Set up an equation:
Numerator is the top number and denominator is the bottom number in a fraction.
(6x)^5 / d = 36
(6x)^5 can be rewritten as 6^5x^5
6^5x^5 / d = 36
Raise 6 tot he power of 5:
7776x^5 /d = 36
Multiply both sides by d:
7776x^5 = 36d
Divide both sides by 36:
d = 7776x^5 / 36
d = 216x^5
what is the ratio of 12 minute to 1 hour
Answer:
12:1
Step-by-step explanation:
12:1Answer:
Step-by-step explanation:
The sum of two polynomials is 8d5 – 3c3d2 + 5c2d3 – 4cd4 + 9. If one addend is 2d5 – c3d2 + 8cd4 + 1, what is the other addend?
Answer:
The second polynomial is:
[tex]6d^5-2c^3d^2+5c^2d^3-12cd^4+8[/tex]
Step-by-step explanation:
Given
[tex]Sum\ of\ polynomials=S=8d^5-3c^3d^2+5c^2d^3-4cd^4+9\\Polynomial\ 1=A=2d^5-c^3d^2+8cd^4+1\\Polynomial\ 2=B=?\\S=A+B\\B=S-A\\=8d^5-3c^3d^2+5c^2d^3-4cd^4+9-(2d^5-c^3d^2+8cd^4+1)\\=8d^5-3c^3d^2+5c^2d^3-4cd^4+9-2d^5+c^3d^2-8cd^4-1\\=8d^5-2d^5-3c^3d^2+c^3d^2+5c^2d^3-4cd^4-8cd^4+9-1\\=6d^5-2c^3d^2+5c^2d^3-12cd^4+8[/tex]
If r(x) = 2 – x2 and w(x) = x – 2, what is the range of (Wºr) (x)
(-∞,0]
(-∞,2]
[0,∞)
[2,∞)
Answer:
(-inf,2]
Step-by-step explanation:
[tex](w \circ r)(x)=w(r(x))[/tex]
[tex]w(2-x^2)[/tex] I replaced r(x) with 2-x^2
[tex](2-x^2)-x[/tex] I replace the x in w(x)=x-2 with 2-x^2
[tex]-x^2-x+2[/tex]
You can graph this to find the range.
But since this is a quadratic (the graph is a parabola), I'm going to find the vertex to help me to determine the range.
The vertex is at x=-b/(2a). Once I find x, I can find the y that corresponds to it by using y=-x^2-x+2.
Comparing ax^2+bx+c to -x^2-x+2 tells me a=-1, b=-1, and c=2.
So the vertex is at x=1/(2*-1)=-1/2.
To find the y-coordinate that corresponds to that I will not plug in -1/2 in place of x into -x^2-x+2.
This gives me
-(-1/2)^2-(-1/2)+2
-1/4 + 1/2 +2
Find a common denominator which is 4.
-1/4 + 2/4 +8/4
8/4
2.
So the highest y value is 2 ( I know tha parabola is upside down because a=negative number)
That mean then range is 2 or less than 2.
So the answer an interval notation is (-inf,2]
What is the value of x in the rhombus below?
Answer:
x = 17Step-by-step explanation:
We know:
1. Diagonals of a rhombus are perpendicular.
2. Diagonals divide the rhombus on four congruent right triangles.
3. The sum of measures of acute angles in a right triangle is equal 90°.
Therefore we have the equation:
(2x + 3) + (3x + 2) = 90 combine like terms
(2x + 3x) + (3 + 2) = 90
5x + 5 = 90 subtract 5 from both sides
5x = 85 divide both sides by 5
x = 17
The value of x is 17. This means that the angles formed by the diagonals of the rhombus are 37 degrees (2 * 17 + 3) and 53 degrees (3 * 17 + 2), and they indeed form congruent right triangles as required in the properties of a rhombus.
To find the value of x in the given equation, we start by understanding the properties of a rhombus and how its diagonals divide it into four congruent right triangles.
Given information:
Diagonals of a rhombus are perpendicular.
Diagonals divide the rhombus into four congruent right triangles.
Let's proceed with the steps to solve for x:
Step 1: Recognize that the angles formed by the diagonals are 2x + 3 and 3x + 2. Since these angles are congruent right angles, their sum is equal to 90 degrees.
Step 2: Set up the equation:
(2x + 3) + (3x + 2) = 90
Step 3: Combine like terms:
5x + 5 = 90
Step 4: Isolate x by subtracting 5 from both sides of the equation:
5x = 85
Step 5: Solve for x by dividing both sides by 5:
x = 85 / 5
x = 17
Hence, the value of x is 17. This means that the angles formed by the diagonals of the rhombus are 37 degrees (2 * 17 + 3) and 53 degrees (3 * 17 + 2), and they indeed form congruent right triangles as required in the properties of a rhombus.
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What does 3(8)+8 equal
Answer: 32
Step-by-step explanation: You need to use PEMDAS. First, multiply the two numbers.
3(8) = 24
Then, add 8.
24 + 8 = 32
32 is your answer.
The second termn in a geometric sequence is 20. The fourth termn in the same sequense is 45/4, or 11.225. What is the common ratio in this sequence?
Answer:
t2=ar^(2-1)
20=ar
then
t4=ar^(4-2)
45/4=ar.r
45/4=20.r
45/80=r
Answer:
r=±0.75
Step-by-step explanation:
Given:
a2= 20
a4= 45/4
As a geometric sequence has a common ratio and is given by:
an=a1(r)^n-1
where
an=nth term
a1=first term
n=number of term
r=common ratio
Now
a2=20=a1(r)^(2-1)
20=a1(r)^1
20=a1*r
Also
a4=45/4=a1(r)^(4-1)
45/4=a1r^3
(a1*r)r^2=45/4
Substituting value of 20=a1*r
(20)r^2=45/4
r^2=45/4(20)
r^2=0.5625
r=±0.75!
Select one answer choice For part A and select one answer choice for part B
[tex]\bf \qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ \stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+6}x\stackrel{\stackrel{c}{\downarrow }}{+9}=0 ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{\underline{one real solution}}~~\textit{\Large \checkmark}\\ positive&\textit{two real solutions}\\ negative&\textit{no solution} \end{cases} \\\\\\ 6^2-4(1)(9)\implies 36-36\implies 0[/tex]
For Valentine's Day, Kelsey got a box of 24 chocolates. After one week, she'd eaten 5/8 of them. How many chocolates had Kelsey eaten?
Answer:
She had eaten 15 chocolates.
Step-by-step explanation:
[tex]\frac{5}{8} * 24 = \frac{120}{8} = 15[/tex]
Final answer:
Kelsey ate 15 chocolates out of the 24 after a week, which is 5/8 of the total. Jenny initially had 14 chocolates before eating two and giving half of the remainder to Lisa.
Explanation:
To solve how many chocolates Kelsey has eaten, we have to calculate 5/8 of 24. Since 24 chocolates multiplied by 5/8 equals 15, Kelsey ate 15 chocolates after one week.
Regarding the second question about Jenny and her chocolates:
If Lisa ends up with 6 chocolates, which represents half of the remainder after Jenny ate two, we can deduce that before giving half to Lisa, there were 12 chocolates.Adding back the two chocolates Jenny ate, she originally had 14 chocolates.In summary, the answer to how many chocolates Jenny initially had is 14.
The table below shows the future value of a certificate of deposit (CD), after x
years. Don states the applied interest is simple interest. True or false?
(number of years)
(future value)
$205.00
$210.00
$215.00
$220.00
$225.00
A. True
B. False
Answer:
A. True.
Step-by-step explanation:
The value increases by the same amount ($5) every year so it is simple interest.
Answer:True
Step-by-step explanation:
h(x)=2x-4/3
o h^-1(x)= 3x-12/2
o h^-1(x)= 3/(2x-4)
o h^-1(x)= 3x+4/2
Answer:
[tex]\large\boxed{h^{-1}(x)=\dfrac{3x+4}{2}}[/tex]
Step-by-step explanation:
[tex]h(x)=\dfrac{2x-4}{3}\to y=\dfrac{2x-4}{3}\\\\\text{Exchange x to y and vice versa}:\\\\x=\dfrac{2y-4}{3}\\\\\text{Solve for y:}\\\\\dfrac{2y-4}{3}=x\qquad\text{multiply both sides by 3}\\\\2y-4=3x\qquad\text{add 4 to both sides}\\\\2y=3x+4\qquad\text{divide both sides by 2}\\\\y=\dfrac{3x+4}{2}[/tex]
For one month Siera calculated her home town’s average high temperature in degrees Fahrenheit. She wants to convert that temperature from degrees Fahrenheit to degrees Celsius using the function . What does C(F) represent?
the temperature of F degrees Fahrenheit converted to degrees Celsius
the temperature of F degrees Celsius converted to degrees Fahrenheit
the temperature of C degrees Fahrenheit converted to degrees Celsius
the temperature of C degrees Celsius converted to degrees Fahrenheit
Answer:
The temperature of F degrees Fahrenheit converted to degrees CelsiusStep-by-step explanation:
[tex]C(F)=\dfrac{5}{9}(F-32)[/tex]
The function C(F) represents the temperature of F degrees Fahrenheit converted to degrees Celsius.
Explanation:The function C(F) represents the temperature of F degrees Fahrenheit converted to degrees Celsius. Temperature conversion is the process of converting between different temperature scales, such as Fahrenheit (°F), Celsius (°C), and Kelvin (K).
Each scale measures temperature differently, so conversions are necessary for various applications. The most common conversion formulas are: Celsius to Fahrenheit: °F = (°C × 9/5) + 32, and Celsius to Kelvin: K = °C + 273.15. These conversions are vital for international communication, weather reports, and scientific calculations.
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please help! what is the value of x when f(x)=8? The graph shows the function f(x)=2^x
Answer:
[tex]f(x) = {2}^{x } \\ f(x) = 8 \\ \\ {2}^{x} = 8 \\ \\ {2}^{x } = {2}^{3} \\ \\ x = 3[/tex]
The value of x when f(x) = 8 is 3 in f(x) = 2^x
How to determine the value of x when f(x)=8?from the question, we have the following parameters that can be used in our computation:
f(x) = 2^x
To find the value of x when f(x) = 8, we need to solve the equation 2^x = 8.
We can rewrite 8 as 2^3
So, the equation becomes:
2^x = 2^3
Since the bases are the same, we can equate the exponents:
x = 3
Hence, the value of x when f(x) = 8 is 3.
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HELP NEED IT PLEASE
Add all of the numbers together
2+3.5+2+3.5
5.5+5.5
= 11 cm
Answer is 11cm - second time
Answer:
11 cm
Step-by-step explanation:
The perimeter is equal to
P =2(l+w)
P = 2(2+3.5)
= 2(5.5)
= 11 cm
An alloy is a mixture of metals. Suppose that a certain alloy is made by mixing 50 grams of an alloy that 52% copper with 78 grams of pure copper. How many grams of copper are in the resulting mixture? What percent of the resulting mixture is copper?
Answer:
See below in bold.
Step-by-step explanation:
The 50 grams of alloy contains 50 * 0.52 = 26 g of pure copper.
So the amount of copper n the mixture = 78 + 26 = 104 g.
The total mass of the mixture = 78 + 50 = 128 g.
% copper = 104 * 100 / 128
= 81.25%.
Final answer:
The resulting mixture contains 104 grams of copper, which constitutes 81.25% of the mixture.
Explanation:
To find out how many grams of copper are in the resulting mixture of the alloy, we need to calculate the amount of copper from both sources and add them together. The first source is 50 grams of an alloy that is 52% copper, and the second source is 78 grams of pure copper.
50 grams of 52% copper alloy contains 50 grams × 0.52 = 26 grams of copper.78 grams of pure copper is of course 78 grams of copper.Now, add the amounts of copper from both sources:
26 grams (from the alloy) + 78 grams (pure copper) = 104 grams of copper.
To determine what percent of the resulting mixture is copper, we add the total weight of the mixture (50 grams + 78 grams = 128 grams) and then calculate the percentage:
(104 grams copper / 128 grams total) × 100 = 81.25%
So, the resulting mixture contains 104 grams of copper and is 81.25% copper.
can You show how to graph this
Answer:
The graph in the attached figure
Step-by-step explanation:
we have that
[tex]f(x)=x-4[/tex] ------> For [tex]x < 2[/tex]
[tex]f(x)=-2x+2[/tex] ------> For [tex]x\geq2[/tex]
To graph this piece wise- defined function
In the interval (-∞,2) ----> graph the line [tex]f(x)=x-4[/tex]
In the interval [2,∞) ----> graph the line [tex]f(x)=-2x+2[/tex]
The function is continue -----> the domain is all real numbers
using a graphing tool
see the attached figure
The area of circle Z is 64 ft2.
What is the value of r?
r = 4 ft
r = 8 ft
r = 16 ft
r = 32 ft
The value of r that satisfies the given area is approximately 5.08 ft, which is closest to 4 ft.
Explanation:The area of a circle can be calculated using the formula A = πr², where A is the area and r is the radius. In this case, the area of the circle is given as 64 ft². So we can substitute the value of A as 64 ft² in the formula to find the value of r.
64 = πr²
To solve for r, we can divide both sides of the equation by π and then take the square root of both sides.
r² = 64/π
r = √(64/π)
To simplify further, we can approximate the value of π as 3.14.
r = √(64/3.14)
r ≈ 5.08 ft
Based on the given options, the value of r that is closest to 5.08 ft is 4 ft.
Answer:
ITS 8FT
Step-by-step explanation:
Given the following information, find the probability that a randomly selected student will be very short. Number of students who are very short: 45, short: 60, tall: 82, very tall: 21
Answer:
[tex]Pr=\dfrac{45}{208}\approx 0.216.[/tex]
Step-by-step explanation:
You are given the information about students:
45 students are very short;60 students are short;82 students are tall;21 students are very tall.In total, there are 45 + 60 + 82 + 21 = 208 students.
Use the definition of the probability:
[tex]Pr=\dfrac{\text{Number of favorable outcomes}}{\text{Number of all possible outcomes}}[/tex]
Number of favorable outcomes = 45
Nomber of all possible outcomes = 208,
hence,
[tex]Pr=\dfrac{45}{208}\approx 0.216.[/tex]
What is the range of possible sizes for side x?
Answer:
1.6 < x < 9.6.
Step-by-step explanation:
Now x cannot be less than 5.6 - 4.0 = 1.6 as a triangle could not be formed if it were.
In fact x must be greater than 1.6.
Also x must be less than the sum of the other 2 sides.
So x must be less than 4.0 + 5.6 = 9.6.
Answer:
1.6 < x < 9.6
Step-by-step explanation:
The range of possible sizes for side x is 1.6 < x < 9.6.
Find the LCD for the following fractions:
(4/15x^3), (5/12x^2). answers: 25^3, 60x^3, 25x^5, 60x^5
Answer:
60x^3
Step-by-step explanation:
Given:
4/15x^3 and 5/12x^2
finding LCM of denominators (15x^3,12x^2)
for variable x, as x^3 is the heighest power so we'll keep x^3
now for the numeric part
15= 3*5
12=3*4
common factor is 3, so
3*4*5 =60
hence LCD= 60x^3!
5. A fan has three thin blades that spin to
produce a breeze. The diameter of the fan is
16 inches.
a. Determine the length of an arc between
two consecutive fan blades.
b. What is the area of each sector formed
by the radii passing through the center of
consecutive fan blades?
c. What is the angular velocity if the tip of
each blade in the fan moves 8m radians
in 2 seconds?
Answer:
a) The length of an arc between two consecutive fan blades is 16.76 inches
b) The area of each sector is 67.02 inches²
c) The angular velocity is 4m rad/sec
Step-by-step explanation:
* Lets explain how to solve the problem
- The fan has three thin blades that spin to produce a breeze
- The diameter of the fan is 16 inches
- The three blades divided the circle into three equal parts
- The circumference of the circle is 2πr
a)
∵ The diameter of the circle = 16 inches
∵ The radius of the circle is half the diameter
∴ The radius (r) = 1/2 × 16 = 8 inches
∵ The length of the circle = 2πr
∴ The length of the circle = 2π(8) = 16π
- The length of an arc between two consecutive fan blades is 1/3
the length of the circle
∴ The length of the arc = 1/3 × 16π = 16.76 inches
* The length of an arc between two consecutive fan blades is
16.76 inches
b)
- The area of a sector in the circle = [tex]\frac{x}{360}(\pi r^{2})[/tex]
where x is the central angle of the sector and r is the radius
of the circle
∵ The angle between each two consecutive blades = 360°/3
∴ x = 360°/3 = 120°
∵ r = 8 inches
∴ The area of each sector = [tex]\frac{120}{360}(\pi )(8^{2})=67.02[/tex]
* The area of each sector is 67.02 inches²
c)
∵ The angular velocity = Ф rad ÷ t, where Ф is the central angle
with radian measure and t is the time in seconds
∴ ω = Ф/t radian/second
∵ Ф = 8m radians
∵ t = 2 seconds
∴ ω = 8m ÷ 2 = 4m rad/sec
* The angular velocity is 4m rad/sec
What is the mean of 11,22,33
Answer:
22
Step-by-step explanation:
11+22+33=66
66/3
=22
Answer:
22
Step-by-step explanation:
The mean is just another word for average
Add up the three numbers and divide by 3
(11+22+33) /3 = 66/3 = 22
two numbers have the sum of 124 and a difference of 32. find the numbers.
Answer:
78 and 46
Step-by-step explanation:
Substitution (look it up it's hard to explain lol)
Write an equation in slope-intercept form for the line passing through the pair of points. (–1, 2), (4, –3)
Answer:
y = - x + 1
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 )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 1, 2) and (x₂, y₂ ) = (4, - 3)
m = [tex]\frac{-3-2}{4+1}[/tex] = [tex]\frac{-5}{5}[/tex] = -1, hence
y = - x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (- 1, 2), then
2 = 1 + c ⇒ c = 2 - 1 = 1
y = - x + 1 ← equation in slope- intercept form
The equation is y = –x + 1.
To find the slope-intercept form of a line passing through two points, calculate the slope using the given points and then use one point to find the y-intercept. The final equation for the line through the points (–1, 2) and (4, –3) is y = –x + 1.
To write an equation in slope-intercept form for the line passing through the points (–1, 2) and (4, –3), we first need to calculate the slope (m) using the formula
m = (y2 - y1) / (x2 - x1). Plugging in our points gives us m = (–3 – 2) / (4 – (–1)) = –5 / 5 = –1. Now that we have the slope, we can use one of the points to find the y-intercept (b). Using the point (–1, 2) and the slope-intercept formula y = mx + b, we plug in the values to get 2 = (–1)×(–1) + b, simplifying to 2 = 1 + b, which yields b = 1. Thus, the equation is y = –x + 1.
What is the solution to the equation
-5 p = 24-p?
What is the arc length of a quarter circle with a radius of 6 inches?
Arc length will be equal to the perimeter divided by 4 since we are talking about quarter circle.
[tex]2\pi r/4=\pi r/2=6\pi/2\approx\boxed{9.42}[/tex]
Hope this helps.
r3t40
Answer:
9.42 inches
Step-by-step explanation:
the cercle length is : 2π×r = 2×3.14 ×6=37.68 inches
the arc length of a quarter circle is : 37.68/4 =9.42 inches
Simplify: ( y^−7 × y^−3 )−1 A. y−21 B. y 21 C. y−10 D. y 10
Answer:
D
Step-by-step explanation:
The rules we need to simplify this are:
[tex]a^x*a^y=a^{x+y}[/tex]
and
[tex](a^x)^y=a^{xy}[/tex]
Now, let's simplify the problem:
[tex](y^{-7}*y^{-3})^{-1}\\(y^{-10})^{-1}\\y^{10}[/tex]
Answer choice D is y^10, so that's correct.
Which of the following are valid names for the given triangle? Check all that apply.
Answer:
B,D, and E
Step-by-step explanation:
They all label the vertices in the correct order and do not label sides when naming it.
Answer:
B. [tex]\Delta TAX[/tex],
D. [tex]\Delta AXT[/tex]
E. [tex]\Delta XTA[/tex].
Step-by-step explanation:
We have been given a triangle. We are asked to choose the valid names for our triangle from the given choices.
We know that labels of the vertices of the triangle are used to name a triangle. In naming triangle, we can start from any vertex and we should keep the letters in order as we go around the triangle.
We can see that vertices of our given triangle are labeled as A, T and X, therefore, we can get three names for our triangle as:
[tex]\Delta TAX[/tex], [tex]\Delta AXT[/tex] and [tex]\Delta XTA[/tex].
Therefore, options B, D and C are correct choices.
Find P(not rolling 1, 3, 4, or 5) with one number cube.
The event "not rolling 1, 3, 4, or 5" is the same event as "rolling 2 or 6".
Since the possible outcomes of a number cube have the same probability, the probability of rolling 2 or 6 is given by
[tex]\dfrac{\text{\# of good outcomes}}{\text{\# of possible outcomes}}=\dfrac{2}{6}=\dfrac{1}{3}[/tex]
What is msu?
49°
77°
98°
161°
Answer:
77°
Step-by-step explanation:
[tex]\\ T = \frac{1}{2} (RU - SU)\\ \\ 21 =\frac{1}{2}(119 - SU)\\ \\ 42 = 119 - SU\\ SU=77[/tex]
The measure of mSU from the given diagram is 77 degrees
Circle geometryThe half of the difference of the intecepted arc is equal to the measure of the angle at the vertex
Applying this theorem to the given figure, we will havea;
1/2(119 - mSU) = 21
119 - mSU = 2(21)
119 - mSU = 42
Determine the measure of mSU
mSU = 119 -42
mSU = 77degrees
Hence the measure of mSU from the given diagram is 77 degrees
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which trinomials are prime?
choose all answers that are correct.
Answer:
A C D
Step-by-step explanation:
A prime Trinomial is one that cannot be reduced into integer factors. It is easier to define a non prime trinomial first.
x^2 - 4x - 12 can be factored into
(x - 6)(x + 2) -6 and 2 are integers.
So B is not prime.
All of the others are prime. You need to use the quadratic formula to solve them.
B factors into
x^2 - 13x + 42
(x - 7)(x - 6)