The sides of the triagle have lengths:
1.1 p + 9.5 q
4.5 p - 5.2 r
5.3 r + 5.4 q
Or:
1.1 p + 0 r + 9.5 q
4.5 p - 5.2 r + 0 q
0 p + 5.3 r + 5.4 q
If we want to calculate the perimeter of the triangle, we just need to sum the three lenghts:
(1.1 + 4.5) p + (-5.2 + 5.3) r + (9.5 + 5.4) q
= 5.6 p + 0.1 r + 14.9 q
A radio announcer asked her listeners which type of music they preferred. The results are below. which answer choice lists the results from greatest to least perefence?F. 0.10, 25%, 0.20, 45/100G. 25%, 45/100, 0.20, 0.10H. 0.10, 0.20, 25%, 45/100J. 45/100, 25%, 0.20, 0.10
To compare the preferences is best to express them using the same form, for example, express all values as decimal values:
To express 25% as a decimal value you have to divide it by 100:
[tex]\frac{25}{100}=0.25[/tex]To express the fraction 45/100 as a decimal value you have to divide 45 by 100
[tex]45\div100=0.45[/tex]So, the observations expressed as decimal values are:
Rap 0.25
Norteno 0.45
Kazz 0.20
Tejano 0.10
Now that all numbers are on the same form you can order them from greatest to least. To do so, you have to compare the digit on the first decimal place, if the first digit is equal, you have to compare the digit on the second decimal place.
The number with the greatest decimal value is 0.45
Then you have 0.20 and 0.25 both have the same first digit, so you have to compare the second digits. "0" is less than "5" so, 0.20 is less than 0.25.
The least value is 0.10.
So ordered from greatest to least the values are:
[tex]\begin{gathered} 0.45;0.25;0.20;0.10= \\ \frac{45}{100};25\%,0.20;0.10 \end{gathered}[/tex]The correct option is J.
I really need help with number 9 find the value of x that makes abcd a parallelogram.
Given:
The adjacent angles of a parallelogram are 78 and x+10.
To find:
The value of x.
Explanation:
We know that,
The sum of the adjacent angles in a parallelogram is supplementary.
So, we can write,
[tex]\begin{gathered} 78+x+10=180 \\ x+88=180 \\ x=180-88 \\ x=92 \end{gathered}[/tex]Thus, the value of x is 92.
Final answer:
The value of x is 92.
Convert the following percent to a simplified fraction: 6%
Given:
6%
To convert the given percent into simplified fraction, we first divide it by 100 as shown below:
[tex]\begin{gathered} 6\%=\frac{6}{100} \\ Simplify \\ =\frac{3}{50} \end{gathered}[/tex]Therefore, the answer is:
[tex]\frac{3}{50}[/tex]HELP ME PLS!!!!!!!
Total consumption of fruit juice in a particular country in 2006 was about 2.15 billion gallons. The population of that country in 2006 was 400 million. What was the average number of gallons of fruit juice consumed per person in the country in 2006? using the per person amount from this problem, about how many gallons would your class consume?
Answer:
5.375 gallons/personStep-by-step explanation:
Total consumption of fruit juice in 2006:
2.15 billion gallonsThe population of the country:
400 million people.Average consumption of fruit juice per person in 2006 was:
2.15 billion / 400 million = 2.15 × 10⁹ / 400 × 10⁶ = 21.5 × 10⁸ / 4 × 10⁸ = 21.5 / 4 = 5.375 gallons/personTo find how many gallons of fruit juice would your class consume multiply the average consumption by the number of your class mates.
The angle of elevation to the top of a Building in New York is found to be 7 degrees from the ground at a distance of 1 mile from the base of the building. Using this information, find the height of the building.
_________ feet
The height of the building is 649.44 feet
Given,
The angle of elevation of the building from ground = 7°
The distance from base of the building to the angle = 1 mile
We have to find the height of the building:
As this information are noted, we will get a right angled triangle(image attached).
So, by trigonometry:
Tanθ = opposite side / adjacent side
here,
θ = 7 degree
opposite side = x
adjacent side = 1 mile
Then,
Tanθ = opposite side / adjacent side
tan(7°) = x / 1
x = tan(7°) × 1
x = 0.123 × 1
x = 0.123 miles
1 mile = 5280 feet
Then,
0.123 miles = 0.123 × 5280 = 649.44 feet
That is,
The height of the building is 649.44 feet.
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Frank will choose 7 colors to use for an art project. If there are 10 colors to choose from, how many different color combinations are possible?
120
Explanation:
total colours = 10
number of colours to be chosen = 7
We apply combination
The different color combinations possible:
[tex]^{10}C_7=\frac{10!}{(10-7)!7!}[/tex][tex]\begin{gathered} =\frac{10!}{3!7!}=\frac{10\times9\times8\times7!}{3\times2\times1\times7!} \\ =\frac{720}{6} \\ \text{= 120} \end{gathered}[/tex]The different color combinations possible is 120
mrs smith took her 3 kids and 3 of thejr friends to the Strawberry field. how many kids are there?
Mrs.Smith took : her 3 kids + 3 of their friends = 3 + ( 3x 3 ) = 12 kids
Answer:
There are 3 kids, and 3 friends.
3 + 3 = 6
there are a total of 6 kids.
-2(6.× -8 - 8 × 4)^0
Every number raised to the power of zero is equal to one.
[tex]-2\cdot1=-2[/tex]The final expression is -2
Find slope and y-intercept of the line. Compare the values to equation y=3x-8
The slope of a line graph, we need to pick two point on the line.
It is better to pick points that meet the grids, so we can have its exactly coordinates.
Also, since we will need the y-intercept, one of the points can be this.
The y-intercept is the point where the line intercepts the y-axis, its x value is always 0, and we can see that it happens, in this case, at y = -8, so the point is (0, -8), and the y-intercept is -8.
Now, we can look at any other point. We can see that one point that meets the grids is the point at x = 3 and y = 1, so at point (3, 1).
The slope, m, can be, then, calculated as:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{1-(-8)}{3-0}=\frac{1+8}{3}=\frac{9}{3}=3 \end{gathered}[/tex]So, the slope is 3.
Answers:
Slope: 3
y-intercept: (0, -8)
The line in the slope-intercept form is:
[tex]y=mx+b[/tex]where m is the slope and b is the y value of the y-intercept.
So, in this case, we have:
[tex]\begin{gathered} m=3 \\ b=-8 \\ y=3x-8 \end{gathered}[/tex]Which is exactly the same as the equation given, y = 3x - 8, so the equation given corresponds to the graph given.
Help me pls on math homework!!!!!
He sold 28 watermelons on Friday.
How to find the number of watermelons sold on Friday?The number of watermelons sold during the entire week is of 60, hence we find the daily amounts and add them, and this has to reach 60. The daily amounts are given as follows:
Monday: x.Tuesday: 2x. (twice as many as Monday).Wednesday: 0.5x. (half as many as Monday).Thursday: 18.Friday: 6x + 4. (four more than twice the amount sold on Monday).Hence the following equation is built, and we can solve for the unknown variable x as follows:
x + 2x + 0.5x + 18 + 6x + 4 = 60.
9.5x = 38
x = 38/9.5
x = 4
Then the amount sold on Friday is calculated as follows:
Friday = 6x + 4 = 6(4) + 4 = 24 + 4 = 28 watermelons.
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He sold 28 watermelons on Friday
What is the number of watermelons he sold on Friday?The total number of watermelons sold for the whole summer week is 60
He sold x watermelons on Monday
On Tuesday, he sold twice the numbers sold on Monday: 2x
On Wednesday, he sold half the numbers sold on Monday: x/2
On Thursday, he sold 18
On Friday, he sold:
= 2(x+2x) + 4 = 2(3x) + 4 = 6x + 4
And we know that the total number of watermelons is 60. Therefore:
x + 2x + x/2 + 18 + 6x+4 = 60
9.5x + 22 = 60
9.5x = 60 - 22
9.5x = 38
x = 4
since the amount sold on Friday is 6x+4:
= 6 x 4 + 4
= 24 + 4 = 28
Therefore, he sold 28 watermelons on Friday
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Find a polynomial f(x) of degree 4 with real coefficients and the following zeros.3 (multiplicity 2) , -i
We are told that we want a polynomial f(x) with the given zeros.
Recall that if we know the zeros oa polynomial, we can write the polynomial by writing the factors (x - zero of the polynomial) and multiply them all together.
For example, if we want a polynomial of degree 2 with zeros at 2 and 3, then the polynomial would be
[tex](x\text{ -2)}\cdot(x\text{ -3)}[/tex]In this case, we have a polynomial f(x) of degree 4. So far, we know that 3 is a zero and that -i is a zero. So we write the following
[tex]f(x)=(x\text{ -a)}\cdot(x\text{ -b)}\cdot(x\text{ -c) }\cdot\text{ (x -d)}[/tex]where a,b,c and d are the zeros of f(x). We know that 3 is a zero and that -i is a zero. So we have
[tex]f(x)=(x\text{ -3)}\cdot(x\text{ -b)}\cdot(x\text{ -( -i)) }\cdot(x\text{ -d)}[/tex]So to fully describe f(x) we need to find the values of b and d. We are told that 3 is a zero of multiplicity 2. This means that the factor (x -3) appears two times in the factorization of f(x). So we can say that b=3. So we have
[tex]f(x)=(x\text{ -3)}\cdot(x\text{ -3) }\cdot(x\text{ +i ) }\cdot(x-d)=(x-3)^2\cdot(x\text{ +i)}\cdot(x\text{ -d)}[/tex]Now, we need to find the value of d. Note that we are told that -i is a zero of the function. -i is a complex number, so one important property of polynomials is that if a complex number a+bi is a zero of the polynomial, then the number a-bi (which is called the complex conjugate) is also a zero. Note that the complex conjugate of a complex number is calculated by leaving the real part intact and multiplying the imaginary part by -1.
In our case we have the complex number -i. So we can write -i= 0 - 1i . Then, its complex conjugate is i.
So, we have that d=i.
Then our polynomial would look like this
[tex]f(x)=(x-3)^2\cdot(x+i)\cdot(x\text{ -i)}[/tex]Note that
[tex](x+i)\cdot(x-i)=x^2\text{ -i}\cdot x\text{ + i}\cdot x+1=x^2+1[/tex]So our polynomial ends up being
[tex]f(x)=(x-3)^2\cdot(x^2+1)[/tex]the sum of the angle measures of a polygon with n sides is given find n1440
Given in the question:
a.) The sum of all angles of a polygon is 1,440 degrees.
To be able to determine what polygon has a total sum of angles of 1,440 degrees, we will be using the following formula:
[tex]\text{ }\Theta=(n-2)x180^{\circ}[/tex]We get,
[tex]\text{ 1},440^{\circ}=(n-2)x180^{\circ}[/tex][tex]\text{ 1},440^{\circ}=180n-360^{\circ}[/tex][tex]180n=1,440^{\circ}\text{ + 360}^{\circ}[/tex][tex]180n=1,800^{\circ}[/tex][tex]\frac{180n}{180}=\frac{1,800^{\circ}}{180}[/tex][tex]n\text{ = 10}[/tex]Therefore, that polygon is a decagon or a polygon with 10 sides.
Find the length and width of a rectangle with the following information belowArea = 2x^2 + 3x Perimeter = 6x + 6
Length: L
Width: W
The area of a rectangle is:
[tex]A=L\cdot W[/tex]The perimeter of a rectangle is:
[tex]P=2W+2L[/tex]Given information:
[tex]\begin{gathered} A=2x^2+3x \\ \\ P=6x+6 \end{gathered}[/tex][tex]\begin{gathered} L\cdot W=2x^2+3x \\ 2W+2L=6x+6 \end{gathered}[/tex]Solve L in the second equation (Perimeter):
[tex]undefined[/tex]Write the equation for a parabola with a focus at (1,-4) and a directrix at x= 2.x=?
The basic form of the equation is;
4p (x- h)= (y - k)²
where (h, k) is the vertex and p is the distance from the vertex to either of its directrix or the focus
But, focus is = (1, -4) adn directrix = 2
So, the perpendicular point is :
(1.5 , -4)
p = -0.5
Putting all the values into the formula
4p (x- h)= (y - k)²
4(-0.5)(x - 1.5) = (y - (-4)²
simplify
-2(x - 1.5) = (y + 4)²
-2(x - 1.5) = y² + 8y + 16
Divide through the equation by -2
x - 1.5 = (-1/2) y² - 4y - 8
Add 1.5 to both-side of the equation
[tex]x\text{ = -}\frac{1}{2}y^2-4y\text{ - 8 + 1.5}[/tex][tex]x=-\frac{1}{2}y^2-4y\text{ - 6.5}[/tex]is y=10 a solution to the inequality y + 6 < 14
The inequality given is
[tex]y+6<14[/tex]Collecting like terms we will have
[tex]\begin{gathered} y+6<14 \\ y<14-6 \\ y<8 \end{gathered}[/tex]With the above solution, we can conclude that y=10 is not a solution to the inequality because the values of y are less than 8
Hence, The answer is NO
College students are offered a 6% discount on a textbook that sells for
$32.50. If the sales tax is 6%, find the cost of the textbook including the sales
tax.
32.383 is the cost of the textbook including the sales tax.
How does sales tax work?
Government-imposed consumption taxes on the purchase of goods and services are known as sales taxes. A typical sales tax is imposed at the moment of sale, paid for by the shop, and then given to the government.The original price of the textbook = $32.50
Also, the discount percentage = 6%
Thus, the price of the textbook after discount = 32.50 - 6 % of 32.50
= 32.50 - 6 * 3250/100
= 32.50 - 1.95
= 30.55
Now, the sales tax = 6 %
Hence, the cost of the textbook including sales tax
= 30.55 + 6 % of 30.55
= 30.55 + 6 * 30.55/100
= 30.55 + 1.833
= 32.383
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James is putting a frame around a rectangular photograph. The photograph is 12 inches long
and 10 inches wide, and the frame is the same width all the way around. What will be the
area of the framed photograph? (Hint: use "x" as your variable.)
Polynomial:________
=_________
=_________
=_________final answer in standard form.
PLEASSEEEEEE i need know this asap
Answer:
The area is 4x² + 44x + 120Step-by-step explanation:
GivenDimensions of rectangle are 12 in and 10 in,Width of the frame is x.To find The area of the framed photographSolutionDimensions of the framed photograph are:
12 + 2x and 10 + 2xArea of the framed photograph is:
A = lwA = (12 + 2x)(10 + 2x) = 12*10 + 12*2x + 10*2x + 2x*2x = 120 + 24x + 20x + 4x²= 4x² + 44x + 120A biologist just discovered a new strain of bacteria that helps defend the human body against the flu virus. To know the dosage that should be given to someone, the doctor must first know if the bacteria can multiply fast enough to combat the virus. To find the rate at which the bacteria multiplies, she puts 10 cells in a petri dish. In an hour, she comes back to find that there are now 12 cells in the dish.
Part 3
An exponential growth function has the general form:
[tex]f(t)=a\cdot(1+r)^t[/tex]where r is the rate of growth, t is the time, and a is a constant. Notice that if calculate f(t) for t = 0, we have (1 + r)º = 1 (any number with exponent 0 equals 1). So, we obtain:
[tex]f(0)=a(1+r)^0=a\cdot1=a[/tex]Thus, the constant a is the initial value of the function.
Now, the rate at which a bacteria grows is exponential. So, the function C(h) is given by:
[tex]C(h)=C(0)\cdot(1+r)^h[/tex]Notice that we represented the time by the letter h instead of t.
Since C(0) = 10 and C(1) = 12, we can replace h by 1 to find:
[tex]\begin{gathered} C(1)=10\cdot(1+r)^1 \\ \\ 12=10+10r \\ \\ 12-10=10r \\ \\ 10r=2 \\ \\ r=0.2 \end{gathered}[/tex]Thus, the number of cells C(h) is given by:
[tex]C(h)=10\cdot(1.2)^h[/tex]Notice that this is valid for C(15) = 154:
[tex]C(15)=10\cdot(1.2)^{15}\cong154.07\cong154_{}[/tex]Part 1
Then, using this formula, we find:
[tex]\begin{gathered} C(2)=10(1.2)^2\cong14 \\ \\ C(3)=10(1.2)^3\cong17.3\cong17 \\ \\ C(4)=10(1.2)^4\cong20.7\cong21 \\ \\ C(5)=10(1.2)^5\cong24.9\cong25 \\ \\ C(6)=10(1.2)^6\cong29.9\cong30 \\ \\ C(7)=10(1.2)^7\cong35.8\cong36 \\ \\ C(8)=10(1.2)^8\cong43 \\ \\ C(9)=10(1.2)^9\cong51.6\cong52 \\ \\ C(10)=10(1.2)^{10}\cong61.9\cong62 \\ \\ C(11)=10(1.2)^{11}\cong74.3\cong74 \\ \\ C(12)=10(1.2)^{12}\cong89.2\cong89 \\ \\ C(13)=10(1.2)^{13}\cong107 \\ \\ C(14)=10(1.2)^{14}\cong128.4\cong128 \end{gathered}[/tex]Part 2
Now, plotting the points, rounded to the nearest whole cell, on the graph, we obtain:
Part 4
Using a calculator, we obtain the following graph of the function C(h):
Comparing the graph to the plot of the data, we see that they match.
Part 5
After a full day, it has passed 24 hours. So, we need to use h = 24 in the function C(h):
[tex]C(24)=10(1.2)^{24}\cong795[/tex]Therefore, the answer is 795 cells.
the diameter of the bagels 4.2 in what is the biggest circumference in inches
Diammeter = 4.2 inch
Radius = diammeter/2 = 4.2/2 =2.1 inch
[tex]\text{Circumference =2}\times\text{ }\pi\times r[/tex][tex]\begin{gathered} \pi\text{ = 3.14} \\ \text{Circumference = 2 }\times3.14\times2.1\text{ =13.188 inches} \end{gathered}[/tex]Translate this phrase into an algebraic expression.Six less than the product of 13 and Mai's heightUse the variable m to represent Mai's height.
If m is the Mai's height you can write for the given description:
13m - 6
The previous expression means six less than the product of 13 and Mai's height.
A red maple sapling was 3 feet tall when planted in 2010. Six years later, the tree was 24 feet tall. The growth rate of the tree is constant over time. Find a linear model for the height H (in ft) of the red maple t years after 2010. Let t = 0 represent 2010.H = __________What is the expected height (in ft) of the red maple in 2020?________ ft
Since the growth rate is linear and constant over time, it means that the sequence formed is an arithmetic sequence. The formula for finding the nth term of an arithmetic sequence is expressed as
an = a1 + d(n - 1)
where
a1 is the first term of the sequence
n = number of terms
d = common difference
In this case, n would be t(number of years
From the information given,
a1 = 3
Since the first term is at t = 0 and it represents 2010, six years letter would be represented by t = 7. Thus, we would took for d given that a7 = 24
We have
24 = 3 + d(7 - 1)
24 = 3 + 6d
6d = 24 - 3 = 21
d = 21/6 = 3.5
The linear model would be
an = 3 + 3.5(t - 1)
Substituting H for an, the linear model is
H = 3 + 3.5(t - 1)
At 2020, t = 11
H = 3 + 3.5(11 - 1) = 3 + 35
H = 38
7. Principal = $39,300, Rate = 4.5%, Time = 6 months. What will that total principal + interest payment be rounded to the nearest dollar? o Lidhe total amount of
Given :
Principal = $39,300,
Rate = 4.5% = 0.045
Time = 6 months = 6/12 year = 0.5 year
Assume simple interest
So,
interest = Principal * rate * time = 39,300 * 0.045 * 0.5 = 884.25
So, the total = Principal + interest = 39,300 + 884.25 = 40,184.25
Rounding the answer to the nearest dollar
So, the total = $40,184
after a 30% discount, Kay's sneakers cost $36, if she would have waited another week to buy them, they would have been on sale for 40% off the original price, how much more money could she have saved
Let the original price of sneakers be x.
Determine the original price of the sneakers.
The function table below is intended to represent the relationship y=-2x-5. However, one of the entries for y does not correctly fit the relationship with x.
x = 1 , f(x) = -2•1 - 5 = -7
Then it doesnt corresponds to f(1) = 6
Answer is OPTION E)
Application machinist is drawing a triangular piece of an industrial machine. Write an equation and solve to find the value of x. Show your work?
Answer:
125
Step-by-step explanation:180=180-(2x+45)+x+80
2x-x=80+45
x=125
Shopping: Discounts Situation: You want to buy three books that are on sale at 20% off. The original prices of the books are $2.50, $4.95, and $6.00. How much will you save? Calculation With Distribution Calculation Without Distribution (Show all steps.) (Show all steps.) I think it is easier: to distribute. to not distribute. Why I Think it is Easier
Let's begin by listing out the information given to us:
Discount = 20%
Book prices: $2.50, $4.95, and $6.00
Taking discount with distribution, we have:
[tex]\begin{gathered} discount=0.2(2.50+4.95+6.00) \\ discount=0.5+0.99+1.2 \\ discount=\text{\$}2.69 \end{gathered}[/tex]Taking discount without distribution, we have:
[tex]\begin{gathered} \text{Sum of books = 2.50 + 4.95 + 6.00 =13.45} \\ discount=0.2(13.45)=2.69 \\ discount=\text{\$}2.69 \end{gathered}[/tex]I think it is easier to not distribute. This is because it reduces significantly the chances of numerical error in computing
on one side of the balance scale, Henry placed gram weight. on the other side of the scale, he placed a ballet slipper. how many milligrams does the slipper weigh?
Solution
Step 1
Convert gram to milligram
1 gram = 1000 milligram
Step 2
Find the answer
Assuming it is 1 gram weight on one side of the balance scale then, the ballet slippers will weigh 1 gram for the scale to be balanced.
I gram = 1000 milligram
Hence the ballet slippers will weigh 1000 milligrams
0=9 means no solution one solution or infinite solution?
Answer:
no solution
Step-by-step explanation:
If you end up with a false equality, then the initial statement is false, meaning that there are no solutions.
I really am struggling with this, could I have some help?
We are to find f(x) - g(x):
We will subtract the expressions of g(x) from f(x)
[tex]\begin{gathered} f(x)-g(x)=x^2\text{ + 1 - (2x - 5)} \\ \end{gathered}[/tex]Expanding the parenthesis using distributive property:
[tex]\begin{gathered} f(x)-g(x)=x^2\text{ + 1 - (2x) -(-5)} \\ mu\text{ltiplication of same signs gives positive sign} \\ m\text{ ultiplication of opposite signs give negative sign} \\ \\ f(x)-g(x)=x^2\text{ + 1 -2x + 5} \end{gathered}[/tex]collect like terms:
[tex]\begin{gathered} f(x)-g(x)=x^2\text{ -2x + 5 }+\text{ 1} \\ f(x)-g(x)=x^2\text{ - 2x + 6} \end{gathered}[/tex]pls help no need for no need for long explanations just a summary
As shown in the figure:
There are two parallel lines of the triangle
Using the ratio and proportional to find the value of x
So,
[tex]\begin{gathered} \frac{x}{6}=\frac{9}{2} \\ \\ x=6\cdot\frac{9}{2}=\frac{54}{2} \\ \\ x=27 \end{gathered}[/tex]So, the answer is: x = 27
