Firstly see what they are in mixed fraction form:
[tex]7 \frac{9}{7} = \frac{58}{7} [/tex]
therefore, 7 9/7 is equal to 58/7
[tex]8 \frac{2}{7} = \frac{58}{7} [/tex]
what is the recursive formula for this geometric sequence -2, -16, ...
[tex]\displaystylea_1=-2\\r=8\\a_n=8a_{n-1}\\\\\left \{ {{a_1=-2} \atop {a_n=8a_{n-1}}} \right.[/tex]
Answer: The sequence is: An = -2*8^(n-1)
Step-by-step explanation:
 geometric sequence is of the form:
An = a*r^(n-1)
where can be any positive integer number.
here the first two numbers are -2 and -16, so we have that:
A1 = a*r^(0) = a = -2
now, we know that our sequence is of the form:
An = -2*r^(n-1)
now, for n= 2 we have that:
A2 = -2*r^(1) = -2*r = -16
r = -16/-2 = 8
now we have determinated our sequence:
An = -2*8^(n-1)
AD and MN are chords that intersect at point B what is the length of line segment MN?
Answer:
[tex]MN=18\ units[/tex]
Step-by-step explanation:
we know that
The Intersecting Chord Theorem, states that When two chords intersect each other inside a circle, the products of their segments are equal.
so
In this problem
[tex]AB*BD=MB*BN[/tex]
substitute
[tex](9)(x+1)=(x-1)(15)\\ \\9x+9=15x-15\\ \\15x-9x=9+15\\ \\ 6x=24\\ \\x=4\ units[/tex]
Find the length of line segment MN
[tex]MN=MB+BN=(x-1)+15=x+14[/tex]
substitute the value of x
[tex]MN=4+14=18\ units[/tex]
Answer:
MN = 18
Step-by-step explanation:
AD and MN are two chords intersecting inside the circle at point B.
As we know from intersecting chords theorem.
AB × BD = BN × BM
So 9(x-1) = 15 (x-1)
9x + 9 = 15x - 15
15x - 9x = 15 + 9
6x = 24
x = 4
and MN = (x-1) + 15
= (x + 14)
= 4 + 14 ( By putting x = 4 )
= (18)
Therefore, MN = 18 is the answer.
he heights of △ABC are drawn from vertices A and C. These heights intersect at point M. Find m∠AMC, if m∠A=70° and m∠C=80°.
Answer: 150°
Step-by-step explanation:
In the given triangle ABC ∠A=70°, ∠C=80°
therefore ∠B=180-(∠A+∠C)=180-(70+80) [sum angle property of triangle]
⇒∠B=30°
Now, heights(altitude) are drawn from vertices A and C on respective bases
they intersect at a point M. Also, we know that heights are perpendicular on the bases.
Also, point of intersection of altitudes is called orthocenter.
Now since M is orthocenter, ∠ABC+∠AMC=180° (property of orthocenter in a triangle)
⇒30°+∠AMC=180°
⇒∠AMC=180°-30°=150°
Hence in the triangle ABC, ∠AMC=150°
Given 0 below, if GH and JK are congruent, what is the measure of KOJ?
Answer:
D
Step-by-step explanation:
Since GH and JK are congruent then the central angles are congruent, that is
∠KOJ = ∠HOG = 68° → D
The measure of KOJ = 68 degree.
What is a sector ?A sector is formed by two radii and the intercepted arc on the circle.
The angle subtended by the sector at the center is called Central Angle.
It is given that the
sector , GH and JK are congruent.
As they are congruent the angle subtended by them at the center will be equal.
The measure of ∠GOH = 68 degree
∠KOJ = ∠GOH = 68 degree
Therefore , The measure of KOJ = 68 degree.
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are alternate interior angles always congruent
Answer:
depends
Step-by-step explanation:
The Alternate Interior Angles theorem states, if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent
Answer:
Yes they are
Step-by-step explanation:
when a line cuts two parallel lines, the alternate interiors angles are congruent. Hope this helps :)
Find the mode of the following data:
10, 16, 15, 14, 8, 21, 10, 5, 19, 18, 4, 5, 16, 12, 10,9
Answer:
The mode is 10.
Step-by-step explanation:
A mode is basically the number that occurs most in a data set, so first to make it easier you can list the number least to greatest. After that look at the data set and see what number occurs the most. In this situation it is 10 because it occurs 3 times.
In a data set, the mode is the value that appears the most frequently. A set of data can have just one mode, multiple modes, or none at all.
HOW TO SOLVE?To solve mode given series is
[tex]10\\16\\15\\14\\8\\21\\10\\5\\19\\18\\4\\5\\16\\12\\10\\9\\[/tex]
Rearranging series we get
[tex]4\\5\\5\\8\\9\\10\\10\\10\\12\\14\\15\\16\\16\\18\\19\\21\\[/tex]
hence, mode is number with highest frequency which is 10 in this series
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Distance between points (-1,2) and (3,-5)
[tex]\huge{\boxed{\sqrt{65}}}\ \ \boxed{\text{approx. 8.06225775}}[/tex]
The distance formula is [tex]\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are the points.
Substitute in the values. [tex]\sqrt{(3-(-1))^2 + (-5-2)^2}[/tex]
Simplify the negative subtraction. [tex]\sqrt{(3+1)^2 + (-5-2)^2}[/tex]
Add and subtract. [tex]\sqrt{4^2 + (-7)^2}[/tex]
Solve the exponents. [tex]\sqrt{16 + 49}[/tex]
Add. [tex]\sqrt{65}[/tex]
[tex]65[/tex] has no square factors, so this is as simple as the answer can get. You can use a calculator to find that [tex]\sqrt{65}[/tex] is approximately [tex]8.06225775[/tex].
The formula for distance between two points is:
[tex]\sqrt{(x_{2} -x_{1})^{2} + (y_{2} -y_{1})^{2}}[/tex]
In this case:
[tex]x_{2} =3\\x_{1} =-1\\y_{2} =-5\\y_{1} =2[/tex]
^^^Plug these numbers into the formula for distance like so...
[tex]\sqrt{(3 -(-1))^{2} + (-5-2)^{2}}[/tex]
To solve this you must use the rules of PEMDAS (Parentheses, Exponent, Multiplication, Division, Addition, Subtraction)
First we have parentheses. Remember that when solving you must go from left to right
[tex]\sqrt{(3 -(-1))^{2} + (-5-2)^{2}}[/tex]
3 - (-1) = 4
[tex]\sqrt{(4)^{2} + (-5-2)^{2}}[/tex]
-5 - 2 = -7
[tex]\sqrt{(4)^{2} + (-7)^{2}}[/tex]
Next solve the exponent. Again, you must do this from left to right
[tex]\sqrt{(4)^{2} + (-7)^{2}}[/tex]
4² = 16
[tex]\sqrt{16 + (-7)^{2}}[/tex]
(-7)² = 49
[tex]\sqrt{(16 + 49)}[/tex]
Now for the addition
[tex]\sqrt{(16 + 49)}[/tex]
16 + 49 = 65
√65 <<<This can not be further simplified so this is your exact answer
Your approximate answer would be about 8.06
***Remember that the above answers are in terms of units
Hope this helped!
~Just a girl in love with Shawn Mendes
product of (6+i)(2+9i)
Answer:
(6 + i)(2 + 9i) = 3 + 56iStep-by-step explanation:
Use FOIL: (a + b)(c + d) = ac + ad + bc + bd
and i² = -1
(6 + i)(2 + 9i) = (6)(2) + (6)(9i) + (i)(2) + (i)(9i)
= 12 + 54i + 2i + 9i²
= 12 + 54i + 2i + 9(-1)
= 12 + 54i + 2i - 9 combine like terms
= (12 - 9) + (54i + 2i)
= 3 + 56i
[tex](6+i)(2+9i)=18+54i+2i-9=9+56i[/tex]
does anyone know this????????
Answer:
3
______
4 | 12
-12
-----
0
Step-by-step explanation:
12/4
The top number always goes inside (larger or not), and the bottom number always goes on the outside (larger or not).
______
4 | 12
Ask yourself how many 4's are in 12.
Let's see one 4 is just 4.
We can probably do more 4's than that.
Two 4's gives us 4+4=8.
Let's see if we can put one 4 in there.
Three 4's gives us 4+4+4=12.
So we can fit three 4's into 12 and there is nothing left over.
3
______
4 | 12
-12 (since 4 times 3 or 4+4+4 is 12)
-----
0
If f(x) = 3x^2
and g(x) = x+2, find (f•g)(x).
A. 3x3 +6x
B. 3x2 +6x
c. xi +2
D. 3x3 +6x2
Answer:
D. (f · g)(x) = 3x³ + 6x²Step-by-step explanation:
(f · g)(x) = f(x) · g(x)
We have f(x) = 3x² and g(x) = x + 2. Substitute:
(f · g)(x) = (3x²) · (x + 2) use the distributive property
(f · g)(x) = (3x²)(x) + (3x²)(2)
(f · g)(x) = 3x³ + 6x²
While shopping at the grocery store, Dan decides to estimate the amount of money he will have to pay for the items he wants to buy. He rounds the individual price of each item to the nearest dollar and then adds up the numbers in his head. Dan adds the following items to his shopping cart: one carton of milk for $\$3.58$, one box of cookies for $\$2.97$, one loaf of bread for $\$2.17$, and one pineapple for $\$2.54$. According to Dan's estimate, how many dollars will he be spending at the store?
Answer:
12 dollars
Step-by-step explanation:
Mile 3.58 rounds to 4 dollars
cookies 2.97 rounds to 3 dollars
bread 2.17 rounds to 2 dollars
pineapple 2.54 rounds to 3 dollars
Adding the whole dollar amounts
4+3+2+3 = 12 dollars
Solution:
Dan will round the price of each item to the nearest dollar. So, the price of milk is rounded to $4, the price of cookies is rounded to $3, the price of bread is rounded to $2, and the pineapple's price is rounded to $3. Adding these numbers up, we get 4+3+2+3=12.Therefore, Dan estimates that he will spend about 12 dollars at the store.
In triangle ABC, a = 3, b = 5, and c = 7. Find the approximate value of angle A. 22° 38° 142° 158°
Answer:
B.
Step-by-step explanation:
B.
Answer:
22
Step-by-step explanation:
law cosines
a^2=b^2+c^2 - 2bc cos A
plug in numbers
21.7 ish
round
22
what is the simplest form of the ratio 40:16?
What is the x-interception of the Logarithmic function??
The answer is:
Why?To find the x-interception of the given function, we just need to isolate the variable "x", by making the function (y) equal to 0.
So, we are given the function:
[tex]F(x)=y=Log_{0.71}(x)[/tex]
Now, making y equal to 0, to isolate "x", we have:
[tex]y=Log_{0.71}(x)\\\\0=Log_{0.71}(x)[/tex]
[tex]0=Log_{0.71}(x)\\\\0.71^{0}=0.71^{Log_{0.71}(x)}} \\\\1=x[/tex]
We have that the x-intercept of the logarithmic function is located at (1,0)
Hence, the correct answer is:
B. (1,0).
Have a nice day!
Note: I have attached a picture for better understanding.
if f(x)=3x^2-9 and g(x)=x^2+1 find (f+g)(x)
Answer:
4x^2 -8
Step-by-step explanation:
f(x)=3x^2-9
g(x)=x^2+1
(f+g)(x)=3x^2-9 +x^2+1
Combine like terms
= 4x^2 -8
Find the percentage of data points that lie between -3.01 and 2.61?
z= (x-u) /o
Answer:
To find the percetage of data points that lie between the points -3.01 and 2.61, on a normal distribution we're going to need the help of a calculator. The result is: 99.42%
Attached you will find the graph that represents the result.
nine times five less than twice x
Answer:
3
Step-by-step explanation:
For this case we must express algebraically the following sentence:
"Nine times five less than twice x"
We have to:
Nine times five represents: [tex]9 * 5 = 45[/tex]
Twice x represents:[tex]2x[/tex]
So we have that "Nine times five less than twice x" is represented as:
[tex]2x-45[/tex]
Answer:
[tex]2x-45[/tex]
which of the following is an arithmetic sequence
Answer:
C
Step-by-step explanation:
For it be an arithmetic sequence it must either be going up by the same number each time or down by the same number each time.
Lets look at the choices:
A. From 2 to 3 that went up by 1. But from 3 to 7, that doesn't continue to go up by 1. So this sequence is not arithmetic.
B. From 2 to 4, that went up by 2. But from 4 to 16, that doesn't continue to go up by 2. So this sequence is not arithmetic.
C. From 3 to 0, that goes down by 3. From 0 to -3, that goes down by 3. From -3 to -6, thar goes down by 3. This sequence is arithmetic.
Which functions have a vertex with a x-value of O?. Select three options.
f(x) = |x|
f(x) = \x{ + 3
f(x) = 5x + 31
f(x) = [x] - 6
f(x) = 5x + 31 - 6
Answer:
Step-by-step explanation:
1) f(x) = |x| has its vertex at (0, 0), so the x-value is 0.
2) Cannot figure out what you meant by \x{ + 3.
3) f(x) = 5x + 31 has a straight line graph, no vertex.
4) [x] - 6 does not have a vertex, or at least not a well-defined one like |x|
5) Unsure of what you meant by 5x + 31 - 6. Did you mean 5x + 25? This does not have a vertex.
Which of the following shapes is the cross-section for a cylinder?
The cross-section of a cylinder is in the shape of a Circle
Cross section for a cylinder is circle in shape.
What is cross section?" Cross section is defined as the intersection of the solid body with a plane along it particular axis."
According to the question,
Given shape,
Cylinder
Cylinder is having a circular base.
Intersection of a plane with the cylinder is circular.
Cross section of cylinder is circle.
Hence, Option(C) is the correct answer.
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Find the rule for (3,1) (6,2) (9,3) (12,4) (15,5)
Answer:
y = [tex]\frac{1}{3}[/tex] x
Step-by-step explanation:
Compare the values of y with the values of x for each ordered pair
x y
3 1 → y = 3 ÷ 3
6 2 → y = 6 ÷ 3
9 3 → y = 9 ÷ 3 = 3
12 4 → y = 12 ÷ 3 = 4
15 5 → y = 15 ÷ 3 = 5
The y value in each case is the x value divided by 3
Hence rule is
y = [tex]\frac{1}{3}[/tex] x
the slope is -4 which of the following is the point -slope form of the line (2,-8)
[tex]\huge{\boxed{y+8=-4(x-2)}}[/tex]
Point slope form is [tex]y-y_1=m(x-x_1)[/tex], where [tex]m[/tex] is the slope and [tex](x_1, y_1)[/tex] is any point on the line.
We can simply plug in the values. [tex]y-(-8)=-4(x-2)[/tex]
Then, just simplify the negative subtraction. [tex]y+8=-4(x-2)[/tex]
What is the difference between the absolute value of 4 and the absolute value of –3?
A) 1
B) 4
C) 7
D) 8
IM TIMED!!!!
Answer:
A) 1
Step-by-step explanation:
|4| - |-3|
4 - 3
1
a cruise ship has a rectangular swimming pool.The width of the pool is 30% of the length of the pool.the perimeter of the pool is 1040 feet.what is the width of the pool?What is the length of the pool?
Answer:
The length of the pool is 400 feet.
The width of the pool is 120 feet.
Step-by-step explanation:
We are given the width (W) is 30% of the length (L).
We are also given the perimeter of the pool is 1040.
So in equation form this is what we have:
W=.3L (of means multiply)
2L+2W=1040
We are going to plug the first equation into the second like so:
2L+2(.3L)=1040
2L+.6L=1040
2.6L=1040
Divide both sides by 2.6
L=1040/2.6
L=400
The length of the pool is 400 feet.
W=.3L
W=.3(400)
W=120
The width of the pool is 120 feet.
We get two equations that we can use for this equation.
2w + 2L = 1040
and
w = 0.3L
We can input w into the first equation:
0.6L + 2L = 1040
2.6L = 1040
L= 400
W = 120
i need help asap thank you
Answer:
363
Step-by-step explanation:
The n th term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
d = - 85 - (- 92) = - 85 + 92 = 7 and a₁ = - 92, hence
[tex]a_{66}[/tex] = - 92 + (65 × 7 ) = - 92 + 455 = 363
Jermiah makes a recipe that calls for 1 1/2 cups of flour and 3/4 stick of butter. If Jermiah uses 3 sticks of butter, how many cups of flour will he need
Answer:
The answer is 6 cups of flour.
To find the amount of flour needed for 3 sticks of butter, a proportion based on the original recipe ratio is used, resulting in 6 cups of flour.
Jermiah's recipe calls for 1 1/2 cups of flour for every 3/4 stick of butter. Therefore, if he uses 3 sticks of butter, we need to find out how many cups of flour that corresponds to.
To determine the amount of flour needed, we set up a proportion, where the original amount of butter and flour are proportional to the new amount of butter and flour.
Since 3/4 stick of butter corresponds to 1 1/2 cups of flour, 3 sticks of butter would be 4 times as much, because 3 divided by 3/4 equals 4. Therefore, he will need 4 times the original amount of flour.
Here is the math: 1 1/2 cups of flour x 4 = 6 cups of flour.
Answer ASAP John is thinking of a number. He gives the following 3 clues. ``My number has 125 as a factor. My number is a multiple of 30. My number is between 800 and 2000.'' What is John's number?
Answer:
1500
Step-by-step explanation:
List of multiples of 125 between 800 and 2000: 875,1000,1125,1250,1375,1500,1625,1750,1875,2000
Of those only 1500 is divisible by 30: 1500 / 30 = 50
The john number should be 1,500,
Calculation of number:The List of multiples of 125 that lies between 800 and 2000 should be 875,1000,1125,1250,1375,1500,1625,1750,1875,2000
Here we can see that there is only 1500 that should be the multiple of 30
Therefore, the john number should be 1500
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Find the area of the shaded region.
Round to the nearest tenth.
9.28 cm
68.90
Area = [?] cm?
I really need help pretty quick on this one. So plz hurry if u can.
Answer:
The area of the shaded region is [tex]11.6\ cm^{2}[/tex]
Step-by-step explanation:
we know that
The area of the shaded region is equal to the area of the sector of circle of angle 68.9 degrees minus the area of the isosceles triangle
step 1
Find the area of sector of the circle
The area of circle is equal to
[tex]A=\pi r^{2}[/tex]
assume
[tex]\pi =3.14[/tex]
[tex]r=9.28\ cm[/tex]
substitute
[tex]A=(3.14)(9.28)^{2}[/tex]
[tex]A=270.41\ cm^{2}[/tex]
Remember that the area of a circle subtends a central angle of 360 degrees
so
using proportion Find out the area of a sector with a central angle of 68.90 degrees
Let
x -----> the area of a sector
[tex]270.41/360=x/68.90\\\\x=68.90*270.41/360\\\\x=51.75\ cm^{2}[/tex]
step 2
Find the area of the isosceles triangle
Applying the law of sines
The area is equal to
[tex]A=(1/2)r^{2}sin(68.90)[/tex]
we have
[tex]r=9.28\ cm[/tex]
substitute
[tex]A=(1/2)(9.28)^{2}sin(68.90)=40.17\ cm^{2}[/tex]
step 3
Find the area of the shaded region
[tex]51.75-40.17=11.58\ cm^{2}[/tex]
Round to the nearest tenth
[tex]11.58=11.6\ cm^{2}[/tex]
The calculated area of the shaded region is 11.6 square cm
How to determine the area of the shaded region.from the question, we have the following parameters that can be used in our computation:
The circle
The area of the shaded region is calculated as
Area of shaded region = Area of sector - Area of triangle
Using the respective formulas, we have
Area of shaded region = 68.9/360 * 3.14 * 9.28 * 9.28 - 1/2 * 9.28 * 9.28 * sin(68.9)
Evaluate
Area of shaded region = 11.6
Hence, the area of the shaded region is 11.6 square cm
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Need answer to A and B!
Answer:
a) [tex]\frac{14}{285}[/tex]
b) [tex]\frac{11}{57}[/tex]
Step-by-step explanation:
We are given that a committee of three people is selected at random from a set of eight teachers, seven parents of students, and five alumni.
We are to find:
a) the probability the committee consists of all teachers is:
Number of ways to select three that are all teachers = [tex]8C3[/tex]
Number of ways to select three randomly = [tex]20C3[/tex]
P (3 all teachers) = [tex]\frac{8C3}{20C3}[/tex] = [tex]\frac{14}{285}[/tex]
b) the probability the committee has no teachers is:
Number of ways to select three that it has no teachers = [tex]12C3[/tex]
Number of ways to select three randomly = [tex]20C3[/tex]
P (no teachers) = [tex]\frac{12C3}{20C3}[/tex] = [tex]\frac{11}{57}[/tex]
6/22 to the nearest whole percent?
is?
1) Divide the numbers
6/22= 0.27 (27 is repeating)
2) Multiply the decimal by 100
0.2727(100)= 27.27
3) Round
27.27 is closer to 27
Therefore, 6/22 to the nearest whole number is 27%.
Hopefully this helps!
Answer: 27%
Step-by-step explanation:
Given the fraction [tex]\frac{6}{22}[/tex], you need to divide the numerator by the denominator in order to rewrite it as a decimal number.
[tex]\frac{6}{22}=0.27[/tex]
Now, to express it in percentage, the final step is to multiply the decimal number by 100.
Therefore, you get that [tex]\frac{6}{22}[/tex] to the nearest whole percent is:
[tex](0.27)(100)=27\%[/tex]