Question: Find the value of x for which “m” is parallel to “n” Can you help me solve this please? (Grade 10, angles)
Let's say 4x-29 = angle 1 and 3x+12 = angle 2; since m and n are parallel, then angle 1 and 2 are corresponding angles, therefore they are the same. for instance we can form the following equation:
[tex]4x-29=3x+12[/tex]Now, let's solve for x
[tex]\begin{gathered} 4x-3x=12+29 \\ x=41 \end{gathered}[/tex]Thus, the value of x is 41
Find the value(s) of k that will cause the equation to have the given number and type of solutions.6x² + kx + 6 +0, 1 real solution
we can use the equation to factor
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]where a=6 , b=k and c=6
replacing
[tex]\begin{gathered} x=\frac{-k\pm\sqrt[]{k^2-4(6)(6)}}{2(6)} \\ \\ x=\frac{-k\pm\sqrt[]{k^2-4(6)(6)}}{2(6)} \\ \\ x=\frac{-k\pm\sqrt[]{k^2-144}}{12} \end{gathered}[/tex]to have a real solution we need the interior of the root to be greater than or equal to 0
so
[tex]\begin{gathered} k^2-144\ge0 \\ k^2\ge144 \\ k\ge\pm\sqrt[]{144} \\ k\le-12ork\ge12 \end{gathered}[/tex]The solution is option B
k can take any value in the interval K<-12 or in the interval k>12
You rake leaves to earn extra cash. You charge clients $10 an hour. On average, you work 20 hours a week. You are thinking about increasing your hourly rate by 15%. If you do begin charging your clients more what will be the difference in how much money you earn each week?
In this case the answer is very simple . .
Step 01:
Data
Initial earnings
1 hour ===> $10
20 hours / week
New earnings
+ 15% hour
$10 * (1.15)
Step 02:
Inicial earnings
[tex]\frac{10\text{ \$}}{\text{hour}}\cdot\frac{20\text{ hour}}{\text{week}}=\text{ 200 \$ / we}ek[/tex]New earnings
[tex]\frac{10\cdot\text{ (1.15) \$}}{\text{hour}}\cdot\frac{20\text{ hour}}{\text{week}}\text{ = }230\text{ \$ / w}eek[/tex]The difference would be:
New earnings - Inicial earnings = $ (230 - 200) = $30
The answer is:
The difference in money you will earn is $ 30.
Which diagram represents the hypothesis of the converse of corresponding angles theorem?mр19yn
Let us check the types of angles in parallel lines
I will draw a figure to explain them
From the figure angles, 1 and 2 are in the corresponding position
Then from the given picture
The figure that represents the hy
Please help with this problem:A rocket is launched vertically from the ground with an initial velocity of 64 ft / sec. (a)Write a quadratic function h(t) that shows the height, in feet, of the rocket t seconds after it was launched.(b)Determine the rocket’s maximum height, the amount of time it took to reach its maximum height, and the amount of time it was in the air. Show work for all steps.(c)Graph h(t) on the coordinate plane using important information from part b.
(a) We are asked to write a quadratic function h(t) that shows the height, in feet, of the rocket t seconds after it was launched.
The initial velocity of the rocket is 64 ft/sec.
Recall from the equations of motion, we have
[tex]s=ut-\frac{1}{2}at^2[/tex]Here s will be replaced by the height h(t), a is the acceleration due to gravity that is 32.17 ft/sec^2 and u is the initial velocity of the rocket.
Plugging the values, the above equation becomes
[tex]\begin{gathered} h(t)=64t-\frac{1}{2}\cdot32.17\cdot t^2 \\ h(t)=64t-16.085t^2 \end{gathered}[/tex]Therefore, we have got the quadratic equation that shows the height of the rocket t seconds after it was launched.
[tex]h(t)=64t-16.085t^2[/tex](b) The amount of time it took to reach its maximum is given by the vertex of the quadratic function.
[tex]t=-\frac{b}{2a}[/tex]From part (a), the coefficients of the quadratic function are
a = -16.085
b = 64
c = 0
[tex]t=-\frac{64}{2(-16.085)}=1.989\;sec[/tex]So, it takes 1.989 seconds to reach the maximum height.
The corresponding maximum height of the rocket can be found by plugging t = 1.989 into the quadratic function.
[tex]\begin{gathered} h(t)=64(1.989)-16.085(1.989)^2 \\ h(t)=127.296-63.634 \\ h(t)=63.662 \end{gathered}[/tex]Therefore, the rocket’s maximum height is 63.662 ft
The amount of time the rocket was in the air is double the time to reach the maximum height.
[tex]2\times1.989=3.978\;sec[/tex]Therefore, the rocket was in the air for 3.978 seconds.
(c) Let us sketch an approximate graph of the function using the information from part (b)
You deposit $1000 in an account that pays 8% interest compounded semiannually. After 4 years, the interest rate is increased to 8.44% compounded quarterly. What will be the value of the account after a total of 8 years?
Answer:
$1,881.28
Step-by-step explanation:
Using the compound interest formula, 1000 dollars 4 years with an interest of 8%, it will be 1360.49 dollars.
After 4 years, the principle becomes 1360.49 dollars, the interest rate becomes 8.44%, and you must calculate for 4 more years.
The final amount after 8 years is 1,881.28. The trick here is compounded separately in 2 parts.
f(x) = 2x+3 and g(x) = x - 7. Find f(3)
ANSWER
f(3) = 9
EXPLANATION
We are given the function:
f(x) = 2x + 3
We want to find f(3).
To do this, we have to replace x with 3 in the function and then simplify:
f(3) = 2(3) + 3
f(3) = 6 + 3
f(3) = 9
That is the value of f(3).
If you know the length of something in centimeters you can calculate it’s length in millimeters
Yes, 1 centimeter is equivalent to 10 millimeters
If a length is known in centimeters, it can be easily known in millimeters
which of the following is true?5/6 > 11/123/4 < 2/39/15 < 4/518/27 = 1/3
To determine which of the following comparisms is true, we will have to convert each of the fractions into whole number using the denominators lowest common multiple (LCM) and then decide on which of the comparisms is true.
Statement 1
[tex]\begin{gathered} \frac{5}{6}>\frac{11}{12} \\ \text{LCM}\Rightarrow12 \\ 12\times\frac{5}{6}=\frac{60}{6}=10 \\ 12\times\frac{11}{12}=\frac{132}{12}=11 \\ \text{ Since 10 is not greater than 11},\text{ then} \\ \frac{5}{6}>\frac{11}{12}\Rightarrow\text{false} \end{gathered}[/tex]Statement 2
[tex]\begin{gathered} \frac{3}{4}<\frac{2}{3} \\ \text{LCM}\Rightarrow12 \\ 12\times\frac{3}{4}=3\times3=9 \\ 12\times\frac{2}{3}=4\times2=8 \\ \text{ Since 9 is not less than 8, then} \\ \frac{3}{4}<\frac{2}{3}\Rightarrow\text{false} \end{gathered}[/tex]Statement 3
[tex]\begin{gathered} \frac{9}{15}<\frac{4}{5} \\ \text{LCM}\Rightarrow15 \\ 15\times\frac{9}{15}=1\times9=9 \\ 15\times\frac{4}{5}=3\times4=12 \\ \text{ Since 9 is less than 12, then} \\ \frac{9}{15}<\frac{4}{5}\Rightarrow\text{true} \end{gathered}[/tex]Statement 4
[tex]\begin{gathered} \frac{18}{27}=\frac{1}{3} \\ \text{LCM}\Rightarrow27 \\ 27\times\frac{18}{27}=1\times18=18 \\ 27\times\frac{1}{3}=9\times1=9 \\ \text{ Since 18 is not equal to 9, then} \\ \frac{18}{27}=\frac{1}{3}\Rightarrow\text{false} \end{gathered}[/tex]Hence, the statement that is true in all the statements is
[tex]\frac{9}{15}<\frac{4}{5}[/tex]multi -4/5×(-1/3)[tex] \\ \\ \\ \\ \\ \\ \\ \times \frac{?}{?} [/tex]
Given data:
[tex]-\frac{4}{5}\times(-\frac{1}{3})[/tex]to miltiply,
[tex]\begin{gathered} -\frac{4}{5}\times.(-\frac{1}{3}) \\ =\frac{4}{5}\times\frac{1}{3} \\ =\frac{4\times\:1}{5\times\:3} \\ =\frac{4}{15} \end{gathered}[/tex]the answer is 4/15.
The first box is to type in the base. The second box is where you fill in the simplified exponent using the multiplication property rule of exponents. Multiply. Write the product as one combined power.
Answer:
b⁵
Explanation:
The multiplication property rule of exponents says that when we have the same base, we can add the exponents, so we can write the given expression as
[tex]b^3*b^2=b^{3+2}=b^5[/tex]Therefore, the answer is
[tex]b^5[/tex]A major supplier has 427 transformers on back order. On the same day they receive 1,000 transformers, they have additional transformer orders placed for 27, 150, 310, and 36. How many transformers are left in stock after filling all orders?
We have that the total transformers is 427 + 1000 = 1427.
Then, if we substract the transformer orders, we get:
[tex]1427-27-150-310-36=904[/tex]therefore, there are 904 transformers left in stock
-4X -8 = -24 Please help me.
Answer:
x = 4
Step-by-step explanation:
Choose all the numbers that make the comparison true 15.44<____A.15.38B. 15.065C. 15.7 D. 15.05E. 15.472F. 15.89please explain thank you very much
Answer
Options C, E and F are all correct.
The numbers that make the comoarison true include
15.7
15.472
15.89
Explanation
In writing inequalities, we should note that the inequality sign faces the bigger number.
So, any number that must satisfy the comparision 15.44 < ___, must be greater than 15.44 since the inequality sign is facing the unknown number.
So, only the options that have numbers that are greater than 15.44 will make the comparison true.
These numbers include
15.7
15.472
15.89
Hope this Helps!!!
Show that this is a countably infinite{2q:q∈Q+}
SOLUTION
Given the question in the question tab, the following are the solution steps to solve the question
STEP 1: Define a countably infinite set
A set is countably infinite if its elements can be put in one-to-one correspondence with the set of natural numbers. In other words, one can count off all elements in the set in such a way that, even though the counting will take forever, you will get to any particular element in a finite amount of time.
STEP 2: Write the given set
[tex]\mleft\lbrace2q\colon q\in Q+\mright\rbrace[/tex]This set is read as a set of values 2q such that q is an element of positive rational numbers
STEP 3: Show the proof
[tex]\begin{gathered} \text{Let }Q_{\pm}=\mleft\lbrace q\in Q\colon q>0\mright\rbrace \\ \text{For ev}ery\text{ q}\in Q_+,\text{ there exists at least one pair (m,n)}\in N\times N \\ \text{such that q}=\frac{m}{n} \end{gathered}[/tex]Therefore, we can find an injection:
[tex]i\colon Q_+\Rightarrow N\times N[/tex]By Cartesian Product of Natural Numbers with Itself is Countable, N×N is countable.
Hence Q+ is countable, by Domain of Injection to Countable Set is Countable.
Note that the function defined by is a bijection. Therefore the composition is a bijection. So the given set is countably infinite.
hello im.stuck.on this and need help tyR = 1.95x + 2.25yVariablesx: number of standard-mixture packagesy: number of deluxe-mixture packages
Variables
• x: number of standard-mixture packages
,• y: number of deluxe-mixture packages
1.
a. From the graph, the coordinates of vertex 1 are (0, 0)
b. At vertex 2, the x- and y-coordinates of the lines 2x+3y = 300 and y = x are the same. Solving this system of equations:
[tex]\begin{gathered} 2x+3y=300\text{ \lparen eq. 1\rparen} \\ y=x\text{ \lparen eq. 2\rparen} \\ \text{ Substituting equation 2 into equation 1} \\ 2x+3x=300 \\ 5x=300 \\ x=\frac{300}{5} \\ x=60 \\ \text{ Substituting x = 60 into equation 2:} \\ y=60 \end{gathered}[/tex]The coordinates of vertex 2 are (60, 60)
c. At vertex 3, the x- and y-coordinates of the lines 2x+3y = 300 and 4x+y = 400 are the same. Solving this system of equations:
[tex]\begin{gathered} 2x+3y=300\text{ \lparen eq. 1\rparen} \\ 4x+y=400\text{ \lparen eq. 2\rparen} \\ \text{ Multiplying equation 1 by 2 and then subtracting equation 2 from it:} \\ 2\left(2x+3y\right)=2\cdot300 \\ 4x+6y=600 \\ 4x+6y-\left(4x+y\right)=600-400 \\ 5y=200 \\ y=\frac{200}{5} \\ y=40 \\ \text{ Substituting y = 40 into the second equation and solving for x} \\ 4x+40=400 \\ 4x=400-40 \\ x=\frac{360}{4} \\ x=90 \end{gathered}[/tex]The coordinates of vertex 3 are (90, 40)
d. From the graph, at vertex 4, the line 4x + y = 400 intersects the x-axis, then the value of the y-variable is zero. Substituting this value into the equation and solving for x:
[tex]\begin{gathered} 4x+y=400 \\ \text{ Substituting y = 0} \\ 4x+0=400 \\ x=\frac{400}{4} \\ x=100 \end{gathered}[/tex]The coordinates of vertex 4 are (100, 0)
2.
[tex]R=1.95x+2.25y[/tex]a. Substituting the point (0, 0) into the function R:
[tex]\begin{gathered} R=1.95\left(0\right)+2.25\left(0\right) \\ R=0 \end{gathered}[/tex]b. Substituting the point (60, 60) into the function R:
[tex]\begin{gathered} R=1.95\left(60\right)+2.25\left(60\right) \\ R=252 \end{gathered}[/tex]c. Substituting the point (90, 40) into the function R:
[tex]\begin{gathered} R=1.95\left(90\right)+2.25\left(40\right) \\ R=265.5 \end{gathered}[/tex]d. Substituting the point (100, 0) into the function R:
[tex]\begin{gathered} R=1.95\left(100\right)+2.25\left(0\right) \\ R=195 \end{gathered}[/tex]3. From item 2, the maximum revenue (265.5) corresponds to vertex 3 (90, 40). Then, she should sell 90 standard-mixture packages and 40 deluxe-mixture packages
Question 12 Multiple Choice Worth 1 points)(04.02 MC)Point A is located at (-2, 2), and point M is located at (1,0). If point M is the midpoint of AB, find the location of point B.(-0.5, 1)(4, -2)(-5, 4)(-1, 1)
The given information is:
A is located at (-2,2)
M is located at (1,0)
M is the midpoint of AB.
To find the location of point B, we need to know the difference in the coordinates of point A and point M, and then, apply it to the coordinates of point M to find the location of point B.
The difference between A and M is:
M-A=(1-(-2), 0-2) = (1+2,-2) = (3,-2)
It means we need to add 3 to the x-coordinate of M and subtract 2 from the y-coordinate of M to find the location of B, thus:
[tex]\begin{gathered} B=(1+3,0-2) \\ B=(4,-2) \end{gathered}[/tex]Answer: point B is located at (4,-2)
Concert tickets cost $15 for general admission but only S9 with a student in Ticket sales total$4500 write an equation in standard form to model this situationHow many student tickets were sold 150 general admission tickets were sold?
There are two kinds of tickets general and student
Total sale is 4500
the equation is 4500 = 15X + 9Y
where X is general and Y is student
if 150 general were sold that means
4500 = 15•150 + 9Y
so then Y = (4500- 2250)/9 = 2250/9 = 250
Remarks
writing in standard form
4500 - 15X - 9Y = 0
Another name for standard form is a scientific notation, that means express the numbers in powers of 10.
it costs #9.00 for a box of 15 cookies. What is the cost for one cookie
The total cost is : $9.00
The number of cookies is: 15
to find the cost for just one cookie, we need to divide the total cost by the number of cookies:
[tex]1\text{ cokie = total cost / number of cookies}[/tex]Thus, we will have:
[tex]\begin{gathered} 1\text{ cookie = \$9.00/15} \\ 1\text{ cookie =\$0.6} \end{gathered}[/tex]Answer: $0.6
what is the triangular square of a obtuse
An Obtuse triangle may be either isosceles ( two equal sides and two equal angles ) or scalene ( no equal sides or angle ) an obtuse triangle has only one inscribed square one of the sides of this square coincides with a part of the longest side of the triangle................!
Write a polynomial function with the realzeros -3, 0, and 3.
Recall that we can factorize any polynomial as:
[tex]P(x)=k(x-a)(x-b)...(x-n),[/tex]where k is a constant and a,b,...n are the root of the polynomial.
Therefore, a polynomial function with the real zeros -3,0, and 3 is:
[tex]f(x)=k(x-3)(x-0)(x+3).[/tex]k can be any constant, therefore, we can set k=1.
Answer: [tex]f(x)=x(x+3)(x-3).[/tex]on a field trip, there there are 42 children for three adults to supervise. how many adults are needed for a 252 children?
18 supervisors are needed.
42 children for 3 adults to supervise:
First, we have to divide the number of children by the number of supervisors:
42/3 = 14 children for each supervisor.
Then we have to divide the new number of children (252) by the number of children that each supervisor supervises.
252 /14 = 18 supervisors.
for the piecewise function, find the values h(-7), h(-3), h(4), and h(6).
So,
definition of function for x=-7 is h(x)=-2x-8
[tex]\begin{gathered} h(-7)=-2(-7)-8 \\ =14-8 \\ =6 \end{gathered}[/tex]definition of function for x=-3 is h(x)=4
[tex]h(-3)=4[/tex]definition of function for x=4 is h(x)=x+5
[tex]\begin{gathered} h(4)=4+5 \\ h(4)=9 \end{gathered}[/tex]definition of function for x=6 is h(x)=x+5
[tex]\begin{gathered} h(6)=6+5 \\ =11 \end{gathered}[/tex]5 ptsQuestion 7=Describe how the graph of y = (x+3)3 + 4 changes from the parent graph ofy = $3.Then name the turning point of the graph.Lyshifts left 3 units, up 4units;(4,3)shifts left 4 units, up 3 units: (4,3)shifts left 3 units, up 4 units (-3,4)O shift left 3 units, up 4 units (3,4)
Shifts left 3 units, up 4 units (-3,4)
Explanations:Given the parent function of the translated function expressed as:
[tex]y=x^3[/tex]If the resulting translated function is given as:
[tex]y=(x+3)^3+4[/tex]This shows that the parent graph shifted to the left by 3units and up by 4 units and the turning point of the graph is (-3, 4). Find the graph shown below:
Enter the equation of the following using line in slope-intercept form. slope = 0; y-intercept is 4
The equation of a line in slope-intercept form is given by
[tex]y=mx+c[/tex]where
[tex]\begin{gathered} m\text{ is the slope} \\ c\text{ is the intercept} \end{gathered}[/tex]From the question given
slope = 0
y-intercept =4
What is 1,664 divided by 65
We want to calculate 1664/65.
We can do this step by step. First, from the original number, we will add digit by digit until we have a number that is greater than 65.
So at first, we have number 1. This number is not greater than 65 so we add the 6.
We get the number 16, which is again less than 65. So we add the other 6.
We get the number 166 which is greater than 65. Now, we want to calculate the maximum number to which we can multiply 65 such that the product is less than 166.
Note that 1*65 = 65,
2 * 65 = 130
3*65 = 195 which is greater than 166. So in this case we keep the number 2 in mind.
NOw, to proceed, we multiply 65 times 2 and then subtract this to 166.
So we get
166 - 2*65 = 166 -130 = 36.
This number is less than 65, so we add the number 4 we had.
We get the number 364. Since it is greater than 65. We do as before: we want to find the maximum number to which we multiply 65 and we get a number that is less than 364.
Note that
65 * 5 = 325
65*6 = 390 which is greater that 364. So the number we are looking for is 5.
We had 2 already from the previous step . So we add the 5 to the 2 to get 25.
Now, we subtract 325 to 364
364 -325 = 39
since 39 is less than 65 and there are no more numbers to add, we stop and we say that 1664/65 is 25 with a residue of 39 . This means that
1665 = 25*65 + 39
A company orders boxed lunches from a deli. Assume each boxedlunch is the same price. The proportional relationship between thenumber of boxed lunches ordered, b, and the total cost in dollars andcents, c, can be represented by the equation c = 9.86. What is theconstant of proportionality from the number of boxed lunches to thetotal cost, in dollars and cents?
Let the number of boxed lunches ordered be b
Let the total cost in dollars and cents be c
The given proportionality between them is c=9.8b.
The constant of proportionality from the number of boxed lunches to the total cost in dollars and cents is the same as the ratio of the number of boxed lunches to the total cost in dollars and cents is the same as the ratio
Simply put b : c;
[tex]b\colon c\equiv\frac{b}{c}[/tex][tex]\begin{gathered} \text{ since }c=9.8b \\ \Rightarrow\frac{c}{9.8}=b\Rightarrow\frac{b}{c}=\frac{1}{9.8} \end{gathered}[/tex]So the constant of proportionality is 1/9.8
If cos(0) = -15/17 and 0 is in Quadrant II, then what is sin (0/2)?Give an exact answer, using radicals as needed. Rationalize the denominator and simplify your answer completely.
Given that Θ is in the second quadrant
[tex]\cos \theta=-\frac{15}{17}[/tex]To Determine:
[tex]\sin (\frac{\theta}{2})[/tex]Solution:
Using Identity
[tex]\sin (\frac{\theta}{2})=\sqrt[]{\frac{1-\cos\theta}{2}}[/tex]Substitute cos Θ into the formula
[tex]\begin{gathered} \sin (\frac{\theta}{2})=\sqrt[]{\frac{1-\cos\theta}{2}} \\ \sin (\frac{\theta}{2})=\sqrt[]{\frac{1-(-\frac{15}{17})}{2}} \\ \sin (\frac{\theta}{2})=\sqrt[]{\frac{1+\frac{15}{17}}{2}} \end{gathered}[/tex][tex]\sin (\frac{\theta}{2})=\pm\sqrt[]{\frac{\frac{17+15}{17}}{2}}=\pm\sqrt[]{\frac{\frac{32}{17}}{2}}=\pm\sqrt[]{\frac{32}{17}\times\frac{1}{2}}=\pm\sqrt[]{\frac{16}{17}}[/tex][tex]\begin{gathered} \sin (\frac{\theta}{2})=\frac{\pm4}{\sqrt[]{17}}=\frac{\pm4}{\sqrt[]{17}}\times\frac{\sqrt[]{17}}{\sqrt[]{17}} \\ \sin (\frac{\theta}{2})=\frac{\pm4\sqrt[]{17}}{17} \end{gathered}[/tex]Hence, the final answer is
[tex]\sin (\frac{\theta}{2})=\frac{\pm4\sqrt[]{17}}{17}[/tex]four points are graphed on the coordinate grid which point is best represented by the ordered pair (2 - 5.5 )?
The point (2,-5.5) has a positive x-coordinate, x=2, and a negative y-coordinate, y=-5.5.
This point will be found in the fourth quadrant (QIV) of the coordinate system which is located at the lower right.
In the fourth quadrant, there are two points, point S has an x-coordinate between 5 and 6, and y- coordinate equal -2
Point W has an x-coordinate at x=2 and y-coordinate between 5 and 6.
So the point on the graph that best represents (2,-5.5) is point W
Solve the system of equationsx + y = 52x - y = -2
Lets number the equations;
x + y = 5 -----i
2x - y = -2 -----ii
Let's solve this using the substitution method, lets rewrite equation i as;
x = 5 - y
Substitute this into the equation ii
2(5 - y) - y = -2
10 - 2y - y = -2
Collect like terms
10 + 2 = 3y
12 = 3y , y = 12/3 = 4
Lets substitute y = 4 in equation i, we would have
x + 4 = 5
x = 5-4 = 1
Therefore,
x = 1
y = 4