(0,0) satisfies y > 2x - 1 but does not satisfy y ≤ x^2 - 4. C
(0,0) satisfies both inequalities.
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.
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
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
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.
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.
Find the distance between the points (6, -4) and (0, 5).
Answer:
3 square root 13
Step-by-step explanation:
I used the distance formula and I got this answer.
Distance is the length of the path linking two sites is the distance between them.
How to solve ?Distance between two points is solved by formula
[tex]=\sqrt{(x1-x2)^2 +(y1-y2)^2}\\=\sqrt{(6-0)^2+(-4-5)^2} \\=\sqrt{36+81} \\=\sqrt{117} \\=10.81[/tex]
Hence distance between points is 10.81
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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
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]
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 :)
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)
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]
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
learn more about the number here: https://brainly.com/question/22439747
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
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]
Need help. Thanks for helping me.
Answer:
F 4 ^ -2
Step-by-step explanation:
4 ^ -5
-----------------
4^-3
We know that a^b/ a^c = a^ (b-c)
4 ^ (-5 - -3)
4 ^ (-5 +3)
4 ^ (-2)
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.
Learn more about cross section here
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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
"Angie read 3 books in 4 days, and each book contained 280 pages. if angie reads the same number of pages each day, how many pages did she read per day?"
Answer:210
Step-by-step explanation:
3 x 280 = 840
840 ÷ 4 = 210
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]
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.
1. Donna bought a coat on sale for $60.
That was 25% off ( less than the regular price).
What was the regular price?
Answer:
$240
Step-by-step explanation:
If x is the missing number and 25% equals to 1/4 then 1/4 times x equals 60.
Then once you multiply x on both sides you get $240.
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
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
what is the simplest form of the ratio 40:16?
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]
pLz help
Graph the linear equation. Find three points that solve the equation, then plot then on the graph.
x -3y= -6
Answer:
So you will want to graph the following 3 points:
(0,2)
(3,3)
(-3,1)
Then connect the points.
Step-by-step explanation:
So we have the equation x-3y=-6.
I'm going to solve for y once so I don't have to do it 3 times when choosing a value for x.
x-3y=-6
Subtract x on both sides:
-3y=-x-6
Divide both sides by -3:
[tex]y=\frac{-x}{-3}+\frac{-6}{-3}[/tex]
Simplify where you can:
[tex]y=\frac{1}{3}x+2[/tex]
So since this in the slope-intercept form, y=mx+b where slope is m and b is y-intercept we have that (0,2) is on our line. If you plug in 0, you will get 2 like this y=1/3 (0)+2=0+2=2.
Now I'm going to choose easy values to plug in, ones that are divisible by 3 since x is being multiplied by 1/3.
So if x=3, then [tex]y=\frac{1}{3}(3)+2=1+2=3[/tex], so (3,3) is on the line.
So if x=-3, then [tex]y=\frac{1}{3}(-3)+2=-1+2=1[/tex]. so (-3,1) is on the line.
So you will want to graph the following 3 points:
(0,2)
(3,3)
(-3,1)
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°
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.
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
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