Answers
2. 44
3. 50
4. 86
5. 44
6. 50
7. 130
8. 50
9. 130
10. 50
11. 86
12. 94
13. 86
14. 94
Remember that the triangle's inner angles should equal 180 for angle 8 and that angles that form a straight line add to 180 as well.
If you would like an explanation for any of these, please comment down below.
Related Questions
Evaluate the following algebraic expressions:1.) 40y-¹, y = 5 2.) 1/m-²(m + 4), m = -8 3.) (p² – 3)-², p = 14.) (x – 1)-² / (x + 1)-², x = 2 5.) y-³ – y-², y = 2
Answers
1. [tex]40y^{-1}, \, y=5.2[/tex]
= 40*y = 40*5.2
= 208
2. [tex] \frac{1}{m^{-2}} (m+4),\, m=-8[/tex]
= m²(m+4)
= (-8)²*(-8+4)
= -256
3. (p² - 3)⁻², p=1
= 1/(p² - 3)²
= 1/(1 - 3)²
= 0.25
4. [tex] \frac{(x-1)^{-2}}{(x+1)^{-2}}, \, x=2.5 [/tex]
[tex]= \frac{(x+1)^{2}}{(x-1)^{2}} [/tex]
= 3.5²/1.5²
= 5.444
5. y⁻³ - y⁻², y=2
= 1/y³ - 1/y²
= 1/8 - 1/4
= -1/8
In the diagram, HGF is a straight line. Given EF = 4 cm and HG = GF = 3 cm, find :
(i) tan x
(ii) sin y
Answers
[tex]tan(x)= \frac{4}{6} = \frac{2}{3}=.6666667 [/tex]
Now use the inverse tan button (2nd-->tan) to get
[tex] tan^{-1} (.66667)=33.69[/tex]
As far as the sin y goes, you have to use the Law of Sines because you are not working with a right triangle in that case. I mean you are as far as having to find out what the hypotenuses are triangle EFH and triangle EFG. The hypotenuse in triangle EFH is 7.211, and the hypotenuse in triangle EFG is 5. Using the Law of Sines to solve for y, you get this:
[tex] \frac{siny}{7.211} = \frac{sin33.69}{5} [/tex]
Solving for y and using the inverse sin gives you that y = 53.12
If you are not familiar with setting up the Law of Sines, nothing I could tell you here would help. If you are familiar, then you get the idea of where the numbers came from and why they are set up that way. Hope that helps. That second part was quite hard.
If [tex] 300cm^{2} [/tex]300 cm of material is available to make a box with a square base and an open top, find the maximum volume of the box in cubic centimeters. Answer to the nearest cubic centimeter without commas. For example, if the answer is 2,000 write 2000.
Answers
[tex]\bf \textit{volume of a rectangular prism}\\\\ V=lwh\quad \begin{cases} l = length\\ w=width\\ h=height\\ -----\\ w=l=x \end{cases}\implies V=xxh\implies \boxed{V=x^2h}\\\\ -------------------------------\\\\ \textit{surface area}\\\\ S=4xh+x^2\implies 300=4xh+x^2\implies \cfrac{300-x^2}{4x}=h \\\\\\ \boxed{\cfrac{75}{x}-\cfrac{x}{4}=h}\\\\ -------------------------------\\\\ V=x^2\left( \cfrac{75}{x}-\cfrac{x}{4} \right)\implies V(x)=75x-\cfrac{1}{4}x^3[/tex]
so.. that'd be the V(x) for such box, now, where is the maximum point at?
[tex]\bf V(x)=75x-\cfrac{1}{4}x^3\implies \cfrac{dV}{dx}=75-\cfrac{3}{4}x^2\implies 0=75-\cfrac{3}{4}x^2 \\\\\\ \cfrac{3}{4}x^2=75\implies 3x^2=300\implies x^2=\cfrac{300}{3}\implies x^2=100 \\\\\\ x=\pm10\impliedby \textit{is a length unit, so we can dismiss -10}\qquad \boxed{x=10}[/tex]
now, let's check if it's a maximum point at 10, by doing a first-derivative test on it. Check the second picture below.
so, the volume will then be at [tex]\bf V(10)=75(10)-\cfrac{1}{4}(10)^3\implies V(10)=500 \ cm^3[/tex]
Which linear function represents the line given by the point-slope equation y + 1 = –3(x – 5)?
Answers
y + 1 = -3x + 15
y = -3x + 15 - 1
y = -3x + 14 <== or f(x) = -3x + 14
Y+1= -3(x+5) in order to solve first write down the function, then find the current of the function.
Y+1=-3x-15 then this is the current of the function. Multiply the -3 times the X and the 5.
Y=-3x-14 finally this is the slope. To get the slope I added the 1 to the -15
Final answer= Y=3x+14
Marisol is making a rectangular wooden frame. She wants the length of the frame to be no more than 12 inches. She has less than 30 inches of wood to use. Which system of inequalities represents the possible length, l, and the possible width, w, that her frame could have?
l ≤ 12
2l + 2w < 30
l > 12
2l + 2w < 30
l ≤ 12
l + w < 30
l > 12
l + w < 30
Answers
2l + 2w < 30
the second and fourth option are saying she can make the length longer than twelve and the third option forgets to double the length and width so it is accurate. The first option is the right answer.
Answer: (A) The first option is the right answer.
Step-by-step explanation:
l ≤ 12
2l + 2w < 30
If a wheel with a radius of 70 inches spins at a rate of 600 revolutions per minute, find the approximate linear velocity in miles per hour.
Answers
ω=600 rev/min=600*2π rad/min=1200 rad/min
v=rω=70*1200π =84,000 in/min
converting the above in miles per hour we get:
84000 in/min
=(84000*1.6*10^(-5)*60)
=80.64 mph
3 on the outside, square root 1/5
Answers
To simplify 1/(5 + √3), multiply both numerator and denominator by the conjugate of the denominator, which is 5 - √3. This results in (5 - √3)/22, which is the simplified form of the expression.
The student has asked to evaluate the expression 1/(5 + √3). To simplify this expression, we can multiply both the numerator and the denominator by the conjugate of the denominator to get rid of the square root in the denominator. The conjugate of 5 + √3 is 5 - √3. So, we multiply the expression by (5 - √3)/(5 - √3).
The resulting expression after multiplication:
Numerator: 1 * (5 - √3) = 5 - √3Denominator: (5 + √3) * (5 - √3) which simplifies to 5² - (√3)² = 25 - 3 = 22
So our final answer after simplification is:
(5 - √3)/22
complete question given below:
Evaluate 1/(5+ square root of 3)
what shows 23^2-17^2 being evaluated using the difference of perfect squares method
Answers
= (23-17)(23+17)
= 6 * 40
= 240
a²-b²=(a-b)(a+b)
so
23²-17²=(23-17)(23+17)=(6)(40)=240
Drive Down is a racing video game. The game gives each player an initial amount of $5,000 in virtual money. After that, a player gets $500 in virtual money for each race won. What function represents the amount of virtual money a player has in terms of the number of races won?
The independent quantity is the , and the dependent quantity is the _________ and the dependent quantity is the _________ The function representing the situation is _________
Answers
dependent quantity f(x)...or y is total virtual money
the function is : f(x) = 500x + 5000 or y = 500x + 5000
Answer:
The game gives each player an initial amount of $5,000 in virtual money. After that, a player gets $500 in virtual money for each race won. This $5000 is fixed.
Let the races won be x
So, the function that represents the amount of virtual money a player has in terms of the number of races won becomes :
[tex]f(x)=500x+5000[/tex]
The independent quantity (x) is : the number of races won
And the dependent quantity f(x) or y is : the total virtual money earned
Determine the slope and y-intercept of the line.
y = 5x + 4
a.
Slope = 4, y-intercept is (0, 5)
c.
Slope = 5, y-intercept is (0, 4)
b.
Slope = -5, y-intercept is (0, 4)
d.
Slope = 4, y-intercept is (0, -5)
Please select the best answer from the choices provided
A
B
Answers
The answer would be C. Slope = 5, y-intercept is (0,4)
Answer:
D
Step-by-step explanation:
Correct on A P E X
A 45 gram sample of a substance that's used to preserve fruit and vegetables has a k-value of 0.1109.
Find the substances half-life in days. Round your answer to the nearest tenth.
Answers
N(t) = N₀ exp(-kt)
where
N₀ = 45 g, original mass
N(t) = mass after time t, days
k = 0.1109, the decay constant.
At half life, N(t) = (1/2)*N₀. Therefore
1/2 = exp(-0.1109t)
Take natural log of each side.
ln(0.5) = -0.1109t
t = ln(0.5)/(-0.1109) = 6.25 days
Answer: 6.3 days (nearest tenth)
N(t) = N₀ exp(-kt)
where
N₀ = 45 g, original mass
N(t) = mass after time t, days
k = 0.1109, the decay constant.
At half life, N(t) = (1/2)*N₀. Therefore
1/2 = exp(-0.1109t)
Take natural log of each side.
ln(0.5) = -0.1109t
t = ln(0.5)/(-0.1109) = 6.25 days
Answer: 6.3 days (nearest tenth)
Sandra calculated the missing side length of one of these triangles using the Pythagorean Theorem. Which triangle is it?
A
B
C
D
Answers
NEED HELP!!!!!!!!!!!!!!!!!!!!!
Answers
Here, a=1, b=13, and c=30.
The only option that fills in the values correctly is D
if the apothem is 6.9 mm and a side length is 8 mm what is the area of the hexagon
Answers
draw it and draw lines from each corner to every other corner... you're left with 6 triangles
work out the area of one of these triangles from your question... area of hexagon = 6 x area of a triangle
how much would $140 invested at 6% interest compounded monthly be worth after 15 years? round your answer to the nearest cent
Answers
The principle amount of $140 invested at a 6% rate of interest compounded monthly be worth after 15 years will be $340.
What is compound interest?Compound interests are those interests where the principle amount always going to change.
For example, if you give $100 to anyone with 5% interest monthly then at the end of your month your value becomes $105 and this will become the principal amount.
Given that the principal amount is $140
P = $140
The rate of interest is 6%
r = 6%
Number of time period 15 years
t = 15
Now by compounding interest formula
A = [tex][1+r/100]^{t}[/tex]
By putting all value we get
A = [tex][1 + 6/100]^{15}[/tex]
A = $340 hence, $340 will be the total amount after 15 years.
For more information about compound interest.
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What is the simplified form of the quantity of x plus 9, all over the quantity of x plus 1 + the quantity of x minus 2, all over 5
the quantity of x squared plus 4x plus 43, all over 5 times the quantity of x plus 1
the quantity of x squared plus 7x minus 18, all over 5 times the quantity of x plus 1
the quantity of x squared plus 7x minus 18, all over the quantity of x plus 6
the quantity of x squared plus 4x plus 43, all over the quantity of x plus 6
Answers
------ + ------
x + 1 5
LCD = 5(x + 1) so we have
5(x + 9) + (x - 2)(x + 1)
------------------------------
5(x + 1)
= 5x + 45 + x^2 - x - 2
--------------------------
5(x + 1)
= x^2 + 4x + 43
------------------
5(x + 1)
That is A
Answer:
= x^2 + 4x + 43
------------------
5(x + 1)
Step-by-step explanation:
A function is shown in the table.
x g(x)
−2 2
−1 −3
0 2
1 17
Which of the following is a true statement for this function?
a. The function is increasing from x = −2 to x = −1.
b. The function is increasing from x = 0 to x = 1.
c. The function is decreasing from x = −1 to x = 0.
d. The function is decreasing from x = 0 to x = 1.
Answers
Only one statement is correct:
B ) The function is increasing from x = 0 to x = 1
Explanation: g ( 0 ) = 2, g ( 1 ) = 17, 2 < 17.
Determine the type and number of solutions of 6x^2-7x-4=0
A. One real solution
B. Two real solution
C. Two imaginary solutions
D. One real solution and one imaginary solution
Answers
How many corners does a cube have? how many faces does a cube have? how many other cubes would share a given corner atom or face atom if several cubes were stacked side-to-side, front-to-back, and top-to-bottom?
Answers
A cube is a 3-dimensional solid figure made by square faces. It would have 8 corners which connects the faces of the cube.
how many faces does a cube have?
There would be 6 faces in a cube
how many other cubes would share a given corner atom or face atom if several cubes were stacked side-to-side, front-to-back, and top-to-bottom?
If several of these cubes are being stacked side-to-side, front-to-back, and top-to-bottom, each corner would share a total of eight cubes. All of the corners would share a different cube. We have eight corners thus eight cubes.
a basketball coach is purchasing 12 shirts for her team, each with a different number. at the checkout counter the clerk places 5 of the shirts in the first bag. how many different ways can a group of 5 shirts be placed in that first bag
Answers
12 * 5
Answer:
792 ways
Step-by-step explanation:
What is a rule that describes the translation ABCD ⇒A' B' C' D'?
A. T <3,-2> (ABCD)
B. T <3,2> (ABCD)
C. T <2,-3> (ABCD)
D. T<-3,2> (ABCD)
A. IS WRONG
Answers
* step 1) move 3 units to the left
* step 2) move 2 units up
The movement in step 1 means x becomes x-3
The movement in step 2 means y becomes y+2
Put this together and (x,y) turns into (x-3, y+2)
That's the same as writing T<-3, 2> as choice D is saying
Answer: Choice D
Final answer:
The question seeks the correct translation rule for the movement of quadrilateral ABCD to A'B'C'D'. Translation in geometry involves moving a shape in a consistent direction and distance. Given option A is incorrect, and considering directionality, T <-3,2> (ABCD) is another possibility for the translation.
Explanation:
The question asks for the rule that describes the translation of quadrilateral ABCD to A'B'C'D'. A translation in geometry is a type of transformation that moves every point of a shape the same distance in the same direction. Since option A, which is T <3,-2> (ABCD), is given as incorrect, let's analyze the remaining options.
To determine the correct rule for translation, we need to look at the relative position of the original points and their corresponding points after the translation. For example, if point A were at (x,y) and A' is at (x+3, y-2), this would correspond to a translation of 3 units to the right and 2 units down, which is described by the vector <3, -2>.
Since option A is incorrect and we know that the transformation corresponds to a translation and not a reflection or rotation, let's consider the other options. Looking at option D, T <-3,2> (ABCD), this would imply that every point of quadrilateral ABCD is moved 3 units to the left (because of -3) and 2 units up (because of 2), which would be the reverse of what is described in option A.
Find the missing terms in the following geometric sequence. -12,__,__, -324
Answers
-324/-12=(ar^4)/(ar^1)
27=r^3
3=r
-12=a(3^1)
-12=3a
-4=a
y=-4(3^n)
y(2)=-36
y(3)=-108
Answer:
The nth term for the geometric sequence is given by:
[tex]a_n = a_1 \cdot r^{n-1}[/tex]
where,
[tex]a_1[/tex] is the first term
r is the common ratio of the terms.
As per the statement:
Given the sequence
-12,__,__, -324
here, [tex]a_1 = -12[/tex] and [tex]a_4 = -324[/tex]
Solve for r:
By definition we have;
[tex]a_4 = a_1 \cdot r^3[/tex]
⇒[tex]-324 = -12 \cdot r^3[/tex]
Divide both sides by -12 we have;
[tex]27 = r^3[/tex]
⇒[tex]r = \sqrt[3]{27} =\sqrt[3]{3^3} = 3[/tex]
We have to find the missing terms [tex]a_2, a_3[/tex]
[tex]a_2=a_1 \cdot r[/tex]
⇒[tex]a_2 = -12 \cdot 3 = -36[/tex]
[tex]a_3=a_1 \cdot r^2[/tex]
⇒[tex]a_2 = -12 \cdot 3^2 = -12 \cdot 9 = -108[/tex]
therefore, the missing terms in the following geometric sequence is,
-12,_-36_,_-108_, -324
The area (A) of a circle with a radius of r is given by the formula A=pier^2 and its diameter (d) is given by d=2r. Arrange the equations in the correct sequence to rewrite the formula for diameter in terms of the area of the circle.
Answers
Final answer:
The diameter d of a circle can be expressed in terms of the area A by first solving the area formula A = πr^2 for r, giving r = √(A/π), and then substituting r into the diameter formula d = 2r, resulting in d = 2√(A/π).
Explanation:
To rewrite the formula for the diameter of a circle in terms of the area, we start with the given formula for area A = πr^2 and the equation for diameter d = 2r. Our aim is to express the diameter d solely in terms of the area A. To achieve this, we rearrange the area formula to solve for the radius r:
A = πr^2r^2 = A/πr = √(A/π)Then, we substitute r into the diameter formula:
d = 2rd = 2√(A/π)Thus, the diameter d can be expressed in terms of the area A as d = 2√(A/π).
In which quadrant is sin positive and tan positive?
Answers
Sin corresponds to the y-value, so sin would be positive at Quadrants 1 and 2.
Tan, which is y/x (sin/cos), is positive at Quadrants 1 and 3.
So at quadrant 1 is where both sin and tan are positive.
Linear Function Graph. Express it in slope intercept form.
Answers
I'm basing this off the points (0,-4) and (3,-3)
Of a group of students 5/8 of them are boys. The girls are put into groups so that each group has 1/6 of the total number of students. How many groups of girls are there?
Answers
In winter, the temperature in northern Wisconsin can be quite cold. When Lauren woke up this morning (6:00am) the temperature outside was -18°F. When she got home from school (4:00pm) the tempature outside was 4°F. What was the change in temperature from 6:00 am to 4:00 pm?
Answers
1 over 111 as a decimal
Answers
what is the sum of the geometric sequence -3, 18, -108,... if there are 7 terms?
Answers
Sn=a(1-r^n)/(1-r)
from our sequence;
a=-3
r=-108/18=-6
n=7
thus the sum of the 7 terms will be:
S7=-3(1-(-6)^7)/(1-(-6))
S7=-3(1+279936)/(1+6)
S7=-3(279937)/7
S7=-119,973
the answer is -119,973
In your own words, define each of the following terms. a. Whole number b. Digit c. Place value d. Rounded number e. Equals
Answers
The following terms are defined below:
a. Whole number, b. Digit, c. Place value, d. Rounded number, and e. Equals.
a. Whole Number: A whole number is a positive integer not having any fractional or decimal parts. Whole numbers include the set of natural numbers(non-negative integers) along with zero.
b. Digit: A digit, in mathematics, means any of the numerical symbols used to denote numbers in the decimal numeral system.
c. Place value: Place values are the values of a digit in a number based on its position or place within that number. Based on powers of ten, in the decimal numeral system, each digit's position determines its place value.
d. Rounded number: An approximation of a numerical value having been adjusted or approximated to a certain level of precision or a specific place value is called a "rounded number".
e. Equals: Mathematically, the term "equals" is utilized to represent that two quantities or expressions have the same value. The equals sign (=) is a symbol used to indicate equality between two mathematical expressions.
Thus, the above terms are defined.
Learn more about whole numbers here:
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Final answer:
Whole numbers are counting numbers without fractions or decimals, digits are symbols used to represent numbers, place value is the value of a digit based on its position, a rounded number is simplified for ease of use, and equals shows that two quantities have the same value.
Explanation:
In the field of mathematics, the terms mentioned refer to basic concepts essential for understanding numbers and arithmetic operations.
a. Whole number
Whole numbers are the basic counting numbers starting from 0 and including all positive integers (1, 2, 3, ...). They do not include fractions, decimals, or negative numbers.
b. Digit
A digit is any one of the ten symbols used to write numbers. These symbols are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
c. Place value
Place value refers to the value of a digit based on its position in a number. For instance, in the number 231.45, the place value of the digit '3' is tens, meaning it represents thirty.
d. Rounded number
A rounded number has been altered to a nearby, often simpler number. Rounding is done to make numbers easier to work with, especially when precision is not crucial.
e. Equals
The term 'equals' is used to signify that two quantities are the same in value, often represented by the symbol '='.