Factoring
Factor the expression:
[tex]72b^2z+96b^2h+90xbz+120xbh[/tex]Divide the expression into two halves:
[tex](72b^2z+96b^2h)+(90xbz+120xbh)[/tex]Factor b^2 from the first group and xb from the second group:
[tex]b^2(72z+96h)+xb(90z+120h)[/tex]Now find the greatest common multiple of 72 and 96:
72= 2*2*2*3*3
96=2*2*2*2*2*2*3
Now we take the common factors with their least number of repetitions:
GCF=2*2*2*3=24
Now we find the GCF of 90 and 120:
90=2*3*3*5
120=2*2*2*3*5
GCF=2*3*5=30
Taking the GCF of each group:
[tex]\begin{gathered} b^224(3z+4h)+xb30(3z+4h) \\ =24b^2(3z+4h)+30xb(3z+4h) \end{gathered}[/tex]Now we finally take out 3z+4h from both groups:
[tex]\mleft(3z+4h\mright)(24b^2+30xb)[/tex]This last expression can be further factored by taking out 6b from both terms:
[tex]6b(3z+4h)(4b+5x)[/tex]This is the final expression factored as much as possible
i need help please and thank youthere are 2 pictures bc i couldn’t get it all in 1!
we have the system
y < -2x^2+4x-2
The solution for this inequality is the shaded area below the vertical dashed parabola
and
[tex]y\ge\frac{2}{3}x-3[/tex]the solution for this inequality is the shaded area above the solid line y=(2/3)x-3
therefore
the solution for this system of inequalities
Is the shaded area below the vertical dashed parabola y=-2x^2+4x-2 and above the solid line y=(2/3)x-3
see the attached figure to better understand the problem
For the given f(x), solve the equation f(x)=0 analytically and then use a graph of y=f(x) to solve the inequalities f(x)<0 and f(x)≥0. f(x)=ln(x+3)(1) What is the solution of f(x)=0?(2) What is the solution of f(x)<0?(3) What is the solution of f(x)≥0?
Explanation:
f(x) is a logarithmic function. Logarithmic functions are zero when the argument is 1:
[tex]\begin{gathered} f(x)=\ln (x+3)=0 \\ x+3=1 \\ x=1-3 \\ x=-2 \end{gathered}[/tex]For greater values, the function is positive and for less values the function is negative.
Answers:
(1) x = -2
(2) x < -2. In interval notation x:(-∞, -2)
(3) x ≥ -2. In interval notation x:[-2, ∞)
If 340 grams of a substance are present initially and 50 years later only 170 grams remain, how much of the substance will be present after 120 years?Round to the nearest tenth of a graim.grams
Given -
Substance present initially = 340 grams
Substance present 50 years later = 170 grams
To Find -
How much of the substance will be present after 120 years =?
Step-by-Step Explanation -
Since the substance was reduced to half of what it is initially in 50 years.
So,
The half-life time of the substance = 50 Years.
It means that every 50 years, the substance will reduce to half of its quantity.
And, we know the formula:
[tex]\text{ A = S\lparen}\frac{1}{2}\text{\rparen}^{\frac{t}{h}}[/tex]Where,
A = the remaining amount of Substance =?
S = the amount of Substance you start with = 340grams
t = the amount of time in years = 120 years
h = the half-life time = 50 years
Simply putting the values, we get:
[tex]\begin{gathered} A\text{ = 340}\times(\frac{1}{2})^{\frac{120}{50}} \\ \\ A\text{ = 17\lparen}\frac{1}{2}\text{\rparen}^{2.4} \\ \\ A\text{ = 17}\times(0.5)^{2.4} \\ \\ A\text{ = 17}\times0.1894 \\ \\ A\text{ = 3.22 gram} \end{gathered}[/tex]Final Answer -
The substance that will remain after 120 years = 3.22 gram
what is the better buy 4GB flash drive for $8 2 GB for $6 or 8 GB for $13
In order to find out which of the options would be better to buy we would have to calculate the better unit price that eacho of the following options offer.
So, unit price for the offers would be:
For 4GB flash drive for $8, unit price=$8/4
unit price=$2
For 2 GB for $6, unit price=$6/2=$3
For 8 GB for $13, unit prince=$13/8=$1.625
Therefore, as the unit price of 8 GB for $13 is the lower one, then the better choice to buy would be 8 GB for $13
A taxi service charges $3 for the first mile and then $2.25 for every mile after that. The farthest the taxi will travel is 35 miles. If X represents the number of miles traveled, and Y represents the total cost of the taxi ride, what is the most appropriate domain for the solutions?
Solution:
Given:
[tex]\begin{gathered} A\text{ taxi service charges \$3 for the first mile} \\ \text{ \$2.25 for every mile after that.} \\ \text{The farthest the taxi will travel is 35 miles.} \end{gathered}[/tex]Since x represents the number of miles traveled
y represents the total cost of the taxi ride
From the description, the number of miles the taxi will travel is between 0 and 35miles since 35 miles is the farthest it could go.
This means the domain which refers to the set of possible input values will be;
[tex]\begin{gathered} x>0\text{ because the service is charged once a certain distance is covered.} \\ \text{when no distance is covered, no charge is made.} \\ \text{Also,} \\ x\le35\text{ because the farthest is 35miles. This means the ta}\xi\text{ can not travel beyond 35miles.} \\ \\ \text{From the descriptions made, the domain will be:} \\ 0Therefore, the most appropriate domain for the solutions is;
[tex]0 The correct answer is OPTION B.Given the following five-number summary, find the IQR.
2.9, 5.7, 10.0, 13.2, 21.1.
The IQR of the given series 2.9, 5.7, 10.0, 13.2, 21.1 is 15.4
In the given question, a five number summary is given as follows
2.9, 5.7, 10.0, 13.2, 21.1
We need to find the IQR
So, first we'll find the median of the given series
The middle value in a sorted, ascending or descending list of numbers is known as the median, and it has the potential to describe a data collection more accurately than the average does.
So, the given series is already in ascending order. And the middle value is 10.0. So the median is 10.0
Now to find the IQR the given formula will be used,
IQR = Q3 - Q1
Where Q3 is the last term in lower series and Q1 is the last term in upper series
Lower series - 2.9, 5.7
Upper series - 3.2, 21.1
Q3 = 5.7 , Q1 = 21.1
IQR = Q3 - Q1 = 21.1 - 5.7 = 15.4 ( IQR is always positive)
Hence, the IQR of the given series 2.9, 5.7, 10.0, 13.2, 21.1 is 15.4
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The table shows the volume of water released by a dam over a certain period of time. Graph a line representing the data in the table, and find the slope and y-intercept of the line from the graph. Then enter the equation for the graph in slope-intercept form.
Okay, here we have this:
Considering the provided information. we are going to calculate the slope, and y-intercept of the line, so we obtain the following:
First we will calculate the slope using the following formula:
m=(y2-y1)/(x2-x1)
m=(80000-40000)/(10-5)
m=40000/5
m=8000
y-intercept:
y=mx+b
40000=(8000)5+b
40000=40000+b
b=0
Finally we obtain that the equation of the line is: y=8000x.
Let's graph the equation:
Which expression is equal to -2i(4 - i)?
Answer:
-8i + 2i^2
I am new but I hope this helps you
Answer:
-8i+2i²
this looks like an equation in factorization
pls help. i dont get it
Answer:
hey what don't u get? u didn't show the question
Look at the expression below.2h + y 4h^2_______ - _____9h^2-y^2 3h+yWhich of the following is the least common denominator for the expression?
Answer:
(3h+y)*(3h-y)
Step-by-step explanation:
We are given the following expression:
[tex]\frac{2h+y}{9h^2-y^2}-\frac{4h^2}{3h+y}[/tex]We want to find the LCD for:
9h²-y² and 3h + y.
3h+y is already in it's most simplified way.
9h²-y² , according to the notable product of (a²-b²) = (a-b)*(a+b), can be factored as:
(3h-y)*(3h+y).
The factors of each polynomial is:
3h + y and (3h-y)*(3h+y)
The LCD uses all unique factors(If a factor is present in more than one polynomial, it only appears once).
So the LCD is:
(3h+y)*(3h-y)
Which is option B.
given the function r(t)=t^2, solve for r(t)=4
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
r(t)=t^2
r(t)=4
t = ?
Step 02:
r(t)=4
t ² = 4
t = √4
t = 2
The answer is:
t = 2
Answer: t=2
Step-by-step explanation:
Because we know that for some value of t, r(t)= 4, and for ALL values of t, r(t)= t^2, then we know for some value of t, that t^2 = 4.
Based off of this information, we can take the square root of both sides, resulting in this equation.
t = [tex]\sqrt{4}[/tex]
This can be simplified.
t=2
A circular pool measures 12 feet across. One cubic yard of concrete is to be used to create a circular border of uniform width around the pool. If the border is to have a depth of 6 inches, how wide will the border be?
SOLUTION:
Step 1:
In this question, we are given the following:
A circular pool measures 12 feet across.
One cubic yard of concrete is to be used to create a circular border of uniform width around the pool.
If the border is to have a depth of 6 inches, how wide will the border be?
Step 2:
From the question, we can see that:
[tex]6\text{ inches = 0. 5 feet}[/tex][tex]1\text{ cubic yard = 3 ft x 3ft x 3ft = }27ft^3[/tex][tex]\begin{gathered} \text{Let the radius of the pool = ( 6+x ) feet} \\ \text{Let the width of the concrete that is used to } \\ \text{create the circular border = 6 feet} \end{gathered}[/tex][tex]\text{Let the depth of the border = 6 inches = }\frac{6}{12}=\text{ 0. 5 inches}[/tex]Step 3:
[tex]\begin{gathered} U\sin g\text{ } \\ \pi R^2h\text{ - }\pi r^2\text{ h = 27} \\ \pi(6+x)^2\text{ 0. 5 - }\pi(6)^2\text{ 0. 5 = 27} \\ \text{0. 5}\pi(x^2\text{ + 12x + 36 - 36 ) = 27} \\ 0.\text{ 5 }\pi(x^2\text{ + 12 x) = 27} \\ \text{Divide both sides by 0. 5 }\pi\text{ , we have that:} \end{gathered}[/tex][tex]x^2\text{ + 12 x - (}\frac{27}{0.\text{ 5}\pi})=\text{ 0}[/tex]Solving this, we have that:
CONCLUSION:
From the calculations above, we can see that the value of the x:
( which is the width of the border ) = 1. 293 feet
(correct to 3 decimal places)
which describes the solution of the inequality y>-15? a) solid vertical line through (0,-15) with shading to the left of the line. b) dashed vertical line through (0,-15) with shading to the left of line. c) solid horizontal line through (0,-15) with shaing below line. d) dashed horizontal line through (0,-15) with shaing above line.
The solution to the inequality y > - 15 is all values of y greater than -15. This means the number -15 itself is not included; therefore, the line is a dashed line that passes through (0, -15). Furthermore, the > sign implies that the shaded region is found above the dashed line. Hence, the solution to our inequality is a dashed horizontal line through (0, -15), with shading above the line.
A cat is stuck in the tree and the fire department needs a ladder to rescue the cat. The fire truck available has a 95-foot ladder, which starts 8 feet above ground. Unfortunately, the fire truck must park 75 feet away from the tree. If the cat is 60 feet up the tree, does the cat get rescued? If not, what ladder length is need to allow the cat to be rescued?
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Draw the given scenario
STEP 2: Describe how to answer the question
The question forms a right angle triangle. where the height of the cat on the tree is the opposite side of the triangle. The distance between the cat and the tree is the adjacent side of the triangle .
Recall the 95 foot ladder can only start 8 feet above the ground .The diagram is represented above:
The ladder height should be the hypotenuse of the triangle.
using Pythagoras's theorem,
[tex]hypotenuse^2=opposite^2+adjacent^2[/tex]STEP 3: Write the given sides
[tex]\begin{gathered} adjacent=75fto \\ opposite=52ft \\ hypotenuse=x\text{ ft} \end{gathered}[/tex]STEP 4: find x
[tex]\begin{gathered} x^2=75^2+52^2 \\ x^2=5625+2704 \\ x^2=8329 \\ x=\sqrt{8329}=91.26335519 \\ x\approx91.26ft \end{gathered}[/tex]The expected length of the ladder should be approximately 91.26ft. Since the ladder is 95 foot, therefore the cat will be rescued with the given ladder.
Quinton will flip a coin and roll a die.What is the probability that he will flip "tails" and roll a "2
Answer:
there is a 50 percent chance he will land tails, and about a 33 percent chance he will rol a 2
Step-by-step explanation:
The graphs depict IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler IQ test).
a.find the Z score. Write that answer to the 2nd decimal place.
b. solve for x
The required Z-score with a value of 120 would be 1.33.
What is Z -score?A Z-score is defined as the fractional representation of data point to the mean using standard deviations.
The given graph depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.
As per the given information, the solution would be as
ц = 100
σ = 15
X = 120 (consider the value)
⇒ z-score = (X - ц )/σ₁
Substitute the values,
⇒ z-score = (120 - 100)/15
⇒ z-score = (20)/15
⇒ z-score = 1.33
Thus, the required Z-score with a value of 120 would be 1.33.
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Use the information given to find the equation of the line using the point-slope formula (y-y_1=m(x-x_1)). Then convert your answer to slope-intercept form (y=mx+b).(0,3) with a slope of 4The point slope form is (y-Answer)=Answer(x-Answer)Converting it to slope intercept form gives us y=Answerx+Answer
we have
m=4
point (0,3)
y-y1=m(x-x1)
substitute given values
y-3=4(x-0) ----> equation in point slope formConvert to slope-intercept form
y=mx+b
y-3=4x
adds 3 both sides
y=4x+3 ----> equation in slope-intercept formava's family drove to disneyland for spring break. Her mom and dad shared the driving duties for a total of 24 hours. Her mom drove 75 miles per hour, and her dad drove 60 miles per hour. If they drove a total of 1,710 miles, how many hours did each person drive for?
Total driving time =24
Mom drove =75 mile per hours
Dad drove = 60 miles per hours
Total distance =1710
Let
[tex]\begin{gathered} \text{ mom driving time =}^{}t_1 \\ \text{dad driviving time=}^{}t_2 \\ \text{Mom driving distance =}x \\ \text{ So dad driving distance=}^{}1710-x \end{gathered}[/tex]Total time:
[tex]t_1+t_2=24[/tex]Formula:
[tex]\text{ Spe}ed=\frac{\text{ Distance}}{\text{ Time}}[/tex]For Ava's mom:
[tex]\begin{gathered} \text{Speed}=\frac{\text{ Distance}}{\text{ time}} \\ 75=\frac{x}{t_1} \\ x=75t_1^{} \end{gathered}[/tex]For Ava's dad:
[tex]\begin{gathered} \text{ Spe}ed=\frac{\text{ Distance}}{\text{ Time}} \\ 60=\frac{1710-x}{t_2} \\ 60t_2=1710-x \\ x=1710-60t_2 \end{gathered}[/tex]Put the value of "x" then:
[tex]\begin{gathered} x=75t_1 \\ x=1710-60t_2 \\ so\colon \\ 75t_1=1710-60t_2 \\ 75t_1+60t_2=1710 \\ 15(5t_1+4t_2)=15\times114 \\ 5t_1+4t_2=114 \end{gathered}[/tex]Solve the both eq then:
[tex]\begin{gathered} t_1+t_2=24 \\ 4t_1+4t_2=96 \\ 5t_1+4t_2=114 \\ \text{then:} \\ 5t_1-4t_1+4t_2-4t_2=114-96 \\ t_1=18 \\ \end{gathered}[/tex]So Ava's mom drive 18 hours
[tex]\begin{gathered} t_1+t_2=24 \\ 18+t_2=24 \\ t_2=24-18 \\ t_2=6 \end{gathered}[/tex]Ava's dad driving 6 houras
If the given is -3x+20=8 What should the subtraction property of equality be?
Given the equation
[tex]-3x+20=8[/tex]To apply the subtraction property of equality, we subtract 20 from both sides.
[tex]-3x+20-20=8-20[/tex]
Solve the inequality and write the solution using:
Inequality Notation:
The solution for the given inequality is x >7.
InequalityIt is an expression mathematical that represents a non-equal relationship between a number or another algebraic expression. Therefore, it is common the use following symbols: ≤ (less than or equal to), ≥ (greater than or equal to), < (less than), and > (greater than).
The solutions for inequalities can be given by: a graph in a number line or numbers.
For solving this exercise, it is necessary to find a number and a graph solution for the given inequality.
The given inequality is [tex]1-\frac{6}{7}x < -5[/tex] . Then,
Move the number 1 for the other side of inequality and simplify.[tex]-\frac{6}{7}x < -5 -1\\ \\ -\frac{6}{7}x < -6[/tex]
Multiply both sides by -1 (reverse the inequality )[tex]-\frac{6}{7}x < -6 *(-1)\\ \\ \frac{6}{7}x > 6[/tex]
Solve the inequality for x[tex]\frac{6}{7}x > 6\\ \\ 6x > 42\\ \\ x > \frac{42}{6} \\ \\ x > 7[/tex]
You should also show the results t > 7 in a number line. Thus, plot the number line. See the attached image.
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Can u help me with my math I’m confused and don’t know
We want to find the area of the rectangle.
The area of a rectangle is given by;
[tex]\text{Area}=\text{Length x Breadth}[/tex]The length is x + 7 and the breadth is given by x + 5.
Thus the area is;
[tex]\begin{gathered} A=(x+7)(x+5) \\ A=x^2+7x+5x+35 \\ A=x^2+12x+35 \end{gathered}[/tex]Therefore, the area is;
[tex]A=x^2+12x+35[/tex]2. A wooden cube with volume 64 is sliced in half horizontally. The two halves are then glued together to form a rectangular solid which is not a cube. What is the surface area of this new solid? A.128 B. 112 C. 96 D. 56
we have that
the volume of the cube is equal to
V=b^3
64=b^3
b^3=4^3
b=4 unit
see the attached figure
the surface area of the new figure is equal to
SA=2B+PH
where
B is the area of the base
P is the perimeter of the base
H is the height
we have
B=4*8=32 unit2
P=2(4+8)=24 unit
H=2 unit
so
SA=2(32)+24*2
SA=64+48
SA=112 unit2
the answer is option B9 - 6 - 19 c) y - 12 OC p = b) y 24 c) = 9
x=70, y= -50 and x=80
1) Let's solve each equation, plugging in the given value for x
y=5x -300
a) y=50
y=5x -300 Plug y=50
50=5x -300 Add 300 to both sides
50+300=5x
350 = 5x Divide both sides by 5
x=70
b) x = 50
y=5x -300 Plug x=50
y=5(50) -300 Distribute the factor
y= 250 -300
y= -50
c) y=100
y=5x -300 Plug y=100
100 = 5x -300 Add 300 to both sides
400 = 5x
x =80
Hence, the answer is
x=70, y= -50 and x=80
A dog walker charges a flat rate of $6 per walk plus an hourly rate of $30. How much does the dog walkercharge for a 45 minute walk? Write an equation in function notation for the situation, and then use it tosolve the problem. Determine if the given statement is True or False.
hello
from the question given, the dog walker charges a flat rate of $6 and an extra $30 per hour.
we can write out an equation in function notation
let the number of hours be represented by x
[tex]f(x)=6+30x[/tex]now we can proceed to solve the cost of the walk for 45 minutes
[tex]\begin{gathered} 1hr=60\min s \\ \text{xhr}=45\min s \\ x=\frac{45}{60} \\ x=\frac{3}{4} \\ \text{therefore 45mins = 3/4 hours} \end{gathered}[/tex]now we can input the value into the equation and know the cost for 45 minutes walk
[tex]\begin{gathered} f(x)=6+30x \\ x=\frac{3}{4} \\ f(x)=6+30(\frac{3}{4}) \\ f(x)=6+22.5 \\ f(x)=28.5 \end{gathered}[/tex]from the calculation above, the cost of 45 minutes walk will cost $28.5
one motorcycle travels 80 miles per hour and the second motor ctcle travels 60 miles per hour if the faster motorcycle travels 1 hour longer than the slower motorcycle and it also travels twice the distance of the slower motorcylce what distace does each of the motorcyle travel
The faster motorcycle travelled 240 miles and the slower motorcycle travelled 120 miles .
In the question ,
let the time travelled by the slower motorcycle be "t" .
given , the faster one travelled 1 hour longer ,
So , the time travelled by faster motorcycle = "t+1" hour .
the speed of slower motorcycle = 60 miles per hour .
the speed of faster motorcycle = 80 miles per hour .
So , the distance covered by slower motorcycle = speed * time
= 60*(t)
the distance covered by the faster motorcycle = 80*(t+1) .
given that faster motorcycle travels twice the distance of the slower motorcycle
So According to the question
80*(t+1) = 2*60*(t)
simplifying further , we get
80t + 80 = 120t
120t - 80t = 80
40t = 80
t = 2 hours
distance covered by slower motorcycle = 60(2) = 120 miles
distance covered by faster motorcycle = 80(2+1) = 80*3 = 240 miles .
Therefore , The faster motorcycle travelled 240 miles and the slower motorcycle travelled 120 miles .
The given question is incomplete , the complete question is
One motorcycle travels 80 miles per hour and the second motorcycle travels 60 miles per hour, if the faster motorcycle travels 1 hour longer than the slower motorcycle and it also travels twice the distance of the slower motorcycle . What distance does each of the motorcycle travel ?
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f(a)=92.39 and the average rate of change of f over the interval from x=a to x=a+266 is 0.16. What is the value of f(a+266)?f(a+266)=
Average rate is f(a+266)-f(a))/266
so f(a+266) equals (0.16 x 266) + f(a)
f (a+266)= (0.16 x 266) + 92.39
In triangle ABC, if AC = 17 cm, CB = 10 cm, AD = x cm, DB = y cm and AB = 21 cm, find the value of (x − y).
The value of (x-y) is 9 cm for the given triangle ABC.
According to the question,
We have the following information:
In triangle ABC, if AC = 17 cm, CB = 10 cm, AD = x cm, DB = y cm and AB = 21 cm.
So, we have:
x+y = 21 cm
y = (21-x) cm
Using Pythagoras theorem in right-angled triangle ADC and CDB:
[tex]AC^{2} = AD^{2} +CD^{2}[/tex] and [tex]BC^{2} = BD^{2}+CD^{2}[/tex]
Now, we have the equal values of [tex]CD^{2}[/tex]:
[tex]17^{2} -x^{2} = 10^{2} -y^{2}[/tex]
289 -[tex]x^{2}[/tex] = 100 - [tex](21-x)^{2}[/tex]
289 - [tex]x^{2}[/tex] = 100 - (441+[tex]x^{2}[/tex]-42x)
289-[tex]x^{2}[/tex] = 100 - 441-[tex]x^{2}[/tex] + 42x
289 = 100 -441+42x
42x-331 = 289
42x = 289+331
42x = 630
x = 630/42
x = 15 cm
y = 21-x
y = 21-15
y = 6 cm
Now, x-y = 15-6
x-y = 9 cm
Hence, the value of (x-y) is 9 cm.
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Each of the letters a through H has one of the 8 values listed. no 2 letters have the same value. The Simple arithmetic problems are clues for determining the value of each letter. Simply guess and check to find the values for letters a through H. You must use numbers listed below.
We have the following:
Let's start from the number C, which has two numbers that when adding it gives a number and subtracting two other numbers gives the same number C
C = 9, therefore:
[tex]\begin{gathered} F-D=9 \\ F=14 \\ D=5 \\ G+B=9 \\ G=3 \\ B=6 \\ 5+E=6\Rightarrow E=1 \\ 6+H=14\Rightarrow H=8 \\ A-9=8\Rightarrow A=17 \end{gathered}[/tex]Find the volume of each rectangular prism. Round to the tenths.
Answer:
To find the volume of the given cuboid.
Length of the cuboid = 6.8 yd
Breadth of the cuboid = 4.5 yd
Height of the cuboid = 3.4 yd
We get,
Volume of a cuboid is,
[tex]=l\times b\times h[/tex]where l,b and h are the length, breadth and height respectively.
Substitute the values we get,
[tex]=6.8\times4.5\times3.4[/tex][tex]=104.04\text{ yd}^3[/tex]Answer is: Volume of the cuboid is 104.04 cubic yards.
¿Por qué NO puede encontrar el punto medio de una línea?
Las líneas en un plano cartesiano son infinitas, no tienen un punto de inicio o final, por lo que no es posible determinar un punto medio para ellas.
