Answer:
area of each sector: 5π ≈ 15.7 square unitsarea of circle: 100π ≈ 314.16 square unitsStep-by-step explanation:
The formula for the area of a circle is ...
A = πr^2
where the radius (r) is half the diameter. For a circle with a diameter of 20 units, the radius is 10 units and the circle area is ...
A = π·(10 units)^2 = 100π units^2 ≈ 314.16 square units
__
When there are 20 congruent sectors, each sector has an area of 1/20 of the circle area, so
sector area = (1/20)·100π unit^2 = 5π units^2 ≈ 15.7 square units
How is this one solved?
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.
in an isosceles triangle ABC, AB=AC and the altitude from A to BC is 20. If the perimeter of the triangle is 80, find the area of the triangle.
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
How do I do this. I don’t understand how to move place values
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]
What is the height of the cylinder below?
8 inches
11 inches
16 inches
22 inches
The answer is: 22 inches.
Why?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.
A box of fruit has three times as many nectarines as grapefruit. Together there are 64 pieces of fruit. Write the equation that represents this situation.
Answer:
4g = 64
Step-by-step explanation:
Let n = the number of nectarines
and g = the number of grapefruit
We have two conditions that must be satisfied to represent the situation:
(1) n = 3g
(2) n + g = 64
If you need one equation, we can substitute (1) into (2) and get
4g = 64
object weighs 8,000 grams, how many kilograms does it weigh? A) 8 kilograms B) 80 kilograms C) 800 kilograms D) 80,000 kilograms
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:
Take the weight of the object in grams, which is 8,000 grams.Divide the weight in grams (8,000) by the number of grams in one kilogram (1,000).The calculation will be 8,000 \/ 1,000 = 8 kilograms.Therefore, an object that weighs 8,000 grams would weigh 8 kilograms, which corresponds to option A.
(There is a picture but I can't put it in the question)
Sides of the triangle: 2x, 4x-2, 3x-1
Find a single expression that represents the perimeter of the triangle.
A) x + 1
B) 5x − 3
C) 3x − 1
D) 9x − 3
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.
Which expression is equivalent to (x2 − 8) − (−2x2 + 4)?
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! ;)
in a circle with a radius of 12.6 ft and an arc is intercepted by a central angle of 2 pi over seven radians what is the arc length
❤️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.
Need math help desperately (Pic included)
Answer:
see the attachment
Step-by-step explanation:
f(x) = x defines a line with a slope of 1 (upward to the right). Only the bottom two graphs have such a line.
The inequality symbol ≥ means the function has this definition for the case when x = 1. That is, f(x) ≥ x for x≥1 means f(1) = 1. The solid dot means that point on the graph is a point that satisfies the function definition.
The graph at lower right is a graph that includes the point f(1) = 3, which is not the same function as the one in the problem statement.
The ratio of the number of skiers who bought season passes to the number of snowboarders is 9:6. If a total of 225 people bought season passes, how many snowboarders bought season passes?
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.
WILL MARK BRAINLIEST!!!NEED HELP ASAP!! Carrie will spin the arrow on the spinner four times. What is the probability that the arrow will stop on A, then B, then C, then D? 3/256 1/64 1/256 3/4
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:
Does anyone understand this
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
Which is the equation of a line that passes through the points (1,4) and (-1,1)
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
f(x) = x +4 and g(x) = 12x -6 what is f(3) + g (-1)
(A) 22
(B) 33
(C) -11
(D) 11
I am having a brain fart can someone explain how I get the answer to this?
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]
How do you simplify 2(3y - 4) without parenthesis
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
A doctor measured a patient’s resting pulse rate at 80 beats per minute. Draw a graph to show the relationship between time and the number of times the patient’s heart beats. Use it to estimate how many times the patient’s heart will beat in 18 minutes. Write an equation in Y = mx + b form.
Answer:
i also need the answer to this question
Step-by-step explanation:
Answer:
y= 8x +18
Step-by-step explanation:
Given: Circumscribed △ELT, EL=14, LT=17, ET=15.
Find: EI, LJ, and ST
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
At 3 p.m. the temperature outside was 5 1/5 degrees Fahrenheit. The temperature then fell steadily by 2 1/2 degree per hour for the next 4 hours. What was the temperature at 7 p.m.
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.
At the beginning of year 1, Mike invests $800 at an annual compound interest rate of 3%. He makes no deposits to or withdrawals from the account. Which example explicit formula can be used to find the account's balance at the beginning of year 7.
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)
5t ≤-15 is....????? i need help and if u guys could maybe explain it to me plz?
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
sophia mandy and alexis are cousins sophia is 3/4 as tall as mandy. alexis is 5/6 as tall as mandy . what is the difference in height between sophia and alexis id mandy is 5 feet tall
1/12
5/12
4 1/6
3 3/4
Answer:
[tex]\frac{5}{12}[/tex] feet
Step-by-step explanation:
Let height of mandy be m, sophia be s, and alexis be a
"sophia is 3/4 as tall as mandy":
[tex]s=\frac{3}{4}m[/tex]
"alexis is 5/6 as tall as mandy":
[tex]a=\frac{5}{6}m[/tex]
Since mandy is 5 feet, we plug in 5 into m in both of the equations to find height of alexis and sophia.
Sophia = [tex]\frac{3}{4}(5)=\frac{15}{4}[/tex]
Alexis = [tex]\frac{5}{6}(5)=\frac{25}{6}[/tex]
Difference in height of Alexis and Sophia is [tex]\frac{25}{6}-\frac{15}{4}=\frac{5}{12}[/tex] feet
Oh Hi there! Can I get some help with Calculus, please? #4,#6, and #8 Don't forget to show your work.
I'll work on the others!
Thank you!
Try this suggested option (see the attached picture).
What is the equation of the circle in standard form see attachment
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.
how to solve In 14 + In x = 0
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
Amy scores an 82% on her math test with Ms. Smith. The average score for her class is a 75% with a standard deviation of 2%. Amy’s friend Karina is taking the same test with Mr. Adams. His class average is a 73% and a standard deviation of 3%. What is the lowest score Karina needs to score higher than Amy relative to the class distributions?
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:
1) Given: circle k(O), ED= diameter ,m∠OEF=32°, m(arc)EF=(2x+10)° Find: x
2)Given: circle k(O), m(arc) FE=56°, FD=ED Find: m∠EFO, m∠EFD
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.
Explanation:In both problems, we're dealing with geometric principles related to circles and angles.
Problem 1: Given that OEF is a central angle standing on the arc EF, we know from circle geometry that the measure of the central angle is equal to the measure of the arc it intercepts. Therefore, 32° = 2x + 10°. Solving this equation, we get x = 11°.Problem 2: Since the angles are located at the circumference and standing on the same arc FE, the angle subtended by an arc at the center is double the angle subtended at the circumference. Therefore, m∠EFO= 56°/2 = 28°. Seeing as ∠EFD is an exterior angle of triangle EFO, its measure is equal to the sum of the two non-adjacent interior angles (angle sum property of a triangle). Therefore, m∠EFD = ∠EFO + ∠FEO = 28° + 56° = 84°.Learn more about Circle Geometry here: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°)
solve the equation. a/6 - 11 = 25
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.
find the zero of y=4x^2-12x-16
HELPP
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]
Please help
problem 3 and 4
show work
find the value of x, y and z
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)