Given
[tex]\mleft(2d+6\mright)\mleft(3d-15\mright)=0[/tex]We have
[tex]\begin{gathered} 2d+6=0 \\ or \\ 3d-15=0 \end{gathered}[/tex]Then solve each one
[tex]\begin{gathered} 2d+6=0 \\ 2d+6-6=0-6 \\ 2d=-6 \\ \frac{2d}{2}=\frac{-6}{2} \\ d=-3 \end{gathered}[/tex]And
[tex]\begin{gathered} 3d-15=0 \\ 3d-15+15=0+15 \\ 3d=15 \\ \frac{3d}{3}=\frac{15}{3} \\ d=5 \end{gathered}[/tex]Answer: d = -3, d = 5
Can you help me to solve the other half of this problem? I don’t know what I’m doing wrong
Let's start by copying the equation:
[tex]-5\cos ^2(x)+4\cos (x)+1=0[/tex]To make it easier to see, let's substitute cos(x) by "u":
[tex]-5u^2+4u+1=0[/tex]To find the values of "u", we can use Bhaskara's Equation:
[tex]\begin{gathered} u=\frac{-4\pm\sqrt[]{4^2-4\cdot(-5)\cdot1}}{2\cdot(-5)} \\ u=\frac{-4\pm\sqrt[]{16+20}}{-10} \\ u=\frac{-4\pm\sqrt[]{36}}{-10} \\ u=\frac{-4\pm6}{-10} \end{gathered}[/tex][tex]\begin{gathered} u_1=\frac{-4+6}{-10}=\frac{2}{-10}=-0.2 \\ u_2=\frac{-4-6}{-10}=\frac{-10}{-10}=1 \end{gathered}[/tex]Now, let's substitute cos(x) back:
[tex]\begin{gathered} \cos (x_1)=-0.2 \\ \cos (x_2)=1 \end{gathered}[/tex]Since it is a trigonometric solution, we have repeating values of "x" that satisfy each equation above.
The first, the one you already got, comes from
[tex]\begin{gathered} \cos (x)=1 \\ x=0+2\pi k \\ x=2\pi k \end{gathered}[/tex]The smallest non negative is for k = 0 which gives
[tex]x=0[/tex]The next following this part would be for k = 1, which gives:
[tex]x=2\pi[/tex]However, we have another equation for solutions:
[tex]\cos (x)=-0.2_{}[/tex]For this equation, the smallest "x" value can be found using arc-cossine of -0.2 in a calculator, which gives:
[tex]\begin{gathered} x=\arccos (-0.2) \\ x=1.772\ldots \end{gathered}[/tex]This is the next non-negative solution for the equation, because it is smaller than the other we found.
So the second part is x = 1.772.
Juan paid $85.00 for 4 concert tickets. Each ticket cost the same amount. What was the cost of each concert ticket in dollars and cents?
Answer:
$21.25
Explanation:
The cost of 4 concert tickets = $85.00
Each ticket cost the same amount.
Thus:
[tex]\begin{gathered} \text{The cost for each concert ticket will be}=\frac{85}{4} \\ =\$21.25 \end{gathered}[/tex]Hey! I need help finding the slope of the Tangent at a given point as depicted in the following image: (Just need help with an explanation to #5)
5.
[tex]\begin{gathered} \frac{d}{dx}(x^n)=nx^{n-1} \\ \end{gathered}[/tex]so:
[tex]\begin{gathered} f(x)=3-5x \\ f(x)^{\prime}=\frac{d}{dx}(3)-\frac{d}{dx}(5x)=\frac{d}{dx}(3)-5\frac{d}{dx}(x) \\ so\colon \\ \frac{d}{dx}(3)=0 \\ \frac{d}{dx}(x)=1x^{1-1}=1x^0=1\cdot1=1 \\ f(x)^{\prime}=0-5 \\ f(x)^{\prime}=-5 \end{gathered}[/tex]6.
[tex]\begin{gathered} g(x)=\frac{3}{2}x+1 \\ g(x)^{\prime}=\frac{3}{2}=m \end{gathered}[/tex]The following is a list of 5 measurements.5, 17, 10, 13, 19Send data to calculatorSuppose that these 5 measurements are respectively labeled X2, X2, ..., Xs. Compute the following.5Σ (4)i=1
We will have the following:
[tex]\sum ^5_{i=1}(x_i)^2=(5)^2+(17)^2+(10)^2+(13)^2+(19)^2\Rightarrow\sum ^5_{i=1}(x_i)=944[/tex]So, the given sum is equal to 944.
1 ) At a local department store, jeans have been reduced to $5. This price is at 20% of theoriginal price for jeans. Given this, what was the original price of the jeans? Roundyour answer to the nearest whole number if necessary.
we have that
$5 ------> represents 20% of the original price
so
Applying proportion
Find out how much represent a percentage of 100%
so
5/20=x/100
solve for x
x=(5/20)*100
x=$25
the answer is $25PLEASE I NEED IT SOON The point (5, 3) has an image of (2, -1) under a translation of left 3 and down 4 units. Which sequence of transformations produces the same image?
Answer:
[tex]undefined[/tex]Explanation: We are going two points P1 and P2 and we need to produce P2 by applying certain transformations on P1. the two points are as follows:
[tex]\begin{gathered} P_1(5,3) \\ P_2(2,-1) \end{gathered}[/tex]By translating P1 3 units left and 2 units down we get a mirror image of P2 over x-axis, then by reflacting over x-axis we get P2, therefore
Match the amplitude, midline, period, and frequency for the cosine equation
Explanation
we can describe the cosine function as
[tex]y=A\cos \mleft(B\mleft(x+C\mright)\mright)+D[/tex]where
amplitude is A
Frequency is B
period is 2π/B
phase shift is C (positive is to the left)
vertical shift is D
Step 1
identify
[tex]5\cos (2x)+3\rightarrow A\cos (B(x+C))+D[/tex]hence
[tex]\begin{gathered} A=5=\text{Amplitude} \\ B=2,C=0,so \\ \text{period}=\frac{2\text{ }\pi}{B}=\frac{2\text{ }\pi}{2}=\pi \\ \text{period}=\pi \\ Frequency=B=2 \\ \text{Vertical shift=D=3} \end{gathered}[/tex]Step 2
midline
The equation of the midline of periodic function is the average of the maximum and minimum values of the function.
a) we have a maximum when
[tex]\begin{gathered} \cos (2x)=1 \\ x=0,\text{ because (cos 0)=1} \\ \text{now, replace} \\ y=5\cos (2x)+3 \\ y=5\cos (2\cdot0)+3=5\cdot1+3=8 \\ y=8,\text{ so the max. is 8} \end{gathered}[/tex]b) we have a minimum when
[tex]\begin{gathered} \cos (2x)=-1 \\ x=\frac{\pi}{2},\text{ because} \\ \cos (2\frac{\pi}{2})=\cos (\pi)=-1 \\ \text{now, replace} \\ y=5\cos (2\cdot\frac{\pi}{2})+3=5\cdot-1+3=-5+3=-2 \end{gathered}[/tex]so, the midline is the average of 8 and -2
[tex]\begin{gathered} \text{midline}=y=\frac{8+(-2)}{2}=\frac{6}{2}=3 \\ y=3 \end{gathered}[/tex]I hope this helps you
A regular hexagon has a radius of 20cm. Find the lengths of the apothem and a side of the hexagon.
A regular hexagon has a radius of 20cm. Find the lengths of the apothem and a side of the hexagon.
Remember that
A regular hexagon can be divided into six equilateral triangles
where
the side of the equilateral triangle is equal to the length side of the regular hexagon and the height of the equilateral triangle is equal to the apothem
in this problem
the radius of the polygon is equal to the length side of the equilateral triangle
therefore
the side of the regular hexagon is 20 cmpart 2
Find the apothem
see the attached figure to better understand the problem
Applying Pythagorean Theorem
20^2=10^2+a^2
a^2=20^2-10^2
a^2=300
a=√300 cm
simplify
a=10√3 cm -----> apothemComplete the explanation to identify the set of numbers that best describes each situation.The change will be whole dollar amount which can be negative, zero, or positive. Thus the change willbe (an) ____[(a)rational, (b)integer, (c)real, (d)irrational] number.
The set of negative integers is represented below:
[tex]-\infty,\cdots-2,-1[/tex]The set of positive integers is represented as:
[tex]1,2,\cdots\infty[/tex]Combining the two sets above and adding zero (0), we have:
[tex]-\infty,\cdots-2,-1,0,1,2\cdots,\infty[/tex]The set which describes the set of negative, zero or positive whole numbers is the set of integers.
Thus the change will be an integer number.
For each pair of statements choose the one that is true ABC or D
EXPLANATION:
Given;
We are given four pairs of statements as indicated in the attached image.
Required;
We are required to determine which statement is true.
Solution;
(A)
[tex]\begin{gathered} \lbrace s\rbrace\subseteq\lbrace g,s\rbrace\text{ }(TRUE) \\ s\subseteq\lbrace g,s\rbrace \end{gathered}[/tex](B)
[tex]\begin{gathered} \lbrace5\rbrace\in\lbrace5,6,7\rbrace \\ \lbrace5\rbrace\subseteq\ne\lbrace6,7,8\rbrace\text{ }(TRUE) \end{gathered}[/tex](C)
[tex]\begin{gathered} \lbrace11,13,15\rbrace\in\lbrace1,3,5,7...\rbrace \\ \lbrace11,13,15\rbrace\subseteq\lbrace1,3,5,7...\rbrace\text{ }(TRUE) \end{gathered}[/tex](D)
[tex]\begin{gathered} \lbrace q\rbrace\in\lbrace n,q\rbrace \\ q\in\lbrace n,q\rbrace\text{ }(TRUE) \end{gathered}[/tex]Select the statement that best describes the pattern.4. 33- 33 = 04-4 = 05- 5 = 0A 33-33= xB X-X=0C x-0= x
X-X=0 (option B)
Explanation:
The pattern is the subtraction of the same number to get 0
33- 33 = 0
4-4 = 0
5- 5 = 0
From the options given, the one that has the difference of the same number resulting to zero is X-X=0
Hence, the statement that best describes the pattern is X-X=0 (option B)
find the equation of the images of the following lines when the reflection line is the x-axis
When the equation is reflected about the x-axis,
(x, y) → (x, - y)
The original equation is y = - x + 7
Therefore,
[tex]\begin{gathered} f(x)=-f(x) \\ replace\text{ y with -y} \\ -y=-x+7 \\ y=x-7 \end{gathered}[/tex]Tom's Bakery recently spent a total of $800 on new equipment, and their average hourlyoperating costs are $10. Their average hourly receipts are $90. The bakery will soon makeback the amount it invested in equipment. What would the total expenses and receipts bothequal?Write a system of equations, graph them, and type the solutionTimelapsedPAUD1.000Smarts.com0300600Dollars (9)400200.103040HoursCESreceiptdollars
The equation for the expenses of the bakery is $800+$10t, where t is given in hours. On the other hand, the equation that models the receipts is $90t, where t is in hours.
To find the value of t such that the expenses are equal to the receipt we need to solve the equation below
[tex]\begin{gathered} 800+10t=90t \\ \Rightarrow800=90t-10t=80t \\ \Rightarrow t=10 \end{gathered}[/tex]In dollars, this is
[tex]90\cdot10=900[/tex]The answer is $900 dollars
The graph of the equations is
The green line represents the expenses and the blue one the receipts
calculate the area height 137, base 203
where b = base and h=height
so for this triangle:
[tex]area=\frac{1}{2}*137*203[/tex]The answer is 13905.5
1 - Determine whether the given function is even, odd, or neither.a. (picture 1)b. (picture 2)2 - Evaluate the piece wise function at the given value of the independent variable. (picture 3)if f(-3)
Here in this question, we want to know if either of the function is even , odd or neither
For an even function, the additive inverse of the value of the independent variable will give the same value of the dependent variable. An odd function will behave otherwise.
What this mean in plain terms is that for an even function;
f(x) = F(-x)
f(x) = 4x^2 + x^4
Let us find f(1)
f(1) = 4(1)^2 + 1^4 = 4 + 1 = 5
f(-1) = 4(-1)^2 + (-1)^4
f(-1) = 4 + 1 = 5
In this case, since f(1) = f(-1), then the function is even.
The graph of f(x) = (1/4)^-x is reflected about the y-axis and compressed vertically by a factor of 1/3 What is the equation of the new function, g(x)?
Given:
[tex]f(x)=(\frac{1}{4})^{-x}[/tex]f(x) is reflected about the y-axis and compressed vertically by a factor of 1/3.
Required:
We need to find the new function g(x).
Explanation:
The reflection of the function y=f(x) about y-axis is y=f(-x).
To reflect the given function f(x) about y-axis:
Replace x =-x in the given function f(x).
[tex]f(-x)=(\frac{1}{4})^{-(-x)}[/tex][tex]f(-x)=(\frac{1}{4})^x[/tex]Multiply both sides by 1/3 to get the function compressed vertically by a factor of 1/3.
[tex]\frac{1}{3}f(-x)=\frac{1}{3}(\frac{1}{4})^x[/tex]The new function is
[tex]g(x)=\frac{1}{3}(\frac{1}{4})^x[/tex]Final answer:
[tex]g(x)=\frac{1}{3}\times(\frac{1}{4})^x[/tex]
The endpoints of segment CD are C(1, 2) and D(5, 4). Graph the image of segment CD after the composition of transformations. C(1, 2) and D(5, 4) Translation: (x, y) + (x, y+ 2) Reflection: over the line y = x
Two segment points, transformation
C (1,2).
D (5,4)
FOR POINT C
Translate C , (x, y) + (x, y+ 2) = (1,2) + (1, 2+2) = (1+1, 2+2+2) = (2,6)
Reflection over y= x
change (x ,y ) in (y,x)
(x,y) = ( 6, 2)
FOR POINT D
Translate D ,(x,y) + (x , y+2) = (5,4) + (5, 4+2) = (5+5, 4+4+2) = (10, 10)
Reflection over y=x
(x,y) = (10,10). (Its same point)
DRAWING
New segment C'D' is drawed in green
In a certain experiment, a coin is tossed and this spinner is spun. Compute the probability of the event.P(heads and no blue)
Consider that the two events (tossing a coin and spinning a spinner) are independent and that the probability of landing on blue is equal to 1/3; thus,
[tex]\begin{gathered} P(heads\&no-blue)=\frac{1}{2}\cdot(1-\frac{1}{3}) \\ \Rightarrow P(heads\&no-blue)=\frac{1}{2}\cdot\frac{2}{3}=\frac{1}{3} \end{gathered}[/tex]Thus, the answer is P(heads&NoBlue)=1/3
describe the effect on the graph of the parent f(x)=x
we know that
the parent function is
f(x)=x
The line passes throught the origin
the slope is m=1
Find the equation of the line g(x)
Billy is comparing gasoline prices at two different gas stations. ·at the first gas station, the equation c = 2.80g gives the relationship between g, the number of gallon of gasoline, and c, the total cost, in dollars.·at the second gas station, the cost of 2.5 gallons of gasoline is $8.30, and the cost of 5 gallons of gasoline is $16.60.how much money, per gallon, would Billy save by going to the less expensive gas station?
For the first gas station,
[tex]c=2.80g[/tex]That is, for one number of gallon of gasoline, the cost is, 2.80
For the second gas station, cost of 2.5 gallons of gasoline is $8.30. Therefore, for one gallon if gasoline, the cost is,
[tex]\frac{8.30}{2.5}=3.32[/tex]Therefore, Billy will save, 3.32 - 2.80 = 0.52 dollars by going to the less expensive gas station.
An end point and one arrow
An end point and one arrow is what is called a vector in mathematical terms.
The end point is where you apply the vector (that could be representing a velocity, or a force, for example.
The arrow indicates the direction of that vector quantity.
the question is really 3(x-8)
Expanding the parenthesis:
[tex]\begin{gathered} 3(x)\text{ - 3(8)} \\ 3x\text{ - 24} \end{gathered}[/tex]Using the image below, identify the type of angle and find the missing angle.
SOLUTION:
Step 1:
In this question, we are given the following:
Using the image below, identify the type of angle and find the missing angle:
Step 2:
The details of the solution are as follows:
[tex]Type\text{ of angle Relationship: Corresponding Angles}[/tex][tex]Missing\text{ Angle: m}\angle1\text{ = 129}^0[/tex]Questionis undefined. If there's more than one value, list them9a - 11Determine the value(s) for which the rational expression-a - 9separated by a comma, e.g. a = 2,3.h
The rational expression is
[tex]\frac{9a-11}{-a-9}[/tex]The values of a which make the rational expression undefined are the values that make the denominator = 0
Then to find them equate the denominator by 0
The denominator is (-a - 9)
[tex]-a-9=0[/tex]Add 9 to each side
[tex]\begin{gathered} -a-9+9=0+9 \\ -a=9 \end{gathered}[/tex]Divide each side by -1
[tex]\begin{gathered} \frac{-a}{-1}=\frac{9}{-1} \\ a=-9 \end{gathered}[/tex]The value of a which makes the rational expression undefined is -9
The answer is a = -9
Como se calcula la hipotenusa de un triángulo
To determine the hypotenuse of the triangle.
The hypotenuse is the opposite side of the right angle in the triangle. It’s also the longest side of the triangle.
If a problem says that to calculate the length of hypotenuse c in a triangle with side a, side b, and hypotenuse c.
Then you are working with a right-angled triangle.
Then by Pythagoras theorem, determine the hypotenuse.
[tex]c^2=a^2+b^2[/tex][tex]c=\sqrt[]{a^2+b^2}[/tex]Then the hypotenuse side is calculated.
A quadrilateral with exactly one pair of parallel sides is: A. squareB. rectangleC. rhombusD. trapezoid
The parallel sides are sides that will never meet and are always the same distance apart.
Given the figures below;
The above shapes has more than a pair of parallel sides, hence they are wrong.
Also,
The trapezoid has only one pair of parallel sides.
CORRECT OPTION: D
mr. Patterson takes 8 minutes to run 2/3 of a Lap. How long would it take to run one full lap.
If it takes Patterson 8 minutes to run 2/3 of a lap.
Let the time to complete on one lap be x,
Then 2/3 of x = 8
cross- multiply, we have :
[tex]\begin{gathered} \frac{2}{3}x=8,_{} \\ 2x=8\times3 \\ \text{Then }x=\text{ }\frac{8\times3}{2} \\ x\text{ = 12 mins} \end{gathered}[/tex]Slope intercept formPlease Solve everything with the exception of 8
The equation of a line in slope intercept form is in the form,
[tex]y=mx+c[/tex]SOLUTION
3) 2y - 6 = -6x
Add 6 to both sides
[tex]\begin{gathered} 2y-6+6=-6x+6 \\ 2y=-6x+6 \end{gathered}[/tex]Divide through by 2
[tex]\begin{gathered} \frac{2y}{2}=-\frac{6x}{2}+\frac{6}{2} \\ y=-3x+3 \end{gathered}[/tex]Hence, the equation in the slope intercept form is
[tex]y=-3x+3[/tex]4) - 11x - 7y = -56
Add +11x to both sides
[tex]\begin{gathered} -11x-7y+11x=-56+11x \\ -7y-11x+11x=11x-56 \\ -7y=11x-56 \end{gathered}[/tex]Divide both sides by - 7
[tex]\begin{gathered} \frac{-7y}{-7}=\frac{11x}{-7}-\frac{56}{-7} \\ y=-\frac{11x}{7}+8 \end{gathered}[/tex]Hence, the equation in the slope intercept form is
[tex]y=-\frac{11x}{7}+8[/tex]How would you find the slope of this line and write an equation for it?
Given the points:
A (-1, 3) and B (0, 4)
slope - intercept form of an equation: y = mx + b.
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex][tex]m\text{ = }\frac{4-3}{0\text{ + 1}}=\text{ 1}[/tex]Now, to find b, we can replace one point in the slope- intercept form:
4 = 1 x 0 + b
b = 4
Slope- intercept equation: y = x + 4
3(3 + 6q) I need to simplify the expression
3(3 + 6q)
By expanding the bracket, we have
3(3) + 3(6q) = 9 + 18q