Answer:
r = 1/2
Step-by-step explanation:
Each entry is diminished by a factor of 1/2 times the previous entry.
so r = 1/2
The next number in the series is 1 and then the one after that is 1/2 and then 1/4 ...
NEED TO FIGURE THIS OUT RIGHT NOW CAN SOMEBODY PLEASE HELP ME? ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Find a quadratic equation with roots -1+4i and -1-4i
Answer:
c
Step-by-step explanation:
Given the roots are x = - 1 + 4i and x = - 1 - 4i then the factors are
(x - (- 1 + 4i))(x - (- 1 - 4i))
= (x + 1- 4i )(x + 1 + 4i )
= (x + 1)² - 16i² → [ i² = - 1 ]
Expand and simplify
= x² + 2x + 1 + 16
Hence
x² + 2x + 17 = 0 → c
Can someone please help me with this question
Answer:
(x−4)² + (y−5)² = 36
Step-by-step explanation:
The equation of a circle is:
(x−h)² + (y−k)² = r²
where (h, k) is the center and r is the radius.
If the center is (4, 5) and the radius is 6, then the equation is:
(x−4)² + (y−5)² = 6²
(x−4)² + (y−5)² = 36
Please prove or explain how to get AC, CM, & CP...
AC = 15
CM = 20
CP = 12
All of the right triangles are similar by AA similarity, so corresponding side lengths are proportional. The ratio of the long leg to the short leg is the same for the two smaller triangles, for example:
CP/AP = MP/CP
CP/9 = 16/CP . . . . . fill in the given numbers
CP² = 9·16 . . . . . . . multiply by 9·CP
CP = 3·4 = 12 . . . . . take the square root
Now, you can use the Pythagorean theorem to find AC and/or CM.
AC = √(9² +12²) = √225 = 15
CM = √(12² +16²) = √400 = 20
In summary, CP = 12, AC = 15, CM = 20.
_____
Once you have CM, you can see these are 3-4-5 right triangles, so you can determine the other lengths by using these side ratios.
3:4:5 = 9:12:15 = 12:16:20
_____
The altitude CP is called the "geometric mean" of AP and MP. It is the square root of their product. This is true for any right triangle, not just one with sides in the ratio 3:4:5. If you know this, you can write down your answers almost immediately. Above, we had to derive this fact using similarity.
Bailey had 75 beads. She used 20 of them on a necklace and 12 of them on a bracelet. Then she bought 25 more beads . How many beads does Bailey have now?
Answer:
68
Step-by-step explanation:
because 75-20= 55 cuz 20 were used
55-12= 43 cuz then 12 more were used
43+25= 68 cuz 25 was added
so 68
What is the area of triangle UVW if the area of triangle RST is 36 cm and the scale
factor is 5\2?
320 cm
90 cm
25 cm
225 cm
Answer:
225 cm²
Step-by-step explanation:
The ratio of areas is the square of the scale factor.
area UVW = (5/2)²·area RST = (25/4)(36 cm²) = 225 cm²
SOMEONE PLEASE HELP ME
IT'S TIMED
Answer:
H = 8 cmStep-by-step explanation:
The formula of a volume of a cylinder:
[tex]V=\pi r^2H[/tex]
We have
[tex]r=6cm,\ V=904.78\ cm^3[/tex]
Substitute:
[tex]\pi(6^2)H=904.78\\\\36\pi H=904.78\qquad\text{use}\ \pi\approx3.14\\\\(36)(3.14)H=904.78\\\\113.04H=904.78\qquad\text{divide both sides by}\ 113.04\\\\H\approx8\ cm[/tex]
A baseball card is originally worth 3$. It increases by 7% every year while the player is still active. After the player retires it increases 10% every year. If a player remains active for 7 years, how much is the baseball card worth after 20 years?
Answer:
[tex]\$16.64[/tex]
Step-by-step explanation:
we know that
The exponential function while the player is still active is equal to
[tex]y=3(1.07)^{x}[/tex]
where
y ----> is the value of the baseball card
x ----> the time in years
Find the value of y for x=7 years (7 years still active)
[tex]y=3(1.07)^{7}=\$4.82[/tex]
After 20 years
x=20-7=13 years (13 years retired player)
The initial value is [tex]\$4.82[/tex]
The new equation is equal to
[tex]y=\$4.82(1.1)^{x}[/tex]
substitute
x=13 years
[tex]y=\$4.82(1.1)^{13}=\$16.64[/tex]
4 pairs of shoes cost 80$.What is the cost of 7 pairs of shoes
Answer:
$140
Step-by-step explanation:
4 pairs of shoes = $80
( ÷ 4 to get the price of one pair of shoes)
1 pair of shoes = $20
( × 7 to get the price of 7 pairs of shoes )
7 pairs of shoes = $140
a kite has diagonals 9.8 ft and 7 ft what is the are of the kite?
33.6ft^2
34.3ft^2
68.6ft^2
8.4ft^2
Answer:
Area of a kite = 34.3 ft^2
Step-by-step explanation:
a kite has diagonals 9.8 ft and 7 ft
WE are given with the diagonals of the kite
Area of a kite = diagonal 1 * diagonal 2 /2
diagonal 1= 9.8 ft
diagonal 2 = 7ft
Area of a kite = [tex]\frac{9.8 * 7}{2}[/tex]
Area of a kite= 34.3 square feet
Trigonometry Ratios
Draw ABC where b = 90 ° and sinA= 12/20
What is the length of AB
What is tan A
What is cos A
[tex]\bf sin(A)=\cfrac{\stackrel{opposite}{12}}{\stackrel{hypotenuse}{20}}[/tex] Check the picture below.
Please help me ASAP! Need to find the surface area of both shapes together.
Answer:
The surface area is [tex]SA=1,108\ in^{2}[/tex]
Step-by-step explanation:
we know that
The surface area of the composite figure is equal to
The lateral area of the rectangular prism plus the area of the base of the rectangular prism plus the area of the two triangular faces of triangular prism plus the area of two rectangular faces of the triangular prism
so
[tex]SA=2(12+20)(5)+(12)(20)+2[\frac{1}{2}(12)(9)]+2(20)(11)[/tex]
[tex]SA=320+240+108+440[/tex]
[tex]SA=1,108\ in^{2}[/tex]
Answer:
1,108in~2
Step-by-step explanation:
Trust us! Acellus 2022
Determine whether the function f(x) = 3(x − 1)4 is even or odd.
Answer:
Other answer.
Step-by-step explanation:
[tex]f(x) = 3(x-1)^4\\ f(-x) = 3(-x-1)^4 = 3\big(-(x+1)\big)^4 = 3(x+1)^4 \\ \\ f(-x)\neq f(x) \\ f(-x)\neq -f(x)\\ \\ \Rightarrow \text{The function is neither odd or even}[/tex]
Answer:
The function is neither even nor odd.
Step-by-step explanation:
Given : Function [tex]f(x)=3(x-1)^4[/tex]
To find : Determine whether the function is even or odd ?
Solution :
Rules to determine the function is even or odd :
If f(x)=f(-x) then the function is even.
If f(x)=-f(x) then the function is odd.
Now, Test for even function
[tex]f(x)=3(x-1)^4[/tex]
[tex]f(-x)=3(-x-1)^4[/tex]
[tex]f(-x)=3(-(x+1)^4[/tex]
[tex]f(-x)=3(x+1)^4[/tex]
[tex]f(x)\neq f(-x)[/tex] so function is not even.
Test for odd function,
[tex]f(x)=3(x-1)^4[/tex]
[tex]-f(x)=-3(x-1)^4[/tex]
[tex]f(x)\neq -f(x)[/tex] so function is not odd.
So, The function is neither even nor odd.
The circumference of a circle can be found using the formula C=2*3.14r
Which is an equivalent equation solved for r?
C=2πr
C=πd
A=πr^2
r=C/2π
r=1/2 d
By the way all you do to solve r is:
C=2πr
C/2π=2πr/2π
C/2π=r
r=C/2π
Hope this helps:)
find the height of a cylinder with a volume of 1215pi mm and a radius of 9mm
Answer: the height would be 15
Step-by-step explanation:
v= pi*radius^2*height
1215pi mm= pi*9^2*height
1215pi mm= pi*81*height
(divide by pi on both sides, which isolates pi on both sides)
1215 mm= 81*height
(divide by 81 on both sides, which would isolate 81 on the right side of the equation)
1215/81= 15= height
The height of the cylinder is 15 mm.
Explanation:To find the height of a cylinder, we can use the formula for the volume of a cylinder, which is V = πr²h, where V is the volume, r is the radius, and h is the height.
Given that the volume is 1215π mm and the radius is 9 mm, we can plug these values into the formula and solve for h.
1215π = π(9)²h
Simplifying the equation, we have:
1215 = 81h
Dividing both sides by 81, we find:
h = 15 mm
Therefore, the height of the cylinder is 15 mm.
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Jordan has decided to purchase a $17,500 car and would like to finance it for five years. Her bank has offered her a standard 6.9% APR, while the dealership has offered her a special 4.9% APR. How much money will she save each month by choosing financing through the dealership
Answer:
Jordan will save $16.25 each month by choosing financing through the dealership.
Step-by-step explanation:
The EMI formula is :
[tex]\frac{p\times r\times(1+r)^{n}}{(1+r)^{n}-1}[/tex]
Case 1:
p = 17500
r = [tex]6.9/12/100=0.00575[/tex]
n = [tex]5\times12=60[/tex]
Putting the values in formula;
[tex]\frac{17500\times0.00575\times(1+0.00575)^{60}}{(1+0.00575)^{60}-1}[/tex]
=> [tex]\frac{17500\times0.00575\times(1.00575)^{60}}{(1.00575)^{60}-1}[/tex]
EMI = $345.70
Case 2:
p = 17500
r = [tex]4.9/12/100=0.004083[/tex]
n = [tex]5\times12=60[/tex]
Putting the values in formula;
[tex]\frac{17500\times0.004083\times(1+0.004083)^{60}}{(1+0.004083)^{60}-1}[/tex]
=> [tex]\frac{17500\times0.004083\times(1.004083)^{60}}{(1.004083)^{60}-1}[/tex]
EMI = $329.45
So, difference per month in payments will be :
[tex]345.70-329.45=16.25[/tex] dollars
Hence, Jordan will save $16.25 each month by choosing financing through the dealership.
What is the definition of an irrational number?
A. a number that can be expressed as a fraction, , where p and q are integers and q is not equal to zero
B. a number that cannot be expressed as a fraction, , where p and q are integers and q is not equal to zero
C. a negative number
D. a number that is more than 10 digits
Answer:
Answer is B
Step-by-step explanation:
A number that cannot be expressed as a fraction ,where p and q are integers and q is not equal to zero
Answer:
a number that cannot be expressed as a fraction, , where p and q are integers and q is not equal to zero
Which function is a quadratic function? a(x) = –2x^3 + 2x – 6 b(x) = 5x^3 + 8x^2 + 3 c(x) = –8x^2 + 3x – 5 d(x) = 6x^4 + 2x – 3
Answer:
c(x) = –8x^2 + 3x – 5 is a quadratic
Step-by-step explanation:
A quadratic function involves the 2nd power of x: x^2, and may (or may not) involve the 1st and zeroth power of x.
a(x) = -2x^3 is not a quadratic because of that exponent 3; in a quadratic, the highest power is always 2.
b(x) = 5x^3 + 8x^2 + 3 is not a quadratic for the same reason that a(x) is not a quadratic.
c(x) = –8x^2 + 3x – 5 is a quadratic: the highest power of x is x^2, the other powers are x^1 and x^0.
What is the measure of angle D to the nearest whole degree?
I hope this diagram explains it and helps you :)
Answer:
Angle D = arc tangent (72 / 21)
Angle D = arc tangent (3.4285714286)
Angle D = 73.74 Degrees
and to the nearest degree it's 74
Step-by-step explanation:
Predict how much money can be saved without having a negative actual net income. monthly budget budgeted amount actual amount income wages savings interest $1150 $25 $900 $25 expenses rent utilities food cell phone savings $400 $100 $250 $75 $200 $400 $80 $200 $75 $____ net income $150 $____
a. it is not possible to save any money this month without having a negative actual net income.
b. $170 can be saved resulting in an actual net income of $0.
c. $200 can be saved resulting in an actual net income of $150.
d. as long as you are saving money, you will not have a negative actual net income.
The amount of money that can be saved without having a negative actual net income is: $170 can be saved resulting in an actual net income of $0.
Explanation:Predict how much money can be saved without having a negative actual net income.
Monthly Budget (is an itemized list of expected income and expenses that helps you to plan how the money will be spent or saved and track of spending habits.)
Budgeted Amount (is an itemized allotment of funds, time for a given period)
Actual Amount (is the particular year in which the amount is spent)
Income (business receives in exchange to provide a good /service /through investing capital )
Wages (is monetary compensation paid by employer to employee in exchange for work done)
Savings Interest (is money the you earn in return for holding your savings in an account.)
$1150
$25
$900
$25
Expenses
Rent
Utilities
Food
Cell Phone
Savings
$400
$100
$250
$75
$200
$400
$80
$200
$75
$____
Net Income
$150
$____
How much money can be saved without having a negative actual net income?
a. It is not possible to save any money this month without having a negative actual net income. b. $170 can be saved resulting in an actual net income of $0. c. $200 can be saved resulting in an actual net income of $150. d. As long as you are saving money, you will not have a negative actual net income.Learn more about money brainly.com/question/1870710
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Answer:
$170 can be saved resulting in an actual net income of $0.
Step-by-step explanation:
Laura's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Laura $5.50 per pound, and type B coffee costs $4.20 per pound. This month's blend used four times as many pounds of type B coffee as type A, for a total cost of $602.10. How many pounds of type A coffee were used?
A: 5.50/p
B: 4.20/p
total 602.10
ratio 1:4 =5
602.10 ÷ 5 =120.42
A= 120.42
(B= 120.42×4= 481.86)
120.42÷ 5.50= 21.8945.....
Answer: 27 pounds
Step-by-step explanation:
We know that Coffee A costs $5.50 per pound, Coffee B costs $4.20 per pound and that this month the total cost was $602.10, then:
[tex]5.50A+4.20B=602.10[/tex] (2)
We know that this month were used used four times as many pounds of type B coffee as type A, then:
[tex]B=4A[/tex] (1)
So, you need to substitute (1) into (2) and solve for A:
[tex]5.50A+4.20(4A)=602.10\\22.3A=602.10\\A=27[/tex]
Nolan uses 3 yards of string .He cuts the string into pieces that are 1/6 yard long. how many pieces does nolan have
Answer:
18 pieces
Step-by-step explanation:
Divide the 3 yd string by 1/6:
[tex]\frac{3}{\frac{1}{6} }[/tex]
Rewrite that to look a little more manageable:
[tex]\frac{3}{1}[/tex]÷[tex]\frac{1}{6}[/tex]
And of course you know that if you want to divide fractions, you flip the one on the bottom upside down and change the sign to multiplication:
[tex]\frac{3}{1}[/tex]×[tex]\frac{6}{1}[/tex]
Do that multiplication and you get 18 pieces.
Answer:
18
Step-by-step explanation:
Please help me with this
Answer:
13.7 cm²
Step-by-step explanation:
area of yellow region = area of square - area of 4 quarter circles
area of square = 8² = 64
area of 4 congruent quarter circles = area of circle
area of circle with radius = 4
A = π × 4² = 16π
yellow region = 64 - 16π ≈ 13.7 cm²
Please please help me out!!!!
Answer:
593.0 cm³
Step-by-step explanation:
The volume (V) of the prism is calculated as
V = area of triangular end face × length
A of Δ = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
here b = 10.2 and h = 10. 2
A of Δ = 0.5 × 10.2 × 10.2 = 52.02 cm², hence
V = 52.02 × 11.4 ≈ 593.0 cm³
use the law of cosines to find the value of cos theta. round your answer to two decimal places
Answer:
The correct answer option is B. 0.21.
Step-by-step explanation:
We are to find the value of [tex]cos \theta[/tex] using the law of cosines.
We know that the formula of the cosine rule is given by:
[tex] c ^ 2 = a ^ 2 + b ^ 2 - 2 a b cos C [/tex]
So substituting the given values in the above formula:
[tex] 10.9 ^ 2 = 5.8 ^ 2 + 10.5 ^ 2 - 2 (5.8) (10.5) cos C [/tex]
[tex]118.81=33.64+110.25-121.8cosC[/tex]
[tex]118.81 - (33.64+110.25) = -121.8cosC[/tex]
[tex]118.81-143.86=-121.8cosC[/tex]
[tex]cosC=\frac{-25.05}{-121.8}[/tex]
cos C = 0.21
Answer:
B. 0.21
Step-by-step explanation:
1. Find sinθ if cosθ=1/2 and θ terminates in Quadrant IV.
2. Find cosθ if sinθ=(√2)/2 and θ terminates in Quadrant I.
3. Find tanθ if cosθ=-1/2 and θ terminates in Quadrant II.
4. Find tanθ if sinθ=-1 and 0≤θ<2π radians.
Answer:-(√3)/2, (√2)/2, -√3, and undefined
Step-by-step explanation:
There are two ways you can solve this. One is with the Pythagorean identity:
sin²θ + cos²θ = 1
The other way is by knowing your unit circle.
1. From the unit circle, we know that cos θ = 1/2 at θ = π/3 and θ = 5π/3. Since θ is in Quadrant IV, then θ = 5π/3. sin (5π/3) = -(√3)/2.
We can check our answer using the Pythagorean identity:
sin²θ + cos²θ = 1
sin²θ + (1/2)² = 1
sin²θ + 1/4 = 1
sin²θ = 3/4
sin θ = ±(√3)/2
Since sine is negative in Quadrant IV, sin θ = -(√3)/2.
We can repeat these steps for the other questions.
2. sin θ = (√2)/2 at θ = π/4 and θ = 3π/4. Since θ is in Quadrant I, θ = π/4. Therefore, cos θ = (√2)/2.
3. cos θ = -1/2 at θ = 2π/3 and θ = 4π/3. Since θ is in Quadrant II, θ = 2π/3. Therefore, sin θ = (√3)/2, and tan θ = sin θ / cos θ = -√3.
4. sin θ = -1 at θ = 3π/2. Therefore, cos θ = 0. tan θ = sin θ / cos θ, so tan θ is undefined.
1. sinθ = √3/2, 2. cosθ = √2/2, 3. tanθ = -√3, 4. tanθ is undefined.
Explanation:1. Given that cosθ=1/2 and θ terminates in Quadrant IV, we can use the Pythagorean identity sin^2θ + cos^2θ = 1 to find sinθ. Substitute the value of cosθ into the equation: sin^2θ + (1/2)^2 = 1. Solve for sinθ: sinθ = ± √(1 - (1/4)) = ± √(3/4) = ± √3/2. Since θ terminates in Quadrant IV, sinθ is positive. Therefore, sinθ = √3/2.
2. Given sinθ=(√2)/2 and θ terminates in Quadrant I, we can again use the Pythagorean identity sin^2θ + cos^2θ = 1 to find cosθ. Substitute the value of sinθ into the equation: (√2/2)^2 + cos^2θ = 1. Solve for cosθ: cosθ = ± √(1 - (1/2)). Since θ terminates in Quadrant I, cosθ is positive. Therefore, cosθ = √(1 - (1/2)) = √(1/2) = 1/√2 = √2/2.
3. Given cosθ=-1/2 and θ terminates in Quadrant II, we can find sinθ using the Pythagorean identity sin^2θ + cos^2θ = 1. Substitute the value of cosθ into the equation: sin^2θ + (-1/2)^2 = 1. Solve for sinθ: sinθ = ± √(1 - (1/4)) = ± √(3/4) = ± √3/2. Since θ terminates in Quadrant II, sinθ is positive. Therefore, sinθ = √3/2. Now, we can find tanθ using the relationship tanθ = sinθ / cosθ. Substitute the values of sinθ and cosθ into the equation: tanθ = (√3/2) / (-1/2) = -√3.
4. Given sinθ=-1 and 0≤θ<2π radians, we can find cosθ using the Pythagorean identity sin^2θ + cos^2θ = 1. Substitute the value of sinθ into the equation: (-1)^2 + cos^2θ = 1. Solve for cosθ: cos^2θ = 1 - 1 = 0. Since 0^2 = 0, cosθ = 0. Now, we can find tanθ using the relationship tanθ = sinθ / cosθ. Substitute the values of sinθ and cosθ into the equation: tanθ = -1 / 0 = undefined.
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PLEASE HELP! What are the values of w and x in the triangle below? Round the answers to the nearest tenth.
w = 13.3; x = 10.3
w = 10.8; x = 6.1
w = 13.3; x = 23.6
w = 10.8; x = 16.9
Answer:
Part 1) The value of w is 13.3 units
Part 2) The value of x is 10.3 units
The answer is the option
w=13.3, x=10.3
Step-by-step explanation:
see the attached figure with letters to better understand the problem
Part 1) Find the value of w
we know that
In the right triangle ABD
tan(42°)=12/w
Solve for w
w=12/tan(42°)=13.3 units
Part 2) Find the value of x
In the right triangle ABC
tan(27°)=12/(w+x)
(w+x)=12/tan(27°)=23.6 units
(w+x)=23.6 units
Solve for x
x=23.6-w
substitute the value of w
x=23.6-13.3=10.3 units
The measure of side lengths w and w are 13.3 and 10.3 units respectively.
The correct option is A) w = 13.3; x = 10.3
What are the measures of side length x and w?The figures in the image are those of two right triangles.
To solve for the measure of side length w and x, we use the trigonometric ratio:
First, we solve for side length w:
Angle θ = 42 degrees
Opposite to angle θ = 12
Adjacent to angle θ = w
tan(θ) = opposite / adjacent
tan( 42 ) = 12 / w
w = 12 / tan( 42 )
w = 13.3
Now we solve for side length x:
Angle θ = 27 degrees
Opposite to angle θ = 12
Adjacent to angle θ = ( w + x )
tan(θ) = opposite / adjacent
tan( 27 ) = 12 / ( w + x )
( w + x ) = 12 / tan( 27 )
( w + x ) = 23.55
Plug in w = 13.3
13.3 + x = 23.55
x = 23.55 - 13.3
x = 10.3
Therefore, the value of x is 10.3 units
Option A) w = 13.3 and x = 10.3 is the correct answer.
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please help
what is 16 -6%
Answer:
15.04
Step-by-step explanation:
.06 % of 16 is .96 and 16- .96= 15.04
Hope this helps!
The answer is 15.94!!
Mary needs to buy 44 cookies for her party.If 6 cookies come in a package how many packages of cookies does she buy
Answer:
She needs to buy 8 packages.
Step-by-step explanation:
Divide 44 (cookies) by 6 (cookies in package) to get 7.33 (packages). Since you can't buy 7.33 packages, you will have to buy 8. Hope this helps!
What is the x-value of the solution to the system of equations?
5х + 4y = 8
2x – Зу = 17
О -3
О-2
O4
O 5
Answer: C. 4
Step-by-step explanation:
How does the graph of [tex]f(x) = -4^{5x}-3[/tex] differ from the graph of [tex]g(x) = -4^{5x}[/tex]?
A. The graph of [tex]f(x)[/tex] is shifted three units to the left of the graph of [tex]g(x)[/tex].
B. The graph of [tex]f(x)[/tex] is shifted three units up from the graph of [tex]g(x)[/tex].
C. The graph of [tex]f(x)[/tex] is shifted thee units to the right of the graph of [tex]g(x)[/tex]
D. The graph of [tex]f(x)[/tex] is shifted three units down from the graph of [tex]g(x)[/tex].
Answer:
D
Step-by-step explanation:
When a number is listed outside the function it is a vertical movement. So negative is down, positive is up!
Inside the function would be left/right. This would have been found in your exponent.
D. The graph of [tex]f(x)[/tex] is shifted three units down from the graph of g(x).
f(x) = [tex]-4^{5x} -3[/tex] and g(x) = [tex]-4^{5x}[/tex]
What is the graph translation Theorem?In general, replacing x with x – h in a mathematical sentence translates its graph h units horizontally. Similarly, replacing y with y – k in a sentence translates its graph k units vertically.
For example, your sketch of Group B should show that the graph of y = x2 + 3 is 3 units above the graph of y = x2.
What is the slope of 4x Y 6?Using the slope-intercept form, the slope is 4 . All lines that are parallel to y=4x−6 y = 4 x - 6 have the same slope of 4 .
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