Answer:
Following are the solution to the question:
Step-by-step explanation:
[tex]Radius= 3\\\\center= (-4,4,1)\\\\x(t)=-4\\\\y(t)=4+3 \cos \ t\\\\z(t)= 1+ 3 \sin \ t[/tex]
What's the solution set of –4x + 1 ≤ 9 or x∕5 + 2 < 3?
Question 3 options:
A)
All real numbers
B)
x ≥ –2 or x < 5
C)
2 ≤ x < 5
D)
There is no solution.
Answer:
B) x ≥ –2 or x < 5
Step-by-step explanation:
We can immediately rule out A) All real numbers, since that will almost never be true for an inequality like this. We can also rule out C) 2 ≤ x < 5, since this is not a compound inequality.
Let's see if B) x ≥ –2 or x < 5 works by plugging in an x value greater than -2 and then, plugging in an x value less than 5.
Plug -1 into x
–4(-1) + 1 ≤ 9
4 + 1 ≤ 9
Combine like terms
5 ≤ 9
This is true, 5 is less than 9, so x ≥ –2 works.
Plug 4 into x
4∕5 + 2 < 3
Combine like terms
2.8 < 3
This is true, 2.8 is less than 3.
It can't be D) no solution now that B works, so B) x ≥ –2 or x < 5 is your answer.
Take care and Have a lovely rest of your day! :)
Give 5 different names for this line.
Answer:
post a pic, OP, to get specific answer
Step-by-step explanation:
You can use any two points, usually uppercase letters, that are on the line, in any order. Also, lines are named with a single script or italicized lowercase letter that is written beside one end of the line. See image for example.
if the m P=4x+1 and m Q=9x-3, find m Q
Answer:
4×9=36
1-3=-2
36÷2=18
Step-by-step explanation:
4×+1,9×-1.
4×9=36
1-3=-2
Show (3 steps) that the function is either continuous or discontinuous at the given value of x
1. f(x) = 1/x at x = 3
2. f(x) = |x+1|/x at x = 2
3. f(x)= [x] at x = 2
Using the continuity concept, the functions are classified as follows:
1) Continuous.
2) Continuous.
3) Discontinuous.
What is the continuity concept?A function f(x) is continuous at x = a if it is defined at x = a, and:
[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]
For functions 1 and 2, the functions are given by simple definitions, hence they are continuous, the limits and the numeric value will al be equal.
In item 3, the function will be discontinuous. This is because the function [x] returns the greatest integer less than x, hence:
[1.999999999999] = 1.[2.000000000001] = 2.Thus:
[tex]\lim_{x \rightarrow 2^-} f(x) = 1[/tex][tex]\lim_{x \rightarrow 2^+} f(x) = 2[/tex]Due to different lateral limits, the function is not continuous at x = 2.
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The price of petrol rose by 650% in the past decade. If the original price was 1 dollar per liter, find the final price
Answer: $ 6.50 per liter of petrol rose
Step-by-step explanation:
Identify which of the following numbers is an integer, rational and real number?
A.
−√5
B.
-1/2
C.
-50, 000, 000
D.
-1.5
From the given numbers :
Integers: -50,000,000
Rational numbers : -1/2 and -1.5
Real numbers : −√5 , -1/2, -50, 000, 000 , -1.5.
As given,
Given numbers:
A. −√5 :It is an irrational number.
Therefore belongs to real numbers.
B. -1/2 :In p/q form .
It is a rational and real number.
C. -50,000,000
It is a negative integer and real number.
D. -1.5 =-15 /10
=3/2
It is a rational and real number.
Therefore, from the given numbers :
Integers: -50,000,000
Rational numbers : -1/2 and -1.5
Real numbers : −√5 , -1/2, -50, 000, 000 , -1.5.
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K
Find the lateral surface area and volume of the solid
object shown below.
9.5"
9"
11"
11"
The base of the pyramid is an equilateral triangle.
...
Answer: 209 square inches, 182 cubic inches
Step-by-step explanation:
The lateral surface area is the sum of the areas each of the four faces.
The area of one face is [tex](1/2)(11)(9.5)[/tex]. Multiplying this by 4, we get 209 square inches.
To find the volume, we use the formula [tex]V=\frac{1}{3}Bh[/tex]. This gives us that the volume is [tex](1/3)[(1/2)(11)(11)](9)[/tex], or about 182 cubic inches.
Pls help BD bisects LABC. Find m LABD, m m LABC = (25x + 34) °
Answer: ABD=67 degrees
CBD=67 degrees
ABC=134 degrees
Step-by-step explanation:
ABC=ABD+CBD
25x+34=ABD+11x+23
14x+34=ABD+23
ABD=14x+11
ABD=CBD ==> Bisected angles are equal to each other since angle ABC is divided into two equal angles when bisected.
14x+11=11x+23
3x+11=23
3x=12
x=4
ABD=14x+11
ABD=14(4)+11
ABD=56+11
ABD=67 degrees
CBD=11x+23
CBD=11(4)+23
CBD=44+23
CBD=67 degrees
ABC=25x+34
ABC=25(4)+34
ABC=100+34
ABC=134 degrees
Answer:
∠ ABD = 67° , ∠ CBD = 67° , ∠ ABC = 134°
Step-by-step explanation:
since BD bisects ∠ ABC , then
∠ ABD = ∠ CBD = 11x + 23
∠ ABC = ∠ ABD + ∠ CBD ( substitute values )
25x + 34 = 11x + 23 + 11x + 23
25x + 34 = 22x + 46 ( subtract 22x from both sides )
3x + 34 = 46 ( subtract 34 from both sides )
3x = 12 ( divide both sides by 3 )
x = 4
Then
∠ ABD = 11x + 23 = 11(4) + 23 = 44 + 23 = 67°
∠ CBD = ∠ ABD = 67°
∠ ABC = 25x + 34 = 25(4) + 34 = 100 + 34 = 134°
Please help! 10 points. If u don’t know don’t js answer for point I really need help. And please explain! Thank u!
Answer:
(b) √(4x+2)√(25x-4)
Step-by-step explanation:
Given two functions f(x) = √(4x+2) and g(x) = √(25x-4), you want the function fg.
SolutionThe product fg is a bit of shorthand notation:
[tex]fg = fg(x) = f(x)\cdot g(x)[/tex]
Substituting the given function definitions, we have ...
[tex]f(x)\cdot g(x) = \sqrt{4x+2}\cdot\sqrt{25x-4}[/tex]
The product of the radicals could be combined into one radical, but that has not been done in your answer choices. This means ...
[tex]\boxed{fg=(\sqrt{4x+2})(\sqrt{25x-4})}[/tex]
Math homework due in 30 min
The missing values are x = 45, t = 90, n = 60, p = 75, m = 30, s = 15, k = 135, w = 30, f = 60 and y = 45.
How to determine the values of the missing angles
Herein we have a geometrical system formed by six triangles, one of them is a equilateral triangle and other one is a right triangle. By geometry we know that the sum of the measures of a triangle is equal to 180°, the angles in a equilateral triangle have the same measure and one of the angles in a right triangle is a right angle.
Then, we have following system of linear equations:
t = 90 (1)
t + 2 · x = 180 (2)
3 · n = 180 (3)
2 · p + m = 180 (4)
p + f + y = 180 (5)
(t + 5) + w + n = 180 (6)
s + k + m = 180 (7)
x + n + p = 180 (8)
f + w = 90 (9)
m + n = 90 (10)
p + s = 90 (11)
By (1) and (2):
x = 45
By (3):
n = 60
By (8):
p = 180 - 45 - 60
p = 75
By (4):
m = 180 - 2 · 75
m = 30
By (11):
s = 90 - 75
s = 15
By (7):
k = 180 - 15 - 30
k = 135
By (6) and (1):
w = 180 - 60 - 90
w = 30
By (9):
f = 90 - 30
f = 60
By (5):
y = 180 - 75 - 60
y = 45
The missing values are x = 45, t = 90, n = 60, p = 75, m = 30, s = 15, k = 135, w = 30, f = 60 and y = 45.
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width= x length =2x+6. Two expressions to represent the perimeter
The two expressions to represent the perimeter of this rectangle include the following:
P = 2(2x + 6 + x).P = 2(3x + 6).What is an expression?An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
How to calculate the perimeter of a rectangle?Mathematically, the perimeter of a rectangle can be calculated by using this formula;
P = 2(L + W)
Where:
P represents the perimeter of a rectangle.L represents the length of a rectangle.W represents the width of a rectangle.Substituting the given variables into the given expression, we have;
P = 2(2x + 6 + x) ......expression 1.
For the second expression, we have:
P = 2(2x + 6 + x)
P = 2(3x + 6) ......expression 2.
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Complete Question:
The length of a rectangle is 2x+6 and the width is x. Write two expressions to represent the perimeter.
I only need the answer for Part 1, thank you.
a The absolute value of ax will be considered while for the second the absolute value of ax + b will be considered.
b The absolute value of ax will be considered while for the second the absolute value of ax + b will be considered.
Given data
a, b, c, and x be real numbers.
How to show the difference in solving |ax| + b = c and |ax + b| = c|ax| + b = c
The equation here contains the modulus sign only for ax hence only the absolute value of ax is considered.
|ax + b| = c
Here the modulus sign covers both ax and b hence the absolute values of ax + b is considered.
How to show the difference in solving |ax| + b ≤ c and |ax + b| ≥ c|ax| + b ≤ c
The equation here contains the modulus sign only for ax hence only the absolute value of ax is considered.
|ax + b| ≥ c
Here the modulus sign covers both ax and b hence the absolute values of ax + b is considered.
Note that absolute values do not consider the signs
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The figure below shows points PQRS on a circle centre O. QP is produced to X Angle XPS = 77 and angle PSO = 68⁰. R Find the size of angle PQO. 0 68% 770 S X
Answer:
Step-by-step explanation:
the ice rink sold 95 tickets for a total of 828.00. general admission tickets are $10.00 each and youth tickets are $8.00 each. how many of each did they sell
There were 61 youth tickets sold and 34 general admission tickets in linear equation .
What in mathematics is a linear equation?
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.GA= GENERAL ADMISSION =$10
Y= YOUTH =$8
GA+Y= 95
GA=95-Y
10GA+8Y=828
10(95-Y)+8Y=828
950-10Y+8Y=828
-2Y= 122 MULTIPLY BY (-1)
2Y= 122
Y= 61
GA= 34
There were 61 youth tickets sold and 34 general admission tickets.
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Micaela and Elisa each Micaela and Elisa each improved their yards by planting rose bushes and geraniums they both bought their supplies from the same store. Micaela spent $122 on 14 rose bushes and. 8 geraniums Elisa spent $120 on 12 rose bushes and 12 geraniums. What is the cost of one geranium?
HELP ASAP
By solving a system of equations, we can see that each geranium costs 3 dollars.
What is the cost of one geranium?
First, let's define the two variables:
x = price of one rose bush.
y = price of one geranium
Now, with the information on the problem we can write two equations, thus, we will have a system of equations:
$122 = 14*x + 8*y
$120 = 12*x + 12*y
We want to solve that system, if we isolate x on the first equation we will get:
x = ($122 - 8y)/14
Now we can replace this on the other equation:
$120 = 12*($122 - 8y)/14 + 12*y
Now we can solve this for y.
14*$120 = 12*($122 - 8y) + 12*14*y
$1,680 = $1,464 + 72y
($1,680 - $1,464 )/72 = y = $3
Each geranium costs 3 dollars.
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what are the length and width in meters of the actual court
The real court is 9 by 18 meters in length and width.
In arithmetic, what does length mean?The length of something is its width or size measured across its entire surface. Or, to put it another way, it is the larger of a geometric shape's higher two or three dimensions.
This statement implies that the court's original dimensions have been reduced by 22.5 for every 1 centimeter in the size of the current drawing, which is 40 cm by 80 cm. To get the original dimension, we will multiply the required dimension by each 22.5 cm as shown. Original length for a 40-cm length = 40 * 22.5 originally 900 cm long 100 cm equals one meter in metres. Multiply 900cm by x to get 9m: 100x = 900*1x = 900/100x Therefore, 900cm = 9m For the 80-cm width: Original width is equal to 80 * 22.5, or 1800 cm. 100 cm equals one meter in metres. multiplying 1800cm by x yields 100x, 1800*1, 1800/100x, and 18m. So 1800cm = 9m. As a result, the real court is 9 meters long and 18 meters wide.
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Jerry surveyed adult males to study the relationship between their High and the length of their Footwear both are measured in centimeters. he found the equation y equals 75 + 3.4 x in which tax is the foot length and why is the height to be a good fit for his data. Based on this equation what would be the expected foot length of an adult male who is 1.8 m tall round your answer to the nearest tenth
The expected foot length of an adult male who is 1.8 m tall is 30.8 cm.
How to illustrate the information?Based on the information given, Jerry surveyed adult males to study the relationship between their high and the length of their footwear both are measured in centimeters and he found the equation y equals 75 + 3.4 x.
This will be illustrated as:
y = 75 + 3.4x..
y = 1.8m = 180
Therefore, y = 75 + 3.4x.
180= 75 + 3.4x
180 = 75 + 3.4x
Collect like terms
3.4x = 180 - 75
3.4x = 105.
Divide
x = 105 / 3.4
x = 30.8 cm
Therefore, the expected foot length of an adult male who is 1.8 m tall is 30.8 cm.
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Q 32. If the length of the adjacent sides of a parallelogram is 16 cm and 30 cm, and the angle between them is 45°, then find
the area of the parallelogram.
Ops: A. 0240,2 sq.cm
B. 022542 sq.cm
C. 0270,2 sq.cm
D. 0180/2 sq.cm
Answer:
Option A
Step-by-step explanation:
When adjacent sides and angle between the adjacent sides are given, then,
[tex]\sf \boxed{\text{\bf Area of Parallelogram = a*b * $Sin \ \theta$}}[/tex]
Here, a and b are the adjacent sides and [tex]\sf \theta[/tex] is the angle between them.
a = 16 cm ; b = 30 cm ; [tex]\sf \theta = 45^\circ[/tex]
Area of parallelogram = 16 * 30 * Sin 45
[tex]\sf = 16 * 30 * \dfrac{\sqrt{2}}{2}\\\\= 8*30*\sqrt{2}\\\\= 240\sqrt{2} \ sq.cm[/tex]
V
The length of a rectangle is six times its width.
If the area of the rectangle is 600 ft², find its perimeter.
Answer:
140
Step-by-step explanation:
→ Find an expression for the area
6x × x = 6x²
→ Equate to area
6x² = 600
→ Solve
x = 10
→ Find length and width
Length = 60 and width = 10
→ Find perimeter
60 + 60 + 10 + 10 = 140
Step-by-step explanation:
you can ask questions for clarification
Simplify each expression. 13. (9 − 3) 2− (5 • 4) 0= _________________ 14. (2 + 3) 5÷ (5 2 ) 2= _________________ 15. 4 2÷ (6 − 2) 4= _________________ 16. [(1 + 7) 2 ] 2• (12 2 ) 0= _________________
The expressions can be simplified as follows-
1. (9 − 3) 2− (5 • 4)0 = 12
2. (2 + 3)5 ÷ (5 × 2)2 = 5/4
3. 4 × 2 ÷ (6 − 2)4 = 1/2
4. [(1 + 7) 2] 2• (12 2 )0 = 0
Let us look at each expression one by one-
1. (9 − 3) 2− (5 • 4)0
Zero multiplied by any number is 0 itself. Thus, the expression becomes-
= (9 - 3) 2
= 6 × 2
= 12
2. (2 + 3)5 ÷ (5 × 2)2
According to the rules of BODMAS, we first solve the brackets-
(5)5 ÷ (10)2
= 25 ÷ 20
= 25/20
= 5/4
3. 4 × 2 ÷ (6 − 2)4
= 4 × 2 ÷ (4)4
= 8 ÷ (4)4
= 8/16
= 1/2
4. [(1 + 7) 2] 2• (12 2 )0
= [(8)2]2• 0
= 0
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SOMEBODY HELP WITH THIS PLEASE
To find the average height over each coaster, we must first add the height of each one together
109+135+115+365+126 = 850
Now divide 850 by the total amount of coasters, 5
850
------- = 170 Feet
5
Since the amusement park claimed their average height was 170 ft, it is not misleading. It is a good strategy because it is an honest statistic, which gives the amusement park more liability.
Aisha is three years older than Mpho . Together their ages add up to 17 years. How old is Aisha
Answer:
Aisha is ten years old and Mpho is seven
The age of Aisha is 10 years old and the age of Mpho is 7 years old.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Aisha is three years older than Mpho. Together their ages add up to 17 years.
Let x be the age of Aisha and y be the age of Mpho. Then the equations are given as,
x = y + 3 ...1
x + y = 17 ...2
From equations 1 and 2, then we have
y + 3 + y = 17
2y = 14
y = 7
Then the value of 'x' is given as,
x = 7 + 3
x = 10
The age of Aisha is 10 years old and the age of Mpho is 7 years old.
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Write an equation of the line that passes through point (−3, 8) and has the slope m=−2.
Do these decorations always come off of jokers or end up falling off when they get old answer asap for brainlist?
Yes or no
Answer:
Step-by-step explanation:
Answer:
yes
Step-by-step explanation:
!!!!!!!Question 3 pls help!!!
Each shape in the diagram below stands for a number.
000
Work out the value of each shape.
50/51 Marks
Total 90
-Total 66
By using the method of division, circle=20 , triangle= 35.
What is division?One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things. It is a mathematical operation used for equal distribution and equal grouping. In this post, let's study more about the division operation in math. One of the fundamental mathematical operations is division, which involves breaking a bigger number into smaller groups with the same number of components.
Given that,
The circles are 3
Which have the total of 60.
So, the total value divided by total number of circles.
60/3= 20
20 is the value of each circle.
The triangles are 2 including one circle
Which have the total of 90
90 - 20(circle)= 70
So, the total value divided by total number of triangles.
70/2= 35.
35 is the value of each triangle.
Therefore, circle=20 , triangle= 35
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Write the equation in slope-intercept form.
1. Slope = 1/3; y-intercept = -1
2. Slope = -2/5; y-intercept = 0
3. Slope = 1; y-intercept = 8
Answer:
[tex]1. \;\;y = \dfrac{1}{3}x - 1\\\\2.\;\;y = -\dfrac{2}{5}x\\\\3.\;\;y = x + 8[/tex]
Step-by-step explanation:
The slope intercept form equation is y = mx + b
where m = slope and b = y-intercept
So for each case, substitute for slope(m) and y-intercept(b)
Answer:
1. y = 1/3x + (-1)
2. y = -2/5x
3. y = 1x + 8 = 1x + 8 or y = x + 8
Step-by-step explanation:
1. First of all, we need to know the slope-intercept form. The formula is y = mx + b. M represent the slope and b represents the y-intercept. So the question asked for the slope-intercept form for the slope that is 1/3 and the interception of -1. So we need figure out how to write it. It asked for -1/3 and -1 and we use the formal y = mx + b and it'll help us on figuring out how to write it. So far we have y = 1/3x + b, b is the intercept. The intercept would be -1. So the way we'd right it out is y = 1/3x + (-1). But first you have to multiply the + with -1. When we would multiply the signs you do it like this: (+) (+) = + and (-) multiplied by (-) is +. As well as (-) multiplied by (+) is -.
So for 1 the slope would be 1/3 and the (0, -1) . But we have to write it in the given form: y = mx + b ... m = slope, b = y intercept. So the way we'd right it is y = mx + b and m = slope, b = y intercept. Therefore the answer for this one is y = 1/3x - 1.
2. First we should know that we have the slope of -2/5 and the y-intercept is 0. The right form for this is y = -2/5x +. So for this one we got y = -2/5x because we said that the first one is 1/3 and -1. As well as the second is -2/5 and 0. The third is 1 and 8 as we wrote it earlier. So that's how we got our answer y = -2/5x for this question. Therefore our answer to this question is y = -2/5x.
3. For this one we first know slope = 1 and intercept =8. This equation is easier than both number 1 and 2 all we need to do is just put every given number in the right place. So we'll need to write the y as it is then add the = sign. Then write the slope which is given above. Then we have to write the x. We'll need to add the + sign and write the intercept given above next to it. After doing these steps you we'd have the answer because this is the general formula. So we would write 1 instead of m and the intercept is 8 so you need to write it instead of b. Therefore our answer would be y = 1x + 8 = 1x + 8 or another way we could write it is y = x + 8 either way would be correct.
I hope this helps, have a blessed day! :)
A rectangular box is 17 cm wide and 26 cm high. If the
surface area of the box is 4238 square centimeters,
find the length of the box.
Answer:
3796 length of the box
Step-by-step explanation:4,238-26×17=3,796
For each of the following polynomials given a power function that best represents the end behavior of the polynomial. Draw the arrows.
Answer:
the answer is the 3rd to the 4th power and
The end behavior of the polynomial y=-4x+8x-21'+3 is y = -4x^3.
What is degree of a polynomial?Degree of a polynomial is the highest power that its terms pertain (for multi-variables, the power of term is addition of power of variables in that term).
Thus, in the degree of the polynomial is 3 as the highest power in its terms is 3.
(power and exponent are same thing)
We are given that;
The functions (a) 1=3x-2x+12
(b) 1-10-8.x2
(c) y=6r-4r+x-120
(d) y=-3x+2x-4x+7
(e) y=5x+2x2
(f) y=-4x+8x-21'+3
Now,
To find the power function that best represents the end behavior of a polynomial, we need to look at the leading term (the term with the highest degree) of the polynomial.
(a) The leading term of this polynomial is 3x. So the power function that best represents its end behavior is y = 3x.
(b) The leading term of this polynomial is -8x^2. So the power function that best represents its end behavior is y = -8x^2.
(c) The leading term of this polynomial is 6r. So the power function that best represents its end behavior is y = 6r.
(d) The leading term of this polynomial is -3x^3. So the power function that best represents its end behavior is y = -3x^3.
(e) The leading term of this polynomial is 2x^2. So the power function that best represents its end behavior is y = 2x^2.
(f) The leading term of this polynomial is -4x^3. So the power function that best represents its end behavior is y = -4x^3.
Therefore, by polynomials the answer will be y = -4x^3.
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During a job interview, Pam Thompson is offered a salary of $50,000. The company gives annual raises of 12 percent. What will be
Pam's salary during her fifth year on the job? Use Exhibit 1-A. (Round time value factor to 3 decimal places and final answer to the
nearest whole number.)
Answer:
$78 700
Step-by-step explanation:
Four time periods year 2 3 4 and 5
50 000 ( 1.12 )^4 = 50 000 ( 1.574) = 78700
( 1.574 is from the table for 12 % and 4 periods )