Answer:
Step-by-step explanation:
Question 1:
x² = -8x - 7
x² + 8x = -7
(x + 4)² = 9
So the answer is (x + 4)² = 9
Question 2:
(x + 4)² = 9
So x = -4 ± 3
3. Given the geometric series 300 +360+432 +518.4+, what is the sum of the first 10 terms?
The sum of the first 10 terms of the given geometric series 300 +360+432 +518.4+..... is 7787.60.
What is the sum of terms of a geometric sequence?Let's suppose its initial term is a , the multiplication factor is r
and let it has total n terms, then, its sum is given as:
[tex]S_n = \dfrac{a(r^n-1)}{r-1}[/tex]
(sum till nth term)
For the given geometric series, the common ratio is,
r = (360/300) = 1.2
Also, the first term of the series is 300. Therefore, the sum of the first ten terms of the series are:
Sum = a(rⁿ-1)/(r-1) = 300(1.2¹⁰-1)/(1.2-1) = 300(5.1917)/0.2 = 7787.60
Hence, the sum of the first 10 terms of the given geometric series is 7787.60.
Learn more about the Sum of terms of geometric sequence:
brainly.com/question/1607203
#SPJ1
A cube has a volume of 0.215ft³. What is te length of each side of the cube?
Answer:
length ≈ 0.599 feet
Step-by-step explanation:
volume = length³
0.215ft³ = length³
cube root both sides to isolate the length
∛(0.215ft³) = length
length ≈ 0.599 feet
Figure A is a scale image of figure B
Answer:
x = 7.5 units
Step-by-step explanation:
10 * .75 = 7.5
Identify the Pre-Image in the diagram below. EXPLAIN your answer.
A transformation's preimage is the shape before the change. The image that is a pre-image is A'B'C', which is in blue colour.
What are an image and pre-image?We have a term for the shape before the transformation and another one for the shape after the transformation. The shape after a transformation is the image of the transformation. A transformation's preimage is the shape before the change.
In maths, the pre-image is the original figure. Therefore, the image that is a pre-image is ABC, which is in red colour.
Learn more about Image and Pre-image:
https://brainly.com/question/1809747
#SPJ1
What is the area of this right triangle?
30 mm²
39 mm²
60 mm²
78 mm²
Answer:
30
Step-by-step explanation:
since we are looking for the area of a right triangle you want to use the legs of the triangle. Basically 5x12 over 2= 30, I think I am correct if not I apologize/
Answer:
the answer is 78
Step-by-step explanation:
12x 5= 60
60x13=180
180+600=780
the answer equals up to 78
The orbit of a planet around the sun is not circular; it is an ellipse with
the Sun at one focus. The aphelion of a planet is the greatest distance
from the sun and the perihelion is its shortest distance. The mean
distance of a planet from the sun is the length of the semimajor axis of
the elliptical orbit. The perihelion of Pluto is 4551 million miles, and the
distance from the center of its elliptical orbit to the sun is 897.5 million
miles. Find the aphelion of Pluto. What is the mean distance of Pluto
from the Sun? Write an equation to represent the orbit of Pluto around
the Sun.
The equation to represent the orbit of Pluto around the Sun will be x²/4659.42 + y²/4566.31 = 1.
How to compute the equation?The distance from the center of the elliptical orbit to the sun is 897.5 million miles. The aphelion will be:
= 5448.5 + 897.5
= 6346 million miles
The equation of ellipse will be:
x²/a² + y²/b² = 1
x²/4659.42 + y²/4566.31 = 1
Learn more about equations on:
https://brainly.com/question/14323743
#SPJ1
What is the volume of a right circular cylinder with a base radius of 6 feet and a height of 10 feet? 900 cubic meters 120 cubic meters 180 cubic meters 360n cubic meters
Step-by-step explanation:
the volume of a cylinder is
base area × height = pi×r² × height
with r being the radius.
so, we get
pi×6² × 10 = pi×36 + 10 = 360pi =
= 1,130.973355... ft³
now we need to look at the conversion rate between feet and meters :
1 ft = 0.3048 m
1 ft² = 0.3048² m² = 0.09290304 m²
1 f³ = 0.3048³ m³ = 0.028316847... m³
1,130.973355... ft³ = 1,130.973355... × 0.028316847... =
= 32.025599... m³
so, something is not right with your answer options. it looks like you put maybe the answer options of a different question in here.
but none of them get even close to the actual solution of the given question.
what's the answer?? please help me
Write and solve an equation to find the value of x.
Answer:
x = 5
Step-by-step explanation:
By the property intersecting chords:
x(16) = (10)(8)
-> x (16) = 80
-> x = 80/16
-> x = 5
Help Please. Solve for x.
Answer:
x = 16
Step-by-step explanation:
sec(60) = 32 /x
2 = 32/x
x2 =32
x = 16
Please help.
fiona asked 150 students to select their favorite fruit and then recorded the results in the bar graph below. fiona will ask another 45 students to select their favorite fruit. based on the information in the bar graph, how many more students from the next 45 are likely to select oranges rather than bananas their favorite fruit?
The number of students that are more likely to select oranges rather than bananas their favorite fruit from the next 45 is; 3.
What no. of students from the next 45 are likely to select oranges rather than bananas their favorite fruit?It follows from the task content that the number of students surveyed initially is 150 and only, 30 -20 = 10 students preferred orange to bananas.
On this note, it follows that the number of students who prefer oranges rather than bananas from the next 45 is; = (45 × 10)/150 = 3.
Read more on ratios;
https://brainly.com/question/13513438
#SPJ1
jackson bought 3 pounds of candy for 9.60. What was the price of this candy in cents per ounce? PLS HELP
Answer:
The price of candies in cents per ounce is 20 cents per ounce.
Step-by-step explanation:
960 cents/(48 oz) = 20 cents/oz
FIND THE EXACT AREA PLEASE HELP ILL GIVE BRAINLIESTTTT
Check the picture below.
[tex]\textit{area of a circular ring}\\\\ A=\pi (R^2-r^2)~~ \begin{cases} r=\stackrel{smaller}{radius}\\ R=\stackrel{larger}{radius}\\[-0.5em] \hrulefill\\ r=2\\ R=3 \end{cases}\implies \begin{array}{llll} A=\pi (3^2-2^2)\implies A=5\pi \\\\\\ A\approx 15.71 \end{array}[/tex]
$6300 at 5% annual rate, compounded semi- annually, for 2 years
Answer:
$6954.02.
Step-by-step explanation:
The formula is
A = P(1 + 0.05/n)^2n where A is the amount compounded, P = initial investment and n is the number of years.
A = 6300(1 + (0.05)/2)"(2*2
= 6954.02
The graph of F(x), shown below, has the same shape as the graph of
G(x) = x4, but it is shifted to the right 3 units. What is its equation?
A. F(x) = - 3
O B. F(x) = (x-3)4
O C. F(x) = (x+3)4
O D. Fx) = 44+ 3
Answer: F(x) = 4x - 16
Step-by-step explanation: G(x) = 4x
if F(x) is the graph G(x) shifted over to the right by 4 then
F(x) = G(x-4) = 4(x-4) = 4x - 16
The general equation is f(x - amount_shifted)
The equation of the graph of the function F(x) is F(x) = (x - 3)⁴.
What is Translation of Functions?Translation of functions is defined as the when each point in the original graph is moved by a fixed units in the same direction.
There are horizontal translation and vertical translation of functions.
Given a function F(x) and G(x).
Given that,
F(x) has the same shape as the graph of G(x) = x⁴.
The difference is that F(x) is shifted to the right 3 units.
A function G(x) when shifted right to k units becomes G(x - k).
So the function F(x) is,
F(x) = G(x - 3)
= (x - 3)⁴
Hence the correct option is B.
Learn more about Translation of functions here :
https://brainly.com/question/29198392
#SPJ7
The swim team is sharing 6 pizzas. There are 36 players on the team. If each member has 1 slice, and each pizza has 8 slices, how much pizza in fraction form is left over?
The amount of pizza left over in the fraction form will be 1/4.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the swim team is sharing 6 pizzas. There are 36 players on the team. If each member has 1 slice, and each pizza has 8 slices.
Total slices = 8 x 6 = 48
Total players = 36
Left slices = 48 - 36 = 12
The portion in fraction left is,
L = 12 / 48
L = 1 / 4
To know more about an expression follow
https://brainly.com/question/3800618
#SPJ2
Please help brainliest who answer's first and correct
Answer:
just start at like 220 i am pretty sure
Step-by-step explanation:
PLEASE HELP WILL MARK BRAINLIEST 45 POINTS
Answer:
I got 58.5
I multiplied 3x9 to get 27
then 3x6 to get 18
then 3x9/2 to get 13.5 and added them all together.
The product of the polynomials (3x 2) and (-x^3 – 3) is . when this product is multiplied by (3 x), the coefficient of x4 in the result is
Answer:
(3x + 2)(-x^3 - 3) =
3x(-x^3 - 3) + 2(-x^3 - 3) =
-3x^4 - 2x^3 - 9x - 6 <== result of multiplying (3x+2)(-x^3-3)
now multiply that by (3+x)...
(3+x)(-3x^4 - 2x^3 - 9x - 6) =
3(-3x^4 - 2x^3 - 9x - 6) + x(-3x^4 - 2x^3 - 9x - 6) =
-9x^4 -6x^3 - 27x - 18 - 3x^5 - 2x^4 - 9x^2 - 6x =
-3x^5 - 11x^4 - 6x^3 - 9x^2 - 33x - 18 <== result of multiplying by (3 + x)
the coefficient of x^4 = -11 <==
Step-by-step explanation:
Answer:
(3x + 2)(-x^3 - 3) =
3x(-x^3 - 3) + 2(-x^3 - 3) =
-3x^4 - 2x^3 - 9x - 6 <== result of multiplying (3x+2)(-x^3-3)
now multiply that by (3+x)...
(3+x)(-3x^4 - 2x^3 - 9x - 6) =
3(-3x^4 - 2x^3 - 9x - 6) + x(-3x^4 - 2x^3 - 9x - 6) =
-9x^4 -6x^3 - 27x - 18 - 3x^5 - 2x^4 - 9x^2 - 6x =
-3x^5 - 11x^4 - 6x^3 - 9x^2 - 33x - 18 <== result of multiplying by (3 + x)
the coefficient of x^4 = -11 <==
Step-by-step explanation:
The list 11, 20, 31, 51, 82 is an example of a list of five strictly positive integers
arranged in ascending order and of which we obtain the third integer by adding the
first and second integers, the fourth by adding the second and third
integers, and the fifth by adding the third and fourth integers. How much
such lists of five positive integers have 124 as the fifth integer?
As of 2016, Illinois has a population of 12, 801,539 people and has a land area of 55,519 square miles. Texas has a population of 27,862,596 people and a land area of 261, 232 square miles. Based on this data, which state has the greater population density? Move the correct state to the first blank, and move numbers into the remaining blanks to justify the answer. The state with the greater population density is because Illinois Texas 107 231 55,519 261, 232 12,801, 539 27,862, 596
Using it's concept, it is found that the state with greater population density is Illinois.
What is population density?Population density is the number of habitants divided by the area.
Considering the data given, for Illinois, the density is given by:
Di = 12,801,539/55,519 = 230.58 habitants per square mile.
For Texas, the density is given by:
Dt = 27,862,596/261,232 = 106.66 habitans per square mile.
Di > Dt, hence the state with greater population density is Illinois.
More can be learned about population density at https://brainly.com/question/26148357
#SPJ1
please help me solve this solve the triangle round to nearest tenth
Answer:
the measurement of the angle A is 39.17°
Write a second degree polynomial with real coefficients and the given root; -2i
Answer: x^2+4
Work Shown:
x = -2i
x^2 = (-2i)^2
x^2 = 4i^2
x^2 = 4(-1)
x^2 = -4
x^2+4 = 0
Side note: Since -2i is one root, this means 2i is the other conjugate root.
[tex]\text{For quadratic equations, if one root is complex, the other root will be its conjugate.}\\\\\text{So, the roots of the second degree polynomial are}~ \alpha = -2i ~~ \text{and}~~ \beta =2i \\\\\text{The equation is,}\\\\~~~~~~~x^2-(\alpha + \beta) x +\alpha \beta = 0\\ \\\implies x^2 -(-2i+2i)x +(2i)(-2i)=0\\\\\implies x^2 -0\cdot x -4i^2 =0\\ \\\implies x^2 -4(-1)=0\\\\\implies x^2 +4=0[/tex]
find four consecutive whole numbers whose sum is 74
Answer:
17, 18, 19, 20
Explanation:
Let the numbers be x, x + 1, x + 2, x + 3
Their sum is equals to 74
x + x + 1 + x + 2 + x + 3 = 74 (group the variables)
x + x + x + x + 1 + 2 + 3 = 74 (simplify)
4(x) + 6 = 74 (subtract both sides by 6)
4x = 68 (divide both sides by 4)
x = 17
Other numbers:
x + 1 = 17 + 1 = 18
x + 2 = 17 + 2 = 19
x + 3 = 17 + 3 = 20
Answer:
17, 18, 19, 20
Step-by-step explanation:
Let four consecutive whole numbers be x, (x + 1), (x + 2) and (x + 3)According to the given condition:x + (x + 1) + (x + 2) + (x + 3) = 74-> 4x + 6 = 74-> 4x = 74 - 6-> 4x = 68-> x = 68/-> x = 17-> x + 1 = 17 + 1 = 18-> x + 2 = 17 + 2 = 19-> x + 3 = 17 + 3 = 20Thus, the four consecutive whole numbers are 17, 18, 19 and 20PLEASE HELP ME I GIVE BRAINLIEST
Answer:
[tex]\frac{2\pi }{3} \ ,\ \pi \ ,\ \frac{4\pi }{3}[/tex]
Step-by-step explanation:
suppose cos(x) = y
Then
[tex]2\cos^{2} \left( x\right) +3\cos x+1=0\Longleftrightarrow \begin{cases}2y^{2}+3y+1=0&\\ y=\cos \left( x\right) \ \ \text{and} &0\leqslant x\leqslant 2\pi \end{cases}[/tex]
2y² + 3y + 1 = 0 ⇒ y = -1 or y = -1/2 (because 2-3+1=0)
y = -1 ⇔ cosx = -1 ⇒ x = π (because x∈[0,2π] )
y = -1/2 ⇔ cosx = -1/2 ⇒ x = 2π/3 or x = 4π/3
Final answer :
x = π or x = 2π/3 or x = 4π/3
Grace collected data from twenty of her friends about the number of pets they have. The median number of pets is two.
What does the median say about Grace's data set?
Answer options with 4 options
A.
Everyone Grace surveyed has two pets.
B.
More of Grace's friends have two pets than any other number.
C.
Two is the middle number when the number of pets in the data set is ordered from least to greatest.
D.
Two is the difference between the greatest and least number of pets Grace's friends have.
The statement which median describe about Grace's data set is 2 is the middle number when the number of pets in the data set is arranged from least to greatest.
What is the median of a data set?The median of the data is the middle value of the data set when it arrange in ascending or descending order.
Grace collected data from twenty of her friends about the number of pets they have. The median number of pets is two.
Median=2
By the definition of median of data set, the median two tells that the middle value of the pet is 2 when arranged in high to low point.
Thus, the statement which median describe about Grace's data set is 2 is the middle number when the number of pets in data set is arranged from least to greatest.
Learn more about the median here;
https://brainly.com/question/14532771
#SPJ1
Find the area of the composite figure below
Answer:
the answer is 25 hope it helps
A solid object was sliced to form two new objects. Each of the two new objects had a circular base. Which of the following solids may have been the original object? Select all that apply.
A: trapezoidal prism
B: cylinder
C: hexagonal prism
D: triangular pyramid
E: cone
solve the system using elimination. show all work. write your answer in the form (x,y) 2x-3y=18 x+y=14
Answer:
x=12 y=2
Step-by-step explanation:
Due to fractions have screen shorted the steps in the image above
What is the sum of the first five terms in this series?
6 - 6/3 + 6/9 - 6/27 + . . .?
Answer:
4 14/27
Step-by-step explanation:
The first five terms
6
-6/3
6/9
-6/27
+6/81
The first thing to do is change all the fractions denominators to 81.
Sum = 6*81/81 - 6(27)/81 + 6*9/81 - 6*3/81 + 6/81
Now add
Sum = 366/81
Sum = 4 14/27
Sum = 4.5185
Note the first term. It has been multiplied by 6*81/81. The 81 over 81 does not change the value of anything 6 * 81/81 is still 6. It just makes it easier to combine with the other members of the series.
