Answers
Solution
Given
[tex]\begin{gathered} m<3=45^0 \\ m<1=50^0 \\ m<6=135^0 \end{gathered}[/tex][tex]\begin{gathered} m<6\text{ = m<1 + m<2 + m<3 \lparen corresponding angles are equal\rparen} \\ 135=50+m<2+45 \\ 135=95+m<2 \\ m<2=135-95 \\ m<2=40^0 \end{gathered}[/tex][tex]\begin{gathered} mRelated Questions
Solve the equation:
√x+8=2
(square root of x+8)
Answers
The solution of the given equation is x = -4.
An algebraic expression is an expression which should include at least one variable connected by at least a single arithmetic operator. These operators can be addition(+), subtraction(-), multiplication(*) or division(/).
an algebraic equation or polynomial equation is an equation of the form
where p = 0
where P is a polynomial with coefficients in some field, often the field of the rational numbers. For many authors, the term algebraic equation refers only to univariate equations, that is polynomial equations that involve only one variable. On the other hand, a polynomial equation may involve several variables. In the case of several variables (the multivariate case), the term polynomial equation is usually preferred to algebraic equation.
We have given that √x+8= 2
To remove the root on the left side of the equation square both sides of equation.
so we get x+8= 4
by solving the equation we will get x= -4.
Thus the solution of the given equation is x= -4.
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Evaluate the expression for x=3 and y=5:(3y - 6)/x
Answers
Let's evaluate the expression by applying the Substitution Method.
Let's substitute x = 3 and y = 6 to the expression:
[tex]\text{ }\frac{3y\text{ - 6}}{x}[/tex]We get,
[tex]\text{ }\frac{3y\text{ - 6}}{x}\text{ = }\frac{3(5)\text{ - 6}}{3}[/tex][tex]\text{ = }\frac{15\text{ - 6}}{3}\text{ = }\frac{9}{3}[/tex][tex]\text{ = }3[/tex]Therefore, the expression (3y - 6)/x at x = 3 and y = 5 will give you a value of 3.
10. A mouse runs a distance of 2metres in 15 seconds. What is its speed?
Answers
We will use the formula;
speed = distance / time
from the question, d= 2 t=15
substitute the value into the formula:
speed = 2/15 = 0.13333 m/s
Evaluate the expression how do you get to (2^-1 x 3^0)^3 times (2^0 x 5^3) ^5
Answers
we have the expression
[tex](2^{-1}\cdot3^0)^{-3}\cdot(2^0\cdot5^3)^5[/tex]Remember that
[tex]\begin{gathered} 2^{-1}=\frac{1}{2} \\ 3^0=1 \\ 2^0=1 \\ 5^3=125 \end{gathered}[/tex]substitute in the original expression
[tex]\begin{gathered} (\frac{1}{2}\cdot1)^{-3}\cdot(1\cdot125)^5 \\ (\frac{1}{2}\cdot)^{-3}\cdot(125)^5 \end{gathered}[/tex][tex]\begin{gathered} (\frac{1}{2})^{-3}=2^3=8 \\ \end{gathered}[/tex]substitute
[tex]\begin{gathered} 8\cdot(125)^5 \\ 8\cdot30,517,578,125 \\ 244,140,625,000 \end{gathered}[/tex]therefore
The answer is
244,140,625,0001)There are fourteen shirts in your closet, four blue, five green, and five red. You randomly select one to wear. It is blue or green2)a magazine contains for teen pages.you open to a random page. The page number is eight to ten.find the probability
Answers
Given:
Total number of shirts is, N= 14.
Number of blue shirts is, n(b) = 4.
Number of green shirts is, n(g) = 5.
Number of red shirts is, n(r) = 5.
The objective is to find the probability of randomly selecting a blue shirt or green shirt.
The required probability ca be calculated as,
[tex]\begin{gathered} P(\text{blue or gr}een)=P(blue)+P(green) \\ =\frac{n(b)}{N}+\frac{n(g)}{N} \\ =\frac{4}{14}+\frac{5}{14} \\ =\frac{9}{14} \end{gathered}[/tex]Hence, the probability of randomly selecting a blue shirt or green shirt is 9/14.
Determine the domain and range of (g ○ f)(x) if f of x is equal to 4 over the quantity x squared minus 4 end quantity and g(x) = x + 2.
Answers
For the function (gof)(x) the Domain is {x∈ R| ,x ≠ –2, 2} , the Range is {(–∞, 1)∪(2, ∞)} .
In the question ,
it is given that
the function f(x) is given as "4 over the quantity x squared minus 4" ,
which means
f(x)=4/(x²-4)
and g(x)=x+2
we know ,
(gof)(x) = g(f(x))= f(x) + 2
= 4/(x²-4) + 2
taking LCM as (x²-4) and solving further ,
we get
= [tex]\frac{4+2x^{2} -8}{x^{2} -4}[/tex]
= (2x²-4)/(x²-4)
the fraction is defined only when the denominator is non zero,
So for Domain
x²-4 ≠ 0
x² ≠ 4
x ≠ +2,-2
So, the domain is all real numbers except the numbers 2,-2 .
For Range , the graph of the function (gof)(x) is plotted below ,
From the graph we can see that the function does not have any value from y=1 to 2 .
So, the Range will be R={(∞, 1)∪(2, ∞)}.
Therefore , for the function (gof)(x) ,the Domain is {x∈ R| ,x ≠ –2, 2} , the Range is R:{(–∞, 1)∪(2, ∞)} .
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Which statement best describes the areas and perimeters of the figures?
O They have the same area and same perimeter.
O
They have the same area but different perimeters.
They have different areas but the same perimeter.
O They have different areas and different perimeters.
Answers
Statement (D) "they each have unique perimeters and areas" best describes the areas and perimeters of the figures.
What are the area and perimeter?The measurement that expresses the size of a region on a plane or curved surface is called an area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina.A closed path that encompasses, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter. There are numerous uses in real life for perimeter calculations.So, according to the given image, we can easily conclude that both the figures have different areas and different perimeters.
Therefore, statement (D) "they each have unique perimeters and areas" best describes the areas and perimeters of the figures.
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The correct question is given below:
Which statement best describes the areas and perimeters of the figures below?
Figures 1 and 2 both have the same perimeter but have different numbers of units inside of the shape.
A. They have the same area and the same perimeter.
B. They have the same area but different perimeters.
C. They have different areas but the same perimeter.
D. They have different areas and different perimeters.
Which of the following are possible equations of a parabola that has no real solutions and opens downward?y > = -(x + 4)2 - 2y > = -(x + 4)2 + 2y > = -x2 - 2y > = (x - 4)2 + 2y > = -(x - 4)2 - 2
Answers
We have to identify the parabola that:
a) has no real solutions (it has complex roots).
b) opens downward.
The equations are in vertex form, so to have no real solutions and be downward, the vertex should have a value of y that is less than 0:
If the vertex had a value of y greater than 0, if it opens downward, there should be two values of x so that f(x) = 0. Then, this would be the real solutions.
The vertex form can be written as:
[tex]y=a(x-h)^2+k[/tex]where (h,k) are the coordinates of the vertex.
Then, we need k <= 0.
The equations that satisfy this are:
y = -(x + 4)² - 2
y = -x² - 2
y = -(x - 4)² - 2
The second condition is that the parabola opens downward. This means a quadratic coefficient "a" with negative value.
All this three equations satisfy this condition.
We can graph them and check if the conditions are satisfied:
Answer:
There are 3 equations that satisfy the two conditions:
y = -(x + 4)² - 2
y = -x² - 2
y = -(x - 4)² - 2
Which of the following expressions can be used to find PQ? A. 12 • sin 42°B. 12 • cos 42°C. 12/cos42°D. 12/sin42°
Answers
PQ is hypotenuse of the triangle
pR is the opposite side
so,
it will come like
sin 42=12/PQ
PQ=12/sin 42
so the answer is D
In his first period, Mr. Mueller had 27 students in his virtual class after 5 students left the class. Whichequation can be used to find b, the number of students in his class before the 5 students left?5+b = 275b = 27b-5 =27b/5 = 27
Answers
she had 27 students after 5 students left her class.
Her present number of student = 27
Initial number of student before 5 left the class = 27 + 5 = 32
number of student in his class before the 5 student left can be represented as follows
where
b = number of student before 5 student left his class
b - 5 = 27
will the square root of 42 be closer to 6 or 7? why?
Answers
The square root of 42 is written mathematically as:
[tex]\sqrt[]{42}[/tex][tex]\sqrt[]{42}=\text{ }6.48[/tex]We can round 6.48 to the
How do I do this? , it doesn’t really explain
Answers
Given:
[tex]\sqrt{y^2}[/tex]To find:
The exponent of y
Explanation:
Using the exponential rule,
[tex]\begin{gathered} \sqrt{y^2}=y^{\frac{2}{2}} \\ =y^1 \end{gathered}[/tex]The exponent of y is 1.
Final answer:
The exponent of y is 1.
The price of regular rice is $1 per pound; that of premium rice is $2. Mix 300 pounds
of regular rice with 400 pounds of premium rice. What is the price of the mixture?
Answers
Answer:
1200 dollars
Step-by-step explanation:
2x400 is 800 + 1x400 =1200
your solution as an inequality in the box below,using "<="fors or ">" for 2 if necessary
Answers
log base √2 8 = x . find the value of x
Answers
(2)^x/2= 2^(3)
So basically x/2 =3
=> x = 6
I need to find the volume and surface area of this 3d composite figure
Answers
Volume:
To find the volume we notice that this figure is made of a cube minus a cone.
The volume of a cube is given as:
[tex]V=l^3[/tex]Here the length of each side is 6 cm.
The volume of a cone is given as:
[tex]V=\frac{1}{3}h\pi r^2[/tex]here the radius of the cone is 2 cm (half the diameter shown) and its height is 6 cm.
Hence the volume of the composite figure is:
[tex]V=(6)^3-\frac{1}{3}(6)\pi(2)^2=190.87[/tex]Surface area:
The surface area of the figure is the surface area of the cube minus the surface area of the cone.
The surface area of the cube is given by:
[tex]SA=6l^2[/tex]in this case the lenght of each side is 6 cm.
The surface area of the cone is given by:
[tex]SA=\pi r^2+\pi rl[/tex]where r is the radius of the cone and l is the slant height. The radius of the cone is 2 cm. To find the slant height we need to remember that this slant height is the hypotenuse of a right triangle with one leg equal to the radius and the other leg equal to the height of the cone. Then, using the pythagorean theorem we have:
[tex]\begin{gathered} l^2=2^2+6^2 \\ l^2=4+36 \\ l=\sqrt[]{40} \end{gathered}[/tex]Once we have all the values we need we have that the surface area is:
[tex]SA=6(6)^2-\pi(2)^2-\pi(2)(\sqrt[]{40)}=163.70[/tex]Summing up we have that:
• The volume is 190.87 cubic cm.
,• The surface area is 163.70 squared cm.
help mee pleasee!!
thank you <3
Answers
An equation that models the number of people employed in some country as medical assistant in the last year x is y = 359 + 14.35x
In this question, we have been given the number of people employed in some country as medical assistant.
We need to write an equation that models the number of people employed in some country as medical assistant in the last year x.
the number of people employed in some country as medical assistant:
in 2004 = 359 thousand
and by 2014 this number is expected to be 560 thousand.
We find the rate of employment.
Consider (x1, y1) = (0, 359) and (x2, y2) = (14, 560)
m = (560 - 359)/(14 - 0)
m = 201/14
m = 14.35
We have been given the line must pass through points (0, 359) and (14, 560)
And, we get the y-intercept c = 359
with slope m = 14.35 and y-intercept c = 359, the equation of the line would be,
y = 14.35x + 359
Therefore, an equation that models the number of people employed in some country as medical assistant in the last year x is y = 359 + 14.35x
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Solve the following simultaneous equation using elimination or substitution method
Answers
Answer:
(15, 10) and (10, 15)
Explanation:
The given system of equation is
x + y = 25
xy = 150
To solve the equation, we will use the subtitution method, so first, we need to solve the first equation for y
x + y = 25
x + y - x = 25 - x
x y= 25 - yx
Then, substitute y = 25 - x on the second equation, we get
xy = 150
x(25 - x) = 150
x(25) - x(x) = 150
25x - x² = 150
Now, we can rewrite the equation as
25x = 15 + x²
0 = 150 + x² - 25x
0 = x² - 25x + 150
Therefore, we need to find the values of x that satisfies
x² - 25x + 150 = 0
Now, we need to factorize this equation, so two numbers that multiply to 150 and add to -25 are -15 and -10. Then
(x - 15)(x - 10) = 0
So, the solutions are
x - 15 = 0
x = 15
or
x 10 = 0
x = 10
Then, the values of y are
If x = 15
y = 25 - x
y = 25 - 15
y = 10
If x = 10
y = 25 - x
y = 25 - 10
y = 15
Therefore, the solutions are (15, 10) and (10, 15)
I
!! CR Algebra 1 B (GP) 21-22 / 8:Radical Expressions and Equations 104 8 6 4 N -10-8 -6 -4 2 0 2 4 6 8 10 -2 6 -8 -10 Match the graph with its function by translating the graph of y = x 4. O O y=&x-2 y = (2 O Oy=√x+2 y x+2 O y=√x+2 O y=√x-2 o Search the web and Windows e it
Answers
The graph of the parent function starts at the origin.
We need to find the translation done on the original function to get the graph in the image.
On the graph, the the line starts at x = 2. This means there was a translation of 2 units to the right sides
[tex]\begin{gathered} \text{for translation:} \\ f(x\text{ + a) : translation of a units to the left} \\ f(x\text{ - a): translation of a units to the right} \end{gathered}[/tex]Since we are translating to the right, the new function becomes:
[tex]f(x\text{ - 2) = }\sqrt[]{x\text{ - 2}}\text{ (option A)}[/tex]What is the rectangular form of the parametric equations?x(t)=t+3, y(t)=2t^2−4, where t is on the interval [−4,0].Enter your answer, in standard form, by filling in the boxes.
Answers
1. Solve t in the first equation:
[tex]\begin{gathered} x=t+3 \\ t=x-3 \end{gathered}[/tex]2. Substitute the t in the second equation by (x-3):
[tex]\begin{gathered} y=2t^2-4 \\ y=2(x-3)^2-3 \end{gathered}[/tex]3. Write the equation you get in previous step in standard form:
[tex]\begin{gathered} (a-b)^2=a^2-2ab+b^2 \\ \\ y=2(x^2-2*x*3+3^2)-3 \\ y=2(x^2-6x+9)-3 \\ y=2x^2-12x+19-3 \\ \\ y=2x^2-12x+16 \end{gathered}[/tex]To find the inverval of x use the equation x=t+3 and the interval of t
[tex]\begin{gathered} t\lbrack-4,0\rbrack \\ x=t+3 \\ x=-4+3=-1 \\ x=0+3=3 \\ \\ x\lbrack-1,3\rbrack \end{gathered}[/tex]Answer:[tex]\begin{gathered} y=2x^2-12x+16 \\ \lbrack-1,3\rbrack \end{gathered}[/tex]Find the perimeter of the window to the nearest hundredth. 3ft
Answers
Answer:
7.71
Step-by-step explanation:
1/2 pi * 3 + 3
3.14 * 3 = 9.42
1/2 of 9.42 = 4.71
4.71 + 3 = 7.71 ft
Examine the following graph, where exponential function P(x) undergoes a transformation.The preimage of the transformation is labeled P(x), and the image is labeled I(x). 2 exponentially decreasing functions. P of x passes through (0,1) & has a horizontal asymptote at y=0. I of x has same horizontal asymptote & passes through (0, 9).© 2018 StrongMind. Created using GeoGebra. What is the function rule for I(x) that represents this transformation?
Answers
Solution
The answer is
Answer:
I(x)=9⋅P(x)
Step-by-step explanation:
I just did the workbook.
Which of these is an example of combination?A. Selecting a president and a vice-president from a group of 8 members.B. Opening a combination lock.C. Picking a team of 5 people from a group of 15D. Arranging the letters of the word "mathematics without repetition.
Answers
By definition:
• a, combination, is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter. ,In combinations, you can select the items in any order,.
• in ,permutations,, the order of the selected items is essential,. For example, the arrangements ab and ba are equal in combinations (considered as one arrangement), while in permutations, the arrangements are different.
From the list of examples we see that:
A) We select a president and a vice president, so order matters → permutation.
B) The order of the numbers of a lock's key matters → permutation.
C) The order of the members of the team doesn't matter → combination.
D) The order of the letter matters → permutation.
Answer: C
Evaluating RadicalsQuestion: Estimate the radical by identifying which two consecutive integers it falls in between.
Answers
Step 1
Given;
[tex]Estimate\text{ the radical by identifying which two consecutive integers it falls between}[/tex]Step 2
An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Examples of integers are: -5, 1, 5, 8, 97, and 3,043. Examples of numbers that are not integers are; -1.43, 1 3/4, 3.14,0.09, and 5,643.1.
We know that the perfect squares between √11 are;
[tex]\begin{gathered} \sqrt{9}\text{ and }\sqrt{16} \\ \sqrt{9}=3 \\ \sqrt{16}=4 \\ \sqrt{11}=3.31662479 \end{gathered}[/tex]Hence, the answer will be;
[tex]\begin{gathered} \sqrt{11}\text{ is between the integers 3 and 4} \\ 3<\text{ }\sqrt{11}\text{ }<4 \end{gathered}[/tex]Find the sum 12 1/9 + 10 2/3
Answers
Answer:
12 1/9 = 109/9
10 2/3 = 32/3
Step-by-step explanation:
109/9 +32/3
=205/9
help meeeeeeeeeeeeeeeeeeeeeee
thank you
Answers
The function g(3) has a value of 0
How to determine the value of the function?The graphs represent the given parameters
The function definition is given as
g(3)
On the two graphs, we have the following highlights
First graph: The function of ySecond graph: The function of g(x)This means that we use the second graph to calculate the value of the function g(3)
The function g(3) means the value of x is 3
On the graph, we have
g(x) = 0 when x = 3
So, we have
g(3) = 0
Hence, the value of the function is 0
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What is the equation of the line that passes through the point (4,-7) and has a slope of -3
Answers
Answer: y=-3x+5
Step-by-step explanation:
1) List in a y = mx + b
y = -3x+b
2) Next fill in x and y with the points given
-7 = -3(4) + b
3) Solve
-7 = -3(4) + b
-7 = -12 + b
5 = b
4) Apply b to the y =mx + b
y=-3x+5
Answer: y= -3x +5
Step-by-step explanation:
Slope: y= mx+ b
m being the slope
b being the y intercept
You're given the slope, so you substitute m for -3
y=mx+b
y = -3x + b
You have the coordinates (4, -7) which you can substitute (the line passes through that point.)
-7 = -3(4) + b
-7 = -12 + b
+12 +12
5= b
y= -3x + b
Check:
-7 = -3(4) + 5
-7 = -12 + 5
-7 = -7
(c)
Calculate the return on investment (as a %) for 2007, 2008, and 2009. (Round your answers to the nearest tenth of a percent.)
2007
Incorrect: Your answer is incorrect.
%
2008
Incorrect: Your answer is incorrect.
%
2009
Incorrect: Your answer is incorrect.
%
(d)
Prepare a trend analysis of the net revenue and total assets for 2005 through 2009. (Round your answers to one decimal place.)
2009 2008 2007 2006 2005
Net Revenue
Incorrect: Your answer is incorrect.
\
Changed: Your submitted answer was incorrect. Your current answer has not been submitted.
100.0
Total Assets
156.8
Correct: Your answer is correct.
158.3
Correct: Your answer is correct.
149.5
Correct: Your answer is correct.
125.2
Correct: Your answer is correct.
100.0
Answers
Answer:
thats confusing is there any other ways you could format it?
Step-by-step explanation:
state if the givin binomial is a factor of the givin polynomial
Answers
19)
Given data:
The given polynomial is
[tex]x^3-5x^2-8x+8^{}[/tex]Substitute -2 for x in the above polynomial.
[tex]\begin{gathered} (-2)^3-5(-2)^2-8(-2)+8 \\ =-8-20+16+8 \\ =-4 \end{gathered}[/tex]As after substituting x=-2 in the polymial is not equal to zero.
Thus, (x+2) is not the factor of the polynomial
[please help!!!]
The manager of a pizza restaurant recorded the total number of pizzas delivered after x weeks in this table. Which statement is true?
A. There was an increase of 83.5 pizzas each week from week 4 to week 6.
B. There was an increase of 34.5 pizzas each week from week 4 to week 6.
C. There was an increase of 50 pizzas each week from week 4 to week 6.
D. There was an increase of 28 pizzas each week from week 4 to week 6.
Answers
Answer:
the answer is a
Step-by-step explanation:
to see which answer is true, we must find the average of the difference between weeks 4-6
356 - 278 = 78
445 - 356 = 89
Now, find the average
89 + 78 = 167
167/2 = 83.5
therefore, answer A is true
