Answer:
x² - 49
Step-by-step explanation:
Identity: (a + b)(a - b) = a² - b²Here a = x and b = 7
(x +7) (a -7) = x² - 7²
= x² - 49
Answer:[tex]x^{2} -49[/tex]
Step-by-step explanation:
determine if the shape is a polyhedron using eulers formula
Answer:
Yes
Step-by-step explanation:
Euler's Formula for Polyhedrons :
Faces + Vertices = Edges + 2
Given :
Vertices = 12Edges = 18Faces = 8Verifying using Euler's Formula :
F + V = E + 2(8) + (12) = (18) + 220 = 20It is a polyhedronThe given shape is a polyhedron using the Euler's formula.
What is Polyhedron?Polyhedron is defined as the three dimensional shape which consists of flat shapes which are polygons.
Cubes, pyramids are all polyhedrons.
Euler's formula for polyhedron states that,
V - E + F = 2
where V, E and F are the number of vertices, number of edges and the number of faces respectively.
For the given polyhedron,
Number of vertices, V = 6 + 6 = 12
Number of edges, E = 6 + 6 + 6 = 18
Number of faces, F = 1 + 6 + 1 = 8
So, V - E + F = 12 - 18 + 8 = -6 + 8 = 2
Hence the given shape is a polyhedron.
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880$ at 5.25% for 2 years
Answer:
$977.20
Step-by-step explanation:
We will use the compound interest formula to solve this: A = P(1 + R) ^ T
Using this formula we plug-in the values that we already have:
A = 880(1 + .0525) ^ 2
Now if we solve this, we end up with 977.20. That is your answer.
Given that ‘z’ is in set of complex number and ‘a’ is any real numbers. Solve the trigonometric equation sin(z) = a for all general solutions.
Recall that for all [tex]z\in\Bbb C[/tex],
[tex]\sin(z) = \dfrac{e^{iz} - e^{-iz}}{2i}[/tex]
so that
[tex]\sin(z) = a \iff e^{iz} - e^{-iz} = 2ia[/tex]
Multiply both sides by [tex]e^{iz}[/tex] to get a quadratic equation,
[tex]e^{2iz} - 2iae^{iz} - 1 = 0[/tex]
Solve for [tex]e^{iz}[/tex]. By completing the square,
[tex]e^{2iz} - 2ia e^{iz} + i^2a^2 = 1 + i^2a^2[/tex]
[tex]\left(e^{iz} - ia\right)^2 = 1 - a^2[/tex]
[tex]e^{iz} - ia = \pm \sqrt{1-a^2}[/tex]
[tex]e^{iz} = ia \pm \sqrt{1-a^2}[/tex]
[tex]iz = \log\left(ia \pm \sqrt{1-a^2}\right)[/tex]
[tex]iz = \ln\left|ia \pm \sqrt{1-a^2}\right| + i \left(\arg\left(ia \pm \sqrt{1-a^2}\right) + 2\pi n\right)[/tex]
[tex]\boxed{z = -i \ln\left|ia \pm \sqrt{1-a^2}\right| + \arg\left(ia \pm \sqrt{1-a^2}\right) + 2\pi n}[/tex]
where n is any integer.
We are given with:
[tex]{\quad \qquad \longrightarrow \sin (z)={\sf a}\:,\:z\in \mathbb{C}}[/tex]
Recall the identity what we have for the sine function of complex numbers
[tex]{\boxed{\bf{\sin (z)=\dfrac{e^{\iota z}-e^{-\iota z}}{2\iota}}}}[/tex]Put the values to thus obtain:
[tex]{:\implies \quad \sf \dfrac{e^{\iota z}-e^{-\iota z}}{2\iota}=a}[/tex]
[tex]{:\implies \quad \sf e^{\iota z}-e^{-\iota z}=2a\iota}[/tex]
Multiply both sides by [tex]{\sf e^{\iota z}}[/tex]
[tex]{:\implies \quad \sf e^{\iota z}\cdot e^{\iota z}-e^{-\iota z}\cdot e^{\iota z}=2a\iota e^{\iota z}}[/tex]
[tex]{:\implies \quad \sf (e^{\iota z})^{2}-2a\iota e^{\iota z}-1=0}[/tex]
Put x = [tex]{\sf e^{\iota z}}[/tex]:
[tex]{:\implies \quad \sf x^{2}-2a\iota x-1=0}[/tex]
Find the discriminant, here D will be, D = (-2ai)² - 4 × 1 × (-1) = 4 - 4a² = 4(1-a²)
Now, By quadratic formula:
[tex]{:\implies \quad \sf x=\dfrac{-(-2a\iota)\pm \sqrt{4(1-a^{2})}}{2}}[/tex]
[tex]{:\implies \quad \sf x=\dfrac{a\iota \pm \sqrt{1-a^{2}}}{2}}[/tex]
[tex]{:\implies \quad \sf e^{\iota z}=\dfrac{a\iota \pm \sqrt{1-a^{2}}}{2}}[/tex]
[tex]{:\implies \quad \sf \iota z=log\bigg(\dfrac{a\iota \pm \sqrt{1-a^{2}}}{2}\bigg)}[/tex]
Using the formula for logarithms, we have:
[tex]{:\implies \quad \sf \iota z=log(a\iota \pm \sqrt{1-a^{2}})-log(2)}[/tex]
[tex]{:\implies \quad \sf z=\dfrac{1}{\iota}log(a\iota \pm \sqrt{1-a^{2}})-\dfrac{1}{\iota}log(2)}[/tex]
The sine function is periodic on 2πn and zero on (π/2), and the logarithmic expression becomes undefined for all ia±√(1-a²) < 0, so we will take modulus of it
[tex]{:\implies \quad \boxed{\bf{z=\dfrac{1}{\iota}log\bigg|a\iota \pm \sqrt{1-a^{2}}\bigg|-\dfrac{1}{\iota}log(2)+\dfrac{\pi}{2}+2\pi n\:\:\forall \:n\in \mathbb{Z}}}}[/tex]
I know the answer but I would like to know how to solve it
Step-by-step explanation:
We can use long division to solve this
First place a 5 in the tens place, this means we are multiplying 5 by 50. This will subtract 250 from 280, leaving us with 30.
Next place a 6 in the ones place, this means we are multiplying 5 by 6. This will subtract 30 from 30, leaving us with 0.
This means we have found our answer of 56.
Answer:
See explanation
Step-by-step explanation:
Basically, division is just saying "how many numbers would go into this number this many times?" We can break this problem down into 200/5 and 80/5. 200/5 is 40, and 80/5 is 16. 40+16 is 56, so the answer is 56.
(I can elaborate further if needed)
Hope this helps!
help________________
Answer:
302cm³
Step-by-step explanation:
The formula for the volume of a hemisphere is [tex]\frac{\frac{4}{3} \pi r^{3}} {2}[/tex] (volume of a sphere over 2)
Plugging in 4 for r we get the answer of [tex]\frac{256}{6}\pi[/tex]
Next we have to find the height of cone. We can get this by subtracting the radius of the hemisphere from the height of the solid. (14-4=10)
We can now find the volume of the cone using the formula [tex]\frac{1}{3} \pi r^{2} h[/tex]
Plugging in 4 for r and 10 for h we get the answer [tex]53 \frac{1}{3} \pi[/tex]
Now we can add our 2 volumes to get the volume of the solid which is 302 in decimal form (3 significant figures)
That is the answer
- Kan Academy Advance
Write an expression that represents the weigh of and object that weighs 12 pounds and increases by 0.5 pound per month, m.
Which number sentence is not true?
A. |-4.5| = 4.5
B. |0| < |-45|
C. |45| > 0
D. |4.5| > |-45|
Answer:
D is not true.
Step-by-step explanation:
[tex] |4.5| = 4.5[/tex]
[tex] | - 45| = 45[/tex]
[tex]4.5 \leqslant 45[/tex]
Find the approximate volume of a cylinder that has a radius of 4 inches and a height of 6 inches. Use 3.14 for Pie
150.72 cubic inches
163.28 cubic inches
301.44 cubic inches
452.16 cubic inches
20% tip on a bill of $53.18
Answer:
$10.64
Step-by-step explanation:
20% out of $53.18 is $10.636 rounded to $10.64
A triangle has sides with lengths of 17 feet, 31 feet, and 36 feet. Is it a right triangle?
yes
no
Vehicle final sale price is $25,000 at 5% interest and offers financing up to 60 months. what is the monthly car payments?
Answer:
$ 471.78
Step-by-step explanation:
This describes an 'ordinary annuity' ====> FORMULA:
PV= C [ 1-(1+i)^-n / i ] Looking for C i = .05/12 n =60 PV = 25000
plug in the numbers and calculate C = 471.78
Boris wants to sort his crayons and give out the
yellow ones. He has 360 crayons altogether.
of the crayons are blue.
18
60% of the crayons are red.
The rest are yellow.
Work out the number of crayon he gives out
Answer:
126 yellow crayons
Step-by-step explanation:
Finding the number of each of the crayons :
Blue = 18Red = 60% of total = 60% x 360 = 0.6 x 360 = 216Number of yellow crayons :
Total - [Blue + Red]360 - [18 + 216]360 - 234126 yellow crayonsCan anyone help me with this area of sector activity? I'm not sure how to solve this. I will reward brainliest! Please tell me how you got your answer as well! this is 10th grade geometry
Answer:
Jenny has worked out the area of the whole circle using the formula π × r² where r is the radius length. She has assumed π is 3.14 which leads to her working of 3.14 × 10² = 314 units². She has to divide the total area by 4 to calculate the sector area.
Let's check
Angle is 90°Radius is 10Area of sector
Ø/360×πr²90/360×pi(10)²1/4×π(100)25π78.5units²P(Head, Diamond AND Head, Heart) = ?
The probability of drawing a head card of diamonds and then a head card of hearts is:
P = 0.003
How to find the probability?
Here we assume that we have a deck of 52 cards, and we want to find:
P(Head, Diamond AND Head, Heart)
This is the probability of drawing a head of diamonds and then a head of hearts.
Remember that for each suit has 3 head cards, J, Q, and K.
Then for the first card, the probability of getting a head of diamonds is equal to the quotient between the number of cards with these properties (3) and the total number of cards (52).
P = 3/52
Then we need to draw a head of hearts, the probability is computed in the same way, but before we drew a card, so now the total number of cards is 51, so we get:
Q = 3/51
Then the joint probability is:
p = (3/52)*(3/51) = 0.003
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PLS HELP ITS WORTH 20 points
Answer:
x=3, Aly is correct.
Step-by-step explanation:
a. angle YWZ
b. ZY = 9
c. the triangles are congruent so 7x-20=2x-5, 5x=15, and x=3
HOWW DO I DO THIS????
WEIRD EXACT TRIG QUESTION (cannot use a calculator)
Answer:
[tex]\huge{\red{\angle ABC = \boxed{30}\degree}}[/tex]
Step-by-step explanation:
[tex]\sin \angle ABC =\frac{p}{30}......(1)[/tex] (Given)In [tex] \triangle ABC,[/tex] sin ratio of [tex] \angle ABC[/tex] can be given as:[tex]\sin \angle ABC =\frac{AC}{AB}[/tex][tex]\implies \sin \angle ABC =\frac{2p+10}{80}......(2)[/tex]From equations (1) and (2), we find:[tex] \frac{p}{30}=\frac{2p+10}{80}[/tex][tex]\implies 80(p)=30(2p+10)[/tex][tex]\implies 80p=60p+300[/tex][tex]\implies 80p-60p=300[/tex][tex]\implies 20p=300[/tex][tex]\implies p=\frac{300}{20}[/tex][tex]\implies p=15[/tex][tex]\implies \sin \angle ABC =\frac{15}{30}[/tex][tex]\implies \sin \angle ABC =\frac{1}{2}[/tex][tex]\implies \sin \angle ABC =\sin 30\degree\:\:\:\:(\because \sin 30\degree=\frac{1}{2})[/tex][tex]\implies \huge{\red{\angle ABC = \boxed{30}\degree}}[/tex]I need the the number
y=3x+3
Step-by-step explanation:
The m is 3 because it is rise over run. For every 3 up it goes one over (3/1) or just 3. The b is 3 because b is where x equals 0 and it is at 3.
Percentage:
A shop has 150 gaming pc. They sold 30.
Find the percentage of the PC that they have not sold.
A box of chocolates contains 10 milk chocolates, 8 dark chocolates and 6 white chocolates. Sung randomly chooses a chocolate, eats it, then randomly chooses another. What is the probability Sung chose a milk chololate then a white chocolate
Using it's concept, it is found that there is a 0.1087 = 10.87% probability Sung chose a milk chocolate then a white chocolate.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, we have that:
Initially, there are 10 + 8 + 6 = 24 chocolates, out of which 10 are milk, hence the probability of eating a milk chocolate first is given by: [tex]\frac{10}{24} = \frac{5}{12}[/tex].Then, there will be 23 chocolates, out of which 6 will be white, hence the probability of eating a white chocolate first is given by: [tex]\frac{6}{23}[/tex].Thus, the probability of milk then white is given by:
[tex]p = \frac{5}{12} \times \frac{6}{23} = \frac{30}{12 \times 23} = 0.1087[/tex]
0.1087 = 10.87% probability Sung chose a milk chocolate then a white chocolate.
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What is the probability that the spinner will land on a number greater than 4 or on a shaded section? two-ninths one-half two-thirds five-sixths
The probability that the spinner will land on a number greater than 4 or on a shaded section is 2/3
How to determine the probability?The given parameters are:
Sections = 6Numbers greater than 4 = 2Shaded section = 3Shaded section and greater than 4 = 1Using the above parameters, we have the following probabilities
P(Greater than 4) = 2/6
P(Shaded) = 3/6
P(Shaded section and greater than 4) = 1/6
The required probability is then calculated using:
P = 2/6 + 3/6 - 1/6
Evaluate
P = 4/6
Simplify
P = 2/3
Hence, the probability that the spinner will land on a number greater than 4 or on a shaded section is 2/3
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Beg someone helps me w this question
Answer:
[tex](x+1)^{2} +4[/tex]
a = 1
b = 4
Step-by-step explanation:
hope this helps!! p.s. i really need brainliest :)
Solve the following quadratic equation for all values of x in simplest form.
4(6 — 5x)² + 11 = 20
Answer:
4-20(6x-5x)^2+11
(6-5x)^2=11+(-16)
6^2-10x+25=-5
6^2-10x+20
PLEASE HELP WILL GIVE BRAINLEST! Which trigonometric function does the graph below represent?
Answer:
Answer In this Picture.
quanto é 756 dividido por 63
Answer:
the answer is 12
Step-by-step explanation:
[tex] \frac{756}{63} \\ = 12[/tex]
Type the correct answer in the box. Use numerals instead of words
In circle A. DB has a length 6.47 centimeters. What is m DAB in radians? Round your answer to two decimal places.
2.9 cm B m DAB= radians
I NEED HELP ASAP!
The measure of angle DAB in the circle shown with the given arc length is: 2.23 radians.
What is the Length of an Arc?Arc length = θ × r, where r is the radius of the circle, and θ is the central angle in radians.
Given the following:
Length of arc = 6.47 cm
Radius (r) = 2.9 cm
θ = m∠DAB
Plug in the values into the arc length formula:
6.47 = θ × 2.9
6.47/2.9 = θ
θ = 2.23 radians
m∠DAB = 2.23 radians
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Answer:
DAB = 2.23 radians
Hope this helps!
Step-by-step explanation:
Ms. Lewis is hiring a carpenter to repair her shed. The cost of Carpenter L is shown in the table.
A table titled Carpenter L Costs is shown. It has three columns and two rows. Row one is labeled Hours, h. Row two is labeled Cost, c. One hour, one hundred eighty-seven dollars. Two hours, two hundred fifty-nine dollars. Three hours, three hundred thirty-one dollars.
Part A. What is the initial cost and hourly rate of Carpenter L?
Part B. Write an equation to represent the function shown in the table.
Part C. Carpenter N charges $60 per hour and an additional $195 for the materials needed. What is the difference in cost between Carpenter N and Carpenter L if the repair takes 6 hours?
Enter the correct answers in the boxes.
Answer:
A. $115; $72/hour
B. c = 72h + 115
C. $8
Step-by-step explanation:
Part A.
1 hour: $187
2 hours: $259
2 hours - 1 hour = 1 hour
$259 - $187 = $72
$72/hour
The hourly rate is $72/hour.
Since for the first hour he charges $187, and only $72 comes from the hourly rate, then the initial cost is $187 - $72 = $115.
The initial cost is $115.
Part B.
c = 72h + 115
Part C.
Carpenter L for 6 hours:
c = 72(6) + 115 = 547
$547
Carpenter N for 6 hours:
60(6) + 195 = 555
$555
Difference: $555 - $547 = $8
What is the value of y?
2
5
7
8
What is the solution of x = 2 startroot x minus 2 endroot?
The solution to the function [tex]f(x) = 2\sqrt{x - 2}[/tex] when x = 2 is 0
How to determine the solution?The equation of the function is given as:
[tex]f(x) = 2\sqrt{x - 2}[/tex]
When x = 2, we have:
[tex]f(x) = 2\sqrt{2 - 2}[/tex]
Evaluate the difference
[tex]f(x) = 2\sqrt{0}[/tex]
Evaluate the exponent of 0
f(x) = 2 * 0
Evaluate the product
f(x) = 0
Hence, the solution to the function when x = 2 is 0
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Solve the right triangle. Round all answers to the nearest tenth.
The trigonometric function gives the ratio of different sides of a right-angle triangle. The length of the side KL is 30.81 units.
What are Trigonometric functions?The trigonometric function gives the ratio of different sides of a right-angle triangle.
[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}\\\\\\Cosec \theta=\dfrac{Hypotenuse}{Perpendicular}\\\\\\Sec \theta=\dfrac{Hypotenuse}{Base}\\\\\\Cot \theta=\dfrac{Base}{Perpendicular}\\\\\\[/tex]
where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.
The measure of ∠J can be written as,
Cos(∠J) = JK/JL
Cos(∠J) = 7/31.6
∠J = 77.2°
Similarly the length of side KL can be written as,
Tan(∠J) = KL/JK
Tan(77.2°) = KL/7
KL = 30.81 units
Hence, the length of the side KL is 30.81 units.
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Using the following figure select all statements that are TRUE. (Write the number of the statement and separate them with a comma)
Answer:
3
Step-by-step explanation:
