Answer:
[tex]a_n=3(-3)^{n-1}[/tex]
Step-by-step explanation:
Geometric sequence
General form of a geometric sequence: [tex]a_n=ar^{n-1}[/tex]
where:
[tex]a_n[/tex] is the nth terma is the first termr is the common ratioGiven:
[tex]a_1=3[/tex][tex]a_2=-9[/tex]To find the common ratio r, divide consecutive terms:
[tex]\implies r=\dfrac{a_2}{a_1}=\dfrac{-9}{3}=-3[/tex]
Therefore, the equation is:
[tex]a_n=3(-3)^{n-1}[/tex]
At a hockey game a vender sold a combined total of 105 sodas and hot dogs. The number of sodas sold was 39 more than the number of hot dogs sold find the number of soda sold and the number is hot dog sold
Answer:
Hot dog sold = 33
Sodas Sold = 72
Step-by-step explanation:
Given:
At a hockey game a vender sold a combined total of 105 sodas and hot dogs. The number of sodas sold was 39 more than the number of hot dogs sold
To Find:
Number of soda/hot dog sold
Solve:
h + ( 39 + h ) = 105
h + 39 + h = 105
2h + 39 = 105
h + 19.5 = 52.5
h = 52.5 - 19.5
This as a system does not use any inequality. "39 more than" means, +39.
h = 33 meaning d= 72
Add to check Answer:
33 + 72 = 105
Thus,
Hot dog sold = 33
Sodas Sold = 72
Kavinsky
Which data set could be represented by the box plot shown below?
Answer:
(D)
Step-by-step explanation:
The box plot is a visual representation of the 5-number summary of the data. It shows the extremes, the quartiles and the median.
__
Each data set has 11 elements, sorted into increasing order.
extremesThe first and last elements of the data set correspond to the ends of the whiskers, so you are looking for a set that ranges from 3 to 18. (This eliminates choice B.)
medianThe median will be the middle element, the 6th from either end. The vertical line in the box identifies its value as 10. (This eliminates choice A.)
quartilesThe first quartile is the middle element of the bottom half of the data set (what remains after the median and above elements are removed). There are 5 elements in the bottom half, so the first quartile is the 3rd one. It is signified by the left end of the box in the box plot. Its value is 7. (This eliminates choice C.)
Similarly, the third quartile is the 3rd element from the right end of the data set. The value 13 in choice D matches the right end of the box in the box plot.
The box plot represents the data set in Choice D.
Find x in this 45°-45°-90° triangle.
22
45
X =
Step-by-step explanation:
45 and 22 multiplied would be your answer
82°
57°
The measure of x is
The measure of y is
The measure of z is
to
Z
102
62⁰
Answers:
x = 16
y = 41
z = 123
==========================================================
Explanation:
Focus on the large triangle on the left.
The three interior angles of any triangle add to 180 degrees.
57+82+y = 180
y+139 = 180
y = 180-139
y = 41
-------------------
Now focus on the large triangle on the right.
We'll use the same idea as before.
x+102+62 = 180
x+164 = 180
x = 180-164
x = 16
-------------------
The last triangle to focus on is the small one in the middle.
Use the values of x and y to find z.
x+y+z = 180
16+41+z = 180
57+z = 180
z = 180-57
z = 123
Answer:
The angles inside of a triangle always add up to 360 therefore we can easily determine what the angle of x and y is because they are a part of two triangles that have two angles each. Let's first determine x.
[tex]x = 180 - (102+ 62)[/tex]
[tex]x = 180 - 164[/tex]
[tex]x = 16[/tex]
The second step that we need to do is to determine y using 82 and 57.
[tex]y = 180 - (82 + 57)[/tex]
[tex]y = 180 - 139[/tex]
[tex]y = 41[/tex]
The final step is to determine z using x and y
[tex]z = 180 - (x + y)[/tex]
[tex]z = 180 - (16 + 41)[/tex]
[tex]z = 180 - 57[/tex]
[tex]z = 123[/tex]
Therefore, x = 15 and y = 41 and z = 123
Hope this helps!
A teacher gave her class two quizzes. 25% of the class passed both quizzes and 40% of the class passed the first quiz. What percent will pass the second quiz given they passed the first quiz?
Answer:
35%
Step-by-step explanation:
40% + 25% = 65% minus that bye 100 you would get 35% the reason the answer isn't 65 is because add 40+25+65=130 which a whole is equal to 100 but if you do 40+25+35= 100 so thr answer is 35% :)
Can someone answer theese 3 questions
Answer:
Which three questions?
Step-by-step explanation:
I've answered this first question, I guess I need two more...
The base diameter and the height of a cone are both
equal to x units.
Answer:
π x³ /12 is the volume of the cone if A cone has a height of x and a diameter of x
Step-by-step explanation:
The base diameter and the height of a cone are both equal to x units
Diameter of cone = x units
Radius = Diameter /2
=> Radius of cone = x/2 units
Height of cone =x units
Volume of cone = (1/3) π r²h
r = radius h = height
=> Volume of cone = (1/3)π (x/2)² * x
= (1/3) π (x²/4) * x
= (1/12) π x³
= π x³ /12 cubic units
Which of the following phrases in bold is an example of informal English?
After basketball practice Julie hit the books.
I really don't want to do my homework today.
Both Kelli and Rosa were late to the party.
Will ran down the street to catch the bus.
PLEASE HELP ME!!!!!!
Will ran down the street to catch the bus.
Hope this helps, thanks,
CoDBiarex
Answer:
After basketball practice Julie hit the books.
Step-by-step explanation:
Informal English often uses slang words that not everyone understands.
Solve for x.
Your answer must be simplified
15<−5x
od
2
(
2 7 1-3
1 3 1-2
6:1-6
b =
d =
IDONE
Answer:
[tex] a = \boxed{1},\: b=\boxed{0}\\\\c=\boxed{0},\: d=\boxed{1}[/tex]
Step-by-step explanation:
[tex]\begin{bmatrix} 2 & 7\\\\1 & 3\end{bmatrix}\:\begin{bmatrix} -3 & 7\\\\1 & -2\end{bmatrix}=\begin{bmatrix} a & b\\\\c & d\end{bmatrix}[/tex]Multiply both the matrices on left side, we find:[tex]\begin{bmatrix} 2(-3)+7(1) & 2(7)+7(-2)\\\\1(-3)+3(1) & 1(7)+3(-2)\end{bmatrix}=\begin{bmatrix} a & b\\\\c & d\end{bmatrix}[/tex][tex]\rightarrow\begin{bmatrix} -6+7 & 14-14\\\\-3+3 & 7-6\end{bmatrix}=\begin{bmatrix} a & b\\\\c & d\end{bmatrix}[/tex][tex]\rightarrow\begin{bmatrix} 1 & 0\\\\0 & 1\end{bmatrix}=\begin{bmatrix} a & b\\\\c & d\end{bmatrix}[/tex]Comparing the corresponding elements of both the matrices on both sides, we find:[tex] a = \boxed{1},\: b=\boxed{0},\:c=\boxed{0},\: d=\boxed{1}[/tex]What is the quotient when (x+3) is divided into the polynomial 2x2 + 3x-9?
O A. 2x-5 with no remainder
B. X+ 3 with a remainder of -2
O c. 2x+ 1 with no remainder
D. 2x-3 with no remainder
Problem: 2x^2+3x-9
For a polynomial of the form, ax^2+bx+c rewrite the middle term as the sum of two terms whose product a·c=2·-9=-18 and whose sum is b=3.
Factor 3 out of 3x
2x^2+3(x)-9
Rewrite 3 as -3 plus 6.
2x^2+(-3+6)x-9
Apply the distributive property
2x^2(-3x+6x)-9
Remove the parentheses
2x^2-3x+6x-9
Factor out the greatest common factor from each group
Group the first two terms and the last two terms
(2x^2-3x) (6x-9)
Factor out the greatest common factor in each group.
x(2x-3)+3(2x-3)
Factor the polynomial by factoring out the greatest common factor, 2x-3
(x+3) (2x-3). So, the quotient is 2x-3
Thus, the correct answer is Option D 2x-3 with no remainder
Solve for x. Round to the nearest tenth, if necessary.
Answer:
x = 1
Step-by-step explanation:
[tex]\sf Sin \ 37^\circ = \dfrac{opposite \ side}{hypotenuse}\\\\[/tex]
[tex]\sf 0.6 = \dfrac{0.6}{x}\\\\Cross \ multiply,\\\\ 0.6*x = 0.6\\\\x = \dfrac{0.6}{0.6}\\\\x = 1[/tex]
i need help with 7th grade math please 30 points need help ASAP in fraction and simplest form.
Answer:
The scale of the drawing to become the statue is 7, and likewise for the statue to become the drawing it is 1/7.
Drawing * Scale = Statue
Take the first dimension:
9 * scale = 63
63/9 = scale
scale = 7
Answer:
7
Step-by-step explanation:
The scale factor is the ratio between the actual size and the model size.
Here, they are termed as "statue" and "drawing" respectively.
Finding scale factor :
Actual size / Model size63/9 710. What mass of carbon dioxide is produced when 6.2
moles of propane, C3Hg is burned in oxygen?
C3H2 + ___ O2 →
O2 → _ CO2 + _ H2O
-
-
Which is a property of polygons?
A polygon is a plane figure.
A polygon is a solid figure.
A polygon has a maximum of 100 sides.
A polygon is an open figure.
Answer:
The answer is, A polygon is a plane figure,
it has no limit in the number of sides, its not an open figure, its not a solid
Step-by-step explanation:
Hope it helps
Answer:
A Polygon is a plane figure
Step-by-step explanation:
Properties of polygon:
1. A polygon is a plane figure with line segments. Two dimensional figure.
2. A polygon has minimum 3 sides and has maximum limit.
3. The sum of all interior angles of the polygon is given by (n -2)*180 where n is the number of sides.
4. The sum of exterior angles of any polygon is 360
A palindrome is a number that reads the same forwards and backwards, such as 22 or 39793.
How many palindromes are there between 10 and 400?
Answer:
There are thirty-nine palindromic numbers between 10 and 400.
Step-by-step explanation:
Listed, they are: 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 202, 212, 222, 232, 242, 252, 262, 272, 282, 292, 303, 313, 323, 333, 343, 353, 363, 373, 383, and 393.
The function (x)-47x
represents the number of jumping jacks j(x) you can do in x minutes. How many jumping jacks can you do in 15 minutes?
Given the function, j(x) = 47x, the number of jumps you can do in 15 minutes is: 705.
What is a Function?A function models the relationship between an input value and its corresponding output value.
Given the function, j(x) = 47x, number of jumping jacks you do in 15 minutes, is:
j(15) = 47(15)
j(15) = 705
Number of jumping jack in 15 minutes is: 705.
Learn more about a function on:
https://brainly.com/question/10439235
#SPJ1
PLS HELP ME
1. What is the length of (AB)?
2. What is the length of (BC)?
3. What is the perimeter of this rectangle?
The length of AB is 4.12 units, length of BC is 8.25 units and Perimeter of rectangle ABCD is 24.74 units.
What is Perimeter of Rectangle?The perimeter of a rectangle is the total distance of its outer boundary. It is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width).
Here,
A (-3, 3) and B (1, 4)
then, Length of AB = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
= [tex]\sqrt{(1-(-3))^2+(4-3)^2 }[/tex]
= [tex]\sqrt{4^2 + 1^2}[/tex]
= [tex]\sqrt{17}[/tex] units.
= 4.12 units
B (1, 4) and C (3, -4)
then, Length of BC = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
= [tex]\sqrt{(3 - 1)^2+(-4 - 4)^2 }[/tex]
= [tex]\sqrt{4 + 64}[/tex]
= [tex]\sqrt{68}[/tex]
= 8.25 units
Perimeter of Rectangle = 2 ( AB + BC )
= 2 ( 4.12 + 8.25 )
= 2 X 12.37
= 24.74 units
Thus, the length of AB is 4.12 units, length of BC is 8.25 units and Perimeter of rectangle ABCD is 24.74 units.
Learn more about Perimeter of Rectangle from:
https://brainly.com/question/15287805
#SPJ1
6 times a number is 16 less than the square of that number. Find the positive solution.
Answer:
x=8
Step-by-step explanation:
Let's say this mystery number is x.
6 times this x is 16 less than the square of x so we can write this as:
[tex]6x = x^2 - 16[/tex]
We can then re-arrange this into a quadratic and simplify it so:
[tex]x^2 -6x-16 =0[/tex]
[tex](x-8)(x+2)[/tex]
x=8, x=-2
And since the question is asking for the positive solution,
x=8
(x+3)^2+4=46
what is the solution of this equation
Answer:
x = -3 + √42
Step-by-step explanation:
1) Expand the square
2) Distribute
3) Distribute
4) Distribute
5) Combine like terms
6) Add the numbers
7) Move terms to the left side
8) Subtract the numbers
9) Use the quadratic formula
10) Simplify
11) Separate the equations
12) Solve
Therefore, the solution of this equation is x = -3 + √42
Step-by-step explanation:
(x + 3)² + 4 = 46
(x + 3)² = 42
x + 3 = ±sqrt(42)
x = ±sqrt(42) - 3
x1 = sqrt(42) - 3 = 3.480740698...
x2 = -sqrt(42) - 3 = -9.480740698...
which statement about the ellipse are true ? select three options.
Answer:
There are three main types of a solar eclipses
Step-by-step explanation:
1. Total solar eclipse: A total solar eclipse is visible from a small area on Earth. The people who see the total eclipse are in the center of the Moon's shadow when it hits Earth. The sky becomes very dark, as if it were night. For a total eclipse to occur, the Sun, Moon and Earth must be in a direct line.
2. Partial solar eclipse: This happens when the Sun, Moon and Earth are not exactly aligned. The Sun appears to have a dark shadow on a small part of its surface.
3. Annular (an-yə-lər) solar eclipse: An annular eclipse happens when the Moon is farthest from Earth. Because the Moon is farther away, it seems smaller. It does not block the entire view of the Sun. The Moon in front of the Sun looks like a dark disk on top of a larger Sun-colored disk. This creates what looks like a ring around the Moon.
Animation of the Moon moving between the Sun and Earth
During a solar eclipse, the Moon blocks the sunlight to Earth. The Moon also casts a shadow onto Earth.
I hope this helps! ;)
To the nearest thousandth, what is the area of the region bounded by y = ex and x = (y-1)²? 0.089 O 1.188 2.880 4.265
The area bounded by the curves will be 0.089. Then the correct option is A.
What is an area bounded by the curve?When the two curves intersect then they bound the region is known as the area bounded by the curve.
The functions are given below.
y₁ = eˣ ....1
x = (y - 1)² ...2
Then equation 2 can be written as
y₂ = √x + 1
The intersection point of the curves will be
eˣ = √x + 1
BY solving, the value of x will be
x = 0, 0.558
Then the area bounded by the curves will be
[tex]\rm A = \int _0^{0.558} (y_2 - y_1) dx\\\\\\A = \int _0^{0.558} (\sqrt{x} + 1 - e^x )dx\\\\\\A = \left [\dfrac{x^{3/2}}{3/2} + x - e^x \right]_0^{0.558} \\\\\\A = \left [\left (\dfrac{0.558^{3/2}}{3/2} + 0.558 - e^{0.558} \right ) - \left ( \dfrac{0^{3/2}}{3/2} + 0 - e^0 \right) \right]\\[/tex]
On further solving we have
A = -0.911 + 1
A = 0.0887
A ≅ 0.089
Then the correct option is A.
More about the area bounded by the curve link is given below.
https://brainly.com/question/24563834
#SPJ1
This morning, Manuel's car had 27.24 gallons of fuel. Now, 5.7 gallons are left. How much fuel did Manuel use?
gallons
Answer:
21.54
Step-by-step explanation:
27.24 - 5.7
= 21.54
An object has a mass of 180 g and a volume of 9 cm³.
Find the density of the object in g/cm³.
g/cm³
Answer:
20 g/cm³
Step-by-step explanation:
mass = 180g
volume = 9 cm³
density =mass/volume
=180/9= 20 g/cm³
Evaluate sin 360°. Round your answer to the nearest hundredth if necessary.
Answer:
0
Step-by-step explanation:
just plug it into a calculator
write two equations that when graphed look like this *see image*. please help its due soon and i will give ya 75 points for answering CORRECTLY thanks, 5 stars, and brainlist.
The graph is showing the equation of circle x²+y²=4
What is a circle?A circle is a two-dimensional geometry on the plane having a centre point and the circular line is drawn equidistant from the centre point.
The given graph in the question represents the equation of the circle cutting the points on the x-axis and y-axis at 4 which is the radius of the circle.
The equation will be as follows:-
x²+y²=4
Hence the graph is showing the equation of circle x²+y²=4
To know more about circles follow
https://brainly.com/question/24375372
#SPJ1
Form an equation whose roots are 2 and -4/3
Answer: x^2 i think
Step-by-step explanation: "be the roots m = 2, n = 3 Sum of the roots = m + n = 2 + 3 m + n = 5 Product of the roots = mn = (2)(3) mn = 6 Standard form is x^2 - (m + n)"
JoAnne wanted to add some accessories to her house. She purchased the following items; 2 decorative bowls for $46 each, a picture for $85, a lamp for $67, and four candles for $12 each. How much did she spend?
$296
$292
$290
$294
Answer:
the answer is $292 :)
have a nice day
FInd the value of x.
Y
D
W
X
(15x-8)
X =
N
226
Let's start with the given arc and its angle.
The angle YWX is going to be half the arc length.
YWX = 1/2 (226) = 113
Angles VWX and YWX form a linear pair (or are supplementary angles), which means that their sum is 180 degrees.
(15x - 8) + 113 = 180
15x + 105 = 180
15x = 75
x = 5
Hope this helps!
Which statement about the line represented by the equation y+2=(x-5) is true
A. The slope is 3 and (-2,5) is on the line
B. The slope is 2 and (3,-5) is on the line
C. The slope is 3 and (5,-2) is on the line
D. The slope is 2 and (-3,5) is on the line
Answer:
A
Step-by-step explanation:
-2+2=5-5
0=0
the correct answer is A