Let $a_1$, $a_2$, . . . , $a_{10}$ be an arithmetic sequence. if $a_1 + a_3 + a_5 + a_7 + a_9 = 17$ and $a_2 + a_4 + a_6 + a_8 + a_{10} = 15$, what is the value of $a_1$?
giving brainliest>

Answer:

[tex]D)~(x+3)^2 = 16[/tex]

Step-by-step explanation:

[tex]~~~~~~x^2 +6x -7 = 0\\\\\implies x^2+6x = 7\\\\\implies x^2 +2 \cdot 3 \cdot x +3^2 -3^2 = 7\\\\\implies x^2 +2 \cdot 3 \cdot x+3^2 = 7+3^2\\\\\implies (x+3)^2 = 7+9\\\\\implies (x+3)^2 = 16[/tex]

The total weight of water and a full tank in the nearest pound is 16328 lb.

Volume of a hemisphere = (2/3) x (n) x (r^3)

3.14 x 5³ x 2/3 = 261.67 ft³

Weight = volume x weight per cubic foot

261.67 ft³ x 62.4 = 16328 lb

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Answer:

$16.37

Step-by-step explanation:

They want to raise $463.72 and they already have $218.22 so if we subtract it

$463.72-$218.22=$245.50

we get $245.50 left to raise.

We have 15 teachers so we do

$245.50/15

we get 16.36 but we round it so we get $16.37.

Answer:

3

Step-by-step explanation:

3÷3=1

cant be divided by 9 and get a whole number

3÷9=.33333

Dilation centred at origin

So new coordinates are same like previous

Now scale factor is 3

So P':-

Option D

Answer:

D)   (−6, −12)

Step-by-step explanation:

Dilation:  A type of transformation that makes the pre-image larger or smaller without changing its shape.

Center of a dilation:  a fixed point about which all points are dilated.

When the center of dilation is the origin (0, 0), simply multiply the coordinates of the points of the pre-image by the scale factor to determine the points of the image after dilation.

Given:

Therefore:

⇒ P' = (-2 × 3, -4 × 3)

⇒ P' = (-6, -12)

Answer:

1, 2, 5, and 10

Step-by-step explanation:

Factors of 30 :

1, 2, 3, 5, 6, 10, 15, 30

Factors of 20 :

1, 2, 4, 5, 10, 20

What numbers go in the shaded overlap?

1, 2, 5, and 10

Answer:

im sorry I just need to us ur page to right on

Answer:

V of both A and B is 100 cm³

Step-by-step explanation:

the volume (V) of a prism is calculated as

V = Ah ( A is the area of the base and h the height )

A

A = 20 and h = 5 , then

V = 20 × 5 = 100 cm³

B

A = 25 and h = 4 , then

V = 25 × 4 = 100 cm³

Answer:

D. 60 ft²

Step-by-step explanation:

Area formula :

Solving :

Answer:

D. 60 ft2

Step-by-step explanation:

Area of a parrelleogram:

bxh

base x hieght

The base is 10ft, the height is 6 ft

(it cannot be 8ft because that line is slanted)

10x6=60ft2

Answer:

200^2

Step-by-step explanation:

Answer:

graph 19 because since it is that means also like the thingy equals that number si then like when the thing is at the highest point it cab maybe actually it will equal that number

Using function concepts, it is found that since the savings account receives no interest, the quantity is changing in a linear fashion.

In this problem, the rate of change is a constant of $723 each month, hence the quantity is changing in a linear fashion.

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Answer:

(5,2)

Step-by-step explanation:

if it’s (x,y) and 4 to the y to get 2

Answer:

-2/3

Step-by-step explanation:

[tex]= 1 \frac{2}{3} - 2 \frac{1}{3}\\=\frac{1 * 3 + 2}{3} - \frac{2 * 3 + 1}{3} \\= \frac{5}{3} - \frac{7}{3}\\ = \frac{5 - 7}{3} \\\\= \frac{-2}{3}[/tex]

Answer:

the answer is b

Step-by-step explanation:

you multiply 0.1% or 0.001 to 4200

the reason I am not multiplying 1.2% is because that is for yearly and 0.1% is for monthly

Answer:

A

Step-by-step explanation:

find 1.2% of £4,200 then multiply it

Answer:

Step-by-step explanation:

One

If the number was 1000, you just count the numbers starting at the right until you get a number that is between 1 and 10

So starting at the right, you get to go 3 places towards the left. You get the number one, so 1000 would be written as 1 * 10^3.

The the given number is a fraction the rule is Add a minus sign

Answer: 1/1000 = 1 * 10^-3

Two

10 is 10^1 in scientific notation

1/10 = 10^-1

Answer: 1/10

Answer:

It's 30.72

Step-by-step explanation:

Take your total and times it by the percentage (20 in this case) and then divide by 100.

total: 25.60$

tip: 20% of total

25.60 * 20 = 512

512/100 = 5.12

25.60 + 5.12 = 30.72

Conic sections are shapes that are formed when the surface of a cone intersects with a plane shape

The types include

The parabola can be applied in solving quadratic equations, functions and graph.

The general equation of a parabola is: y = a(x - h)² +k

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Answer:

1. False

2. True

3. true

Step-by-step explanation:

The first answer is false, the second one is true and the third is true

Answer:

i think its D but i'm not very sure. try it

Step-by-step explanation:

Answer:

8.2

Step-by-step explanation:

the bigger numbers are 9.21 and 9.73 because they have a higher number and 8.9 and 8.2 are the lower ones but 9 is a bigger number than 2.

Answer:

1. Binary number system only uses 2 digits: 0 and 1.

2. Octal number system uses 8 digits: 0,1,2,3,4,5,6,7 with the base of 8.

3. Decimal number system uses 10 digits: 0,1,2,3,4,5,6,7,8,9 with a base of 10.

4. Hexadecimal number system uses 16 digits and alphabets: 0,1,2,3,4,5,6,7,8,9 and A,B,C,D,E,F with the base of 16.

5. Quinary number system uses 0,1,2,3,4 with 5 as the base.

Absolute value is a number's distance from 0 on the number line.

A prime factor is a number with no factors other than one and itself.

The smallest quantity divisible by every number of the set is known as the least common multiple.

The denominator of a fraction can never be zero since a number divided by zero is not defined.

If the numerator is greater than or equal to the denominator, the fraction is called an improper fraction.

A mixed fraction is the sum of a whole number and a fraction.

To simplify a fraction is to convert it into a form which the numerator and denominator have no common factor other than one.

Step-by-step explanation:

Hope this helps :)

To solve this problem, we need to factor both

 ⇒ numerator: [tex]x^2-4x+4[/tex]

 ⇒ denominator: [tex]x^2-4[/tex]

Let's factor:

 ⇒ [tex]x^2-4x+4=(x-2)(x-2)\\[/tex]

 ⇒ [tex]x^2-4=(x+2)(x-2)[/tex]

Let's put it back into the fraction:

[tex]\frac{x^2-4x+4}{x^2-4}=\frac{(x-2)(x-2)}{(x+2)(x-2)} =\frac{x-2}{x+2}*\frac{x-2}{x-2} =\frac{x-2}{x+2} *1=\frac{x-2}{x+2}[/tex]

Answer: Choice (3) or [tex]\frac{x-2}{x+2}[/tex]

Answer:

[tex]\frac{x-2}{x+2}[/tex]

Step-by-step explanation:

First, let's factor out the fraction into [tex]\frac{(x-2)^2}{(x+2)(x-2)}[/tex], now we can cancel out the [tex]x-2[/tex]. After we do that, our final answer is [tex]\frac{x-2}{x+2}[/tex].

Hope this helps! :)

Answer:D

Step-by-step explanation:

Answer:

Step-by-step explanation:

45° Corresponds to (π÷4) which is a remarkable measure

We are all supposed to learn by heart the values of it’s ‘sin’ , ‘cos’ , ‘tan’ and ‘cot’ .

the same apply to 30° (corresponds to (π÷6))

……………………………………………………………

So without a calculator:

tan 45° = 1

cot 45° = 1

sin 30°​ = 1/2

therefore ,

tan 45°.sin 30° - cot45°​ = 1 × (1÷2) − 1 = (1÷2) − 1 = −(1÷2) = −0.5

Answer:

She has not got enough spice for 6 weeks.

Step-by-step explanation:

Remark

0.35 kg = 0.35 * 1000 grams / kg = 350 grams.

Since she will use 6 * 80 = 480 grams for 6 weeks, and since 350 is less than 480, she does not have enough spice for six weeks.

Answer:

B)  35.4 ft²

Step-by-step explanation:

Area of a sector

[tex]\textsf{Area of a sector of a circle}=\left(\dfrac{\theta}{360^{\circ}}\right) \pi r^2[/tex]

[tex]\textsf{(where r is the radius and the angle }\theta \textsf{ is measured in degrees)}[/tex]

Given:

Substitute the given values into the formula:

[tex]\begin{aligned}\implies \textsf{Area} & =\left(\dfrac{110^{\circ}}{360^{\circ}}\right) \cdot3.14 \cdot 6^2\\\\& =\left(\dfrac{11}{36}}\right) \cdot3.14 \cdot 36\\\\& =34.54\\\\ & = 35.4\: \sf ft^2 \: (nearest\:tenth)\end{aligned}[/tex]

Hi Student!

Looking at the problem, we first need to determine the important information that is given to us.  We can see that we are given a radius of 6 feet and a central angle of 110 degrees.  We will need to use both of these given values in our problem.

The second step that we need to take, after gathering our information, is to convert our degrees to radians.  The purpose of this is because in our formula we must use radians instead of degrees.  To convert degrees to radians, we multiply it by π/180.

[tex]110\ degrees\ *\ \frac{3.14}{180\ degrees}[/tex]

[tex]1.919[/tex]

Now that we have our angle converted to radians, we can plug our information into the formula and solve.

[tex]Sector\ Area = r^2\ *\ \frac{angle}{2}[/tex]

[tex]Sector\ Area = (6\ ft)^2\ *\ \frac{1.919}{2}[/tex]

[tex]Sector\ Area = 36\ ft^2\ *\ 0.9595[/tex]

[tex]Sector\ Area = 34.542\ ft^2[/tex]

Therefore, after solving the entire equation down to the end, we can see that our answer is 34.542 feet squared.  This matches option B which would be our answer.

Answer:

1) The smaller t is -6

The larger t is 7

2) The vertex of the parabola is (1/2, -42.25)

Step-by-step explanation:

Hey there!

To find the zeros of a function, you need to find two values that add up to "b" and multiply together to get "ac"

The b and ac come from the standard form of a parabola which this statement is given to us right now

t^2-t-42

1 is the "a" value, -1 is the "b" value, and -42 is the "c" value

What are two numbers that multiply together and get -42 and those same two numbers add up to -1

Those two numbers are -7 and 6

When you multiply those numbers together, you get -24

And when you add them together, you get -1

Now you can split the -t in the equation

The new equation after splitting the original equation will look like this

t^2-7t+6t-42

Now we group the equation into two parts

(t^2-7t) + (6t-42)

Since t is the common variable in the first set of parentheses, we can take it out

t(t-7)+(6t-42)

Now in the second pair of parentheses, 6 is the constant term

You can also take that out

t(t-7)+6(t-7)

Now we have our zero pairs

We take one of the parentheses and the terms that are outside of the parentheses

Now we have

(t+6)(t-7)=0

Now we can find our two zeros

The smaller t is -6

The larger t is 7

Now we have to find the vertex

The formula to solving the x-coordinate of the vertex is -b/2a

The "b: value is -1 and the "a" value is 1

So, the x-coordinate of the vertex is 1/2

Now we plug that into the equation

(1/2)^2 - 1/2 - 42

1/4 - 1/2 - 42

-1/4 - 42

-169/4 --> -42.25

So, the y-coordinate of the vertex s -42.25

This means,

The vertex of the parabola is (1/2, -42.25)

Answer:

$826.28

Step-by-step explanation:

Given:

[tex]P = 600[/tex]

[tex]r = 6% or 0.06[/tex]% or [tex]0.06[/tex]

[tex]t = 6[/tex]

Work:

[tex]A=Pe^{rt}[/tex]

[tex]A=600e^{0.06*6}[/tex]

[tex]A=600e^{0.36}[/tex]

[tex]A=826.28[/tex]

Therefore, the balance after 6 year is 826.28.