To solve this expression, we just have to subtract because they are like terms
[tex]6q-q=5q[/tex]Hence, the answer is 5q.
After how many cakes will their savings be the same for both? b) What will their savings be?
Let "s" represent the amount saved in the bank account and "c" the number of cakes sold.
Jane (J)
Has a starting balance of $70 and she sells "c" cakes for $25 each, you can symbolize the earnings of the cake sales as 25c
You can express the total amount saved using the following expression
[tex]s_J=70+25c[/tex]Miriam (M)
Has a starting balance of $100 and shells cakes for $20 each, you can symbolize the total earnings for her cakes sales as 20c
So the total amount saved can be expressed as:
[tex]s_M=100+20c[/tex]a) To determine how many cakes they must sell so that their savings will be the same, you have to equal both expressions and calculate the value of c:
[tex]\begin{gathered} s_J=s_M \\ 70+25c=100+20c \end{gathered}[/tex]To calculate for c, the first step is to pass the term containing the variable to the left by applying the opposite operation to both sides of the equal sign:
[tex]\begin{gathered} 70+25c-20c=100+20c-20c \\ 70+5c=100 \end{gathered}[/tex]Repeat the process to pass 70 to the right side of the expression
[tex]\begin{gathered} 70-70+5c=100-70 \\ 5c=30 \end{gathered}[/tex]And divide both sides by 5 to reach the value of c
[tex]\begin{gathered} \frac{5c}{5}=\frac{30}{5} \\ c=6 \end{gathered}[/tex]After selling 6 cakes both Jae and Miriam will have saved the same amount.
b)
To determine what will their savings be, you have to replace either one of the expressions with c=6 and calculate for s:
[tex]\begin{gathered} s_J=70+25c \\ s_j=70+25\cdot6 \\ s_j=220 \end{gathered}[/tex]If you solve it using Miriam's expression the result must be the same:
[tex]\begin{gathered} s_M=100+20c \\ s_M=100+20\cdot6 \\ s_M=220 \end{gathered}[/tex]As you see using either equation we arrived to the same result, after selling 6 cakes their total saves will be $220
Find the volume of this object.Use 3 for T.Volume of a CylinderV=Tir2h6 in8 in10 in] 2 in V ~ [?]in3
Solution:
Given:
Two cylinders on each other;
[tex]\begin{gathered} \text{For the cylinder at the top, the following were given;} \\ d=6in \\ \text{radius is half of a diameter,} \\ \text{Hence,} \\ r=\frac{d}{2}=\frac{6}{2} \\ r=3in \\ h=8in \\ \pi=3 \end{gathered}[/tex]Using the formula of the volume of a cylinder;
[tex]\begin{gathered} V=\pi r^2h \\ V=3\times3^2\times8 \\ V=216in^3 \end{gathered}[/tex]For the cylinder at the bottom, the following were given;
[tex]\begin{gathered} \\ d=10in \\ \text{radius is half of a diameter,} \\ \text{Hence,} \\ r=\frac{d}{2}=\frac{10}{2} \\ r=5in \\ h=2in \\ \pi=3 \end{gathered}[/tex]Using the formula of the volume of a cylinder;
[tex]\begin{gathered} V=\pi r^2h \\ V=3\times5^2\times2 \\ V=150in^3 \end{gathered}[/tex]Hence, the volume of the object is the total volume of both cylinders.
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Therefore, the volume of the object is 366 cubic inches.
Determine if the measures create aight triangle.13m5m12m
use the pythagorean theorem to see if the measurements create a right trinangle.
remember the addition of the squared shorter sides must be equal to the largest side squared
[tex]a^2+b^2=c^2[/tex][tex]5^2+12^2=13^2[/tex][tex]\begin{gathered} 5^2+12^2=169 \\ 13^2=169 \\ \\ 169=169 \end{gathered}[/tex]3. Are the triangles congruent? If so, how? b. yes, AAS ves, SSS yes, SAS + d
Yes are congruent , SSS because the graph shows us two equal sides, if they are equal, then the upper and lower sides of the quadrilateral will be equal, for this reason we already have two equal sides, and since the triangles share the diagonal we can say that their three sides are equal
red and green sides are equal one by one,the red ones are the same because the drawing says so, and the green ones are the same because in a parallelogram the opposite sides have the same measure.
we already have that two of the three sides of each triangle are equal,and we can conclude that the third side is also the same, since the triangles share it
then the triangles are equivalent since their three sides are equal SSS
1. Which of the following pairs of figures are congruenta which are not ? How do you know Be sure to use the following vocabulary words congruent .
Congruent and similar goes by:
Two figures are congruent if they have the same shape and size.
and,
When two figures are similar, the ratios of the lengths of their corresponding sides are equal.
Now, check the images.
First figure (two houses) are congruent.
Second figures (two triangles) are not congruent.
How is seeing the parts of a partitioned number line the same as seeing the parts of a partitioned rectangle? How is it different?
Partitioning a number line:
If you have a number line, you can partition into fractions. This is done by dividing the number lines into equal portions and summing up the portions to give the total part that you need.
For example, to partition a number line into 3/4 portion of a number line, you can partition the number line into 4 portions of 1/4 each and take 3 portions out of the four to get 3/4.
The same strategy is used for a rectangle:
To divide a rectangle into two portions of 3/4 and 1/4, you can use similar method as above:
Difference:The difference is that in a number line, you only have the length and you can partition only across the length
In a rectangle you can partition both the length and the width of the shape
Billy is comparing gasoline prices at two different gas stationsAt the first gas station the equation c = 2.80g gives the relationship between g the number of gallons of gasoline and c the total cost in dollarsAt the second gas station the cost of 2.5 gallons of gasoline is $8.30 and a cost of $5 of gasoline is $16.60how much per gallon would Billy save by going to the less expensive gas station
Answer
Billy would save $0.52 by going to the less expensive gas station (which is the first gas station).
Explanation
At the first station,
c = 2.80g
c = cost of gasoline
g = number of gallons of gasoline
The cost of 1 gallon of gasoline at this station will be obtained by putting in g = 1
c = 2.80g
g = 1 gallon
c = 2.80 (1)
c = 2.80 dollars per gallon
Cost per gallon = 2.80 dollars
At the second station,
2.5 gallons = 8.30 dollars
5 gallons = 16.60 dollars
The cost of 1 gallon at this station will be
1 gallon = (8.30/2.5) = (16.60/5) = 3.32 dollars
Cost per gallon = 3.32 dollars
We can see that gasoline is cheaper at the first station and the difference in price per gallon (which is the amount that will be saved by going to the less expensive gas station) is
3.32 - 2.80 = 0.52 dollars
Hope this Helps!!!
The time required for the stone to hit the ground is ( ) seconds?
we have the equation
[tex]h=-16t^2+144[/tex]Remember that
when the stone hit the ground, the value of h is zero
so
For h=0
[tex]-16t^2+144=0[/tex]solve the quadratic equation
[tex]\begin{gathered} 16t^2=144 \\ t^2=\frac{144}{16} \\ t=\pm\frac{12}{4} \\ t=\pm3 \end{gathered}[/tex]the solution is the positive value
t=3 sec
These tables represent an exponential function. Find the average rate ofchange for the interval from x = 8 to x = 9.хyInterval0110 to 13291 to 2Average rateof change2]x36]x318]*3543x3162]*34863272 to 34813 to 44 to 5524367295 to 6O A. 13,122O B. 3O C. 19,683D. 6561
Average rate can be calculated like the slope
[tex]\frac{y2-y1}{x2-x1}[/tex]where (x2,y2) is a right point yo (x1,y1)
But we need the values of x=8 and x=9
we realize the change between values of y is the last value by 3 then if
[tex]\begin{gathered} 6\longrightarrow729 \\ 7\longrightarrow729\times3=2187 \\ 8\longrightarrow2187\times3=6561 \\ 9\longrightarrow6561\times3=19683 \end{gathered}[/tex]we have the corresponding values for x=8 and x=9
now replace on the formula of the slope using the points (8 , 6561) and (9 , 19683)
where (9 , 19683) is (x2,y2) and (8 , 6561) is (x1,y1)
[tex]\begin{gathered} \frac{19683-6561}{9-8} \\ \\ \frac{13122}{1}=13122 \end{gathered}[/tex]the avreage rate of change for the interval 8 to 9 is 13122
We realize the values of the average are multiplied by 3 too, then we can fi
PLEASE HELP ME!!!!
What is the value of this expression when p = 5 and q=−2?
−3(p−q)2
Enter your answer in the box.
Answer:
-147
Step-by-step explanation:
We can solve this by plugging in p = 5 and q=−2 and then evaluating using PEMDAS which tells us the order we do the math in by operation
Remember,
PEMDAS means
Parenthesis
Exponents
Multiplication and Division ( perform going left to right )
Addition and Subtraction ( perform going left to right )
-3(p-q)²
==> plug in p = 5 and q = -2
-3(5-(-2))²
==> remove parenthesis on -2
-3(5 + 2)²
==> do the operations inside of the parenthesis
-3(7)²
==> do the exponents
-3(49)
==> multiply -3 and 49
=-147
Mona bought 3 3/8 pounds of cheese. She used 2 3/4 pounds to make sandwiches. Write and solve an equation to find how much cheese is left.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
cheese:
purchased amount = 3 3/8 lb
used amount = 2 3/4
Step 02:
equation:
remaining amount = purchased amount - used amount
[tex]\begin{gathered} \text{remaining amount = 3 3/8 - 2 3/4 }=\text{ (3 + }\frac{3}{8})\text{ - (2 + }\frac{3}{4}) \\ \text{ } \end{gathered}[/tex][tex]\text{remaining amount = }\frac{27}{8}\text{ - }\frac{11}{4}=\frac{5}{8}[/tex]The answer is:
5/8 lb = 0.625 lb
why is this correct?
Trapezoid area = (7+3)/2• height = 10/2 •height
Parallelogram area= 5 • height
Then ,Candy is correct ,both areas are EQUAL
The area of parallelogram is 5•H
The area of trapezoid is 10•H divided by 2 ,or. 5•H
2. Which graph represents the solution set to the following system of inequalities?y +6 > (x + 1)^2 + 2-x+2<= -1/2y+3
Solution:
The inequalities are given below as
[tex]\begin{gathered} y+6>(x+1)^2+2 \\ -x+2\leq-\frac{1}{2}y+3 \end{gathered}[/tex]Using a graphing calculator, we will have the graph be
Solve using the elimination method:4x + y + 5z = -40-3x + 2y + 4z = 10x - y - 2z = -2
Let's take
4x + y + 5z = -40 (Eq1)
-3x + 2y + 4z = 10 (Eq2)
x - y - 2z = -2 (Eq3)
Now create a new system using elimination
-2* (4x + y + 5z = -40) (Eq1)
1* (-3x + 2y + 4z = 10) (Eq2)
----------------------------------
-11x - 6z = 90 (Eq4)
Use elimination again
1* (-3x + 2y + 4z = 10) (Eq2)
2* (x - y - 2z = -2) (Eq3)
---------------------------------------
-x = 6 (Eq5)
From Equation 5 we have that
x = -6
Replace the value of x in Equation 4 and clear z
-11(-6) - 6z = 90
-6z = 90 - 66
-6z=24
z = 24/-6
z = -4
Replace x and z in equation 3 and clear y
-6 - y - 2*(-4) = -2
-y + 8= -2 +6
-y = 4 - 8
-y= -4
y = 4
a surveyor locating the corners of a four-sided of property started at one corner and walk 200 feet in the direction of N80°E 5o reach the next corner he turned and walked to north 160 feet to the next corner of the property he did turn and walk due west to get to the 4th corner of the property finally he walked in the direction S15°E to get back to the starting point. What is the area of the property is in square feet?
we have three figures, we must find the area of each one and at the end, add them
lower triangle
we must find x and y to calculate the area, we will use trigonometric ratios
[tex]\begin{gathered} \sin (80)=\frac{x}{200} \\ \\ x=200\sin (80) \\ x=197 \end{gathered}[/tex][tex]\begin{gathered} \sin (10)=\frac{y}{200} \\ \\ y=200\sin (10) \\ y=34.73 \end{gathered}[/tex]now calculate the area
[tex]\begin{gathered} A_{T1}=\frac{b\times h}{2} \\ \\ A_{T1}=\frac{y\times x}{2}=\frac{34.73\times197}{2} \\ \\ A_{T1}_{}=3420.9 \end{gathered}[/tex]the area of the triangle is 3420.9 square feet
Rectangle
we have the height (160ft) and the base we calculate it in the previous step (x=197ft)
the area is
[tex]\begin{gathered} A_R=b\times h \\ A_R=197\times160 \\ A_R=31520 \end{gathered}[/tex]the area of the rectangle is 31520 square feet
Left Triangle
we must use trigonometric ratios to calculate Z
[tex]\begin{gathered} \tan (15)=\frac{Z}{160+34.73} \\ \\ Z=194.73\tan (15) \\ Z=52.18 \end{gathered}[/tex]and the area of the triangle is
[tex]\begin{gathered} A_{T2}=\frac{b\times h}{2} \\ \\ A_{T2}=\frac{Z\times(160+34.73)}{2}=\frac{52.18\times194.73}{2} \\ \\ A_{T2}=5080.5 \end{gathered}[/tex]Total area
[tex]\begin{gathered} A=A_{T1}+A_R+A_{T2} \\ A=3420.9+31520+5080.5 \\ A=40021.4 \end{gathered}[/tex]the total area is 40,021.4 square feet
Sharon Nguyen has $25,000 to invest and believes that she can earn 8% compounded semiannually. Find the amount if she invests for 10 years
Solution:
Given:
[tex]\begin{gathered} P=\text{ \$25,000} \\ r=8\text{ \%}=\frac{8}{100}=0.08 \\ t=10\text{years} \\ n=\text{twice a year(semiannually),}n=2 \end{gathered}[/tex]
To get the amount, we use the compound interest formula;
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Substituting the given values into the formula,
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A=25000(1+\frac{0.08}{2})^{2\times10} \\ A=25000(1+0.04)^{20} \\ A=25000(1.04)^{20} \\ A=25000\times1.04^{20} \\ A=\text{ \$54,778.08} \end{gathered}[/tex]
Therefore, the amount after 10 years is $54,778.08
how do I find which coordinate pairs represent vertices of P'Q'R'S after these two transformations?
We have two transformations.
We will apply them to a generic point P=(x,y), and then we can replace them with any coordinates as inputs.
First transformation: translating 6 units to the right.
This changes the x-coordinate by adding 6 units (x=0 becames x'=6, for example), so we can write:
[tex]P=(x,y)\longrightarrow P^{\prime}=(x+6,y)[/tex]Second transformation: rotate 90 degrees clockwise.
This changes both x and y coordinates. We can look at a drawing to understand the transformation.
The x-coordinate becomes the y-coordinate, and the y-coordinate becomes the negative x-coordinate.
We can then write:
[tex]P^{\prime}=(x+6,y)\longrightarrow P^{\prime}^{\prime}=(y,-x-6)[/tex]So now we know that the final image of a point (x,y) after the two transformations is (y,-x-6).
Then, we can list all four points:
[tex]P=(-3,7)\longrightarrow P^{\prime}^{\prime}=(7,-(-3)-6)=(7,-3)[/tex][tex]Q=(4,12)\longrightarrow Q^{\prime}^{\prime}=(12,-4-6)=(12,-10)[/tex][tex]R=(4,-2)\longrightarrow R^{\prime}^{\prime}=(-2,-4-6)=(-2,-10)[/tex][tex]S=(-3,-7)\longrightarrow S^{\prime}^{\prime}=(-7,-(-3)+6)=(-7,-3)[/tex]Final coordinates: (7,-3), (12,-10), (-2,-10) and (-7,-3).
The equation d=16t^2 gives the distance in feet that a golf ball falls in t seconds.How many seconds will it take the gol to drop to the ground from a height of 4 feet?64 feet?
We are given the following function of distance in terms of time:
[tex]d=16t^2[/tex]Where:
[tex]\begin{gathered} d=\text{ distance} \\ t=\text{ time} \end{gathered}[/tex]We are asked to determine the time when the distance is 4ft. To do that we will solve for "t". First, we will divide both sides by 16:
[tex]\frac{d}{16}=t^2[/tex]Now, we take the square root to both sides:
[tex]\sqrt{\frac{d}{16}}=t[/tex]Simplifying we get:
[tex]\frac{1}{4}\sqrt{d}=t[/tex]Now, we substitute the value of the distance:
[tex]\frac{1}{4}\sqrt{4}=t[/tex]Solving the operations:
[tex]\begin{gathered} \frac{1}{2}=t \\ \\ 0.5=t \end{gathered}[/tex]Therefore, the time is 0.5
The same procedure is used to determine the time for 64 feet.
Select the correct choices to complete the sentence.
AIR SHOW At a flight demonstration, two planes are flying in a synchronized pattern. The planes start their demonstration at (−20,−15) and (5, −15) . Select the transformation that represents the planes’ flight pattern to their final destinations at (−30, 20) and (0, 20) .
Options:
A. (-2, 7)
B. (-10, 35)
C. (-12, 48)
Answer:
The coorect option is letter C
Find dy/dx by implicit differention.1) x^4 + x^2y^2 + y^3 = 5(2) Sin (x+y) = cosx + casy
The given equation is:
[tex]x^4+x^2y^2+y^3=5[/tex]The differential is given as:
[tex]4x^3+2xy^2+2yx^2\frac{dy}{dx}+3y^2\frac{dy}{dx}=0[/tex]Make dy/dx the subject of the formula:
[tex]\begin{gathered} 2yx^2\frac{dy}{dx}+3y^2\frac{dy}{dx}=-(4x^3+2xy^2) \\ \\ \frac{dy}{dx}(2x^2y+3y^2)=-(4x^3+2xy^2) \\ \\ \frac{dy}{dx}=\frac{-(4x^3+2xy^2)}{2x^2y+3y^2} \end{gathered}[/tex]g(n) = 2n^2 - 4; Find g(-2)
ANSWER
g(-2) = 4
EXPLANATION
We are given the function g(n) as:
[tex]g(n)=2n^2\text{ - 4}[/tex]To find g(-2), we have to replace n with -2 in g(n) and simplify it.
[tex]\begin{gathered} g(-2)=2(-2)^2\text{ - 4 = 2}\cdot4\text{ - 4} \\ g(-2)\text{ = 8 - 4} \\ g(-2)\text{ = 4} \end{gathered}[/tex]That is the value of g(-2)
Nicole can run 4
laps in 2/5 hour.
How long will it
Hake her to run 5
laps?
Answer:
1/2 hour
Step-by-step explanation:
Each lap is 1/10 hours times that by 5 and you get 5/10 and simplified is 1/2
how do i findFind the domain of f ∘ g in the equation
First, we need to find the composite function of f ∘ g.
We need to write the function f(x) in terms of g(x).
Then:
[tex]\begin{gathered} (fog)(x)=\frac{6}{g(x)+7}=\frac{6}{x+5+7} \\ =\frac{6}{x+12} \end{gathered}[/tex]Now, to find the domain we need to look at the x values that the function can take.
The function is a rational function, then the domain is given using the denominator because it can be equal to zero.
x+12 = 0
x=-12
Therefore, the domain is the interval (-∞.-12)U(-12,∞)
How to create a table like the following for the following problem:
We have to graph the function:
[tex]y=-\frac{5}{2}+\cos \lbrack3(x-\frac{\pi}{6})\rbrack[/tex]We can start from known points of the cosine function and then find the values of y.
We know the exact values of cosine for the following angles:
[tex]\begin{gathered} \cos (0)=1 \\ \cos (\frac{\pi}{6})=\frac{\sqrt[]{3}}{2} \\ \cos (\frac{\pi}{4})=\frac{\sqrt[]{2}}{2} \\ \cos (\frac{\pi}{3})=\frac{1}{2} \\ \cos (\frac{\pi}{2})=0 \\ \cos (\frac{2\pi}{3})=-\frac{1}{2} \\ \cos (\frac{3\pi}{4})=\frac{-\sqrt[]{2}}{2} \\ \cos (\frac{5\pi}{6})=\frac{-\sqrt[]{3}}{2} \\ \cos (\pi)=-1 \end{gathered}[/tex]We have half the cycle here. We will complete the values later.
We then can find the value of x that matches the arguments of the known vlaues of the cosine as:
[tex]\begin{gathered} \alpha=3(x-\frac{\pi}{6}) \\ x=\frac{\alpha}{3}+\frac{\pi}{6} \end{gathered}[/tex]where α is the argument of the known values of cosine (0, π/6, π/4, ...).
We then can calculate the values of x for each one as:
[tex]\begin{gathered} x_1=\frac{0}{3}+\frac{\pi}{6}=\frac{\pi}{6} \\ x_2=\frac{1}{3}\cdot\frac{\pi}{6}+\frac{\pi}{6}=\frac{\pi}{18}+\frac{\pi}{6}=\frac{4\pi}{18} \\ x_3=\frac{1}{3}\cdot\frac{\pi}{4}+\frac{\pi}{6}=\frac{\pi}{12}+\frac{\pi}{6}=\frac{3\pi}{12}=\frac{\pi}{4} \\ x_4=\frac{1}{3}\cdot\frac{\pi}{3}+\frac{\pi}{6}=\frac{\pi}{9}+\frac{\pi}{6}=\frac{5\pi}{18} \\ x_5=\frac{1}{3}\cdot\frac{\pi}{2}+\frac{\pi}{6}=\frac{\pi}{6}+\frac{\pi}{6}=\frac{\pi}{3} \\ x_6=\frac{1}{3}\cdot\frac{2\pi}{3}+\frac{\pi}{6}=\frac{2\pi}{9}+\frac{\pi}{6}=\frac{7\pi}{18} \\ x_7=\frac{1}{3}\cdot\frac{3\pi}{4}+\frac{\pi}{6}=\frac{\pi}{4}+\frac{\pi}{6}=\frac{5\pi}{12} \\ x_8=\frac{1}{3}\cdot\frac{5\pi}{6}+\frac{\pi}{6}=\frac{5\pi}{18}+\frac{\pi}{6}=\frac{4\pi}{9} \\ x_9=\frac{1}{3}\pi+\frac{\pi}{6}=\frac{\pi}{2} \end{gathered}[/tex]We then can calculate the value of y for each of this points, using the known values of the cosine, as:
[tex]\begin{gathered} x=\frac{\pi}{6}\Rightarrow y=-\frac{5}{2}+1=-\frac{3}{2} \\ x=\frac{4\pi}{18}\Rightarrow y=-\frac{5}{2}+\frac{\sqrt[]{3}}{2}=\frac{\sqrt[]{3}-5}{2} \\ x=\frac{\pi}{4}\Rightarrow y=-\frac{5}{2}+\frac{\sqrt[]{2}}{2}=\frac{\sqrt[]{2}-5}{2} \\ x=\frac{5\pi}{18}\Rightarrow y=-\frac{5}{2}+\frac{1}{2}=-\frac{4}{2}=-2 \\ x=\frac{\pi}{3}\Rightarrow y=-\frac{5}{2}+0=-\frac{5}{2} \\ x=\frac{7\pi}{18}\Rightarrow y=-\frac{5}{2}-\frac{1}{2}=-\frac{6}{2}=-3 \\ x=\frac{5\pi}{12}\Rightarrow y=-\frac{5}{2}-\frac{\sqrt[]{2}}{2}=\frac{-5-\sqrt[]{2}}{2} \\ x=\frac{4\pi}{9}\Rightarrow y=-\frac{5}{2}-\frac{\sqrt[]{3}}{2}=\frac{-5-\sqrt[]{3}}{2} \\ x=\frac{\pi}{2}\Rightarrow y=-\frac{5}{2}-1=-\frac{7}{2} \end{gathered}[/tex]We can repeat this process for the rest of the cycle, but in this case, we will only graph the mean value (when cosine is 0) and the extreme values (when cosine is -1 or 1).
We can list this as:
[tex]\begin{gathered} \cos (\pi)=-1 \\ \cos (\frac{3\pi}{2})=0 \\ \cos (2\pi)=1 \end{gathered}[/tex]We can relate this values to x using the formula we used before:
[tex]\begin{gathered} x_{10}=\frac{1}{3}(\pi)+\frac{\pi}{6}=\frac{\pi}{3}+\frac{\pi}{6}=\frac{\pi}{2} \\ x_{11}=\frac{1}{3}(\frac{3\pi}{2})+\frac{\pi}{6}=\frac{\pi}{2}+\frac{\pi}{6}=\frac{2\pi}{3} \\ x_{12}=\frac{1}{3}(2\pi)+\frac{\pi}{6}=\frac{2\pi}{3}+\frac{\pi}{6}=\frac{5\pi}{6} \end{gathered}[/tex]Now, we calculate the values of y as:
[tex]\begin{gathered} x=\frac{\pi}{2}\Rightarrow y=-\frac{5}{2}-1=-\frac{7}{2} \\ x=\frac{2\pi}{3}\Rightarrow y=-\frac{5}{2}+0=-\frac{5}{2} \\ x=\frac{5\pi}{6}\Rightarrow y=-\frac{5}{2}+1=-\frac{3}{2} \end{gathered}[/tex]Using this particular values for the complete cycle we can complete the table as:
In how many ways can a committee of four Democrats and five Republicans be formed from a group of seven Democrats and eleven Republicans?
The percentage of majority and minority party members on each committee is also decided by party leaders.
How many Republicans and Democrats are there in each committee?The percentage of majority and minority party members on each committee is also decided by party leaders. Each standing committee (apart from Standards) is required under the Democratic Caucus Rules to have at least three Democrats for every two Republicans.The percentages of Democrats and Republicans in the committees generally correspond to their representation in the House and the Senate overall.In the House, there are now 20 standing committees and 1 permanent select committee. Please visit the Clerk of the House website for the most recent committee information.Individual Senators are typically only allowed to serve on two Class A committees and one Class B committee.To learn more about standing committees refer to:
https://brainly.com/question/2609442
#SPJ1
The percentage of majority and minority party members on each committee is also decided by party leaders.
How many Republicans and Democrats are there in each committee?The percentage of majority and minority party members on each committee is also decided by party leaders. Each standing committee (apart from Standards) is required under the Democratic Caucus Rules to have at least three Democrats for every two Republicans.
The percentages of Democrats and Republicans in the committees generally correspond to their representation in the House and the Senate overall. In the House, there are now 20 standing committees and 1 permanent select committee.
Please visit the Clerk of the House website for the most recent committee information. Individual Senators are typically only allowed to serve on two Class A committees and one Class B committee.
To learn more about standing committees refer to:
brainly.com/question/2609442
#SPJ1
combining functionsConsider the following functions. f(-2) = -10 and g(-2) = -11Find (f +g)(-2). (f + g) (-2) =
f(-2) = -10 and g(-2) = -11
Find (f +g)(-2).
we have that
(f +g)(-2)=f(-2)+g(-2)
substitute the given values
(f +g)(-2)=-10+(-11)=-21
if I can...give me any word problems that have to deal with multiply and dividing rational numbers
Determine whether the given numbers are rational or irrational.
(a) 1.75 (b) 0.01 (c) 0.5 (d) 0.09 (d) √3
So, rational can be any fraction number, but it can not be in under root form.
Thus the only option (d) is irrational number. all other are rational number.
[tex]\begin{gathered} \text{The product of rational number }\frac{4}{7}\text{ and }\frac{3}{5\text{ }}is? \\ \Rightarrow\frac{4}{7}\times\frac{3}{5} \\ \Rightarrow\frac{12}{35} \end{gathered}[/tex]12. A local poll finds that 0.35 of all citizens approve of the mayor's policies. What fraction of citizens approve? Write the answer in lowest terms. O 3/5 035/100 O 7/20 O 35/50
Explanation:
Writing 0.35 as a fraction we have:
[tex]\frac{35}{100}[/tex]And we can simplify dividing both numerator and denominator by 5:
[tex]\frac{\frac{35}{5}}{\frac{100}{5}}=\frac{7}{20}[/tex]Answer:
7/20
Check for Understanding 1eteofLook at the function table below and select the correct equation rule.tly510714918Select one:Of(0) =Of(0) = 21 +1Of(1) = 20Of(1) = 21 - 1Check
C) y= 2x
1) Examining that table, we can notice that the value of y is precisely twice the value of x
x | y
5 10
7 14
9 18
2) Hence, we can state since y is twice x that the function can be written as:
y=2x
3) So the answer is C) y= 2x
what is the slope and x and y intercepts on these graphs
ANSWER:
Slope: -1
Y intercept: (0, -3)
X intercept: (-3, 0)
STEP-BY-STEP EXPLANATION:
The slope of a function is calculated using the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]To calculate the slope we use the indicated points (-4, 1) and (-2, -1), we substitute:
[tex]m=\frac{-1-1}{-2-(-4)}=\frac{-2}{-2+4}=\frac{-2}{2}=-1[/tex]The y-intercept is when it crosses the y-axis and the x-intercept is when it crosses the x-axis.
Therefore:
Y intercept: (0, -3)
X intercept: (-3, 0)