Suppose that a1, a2, a3, . . . is an arithmetic sequence, in which a3 = 19 and a14 = 96. Find a1.

Answer:

[tex]\approx 13.0[/tex]

Step-by-step explanation:

The Pythagorean theorem is a formula that relates the sides of a right triangle. This formula states the following:

[tex]a^2+b^2=c^2[/tex]

Where (a) and (b) are the legs or the sides adjacent to the triangle angle of the right triangle. Parameter (c) represents the hypotenuse or the side opposite the right angle of the right triangle. Substitute the given values into the formula and solve for the unknown:

[tex]a = 7\\b = 11[/tex]

[tex]a^2+b^2=c^2[/tex]

[tex]7^2+11^2=c^2[/tex]

Simplify,

[tex]7^2+11^2=c^2\\\\49 + 121= c^2\\\\170=c^2[/tex]

Inverse operations,

[tex]170=c^2\\\\\sqrt{170}=c\\\\\\c \approx 13.0384[/tex]

Answer:

29.83 ft

Step-by-step explanation:

First, you find the square root of 445, which is 21.09.

Then you use the Pythagorean theorem, which is a^2 + b^2 = c^2

because a and b are the same value you plug it in

21.09^2+21.09^2 = c^2

You end up getting:

c^2=889/5762

You then square root both sides to get:

c = 29.83, which is option 3

Answer:

It's A

Step-by-step explanation:

DO FOIL

-10d^4+(5+12)d^2s-6s^2=-10d^4+17d^2s-6s^2

Answer:

the first answer: -10a^4 + 17a^2s-6s^2

Step-by-step explanation:

Answer:

x = 69

Step-by-step explanation:

since AB is parallel to CD we can find the value of y with the following equation :

2y - 40 = 66 add 40 to both sides

2y = 110 divide both sides by 2

y = 55

from supplementary angles, we know that the exterior angle's measure is 124

since the sum of two interior angles in a triangle is equal to an exterior angle that is supplementary to the third interior angle

y + x = 124 we found value of y earlier

55 + x = 124 subtract 55 from both sides

x = 69

Answer:

54piecm^3

Step-by-step explanation:

pie x radius ^2 x h

= v

pie x 9

= 9pie x 6

= 54pie

Answer:

A' (9,4)

B' (8,-1)

C' (5,1)

Answered by GAUTHMATH

Answer:

A' = 9,4

B' = 8,-1

C' = 5,1

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

C. 37 degrees

Step-by-step explanation:

27, 36, 45 is just a larger 3, 4, 5 triangle. The smallest angle is across from the smallest side. With those in mind, we have 37, 53, and 90 degrees as the angles for a 3, 4, 5 triangle. We pair the 27, (the three when we reduce) with the smallest angle, the 37.

I'm sure you can do it with an actual formula, but i can't recall. Cheers

Answer:

$7.47

Step-by-step explanation:

Take the number of pounds and multiply by the price per pound

3 * 2.49

7.47 for 3 pounds of apples

Answer:

7.49

Step-by-step explanation:

Given: 3 pounds, and 2.49 for each pound

Multiply:

2.49 × 3

 ₁   ₂    

 2.49

×      3

----------

 7. 47

Mrs. Ella bought 3 pounds of apples for $7.49

Answer:

see explanation

Step-by-step explanation:

Given f(x) then f(x) + c is a vertical translation of f(x)

• If c > 0 then a shift up of c units

• If c < 0 then a shift down of c units

The graph of g(x) is the graph of f(x) shifted up by 4 units

Answer: 23, 27,29

Those im absolutely positive about.

Im not sure abt the rest

Step-by-step explanation:

Answer:

5 + 20 + 6

Step-by-step explanation:

that's how you get

Answer:

-6

Step-by-step explanation:

2n can be the smallest integer, and 2n + 18 will be the largest integer.

The sum of this, divided by two, will result in the average/mean.

(2n + 2n + 18)/2 = 3

Multiply each side by 2:

(2n + 2n + 18)/2 ⋅ 2 = 3 ⋅ 2

2n + 2n + 18  =  6

Combine the like terms:

4n + 18 = 6

Subtract 18 from both sides:

4n + 18 - 18 = 6 - 18

4n = -12

Divide each side by 4:

4n/4 = -12/4

n = -3

Since we decided to go by 2n:

2n = 2(-3) = -6

Answer:

5.1 cm

Step-by-step explanation:

(Probable) Question;

Given a circle with center O and radius 2.4 cm. P is a point on the tangent that touches the circle at point Q, such that the length of the tangent from P to Q is 4.5 cm. Find the length of OP

The given parameters are;

The radius of the circle with enter at O, [tex]\overline{OQ}[/tex] = 2.4 cm

The length of the tangent from P to the circle at point Q, [tex]\overline{PQ}[/tex] = 4.5 cm

The length of OP = Required

By Pythagoras's theorem, we have;

[tex]\overline{OP}[/tex]² = [tex]\overline{OQ}[/tex]² + [tex]\overline{PQ}[/tex]²

∴ [tex]\overline{OP}[/tex]² = 2.4² + 4.5² = 26.01

[tex]\overline{OP}[/tex] = √26.01 = 5.1

The length of OP = 5.1 cm

Step-by-step explanation:

c. 2x-11 this is the answer

hope this helps you

have a nice day:)

Answer:

x = 10

Step-by-step explanation:

8x-12 = 6x+ 8

or, 8x -6x = 8 + 12

or, 2x = 20

or, x = 20/2

so, x = 10

Answer:

10

there is a problem with the question...

IF it was : 8x - 12 = 6x + 8

then the answer would be: 2x = 20 .... x = 10

Step-by-step explanation:

Given:- 7x + 1 < 4(x - 2)

7x + 1 < 4(x - 2)

7x + 1 < 4x - 8

7x - 4x < -8 -1

3x < -9

x < -9/3

x < -3

Answer:

See answers below

Step-by-step explanation:

For the expression

The sum of two numbers is  25.  The first number is 37 more  than 2 times the second  number

Let the two numbers be x and y

If the sum is 25, then;

x + y = 25 .... 1

37 more  than 2 times the second  the number is expressed as;

37+2y

If the first number is 37 more  than 2 times the second  number, then;

x = 37 + 2y

x - 2y = 37 ...2

This shows that the simultaneous equation that fits the expressions are;

x - 2y = 37

x + y = 25

For the expression

A child has a piggy bank full  of $1 and $2 coins totaling  $37.  There are 25 more $1 coins  than there are $2 coins.

Let x be the $1 coins

Let y be the $2 coins

If a child has a piggy bank full  of $1 and $2 coins totaling  $37, then;

x + 2y = 37 ... 1

Also, if there are 25 more $1 coins  than there are $2 coins, then;

x = 25 + y

x - y = 25 ...2

The equivalent expressions for the statement will be;

x + 2y = 37

x - y = 25

This hence leaves us with the last;

An exam that is worth 37  marks contain 25  questions.  The questions are either  worth 1 mark or 2 marks. The resulting simultaneous equation will be;

x + 2y = 37

x + y = 25

Answer:

47.12

Step-by-step explanation:

C=2πr=2·π·7.5≈47.12389

Answer:

8 1/4 kg

Step-by-step explanation:

Add the weight of the fruits together

3 1/2 + 4 3/4

Get a common denominator of 4

3 2/4 + 4 3/4

7 5/4

7 4/4 + 1/4

8 1/4 kg

Answer:

the third option - they are perpendicular to each other.

Step-by-step explanation:

for a perpendicular slope we need to exchange the x and y values (remember, a slope is the ratio of y/x) and flip the sign.

and that is exactly what happened here.

Answer:

648

Step-by-step explanation:

18√2×18√2= (18√2)²

                  = (18)²×(√2)²

                  = 324×2

                  = 648

Presumably, ln⁵(x) is the same as (ln(x))⁵ (as opposed to a quintuply-nested logarithm, log(log(log(log(log(x)))))).

Then substituting u = ln(x) and du = dx/x gives

[tex]\displaystyle\int\frac{\mathrm dx}{x\ln^5(x)} = \int\frac{\mathrm du}{u^5} = -\frac1{4u^4}+C = \boxed{-\frac1{4\ln^4(x)}+C}[/tex]

Answer:

A/w = l

Step-by-step explanation:

A = lw

Divide each side by w

A/w = lw/w

A/w = l

Answer:

10

Step-by-step explanation:

not sure please verify

Answer:

(5,-3) in the 4th quadrant

Step-by-step explanation:

You have the right idea. You'll apply a y-axis reflection to go from above the x axis to below it. This allows us to move the red line into the correct vertical position without having to use a vertical translation.

Afterward, you'll shift the red line 4 units to the right to have it line up perfectly with the blue line.

Going from f(x) to -f(x) is the y-axis reflection part

Going from -f(x) to -f(x-4) will shift the line 4 units to the right.

Answer:

A is the correct one

cause according to function rule the vertical line should cut only on a one point to be function

as here we can see that vertical line cuts here at two point

Answer:

the polygon above has 6 sides . It is a hexagon with 6 obtuse angles interior angles equal to 720° .

Answer:

the polygon above has 6 sides . It is a hexagon with 6 obtuse angles interior angles equal to 720° .

Step-by-step explanation:

Answer:

32:3/4

33:4/3

34:40

35:48