(3+ 1i) (2 - 2i)
open the parenthesis
3(2 - 2i) + 1i(2 - 2i) (note: i² = -1)
6 - 6i + 2i + 2
Rearrange
6 + 2 - 6i + 2i
8 - 4i
comparing with a + bi
The real number a equals 8
The real number b equals -4
Simplify 2(2x-7) show work
Given:
[tex]2(2x-7)[/tex]Aim:
We need to simplify the given expression.
Explanation:
Use the distributive property.
[tex]a(b+c)=ab+ac.\text{ Here a =2, b=2x and c=-7.}[/tex][tex]2(2x-7)=(2\times2x)+(2\times(-7))[/tex]Multiply 2 and 2x, we get 4x and multiply 2 and (-7), we get (-15).
[tex]=4x+(-14)[/tex][tex]Use\text{ \lparen +\rparen\lparen-\rparen=\lparen-\rparen.}[/tex][tex]=4x-14[/tex]Final answer:
[tex]2(2x-7)=4x-14[/tex]How many ounces of a 5% alcohol solution must be mixed with 17 ounces of a 10% alcohol solution to make a 6% alcohol solution?
Let x be number or ounces of a 5% alcohol solution, then:
[tex]x(0.05)+17(0.10)=(x+17)(0.06)[/tex]Solving the above equation for x, we get:
[tex]\begin{gathered} 0.05x+1.7=0.06x+1.02 \\ 0.01x=1.7-1.02 \\ 0.01x=0.68 \\ x=68 \end{gathered}[/tex]Therefore, you must add 68 ounces of the 5% alcohol solution.
Find the equation of the line with the given properties. Express the equation in general form or slope-intercept form.
To asnwer this questions we need to remember that two lines are perpendicular if and only if their slopes fullfil:
[tex]m_1m_2=-1[/tex]Now to find the slope of the line
[tex]-7x+y=43[/tex]we write it in slope-intercept form y=mx+b:
[tex]\begin{gathered} -7x+y=43 \\ y=7x+43 \end{gathered}[/tex]from this form we conclude that this line has slope 7.
Now we plug this value in the condition of perpendicularity and solve for the slope of the line we are looking for:
[tex]\begin{gathered} 7m=-1 \\ m=-\frac{1}{7} \end{gathered}[/tex]Once we hace the slope of the line we are looking for we plug it in the equation of a line that passes through the point (x1,y1) and has slope m:
[tex]y-y_1=m(x-x_1)[/tex]Plugging the values we know we have that:
[tex]\begin{gathered} y-(-7)=-\frac{1}{7}(x-(-7)) \\ y+7=-\frac{1}{7}(x+7) \\ y+7=-\frac{1}{7}x-1 \\ y=-\frac{1}{7}x-8 \end{gathered}[/tex]Therefore the equation of the line is:
[tex]y=-\frac{1}{7}x-8[/tex]Three ships, A, B, and C, are anchored in the atlantic ocean. The distance from A to B is 36.318 miles, from B to C is 37.674 miles, and from C to A is 11.164 miles. Find the angle measurements of the triangle formed by the three ships.A. m∠A=88.28267; m∠B=17.22942; m∠C=74.4879B. m∠A=74.4879; m∠B=17.22942; m∠C=88.28267C. m∠A=17.22942; m∠B=74.4879; m∠C=88.28267D. m∠A=88.28267; m∠B=74.4879; m∠C=17.22942
Question: Three ships, A, B, and C, are anchored in the Atlantic ocean. The distance from A to B is 36.318 miles, from B to C is 37.674 miles, and from C to A is 11.164 miles. Find the angle measurements of the triangle formed by the three ships.
Solution:
Note: In finding the angles of a triangle given its three sides, we will use the Cosine Law.
[tex]\begin{gathered} c^2=a^2+b^2\text{ -2abcosC} \\ or\text{ it can be written as:} \\ \text{Cos(C) = }\frac{a^2+b^2-c^2}{2ab} \end{gathered}[/tex]
In finding angle C, we use the formula given above.
[tex]\begin{gathered} \text{Cos(C) = }\frac{37.674^2+11.164^2-36.318^2}{2\cdot37.674\cdot11.164} \\ \text{Angle C = 74.4879 degrees} \end{gathered}[/tex]Note: Side a is the side opposite Angle A, side b is the side opposite Angle B, and side c is the side opposite Angle C.
Let's find the next angle.
[tex]\begin{gathered} \text{Cos(B) = }\frac{a^2+c^2-b^2}{2ac} \\ \text{Cos(B) = }\frac{37.647^2+36.318^2-11.164^2}{2\cdot37.647\cdot36.318} \\ \text{Angle B = 17.2294}2\text{ degrees} \end{gathered}[/tex]Note: We can still use the cosine law in finding Angle A. But another solution is subtracting the Angles A and B from 180 degrees. The measure of the internal angle of a triangle is always 180 degrees no matter what type of triangle it is.
[tex]\begin{gathered} \text{Angle A = 180-74.4849 -17.22942} \\ \text{Angle A = 88.28 degrees} \end{gathered}[/tex]ANSWER:
A. m∠A=88.28267; m∠B=17.22942; m∠C=74.4879
You are a landscaper working on the design of a parking lot in a new shopping center. You are measuring the length of a grass median that will be exactly as long as four parking spots and their dividing lines. One of these spots is a handicapped spot, which is 1018 feet wide and next to the curb. The other three spots are 838 feet wide. There are four dividing lines between the spots, and each measures 18 foot. What is the length of the grass median, D?
SOLUTION
From the given information:
one of the spots is
[tex]10\frac{1}{8}ft[/tex]Other three spots are
[tex]8\frac{3}{8}ft\text{ wide}[/tex]There are four dividing line of
[tex]\frac{1}{8}\text{foot}[/tex]The total length of the grass median is:
[tex]10\frac{1}{8}+3(8\frac{3}{8})+4(\frac{1}{8})[/tex]Calculate the value
[tex]\begin{gathered} \frac{81}{8}+3(\frac{67}{8})+\frac{4}{8} \\ =\frac{81}{8}+\frac{201}{8}+\frac{4}{8} \\ =\frac{81+201+4}{8} \\ =\frac{286}{8} \end{gathered}[/tex]Reduce the fraction
[tex]\frac{286}{8}=35\frac{6}{8}=35\frac{3}{4}[/tex]Therefore the length of the grass median is
[tex]35\frac{3}{4}[/tex]in a classroom there are 28 tablets which includes 5 that are defective. if seven tablets are chosen at random to be used by student groups. 12. how many total selections can be made? a. 140 b. 98280 c. 11793600 d. 4037880 e. 1184040 13. how many selections contain 2 defective tablets? a. 10 b. 21 c. 336490 d. 706629 e. 33649
Using the combination formula, it is found that:
The number of total selections that can be made is: e. 1184040.The number of selections that contain two defective tablets is: c. 336490.Combination formula[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula, involving factorials. It is used when the order in which the elements are chosen does not matter.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In the context of this problem, we have that seven tablets are chosen from a set of 28 tablets, hence the number of selections that can be made is given by:
[tex]C_{28,7} = \frac{28!}{7!21!} = 1,184,040[/tex]
For two defective tablets, the selections are given as follows:
Two defective from a set of five.Five non-defective from a set of 23.Hence the number of selections is calculated as follows:
[tex]C_{23,5}C_{5,2} = \frac{23!}{5!18!} \times \frac{5!}{2!3!} = 336,490[/tex]
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Advantage Cellular offers a monthly plan of $25 for 500 minutes. What is the cost per minute? Round to the nearest hundredths place.
The cost per minute is $0.05 and it is round off to the nearest hundredths place.
Round off:
Rounding off means a number is made simpler by keeping its value intact but closer to the next number. It is done for whole numbers, and for decimals at various places of hundreds, tens, tenths, etc.
Given,
Advantage Cellular offers a monthly plan of $25 for 500 minutes.
Here we need to find the cost per minute and we have also need to round off the result to the nearest hundredth place.
We know that,
500 minutes cost = $25
So, to calculate the price for one minute, then we have to divide the cost by the total number of minutes.
So, it can be written as,
=> 25 ÷ 500
So, the cost for one minute is.
=> 0.050
When we rounded to the nearest hundredths place.
The 5 in the hundredths place rounds down to 5, or stays the same, because the digit to the right in the thousandths place is 0.
Therefore, the cost per minute is $0.05.
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Rain equation for the line that is parallel to the given line and that passes through the given point
From the properties of line
If two lines are parallel, then thier slope are equal.
The general equation of line with slope m is; y = mx + b
The given equation of line us y = -5x + 3, slope of the given line is (-5)
The line is passes through the point (-6,3) and slope (-5)
The general equation of line is;
[tex]y-y_1=m(x-x_1)[/tex]Substitute the coordinates as;
[tex]x_1=-6,y_1=3[/tex]Thus;
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-3=-5(x+6) \\ y-3=-5x-30 \\ y+5x-3+30=0 \\ 5x+y+27=0 \\ y=-5x-27 \end{gathered}[/tex]Answer : y = -5x - 27
,,,
For the function f(x). describe, in words, the effects of each variable alb,h,k on the graph of a*f(bx+h)+k
Answer:
a: a produces vertical stretch
b: b produces a horizontal stretch
h: h produces a translation to the left of the X-axis
k: k produces a translation on the new function upward of the Y-axis
Step-by-step explanation:
An intermediate function is produced by adding each variable in the following order:
1) f(x) to f(bx):
Effect:
the horizontal stretch of f(x) along the x-axis with stretch factor b
2) f(bx) to f(bx+h):
Effect:
translation of f(bx) to the left of the X-axis by h units
3) f(bx+h) to a*f(bx+h):
Effect:
vertical stretching of f(bx+h) by a factor equal to a
4) Finally, a*f(bx+h) to a*f(bx+h)+k:
Effect:
vertical translation of a*f(bx+h) by h units upwards along the Y-axis.
Blaise M.
What types of solutions will a quadratic equation have when the discriminant b2 − 4ac in the quadratic formula is negative?
Explanation
When the discriminant is negative, this implies that
[tex]b^2-4ac<0[/tex]Answer: In this case, the equation has no real solutions;
A local children's center has 46 children enrolled, and 6 are selected to take a picture for the center'sadvertisement. How many ways are there to select the 6 children for the picture?
The question requires us to find how many ways we can select 6 children from a total of 46.
The formula for combinations is given as follows;
[tex]nC_r=\frac{n!}{(n-r)!r!}[/tex]Where n = total number of children, and r = number of children to be selected. The combination now becomes;
[tex]\begin{gathered} 46C_6=\frac{46!}{(46-6)!6!} \\ 46C_6=\frac{46!}{40!\times6!} \\ 46C_6=\frac{5.5026221598\times10^{57}}{8.1591528325\times10^{47}\times720} \\ 46C_6=\frac{5.5026221598\times10^{10}}{8.1591528325\times720} \\ 46C_6=\frac{0.674410967996781\times10^{10}}{720} \\ 46C_6=\frac{6744109679.967807}{720} \\ 46C_6=9,366,818.999955287 \\ 46C_6=9,366,819\text{ (rounded to the nearest whole number)} \end{gathered}[/tex]Does the point (3,-1) lie on the circle (x + 1)2 + (y - 1)1)2 = 16?no; the point is not represented by (h, k) in the equationyes; when you plug the point in for x and y you get a true statementno; when you plug in the point for x and y in the equation, you do not get a trueyes; the point is represented by (h, k) in the equation
We are given an equation of a circle and a point. We are then asked to find if the point lies on the circle. The equation of the circle and the point is given below
[tex]\begin{gathered} \text{Equation of the circle} \\ (x+1)^2+(y-1)^2=16 \\ \text{Given point =(3,-1)} \end{gathered}[/tex]To find if the point lies in the circle, we can use the simple method of substituting the coordinates into the equation of the circle.
This can be seen below:
[tex]\begin{gathered} (3+1)^2+(-1-1)^2=16 \\ 4^2+(-2)^2=16 \\ 16+4=16 \\ \therefore20\ne16 \end{gathered}[/tex]Since 20 cannot be equal to 16, this implies that the point does not lie on the circle.
ANSWER: Option 3
Andrew says the scale factor used was 3\2. Annie says the scale factor used was 2\3.Which student is correct and why?
Answer:
Annie is right, beause the coordinates of the points A'B'C' are 2/3 of the coodinates of the points ABC
and the size of the triangle A'B'C' is 2/3 of the size of the triangle ABC
for example:
Side AC lenght is 6 units and A'C' is 4
To go from 6 to 4, the factor must be 2/3
y= 3(x-3)^2-12E) Find two more points on The Graph. You can choose what x-values to use. Write your points as coordinates x y
Given:
[tex]y=3(x-3)^2-12[/tex]The quadractic equation above is written in vertex form:
[tex]y=a(x-h)^2+k[/tex]Where:
(h, k) is the coordinate of the vertex of the parabola
We have
a = 3
h = 3
k = -12
Let's find the following:
A.) Identify the coefficients, a, h, and k
Comparing the equation with the vertex form, we have:
a = 3
h = 3
k = -12
B.) Identify whether the graph opens up or opens down.
If a is greater than zero, then the graph opens up
If a is less than zero, then the graph opens downwards
Here, a = 3
Since a is greater than zero, the graph opens up.
The graph of the equation opens up
C.) Find the vertex.
The coordinates of the vertex is = (h, k)
Given:
h = 3
k = -12
Therefore, the vertex is: (3, -12)
D.) Find the axis of symmetry.
The axis of symmetry is the line that passes through the vertex and the focus.
To find the axis of symmetry we have:
x = h
where h = 3
Thus, the axis of symmetry is:
x = 3
E.) Let's find two more points.
Point 1 ==> (x, y)
Let's take x = 1
Substitute 1 for x and solve for y:
[tex]\begin{gathered} y=3\mleft(x-3\mright)^2-12 \\ \\ y=3(1-3)^2-12 \\ \\ y=3(-2)^2-12 \\ \\ y=3(4)-12 \\ \\ y=12-12 \\ \\ y=0 \end{gathered}[/tex]When x is 1, y is 0.
Therefore, we have the point:
(x, y) ==> (1, 0)
Point 2:
Let's take x = 2
Substitute 2 for x and solve for y:
[tex]\begin{gathered} y=3\mleft(x-3\mright)^2-12 \\ \\ y=3(2-3)^2-12 \\ \\ y=3(-1)^2-12 \\ \\ y=3(1)-12 \\ \\ y=3-12 \\ \\ y=-9 \end{gathered}[/tex]When x is 2, y is -9.
Therefore, we have the points:
(x, y) ==> (2, -9)
ANSWER:
A.) a = 3
h = 3
k = -12
B.) The graph opens up
C.) (3, -12)
D.) x= 3
E.) (1, 0), (2, -9)
11. The population of the District of Columbia was approximately 572 thousand in 2000 and had been growing by about 1.15% per year.(a) Write an explicit formula for the population of DC t years after 2000 (i.e. t=0 in 2000), where Pt is measured in thousands of people.Pt = (b) If this trend continues, what will the district's population be in 2025? Round your answer to the nearest whole number. thousand people(c) When does this model predict DC's population to exceed 800 thousand? Give your answer as a calendar year (ex: 2000).During the year
Given:
Population in 2000 = 572 thousand
Rate of growth per year = 1.15%
Let's solve for the following:
(a) Explicit formula for the population years after 2000.
Where:
In year 2000, t = 0
To write the explicit formula, apply the exponantial growth function formula:
[tex]f(t)=a(1+r)^t[/tex]Where:
a is the initial amount
r is the growth rate.
Thus, we have:
[tex]\begin{gathered} P_t=572(1+\frac{1.15}{100}_{^{}})^t \\ \\ P_t=572(1+0.0115)^t \end{gathered}[/tex]Therefore, the explicit formula for the population years after 2000 is:
[tex]P_t=572(1.0115)^t[/tex](b) What will be the district's population in 2025.
Where:
In the year 2000, t = 0
In the year 2025, t will be = 25
To find the population in 2025, substitute 25 for t in the explicit formula for evalaute:
[tex]\begin{gathered} P_{25}=572(1.0115)^{25} \\ \\ P_{25}=572(1.330905371) \\ \\ P_{25}=761.28\approx761 \end{gathered}[/tex]The population in 2025 if the trend continues will be approximately 761 thousand.
(c) When does the model predict the population to exceeed 800 thousand.
Substitute 800 for Pt and solve for t.
We have:
[tex]\begin{gathered} P_t=572(1.0115)^t \\ \\ 800=572(1.0115)^t \end{gathered}[/tex]Divide both sides by 572:
[tex]\begin{gathered} \frac{800}{572^{}}=\frac{572(1.0115)^t}{572} \\ \\ 1.3986=1.0115^t \end{gathered}[/tex]Take the natural logarithm of both sides:
[tex]\begin{gathered} \ln (1.3986)=\ln (1.0115)^t \\ \\ \ln (1.3986)=t\ln (1.0115) \\ \\ 0.33547=0.01143t \end{gathered}[/tex]Divide both sides by 0.01143:
[tex]\begin{gathered} \frac{0.33547}{0.01143}=\frac{0.01143t}{0.01143} \\ \\ 29.3=t \\ \\ t=29.3\approx29 \end{gathered}[/tex]When t = 29, the year is 2000 + 29 = 2029
Therefore, using this model, DC's population will exceed 800 thousand in the year 2029.
ANSWERS:
[tex]\begin{gathered} (a)P_t=572(1.0115)^t \\ \\ (b)=761\text{ thousand people} \\ \\ (c)\text{ 20}29 \end{gathered}[/tex]Triangle UVW, with vertices U(-5,5), V(-4,7), and W(-9,8), is drawn on the coordinate grid below.
The area formula of a triangle given the coordinates of the vertices :
[tex]U(-5,5),V(-4,7),W(-9,8)[/tex][tex]A=\lvert\frac{U_x(V_y-W_y)+V_x(W_y-U_y)+W_x(U_y-V_y)}{2}\rvert[/tex]Using the formula above, the area will be :
[tex]\begin{gathered} A=\lvert\frac{-5(7-8)-4(8-5)-9(5-7)}{2}\rvert \\ A=\lvert\frac{5-12+18}{2}\rvert \\ A=\lvert\frac{11}{2}\rvert \\ A=\lvert5.5\rvert \\ A=5.5 \end{gathered}[/tex]The answer is 5.5 square units
find the explict formula for 15, 12, 9, 6
Given:
15, 12, 9, 6
To write the explicit formula, use the form:
[tex]a_n=a_1+d(n-1)[/tex]Where
a1 = first term = 15
d = common difference = 12 - 15 = -3
n = number of terms
Therefore, the explicit formula is:
[tex]\begin{gathered} a_n=15-3(n-1) \\ \\ a_n=15-3n+3 \\ \\ a_n=18-3n \end{gathered}[/tex]ANSWER:
[tex]a_n=18-3n[/tex]Sx-3y =-3
(2x + 3y = -6
a. by graphing,
What are
y =
Y2=
Given,
x-3y=-3
2x+3y=-6
Plotting it in graph we have,
Since we have only one point of intersection so that would be only one solution.
The point of intersection is (-3,0)
Thus x=-3 and y=0
a. Draw any obtuse angle and label it angle AXB. Then draw ray XY so that it bisects < AXB.b. if m AXB = 140°, then what is m ZYXB?
The obtuse angle is shown in the diagram below:
The word, "bisect" means to divide an angle into 2 equal parts. Given that ray XY bisects angle AXB, it mean that it divides it into two equal halves. Theregfore, angle YXB is 140/2 = 70 degrees
Sharon's house, the library, and Lisa's house are all on the same straight road. Sharon has to ride her bike 1 3/5 miles to get from her house to the library and another 2 3/4 miles to get from the library to Lisa's house. How far does Sharon live from Lisa? Explain how you got your answer.
Sharon lives [tex]4\frac{7}{20}[/tex] miles away from Lisa .
In the question ,
it is given that
distance between Sharon and Library is [tex]1\frac{3}{5}[/tex] miles .
distance between Library to Lisa's house is [tex]2\frac{3}{4}[/tex] miles .
So according to the question
distance between Sharon's house and Lisa's house = (distance between Sharon and Library) + (distance between Library to Lisa's house) .
On substituting the values from above ,
we get ,
distance between Sharon's house and Lisa's house = [tex]1\frac{3}{5}[/tex] + [tex]2\frac{3}{4}[/tex]
= (5+3)/5 + (8+3)/4
= 8/5 + 11/4
taking LCM as 20 and solving further we get
= 32/20 + 55/20
= 87/20
= [tex]4\frac{7}{20}[/tex]
Therefore , Sharon lives [tex]4\frac{7}{20}[/tex] miles away from Lisa .
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If there are 40 seats per row how many seats are in 90 rows?
Answer:
3,600 seats
Step-by-step explanation:
If you have 40 seats in a row, and there are 90 rows, you simply take the amount of seats, and multiply that by the amount of rows.
-Hope this helps
Answer:
Step-by-step explanation:
3600
If you were to multiply 40 seats by 90 rows, you would result with 3600 seats!
find an ordered pair for 5x+y=1
An ordered pair for the equation 5x + y = 1 is (0, 1)
How to determine the ordered pair?The equation of the function is given as
5x + y = 1
To determine the ordered pair, we simply set the value of x to any value.
And then calculate the value of y
Using the above parameters as a guide, we can assume that
x = 0
Substitute x = 0 in 5x + y = 1
5(0) + y = 1
Evaluate the product
0 + y = 1
So, we have
y = 1
Express as ordered pairs
(x, y) = (0, 1)
Hence, the ordered pair in the solution is (0, 1)
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An ordered pair of the equation 5x + y = 1 is (1, - 4).
What is an ordered pair?An ordered pair (a,b) is a set of values for x and y coordinates.
As the name suggests (a, b) and (b, a) are two different ordered pairs.
Given, 5x + y = 1.
Or,
y = 1 - 5x.
Now we can choose any arbitrary value of x that corresponds to a value
of y.
At x = 1,
y = 1 - 5(1).
y = 1 - 5,
y = - 4.
∴ An ordered pair o the given equation 5x + y = 1 is (1, - 4).
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find the LCD of the list of fractions 7/20, 5/15
Explanation:
First we have to find multiples of each of the denominators:
[tex]\begin{cases}20\rightarrow20,40,60,80,100\ldots \\ 15\rightarrow15,30,45,60,75,90\ldots\end{cases}[/tex]From those multiples we have to find which one is the least that is in both lists. In this case, the least number that's in both lists is 60
Answer:
LCD = 60
Need some help thanks
In the given equations, the value of variables are:
(A) a = -10(B) b = -0.2(C) c = 0.25What exactly are equations?When two expressions are equal in a mathematical equation, the equals sign is used to show it.A mathematical statement is called an equation if it uses the word "equal to" in between two expressions with the same value.Using the example of 3x + 5, the result is 15.There are many different types of equations, such as cubic, quadratic, and linear.The three primary categories of linear equations are point-slope, standard, and slope-intercept equations.So, solving for variables:
(A) 1/5a = -2:
1/5a = -2a = -2 × 5a = -10(B) 8 + b = 7.8:
8 + b = 7.8b = 7.8 - 8b = -0.2(C) -0.5 = -2c:
-0.5 = -2cc = -0.5/-2c = 0.25Therefore, in the given equations, the value of variables are:
(A) a = -10(B) b = -0.2(C) c = 0.25Know more about equations here:
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21. A seamstress made 3 different skirts out of the same material. Each skirt required a dif- ferent amount of material. The chart below shows the number of yards y required for each skirt and the total cost C of the ma- terial. What is the equation for finding the cost per skirt made from the same material? Skirt А B C у 2.5 3.5 4 C С $15.60 $21.84 $24.96
Could you please share the chart the problem refers to?
We are asked to find an equation that gives the cost (C) of the skirt as a function of the number of yards (y) of material used.
The information given is:
y = 2.5 then C = $15.60
y = 3.5 then C = $21.84
y = 4 then C = $24.96
when the cost is $15.60, the amount of material in yards is 2.5 yards
so let's find the cost per yard as the quotient cost in $ divided by yard of material
Cost/yards = $21.84/3.5 = 6.24 $ per yard
The quotient gives the same value for all the three cases:
$15.60 / 2.5 = $6.24 per yard
$24.96 / 4 = $6.24 per yard
then the cost is going to be given by the equation:
C = 6.24 * y
This is the equation they asked you to find (naming "C" the cost, and "y" the number of yards of material used.
The equation contains ""unknowns"
Recall that the question is:
What is the equation for finding the cost per skirt made from the same material?
So they want a mathematical formula/equation that allows everyone to estimate the cost (C) given the number of yards of mwterial used (y)
So if you give the following equation (called equation because it must contain an "equal" sign):
C = 6.24 * y
A second problem gives you the amount paid for number of pounds of blueberries
The data says:
3 pounds cost $5.4
7 pounds cost $12.6
We proceed as before, and get that the amount per pound is obtained via the quatient: Price (C) divided by number of pounds (p)
C / p = $5.4 / 3 = $1.8 per pound
that gives us the equation:
C = $1.8 * p
In parallelogram PQRS, diagonals PR and QS intersect at point T.Which statement would prove PQRS is a rhombus?PT > QTPT QTPR QSSTQT
We can have more arguments to prove that PQRS is a rhombus, but, the argument that we will use here is:
Let's look at the first statement, we have
[tex]PT>QT[/tex]That's not correct, it would just prove that QR/2 > PS/2,
[tex]PR=QS[/tex]This statement implies
[tex]\begin{gathered} PR^2=QS^2 \\ \\ PS^2+SR^2=PQ^2+QR^2 \end{gathered}[/tex]We cannot conclude that
[tex]PS=SR=PQ=QR[/tex]The next statement is
[tex]PT=QT[/tex]A rhombus can have different diagonals, and in fact they have. Then let's go to the next one
[tex]ST=QT[/tex]That also not exactly says it's a rhombus, it's a pallelogram property.
[tex]\angle SPT=\angle QPT[/tex]By doing that we have that the diagonal bissects the angle
That implies that the angle b is also bissect.
The last statment is
[tex]\angle PTQ=\angle STR[/tex]That's literally the vertex angle, it's true always, not only in that case, therefore the only possible answer is
[tex]\angle SPT=\angle QPT[/tex]Pro
A polynomial function with degree 5 can have a maximum of how many turning points? It would be 5 right?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
polynomial function
Step 02:
turning points:
The maximum number of turning points of a polynomial function is always one less than the degree of the function.
5th degree polynomial function and has 4 turning points.
The answer is:
5th degree polynomial function and has 4 turning points.
What’s the correct answer answer asap for brainlist please
y + 7x= 11; x= -1,0, 4
We have an expression with 2 unknowns, and we have values for one unknown. We have to calculate then the other unknown value:
Expression:
[tex]\begin{gathered} y+7x=11 \\ y=11-7x \end{gathered}[/tex]Then, when x=-1
[tex]y=11-7x=11-7(-1)=11+7=18[/tex]When x=0
[tex]y=11-7(0)=11[/tex]When x=4
[tex]y=11-7(4)=11-28=-17[/tex]([20 + 10.4^2 - 116,870) / (20/ 1/3 x 15 - 10.4/ (116,870/6808))] ^-1
Answer:
[tex]8\frac{875730264}{8491541359}[/tex]Explanation:
Given the values of the variables below:
• D = 116,870
,• E=1/3
,• L =15
,• M = 20
,• O = 10.4
,• Y = 6,808
We are required to evaluate:
[tex]\begin{gathered} \lbrack(M+O^2-D\div Y)\div(M\div E\cdot L-O\div(D\div Y))\rbrack^{-1} \\ =\mleft(\frac{(M+O^2-D\div Y)}{(M\div E\cdot L-O\div(D\div Y))}\mright)^{-1} \end{gathered}[/tex]Substitute the given values:
[tex]=\mleft(\frac{20+10.4^2-116,870\div6,808}{20\div\frac{1}{3}\cdot15-10.4\div(116,870\div6,808)}\mright)^{-1}[/tex]We simplify using the order of operations PEMDAS.
First, evaluate the parentheses in the denominator.
[tex]=\mleft(\frac{20+10.4^2-116,870\div6,808}{20\div\frac{1}{3}\cdot15-10.4\div\frac{116,870}{6,808}}\mright)^{-1}[/tex]Next, evaluate the exponent(E): 10.4²
[tex]=\mleft(\frac{20+108.16-116,870\div6,808}{20\div\frac{1}{3}\cdot15-10.4\div\frac{116,870}{6,808}}\mright)^{-1}[/tex]Next, we take multiplication and division together:
[tex]\begin{gathered} =\mleft(\frac{20+108.16-\frac{116,870}{6,808}}{20\times3\times15-10.4\times\frac{6808}{116,870}}\mright)^{-1} \\ =\mleft(\frac{20+108.16-\frac{116,870}{6,808}}{900-\frac{13616}{22475}}\mright)^{-1} \end{gathered}[/tex]Finally, take addition and subtraction and then simplify.
[tex]\begin{gathered} =\mleft(\frac{9445541}{85100}\div\frac{20213884}{22475}\mright)^{-1} \\ =(\frac{9445541}{85100}\times\frac{22475}{20213884})^{-1} \\ =(\frac{8491541359}{68808061136})^{-1} \\ =1\div\frac{8491541359}{68808061136}=1\times\frac{68808061136}{8491541359} \\ \\ =\frac{68808061136}{8491541359} \\ =8\frac{875730264}{8491541359} \end{gathered}[/tex]The result of the evaluation is:
[tex]8\frac{875730264}{8491541359}[/tex]