Answer:
hypotenuse = 20
leg = x + 4
other leg = x
From the Pythagorean Theorem we know that
20^2 = (x + 4)^2 + x^2
400 = x^2 + 8x + 16 + x^2
2 x^2 + 8x -384 = 0
Solving the quadratic equation we get
x = 12 and x = -16
x = 12 and so the lengths of the 2 legs are:
12 and 16
Right Triangle Area = (leg1 * leg2) / 2
Right Triangle Area = (12 * 16) / 2
Area = 192 / 2
Area = 96 square centimeters
Step-by-step explanation:
To find the area of the triangle, we used the Pythagorean theorem to solve for the legs, obtaining lengths of 16 cm and 12 cm. The area is then calculated using the formula for the area of a right triangle (1/2 * base * height), resulting in an area of 96 cm².
We are given a right triangle with a hypotenuse of 20 cm and two legs where one leg (let's call it a) is 4 cm longer than the other leg (let's call it b). Using the Pythagorean theorem, we can express the relationship between the legs and the hypotenuse: a² + b² = 20². We know that a = b + 4, so if we substitute a into the equation, we get:
(b + 4)² + b² = 400
b² + 8b + 16 + b2 = 400
2b² + 8b - 384 = 0
Dividing everything by 2, we get:
b² + 4b - 192 = 0
Using the quadratic formula or factoring, we find that b = 12 (b can't be negative). Consequently, a = 16. The area of the triangle is given by 1/2 * base * height, which is:
Area = 1/2 * a * b
Area = 1/2 * 16 * 12
Area = 1/2 * 192
Area = 96 cm²
work out the area of the rectangle
Answer:
48 cm²
Step-by-step explanation:
Let's call the width and height of the rectangle w and h.
w / h = 3 / 4
2w + 2h = 28
Solve the system of equations with substitution.
w = 3/4 h
2 (3/4 h) + 2h = 28
3/2 h + 2h = 28
7/2 h = 28
h = 8 cm
So the width is:
w = 3/4 (8)
w = 6 cm
So the area is:
A = wh
A = 48 cm²
Solve 65x = 20.
Round to the nearest ten-thousandth.
Answer:
I think it's 0.30
Step-by-step explanation:
17. Which of the following is the correct formula for finding power in a DC circuit? A. P = I2R B. P = VR C. P = IR D. P = V2I
Answer:
Choice A. P = I² · R where
P is the power in the DC circuit,I is the current through the circuit, andR is the total resistance of the circuit.Step-by-step explanation:
Electrical power is the rate at which the electrical force does work. So what is electrical work? That's the work [tex]W[/tex] that the electrical force do when it moves charges [tex]Q[/tex] across a potential difference [tex]V[/tex]:
W = [tex]V\cdot Q[/tex].
The power is the rate at which the electrical force do the work:
[tex]\displaystyle P = \frac{W}{t} = V \cdot \frac{Q}{t}[/tex].
On the other hand, current [tex]I[/tex] is the charge through a cross-section of the circuit in unit time. By the definition of current:
[tex]\displaystyle\frac{Q}{t} = I[/tex].
[tex]\displaystyle P =V \cdot \frac{Q}{t} = V\cdot I[/tex].
Consider Ohm's Law:
[tex]V = I \cdot R[/tex].
Therefore
[tex]\displaystyle P = V\cdot I = (I \cdot R) \cdot I = I^{2}\cdot R[/tex].
Choice-A is one of several useful, correct formulas for electrical power. It's true in AC circuits as well as DC ones.
The volume of a sphere is 2 comma 143.57 m cubed. To the nearest meter, what is the radius of the sphere? Use 3.14 for pi.
[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\ \cline{1-1} V=2,143.57 \end{cases}\implies 2143.57=\cfrac{4\pi r^3}{3}\implies 6430.71=4\pi r^3 \\\\\\ \cfrac{6430.71}{4\pi }=r^3\implies \sqrt[3]{\cfrac{6430.71}{4\pi }}=r\implies \stackrel{\pi =3.14}{7.9999956 \approx r}\implies \stackrel{\textit{rounded up}}{8=r}[/tex]
drag the tiles to the boxes to form the correct pairs. not all tiles will be used.
Expand or factor each of the following expressions to determine which expressions are equivalent.
Answer:
[tex]9x^{2}+3x-20=(3x+5)(3x-4)[/tex]
Step-by-step explanation:
We need to drag the tiles and place them in boxes to form the correct pairs.
The given options are:-
1) [tex]9x^{2}+3x-20[/tex]
2) [tex](4x-3y)^{2}[/tex]
3) [tex](3x+5)(3x-4)[/tex]
4)[tex](3x+2)(9x^{2} -6x+4)[/tex]
First we simplify the all given factor and then compare with provided options
2) [tex](4x-3y)^{2}[/tex]
=[tex]16x^{2}+9y^{2}-24xy[/tex]
3) [tex](3x+5)(3x-4)[/tex]
[tex]9x^{2}-12x+15x-20[/tex]
[tex]9x^{2}+3x-20[/tex]
Here we can see equation (3) match with (1)
so, [tex]9x^{2}+3x-20=(3x+5)(3x-4)[/tex]
Hence, the correct match is shown in figure-1
The expressions that are equivalent should be matched as follows;
9x² + 3x - 20 ↔ (3x + 5)(3x - 4)
How to match the equivalent expressions?In order to match the equivalent expressions, we would have to either expand or factor each of the given expressions as follows;
9x² + 3x - 20
By applying the sum-product pattern, we have:
9x² + 15x - 12x - 20
By writing the common factor from the two pairs, we have:
(9x² + 15x) + (-12x - 20)
3x(3x + 5) - 4(3x + 5)
(3x + 5)(3x - 4)
Next, we would expand the expression (4x - 3y)²;
(4x - 3y)(4x - 3y)
16x² - 12xy - 12xy + 9y²
16x² - 24xy + 9y²
9y² - 24xy + 16x²
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In the pulley system shown in this figure, MQ = 30 mm, NP = 10 mm, and QP = 21 mm. Find MN.
MN is 63 mm.
Since triangles MPQ and NQP are similar, we have the following
proportion:
[tex]\frac{MQ}{NP} = \frac{QP}{MN}[/tex]
Substituting the given values, we have:
[tex]\frac{30}{10} = \frac{21}{MN}[/tex]
Solving for MN, we get:
[tex]MN = \frac{21 \times 30}{10} = 63 mm[/tex]
Therefore, MN is 63 mm.
What is the range of the function f(x) = 3x^2 + 6x - 8?
R; all quadratic functions are going to have ranges and domains of *ALL REAL NUMBERS*.
What is the value of s in the figure below?
The value of 's' is calculated using the formula s = re, where e is the angle in radians and r is the radius in meters, which can also be determined statistically.
Explanation:The value of s in the given physics problem represents the distance between two objects separated by an angle, when they are a certain distance r apart. According to the information and by using the formula s = re, where e is the angle in radians and r is the radius in meters (converted from millimeters), we can substitute the known values to find s. Since S = 80×109 N/m² is the shear modulus and given the small value of Kåp, we assume that s will be significantly small compared to 0.040. Additionally, the value of s can also be found using statistical methods, as indicated by a computer or calculator output showing s = 16.4 as the standard deviation in a set of residuals.
Which of the following statements would be the reason in line 4 of the proof?
A.) Definition of supplementary
B.) Two <'s supplementary to equal <'s are =
C.) Substitution
Answer:Two <‘s supplementary to equal <‘are=
I got this correct on Odyssey:)
Answer:
Option B.
Step-by-step explanation:
∠1 and ∠3 are supplementary and ∠2 and ∠4 are supplementary.
Because they are exterior sides in opposite rays.
In other words ∠1 + ∠3 = 180° and ∠2 + ∠4 = 180°
and it is given that ∠1 ≅ ∠2
So ∠3 ≅ ∠4
Since Two angles supplementary to equal angles are equal will be the reason.
Option B is the correct option.
The volume of box A is 2/5 the volume of box b. What is the height of box A if it has a base area 32 square centimeters
The length of the edge of the bases is x = 4 and x=1.79.
What is the volume of the box?The volume of a rectangular box can be calculated if you know its three dimensions: width, length, and height.
The volume of a box with a square base and a height of 2 cm is 32cm for box A and the volume of a box with a square base and a height of 10cm is 32cm.
What is the length of the edge of the bases?
The volume of the box = length × width × height
Therefore, we are going to make use of Equation (1) to determine the solution to this question, so that we have;
For Box A; We are given our volume to be equal to 32cm^3, height = 2cm, length and width = x cm.
For Box B IS;
[tex]\rm 32 = 2x^2\\\\x^2 = 16\\\\x^2=4^2\\\\x=4[/tex]
Here Length = width.
For box B;
[tex]\rm 32 = 10x^2\\\\x^2=\dfrac{32}{10}\\\\x^2=3.2\\\\x=1.79[/tex]
Hence, the length of the edge of the bases is x = 4 and x=1.79.
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The Greatest common factor between 14 and 24
The greatest common factor between 14 and 24 is 2 because
The factors of 14 that divides 14 without a remainder are 1,2, and 7
The factors of 24 that divides 14 without a remainder are 1,2,3,4,6,8,and 12
Therefore 2 is the greatest factor between 14 and 24.
For this case we have that by definition, the Greatest Common Factor or GFC of two numbers is given by the biggest factor that divides both without leaving residue. We should look for the GFC of 14 and 24.
14: 1,2,7,14
24: 1,2,3,4,6,8,12,24
Thus, it is observed that the GFC of both numbers is 2.
Answer:
2
A. 3
B. 5
C.9
D. 15
Answer: 15
Step-by-step explanation
Answer:
3Step-by-step explanation:
[tex]\underline{+\left\{\begin{array}{ccc}2x+3y=9\\-2x+2y=6\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad5y=15\qquad\text{divide both sides by 5}\\.\qquad\qquad\boxed{y=3}[/tex]
Suppose y varies jointly as x and z. Find y when x = 5 and z = 16, if y = 136 when x = 5 and z = 8. Round your answer to the nearest hundredth, if necessary.
Answer:
The value of y when x = 5 and z = 16 is 272
Step-by-step explanation:
* Lets Talk about the direct variation
- y is varies jointly (directly) as x and z, that means there are direct
relation between y , x and z
- y increases if x increases or z increases
∴ y ∝ x × z
- To change this relation to equation we use a constant k
∴ y = k (x) (z), where k is the constant of variation
- To find the value of k we substitute the values of x , y and z in
the equation above
∵ y = 136 when x = 5 and z = 8
∴ 136 = k × 5 × 8
∴ 136 = 40 k ⇒ divide both sides by 40
∴ k = 3.4
- Substitute this value in the equation
∴ y = 3.4 (x) (z)
∵ x = 5 , z = 16
∴ y = 3.4 (5) (16) = 272
∴ The value of y when x = 5 and z = 16 is 272
Answer:
The correct answer is B.
Step-by-step explanation:
If y varies jointly as x and z, then we can write the join variation equation.
[tex]y=kxz[/tex], where 'k' is the constant of proportionality.
If y = 136 when x = 5 and z = 8,then
[tex]136=k(5)(8)[/tex],
[tex]\implies 136=40k[/tex]
[tex]\implies \frac{136}{40}=k[/tex]
[tex]\implies \frac{17}{5}=k[/tex].
The variation equation now becomes:
[tex]y=\frac{17}{5}xz[/tex]
when x = 5 and z = 16, then
[tex]y=\frac{17}{5}(5)(16)[/tex]
[tex]y=17(16)[/tex]
[tex]y=272[/tex]
The correct answer is B.
what happens when you move a decimal point left or right?
Answer:
when you move a decimal point to the left you are increasing the number
when you move a decimal to the right you are decreasing the number
The lateral area of a right cylinder which has a base diameter of 12 cm and a height of 8 cm is?
Answer:
[tex]A = 301.59\ cm^2[/tex] or [tex]A=96\pi\ cm^2[/tex]
Step-by-step explanation:
The lateral area of a cylinder is calculated by the following formula
[tex]A = 2\pi r * h.[/tex]
Where r is the radius of the right cylinder and h is the height
In this case we know that the diameter d of the cylinder is
[tex]d=2r\\\\r=\frac{d}{2}\\\\r=\frac{12}{2}\\\\r=6\ cm[/tex]
[tex]h=8\ cm[/tex]
Therefore the lateral area is:
[tex]A = 2\pi*6 * 8.[/tex]
[tex]A = 96\pi[/tex]
[tex]A = 301.59\ cm^2[/tex]
Answer:
The lateral area of a right cylinder = 96π cm²
Step-by-step explanation:
Points to remember
The lateral area of a right cylinder = 2πrh
Where r - Radius of cone and
h - Height of cone
To find the lateral surface area
Here diameter d = 12 cm
then radius r = d/2 = 12/2 = 6 cm
And h = 8 cm
Lateral surface area = 2πrh
= 2 * π *6 * 8 = 96π cm²
Therefore the lateral area of a right cylinder = 96π cm²
A 254–foot tall radio tower is located partway between a building and a tree. The angle of elevation from the base of the building to the top of the tower is 36°, and the angle of elevation from the base of the tree to the top of the tower is 62°. What is the distance from the base of the building to the base of the tree (rounded to the nearest foot)?
Answer:
485 ft
Step-by-step explanation:
step 1
Find the distance from the base of the building to the base of the radio tower
Let
x -----> the distance from the base of the building to the base of the radio
we know that
tan(36°)=254/x
x=254/tan(36°)=349.60 ft
step 2
Find the distance from the base of the tree to the base of the radio tower
Let
x -----> the distance from the base of the tree to the base of the radio tower
we know that
tan(62°)=254/x
x=254/tan(62°)=135.05 ft
step 3
Find the distance from the base of the building to the base of the tree
Adds the distances
349.60 ft+135.05 ft=484.65 ft
Round to the nearest foot
484.65 ft=485 ft
The final distance is approximately 485 feet.
Calculating the Distance from the Building to the Tree
To determine the distance from the base of the building to the base of the tree given the angles of elevation to the top of the radio tower, we can use trigonometry.
Let the height of the radio tower be 254 feet. Assume the distance from the base of the building to the base of the tower is x feet, and the distance from the base of the tree to the base of the tower is y feet.
Step-by-Step Solution:
Using the angle of elevation from the building, 36°, we can write:
tan(36°) = 254 ÷ x
Solving for x: x = 254 / tan(36°)
Using the angle of elevation from the tree, 62°, we can write:
tan(62°) = 254 ÷ y
Solving for y: y = 254 / tan(62°)
Calculate the values:
tan(36°) ≈ 0.7265
x = 254 / 0.7265 ≈ 349.6 feet.
tan(62°) ≈ 1.8807
y = 254 ÷ 1.8807 ≈ 135.1 feet.
The total distance from the base of the building to the base of the tree is x + y:
Total distance = 349.6 + 135.1 ≈ 485 feet.
Thus, the distance from the base of the building to the base of the tree is approximately 485 feet.
A function of the form f(x)=ab^x is called an exponential ___________function, when b is greater than 1
A function of the form f(x)=ab^x is called an exponential exponential growth function, when b is greater than 1
What is an exponential function?
An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
It is a relation of the form y = aˣ in mathematics, where x is the independent variable.
It is given the exponential function :
f(x) = abˣ and b>1
Therefore, If the base (b) is greater than one is called an exponential growth, if it smaller than one it called an exponential decay.
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What is the scale factor from figure A to figure B?
Answer:
Figure A sides are 1/4 the size of Figure B
The top of Figure A = 4, the top of Figure B = 1.
Divide 1 by 4 to get the scale factor, which is 1/4 as a fraction or 0.25 as a decimal.
Step-by-step explanation:
True or false: When it's argument is restricted to (0,2pi), the polar form of a complex number is *not unique*.
Answer:
The CORRECT answer is False
Step-by-step explanation:
I just took the test and got it correct!!
cos x + i sin x in the range 0 to 2pi will be unique so false.
What do you mean by complex number?Complex numbers exist the numbers that exist expressed in the form of a+ib where, a, and b are real numbers, and 'i' exists an imaginary number named “iota”. The value of i = (√-1).
The abbreviated polar form of a complex number exists z = rcis θ, where r = √(x2 + y2) and θ = tan-1 (y/x).
The range is the difference between the highest and lowest values in a set of numbers. To find it, subtract the lowest number in the distribution from the highest.
The range in statistics for a given data set is the difference between the highest and lowest values. For example, if the given data set is {2,5,8,10,3}, then the range will be 10 – 2 = 8. Thus, the range could also be defined as the difference between the highest observation and lowest observation.
Hence, cos x + i sin x in the range 0 to 2pi will be unique so false.
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The square of the sum of two consecutive positive even integers is 4048 more than the sum of the squares of these two numbers. Find the two numbers.
Answer:
44, 46
Step-by-step explanation:
The integers are both even, so if the smaller one is x, then the larger one is x+2.
Therefore:
((x) + (x+2))² = 4048 + (x)² + (x+2)²
(2x + 2)² = 4048 + x² + x² + 4x + 4
4x² + 8x + 4 = 2x² + 4x + 4052
2x² + 4x - 4048 = 0
x² + 2x - 2024 = 0
(x + 46) (x - 44) = 0
x = -4+, 44
Since x must be positive, x = 44. And x+2 = 46. So the numbers are 44 and 46.
Let's check:
(44 + 46)² = 8100
4048 + 44² + 46² = 8100
Help with this, thanks.
Answer:
The first blank is "y", the second blank is "x", and the third blank is 1:3.
Which of the following statements are true?
1. The difference between -14 and -8.3 is positive.
II. -14 + 8.3 has the same value as the difference between -1.4 and -8.3.
HII. The between -8.3 and -14 has the same value as the difference between -1.4 and -8.3.
É
only
A of the statements are true.
None of the statements are true
Answer:
None of the statements are true
Step-by-step explanation:
Given statements are:
I. The difference between -14 and -8.3 is positive.
II. -14 + 8.3 has the same value as the difference between -1.4 and -8.3.
III. The between -8.3 and -14 has the same value as the difference between -1.4 and -8.3.
Test for statement (I).
difference = -14-(-8.3) = -14+8.3 = -5.7
which is negative so statement I is FALSE.
Test for statement (II).
-14+8.3 = 5.7
difference = -14-(-8.3) = -14+8.3 = -5.7
which are different so statement II is FALSE.
Test for statement (III).
difference = -8.3-(-14) = -8.3+14 = 5.7
which is different than difference value -5.7 for statement I.
so statement III is FALSE.
So the correct choice is "None of the statements are true".
Please help me with this. I want to get an A
Answer:
Question 1: x = 3
Question 2: x = -4
Question 3: x = -2
13: x=3
14: x=-4
15: x=-2
All I did was use an calculator to find out the missing variables or u could have just put all the answer chooses in it and see which one is right.
Zero is _____ a divisor.
a.always
b.sometimes
c.never
ANSWER
c. never
EXPLANATION
When we have
[tex]\frac{a}{b}[/tex] in mathematics, we call b the divisor.
In mathematics, division by zero is not defined.
We cannot divide a function, or a number by zero and get a value.
That is why, there is the restriction, b≠0
Therefore, zero is never a divisor.
The correct answer is C
How many defective telephones
Answer:
Option 3: 300 phones
Step-by-step explanation:
Given
Phone produces each day: 1000
Number of phones that were checked = 30
Defective phones = 9
So the probability of defective phones will be calculated by dividing the number of defective phones by total number of phones checked.
So, the probability of defective phones
= 9/30
= 0.3 or 30%
So, from 1000 phones the defective phones will be:
1000*0.3
= 300 Phones ..
The table shows the estimated number of lines of code written by computer programmers per hour when x people are working.
Need the table, please include an attachment!
Answer:
(C) Y=26.9x-1.3 is the answer
Step-by-step explanation:
Which of the following points satisfies the inequality 2x - 3y < 1?
(-2, 1)
(, 0)
(2, -1)
I'm not sure about the second point you posted, but I believe the answer is (-2, 1). Here is my work:
Answer:-2,1
Step-by-step explanation:
Jared has two ropes. Each rope is 9 inches long. How many inches of rope does he have in all?
Answer:
18 Inches total of rope
Step-by-step explanation:
9+9=18
or
9 x 2 = 18
You can do this two ways:
1. You can multiply 9 (how long the rope is) by 2 (how many ropes you have. so...
length of rope * number of ropes
9 * 2 = 18
2. Or you can add 9 plus nine together and it will give you the same answer. so...
9 + 9 = 18
Hope this helped!
Multiply or divide as indicated. x^-8 • x^-2
ANSWER
[tex]\frac{1}{ {x}^{10} }[/tex]
EXPLANATION
The given exponentiial expression is
[tex] {x}^{ - 8} \bullet {x}^{ - 2} [/tex]
We simplify using the rule:
[tex] {a}^{m} \times {a}^{n} = {a}^{m + n} [/tex]
We apply this property to get:
[tex]{x}^{ - 8} \bullet {x}^{ - 2} = {x}^{ - 8 + - 2}[/tex]
We simplify to get;
[tex]{x}^{ - 8} \bullet {x}^{ - 2} = {x}^{ - 10}[/tex]
We rewrite as a positive index to get;
[tex]{x}^{ - 8} \bullet {x}^{ - 2} = \frac{1}{ {x}^{10} } [/tex]
What are the zeros of the function? f(x)=3x^2−24x+36 Enter your answers in the boxes. The zeros of f(x) are and
[tex]
f(x)=3x^2-24x+36 \\
0=3(x-2)(x-6) \\
0=(x-2)(x-6)
[/tex]
There will be 2 solutions.
[tex]
x-2=0\Longrightarrow\boxed{x_1=2} \\
x-6=0\Longrightarrow\boxed{x_2=6}
[/tex]
Hope this helps.
r3t40
The zeros of the function f(x) = 3x^2 - 24x + 36 are found using the quadratic formula to be x = 6 and x = 2.
The zeros of the function f(x) = 3x2 \- 24x + 36 are the values of x for which f(x) equals zero. To find the zeros, we set the quadratic equation equal to zero and solve for x. This can be done using the quadratic formula x = (-b \\pm (sqrt{b2 \(- 4ac})/(2a), where a = 3, b = -24, and c = 36. Applying the quadratic formula:
Calculate the discriminant: \(( -24 )2 \- 4 * 3 * 36 = 576 \- 432 = 144)Take the square root of the discriminant: \sqrt{144} = 12Apply the values to the quadratic formula: \x = (24 \pm 12) / 6Solve for the two possible values of x: \x = 6, \x = 2Therefore, the zeros of the function are x = 6 and x = 2.