[tex]\bf ~~~~~~~~~~~~\textit{angle between two vectors } \\\\ cos(\theta)=\cfrac{\stackrel{\textit{dot product}}{u \cdot v}}{\stackrel{\textit{magnitude product}}{||u||~||v||}} \implies \measuredangle \theta = cos^{-1}\left(\cfrac{u \cdot v}{||u||~||v||}\right) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} u=i+\sqrt{7}j\implies &<1,\sqrt{7}>\\\\ v=-i+9j\implies &<-1,9> \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf u\cdot v\implies (1)(-1)~+~(\sqrt{7})(9)\implies -1+9\sqrt{7}\implies 9\sqrt{7}-1~\hfill dot~product \\\\[-0.35em] ~\dotfill\\\\ ||u||\implies \sqrt{1^2+(\sqrt{7})^2}\implies \sqrt{1+7}\implies \sqrt{8}~\hfill magnitudes \\\\\\ ||v||\implies \sqrt{(-1)^2+9^2}\implies \sqrt{1+81}\implies \sqrt{82} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \theta =cos^{-1}\left( \cfrac{9\sqrt{7}-1}{\sqrt{8}\cdot \sqrt{82}} \right)\implies \theta =cos^{-1}\left( \cfrac{9\sqrt{7}-1}{\sqrt{656}} \right) \\\\\\ \theta \approx cos^{-1}(0.8906496638868531)\implies \theta \approx 27.05[/tex]
make sure your calculator is in Degree mode.
What is the conjugate of 7 - 24i
Answer:
7+24i
Step-by-step explanation:
A math conjugate is formed by changing the sign between two terms in a binomial. For instance, the conjugate of x + y is x - y. We can also say that x + y is a conjugate of x - y. In other words, the two binomials are conjugates of each other.
The conjugate of a complex number is obtained by negating its imaginary part while keeping the real part unchanged. So, for 7 - 24i, the conjugate is 7 + 24i. The real part remains 7, and the imaginary part changes from -24i to +24i.
Explanation:In the field of mathematics, specifically complex numbers, the conjugate of a complex number is formed by changing the sign of its imaginary part. Given the complex number 7 - 24i, its conjugate is obtained by changing the sign of the imaginary part (-24i) to a positive. So, the conjugate of 7 - 24i is 7 + 24i.
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What is the value of X
Answer:
120
Step-by-step explanation:
it is an obtuse angle
The answer is:
The missing angle "x" is equal to 130°.
Why?We need to remember that the sum of all of the angles of any polygon will be all equal to 360°.
So, we are given the following exterior angles:
[tex]140\°\\34\°\\56\°\\[/tex]
Now, if the sum of all the exterior angles is equal to 360°, we can use it to calculate "x", so:
[tex]360\°=140\°+34\°+56\°+x\\\\x=360\°-(140\°+34\°+56\°)=360\°-230\°\\\\x=130\°[/tex]
Hence, the missing angle "x" is equal to 130°.
Have a nice day!
Dante bought a new graduated cylinder for his chemistry class. It holds 847 milliliters of liquid. If the cylinder has a radius of 5.5 cm, then how tall is the cylinder? (Note: 1 milliliter is equal to 1 cubic centimeter)
a. 28
b. 154
c. 23,716
d. 77
Answer:
Option a) [tex]h=28\ cm[/tex]
Step-by-step explanation:
we know that
The volume of a cylinder is equal to
[tex]V=\pi r^{2}h[/tex]
we have
Note In this problem the volume is equal to [tex]847\pi\ ml[/tex] instead of [tex]847\ ml[/tex]
so
[tex]847\pi\ ml=847\pi\ cm^{3}[/tex]
[tex]r=5.5\ cm[/tex]
substitute in the formula and solve for h
[tex]847\pi=\pi(5.5)^{2}h[/tex]
simplify
[tex]847=(5.5)^{2}h[/tex]
[tex]h=847/(5.5)^{2}[/tex]
[tex]h=28\ cm[/tex]
Which expressions can be used to find m∠ABC? Check all that apply.
Answer:
[tex]\cos^{-1}(\frac{6.3}{9.8})[/tex]
[tex]\sin^{-1}(\frac{7.5}{9.8})[/tex]
Step-by-step explanation:
Recall the mnemonics SOH-CAH-TOA
The sine ratio is the length of the opposite side expressed over the hypotenuse.
[tex]\sin m\angle ABC=\frac{7.5}{9.8}[/tex]
Take the sine inverse of both sides to get;
[tex]m\angle ABC=\sin^{-1}(\frac{7.5}{9.8})[/tex]
The cosine ratio is the length of the adjacent side expressed over the hypotenuse.
[tex]\cos m\angle ABC=\frac{6.3}{9.8}[/tex]
Take the cosine inverse of both sides to get;
[tex]m\angle ABC=\cos^{-1}(\frac{6.3}{9.8})[/tex]
Which statement is true about the distribution
Answer:
dssdac
Step-by-step explanation:
What is the area of point ?
Answer:
314 cm²
Step-by-step explanation:
It's not the point O, but the circle O, a point has no area.
The area of a circle is given by the formula A = π r²
We don't have r (radius), but we have the diameter, which is double the radius. So, r = d / 2 = 20 cm / 2 = 10 cm
Now, we can plug r directly into the equation:
A = π r² = π 10² = 100π = 314 cm²
An astronaut visited Mars. His weight on Earth was 180 pounds, and his weight on Mars was only 72 pounds. He removed a rock with a weight of 16 pounds on Mars. What is the weight of the rock on Earth? a. 1.4 pounds c. 6.4 pounds b. 4 pounds d. 40 pounds Please select the best answer from the choices provided A B C D
Answer:
d. 40 pounds
Step-by-step explanation:
We know both weights of the astronaut, and we know one of the weight of the rock... we need to find the other weight of the rock (on Earth).
The easiest way to deal with those problems is to use a cross-multiplication.
We'll place on top the weights on Earth and as denominators the weights on Mars:
[tex]\frac{x}{16} = \frac{180}{72}[/tex]
So we isolate x = (16 * 180) / 72 = 2,880 / 72 = 40 pounds.
The rock then weights 40 pounds on Earth.
what is the area of a hexagon with an apothem of 10
Since the perimeter of said hexagon is 120√3, we simply multiply this number by 10 and divide it by 2.
1200√3/2 = 600√3
If f(x) and its inverse function, f–1(x), are both plotted on the same coordinate plane, what is their point of intersection?
Answer:
-3
Step-by-step explanation:
f(-1) = 3(-1)
f(-1) = -3
Answer with explanation:
The given function is:
⇒ y =3 x
And it's inverse function can be Calculated by, replacing , x by y, and , y by x, in the above equation
⇒x=3 y, is the equation of inverse function.
Both the original function , and inverse function passes through origin, As well as Origin is the point of Intersection, which can be shown as follows:
3 x-y=0-----(1)
x-3 y=0
3 x - 9 y =0 ------(2)
EQ.(1) - Eq.(2)
3 x - y - (3 x- 9 y)=0
-y + 9 y=0
8 y=0
y=0
Putting the value of , y in equation (2)
x=3 × 0
x=0
⇒Point of intersection of ,f(x) and it's inverse =(0,0)
Kyle bought x pencils. He paid $1.24, including tax, per pencil. He gave the
cashier $20 and received $5.12 in change. How many pencils did Kyle purchase?
Answer:
Kyle purchased 12 pencils
Step-by-step explanation:
p= pencils
1.24p - 5.12 = 20
or, you can do this back wards like this....
20 - 5.12 = 14.88
14.88 / 1.24 = 12
p=12
(sorry for any confusion, this is just how my brain works...)
Kyle bought 12 pencils at $1.24 each. This determination is based on subtracting the amount of change he received from his $20 payment and dividing by the cost per pencil.
Explanation:Kyle bought x pencils for $1.24 each, paid with a $20 bill, and received $5.12 in change. Therefore, the total amount he spent can be calculated by subtracting the change from the total payment ($20 - $5.12 = $14.88). As he spent this amount on pencils that cost $1.24 each, the number of pencils he bought can be determined by dividing the total spent by the cost per item ($14.88 / $1.24). Therefore, Kyle bought approximately 12 pencils (the exact result is 12.003, but as pencils cannot be fractional, we round down to the nearest whole number).
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If x = 6 cm, what is the surface area of the geometric shape formed by this net?
A. 144 square cm.
B. 432 square cm.
C. 216 square cm
D. 576 square cm
Please explain because these still stump me
Answer:
the answer is D. 576 square cm
Step-by-step explanation:
Find the area of one of the rectangular faces using the formula, Area = lw.
A = (12 cm) (6 cm)
A = 72 square cm
Since there are 4 rectangular faces, multiply the area of one rectangular face by 4 to get a total of 288 square cm.
The area of one of the congruent squares is 12 cm × 12 cm, or 144 cm2. Multiply 144 cm2 by 2 to get a total of 288 cm2.
To find the surface area of the rectangular prism, add the area of the four rectangular faces to the area of the two square faces.
288 square cm + 288 square cm = 576 square cm
What is the slope of the line through the points (-2,-1) and (8,-3)?
Answer:
- 1/5
Step-by-step explanation:
Slope of a line passing through two points can be calculated as:
[tex]\text{slope}=\frac{\text{rise}}{\text{run}} \\\\ \text{slope}=\frac{\text{Difference of y coordinates}}{\text{Difference of x coordinates}}[/tex]
The given points are (-2, -1) and (8, -3). Using the values in above formula, we get:
[tex]\text{slope}=\frac{-3-(-1)}{8-(-2)}\\\\ \text{slope}=\frac{-3+1}{8+2}\\\\ \text{slope}=\frac{-2}{10}\\\\ \text{slope}=\frac{-1}{5}[/tex]
Thus the slope of the line through the given points is -1/5. So 2nd option gives the correct answer
Answer:
The correct answer is second option
-1/5
Step-by-step explanation:
Points to remember
The slope of line passing through (x₁, y₁) and (x₂, y₂) is given by,
Slope = (y₂ - y₁)/(x₂ - x₁)
To find the slope of given line
Here, (x₁, y₁) = (-2, -1) and (x₂, y₂) = (8, -3)
Slope = (y₂ - y₁)/(x₂ - x₁) = ( -3 - - 1)/(8 - -2)
= (-3 + 1)/(8 + 2) = -2/10
= -1/5
Therefore the correct answer is second option -1/5
Part 2 of “I don’t know what the heck i’m doing”
Plot the points ( -4,2.5), (-3,3), (-2,1.5), (-1,2), (0,1), (1,2), (2,3.5), (3,0.5), (4,2.5) then connect them with a line
Find the surface area of the cone. Leave your answer in terms pi
Answer:
The answer is C. 119cm³
Step-by-step explanation:
SA= [tex]\pi r^{2} +\pi rl[/tex]
= 49[tex]\pi +\pi 7(10)[/tex]
= 49[tex]\pi +20\pi[/tex]
SA= 119[tex]\pi[/tex]
Answer:
The correct answer is option C. 119π cm²
Step-by-step explanation:
Points to remember
Surface area of cone = πrl + πr²
Where r is the base radius and l is the lateral edge
To find the surface area of given cone
Here r = 7 cm and l = 10 cm
Surface area = πrl + π r² =( π * 7 * 10) + (π *7²)
= 70 π + 49π
= 119π cm²
Therefore correct answer is option C. 119π cm²
what is 15.36 times negative 0.45
Answer:
-6.912
Step-by-step explanation:
Answer: -6.912
Step-by-step explanation: -6.912 Would Be Your Answer. Have A Great Day!
A concert hall is in the shape of a rectangle. Its floor has a length of (x + 6) meters and a width of (2x - 3) meters. Write a simplified expression that represents the area of the floor of the concert hall, in square meters?
Answer:
[tex]A=(2x^{2}+9x-18)\ m^{2}[/tex]
Step-by-step explanation:
Let
L-----> the length of the concert hall
W----> the width of the concert hall
we know that
The area of a rectangle ( concert hall) is equal to
[tex]A=LW[/tex]
we have
[tex]L=(x+6)\ m[/tex]
[tex]W=(2x-3)\ m[/tex]
substitute the values
[tex]A=(x+6)(2x-3)\\ \\A=2x^{2} -3x+12x-18\\ \\A=(2x^{2}+9x-18)\ m^{2}[/tex]
The area of the concert hall's floor, in square meters, is represented by the simplified algebraic expression 2x² + 9x - 18, which is derived by multiplying the hall's length (x + 6) by its width (2x - 3) then simplifying the resulting expression.
Explanation:The area of a rectangle is calculated by multiplying the length by the width. In this case, the length of the concert hall is given as (x + 6) meters and the width as (2x - 3) meters. Therefore, the area of the concert hall's floor, expressed in square meters, is the product of these two expressions.
So, you multiply (x + 6) by (2x - 3) to get the area, which gives you the following expression: 2x² - 3x + 12x - 18. Now, simplify this expression by combining like terms.
The simplified expression for the area of the floor in square meters is then 2x² + 9x - 18.
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13. Which of the following is the graph of y = 3(1⁄5)x?
Answer:
Second graph
Step-by-step explanation:
The second graph is the correct one. Why? because the y intercept is (0, 3), and also because the base, 1/5, is between 0 and 1, which leads to a decaying exponential graph.
How would you do this? I’m lost.
Find the x intercepts by setting each x to equal 0:
(4-x)=0
4 -4 = 0
First x intercept = (4,0)
(x+2) = 0
-2 + 2 = 0
Second x intercept = (-2,0)
Now find the Y intercept by setting the x's to 0 and solve for y:
y = (4-0)(0+2)
y = 4*2
y = 8
The Y intercept is (0,8)
Now find the graph the the parabola crosses the x axis at -2 and 4 and also crosses the Y axis at 8.
Graph A is the correct one.
if you apply the changes below to the absolute value parent function f(x)=lxl, what is the equation of the new function?
Shift 4 units left
Shift 2 units up
Answer:
[tex]f(x)=|x+4|+2[/tex]
Step-by-step explanation:
The given absolute value function is
[tex]f(x)=|x|[/tex]
This is the base or the parent function.
The transformation [tex]f(x)=|x+b|+c[/tex] will shift the parent function b units to the left and c units up.
From the question, b=4 units and c=2 units.
The new equation is [tex]f(x)=|x+4|+2[/tex]
Answer: The equation of the new function is [tex]f(x)=|x+4|+2.[/tex]
Step-by-step explanation: We are given to find the equation of the new function if we apply the following changes to the absolute value parent function f(x)=lxl :
Shift 4 units left and Shift 2 units up.
We know that
if we shift the absolute value parent function f(x) = |x| to h units left and k units up, then the new equation will be
[tex]f(x)=|x+h|+k.[/tex]
Therefore, if the function is shifted 4 units left and 2 units up, then the equation of the new function will be
[tex]f(x)=|x+4|+2.[/tex]
Thus, the equation of the new function is [tex]f(x)=|x+4|+2.[/tex]
What is the average rate of change of the function over the interval x = 0 to x = 8?
Answer:
The average rate of change is:
[tex]\frac{13}{161}[/tex]
Step-by-step explanation:
The rational function given to us is;
[tex]f(x)=\frac{3x+4}{2x+7}[/tex]
[tex]f(0)=\frac{3(0)+4}{2(0)+7}[/tex]
[tex]f(0)=\frac{4}{7}[/tex]
[tex]f(8)=\frac{3(8)+4}{2(8)+7}[/tex]
[tex]f(0)=\frac{28}{23}=1[/tex]
The average rate of change of this function from x=0 to x=8 is the slope of the secant line connecting:
(0,f(0)) and (8,f(8))
Average rate of change =[tex]=\frac{f(8)-f(0)}{8-0}[/tex]
[tex]=\frac{\frac{28}{23}-\frac{4}{7} }{8}[/tex]
[tex]=\frac{13}{161}[/tex]
Solve the equation. 5/2s + 3/4 = 9/4s
Answer:0.15789474
Step-by-step explanation:
5/2=2.5s+ 3/4=0.75 = 9/4=2.25
add 5/2/2.5 to the other side{like terms because of the letter s} which would=4.75s
now divide that to other side of .75 divided by 4.75 which would equal= 0.15789474
(i think, sorry if its incorrect)
Answer:
The value of s is -0.33
Step-by-step explanation:
Given the equation
[tex]\frac{5}{2s}+\frac{3}{4}=\frac{9}{4s}[/tex]
we have to solve the above equation
[tex]\frac{5}{2s}+\frac{3}{4}=\frac{9}{4s}[/tex]
[tex]\frac{5}{2s}-\frac{9}{4s}=-\frac{3}{4}[/tex]
[tex]\frac{10-9}{4s}=-\frac{3}{4}[/tex]
[tex]\frac{1}{4s}=-\frac{3}{4}[/tex]
[tex]s=-\frac{1}{3}=-0.33[/tex]
The value of s is -0.33
If ∠3 = 5x - 1, and ∠5 = 3x + 11, then x =
Answer:
6
Step-by-step explanation:
cause we will add them together
5x -1 = 3x +11
2x=12
x=6
The value of x if ∠3 = 5x - 1, and ∠5 = 3x + 11, is 6.
What is angle?An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively.
Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles.
Given;
∠3 = 5x - 1, and ∠5 = 3x + 11,
Calculate the value of x as shown below,
∠3 = ∠5 (Alternate interior angles between parallel lines are equal)
5x - 1 = 3x + 11
5x - 3x = 11 + 1
2x = 12
x = 12 / 2
x = 6
Thus, the value of x is 6.
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a man can do a job in 4 days working alone and his helper can do the same job in 12 days working alone what part of the job can they do in one day when working together at their respective rates?
Solution:
Let t = working together in terms of days
(1/4) + (1/12) = 1/t
Solve for t.
Multiply both sides by the LCD.
LCD = 12t
3t + t = 12
4t = 12
t = 12/4
t = 3
Together, they can do the job in 3 days.
How do you Graph y-3=1/3(x+1)
Answer:
You can find the point of intersection of the line with the y-axis and the the point of intersection of the line with the x-axis. See the graph attached.
Step-by-step explanation:
Find the intersection with the y-axis. Substitute [tex]x=0[/tex] into the equation and solve for y:
[tex]y-3=\frac{1}{3}(x+1)\\\\y-3=\frac{1}{3}(0+1)\\\\y-3=\frac{1}{3}(1)\\y=\frac{1}{3}+3\\\\y=\frac{10}{3}[/tex]
[tex]y[/tex]≈3.33
Find the intersection with the x-axis. Substitute [tex]y=0[/tex] into the equation and solve for x:
[tex]y-3=\frac{1}{3}(x+1)[/tex]
[tex]0-3=\frac{1}{3}(x+1)\\(-3)(3)=x+1\\-9-1=x\\x=-10[/tex]
Now, you know that the line passes through the point (0,3.33) and (-10,0). Now you can graph the function. (Observe the graph attached)
Mark earns $300 per month plus an additional 2% on all of his sales. Last month he sold $59,000. What was Mark’s income for the month?
Answer:
59,000 * .02= $1,180 commission plus $300 = $1480
what is the mean between the numbers 3,19,21,6.8,9.3,21.7,2.9
Answer:
About 11.96
Step-by-step explanation:
The mean of a data set is basically the average.
To find the average, add up all of the data values and then divide by the amount of numbers there are.
First, add the numbers.
3 + 19 + 21 + 6.8 + 9.3 + 21.7 + 2.9 = 83.7
There are 7 numbers in this data set so divide 83.7 by 7
83.7/7 = 11.95714285714286
Round this number to the nearest hundreth, to get 11.96
So, the mean of this data set is 11.96
I hope this helps!
Calculate the finance charge and new balance using the previous balance method. Previous balance = $199.19 Annual rate = 14%
Answer:
Finance charge = $2.32
new balance = $201.51
Step-by-step explanation:
Finance charge = Previous balance×Periodic percentage rate
The previous balance is 199.19
The annual percentage rate is 0.14. Therefore, the periodic percentage rate is; (0.14/12)
Finance charge = 199.19 * (0.14/12)
= 2.3239 = $2.32
new balance = previous balance + finance charge
= 199.19 + 2.32
= $201.51
The number 18.34 has four significant figures
Answer:
True
Step-by-step explanation:
The number 18.34 has four significant figures. Yes it is true that it has four significant figures.
For significant figures, we start counting from the first non zero digit.
The first non zero digit in 18.34 is 1.
Count from this number to the last number, we have four numbers.
Therefore, it is true that the number 18.34 has four significant figures.
Department A had sales of $200,000.00, Department B had sales of $600,000.00, and total overhead expenses were $32,000.00. The allocation of overhead to Department A should be ________.
Answer:
the allocation of overhead to department A is $8,000.00
Step-by-step explanation:
Given that Department A had sales of $200,000.00 and Department B had sales of $600,000.00, the ratio of department A's sales to that of department B is 200,000.00 / 600,000.00 = 1/3.
The total overhead expenses were $32,000.00, the allocation of overhead to department A is 32,000.00 / (3 + 1) = $32,000.00 / 4 = $8,000.00
15 over 1000 wrote in scientific notation
Answer:
1.5*10^-2
Step-by-step explanation:
You mean 15/1000 written in scientific notation?
In this case, it would be- 1.5*10^-2.