Answers
Daily dosage of medicine for every 20 pounds of body weight = 70 mg
Daily dosage of medicine for every 1 pound of body weight = 70/20 mg
Daily dosage of medicine for every 1 pound of body weight = 3.5 mg
Daily dosage of medicine for every 175 pounds of body weight = 175 x 3.5
Daily dosage of medicine for every 175 pounds of body weight = 612.5 mg
Therefore, the daily dose for a man who weighs 175 pounds is 612.5 mg
If the man is to receive 900 mg in 8 hours
Dosage he will receive in 1 hour = 900/8
Dosage he will receivw in 1 hour = 112.5 mg
Dosage he will receive in 24 hours = 112.5 x 24
Dosage he will receive in 24 hours = 2700 mg
This means the man will take 2700 mg instead of the normal 612.5 mg. He is receiving the wrong dosage
Related Questions
Which choice best represents the sum of (5 + 8x -3) and (9x -6)1: 17x + -42: 17x + 43: x + 144: x + - 14
Answers
We can solve the expression as:
[tex]\begin{gathered} (5+8x-3)+(9x-6) \\ 2+8x+9x-6 \\ 17x-4 \end{gathered}[/tex]The answer is 1. 17x-4.
can someone please help me with this please explain (and if you can please add an example)
Answers
Given: A square pyramid with a base length of 5 inches and a height of 9 inches.
Required: To find the volume of the given square pyramid.
Explanation: The volume of the square pyramid is given by the formula
[tex]V=\frac{a^2\times h}{3}[/tex]Where a is the base length, and h is the height of the square pyramid.
Hence,
[tex]\begin{gathered} V=\frac{5^2\times9}{3} \\ =75\text{ in}^3 \end{gathered}[/tex]Final Answer: The volume of the square pyramid is 75 cubic inches.
A spinner with 10 equally sized slices has 10 yellow slices. The dial is spun and stops on a slice at random. What is the probability that the dial stops on a yellow slice? Write your answer as a fraction in simplest form. Explanation Check U 00 00 X. S ? Esp E D 5 E [2]
Answers
Step 1
Given;
Step 2
The probability of an event is given as;
[tex]P(event)=\frac{Required\text{ number of events }}{Total\text{ number of events}}[/tex][tex]\begin{gathered} Required\text{ number of events=Yellow slice=10} \\ Total\text{ number of events= 10 slices} \end{gathered}[/tex]Thus,
[tex]P(yellow\text{ slice\rparen=}\frac{10}{10}=1[/tex]Answer;
[tex][/tex]Daryl loaned his friend $2,500 to help him with his business. If his friend pays Daryl back in one year with 15% simple interest how much will he owe Daryl all together?
Answers
Answer:
$2875
Explanation
Given
Principal P = $2,500
Rate R = 15%
Time T = 1year
Get the interest on $2500
Simple Interest = PRT/100
Simple Interest = 2500 * 15 * 1/100
Simple Interest = 25*15
Simple Interest = $375
Amount owed altogether = Pricipal + Interest
Amount owed altogether = $2500 + $375
Amount owed altogether = $2875
I need help with finding the area and perimeter of the letter o
Answers
Check below, please.
1) In this question, we're going to remember two concepts: The perimeter is the sum of the lengths of each segment of each letter.
2) So let's start counting each tiny square so that we can get to know the length.
The letter "L" is actually, with this typography, two rectangles:
So, the perimeter (2P) is equal to:
2P =15 +15 +7+3+3+10+3
2P= 56 units
As for the area:
Using the Rectangle formula, then we can write down the area as:
Area:
[tex]\begin{gathered} A=l\cdot w \\ A_1=3\cdot15=45u^2 \\ A_2=10\cdot3=30u^2 \\ A_L=30+45=75u^2 \end{gathered}[/tex]3) In this letter "O" we can divide it into two trapezoids, and two parallel rectangles:
Note that we need to find the length of those corners shaped like triangles, we can use the Pythagorean Theorem, considering the "rise over run" and write:
[tex]\begin{gathered} a^2=3^2+2^2 \\ a^2=9+4 \\ a^2=13 \\ \sqrt[]{a^2}=\sqrt[]{13} \\ a=3.6 \end{gathered}[/tex]So the Perimeter can be written:
[tex]\begin{gathered} 2P=3.6+3.6+3.6+3.6+5+5+12+12+12+12+3+3 \\ 2P_O=78.4 \end{gathered}[/tex]And for the area, we can find the area of those two trapezoids and two rectangles writing this:
[tex]\begin{gathered} A_O=2(\frac{(B+b)h}{2})+2(w\times l) \\ A_O=2(\frac{(9+3)3}{2})+2(12\times3)_{} \\ A_O=108u^2 \end{gathered}[/tex]4) And now, finally the letter "u":
For the corners let's assume they are triangles, and then we can write the following since those corners are like hypotenuses:
[tex]\begin{gathered} a^2=5^2+2^2 \\ a^2=25+4 \\ a=\sqrt[]{29}\approx5.4 \end{gathered}[/tex]And for the inclined lower part of the letter "u", we can write:
[tex]\begin{gathered} a^2=1^2+2^2 \\ a=\sqrt[]{5}\approx2.2 \end{gathered}[/tex]Therefore, we can write the Perimeter as:
[tex]\begin{gathered} 2P=2(5.4)+2(2.2)+4+3(2)+4(13) \\ 2P_U=77.2 \end{gathered}[/tex]And for the area, we can see from bottom to top: One trapezoid, a par of parallelograms, and two rectangles. Hence, we can write:
[tex]\begin{gathered} A_U=\frac{(B+b)h}{2}+2(l\cdot w)+2(l\cdot w) \\ A_U=\frac{(6+4)3}{2}+2(2\cdot2)+2(2\cdot13) \\ A_U=75u^2 \end{gathered}[/tex]5) So, each letter by area and perimeter:
[tex]\begin{gathered} A_L=75u^2 \\ 2P_L=56u \\ -- \\ A_O=108u^2 \\ A_O=78.4u \\ -- \\ A_U=75 \\ 2P_U=77.2 \end{gathered}[/tex]Can anyone help me? I don't know the answer.
Answers
Hence, the area of the rectangle is [tex]\frac{21}{32}m^2[/tex].
What is the rectangle?
A rectangle is a two-dimensional flat shape. In an [tex]XY[/tex] plane, we can easily represent a rectangle, where the arms of x-axis and y-axis show the length and width of the rectangle, respectively.
Area of rectangle = Length × Width
Here given that,
[tex]L=\frac{7}{8}m[/tex]
[tex]W=\frac{3}{4}m[/tex]
So,
Area of rectangle = [tex](\frac{7}{8}m)*(\frac{3}{4}m)\\[/tex]
[tex]=\frac{21}{32}m^2[/tex]
Hence, the area of the rectangle is [tex]\frac{21}{32}m^2[/tex].
To know more about the rectangle
https://brainly.com/question/8663941
#SPJ1
what is the driving distance from the hospital to City Hall
Answers
Coordinate of the Hospital = (-6, -4)
Coordinate of City Hall = (0,0)
[tex]\begin{gathered} \text{Distance betw}en\text{ two points = }\sqrt[]{(x_2-x_{1)^2+}(y_2-y_1)^2} \\ \\ =\sqrt[]{(0-(-6))^2+(0-(-4))^2} \\ =\sqrt[]{(0+6)^2+(0+4)^2} \\ =\sqrt[]{6^2+4}^2 \\ =\sqrt[]{36\text{ +16}} \\ =\sqrt[]{52} \\ =2\sqrt[]{13}\text{ or 7.21} \end{gathered}[/tex]Roselle has three cups of popcorn and 6 oz of soda for a total of $246 calories. Carmel has one cup of popcorn and 14 oz of soda for a total of $274 calories. determine the number of calories per cup of popcorn and per ounce of soda
Answers
Let 'x' be the number of calories per cup of popcorn, and 'y' be the number of calories per ounce of soda.
Given that 3 cups of popcorn and 6 oz of soda constitute 246 calories,
[tex]3x+6y=246[/tex]Also given that 1 cups of popcorn and 14 oz of soda constitute 274 calories,
[tex]x+14y=274[/tex]Solve the equations using Elimination Method.
Subtract 3 times equation 2 from equation 1,
[tex]\begin{gathered} (3x+6y)-3(x+14y)=246-3(274) \\ 3x+6y-3x-42y=246-822 \\ -36y=-576 \\ y=16 \end{gathered}[/tex]Substitute this value in equation 1, to obtain 'x' as,
[tex]\begin{gathered} 3x+6(16)=246 \\ 3x+96=246 \\ 3x=150 \\ x=50 \end{gathered}[/tex]Thus, the solution of the system of equations is x=50 and y=16.
Therefore, there are 50 calories per cup of popcorn, and 16 calorie per ounce of soda.
i don’t understand this very well, i think growth and decay but not sure
Answers
She bought the bike by 3,000 six years ago, we are assuming the value of her mountain bike depreciated 20% each year
1 year
3,000*20% = 600
2year
3,000-600 = 2,400*20% = 480
3year
2,400-480 = 1920*20% = 384
4 year
1920-384= 1,536*20% = 307.2
5 year
1,536-307.2= 1,228.8*20% = 245.76
6year
1,228.8 - 245.76 = 1,043.04*20% = 208.608
1,043.04 - 208.608 =834.432
Rounded to the nearest dollar
= 834
7/5-6/5+3/2=17/10=1 7/10
Answers
Question:
Solution:
Let us denote by x the blank space in the given equation. Then, we get:
[tex]\frac{7}{5}-x+\frac{3}{2}=\frac{6}{5}[/tex]this is equivalent to:
[tex]\frac{7}{5}+\frac{3}{2}-x=\frac{6}{5}[/tex]this is equivalent to:
[tex]\frac{14+15}{10}-x=\frac{6}{5}[/tex]that is:
[tex]\frac{29}{10}-x=\frac{6}{5}[/tex]solving for x, we obtain:
[tex]\frac{29}{10}-\frac{6}{5}=x[/tex]that is:
[tex]x=\frac{29}{10}-\frac{6}{5}=\frac{29-12}{10}=\frac{17}{10}[/tex]so that, the blank space would be:
[tex]\frac{17}{10}[/tex]and the complete expression would be:
[tex]\frac{7}{5}-\frac{17}{10}+\frac{3}{2}=\frac{6}{5}[/tex]Julia has been measuring the length of her baby's hair. The first time it was 6 cm long and after one month it was 2 cm longer. If the hair continues to grow at this rate, determine the function that represents the hair growth and graph it.
Answers
Given that,
The length of baby's hair at first time = 6cm
After a month, the length was 2 cm longer = 6 + 2 = 8 cm
As mentioned in the question, the hair continues to grow at this rate. Therefore, after two months, the length would be = 8 + 2 = 10 cm
It results in a sequence with a common difference of 2,
6, 8, 10, 12, ............
If a sequence has a common difference, it is called an arithmetic sequence. In such sequences, the nth term is calculated as:
an = a1 + (n-1)*d
Here,
a1 = first term = 6
d = common difference = 2. (8-6 or 10 - 8 = 2)
Now, put all the values in the equation,
an = a1 + (n-1)*d
an = 6 + (n-1)*2
an = 6 + 2n - 2
an = 2n + 4
an = 2(n+2)
Hence, the function that represents growth is an = 2(n+2).
By varying the value of 'n', you can get the values of 'an'. Both will generate ordered pairs that will help you in plotting. For example:
n = 1
an = 2(n+2) = 2(1+2) = 2 (3) = 6
=> ordered pair (1, 6)
n = 2
an = 2(n+2) = 2(2+2) = 2 (4) = 8
=> ordered pair (2, 8)
n = 3
an = 2(n+2) = 2(3+2) = 2 (5) = 10
=> ordered pair (3, 10)
n = 4
an = 2(n+2) = 2(4+2) = 2 (6) = 12
=> ordered pair (4, 12)
With the ordered pairs, you can plot the graph.
Explain how to estimate the product ofof 12 3/8 x 6 7/8Use complete sentences in your answer.
Answers
Given:
12 3/8 x 6 7/8
We can round 12 3/8 down to 12 because converting 12 3/8 to decimal will give 12.375.
We can round up 6 7/8 which is equivalent to 6.875 to 7
Hence, the estimate is 12 x 7 = 84
The US consumes an average of 5.25 million metric tons of bananas per year. There are 317 million people in the US and there are 1000 kg in 1 metric ton. How many kilogram of bananas are consumed per person in a year? Round answer (except last one) to three significant digits. 365 days in a year.
Answers
The US consume 5.25 million metric tons of banana per year.
This is equivalent to 5.25 million x 1000kg = 5250 000 000 kg
US population = 317 million = 317 000 000
The number of kilogram of bananas consumed per person per year
= 5250 000 000 kg / 317 000 000
=16.6 kg
Therefore, the number of kilogram of bananas that are consumed per person per year is 16.6kg
See attached pic of problem. I have to show cancelling of units and answer has to show proper number of significant figures.
Answers
We have that 1 cubic meter is equivalent to 1.308 cubic yards. Then, we can use a rule of three to find the value in yards of 1.37 cubic meters:
[tex]\begin{gathered} 1m^3\rightarrow1.308yd^3 \\ 1.37m^3\rightarrow x \\ \Rightarrow x=\frac{(1.37m^2)(1.308yd^3)}{1m^3}=1.37(1.308yd^3)=1.792yd^3 \\ \Rightarrow x=1.792yd^3 \end{gathered}[/tex]therefore, 1.37m³ is equivalent to 1.792yd³
6) What is the equation of the following graphed function?Is the vertex a maximum or minimum?What are the solutions to the function?What is the y-intercept?уmobruo uove56$ x
Answers
If we know the roots (solutions) we can find the equation of the second-degree function using the formula above:
[tex]f(x)=a(x-x_1)(x-x_2)[/tex]In this case, a = -1, x1 = 2 and x2 = 4. Therefore the equation will be:
[tex]f(x)=-1(x-2_{})(x-4_{})[/tex][tex]f(x)=-x^2+6x-8[/tex]The vertex is maximum (see that the function has a clear max value).
The solutions to the function are the roots (place in the x-axis where the function cross). They are 2 and 4.
The y-intercept is the point with the format (0,y). Thus to find this point we can substitute 0 into the function:
[tex]f(0)=-0^2+6\times0-8[/tex][tex]f(0)=-8[/tex]The y-intercept will be y = -8.
2. Yan also has three times as many apples as Xavier. Write a second expression for how many apples Yanhas.
Answers
For this case, let be "x" the number of apples Xavier has and "y" the number of apples Yan has.
According to the information given in the exercise, you know that Yan has three times as many apples as Xavier. In other words, to find the number of apples Yan has, you need to multiply the number of apples Xavier has by 3.
Then, knowing the above, you can write the following equation:
[tex]y=3x[/tex]Therefore, you can determine that an expression that represents how many apples Yan has, is the one shown below:
[tex]3x[/tex]in the function y=-2(x-1)+4 what effect does the number 4 have onthe graph, as compared to the graph of the function 7OA. t shifts the graph down 4 unitsO B. t shifts the graph 4 units to the leftOcHshifts the graph up 4 unitsOD.t shifts the graph 4 units to the right
Answers
Given:
y = -2(x - 1) + 4
The effect the number 4 has on the graph of the function is that there will be a vertical shift of 4 units up.
+4 here indicates a vertical shift of 4 upwards
ANSWER:
C) It shifts the graph up 4 units
Match these equation balancing steps with the description of what was done in each step.Step 1:12x - 6 = 10 6x - 3 = 5 -Add 3 to both sides -Divide both sides by 6 -Divide both sides by 2 Step 2: 6x - 3 = 5 6x = 8 -Add 3 to both sides -Divide both sides by 6 -Divide both sides by 2 Step 36x = 8 x= 4/3 -Add 3 to both sides -Divide both sides by 6 -Divide both sides by 2
Answers
Step 1:
6x - 3 = 5
[tex]\begin{gathered} \text{add 3 to both sides} \\ 6x-3+3=5+3 \\ 6x=8 \end{gathered}[/tex]step 2:
6x = 8
[tex]\begin{gathered} \text{Divide both sides by 6} \\ \frac{6x}{6}=\frac{8}{6} \\ x=\frac{4}{3} \end{gathered}[/tex]Step 3:
x = 4/3
[tex]\begin{gathered} \text{divide both sides by 2} \\ x=\frac{8}{6}=\frac{4}{3} \end{gathered}[/tex]
The Hill family and the Stewart family each used their sprinklers last summer. The water output rate for the Hill family's sprinkler was 15 L per hour. Thewater output rate for the Stewart family's sprinkler was 25 L per hour. The families used their sprinklers for a combined total of 55 hours, resulting in atotal water output of 1025 L. How long was each sprinkler used?Note that the ALEKS graphing calculator can be used to make computations easier.Х5?Hill family's sprinkler: hoursStewart family's sprinkler: [hoursM
Answers
The Hill family and the Stewart family each used their sprinklers last summer. The water output rate for the Hill family's sprinkler was 15 L per hour. The
water output rate for the Stewart family's sprinkler was 25 L per hour. The families used their sprinklers for a combined total of 55 hours, resulting in a
total water output of 1025 L. How long was each sprinkler used?
Let
x ------> the number of hours of Hill family's sprinkler
y ------> the number of hours of Stewart family sprinkler
so
we have that
x+y=55 -------> x=55-y ------> equation 1
15x+25y=1025 ------> equation 2
Solve the system
Substitute equation 1 in equation 2
15(55-y)+25y=1025
solve for y
825-15y+25y=1025
10y=1025-825
10y=200
y=20
Find the value of x
x=55-20) -----> x=35
therefore
Hill family's sprinkler: 35 hoursStewart family's sprinkler:20 hoursJennie has $300 and spends $15.What percent of her money is spent?
Answers
ok
Total money = $300
money spend = $15
300 ---------------------- 100
15 ---------------------- x
x = (15 x 100)/300
x = 1500/300
x = 5
Jennie spent 5% of her money
To solve it, use a rule of three. $300 is 100%, so we need to calculate which percent is $15 of the total amount.
In a rule of three, it's necessary to use cross multiplication and then division.
That's why I multiplied 15 by 100 and then I divided by 300.
15 is 5% of $300
Two points A(0,-4), B(2,-1)determine line AB.What is the equation of the line AB? y= _1_x + _2_What is the equation of the line perpendicular to lineAB, passing through the point (2,-1)? y= _3_x + _4
Answers
1.
Let:
[tex]\begin{gathered} (x1,y1)=(0,-4) \\ (x2,y2)=(2,-1) \\ so\colon \\ m1=\frac{y2-y1}{x2-x1}=\frac{-1-(-4)}{2-0}=\frac{3}{2} \end{gathered}[/tex]Using the point-slope equation:
[tex]\begin{gathered} y-y1=m1(x-x1) \\ y-(-4)=\frac{3}{2}(x-0) \\ y+4=\frac{3}{2}x \\ y=\frac{3}{2}x-4 \end{gathered}[/tex]2.
If two lines are perpendicular, then:
[tex]\begin{gathered} m1\times m2=-1 \\ \frac{3}{2}\times m2=-1 \\ m2=-\frac{2}{3} \end{gathered}[/tex]Let:
[tex](x1,y1)=(2,-1)[/tex]Using the point slope equation:
[tex]\begin{gathered} y-y1=m2(x-x1) \\ y-(-1)=-\frac{2}{3}(x-2) \\ y+1=-\frac{2}{3}x+\frac{4}{3} \\ y=-\frac{2}{3}x+\frac{1}{3} \end{gathered}[/tex]Consider the following function. Complete parts (a) through (e) below.f(x)=x²-2x-8The vertex is.(Type an ordered pair.)c. Find the x-intercepts. The x-intercept(s) is/are(Type an integer or a fraction. Use a comma to separate answers as needed.)d. Find the y-intercept. The y-intercept is(Type an integer or a fraction.)e. Use the results from parts (a)-(d) to araph the quadratic function.
Answers
Given the function:
[tex]f(x)=x^2-2x-8[/tex]It is a quadratic function where:
a=1
b= -2
c= -8
The x-coordinate of the vertex is given by:
[tex]x=-\frac{b}{2a}[/tex]Substitute a and b:
[tex]x=-\frac{-2}{2(1)}=\frac{2}{2}=1[/tex]Substituting in the original equation to obtain the y-coordinate, we obtain:
[tex]y=(1)^2-2(1)-8=1-2-8=-9[/tex]So, the vertex is (0, -9)
c. For the intercept at x we make y = 0:
[tex]0=x^2-2x-8[/tex]And solve for x by factorization:
[tex]\begin{gathered} (x-4)(x+2)=0 \\ Separate\text{ the solutions} \\ x-4=0 \\ x-4+4=0+4 \\ x=4 \\ and \\ x+2=0 \\ x+2-2=0-2 \\ x=-2 \end{gathered}[/tex]So, the x-intercepts are:
(-2, 0) and (4,0)
Answer: (-2,0), (4,0)
d. For the intercept at y we make x = 0:
[tex]y=(0)^2-2(0)-8=-8[/tex]So the y-intercept is (0, -8)
Answer: (0, -8)
e. Graphing the function:
15x²y/(x+1)^3* (x+1)/24x^5y
Answers
The simplified value of the given expression in the form of a fraction is [tex]\frac{5}{8\cdot(x+1)^2\cdot x^3}[/tex] .
The given expression is: [tex]\frac{15x^2y}{(x+1)^3}\cdot\frac{(x+1)}{24x^5y}[/tex]
we will use the properties of exponents to simplify the expression.
Taking the powers of the like terms and combining we get :
[tex]\implies \frac{15x^2y}{(x+1)^3}\cdot\frac{(x+1)}{24x^5y}[/tex]
[tex]\implies \frac{15}{24} \times \frac{x^{2-5}y^{(1-1)}}{(x+1)^{3-2}}[/tex]
[tex]\implies \frac{5}{8\cdot(x+1)^2\cdot x^3}\\[/tex]
Therefore we get the simplified equation for the expression.
Expressions are mathematical statements that comprise either numbers, variables, or both and at least two terms associated by an operator. Mathematical operations include addition, subtraction, multiplication, and division.
In mathematics, there are two different types of expressions: algebraic expressions, which also include variables, and numerical expressions, which solely comprise numbers. A set sum of money appears to be a constant.
A variable is a symbol that has no predetermined value. A term may consist of one constant, one variable, or a combination of variables and constants multiplied or divided. A number that is additionally multiplied by a variable is referred to as the coefficient in an expression.
To learn more about expression visit:
https://brainly.com/question/22860327
#SPJ9
Find the equation of the line containing the points (42.3,82) and (42.8,94) more
Answers
Let's remember that the equation of a line always has the form:
[tex]y=m\cdot x+b[/tex]where "m" and "b" are constant numbers that we must find. Now, let's find "m" first. "m" is called the slope of the line, and it represents the relationship between the changes in y (second component) and the changes in x (first component). So it isn't surprising that we can compute it by:
[tex]m=\frac{94-82}{42.8-42.3}=\frac{12}{0.5}=24[/tex]Having calculated "m", we know that, (for the point (42.3,82) must lie in the line)
[tex]82=24\cdot(42.3)+b[/tex]Then,
[tex]b=82-24\cdot(42.3)=933.2[/tex]This implies that the equation of our line is
[tex]y=24\cdot x-933.2[/tex]Here is a graph of the line:
Comment: Our line is represented with a red color.
I need this practice problem from my prep guide answered and explained
Answers
To rewrite the equation in the indicated form, isolate the variable terms on the left side of the equation.
[tex]8x^2+9y^2-16x-9y=-2[/tex]Group the variable terms and then complete the squares. Add the same terms on the right side of the equation to make it balance.
[tex]\begin{gathered} (8x^2-16x)+(9y^2-9y)=-2 \\ 8(x^2-2x)+9(y^2-y)=-2 \\ 8(x^2-2x+1)+9(y^2-y+\frac{1}{4})=-2+8+9(\frac{1}{4}) \end{gathered}[/tex]Rewrite the trinomials as squares of binomials and then simplify the right side of the equation.
[tex]8(x-1)^2+9(y-\frac{1}{2})=\frac{33}{4}[/tex]To make the right side of the equation equal to 1, multiply both sides of the equation by 4/33.
[tex]\begin{gathered} \mleft(\frac{4}{33}\mright)(8)(x-1)^2+\mleft(\frac{4}{33}\mright)(9)(y-\frac{1}{2})=\mleft(\frac{4}{33}\mright)\mleft(\frac{33}{4}\mright) \\ \frac{32\mleft(x-1\mright)^2}{33}+\frac{12(y-\frac{1}{2})}{11}=1 \end{gathered}[/tex]Need help with solving equations and also need help understanding what moves to the lowest variable term mean.
Answers
An equation is a mathematical expression that contains an equal sign. The objective of an equation is usually to determine the value of an unkown variable, commonly referred to x or y. In order to do that, however, we need to isolate the variable on the left side and this has to be done in a way that mantains the balance in the equation. This means that whatever operation we do on one side we have to perform the same exact operation on the other side. Let's take a look at an example.
[tex]3x+9=x+40[/tex]For this equation we have the unknown variable x, which is the value we want to find. Our goal is to isolate the variable on the left side, however we can see that there is one x on the right side, the first step will be to move this to the left side, this is what means to move the lowest variablem term first, because if we were to move "3x", which is the highest variable term, we would have to perform more steps to solve the equation.
To move the term "x" from the right to the left we need to subtract both sides by "x", this is because when we subtract "x-x" on the right side, the result will be 0 and we will be left with unkown variables only on the left. Let's check this out:
[tex]\begin{gathered} 3x+9-x=x+40-x \\ 3x-x+9=x-x+40 \\ 2x+9=40 \end{gathered}[/tex]As we can see by doing so we eliminated the variable on the right side. Now we want to remove the 9 from the left side, we will have to perform a similar operation by subtracting 9 from both sides.
[tex]\begin{gathered} 2x+9-9=40-9 \\ 2x=31 \end{gathered}[/tex]Now we have only a variable term on the left side, but it still being multiplied by 2 and we don't want that, so we have to divide both sides by 2.
[tex]\begin{gathered} \frac{2x}{2}=\frac{31}{2} \\ x=\frac{31}{2} \end{gathered}[/tex]With this we achieved the goal of the equation, which was to find the value of x. In short we always want to isolate the variable on the left side and to do that we will have to perform the inverse operation of the other terms in both sides of the equation, if a term is adding we need to subtract on both sides, if it is multiplying we need to divide on both sides and so on. We have to do that first with the term that contains the letter of lowest value, like we did with this one.
A principal of $600 earns 3.2% interest compounded monthly. What is the effective interest (growth) rate? (Hint: make the equation look like abt.) About how long does it take to reach $1000?
Answers
Answer:
Explanation:
The formula for calculating the effective interest rate is expressed as
R = (1 + i/n)^n - 1
where
R is the effective interest rate
i is the nominal rate
n is the number of compounding periods in a year
From the information given,
n = 12 because it was compounded monthly
i = 3.2% = 3.2/100 = 0.032
Thus,
R = (1 + 0.032/12)^12 - 1
R = 0.03247
Multiplying by 100, it becomes 0.03247 x 100
Effective interest rate = 3.25%
We would apply the formula for calculating compound interest which is expressed as
A = a(1 + r/n)^nt
where
a is the principal or initial amount
t is the number of years
A is the final amount after t years
From the information given,
A = 1000
a = 600
n = 12
We want to find t
By substituting these values into the formula, we have
1000 = 600(1 + 0.032/12)^12t
1000/600 = (1.00267)^12t
Taking natural log of both sides, we have
ln (1000/600) = ln (1.00267)^12t = 12tln(1.00267)
12t = [ln (1000/600)]/ln (1.00267) = 191.5758
t = 191.5758/12
t = 16
It takes 16 years for the amount to reach $1000
Find the real and imaginary solution of (w^3) - 1000=0
Answers
Explanation
Given
[tex]w^3-1000=0[/tex]We will have;
[tex]\begin{gathered} w^3=1000 \\ \mathrm{For\:}x^3=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt[3]{f\left(a\right)},\:\sqrt[3]{f\left(a\right)}\frac{-1-\sqrt{3}i}{2},\:\sqrt[3]{f\left(a\right)}\frac{-1+\sqrt{3}i}{2} \\ therefore;\text{ }w=\sqrt[3]{1000},\:w=\sqrt[3]{1000}\frac{-1+\sqrt{3}i}{2},\:w=\sqrt[3]{1000}\frac{-1-\sqrt{3}i}{2} \\ hence;w=10,w=10\times\frac{-1+\sqrt{3}i}{2},\:w=10\times\frac{-1-\sqrt{3}i}{2} \\ w=10,\:w=-5+5\sqrt{3}i,\:w=-5-5\sqrt{3}i \end{gathered}[/tex]Answer: Option D
In AOPQ, OQ is extended through point Q to point R, m PQR = (7x – 19)º, mZOPQ = (2x – 3)°, and mZQOP = (x + 16). Find mZPQR.
Answers
Solution
For this case we can do the following:
m < PQR = 7x -19
m < OPQ= 2x-3
m < QOP= x+16
We need to satisfy that:
(180- m Replacing we got:
(180- 7x +19) + 2x -3 + x+16= 180
-7x +2x +x = -19+3 -16
-4x = -32
x= 8
Then m
A science fair poster is a rectangle 36 inches long and 24 inches wide what is the area of the poster in square feet with sure to include the correct unit in your answer
Answers
Okay, here we have this:
Considering the provided information, we are going to calculate the area of the rectangle ins square inches and after we are going to convert it to square feet, so we obtain the following:
Area of the rectangle=36 inches * 24 inches = 864 square inches
Now, let's convert it to square feet, then we have:
[tex]\begin{gathered} 864in^2\cdot\frac{1ft^2}{144in^2} \\ =6ft^2 \end{gathered}[/tex]Finally we obtain that the area in square feet of the rectangle is 6 square feet.