to find vectors v such that v⋅u = 0 for all u in S. To do this, we can use the dot product: v⋅u = v1u1 + v2u2 + v3u3 + v4u4 + v5u5= v1u1 + v2u2 + v5u5We want this to be zero for all u in S. This implies:v1 + v2 = 0 andv5 = 0Therefore, S⊥ is given by the set of all vectors in R5 of the form (a,-a,b,c,0), where a, b, and c are arbitrary constants. The orthogonal complement S⊥ has dimension three, and a basis for it is {f1, f2, f3}, where:f1 = (1,-1,0,0,0)f2 = (0,0,1,0,0)f3 = (0,0,0,1,0)The above result gives us a complete characterization of S⊥.

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If you have 240 cards and collect 20 cards per week, you have 96 cards after 8 weeks and your freind have 240 cards in 7.5 weeks.

First, we need to find the total number of cards collected per week by both you and your friend

Total cards collected per week = your cards + friend's cards

Total cards collected per week = 20 + 12

Total cards collected per week = 32

Now, we can find the number of weeks it would take for your friend to collect 240 cards

240 cards ÷ 32 cards per week = 7.5 weeks

Since we cannot have a fractional number of cards, we need to round up to the nearest whole number of weeks. Therefore, it would take your friend 8 weeks to collect 240 cards.

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Answer:

caste system, they were commonly used to show the groups of people in their social hierarchies

\(x=106^{\circ}\) (linear pair)

\(y=106^{\circ}\) (corresponding angles with \(x\))

\(z=106^{\circ}\) (vertical angles with \(y\))

Answer: 22x-12

Step-by-step explanation:

4x + 6(3x - 2)

= 4x+18x-12

= 22x-12

= 2(11x-6)

Answer:

\(4x + 6(3x - 2) \\ = 4x + 18x - 12 \\ = 22x - 12 \\ \\ \)

The rate in centimeters per second, at which the radius is increasing at the instant when the radius is 5 centimeters is 0.16 cm/s.

Using a known value of a function at a certain point along with its rate of change at that moment, one application of derivatives is to estimate an unknown value of a function at a particular point.

Given:

Both radius r and area A is a function of time, so in fact:

A(t) = π [r(t)]²

Deriving this we get that the area changes and the radius changes as:

\(\frac{dA(t)}{dt} = 2\pi r(t)\frac{dr(t)}{dt}\)

But,

\(\frac{dA(t)}{dt} = 5 \frac{cm^{2} }{s}\)

Considering when r(t) = 5cm at the instant we get,

\(5 = 2\pi . 5\frac{dr(t)}{dt}\)

Simplify 5 and take 2π to the other side and divide,

The rate of change of radius is given by:

\(\frac{dr(t)}{dt} =\frac{1}{2\pi } = 0.16 cm/s\)

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Answer:

y<-15

Step-by-step explanation:

2y+5/y=2y/y-3

2y^2=2y^2-6y+5y-15

y=-15

Answer:

\(x=7\)

Step-by-step explanation:

So we have the equation:

\(7x-27=3x-5+x-1\)

Combine like terms:

\(7x-27=4x-6\)

Subtract 4x from both sides:

\(3x-27=-6\)

Add 27 to both sides:

\(3x=21\)

Divide both sides by 3:

\(x=7\)

So, the value of x is 7.

And we're done!

Steps to solve:

7x - 27 = 3x - 5 + x - 1

~Combine like terms

7x - 27 = 4x - 6

~Add 27 to both sides

7x = 4x + 21

~Subtract 4x to both sides

3x = 21

~Divide 3 to both sides

x = 7

Best of Luck!

the products are equal, we can conclude that the two ratios form a proportion. Therefore, we can say that the ratio of large staplers to small staplers is the same in both cases,

what is ratios ?

A ratio is a comparison of two or more quantities that can be expressed in the form of a fraction. Ratios can be used to describe the relationship between two quantities, such as the number of boys to the number of girls in a class, the ratio of sugar to flour in a recipe

In the given question,

To determine if these ratios form a proportion, we need to check if the two ratios are equal to each other. We can do this by cross-multiplying and checking if the products are equal.

The first ratio can be written as:

3 large staplers : 17 small staplers

We can also write it as:

3/17 = x

where x is the ratio of large staplers to small staplers.

The second ratio can be written as:

6 large staplers : 34 small staplers

We can also write it as:

6/34 = x

Now, we can cross-multiply to check if the two ratios are equal:

3/17 = 6/34

Cross-multiplying gives:

3 x 34 = 6 x 17

Simplifying:

102 = 102

Since the products are equal, we can conclude that the two ratios form a proportion. Therefore, we can say that the ratio of large staplers to small staplers is the same in both cases, and we can use this proportion to make calculations involving these ratios.

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Answer:

l = 194999.45

Step-by-step explanation:

I'm going to assume that you meant 3.14 by 3,14.

336,765 = 3.14 × 0.55 × (l + 0.55)

336,765 ÷ (3.14 × 0.55) = l + 0.55

(336,765 ÷ (3.14 × 0.55)) - 0.55 = l

l = 194999.45

A)an = 2*2^(n-1)`. B) `The sum of the first n fractions is `2*(2^n - 1)`.

a. The sequence is a geometric sequence with the first term `a1 = 2` and common ratio `r = 2`.Therefore, the nth term `an` is given by:`an = a1*r^(n-1)`

Substituting `a1 = 2` and `r = 2`, we have:`an = 2*2^(n-1)`

b. To find the sum of the first n terms, we use the formula for the sum of a geometric series:`S_n = a1*(1 - r^n)/(1 - r)

`Substituting `a1 = 2` and `r = 2`, we have:`S_n = 2*(1 - 2^n)/(1 - 2)

`Simplifying:`S_n = 2*(2^n - 1)

`The sum of the first n fractions is `2*(2^n - 1)`.As `n` gets larger and larger, the sum approaches `infinity`.

Thus, the sum is getting closer and closer to infinity.

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The dimensions of the living room on the drawing is 2 inches by 2 1/2 inches.

The scale drawing is a smaller version of the living room. The scale drawing is reduced at a constant rate using the scale.

The scale is used to keep the proportion of the dimensions between the scale drawing and the original diagram similar.

Length of the scale drawing = (3/4 x 16) / 6 = 2 inches

Width of the scale drawing = (3/4 x 20) / 6 = 2 3/6 = 2 1/2 inches

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The angle whose vertex is on the circle and the sides of the angle are the chords is called an Inscribed Angle .

What is an Inscribed Angle ?

An inscribed angle in the circle is formed by the two chords which have a common end point on circle and this common end point is called the vertex of inscribed angle.

The arc formed by the inscribed angle in the circle is called as the intercepted arc .

also the Inscribed Angle Theorem states that inscribed angle on the circle is half the measure of central angle that subtends the same arc .

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SOLUTION

Line 1 is given as

let's find the equation of line 2, it passes through points (2, 3) and (4, 4)

The slope is

The slope of line 2 is 1/2

If the two lines are perpendicular, then the product of their slope will be = -1, that is

Since the product of their slope = -1

Hence Line 1 and Line 2 are perpendicular

You have the following function:

As you can notice, the function does not have exponentials, logarithms, denominators and roots. Then there are no restrictions to the domain of the function neither the range of the function.

The range are all real numbers. In interval notation is:

(-∞,∞)

answer: (-∞,∞)

Answer:

The percent of interest is 12.3% per year

Step-by-step explanation:

According to the question Elwood invested 5000 $ in market account

The market account gives the compound interest annually

let p be the interest per year then

At the end of 1st year

amount =(1+0.p) x 5000  = 1.p x 5000

similarly at the end of 2nd year

amount =(1+0.p) x(1+0.p)x 5000  = \((1.p)^{2}\) x 5000

similarly at the end of 3rd year

amount = 7100 $ = \((1.p)^3\) x 5000

⇒ \(\frac{71}{50}\) = \((1.p)^3\)  

1.392 =  \((1.p)^3\)

on further solving we get

1.p = \((1.42)^{1/3}\) = 1.123

thus 1.p = 1 + 0.p = 1.123

thus p = 0.123

thus the percent of interest is 12.3% per year

Answer:

drop down 1 a slower rate per year

drop down 2 670

Step-by-step explanation:

as in three years you get $7100

you take that and subtract it by your starting amount (5000)

7100-5000= 2100

then divide 2100 by the number of years (3)

to get your annual rate of 700$

then you take the 8 year total and subtract it from your 3 year total

10350-7100= 3250

Then divide that by 5 because that how many years it has been

to get the annual rate of 650

making the 5 year rate slower.

The to find the average rate over all 8 year you take 10350 and subtract it from your starting number 5000

10350-5000= 5350

then take 5350 and divide it by the number of years (8)

you then get you average rate of 668.75

668.75=670

Hope this helps!

The gut lining and circulation are both helped by special cells that aid in the absorption of nutrients.

One of the eleven organ systems that make up the human body is the circulatory system, which is a component of the "cardiovascular" system. Its primary job is to move waste products away from cells and nutrients toward them. The heart, blood, and blood vessels make up this system.

The circulatory system rids the body of wastes and feeds and oxygenates cells. Different sides of the heart pump both oxygenated and deoxygenated blood. Arteries, capillaries, and veins are the different types of blood vessels.

Small intestine villi that line the walls absorb nutrients into lymphatic lacteals and capillaries of the circulatory system. Capillary beds and lacteal-like lymphatic channels can be found in villi. The lacteals take in fatty acids from the chyme after it has been broken down.

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Answer:

2/5

Step-by-step explanation:

2:3

If we write an equation: 2x+3x=150

5x=150, so x=30

Goldfish= 2x= 60

Betta fish= 3x= 90

60/150= 6/15 = 2/5

OR

2x+3x= 5x

2x/5x, cancel out x, 2/5

Answer:

18 - 9i

can also be written as 9(2 - i)

Step-by-step explanation:

Please let me know if you want me to add an explanation as to why this is the answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)

Answer:

(0,0) is a saddle point

(-4,4) is a local maximum

Step-by-step explanation:

\(\displaystyle z=3x^3-36xy-3y^3\\\\\frac{\partial z}{\partial x}=9x^2-36y\\\\\frac{\partial z}{\partial y}=-36x-9y^2\)

Determine critical points

\(9x^2-36y=0\\9x^2=36y\\\frac{x^2}{4}=y\)

\(-36x-9y^2=0\\-36x-9(\frac{x^2}{4})^2=0\\-36x-\frac{9}{16}x^4=0\\x(-36-\frac{9}{16}x^3)=0\\\\x=0\\\\-36-\frac{9}{16}x^3=0\\-36=\frac{9}{16}x^3\\-64=x^3\\-4=x\)

When x=0

\(9x^2-36y=0\\9(0)^2-36y=0\\-36y=0\\y=0\)

When x=-4

\(9x^2-36y=0\\9(-4)^2-36y=0\\9(16)-36y=0\\144-36y=0\\144=36y\\4=y\)

So, we need to check what kinds of points (0,0) and (-4,4) are.

For (0,0)

\(\displaystyle H=\biggr(\frac{\partial^2 z}{\partial x^2}\biggr)\biggr(\frac{\partial^2 z}{\partial y^2}\biggr)-\biggr(\frac{\partial^2 z}{\partial x\partial y}\biggr)^2\\\\H=(18x)(-18y)-(-36)^2\\\\H=(18(0))(-18(0))-(-36)^2\\\\H=-1296 < 0\)

Therefore, (0,0) is a saddle point since \(H < 0\).

For (-4,4)

\(\displaystyle H=\biggr(\frac{\partial^2 z}{\partial x^2}\biggr)\biggr(\frac{\partial^2 z}{\partial y^2}\biggr)-\biggr(\frac{\partial^2 z}{\partial x\partial y}\biggr)^2\\\\H=(18x)(-18y)-(-36)^2\\\\H=(18(-4))(-18(4))-(-36)^2\\\\H=(-72)(-72)-1296\\\\H=5184-1296\\\\H=3888 > 0\)

Because \(H > 0\) and since \(\frac{\partial^2z}{\partial x^2}=-72 < 0\), then (-4,4) is a local maximum

Given the function:

We will find the y-intercept of the function

The y-intercept is the value of (y) when (x = 0)

so, when x = 0

so, the answer will be option 1)

1) The y-intercept is 2.

The equation of the axis of symmetry is x = 1.

Thus, to determine whether Intel's stock and Southwest Airlines' stock have similar rates of return, we can use a statistical analysis of the daily rate of return for each stock over a 50-day period. However, the small sample size means that we must be cautious when interpreting the results.

To determine whether Intel's stock and Southwest Airlines' stock have similar rates of return, we can conduct a statistical analysis using the sample data collected. The sample size of 50 days is relatively small, so we must be cautious when interpreting the results.

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It is given that:

1) f(g(x)) will be:

2)The domain will be all real numbers except x=-4.

3)g(f(x)) will be:

4) The domain of g(f(x)) is:

5) f(f(x)) is given by:

6)The domain of f(f(x)) is:

7) g(g(x)) is calculated as:

8)The domain of g(g(x)) is: