PLEASE HELP!!!!!! 20 POINTS!!! (BOTH QUESTIONS) VERY EASY!!!!!

Answer:

x = 1/14

Step-by-step explanation:

You can work it as is by subtacting ln(14), then taking antilogs:

ln(x) = -ln(14)

x = 14^-1

x = 1/14

___

Or you can rewrite to a single log and then take antilogs:

ln(14x) = 0

14x = 1

x = 1/14 . . . . . divide by the coeffient of x

The answer is: 22 inches.

We are given a cylinder shape, with the information about it's diameter, meaning that we also can know the radius.

The height of a cylinder goes from the bottom to the top of the shape, so, from the given shape, the height is 22 inches.

With the information, we can also calculate the volume of the cylinder using the following formula:

[tex]V=\pi *r^{2}*h\\\\V=\pi *(\frac{Diameter}{2})^{2} *h\\\\\V=\pi *(\frac{16}{2})^{2}*22=\pi *8^{2} *22=4423.4inches[/tex]

Have a nice day!

Answer:

22 inches

Step-by-step explanation:

We are given a figure of a cylinder with two known lengths. We are to determine whether which of them is the height of the cylinder.

We know that the base of the cylinder is round so the length mentioned on the round base is its diameter.

While the other length running from the top to bottom (or from left to right as shown in the picture) is the height of the cylinder which is 22 inches.

Answer:

  see below

Step-by-step explanation:

This is solved by simplifying each expression and identifying the column heading it matches.

1. (6 x^2/(x^2 - 7 x + 10)) / (2 x)/(x - 5))

= (6 x^2/(x^2 - 7 x + 10)) · (x -5)/(2 x) . . . . invert and multiply

= (6x^2)/(2x) · (x -5)/((x -2)(x -5)) . . . . . . . factor so common factors can cancel

= 3x/(x -2) . . . . matches column 1

__

2. (x - 4) (x + 2)/(x^2 + 5 x + 6) + (-3 x^2 + 24 x - 20)/((x + 3) (4 x - 5))

= (x -4)(x +2)/((x +3)(x +2)) + (-3x^2 +24x -20)/((x +3)(4x -5)) . . . factor

= (x -4)/(x +3) + (-3x^2 +24x -20)/((x +3)(4x -5)) . . . . cancel common factor

= ((x -4)(4x -5) +(-3x^2 +24x -20))/((x +3)(4x -5)) . . . . use common denominator

= (4x^2 -21x +20 -3x^2 +24x -20)/((x +3)(4x -5)) . . . expand product

= (x^2 +3x)/((x +3)(4x -5)) . . . . . . collect terms

= (x)(x +3)/((x +3)(4x -5)) . . . . . . factor numerator

= x/(4x -5) . . . . . . . . . . . . . . . . . . cancel common factor ... matches column 2

__

3. 3 x^2/(x + 3) · (2 x + 6)/(2 x^2 - 4 x)

= 3·2·x·(x +3)/((x +3)(2·x)(x -2)) = 3/(x -2) . . . . matches column 1

__

4. 3 x/(4 x - 5) - 4 x^2/(8 x^2 - 10 x)

= 3x/(4x -5) - 4x^2/(2x(4x -5)) = (3x -2x)/(4x -5) = x/(4x -5) ... matches col 2

__

5. 5 x^2/(x - 2) · (2 x + 6)/(8 x^2 - 4 x) . . . . no match (has a denominator factor of 2x-1 that doesn't cancel any numerator factors)

__

6. -x/(4 x - 5) - 4 x^2/(16 x^2 - 22 x)

In order to match one of the columns, the term on the right must reduce to 2x/(4x-5), which it does not, or must have a denominator factor of x-2, which it also does not. no match.

Answer:

y = (5/2)x

Step-by-step explanation:

A proportional relation can be written as ...

y = kx

Solving for k, you divide by x to get ...

y/x = k

The contant of proportionality is the ratio of y to x. Any pair of x and y will do for computing k. The first pair requires no reduction in the fraction that results:

5/2 = k

So, your equation is ...

y = (5/2)x

Answer:

The constant of proportionality is

✔ 2.5

The equation that represents this proportional relationship is

✔ y = 2.5x

Step-by-step explanation:

hope this helps:)

The value of x in Problem 1 is 11 degrees. The measures of angles EFO and EFD in Problem 2 are 28 degrees and 84 degrees respectively.

In both problems, we're dealing with geometric principles related to circles and angles.

https://brainly.com/question/27802544

#SPJ12

1. The value of x is 11

2. angle EFO = 28°

3. angle EFD = 90°

In geometry, the central angle of a circle's arc is equal to the subtended arc's measure.

The relationship is given by

Central Angle = Arc Measure

Central Angle=Arc Measure in degrees. This property is fundamental in circular geometry.

1. Since arc EF = 2x + 10

2x + 10 = 32( angle at the centre equal measure of arc it intercept)

2x = 32 - 10

2x = 22

x = 11

Since FE = 56

EFO = 1/2 × 56 ( angle at the center is 2× angle at the circumference)

EFO = 28°

angle EFD = 90° ( angle substended from the diameter of a circle to the circumference is 90°)

Answer:

The equation of the line is y = 3/2x + 5/2

Step-by-step explanation:

To find the equation of this line, start by using the two points with the slope formula to find the slope.

m(slope) = (y2 - y1)/(x2 - x1)

m = (4 - 1)/(1 - -1)

m = 3/(1 + 1)

m = 3/2

Now that we have the slope, we can use that and either point in point-slope form to find the equation.

y - y1 = m(x - x1)

y - 4 = 3/2(x - 1)

y - 4 = 3/2x - 3/2

y = 3/2x + 5/2

Answer:

The lateral area of the cylinder is [tex]24 \pi\ units^{2}[/tex]

Step-by-step explanation:

we know that

The lateral area of the cylinder is equal to

[tex]LA=2\pi rh[/tex]

step 1

Find the radius of the base of the cylinder

The area of the base is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]A=36 \pi\ units^{2}[/tex]

so

substitute and solve for r

[tex]36 \pi=\pi r^{2}[/tex]

Simplify

[tex]r=6\ units[/tex]

step 2

Find the lateral area

we have

[tex]r=6\ units[/tex]

[tex]h=2\ units[/tex]

substitute the values

[tex]LA=2\pi (6)(2)=24 \pi\ units^{2}[/tex]

Answer:

i also need the answer to this question

Step-by-step explanation:

Answer:

y= 8x +18

Step-by-step explanation:

Example:

 a) mutually exclusive

 b) not mutually exclusive

 c) not mutually exclusive

Your Turn:

 a) not mutually exclusive

 b) not mutually exclusive

 c) not mutually exclusive

 d) mutually exclusive

Events are mutually exclusive if they cannot both occur together. Otherwise, they are not mutually exclusive.

Example

 a) the winner cannot be both a junior and a senior — mutually exclusive

 b) the winner could be a female sophomore — not mutually exclusive

 c) the winner could be a male freshman — not mutually exclusive

___

Your Turn

 a) the card could be the ace of clubs — not mutually exclusive

 b) the number could be divisible by both 5 and 10 — not mutually exclusive

 c) the card could be the 5 of hearts — not mutually exclusive

 d) the result cannot be both 6 and 7 — mutually exclusive

Answer:

  C. not similar, dilations are involved

Step-by-step explanation:

For geometric figures, such as triangles, we generally study a couple of kinds of transformations.

One is the "rigid transformation" which lets us move, rotate, or reflect the figure any way we like, but we keep it the same size—as though it were cut from cardboard or anything else that holds its shape and size. Any figures transformed by a rigid transformation are congruent.

Another is very much like the "rigid transformation", but dilation is involved. That is, the figure is allowed to be stretched or shrunk uniformly (by the same factor in every direction). Figures transformed in this way are similar, but are not congruent.

In this diagram, your triangle has been reflected and changed in size by a different factor horizontally than vertically. Hence dilation is involved (answer choices A or C), but because the factors are different, the figures are not similar (answer choice C).

_____

Comment on the answer choices

Rotations may be involved in similarity transformations, too. For some reason, that possibility was left off of choices A and C. (On the other hand, rotation is equivalent to a suitable set of reflections.)

i jus want some point bro

For this case we must indicate the value of the following expression, expressed in scientific notation:

[tex](1.2 * 10^{-3}) * (1.1 * 10^{8}) =[/tex]

We have that for multiplication properties of powers of the same base, the same base is placed and the exponents are added:

[tex]a ^ n * a ^ m = a ^ {n + m}[/tex]

Then, rewriting the expression we have:

[tex](1.2 * 1.1) * 10 ^{- 3 + 8} =\\1.32 * 10 ^ 5[/tex]

Answer:

[tex]1.32 * 10 ^ 5[/tex]

Answer: 6(x-2)

Step-by-step explanation:

(x·2-8)-(2x·2+4)

(2(x-4))+2x·2-4

2(x-4)+2x·2-4

2(x-4)+4x-4

2(x-4+2x-2)

2(3x-4-2)

2(3x-6)

2·3(x-2)

6(x-2)

Answer:

3x^2-12

Step-by-step explanation:

Just took it on USATestPrep, if that's where the question came from! ;)

Answer:

-1, 4

Step-by-step explanation:

factor out common term 4

4(x^2 - 3x - 4)        find factors of -4      1 (-4)= -4  (c term)  also 1 - 4 = -3  (b term)

4(x+1)(x-4)  = 0

zeros are -1, 4

Answer:

[tex]\large\boxed{x=-1\ or\ x=4}[/tex]

Step-by-step explanation:

[tex]y=4x^2-12x-16\\\\\text{the zeros are for}\ y=0:\\\\4x^2-12x-16=0\qquad\text{divide both sides by 4}\\\\x^2-3x-4=0\\\\x^2+x-4x-4=0\\\\x(x+1)-4(x+1)=0\\\\(x+1)(x-4)=0\iff x+1=0\ \vee\ x-4=0\\\\x+1=0\qquad\text{subtract 1 from both sides}\\\boxed{x=-1}\\\\x-4=0\qquad\text{add 4 to both sides}\\\boxed{x=4}[/tex]

Answer:

  (2a +b)·(13a^2 -5ab +b^2)

Step-by-step explanation:

The factorization of the difference of cubes is a standard form:

  (p -q)^3 = (p -q)(p^2 +pq +q^2)

Here, you have ...

so the factorization is ...

  (3a -(a -b))·((3a)^2 +(3a)(a -b) +(a -b)^2) . . . . substitute for p and q

  = (2a +b)·(9a^2 +3a^2 -3ab +a^2 -2ab +b^2) . . . . simplify a bit

  = (2a +b)·(13a^2 -5ab +b^2) . . . . . . collect terms

Answer:

  300 square units

Step-by-step explanation:

Let M be the midpoint of BC. Then AM =20 is the altitude. Let x represent the length BM=MC, and let y represent the length AB=AC. Then the perimeter is ...

  2x +2y = 80

  x +y = 40 . . . . divide by 2 . . . . . [eq A]

The Pythagorean theorem tells us ...

  x^2 + 20^2 = y^2 . . . . . . . y is the hypotenuse of right triangle AMC

Rearranging, we have ...

  y^2 -x^2 = 400

  (y -x)(y +x) = 400

  (y -x)·40 = 400

  y -x = 10. . . . . . . . . [eq B]

Subtracting [eq B] from [eq A], we find ...

  (x +y) -(y -x) = (40) -(10)

  2x = 30

  x = 15

The area of interest is 20x, so is ...

  A = 20·x = 20·15 = 300 . . . . square units

Answer:

A) 8 kilograms

Step-by-step explanation:

"kilo-" is a prefix meaning 1000. So, 8 kilo-grams = 8 thousand grams = 8,000 grams.

To convert 8,000 grams to kilograms, divide by 1,000, resulting in 8 kilograms. Therefore, an object that weighs 8,000 grams would indeed weigh 8 kilograms, which is option A.

If an object weighs 8,000 grams and you want to convert it to kilograms, you need to know the conversion between grams and kilograms. In the metric system, one kilogram is equal to 1,000 grams. So, to convert grams to kilograms, you divide the number of grams by 1,000.

To calculate the weight of the object in kilograms from grams:

Therefore, an object that weighs 8,000 grams would weigh 8 kilograms, which corresponds to option A.

Answer:

a=216.

Step-by-step explanation:

What you do is you need to get a by itself.

a/6-11=25. You first add 11 to both sides.

a/6=36. Next you will times 6 on both sides to get

a=216 as your answer.

The perimeter of a triangle is just adding all the sides.

So, (2x)+(4x-2)+(3x-1)= 9x-3

So, the answer is D, 9x-3

Answer:

D.

Step-by-step explanation:

The perimeter = the sum of the 3 sides.

Perimeter = 2x + 4x - 2+ 3x - 1

=  9x - 3.

Answer:

C. A(7) = 800·(1 +0.03)^(7-1)

Step-by-step explanation:

Note that the times are described as "the beginning of year 1" and "the beginning of year 7." If you consider the formula to be the one marked (choice D), you find the general case is ...

A(n) = 800·1.03^n

When you put in 1 for n, you see it gives you ...

A(1) = 800·1.03^1 = 824 . . . . . . . incorrect value for "the beginning of year 1"

The exponent of 1.03 needs to be the difference in year numbers: 7-1, as in choice C.

The appropriate formula is ...

A(7) = 800·(1 +0.03)^(7-1)

Answer:

t ≤ -3

Step-by-step explanation:

5t ≤ -15

You are solving for t. That means you want t alone on the left side. t is being multiplied by 5. To get rid of a multiplication by 5, you do the opposite operation, and you divide by 5. You must do the same operation to both sides of an inequality, so you must divide both sides by 5.

5t/5 ≤ -15/5

t ≤ -3

Answer:

  6y -8

Step-by-step explanation:

Use the distributive property. It tells you the product can be simplified to the product of the outside factor and each of the individual terms in parentheses:

  2(3y - 4) = 2·3y + 2·(-4) = 6y -8

Answer:

  90

Step-by-step explanation:

The total number of "ratio units" is 9+6 = 15, so each one must stand for 225/15 = 15 people. Then 6·15 = 90 people were snowboarders who bought season passes.

Answer:

(C) -11

Step-by-step explanation:

The given functions are;

[tex]f(x)=x+4[/tex]

Plug in x=3.

This implies that; [tex]f(3)=3+4=7[/tex]

and

[tex]g(x)=12x-6[/tex]

Plug in x=-1

This implies that; [tex]g(-1)=12(-1)-6=-18[/tex]

[tex]f(3)+g(-1)=7+-18=-11[/tex]

Center (-1,1), radius 5 so

[tex](x - -1)^2 + (y - 1)^2 = 5^2[/tex]

[tex](x+1)^2 + (y-1)^2 = 25[/tex]

Third choice

Answer:

○ (x + 1)² + (y - 1)² = 25

Step-by-step explanation:

According to one of the Circle Equations, (X - H)² + (Y - K)² = R², all the negative symbols give the OPPOSITE terms of what they really are, so be EXTREMELY careful inserting the center into the formula with their CORRECT signs. Then in the end, square the radius.

The radius is five, so squaring this will give you twenty-five.

I am joyous to assist you anytime.

Answer:

[tex]-4.8[/tex] degrees Fahrenheit

Step-by-step explanation:

Let [tex]t[/tex] be temperature.

[tex]t[/tex] at 3:00PM: [tex]5.2[/tex] degrees.

Every hour, the temperature falls by [tex]2.5[/tex] degrees per hour for the next four hours. Let's multiply 2.5 by 4 to find out the total temperature drop in four hours.

[tex](2.5)(4)=10[/tex]

In four hours, the temperature dropped 10 degrees. Since it is getting colder, let's subtract this from the original 5.5 degrees to get the temperature at 7:00PM.

[tex]5.2-10=-4.8[/tex]

The temperature at 7:00PM was -4.8 degrees Fahrenheit.

The probability that the arrow will land on any of them once is 1/4.

The probability that the arrow will land on any of them twice is 1/4 * 1/4. This is because the probability of Event A and Event B is P(B) * P(A).

Based on this:

[tex]P(a\cap b\cap c\cap d) = \frac{1}{4}\times \frac{1}{4}\times\frac{1}{4}\times\frac{1}{4}\\\\=\frac{1}{4\times4\times4\times 4}\\=\frac{1}{256}[/tex]

1/256

Hope this helps, let me know if I missed anything!

Answer:

1/256 or 2/512

Step-by-step explanation:

Answer:

EI=6 units

LJ=8 units

ST=9 units

Step-by-step explanation:

step 1

we know that

The triangle ELT is a circumscribed triangle

so

EI=ES

LI=LJ

TS=TJ

EL=EI+LI ------> 14=EI+LI -----> 14=EI+LJ -----> equation A

LT=LJ+TJ----> 17=LJ+TJ ----> 17=LJ+TS ----> equation B

ET=ES+TS ---> 15=ES+TS----> 15=EI+TS ----> equation C  

Subtract equation A from equation C

15=EI+TS

14=EI+LJ

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

15-14=TS-LJ

TS=1+LJ ------> equation D

substitute equation D in equation B and solve for LJ

17=LJ+(1+LJ)

17=2LJ+1

2LJ=17-1

LJ=8

Find the value of TS

TS=1+LJ -----> TS=1+8=9

Find the value of EI

14=EI+LJ ------> 14=EI+8 ----> EI=14-8=6

therefore

EI=6 units

LJ=8 units

ST=9 units

Answer:

Step-by-step explanation:

The altitude to the hypotenuse of a right triangle create two smaller triangles, all of which are similar to the original. This means corresponding sides are proportional.

3. Using the above relationship, ...

short-side/hypotenuse = 8/y = y/(8+23)

y^2 = 8·31

y = 2√62

__

long-side/hypotenuse = z/(8+23) = 23/z

z^2 = 23·31

z = √713

__

short-side/long-side = 8/x = x/23

x^2 = 8·23

x = 2√46

_____

4. The picture is fuzzy, but we think the lengths are 25 and 5. If they're something else, use the appropriate numbers. Using the same relations we used for problem 3,

y = √(5·25) = 5√5 . . . . . . . = √(short segment × hypotenuse)

z = √(20·25) = 10√5 . . . . . = √(long segment × hypotenuse)

x = √(5·20) = 10 . . . . . . . . . = √(short segment × long segment)

Assuming scores are normally distributed, a score of 82% on Ms. Smith's test corresponds to the [tex]p[/tex]-th percentile, i.e.

[tex]P(X_S\le82)=p[/tex]

where [tex]X_S[/tex] is a random variable denoting scores on Ms. Smith's test.

Transform [tex]X_S[/tex] to [tex]Z[/tex], which follows the standard normal distribution:

[tex]P(X_S\le82)=P\left(\dfrac{X_S-75}2\le\dfrac{82-75}2\right)=P(Z\le3.5)\approx0.9998[/tex]

which means Amy scored at the 99.98th percentile.

This makes it so that Karina needs to score [tex]X_A=x[/tex] on Mr. Adams' test so that

[tex]P(X_A\le x)=0.9998[/tex]

Their test scores have the same [tex]z[/tex] score computed above, so

[tex]\dfrac{x-73}3=3.5\implies x=83.5[/tex]

so Karina needs to get a test score of at least 83.5%.

Answer:

the answer is 84%

Step-by-step explanation:

❤️Hello!❤️ The answer is 11.31 feet                                                                    arc length = radius * central angle (in radians)

arc length = 12.6 * 2*PI/7

arc length = 25.2 * PI/7  

arc length = 11.31 feet ☯️Hope this helps!☯️  ↪️ Autumn ↩️

Answer:

11.31 ft is the arc length.

Step-by-step explanation:

We have given the radius r = 12.6 ft and arc intercept by central angle

Ф = 2π/7.

We have to find the arc length.

We know the formula to find the arc length that is:

L = rФ

Putting the values we get,

 L= 12.6 × 2π/7

L = 25.2 π/7

L = 11.31 ft  is the answer.

11.31 ft is the arc length.