To solve for x in any specific equation, we need to isolate x in one side of the equation. we can do that by adding, subtracting, multiplying, or dividing by a specific number on both sides of the equation.
For example:
X + 3 = 7
X + 3 - 3 = 7 - 3
X = 4
We solve for x when we subtract 3 on both sides of the equation.
an unusually shaped section of a park is to be paved. this section is drawn to scale below. the length of a single grid segment is 1 m.
Since the length of a single grid square is 1m, then its area is:
[tex]A=1m\times1m=1m^2\text{.}[/tex]Now, to compute the area of the given section we will use the following diagram.
To compute the area of each triangle we will use the following formula for the area of a triangle:
[tex]\begin{gathered} A=\frac{bh}{2}, \\ \text{where b is the base of the triangle and h is its height.} \end{gathered}[/tex]And to compute the area of the rectangle we will use the following formula:
[tex]\begin{gathered} A=bh, \\ \text{where b is the base of the rectangle and h is its height.} \end{gathered}[/tex]Therefore the area of triangle A is:
[tex]A_A=\frac{6m\cdot2m}{2}=6m^2\text{.}[/tex]The area of triangle B is:
[tex]A_B=\frac{4m\cdot2m}{2}=4m^2\text{.}[/tex]The area of triangle C is:
[tex]A_C=\frac{3m\cdot1m}{2}=1.5m^2\text{.}[/tex]The area of triangle D is:
[tex]A_D=\frac{5m\cdot1m}{2}=2.5m^2\text{.}[/tex]The area of rectangle E is:
[tex]A_E=12m^2\text{.}[/tex]Finally, the area of the given section is:
[tex]\begin{gathered} A=A_A+A_B+A_C+A_D+A_E \\ =6m^2+4m^2+1.5m^2+2.5m^2+12m^2=26m^2\text{.} \end{gathered}[/tex]Answer:
The area of a single grid square is:
[tex]1m^2\text{.}[/tex]The approximate area of the section that will be paved is:
[tex]26m^2\text{.}[/tex]
use the given actual and magnified lengths to determine which of the following insects were looked at using the same magnifying glass (with the same scale factor)
Grasshoper
Actual: 2 in
Magnified: 15 in
The scale factor is given by:
[tex]k=\frac{15}{2}=7.5[/tex]Black beetle
Actual: 0.6 in
Magnified: 4.2 in
The scale factor is:
[tex]k=\frac{4.2}{0.6}=7[/tex]Honybee
Actual: 5/8 in
Magnified: 75/16 in
The scale factor is:
[tex]k=\frac{\frac{75}{16}}{\frac{5}{8}}=\frac{75\cdot8}{16\cdot5}=\frac{600}{80}=\frac{15}{2}=7.5[/tex]Monarch butterfly
Actual: 3.9 in
Magnified: 29.25 in
The scale factor is:
[tex]k=\frac{29.25}{3.9}=\frac{15}{2}=7.5[/tex]Answer:
Grasshoper, Honybee and Monarch butterfly have the same factor scale = 7.5
Black beetle has a factor scale = 7
In ABC, AB = 10 and BC = 5. Which expression is always true?
Using the Triangle inequality:
In every triangle the sum of the lengths of any two sides is always greater than the length of the remaining side, so:
[tex]\begin{gathered} AB+BC>AC \\ so\colon \\ 5Write a equation of a line in slope intercept form that is perpendicular to the line y= [tex] \frac{1}{4} x[/tex]and crosses through the point (-3, -2)
Here, we want to write the equation of a line that passes through the given point and is perpendicular to the given line
When two lines are perpendicular to each other, what this mean is that the product of their slopes are equal to -1
Generally, the equation of a straight line can be written in the form;
[tex]y\text{ = mx + b}[/tex]where m is the slope of the line and b is the y-intercept of the given line
Now from the given equation, we can see that the coefficient of x is 1/4. What this mean is that the slope of the line is 1/4 (the line's y-intercept is zero)
We can then proceed from here to get the slope of the second line
Mathematically, since the two lines are perpendicular;
[tex]m_{1\text{ }\times\text{ }}m_2\text{ = -1}[/tex]Thus;
[tex]\begin{gathered} \frac{1}{4}\text{ }\times m_2\text{ = -1 } \\ \\ m_2\text{ = -1 }\times\text{ 4 = -4} \end{gathered}[/tex]This shows that the slope of the second line is -4
We can write the equation of the second line as;
[tex]y\text{ = -4x + c}[/tex]To completely write the equation of the second line, we need to get the value of c
To do this, we substitute the coordinates of the point that lies on the line
The point we are given is (-3,-2)
So in this case, we substitute the value x = -3 and y = -2
Thus, we have;
-2 = -4(-3) + c
-2 = 12 + c
c = -2 -12
c = -14
A. Substitute the x-values shown to the right into y = xand y = |x| to find several points on their graphs. Usethe probe to check your work.
For the function y=x we just have to replace the values in the table for the x so:
[tex]\begin{gathered} -3\to x=-3 \\ -2\to x=-2 \\ -1\to x=-1 \\ 0\to x=0 \\ 1\to x=1 \\ 2\to x=2 \\ 3\to x=3 \end{gathered}[/tex]and for y = |x| we have to change all the negative values for positive:
[tex]\begin{gathered} -3\to\mleft|x\mright|=3 \\ -2\to|x|=2 \\ -1\to|x|=1 \\ 0\to|x|=0 \\ 1\to|x|=1 \\ 2\to|x|=2 \\ 3\to|x|=3 \end{gathered}[/tex]Which expression is equivalent to75a7b"40213,9 ? Assume a=1 and C=0.
we have the expression
[tex]\sqrt[3]{\frac{75a^7b^4}{40a^{(13)}c^9}}[/tex]Remember that
[tex]\frac{75}{40}=\frac{15}{8}=\frac{15}{2^3}[/tex][tex]\frac{a^7}{a^{(13)}}=\frac{1}{a^6}[/tex]substitute
[tex]\sqrt[3]{\frac{75a^7b^4}{40a^{(13)}c^9}}=\sqrt[3]{\frac{15b^4}{2^3a^6c^9}}[/tex]we have that
[tex]2^3a^6c^9=(2a^2c^3)^3[/tex]substitute
[tex]\sqrt[3]{\frac{15b^4}{2^3a^6c^9}}=\frac{\sqrt[3]{15b^4}}{(2a^2c^3)}=b\frac{\sqrt[3]{15b^{}}}{(2a^2c^3)}[/tex]answer is the second optionYou poured 1/4 of the juice from a 2-liter bottle while serving guests at a party. How much juice, in liters, is still left in the bottle?
How much juice was used?
How much is left?
Answer:
1.5 litters is left and 0.5 litters was used
Step-by-step explanation:
2 litters divided by 4 = 0.5 litters and you can do the rest of the math if needed
The count in a bacteria culture was 800 after 15 minutes and 1000 after 30 minutes. Assuming the count grows exponentiallyA)What was the initial size of the culture? B)Find the doubling period. C)Find the population after 60 minutes. D)When will the population reach 13000.
Answer:
A) The initial size o the culture is 640
B) The doubling period is 47 minutes
C) The population after 60 minutes is 1563
D) The population will reach 13000 after 3 hours 22 minutes
Explanation:
The form of an exponential grow model is:
[tex]S=Pb^t[/tex]Where:
S is the population after t hours
P is the initial population
b is the base of the exponent
t is the time, in hours
We know that after 15 minutes, the population was 800. 15 minutes is a quarter of an hour. Thus, t = 1/4, S = 800:
[tex]800=Pb^{\frac{1}{4}}[/tex]Also, we know that after 30 minutes, the population was 1000. Thus, t = 1/2, S = 1000
[tex]1000=Pb^{\frac{1}{2}}[/tex]Then, we have a system of equations:
[tex]\begin{cases}800=Pb^{\frac{1}{4}}{} \\ 1000=Pb^{\frac{1}{2}}{}\end{cases}[/tex]We can solve the first equation for P:
[tex]\begin{gathered} 800=Pb^{\frac{1}{4}} \\ P=\frac{800}{b^{\frac{1}{4}}} \end{gathered}[/tex]And substitute in the other equation:
[tex]1000=\frac{800}{b^{\frac{1}{4}}}b^{\frac{1}{2}}[/tex]And solve:
[tex]\frac{1000}{800}=\frac{b^{\frac{1}{2}}}{b^{\frac{1}{4}}}[/tex][tex]\begin{gathered} \frac{5}{4}=b^{\frac{1}{2}-\frac{1}{4}} \\ . \\ \frac{5}{4}=b^{\frac{1}{4}} \end{gathered}[/tex][tex]\begin{gathered} b=(\frac{5}{4})^4 \\ . \\ b=\frac{625}{256} \end{gathered}[/tex]Now, we can find the initial population P:
[tex]P=\frac{800}{(\frac{625}{256})^4}=\frac{800}{\frac{5}{4}}=\frac{800\cdot4}{5}=640[/tex]The initial population is 640
To find the doubling period, we want that the population equal to twice the initial population:
[tex]S=2P[/tex]Then, since we know the equation, we can write:
[tex]2P=P(\frac{625}{256})^t[/tex]Then:
[tex]\begin{gathered} \frac{2P}{P}=(\frac{625}{256})^t \\ . \\ 2=(\frac{625}{256})^t \\ \ln(2)=t\ln(\frac{625}{256}) \\ . \\ \frac{\ln(2)}{\ln(\frac{625}{256})}=t \\ . \\ t\approx0.7765 \end{gathered}[/tex]If an hour is 60 minutes:
[tex]60\cdot0.7765=46.59\approx47\text{ }minutes[/tex]To find the population after 60 minutes, we use t = 1 hour and we want to find S:
[tex]\begin{gathered} S=640(\frac{625}{256})^1 \\ . \\ S=640\cdot\frac{625}{256}=1562.5 \end{gathered}[/tex]To find when the population is 13000, then we use S = 13000 and solve for t:
[tex]\begin{gathered} 13000=640(\frac{625}{256})^t \\ . \\ \frac{13000}{640}=(\frac{625}{256})^t \\ . \\ \frac{325}{16}=(\frac{625}{256})^t \\ . \\ \ln(\frac{325}{16})=t\ln(\frac{625}{256})^ \\ . \\ t=\frac{\ln(\frac{325}{16})}{\ln(\frac{625}{256})}\approx3.373 \\ \\ \end{gathered}[/tex]We have 3 full hours and 0.373. Since one hour is 60 minutes:
[tex]60\cdot0.373\approx22[/tex]The population reach 13000 after 3 hours 22 minutes
The distance from Becca’s house to Liz’s house is 13 kilometers. Approximately how many miles does Becca live from Liz? Use the conversion factor shown below.
Data:
13 km
Convert to miles
(1 km is equal to 0.6214 miles)
[tex]13\operatorname{km}\cdot\frac{0.6214mi}{1\operatorname{km}}=8.078mi[/tex](1 mile is equal to 1.6093km)
[tex]13\operatorname{km}\cdot\frac{1mi}{1.6093\operatorname{km}}=8.078mi[/tex]Then, Becca lives 8.078 miles (aprroximately 8.1 miles) from LizOrder the angles of the triangle from smallest to biggest T R 12 addre S
It's important to know that each side is related to its angle in front. In other words, the greatest side has the greatest angle in front, and so on.
Having said that, the order of the angles from least to greatest is
[tex]\begin{gathered} 6<11<12 \\ \angle S<\angle R<\angle T \end{gathered}[/tex]Therefore, the order is S, R, and T.Use the standard deviation values of the two samples to find the standard deviation of the sample mean differences.Sample Standard Deviationred box 3.868blue box 2.933
Given:
The standard deviation are given as,
[tex]\begin{gathered} \sigma_{m_1}=\text{ 3.868} \\ \sigma_{m_2}\text{ = 2.933} \\ \end{gathered}[/tex]Required:
The standard deviation of the sample mean differences.
Explanation:
The formula for the deviation of the sample mean difference is given as,
[tex]\begin{gathered} \sigma_{m_1}-\text{ }\sigma_{m_2}\text{ = }\sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}} \\ \end{gathered}[/tex]Substituting the values in the above formula,
[tex]\begin{gathered} \sigma_{m_1}-\text{ }\sigma_{m_2}\text{ = }\sqrt{\frac{3.868^2}{n_1}+\frac{2.933^2}{n_2}} \\ \sigma_{m_1}-\text{ }\sigma_{m_2}\text{ = }\sqrt{\frac{14.9614}{n_1}+\frac{8.6025}{n_2}} \end{gathered}[/tex]Answer:
Thus the required answer is,
[tex]\sigma_{m_1}-\text{\sigma}_{m_2}=\sqrt{\frac{\text{14.9614}}{n_1}+\frac{\text{8.6025}}{n_2}}[/tex]
The prices of cell phone cases in a store are normally distributed.The mean of the prices is $22.90,and the standard deviation is $4.90.If you want to look at the bottom 45% of cases in terms of price,what is the cutoff price so that 45% of all cases are priced below that amount?
Given:
Mean = 22.90
Standard Deviation = 4.90
Find the cutoff price so that 45% of all cases are priced below that amount.
To solve this problem, the first thing we need to do is to find the z-score for 45% or 0.45.
The z-score for 0.45 is -0.126.
Now, to find the cutoff price or the "score", we will use the following equation
[tex]z=\frac{x-\mu}{\sigma}[/tex]Where:
z = z-score
x = score
μ = mean
σ = standard deviation
We are looking for the "x"
Derive the formula and substitute the given data.
[tex]z=\frac{x-\mu}{\sigma}[/tex][tex]\sigma z=x-\mu[/tex][tex]x=z\sigma+\mu[/tex][tex]x=(-0.126)(4.90)+22.90[/tex][tex]x=22.28[/tex]We got a value of 22.28 for our score, therefore, the cutoff price must be $22.28.
About 1% of the population has a particular genetic mutation. 100 people are randomly selected.Find the standard deviation for the number of people with the genetic mutation in such groups of 100. (Remeber that standard deviation should be rounded to one more decimal place than the raw data, in this case 1 decimal place is necessary.)
ANSWER:
1.0
STEP-BY-STEP EXPLANATION:
Given:
p = 1% = 0.01
q = 1 - p = 1 - 0.01 = 0.99
n = 100
The standard deviation is calculated using the following formula:
[tex]\begin{gathered} \sigma=\sqrt{n\cdot p\cdot q} \\ \\ \text{ We replace each value and obtain the standard deviation:} \\ \\ \sigma=\sqrt{100\cdot0.01\cdot0.99} \\ \\ \sigma=\sqrt{0.99} \\ \\ \sigma=0.99498 \\ \\ \sigma=0.995\rightarrow1\text{ decimal place}\rightarrow1.0 \end{gathered}[/tex]Therefore, the standard deviation is equal to 1.0
a landscaper is hired to take care of the lawn and shrubs around the house. the landscaper claims that the relationship between the number of hours worked and the total work fee is proportional. the fee for 4 hours of work is $140.
which of the following combinations of values for the landscapers work hours and total work fee support the claim that the relationship between the two values is proportional?
A. 3 hours for $105 B. 3.5 hours for $120 C. 4.75 hours for $166.25 D. 5.5 hours for $190 E. 6.25 hours for $210.25 F. 7.5 hours for $262.50
The two combinations that shows that the landscapers work hours and total work fee are proportional are: 3 hours for $105 and 7.5 hours for $262.50(option A and F)
What is direct proportion?Direct proportion or direct variation is the relation between two quantities where the ratio of the two is equal to a constant value. It is represented by the proportional symbol.
Direct proportion is given by y= kx, where k is the constant and y and x are the variables.
If x represents the landscapers work hours and y represents the total work fee.
y= kx
when y = $140 and x= 4hours
k= 140/4= 35
therefore when x= 3 then y= 3×35=105
similarly when x= 7.5, y= 35×7.5=262.50
Only option A and F obeys the proportional relationship.
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what is the value of f(0)=
SOLUTION:
Case:
Given:
Required:
Method:
Step 1:
Step 2:
Step 3:
Final answer:
What type of number is 4π?whole numberintegerrational numberirrational number
Answer:
(D)Irrational number
Explanation:
The number π is Irrational because the digits after the decimal point go on indefinitely.
Therefore, a product of a number and π is also an Irrational Number.
Perform the operations and simplify the final answer if possible
Answer:
-23
Explanation:
To perform the operations, we first need to solve the operations in parenthesis, then the power, and finally, the sum.
So, the expression is equal to:
2 - (4 - 9)²
2 - (-5)²
2 - (25)
2 - 25
-23
Therefore, the answer is -23
True or false: if the determinant is 0, then the system has no solution?
If the determinat of a matrix is 0, then the linear system of equations it represents has no solution.
Then, the statement is true.
I need help with this question please (just question 10, not the one below)
Let the cost of each packet of cheese is $x
Let the cost of each burger $y
Calvin bought 5 packets of cheese and 3 burgers for $29.99
Mathematically we can write
[tex]5x+3y=29.99\text{ ..(1)}[/tex]Alex bought 3 packets of cheese and 7 burgers for $32.71
Mathematically we can write
[tex]3x+7y=32.71\text{ ..(2)}[/tex]Now we have to solve equations (1) and (2) for x and y
Now 7*(1)-3*(2) implies
[tex]7\times(1)-3\times(2)\Rightarrow35x+21y-9x-21x=209.93-98.13\Rightarrow26x=111.8\Rightarrow x=\frac{111.8}{26}\Rightarrow x=4.30[/tex]Hence the price of each packets of cheese is $4.30
Part 2 out of 2If you plan to cancel your internet service after 11 months, which is the cheaper option
m = number of months
Option 1 cost = 35 + 20m
Option 2 cost = 25m
Part 1: If the cost is equal for both otpions, then we can write: 35 + 20m = 25m, solving for m:
5m = 35 ==> m = 35/5 = 7
m = 7
In month 7, the cost is 35 + 20(7) = 35 + 140 = 175
Part 2:
Option1 cost when m = 11: 35 + 20(11) = 35 + 220 = 255
Option2 cost when m = 11: 25(11) = 275
Option 2 costs more than option 1, so Option 1 is cheaper
Tell which choice, 100, 500, or 1,000, is the best estimate of the solution.39.4x = 37,627a. 1,000b.500c.100Please select the best answer from the choices providedΑВС
39.4 x = 37627
Divide both sides by 39.4
[tex]\begin{gathered} \frac{39.4x}{39.4}=\frac{37627}{39.4} \\ x=955 \end{gathered}[/tex]955 is nearest to 1000 than 500 or 100
Then the best estimate is 1000
The answer is A
108A) 54B) 60C) 68D) 72BCNote: Figure not drawn to scale.In the figure above, lines and m are paralleland BD bisects ZABC. What is the value of x?
Given the shown figure:
lines l and m are parallel
So, m∠A = m∠ABC
Because the alternative angles are congruent
So, m∠ABC = 108°
And BD bisects the m∠ABC
So, m∠CBD = 1/2 * m∠ABC = 1/2 * 108 = 54°
As the lines l and m are parallel
So, m∠CBD = m∠D = x
So, the answer will be x = 54
The answer will be A) 54
Enter an equation for the function. Give your answer in the form a(6"). In theevent that a = 1, give your answer in the form b".A laser beam with an output of 4 milliwatts is directed into a series of mirrorsThe laser beam loses 6% of its power every time it reflects off of a mirror. Thepower p(n) is a function of the number n of reflections.The equation is p(n) = 0
From the data provided, we have the following;
Initial power output = 4 milliwatts
Power lost per reflection = 6% (OR 0.06)
We need to find a function that shows the power each time the laser beam is reflected off a mirror.
Note that the general equation for an exponential decay/loss is given as;
[tex]\begin{gathered} y=a(1-r)^x \\ OR \\ f(x)=a(1-r)^x \end{gathered}[/tex]Note also that (1 - r) is often replaced by b. Therefore, the equation can be written as;
[tex]\begin{gathered} f(x)=a(1-r)^x^{} \\ f(x)=ab^x \end{gathered}[/tex]Where the number of reflections is given by n and p(n) is a function of the number of reflections, we now have;
[tex]p(n)=ab^n[/tex]Where the variables are;
[tex]\begin{gathered} a=4\text{ milliwatts (initial value)} \\ r=0.06 \end{gathered}[/tex]We now have the function as;
[tex]\begin{gathered} p(n)=a(1-0.06)^n \\ p(n)=a(0.94)^n \end{gathered}[/tex]ANSWER:
[tex]p(n)=a(0.94)^n[/tex]Is position on an x or y axis
Usually, time is the independent variable, so it goes in the x-axis.
Position is similar to distance, and spedd is the rate of variation of position or distance. All of these three are usually graphed in the y-axis, as they depend on time.
Express the following ratio in simplest form 39:10
ok
If we have
[tex]\text{ }\frac{39}{10}[/tex]It was not possible to simplify it anymore so the answer will be the same.
It is not possible to implify it because the are no common fators between 39 and |0.
I have a triangle and diamond on an equation which is =1.05so I am asking am I suppose to divide by 2 to get the answer?
Let,
T = Triangle
S = Semi Circle
R = Star
D = Diamond
Given:
a.) 4 Triangles = 2 Semi Circle + 2 Star → 4T = 2S + 2R
b.) 1 Triangle + 1 Diamond = 1.05 → 1T + 1D = 1.05
c.) 1 Star + 1 Semi Circle = 0.525 → 1R + 1S = 0.525
d.) Diamond = ?
For us to be able to determine the value of the diamond, we must be able to determine the value of the Triangle.
For us to get it, we will be using first the equation at a and c.
4T = 2S + 2R
1R + 1S = 0.525
We get,
2S + 2R = 2(1S + 1R)
2S + 2R = 2(0.525)
2S + 2R = 1.05
Let's now get the value of the triangle,
4T = 2S + 2R
4T = 1.05
T = 1.05/4
T = 0.2625 (Value per triangle)
Let's now determine the value of the DIAMOND.
1 Triangle + 1 Diamond = 1.05 → 1T + 1D = 1.05
1T + 1D = 1.05
1(0.2625) + 1D = 1.05
0.2625 + 1D = 1.05
1D = 1.05 - 0.2625
1D = D = 0.7875
ANSWER: The value of the diamond is 0.7875
Write a formula for the function obtained when the graph is shifted as described. When typing exponents use the carrot key ^ by pressing SHIFT and 6. For example x squared can be typed as x^2. Do not put spaces between your characters and remember to use parentheses in the appropriate places!f(x)=x^3 is shifted up 3 unit and to the left 7 units.The new equations f(x)=Answer
Given the function
[tex]f(x)=x^3[/tex]We are asked to shift the function up 3 units and to the left 7 units.
Explanation
1) To shift upwards, we will add outside of the argument
2) To shift to the left, we will add inside of the argument
Therefore;
[tex]x^3\rightarrow(x+7)^3+3[/tex]Answer:
[tex]f(x)=(x+7)^3+3[/tex]The ratio of the quantities of sugar and flour needed to bake a cake is 2:5. What is the quantity of sugar needed for a cake, if 750 grams of flour are used to bake it?
The quantity of sugar needed for a cake, if 750 grams of flour are used to bake it is 300 grams.
What is ratio?Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them.
In this case, the ratio of the quantities of sugar and flour needed to bake a cake is 2:5.
The quantity of sugar needed is illustrated by x.
This will be:
2/5 = x/750
Cross multiply
5x = 2 × 750
5x = 1500
Divide
x = 1500/5
x = 300
The sugar needed is 300 grams.
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Four gallons of gasoline cost $17.56. What is the price per gallon?
write a relationship between the cost and the amount of gasoline
[tex]\begin{gathered} 4gal\Rightarrow17.56 \\ 1gal\Rightarrow x \end{gathered}[/tex]solve for the x
[tex]\begin{gathered} x=\frac{1gal\cdot17.56}{4gal} \\ x=4.39 \end{gathered}[/tex]the price per gallon is $4.39
Anjali's Bikes rents bikes for $15 plus $7per hour. Aliyah paid $57 to rent a bike.For how many hours did she rent the bike?
From the question;
Anjali's Bikes rents bikes for $15 plus $7 per hour.
Let h represent the number of hours she rent the bike;
the total amount she will pay for h hours is;
[tex]T=15+7h[/tex]Given that; Aliyah paid $57 to rent a bike.
T = $57
The equation becomes;
[tex]T=15+7h[/tex]