The 3rd option is right as both contain the sum
50/7 + 8/15
write the number in standard notation:3.92x10^7
We will write it as follows:
[tex]3.92\cdot10^7=39200000[/tex]Find greatest common factor for each group,factor completely and find real roots
SOLUTION
Write out the polynomial given
The first group of the expresion is
[tex]\begin{gathered} 3x^3+4x^2 \\ \text{Then the GCE is } \\ x^2(\frac{3x^3}{x^2}+\frac{4x^2}{x^2}) \\ \text{GCE}=x^2 \end{gathered}[/tex]GCE is x²
For the second group, we have
[tex]\begin{gathered} 75x+100 \\ \text{GCE}=25(\frac{75x}{25}+\frac{100}{25}) \\ \text{GCE}=25 \end{gathered}[/tex]The GCE for the secod group is 25
To factorise completely, we have
[tex]\begin{gathered} 3x^3+4x^2+75x+100 \\ \\ x^2(\frac{3x^3}{x^2}+\frac{4x^2}{x^2})+25(\frac{75x}{25}+\frac{100}{25}) \end{gathered}[/tex]Then by simplification, we have
[tex]\begin{gathered} x^2(3x+4)+25(3x+4) \\ \text{Then, we factor completely to get} \\ (3x+4)(x^2+25) \end{gathered}[/tex]Then factors are (3x +4)(x²+ 25)
To find the real root, we equate each of the factors to zero, hence
[tex]\begin{gathered} (3x+4)(x^2+25)=0 \\ \text{Then} \\ 3x+4=0orx^2+25=0 \\ 3x=-40rx^2=-25 \\ \end{gathered}[/tex]Thus
[tex]\begin{gathered} \frac{3x}{3}=-\frac{4}{3} \\ x=-\frac{4}{3}\text{ is a real root } \\ or\text{ } \\ x^2=-25 \\ \text{take square root} \\ x=\pm_{}\sqrt[]{-25}\text{ not a real root} \end{gathered}[/tex]Therefore, since the root of -25 is a complex number,
The only real root is x = -4/3
A person can join The Fitness Center for $50. A member can rent the tennis ball machine for $10 an hour. Write a linear function to model the relationship between the number of hours the machine is rented (x) and the total cost (y).
Answer: y=10x+50
Step-by-step explanation:
Given the triangle congruence statement ΔUVW≅ΔABC and the triangles below, mark each of the triangles appropriately for corresponding angles and sides. Then create a list of congruent sides and angles using the tableCorresponding SidesCorresponding Angles
Given:
[tex]\Delta UVW\cong\Delta ABC[/tex]Corresponding sides are:
[tex]\begin{gathered} UV\cong AB \\ VW\cong BC \\ UW\cong AC \end{gathered}[/tex]Corresponding angles are:
[tex]\begin{gathered} \angle U\cong\angle A \\ \angle V=\angle B \\ \angle W=\angle C \end{gathered}[/tex]Convert percent 26% of a number is what fraction of that number
Express 26% as a fraction:
26% = 26/100
[tex]\frac{26}{100}=\frac{13}{50}=0.26[/tex]Which of the geometric objects are scaled versions ofeach other?For the objects that are scaled versions of each otherfill out the table withFigure Type- Figure Labels (smallest to largest)-Figure Ratio (might be extended ratio)Ive filled out the circles for you as an example and because the ratio involves radials. Figure labels| figure ratioCircle- J,L,G | √2: √ 5 :3
I will do the squares for you
All squares are similar
E K and C are squares so they are scaled versions of each other
The length of the top side of E 2 is units
The length of the top side of K is 3 units
The length of the top side of C is 5 units
From smallest to largest is E, K, C
Figure ratio is 2,3,5
The rectangles are done in the same manner
D is a 2 by 4
F is a 2 by 6
I is a 3 by 6
D and I are similar
D,I the ratio is 2:3
Triangles work like rectangles
B is a 2 by 3
H is a 3 by 5
A is a 4 by 6
B and A are similar
B,A the ratio is 2:4
in the graph of y= 8x + 5, 8 is theof the line
the function is:
[tex]y=8x+5[/tex]where 8 is the slope of the function
-Determine whether each relation is a function. Explain your answerA. {(7,4),(6,3),(5,2)}B. {(15,0),(15,-2)}C. {(0,1),(2,1),(0,3)}
A. it is a fuction because for every number in the first position of the pairs it is one and only one second position number.
B. it's not a function because the number 15 has two different pairs
C. it's not a function because zero has two different pairs, 1 and 3.
Solve the equation below for x. log(5x) + log(2x) = 1 O A. x = 10/7 O B. x = 1; x = -1 O c. x= 1 O D. There is no solution.
So we need to solve the following equation:
[tex]\log (5x)+\log (2x)=1[/tex]There are a few properties of logarithmic functions that we should remember. First, the logarithm of a negative number doesn't exist which means that x must be a positive number. Second, the addition of logarithms meets the following property:
[tex]\log (a)+\log (b)=\log (a\cdot b)[/tex]If we apply this to our equation we get:
[tex]\log (5x)+\log (2x)=\log (5x\cdot2x)=\log (10x^2)=1[/tex]Now we can pass the logarithm to the right side of the equation:
[tex]\begin{gathered} \log (10x^2)=1 \\ 10x^2=10^1=10 \\ 10x^2=10 \\ x^2=1 \end{gathered}[/tex]There are two possible solutions for x^2=1. These are x=1 and x=-1, however as I stated before x can't be a negative number which means that the solution of the equation is:
[tex]x=1[/tex]Then option C is the correct one.
Modeling System of Equations Per 2
Based on the given information, you can write the following equations for the costs:
y1 = 35x + 75
y2 = 38x
If the cost is the same for both companies, you have:
35x + 75 = 38x
you can solve the previous equation for x to determine the number of people:
35x + 75 = 38x subtract 35x both sides
75 = 38x - 35x
75 = 3x divide by 3 both sides
75/3 = x
25 = x
Hence, the number of people is 25
Sarah wanted to catch Jim. However , although they started at the same time, Jim traveled at 80 km/h and Sarah traveled at 120 km/h . How much of a head start did Jim have if it took three hours for Sarah to catch him ?
Jim traveled at 80 km/h and Sarah traveled at 120 km/h
It took 3 hours for Sarah to catch Jim.
Let's find out how much distance both covered.
[tex]Jim\colon\; d=r\cdot t=80\cdot3=240\: km[/tex]So, Jim traveled 240 km
[tex]Sarah\colon\; d=r\cdot t=120\cdot3=360\: km[/tex]So, Sarah traveled 360 km
This means that Jim must have started 360 - 240 = 120 km ahead.
Therefore, Jim had a head start of 120 km
Solve each equation for the variable. -10 = Зm +5
-10 = Зm +5
Subtract 5 from both sides of the equation:
-10-5 = 3m+5-5
-15 = 3m
Divide both sides by 3
-15/3 = 3m/3
-5= m
m= -5
Given a student has a dog, what is the probability that a student also has a cat?62.9%57.1%41.8%36.3%
The given problem is a conditional probability problem.
Probability that a student has a cat given that he/she has a dog is represented as:
[tex]Pr(C|D)=\frac{Pr(CnD)}{Pr(D)}[/tex][tex]\begin{gathered} \text{CnD}=16 \\ \text{Sample space=28+16+24}=68 \end{gathered}[/tex]Thus,
[tex]Pr(\text{CnD)}=\frac{16}{68}=0.2353[/tex][tex]\begin{gathered} Number\text{ of dogs only=28} \\ Pr(D)=\frac{28}{68}=0.4117 \end{gathered}[/tex]Therefore,
[tex]undefined[/tex](5 points each for a and b) A bacteria colony starts with 20 bacteria andgrows continuously at a rate of 28% per hour.a. How long will it take for the colony to:i. Double its size?ii. Reach 500,000 bacteria?b. How many bacteria will there be in:i. 3 hours?ii. 3.5 days?
Given:
The initial population of bacteria, I = 20
Growth rate, r = 28%
Explanation:
a) To find: The time
i) Double its size
Using the formula,
[tex]F=I(1+r)^t,\text{ Where I denotes initial and F denotes Final size.}[/tex]On substitution we get,
[tex]\begin{gathered} 40=20(1+0.28)^t \\ 1.28^t=\frac{40}{20} \\ t=\log _{1.28}2 \\ t=2.81 \end{gathered}[/tex]Thus, the answer is 2.81 hours.
ii) To reach 500000 bacteria:
[tex]\begin{gathered} 500000=20(1+0.28)^t \\ 1.28^t=\frac{500000}{20} \\ t=\log _{1.28}(25000) \\ t=41.02\text{ hours} \end{gathered}[/tex]Thus, the answer is 41.02 hours.
b) To find the bacteria size:
i) In 3 hours,
[tex]\begin{gathered} F=20(1+0.28)^3 \\ =41.94304 \\ \approx42 \end{gathered}[/tex]Thus, the size of bacteria in 3 hours is 42.
i) In 3.5 days,
That is, 84 hours
[tex]\begin{gathered} F=20(1+0.28)^{84} \\ =20261306488.67 \\ \approx20261306489 \end{gathered}[/tex]Thus, the size of bacteria in 3.5 days is 20261306489.
I just need the answer for this, no process or explanation needed, thank you!
1) Considering that the initial amount of Carbon 14 is 40% (0.4) and each year "t" is given in whole numbers. And we were told the amount of k we can insert into the equation:
[tex]\begin{gathered} N=N_0e^{-kt} \\ 0.6=\left(1\right)e^{-0.0001*t} \\ e^{\left\{-0.0001t\right\}}=0.6 \\ lne^{\left\{-0.0001t\right\}}=ln\left(0.6\right) \\ -0.0001t=ln\left(0.6\right) \\ t=5108.25623 \\ t\approx5108years \end{gathered}[/tex]Note that the initial value is 1 and the last one is 0.6 (40% less).
I need help with the Try it! section. i will flow a walk through if you can give one
Solution
For this case we need to remember that the general equation for a line is given by:
y= mx+ b
Where m represent the slope and b the intercept
And we can find the slope with this formuala:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]And we can use (50, 725) and (100,1325) and we have:
[tex]m=\frac{1325-725}{100-50}=12[/tex]And the intercept would be:
725 = 50*12 +b
b= 725 - 600
b= 125
and the equation would be given by:
y= 12 x + 125
And the y intercept represent the starting value of 125$ no matter the number of guests
A fireworks rocket is launched from a hill above a lake. The rocket will fall into the lake after exploding in the air. The rocket’s height above the surface of the lake is given by the function g(x)= -16x2 + 64x + 80 where x is the number of seconds after the rocket is launched. The function can also be written in factored form as g(x) = -16 (x + 1)(x - 5).When does the rocket hit the ground?
We are giving the function as;
[tex]g(x)=-16x^2+64x+80[/tex]If we factorize g(x) we have that
[tex]g(x)=-16(x+1)(x-5)[/tex]T0 find if the object has be launched and find the x value of the object
Therefore,
[tex]\begin{gathered} -16(x+1)(x_{}-5)=0 \\ \Leftrightarrow(x+1)(x_{}-5)=0 \\ \leftrightarrow x=-1\text{ or x=5} \end{gathered}[/tex]it will take the rocket 5 seconds to reach the ground.
Complete the square to findthe vertex of this parabola.x² - 2x + y - 4 = 0([?], [ ])
Given:
[tex]x^2-2x+y-4=0[/tex]Let's complete the square to find the vertex of the parabola.
To solve first move all terms not containing y to the right side of the equation:
[tex]y=-x^2+2x+4[/tex]Now, take the vertex form of a parabola:
[tex]y=a(x-h)^2+k[/tex]Apply the standard form of a parabola:
[tex]\begin{gathered} ax^2+bx+c \\ \\ -x^2+2x+4 \end{gathered}[/tex]Thus, we have:
a = -1
b = 2
c = 4
Now, to find the value of h, we have:
[tex]\begin{gathered} h=-\frac{b}{2a} \\ \\ h=-\frac{2}{2(-1)} \\ \\ h=-\frac{2}{-2} \\ \\ h=1 \end{gathered}[/tex]To find the value of k, we have:
[tex]\begin{gathered} k=c-\frac{b^2}{4a} \\ \\ k=4-\frac{2^2}{4(-1)} \\ \\ k=4-\frac{4}{-4} \\ \\ k=4+1 \\ \\ k=5 \end{gathered}[/tex]We have the values:
h = 1
k = 5
The vertex of the parabola is:
(h, k) ==> (1, 5)
ANSWER:
(1, 5)
If the fish tanks dimension are 60 by 15 by 34 and its is completely empty, what volume of water is needed to fill three fourths of the aquarium? Please help what would the volume if you only filled 3/4 of the tank
First let's find the volume of the fish tank. Given that the dimensions are 60 by 15 by 34, then:
[tex]V=(60)(15)(34)=30600[/tex]we have that the total volume of the fish tank is 30600 u³. But we only want to know how much is 3/4 of the total volume, then:
[tex](30600)(\frac{3}{4})=22950[/tex]therefore, to fill three fourths of the aquarium we will need 22950 u³ of water
The volume of a gas, such as helium or air, varies inversely with the pressure on it. If the volume of air is 325 cubic inches under a pressure of 11 psi, what pressure has to be applied to decrease the volume to 143 cubic inches?
ANSWER
The pressure is 25 psi
STEP-BY-STEP EXPLANATION:
From the question provided, you can see that the relationship between the volume of a gas and the pressure is an inverse relationship.
The volume of a gas varies inversely with the pressure on it
This implies that as the volume of the gas increases the pressure of the gas decreases and vice versa.
The next thing is to assign variables
Let the volume of the gas be V
Let the pressure of the gas be P
Mathematically, this can be represented as
[tex]\begin{gathered} V\text{ }\propto\text{ }\frac{1}{P} \\ \text{Introduce a proportionality constant K} \\ V\text{ = }\frac{K}{P} \\ \text{Cross multiply} \\ K\text{ = VP -------- equation 1} \\ \end{gathered}[/tex]The next step is to find the value of K from the given information in the question
• Volume = 325 cubic inches
,• Pressure = 11 psi
Recall that, K = VP
K = 325 * 11
K = 3,575
Since you have gotten the value of K, then, you can now find your pressure when the volume Is 143 cubic inches
[tex]\begin{gathered} V=143inches^3 \\ K\text{ = 3,575} \\ K\text{ = VP} \\ \text{Divide both sides by V} \\ \frac{K}{V}\text{ = }\frac{VP}{V} \\ P\text{ = }\frac{K}{V} \\ P\text{ = }\frac{3575}{143} \\ P\text{ = 25 ps}i. \end{gathered}[/tex]Hence, the pressure is 25 psi
Which point satisfies both of the following inequalities? -3x + 5y< 15. 5x+y>-5
Explanation.
eWe are told to find the points that satisfy the systems of inequalities
The systems of equations are
[tex]undefined[/tex]WhT is the slop of (0,3)
Step 1;
Write the coordinates of the given points
The number a exceeds the number b by 50% by what percent is the number b smaller than the number a
Number a exceeds the number b by 50%:
[tex]\begin{gathered} a=b+0.5b \\ a=1.5b=\frac{3}{2}b \\ b=\frac{2}{3}a \end{gathered}[/tex]That means, 1/3 smaller=33, 1/3% smaller or 33% smaller.
I don't understand how to do a certain equation i have no clue what its called
Answer:
y =24 -x
Explanation:
Mr Ledger has 24 donuts and if he uses x donuts then the amount he will have left will be
[tex]24-x[/tex]and since we are calling this amount left y, we can say
[tex]y=24-x[/tex]which is our answer!
When Mr Ledger uses 18 donuts, the number left will be
[tex]\begin{gathered} y=24-18, \\ y=6. \end{gathered}[/tex]And when Mr Ledger uses 22 donuts, we will have left
[tex]\begin{gathered} y=24-22, \\ y=2. \end{gathered}[/tex]donuts.
The graph of the two points is given below.
Identify any misrepresentation issues in the given graph. ▪︎The horizontal axis scale is not appropriate. ▪︎The horizontal axis ticks are not placed correctly.▪︎ The vertical axis scale is not appropriate. ▪︎The vertical axis ticks are not placed correctly. ▪︎The axis labeling is not complete. ▪︎There are distracting visual effects. ▪︎The graph is designed appropriately.
Looking at the graph, we can see that the x-axis has a lot of unused values, it goes until 50 but the graph only goes until around 25, so the horizontal axis scale is not appropriate.
Also, the x-axis does not have a label, so The axis labelling is not complete.
Last, this is a good graph to represent the temperature over the time, so the graph is designed appropriately.
What is the area of trapezoid KLMO?A) 224cm^2B) 112 cm^2C) 128 cm^2D) 96 cm^2
Given:
The length of the bases of the trapezoid
[tex]\begin{gathered} KL=a=12cm \\ \\ OM=b=16cm \end{gathered}[/tex]Height of the trapezoid:
[tex]LN=h=8cm[/tex]Required:
The area of trapezoid KLMO
Explanation:
The formula for area of trapezoid is given by
[tex]A(trapezoid)=\frac{a+b}{2}\times h[/tex]Substituting the given values in the above equation we get
[tex]\begin{gathered} A(trapezoid\text{ }KLMO)=\frac{a+b}{2}\times h \\ \\ A(trapezoid\text{ }KLMO)=\frac{12+16}{2}\times8=\frac{28}{2}\times8=14\times8=112cm^2 \end{gathered}[/tex]Final answer:
The area of trapezoid KLMO is 112 sq.cm
y = -x - 2 y + 2 = -x Graph each system. Tell whether the system hasA.no solutionB.one solutionC. infinitely many solutionsD. Cannot determine
To graph each equation in the system, you can give it x-values, plug into the equations, and get values for Y.
Since a single line passes through two points, just take two values of x for each equation. So, for the first you have for example
*If x = 3
[tex]\begin{gathered} y=-x-2 \\ y=-3-2 \\ y=-5 \\ \text{ So} \\ (3,-5) \end{gathered}[/tex]*If x = -4
[tex]\begin{gathered} y=-x-2 \\ y=-(-4)-2 \\ y=4-2 \\ y=2 \\ \text{ So,} \\ (-4,2) \end{gathered}[/tex]For the second equation you have for example
*If x = 1
[tex]\begin{gathered} y+2=-x \\ y+2=-1 \\ y+2-2=-1-2 \\ y=-3 \\ \text{ So,} \\ (1,-3) \end{gathered}[/tex]*if x = -1
[tex]\begin{gathered} y+2=-(-1) \\ y+2=1 \\ y+2-2=1-2 \\ y=-1 \\ \text{ So,} \\ (-1,-1) \end{gathered}[/tex]Now, graphing the equations you have
As you can see, the lines associated with this system of equations overlap, that is, they share infinite solution points.
Therfore, the correct answer is C. infinitely many solutions.
The doctor orders 3000 mL D5RL to run at 300 ml/hr. How long will this IV infusion run
we know that
the infusion run at 300 ml/hr
so
Applying proportion
Find out how long for 3,000 ml
Use a net to find the surface area of the prism. The surface area of the prism is ___cm² (Simplify your answer.)
Answer:
1,417 cm²
Explanation:
The net of the prism is attached below:
The surface area of the prism is the area of each of the triangles.
[tex]\begin{gathered} \text{Surface Area=}(13\times32)+(32\times6.5)+(13\times32)+(32\times6.5)+(13\times6.5)+(13\times6.5) \\ =416+208+416+208+84.5+84.5 \\ =1417\operatorname{cm}^2 \end{gathered}[/tex]The surface area of the prism is 1,417 cm².
a railroad tracks can be determined using the following graph. Several different rosdways are in the same region as the railroad. Part B: A turnpikes route is determined by the equation y=1/3x^2. Prove algebraically how many intwrsections there will be between the railroad abd the turnpike,showing all necessary work
Given
[tex]y=\frac{1}{3x^2}[/tex]2x+3y=18
Find
Prove algebraically how many intwrsections there will be between the railroad
Explanation
The graph of 2x+3y=18 is as the picture
2x+3y=18
when x=0, 0+3y=18 => y=6 =>(0,6)
when y=0, 2x+0=18 => x=9 => (9,0)
The intersection between the railroad and the highway is 0 because the graph of the railroad and the graph of the highway are parallel, that means they have no intersection
(b)
Assume the railroad can be found using the equation y=3/2x+b
when x=0 => y=8
[tex]\begin{gathered} \frac{1}{3}x^2=\frac{3}{2}x+8 \\ 2x^2-9x-48=0 \\ D=9^2-4(2)(-48)=465 \\ =>D>0 \\ \frac{1}{3}x^2=\frac{3}{2}x+8 \end{gathered}[/tex]has two roots, and there are 2 intersections
Final Answer
(a) No intersection
(b) Two intersections