Find d:
d=| 5 1 |
|-1 10 |
D= 51

[2 4 ]
[-3 9]
the determinant of the above matrix: 30

Answer:

The sum of the first 20 terms is -1440.

Step-by-step explanation:

We want to find the sum of the first 20 terms of the arithmetic sequence:

4, -4, -12, -20...

The sum of an arithmetic sequence is given by:

[tex]\displaystyle S=\frac{k}{2}(a+x_k)[/tex]

Where k is the number of terms, a is the initial term, and x_k is the last term.

Since we want to find the sum of the first 20 terms, k = 20.

Our initial term a is 4.

Our last term is also the 20th term as we want the sum of the first 20 terms.

To find the 20th term, we can write an explicit formula for our sequence. The explicit formula for an arithmetic sequence is given by:

[tex]x_n=a+d(n-1)[/tex]

Where a is the initial term, d is the common difference, and n is the nth term.

Our initial term is 4. From the sequence, we can see that our common difference is -8 since each subsequent term is eight less than the previous term. Therefore:

[tex]x_n=4-8(n-1)[/tex]

Then the last or 20th term is:

[tex]x_{20}=4-8(20-1)=4-8(19)=-148[/tex]

Therefore, the sum of the first 20 terms are:

[tex]\displaystyle\begin{aligned} S_{20}&=\frac{(20)}{2}\left((4)+(-148))\\&=10(-144) \\&= -1440\end{aligned}[/tex]

Answer:

- 1440

Step-by-step explanation:

First-term is 4 and we subtract 8 to get the next term so the general term is

a(n) = 4 - 8(n -1)

The sum of the sequence is the average of the first and last terms multiplied by the number of terms: (a1 + an)/2 * n

We need the 20th term: a20 = 4 - 8(20–1) = 12 - 160 = - 148

The sum is (4 - 148)/2 * 20 = 10*(-144) = - 1440

Answer: D) Increase the sample size and decrease the confidence level.

Step-by-step explanation:

A reduced interval width means that the data is more accurate. This can only be achieved if the sample size is increased because a larger sample size is able to capture more of the characteristics of the variables being tested.

A smaller confidence interval will also lead to a reduced interval width because it means that the chances of the prediction being correct have increased.

Answer:

x is ( -∞, 6-√(33) ) U ( 6+√(33) , -∞ )

Step-by-step explanation:

I have attached the explanation on the image above, hopefully this help

Answer:40

step by step explanation

3*23÷46=6

46-6=40

there are 40 pies in each plate

Answer:

Answer: 10 pies on each plate.

Step-by-step explanation:

Okay, to solve this problem we first need to find 3/23 of 46.

But before we do that, we need to know 1/23 of 46.

To solve this, we do 64 divided by 23 which equals 2.

then we multiple 2 by 3 to get 3/23 of 46 and that equals 6.

To find out how many pies remain, we subtract 6 pies from 46 pies, which gives us 40 pies. Then we divide 40 by 4, which is 10.

Hello,

I am going to calculate all the surface areas of the prism:

1) the bases: 2*(6*9)/2=64 (cm²)

2) perimeter of the base: 7+9+7=23 (cm)

3 lateral area: 23*5=115 (cm²)

All surface areas= 64+115=179 (cm²)

What does it means sq ? (for a foreigner) ?

All surface areas= 64+115=179 (cm²)

A three-sided polyhedron consisting of a triangle base, a translated copy, and three faces connecting equivalent sides is known as a triangular prism in geometry. If the sides of a right triangular prism are not rectangular, the prism is oblique.

Given

the bases: 2*(6*9)/2=64 (cm²)

perimeter of the base: 7+9+7=23 (cm)

3 lateral area: 23*5=115 (cm²)

All surface areas= 64+115=179 (cm²)

To know more about triangular prisms refer to:

https://brainly.com/question/3160908

#SPJ2

Answer:

The friend would pay $100

Step-by-step explanation:

The price of the card was $20 when Daniel bought it, it gained a value of $10 every year,

since Daniel bought it 3 years ago we will add $30 to $20 as the value increased by $10/year

so the price becomes $50, but his friend says he'll pay twice the value so,

$50×2= $100

Answer:

[tex]f(n) = \frac{32}{3}(\frac{3}{2})^n[/tex]

Step-by-step explanation:

Given

[tex]r = \frac{3}{2}[/tex]

[tex]f(5) = 81[/tex]

Required

The geometric sequence

A geometric sequence is represented as:

[tex]f(n) = ar^{n-1}[/tex]

Replace n with 5

[tex]f(5) = ar^{5-1}[/tex]

[tex]f(5) = ar^4[/tex]

Substitute values for f(5) and r

[tex]81 = a* (\frac{3}{2})^4[/tex]

Open bracket

[tex]81 = a* \frac{81}{16}[/tex]

Make a the subject

[tex]a = \frac{81 * 16}{81}[/tex]

[tex]a = 16[/tex]

So, the explicit function is:

[tex]f(n) = ar^{n-1}[/tex]

[tex]f(n) = 16 * (\frac{3}{2})^{n-1}[/tex]

Split

[tex]f(n) = 16 * (\frac{3}{2})^n \div (\frac{3}{2})[/tex]

Convert to multiplication

[tex]f(n) = 16 * (\frac{3}{2})^n * \frac{2}{3}[/tex]

[tex]f(n) = \frac{32}{3}(\frac{3}{2})^n[/tex]

Answer:

f(x) = 16*(3/2)^(x-1)

Step-by-step explanation:

right on edge

Answer:

library 2,3

park 8,2

market 3,7

red centers 4,10

pool 6,6

movie theater 9,9

ice cream shop 5,4

Answer:

See Explanation

Step-by-step explanation:

Given

Let

[tex]S \to[/tex] Strawberry

[tex]B \to[/tex] Banana

[tex]S : B = 2 : 3[/tex]

Solving (a):

Complete the table

The table, to be complete, is not given; so, I will generate one myself.

[tex]\begin{array}{cccccc}S & {2} & {3} & {4} & {5} & {6} \ \\ {B} & {3} & {4.5} & {6} & {7.5} & {9} \ \end{array}[/tex]

The table is generated as follows:

[tex]S : B = 2 : 3[/tex]

Multiply by 1.5

[tex]S : B = 2 * 1.5 : 3 * 1.5[/tex]

[tex]S : B = 3 : 4.5[/tex]

Multiply by 2

[tex]S : B = 2*2 : 3*2[/tex]

[tex]S : B = 4 : 6[/tex]

And so on....

In summary, whatever factor is multiplied to S must be multiplied to B; in order to keep the ratio constant

Solving (b): Why the amount are proportion

Because the ratio is constant and it remains unchanged all through.

Step-by-step explanation:

Only 1 number works. 1 will make 819 which is divisible by 9.

Since it is 1 of ten numbers can go in the blank, the answer is 1/10 which is 0.1

The 10 number choices are

0,1,2,3,4,5,6,7,8,9

The only one that works is 1 as I've stated.

Answer:

$4,562.5

Step-by-step explanation:

The amount Arvin has to invest, P = $10,000

The interest paid on the investment in the term deposit = 5%/year

The interest paid om the investment in Canada savings bonds = 3.4%/year

The amount Arvin earned at the of the year as simple interest, A = $413

Let, x, represent the amount Arvin invested in the term deposit and let, y, represent the amount he invested in Canada savings bonds, we can get the following system of equations

x + y = 10,000...(1)

0.05·x + 0.034·y = 413...(2)

Making y the subject of equation (1) and substituting the value in equation (2), we get;

From equation (1), we get, y = 10,000 - x

Plugging the above value of y in equation (2) gives;

0.05·x + 0.034 × (10,000 - x) = 413

∴ 0.05·x - 0.034·x + 340 = 413

x = (413 - 340)/(0.05 - 0.034) = 4,562.5

Therefore, the amount Arvin invested in the term deposit at 5%, x = $4,562.5

(y = 10,000 - x

∴ y = 10,000 - 4,562.5 = 5,437.5

The amount Arvin invested in Canada savings bonds, y = $5,437.5.)

Hello!

(3n + 2) - 10 =

= (3 × 3 + 2) - 10 =

= (9 + 2) - 10 =

= 11 - 10 =

= 1

Good luck! :)

[tex]\displaystyle\bf (3n+2) -10 \ if \ n=3\Longrightarrow 3\cdot3+2-10=11-10=\boxed{1}[/tex]

Answer:

slope= -8/1

y-intercept= 0,0

Answer:

m = -8

c = 0

Step-by-step explanation:

The given equation of the line is ,

[tex]\implies y = -8x[/tex]

We know that the Standard equation of Slope Intercept Form of the line is,

[tex]\implies y = mx + c[/tex]

Where ,

On comparing to the Standard form of the line we get ,

[tex]\implies Slope = -8 [/tex]

[tex]\implies y - intercept= 0 [/tex]

Answer:

hi, it's 16 because:

[tex]ab = bc \\ ab = 8 \\ ac = 2 \times 8 = 16 \\ ac = 16[/tex]

Answer:

16

Step-by-step explanation:

Theorem: In a circle, if a radius is perpendicular to a chord, then the radius is the perpendicular bisector of the chord.

In this case, the radius containing points O and B is perpendicular to chord AC, so the radius bisects chord AC making AB = BC.

Also,

AB + BC = AC

By substitution, we have

AB + AB = AC

AC = 2AB

AC = 2(8)

AC = 16

Step-by-step explanation:

simply take the average of the x and y coordinates

Answer:

(7x + 2)(x - 2)(x + 2)

Step-by-step explanation:

Given

7x³ + 2x² - 28x - 8 ( factor the first/second and third/fourth terms )

= x²(7x + 2) - 4(7x + 2) ← factor out (7x + 2) from each term

= (7x + 2)(x² - 4) ← x² - 4 is a difference of squares

= (7x + 2)(x - 2)(x + 2)

Step-by-step explanation:

In a direct proportion, the ratio between matching quantities stays the same if they are divided. (They form equivalent fractions). In an indirect (or inverse) proportion, as one quantity increases, the other decreases.  In an inverse proportion, the product of the matching quantities stays the same.

Answer:

Both direct and indirect proportion are a comparison between two quantities (usually with different units).

In a direct proportion, as one quantity increases, the other also increases.

Examples would include:

If you buy more packets, it will cost more money.

If you have further to travel it will take more time.

If more people are to be fed, more food will be need.

If more people are to be transported, more cars/buses are needed.

More petrol is needed for longer distances.

Bigger area of floor will require more tiles/paint/wood.

A longer distance will need more paces to cover.

More dresses to be made will require more material.

In a direct proportion, the ratio between matching quantities stays the same if they are divided. (They form equivalent fractions).

k

=

x

y

In an indirect (or inverse) proportion, as one quantity increases, the other decreases.

If more people share a task, it will be done in less time.

Travelling at a faster speed means a trip will take less time.

If sugar is packed in smaller packets, more packets will be needed for the same mass.

For the same amount of money, a small parcel can be sent further than a bigger parcel.

If more people are being fed, food will be used up quicker.

For a fixed amount of money, as the price of presents increases, fewer can be bought.

Walking with longer strides means fewer paces are needed.

In an inverse proportion, the product of the matching quantities stays the same.

k

=

x

×

y

A hyperbola is the graph of inverse proportion.

Step-by-step explanation:

, .

Answer:

B

Step-by-step explanation:

[tex]y = \sqrt{x } - 4 \\ \sqrt{x} = y + 4 \\ x = (y + 4) {}^{2} \\ [/tex]

Domain of inverse = Range of f = x>-4

Hence B

The correct option is B which is f⁻¹(x) = ( x + 4 )² and x ≥ -4.

The inverse function of a function f in mathematics is a function that reverses the operation of f. If and only if f is bijective, the inverse of f is true.

A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

The given function is f(x) = √x - 4. The inverse function will be calculated as:-

y = √x - 4

√x = y + 4

Squaring on both sides.

x = ( y + 4 )²

Replace x with y.

y = ( x + 4 )²

The range of the function is x ≥ -4.

Therefore, the correct option is B which is f⁻¹(x) = ( x + 4 )² and x ≥ -4.

To know more about an inverse function follow

https://brainly.com/question/3831584

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Answer:

{5,7,8}

Step-by-step explanation:

A-B = {2,4,6} => A={2,4,6}

B - A = {0,1,3} => B= {0,1,3}

A∪B = {0,1,2,3,4,5,6,7,8}

=> A = {2,4,5,6,7,8}

B= {0,1,3,5,7,8}

=> A∩B = {5,7,8}

Answer:

I believe that the answer is B as well

Step-by-step explanation:

This might be for Ap3x but not 100% sure

Answer:

C

Step-by-step explanation:

The vertex is the point where the 2 lines meet on the V shape

The vertex is at (3, 2 ) → C

Answer:

Option c is the answer I think so if the answer is correct plz mark me as brainliest

Answer:

C

Step-by-step explanation:

its asking for y, on the graph, the line is placed on point 4

Answer: Choice A

L = 65 - 15d; discrete

===============================================

Explanation:

He starts with 65 cm of bread. After the first day he has 65-15 = 50 cm left over. After the second day he has 65-15*2 = 35 cm left over, and so on.

In general, he has 65-15d centimeters left over after d number of days have elapsed. For example, if d = 3 days pass by, then he has 65-15d = 65-15*3 = 65-45 = 20 cm left over.

So that's why the equation we're after is L = 65-15d where d is the number of days, and L is the amount left over in cm.

The number of days is discrete because we're dealing with the set of nonnegative numbers {0,1,2,3,4,...}. We can't have d = 2.5 for instance.

Because the input variable d is discrete, this automatically means L is discrete as well. Consider a finite domain such as {0,1,2,3}. This finite domain would map to the finite range {65,50,35,20}. These two finite sets are sufficient to say we have a discrete function.

A discrete function leads to a discrete graph which is simply a set of points. You would not connect the dots to form a straight line (simply leave the points as separate islands).

ANSWER:-

[tex] 210,000 \: divied \: by \: 0.12 \\ - - > \frac{210000}{0.12} \\ - - > \frac{210000 \times 100}{12} \\ - - > 1,750,000[/tex]

Answer:

1750000

Step-by-step explanation:

when dividing a non decimal number by a decimal number you have to first multiply both the numbers by the number of decimal places of the numbers that has has a decimal,In this case will multiply both numbers by 100 because there are decimal places on 0.12, giving us

21000000/12

=1750000

Step-by-step explanation:

To Find :-

Solution :-

Using Distance Formula ,

> d = √{ ( 2-3)² + (0-1)² + (-1-4)² }

> d = √{ (-1)² + (-1)² + (-5)² }

> d = √{ 1 + 1 + 25 }

> d = √26 .

Using midpoint formula ,

> m = ( 2+3/2 , 0+1/2 , -1+4/3 )

> m = ( 5/2 , 1/2 , -3/3 )

> m = ( 2.5 , 0.5 , -1 )

99 boys and 1 girl makes 99 percent of boys. To make it 98%, 50 boys must leave the theatre, so there are 49 boys and 1 girl, making 98% of boys.

Answer:

[tex]f) \: r2 \div r1 \: = 5 \div 1[/tex]

Step-by-step explanation:

[tex] \frac{a1}{a2} = \frac{1}{25} = \frac{\pi \times (r1)^{2} }{\pi \times (r2)^{2}} [/tex]

[tex] {(\frac{r2}{r1})}^{2} = 25[/tex]

[tex] \frac{r2}{r1} = 5[/tex]

Answer:

2.4cm

Step-by-step explanation:

the area of a triangle is

baseline × height / 2

that means two lengths of the triangle have to be multiplied.

and to have 2 similar triangles means that all lengths inside one triangle are the corresponding lengths inside the other triangle multiplied by the scaling factor f.

multiplying 2 if these lengths with each other means also including the square of the scaling factor (multiplying with the scaling factor twice).

so, if the area of triangle 1 is

"baseline 1" × "height 1" / 2 = 45 cm²

then the area of triangle 2 is

"baseline 2" × "height 2" / 2 =

= "baseline 1"×f × "height 1"×f /2 =

= "baseline 1" × "height 1" × f² / 2 =

= ("baseline 1" × "height 1" / 2) × f² =

= 45 × f² = 20 cm²

f² = 20/45 = 4/9

f = 2/3

so, for a side of ABC being 3.6cm long, that means the corresponding side in DEF is

3.6 × f = 3.6 × 2/3 = 7.2/3 = 2.4cm

Answer:

4 number

Step-by-step explanation:

16p+32q=1,280