Find the 8th term of the geometric sequence 7,−21,63,
Answer:
8th term is -15309
Step-by-step explanation:
[tex]{ \boxed{ \bf{u_{n} = a( {r}^{n - 1} ) }}} \\ { \tt{u_{8} = 7( {( - 3)}^{8 - 1}) }} \\ { \tt{u_{8} = 7( - 2187)}} \\ { \tt{u _{8} = - 15309}}[/tex]
r is the common difference, r = -21/7 = -3
Answer:
a₈ = - 15309
Step-by-step explanation:
The nth term of a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
Here a₁ = 7 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-21}{7}[/tex] = - 3 , then
a₈ = 7 × [tex](-3)^{7}[/tex] = 7 × - 2187 = - 15309
The average age of a preschool class is 4.5 years old. If there is one 3-year-old, five 5-year-olds, and two other children both of the same age, what is the age, in years, of the other two children?
Answer:
3.1
Step-by-step explanation:
5 x5 =25
25+3=28
the other children are 4 years old
If the diameter of a cylinder is 18 inches, the radius of the cylinder is 9 inches.
True False
Answer:
True
Step-by-step explanation:
A cylinder has two circles as its bases, and the diameter formula is:
2r = d
So if you plug in:
2r = 18
--- ---
2 2
r = 9
So it will be true.
Hope this helped.
A regular square pyramid has a slant height of 5 in and a base area of 49 in2. Find the surface area of the pyramid. ------------------------------------------------------------------------------------------- 171.5 square inches 70 square inches 119 square inches 245 square inches
Answer:
C: 119 square inches
Step-by-step explanation:
We are given;
Slant height; L = 5 in
Base area; B = 49 in²
Since it's a square pyramid, the base portion has a square shape.
Thus, area of base = x²
Where x is a side of the square.
Thus;
x² = 49
x = √49
x = 7
Perimeter of base = 7 × 4 = 28 in
Area of pyramid = ½PL + B
Plugging in the relevant values;
Area of pyramid = (½ × 28 × 5) + 49
Area of pyramid = 119 in²
mary stated that 2.01 x 10⁶ is less than 4.8 x 10⁴ because 2.01 is less than 4.8. what was mary's mistake ?
I'm horrible at scientific notation so some help would be nice. =]
Answer:
Step-by-step explanation:
Scientific notation is always written as a number between 1 and 9.9999999 repeating. There follows a power of 10. I'm not sure which answer would help you see it clearer but
4.8 * 10^4 the decimal is shifted 4 places the right which is 48000 where you have no numbers, you use zeros.
2.01 * 10^6 means that you shift the decimal 6 places to the right.
2010000
So 2 million is larger than 48 thousand.
The other way to do it is just to look at the power. 6 is more than 4. 6 describes the number of places you move. So does 4. 6>4 so that's the larger number.
If cos(27) =p, express sin(27) in terms of p
Answer:
√(p²-1)
Step-by-step explanation:
sin (27°) = √(p²-1) / 1
= √(p²-1)
According to the rules of Major League Baseball, the infield must be 30 feet by 30 feet in a diamond shape with perpendicular (90°) corners. Answer the following questions regarding the shape of the infield.
Answer:
No Major League ballparks are exactly alike, but certain aspects of the field of play must be uniform across baseball.
The infield must be a square that is 90 feet on each side, and the outfield is the area between the two foul lines formed by extending two sides of said square (though the dirt portion of the field that runs well past the 90-foot basepaths in all Major League parks is also commonly referred to as the infield). The field must be constructed so that the bases are the same level as home plate.
The rulebook states that parks constructed by professional teams after June 1, 1958, must have a minimum distance of 325 feet between home plate and the nearest fence, stand or other obstruction on the right- and left-field foul lines, and 400 feet between home plate and the nearest fence, stand or other obstruction in center field. However, some clubs have been permitted to construct parks after that date with dimensions shorter than those specified.
The pitcher's plate must be a 24-inch by 6-inch slab of whitened rubber that is 10 inches above the level of home plate and 60 feet, 6 inches away from the back point of home plate. It is placed 18 inches behind the center of the mound -- which is erected within an 18-foot diameter circle -- and surrounded by a level area that is 5 feet by 34 inches. The slope of the pitcher's mound begins 6 inches in front of the pitcher's plate and must gradually decrease by 1 inch every foot for 6 feet in the direction of home plate.
Home plate is a 17-inch square of whitened rubber with two of the corners removed so that one edge is 17 inches long, two adjacent sides are 8 1/2 inches each and the remaining two sides are 12 inches each and set at an angle to make a point. The 17-inch side faces the pitcher's plate, and the two 12-inch edges coincide with the first- and third-base lines. The back tip of home plate must be 127 feet, 3 and 3/8 inches away from second base.
The other bases must be 15-inch squares that are between 3 and 5 inches thick, covered by white canvas or rubber and filled with soft material.
Step-by-step explanation:
Find the general solution for:-
[tex]sin\:x \:cos\: 3x+cos\:x\: sin\:3x=tan140[/tex]
~Please show your work
~Thank you!
Answer:
[tex] \rm \displaystyle x \approx \bigg \{ {59.3}^{ \circ} + \frac{n\pi}{2} , - {14.3}^{ \circ} + \frac{n\pi}{2} \bigg \}[/tex]
Step-by-step explanation:
we would like to solve the following trigonometric equation:
[tex] \rm \displaystyle \sin(x) \cos(3x) + \cos(x) \sin(3x) = \tan( {140}^{ \circ} ) [/tex]
the left hand side can be rewritten using angle sum indentity of sin which is given by:
[tex] \rm \displaystyle \sin( \alpha + \beta ) = \sin( \alpha ) \cos( \beta ) + \cos( \alpha ) \sin( \beta ) [/tex]
therefore Let
[tex] \alpha = x[/tex][tex] \beta = 3x[/tex]Thus substitute:
[tex] \rm \displaystyle \sin(x + 3x) = \tan( {140}^{ \circ} ) [/tex]
simplify addition:
[tex] \rm \displaystyle \sin(4x) = \tan( {140}^{ \circ} ) [/tex]
keep in mind that sin(t)=sin(π-t) saying that there're two equation to solve:
[tex] \begin{cases} \rm \displaystyle \sin(4x) = \tan( {140}^{ \circ} ) \\ \\ \displaystyle \sin(\pi - 4x) = \tan( {140}^{ \circ} ) \end{cases}[/tex]
take inverse trig and that yields:
[tex] \begin{cases} \rm \displaystyle 4x= { \sin}^{ - 1} ( \tan( {140}^{ \circ} ) ) \\ \\ \displaystyle \pi - 4x = { \sin}^{ - 1}( \tan( {140}^{ \circ} ) ) \end{cases}[/tex]
add π to both sides of the second equation and that yields:
[tex] \begin{cases} \rm \displaystyle 4x= { \sin}^{ - 1} ( \tan( {140}^{ \circ} ) ) \\ \\ \displaystyle - 4x = { \sin}^{ - 1}( \tan( {140}^{ \circ} ) ) + \pi\end{cases}[/tex]
sin function has a period of 2nπ thus add the period:
[tex] \begin{cases} \rm \displaystyle 4x= { \sin}^{ - 1} ( \tan( {140}^{ \circ} ) ) + 2n\pi\\ \\ \displaystyle - 4x = { \sin}^{ - 1}( \tan( {140}^{ \circ} ) ) + \pi + 2n\pi\end{cases}[/tex]
divide I equation by 4 and II by -4 which yields:
[tex] \begin{cases} \rm \displaystyle x= \frac{ { \sin}^{ - 1} ( \tan( {140}^{ \circ} ) ) }{4} + \frac{n\pi}{2} \\ \\ \displaystyle x = - \frac{{ \sin}^{ - 1}( \tan( {140}^{ \circ} ) ) + \pi}{4} - \frac{n\pi}{2} \end{cases}[/tex]
recall that,-½(nπ)=½(nπ) therefore,
[tex] \begin{cases} \rm \displaystyle x= \frac{ { \sin}^{ - 1} ( \tan( {140}^{ \circ} ) ) }{4} + \frac{n\pi}{2} \\ \\ \displaystyle x = - \frac{{ \sin}^{ - 1}( \tan( {140}^{ \circ} ) ) + \pi}{4} + \frac{n\pi}{2} \end{cases}[/tex]
by using a calculator we acquire:
[tex] \begin{cases} \rm \displaystyle x \approx - {14.3}^{ \circ} + \frac{n\pi}{2} \\ \\ \displaystyle x \approx {59.3}^{ \circ} + \frac{n\pi}{2} \end{cases}[/tex]
hence,
the general solution for: for the trig equation are
[tex] \rm \displaystyle x \approx \bigg \{ {59.3}^{ \circ} + \frac{n\pi}{2} , - {14.3}^{ \circ} + \frac{n\pi}{2} \bigg \}[/tex]
PLEASE HELP WILL GIVE BRAILNLIEST! Find the value of x
Answer:
x = 14.63
Step-by-step explanation:
Select the false statement
A. Vertical angles are always congruent
B.Vertical angles are sometimes complimentary
C.Two right angles are always supplementary
D. Angles that form a linear pair are sometimes supplementary. Plz answer ASAP
Answer: D. Angles that form a linear pair are sometimes supplementary.
That is not true, linear pairs are always supplementary.
Answer:
D. Angles that form a linear pair are sometimes supplementary.
~OAmalOHopeO
What is an
equation of the line that passes through the points (-3,-1) and (-4,-4)
Answer:
y= 3x+8
Step-by-step explanation:
not a 100% sure...
sry if its wrong
(try using Math-way, its rly helpful)
Answer:
Step-by-step explanation:
y=mx+b
To find slope: -4+1/-4+3
Slope=3
y=3x+b
Plug in either points ,as an example, i'll plug in (-3,-1)
-1=3(-3)+b
-1=-9+b
8=b
Finished formula: y=3x+8
_(9)=(2(1-2(2)^(9)))/(1-2(2))
PLEASE HELP ME OUT.
Answer:
the answer = um ok
Step-by-step explanation:
Angie used 4 apples and 5 strawberries in her fruit salad. Salim used 7 apples and 9 strawberries. Did Angie and Salim use the same ratio of apples to strawberries? If not, who used the greater ratio of apples to strawberries?
Answer:
We can write a ratio between two quantities, x and y, as:
x to y.
To find if two ratios:
"a to b" and "c to d" are equal, we need to see if the quotientes:
a/b and c/d are equal.
Here we know that the ratios are:
4 apples to 5 strawberries, this gives the quotient 4/5 = 0.8
7 apples to 9 strawberries, this gives the quotient 7/9 = 0.78
So the quotients are different, which means that the ratios are not equal.
Now we want to see who used a greater ratio of apples to strawberries.
notice that in the numerator we used the number of apples, so as larger is the quotient, larger is the ratio of apples to strawberries.
We can see that the quotient of Angie is larger, then Angie used the greater ratio of apples to strawberries.
PLEASE HELP! I HAVE BEEN AT THIS FOR A LONG TIME!.
For each investement, 25 000 is deposited in an account. How much is each payment?
(a. 8% per annum, compounded annually, with annual payments starting in a year.
Answer:
Annual payment wil be 2,001 and total amount after compounded annually will be 27,001
The triangle on the grid will be translated two units down.
On a coordinate plane, triangle A B C has points (2, 1), (0, negative 1), (2, negative 1).
Which shows the triangle when it is translated two units down?
On a coordinate plane, triangle A prime B prime C prime has points (0, negative 1), (0, negative 3), (2, negative 3).
On a coordinate plane, triangle A prime B prime C prime has points (0, 1), (negative 2, negative 1), (0, negative 1).
On a coordinate plane, triangle A prime B prime C prime has points (2, negative 1), (2, negative 3), (0, negative 3).
On a coordinate plane, triangle A prime B prime C prime has points (2, negative 1), (2, negative 3), (0, negative 1).
Given:
The vertices of the triangle ABC are A(2, 1), B(0,-1), C(2, -1).
To find:
The vertices of the image of triangle ABC if ABC is translated two units down.
Solution:
It is given that the triangle ABC is translated two units down. So, the rule of translation is:
[tex](x,y)\to (x,y-2)[/tex]
Using this rule, we get
[tex]A(2,1)\to A'(2,1-2)[/tex]
[tex]A(2,1)\to A'(2,-1)[/tex]
Similarly,
[tex]B(0,-1)\to B'(0,-1-2)[/tex]
[tex]B(0,-1)\to B'(0,-3)[/tex]
And,
[tex]C(2.-1)\to C'(2,-1-2)[/tex]
[tex]C(2.-1)\to C'(2,-3)[/tex]
The vertices of the image are A'(2,-1), B'(0,-3), C'(2,-3).
Therefore, the correct option is C.
Answer:
C.
Step-by-step explanation:
A baker finds several new recipes to try. Of the new recipes, there are 11 for cookies, 10 for muffins, and 4 for cakes. If the baker selects a recipe at random, what is the probability the recipe is for a cake?
Answer:
4/25
Step-by-step explanation:
All the amount of recipes is 11+10+4=25 . There are 4 recipes for cakes
so probability is 4/25
A sports scientist has made the formula below that gives the energy in joules provided,
e
per
ml
,
a
consumed of a power drink.
e=a×0.2
Substitute in
660
for the amount consumed,
a
, in an energy shake and give the energy provided,
e
.
Please help me ASAP I’m stuck on these questions
Answer:
4, yes through the middle 5, yes through the middle 6, yes through the middle all of them reflect from the center
Step-by-step explanation:
equation of the line which passes through point (0,5) at gradient of - 1
Answer:
y = - x + 5
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here gradient (slope) = - 1 and (0, 5) ⇒ c = 5
y = - x + 5 ← equation of line
At a particular school, all students participate in at least one out of three activities: debate, music, and community service. 3 students do all three activities, 21 students do two or more activities, half of all students participate in music, and the ratio of participants in debate, music, and community service, respectively, is $5:4:3$. What is the total number of students at the school
Answer:
48
Step-by-step explanation:
The given parameters are;
The activities in which the students of the school participate = 1) Debate, 2) Music, and 3) Community services
The number of students that do all three activities = 3
The number of students that do two or more activities = 21
The number of the students that participate in music = Half of the students
The ratio of the students that take part in debate, music, and community service = 5 : 4 : 3
Let x represent a common number factor of participants in each of the given three activities, we have;
5·x participate in debate, A
4·x participate in music, B
3·x participate in community service, C
We get;
The sum of the students in the school = A∪B∪C = A + B + C - A∩B - A∩C - B∩C + A∩B∩C
Given that the number of students that do two or ore activities = 21, we have;
(A∩B)∪(A∩C)∪(B∩C) = 21
However, we have;
(A∩B)∪(A∩C)∪(B∩C) = (A∩B) + (A∩C) + (B∩C) - A∩B∩C - B∩A∩C - C∩B∩A + A∩B∩C
∴ 21 = (A∩B) + (A∩C) + (B∩C) - 3 - 3 - 3 + 3
(A∩B) + (A∩C) + (B∩C) = 21 + 3 + 3 + 3 - 3 = 21 + 6 = 27
∴ -(A∩B) - (A∩C) - (B∩C) = -27
Therefore;
A + B + C - A∩B - A∩C - B∩C + A∩B∩C = 5·x + 4·x + 3·x - 27 + 3
5·x + 4·x + 3·x - 27 + 3 = 12·x - 24
The total number of students = A∪B∪C = 12·x - 24
The number of students participating in music, B = 4·x = Half the total number of students = (12·x - 24)/2
∴ 4·x = (12·x - 24)/2
8·x = 12·x - 24
12·x - 8·x = 24
4·x = 24
x = 24/4 = 6
The total number of students at the school = 12·x - 24 = 12 × 6 - 24 = 48
Since opening night, attendance at Play A has increased steadily, while attendance at Play B first rose and then fell. Equations modeling the daily attendance y at each play are shown below, where x is the number of days since opening night. On what day(s) was the attendance the same at both plays? What was the attendance?
Play A: y=25x+136
Play B: y=-x^2+44x+76
Answer: Day 4 and 15
Step-by-step explanation:
Set up system of equations:
[tex]25x+136=-x^2+44x+76[/tex]
Simplify:
[tex]x^2-19x+60=0[/tex]
Factor: Both factors must be positive as the days can only be natural numbers.
[tex](x-15)(x-4)=0[/tex]
x=4,15
Identify the equation of the circle that has its center at (16, 30) and passes through the origin
To solve this question, we have to find the equation of the circle with given center and where it passes. Doing this, we get that the equation of the circle is:
[tex](x - 16)^2 + (y - 30)^2 = 1156[/tex]
Equation of a circle:
The equation of a circle with center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
Center at (16, 30)
This means that [tex]x_0 = 16, y_0 = 30[/tex]
Thus
[tex](x - 16)^2 + (y - 30)^2 = r^2[/tex]
Passes through the origin:
We use this to find the radius squared, as this means that [tex]x = 0, y = 0[/tex] is part of the circle. Thus
[tex](x - 16)^2 + (y - 30)^2 = r^2[/tex]
[tex](0 - 16)^2 + (0 - 30)^2 = r^2[/tex]
[tex]r^2 = 16^2 + 30^2 = 1156[/tex]
Thus, the equation of the circle is:
[tex](x - 16)^2 + (y - 30)^2 = 1156[/tex]
For another example to find the equation of a circle, you can look at https://brainly.com/question/23719612
What is 2:50 is simplest form
Answer:
0.04
Step-by-step explanation:
2 / 50 is the same as 1 / 25.
1 / 25 = 0.04
Answer:
0.04
Step-by-step explanation:
Any help, I would highly appreciate it
Answer:
B
Step-by-step explanation:
We are given the equation:
[tex]\displaystyle x(b-c) = y+x[/tex]
And that:
[tex]2b=3c=7[/tex]
And we want to find the value of y / x.
To start, subtract x from both sides in the first equation:
[tex]x(b-c) -x = y[/tex]
Divide both sides by x:
[tex]\displaystyle \frac{x(b-c)-x}{x}=\frac{y}{x}[/tex]
Simplify:
[tex]\displaystyle (b-c)-1 = \frac{y}{x}[/tex]
Next, in the second equation, divide everything by two:
[tex]\displaystyle b = \frac{3}{2} c = \frac{7}{2}[/tex]
Substitute:
[tex]\displaystyle \left(\frac{3}{2} c - c \right) - 1= \frac{y}{x}[/tex]
Simplify:
[tex]\displaystyle \frac{1}{2} c - 1 = \frac{y}{x}[/tex]
From the modified second equation, we can multipy both sides by 1/3:
[tex]\displaystyle \frac{1}{2} c = \frac{7}{6}[/tex]
Substitute:
[tex]\displaystyle \left(\frac{7}{6}\right) -1 = \frac{y}{x}[/tex]
Subtract:
[tex]\displaystyle \frac{y}{x} = \frac{7}{6} - \frac{6}{6} = \frac{1}{6}[/tex]
Therefore, our answer is B.
graph the equation y=5/7x
Answer:
Step-by-step explanation:
simplify (2^2×4^-2)×5^8+2+3^0
See pic below! Need help solving
Answer:
383.54 m
Step-by-step explanation:
The length of the training track running around the field = circumference of the circle formed by the two semicircles + 2(length of the rectangle)
The two semicircles forms a fill circle with diameter (d) = width of rectangle = 61 m
Length of rectangle (L) = 96 m
π = 3.14
The length of the training track running around the field = πd + 2(L)
Substitute the values
The length of the training track running around the field = 3.14*61 + 2(96)
= 191.54 + 192
= 383.54 m
help please area geometry !!
Answer:
37.5 cm^2
Step-by-step explanation:
The area of a parallelogram is
A = bh where b is the base and h is the height
A = 7.5 * 5
A = 37.5 cm^2
Answer:
A = 37.5 cm²
Step-by-step explanation:
The area of a parallelogram is calculated as
A = bh ( b is the base and h the perpendicular height )
Here b = 7.5 and h = 5 , then
A = 7.5 × 5 = 37.5 cm²
The graph below shows a proportional relationship between y and x .
What is the constant of proportionality?
y/x?
Answer:
49/1
Step-by-step explanation:
The point is on (1,49)
How do you express a gain of 4 yards in a football game as a rational number?
OA 4.5 yards
OB. 4 yards
OC. yards
OD. - yards
OE-4 yards
PLEASE HELP
Answer:
B- 4 yards
4 is a rational number along with the number of yards gained.
