hello
the distance or length of the path is 8 miles.
Max is 375% of the way to the end. Let's find he distance of 375% on 8 miles
[tex]\begin{gathered} 375\text{ \% of 8} \\ \frac{375}{100}=\frac{x}{8} \\ \text{cross multiply both sides} \\ 100\times x=375\times8 \\ 100x=3000 \\ \frac{100x}{100}=\frac{3000}{100} \\ x=30 \end{gathered}[/tex]from the calculation above, Max is 30 miles away from the path
(2n^3+15n^2+11n-42)÷(n+6)
we have the following:
A carnival ride is in the shape of a wheel with a radius of 25 feet. The wheel has 20 cars attached to the center of the wheel. Use 3.14 for pi and round answers to the nearest hundredth, if applicable.a.) What is the measure of each central angle between any two cars? (4 points)b.) What is the arc length of each sector between any two cars? (4 points)c.) What is the area of each sector between any two cars?
The carnival ride is in shape of wheel with 25ft radius.
The wheel has 20 cars attached to the center of the wheel. Since the cars are evenly distributed, we can thus find the
the measure of the angle between each car by dividing 360 degrees by 20.
#A:
The measure of each central angle between any two cars is:
[tex]\frac{360}{20}=18^0[/tex]#B:
Hence, we can find the length of the arch between any two cars is given by the length of arc formula given below:
[tex]\begin{gathered} \frac{\theta}{360}\times2\pi r \\ \text{where,} \\ r=\text{radius} \\ \theta=\text{measure of each central angle betw}een\text{ two cars} \end{gathered}[/tex]Let us calculate this length below:
[tex]\begin{gathered} \theta=18^0 \\ \frac{18}{360}\times2\pi\times25 \\ =2.5\pi=7.85\text{ (to the nearest hundredth)} \end{gathered}[/tex]#C:
We are asked to find the area of each sector between two cars.
The area of a sector of a circle is:
[tex]\frac{\theta}{360}\times\pi\times r^2[/tex]Since we have all the parameters, let us calculate this area:
[tex]\begin{gathered} Area=\frac{18}{360}\times\pi\times25^2 \\ \\ Area=98.13\text{ (to nearest hundredth)} \end{gathered}[/tex]Therefore, the final answers are:
#A: angle = 18 degrees
#B length = 7.85 feet
#C Area = 98.13 squared feet
Question 2(Multiple Choice Worth 1 points)(07.02 MC)Factor completely x³ + 4x² + 8x + 32.O(x + 4)(x² + 8)O(x-4)(x²-8)O(x-4)(x² + 8)○ (x + 4)(x² − 8)
Given -
x³ + 4x² + 8x + 32
To Find -
Factor completely =?
Step-by-Step Explanation -
x³ + 4x² + 8x + 32 can be written as:
= (x³ + 4x²) + 8x + 32
= x²(x + 4) + 8(x + 4)
Now it can be written as:
(x² +8)(x + 4)
So, the complete factor of x³ + 4x² + 8x + 32 is (x + 4)(x² + 8)
Final Answer -
A. (x+4)(x² + 8)
A. Step 1 B. Step 2 C. Omar did not make a mistake
To find out if Omar made a mistake, we must solve the equation step by step.
Step 1
[tex]\begin{gathered} 3x=4.5 \\ \text{divide through by 3} \\ \frac{3x}{3}=\frac{4.5}{3} \end{gathered}[/tex]Step 2
Simplify the final part in step 1
[tex]\begin{gathered} \frac{3x}{3}=\frac{4.5}{3} \\ x=\frac{3}{2}=1.5 \end{gathered}[/tex]Since, we have gone through all the steps and gotten exactly the same steps and solution as Omar, we can conclude that Omar did not make a mistake.
The sum of 3 times a number and another number is 34. Five times the first number minus the other number is 38. What are the two numbers. The numbers are 3 and 11. The numbers are 9 and 7.
The sum of 3 times a number and another number is 34. Five times the first number minus the other number is 38. What are the two numbers. The numbers are 3 and 11. The numbers are 9 and 7.
Let
x -----> first number
y -----> another number
we have that
3x+y=34 -------> equation A
5x-y=38 -----> equation B
solve by elimination
Adds the equations
so
8x=72
x=72/8
x=9
substitute
3(9)+y=34
y=34-27
y=7
therefore
the numbers are 9 and 77. Find two consecutive even integers such that twice the smaller diminished by twenty is equal to thelarger.
Given two consecutive even integer numbers x and x + 2, we know that twice the smaller number diminished by twenty is equal to the larger:
[tex]2x-20=x+2[/tex]Solving for x:
[tex]\begin{gathered} 2x-x=20+2 \\ \\ \Rightarrow x=22 \end{gathered}[/tex]And the numbers are:
[tex]22\text{ and }24[/tex]hello, please help me solve to find the correct polynomials!
INFORMATION:
We have the next polynomials
And we must factor them to complete the next table
STEP BY STEP EXPLANATION:
1.
[tex]x^2-8x+15[/tex]To factor it, we must look for two number that multiplied be equal to 15 and added up be equal to -8.
These two numbers would be -5 and -3.
- -5 x -3 = 15
- -5 - 3 = -8
So, when we factor this polynomial, we obtain
[tex]\begin{gathered} x^2-8x+15=(x-5)(x-3) \\ \text{ So, }a=1,b=-5,c=1,d=-3 \end{gathered}[/tex]2.
[tex]2x^3-8x^2-24x[/tex]To factor it, we must first take the common factor 2x from the expression
[tex]2x(x^2-4x-12)[/tex]Now, we must factor the terms in the parenthesis. We must look for two number that multiplied be equal to -12 and added up be equal to -4. These two numbers would be -6 and 2.
- -6 x 2 = -12
- -6 + 2 = -4
So, when we factor this polynomial, we obtain
[tex]\begin{gathered} 2x(x+2)(x-6) \\ \text{ So, }a=1,b=2,c=1,d=-6 \end{gathered}[/tex]3.
[tex]6x^2+14x+4[/tex]To factor it, we must first take the common factor 2 from the expression
[tex]2(3x^2+7x+2)[/tex]Then, we divide the 7x term in the parenthesis in two terms
[tex]2(3x^2+6x+x+2)[/tex]Now, we can take the common factor x + 2 in the parenthesis
[tex]2(3x(x+2)+(x+2))[/tex]Finally, we can take the common factor x + 2 in the complete expression
[tex]\begin{gathered} 2(x+2)(3x+1) \\ \text{ Simplifying,} \\ =\left(3x+1\right)(2x+4) \\ \text{ So, }a=3,b=1,c=2,d=4 \end{gathered}[/tex]ANSWER:
A training field is formed by joining a rectangle and two semicircle. The rectangle is 87m long and 64m wide. What is the length of a training track running around the field? ( Use the value 3.14 pie, and do not round your answer. Be sure to include the correct unit in your answer.)
The legth of running around this track will be the length of both semi-circles plus the two bigger sidesof the rectangle.
The length of a semi -circle is half the length of a circle, and can be expressed as:
[tex]S=\frac{2\pi r}{2}=\pi r[/tex]Where r is the radius of the semi-circle. The diameter of the semi-circles is the same as the smaller sides of the rectangle and its radius is half the diameter, so:
[tex]r=\frac{d}{2}=\frac{64}{2}=32[/tex]So, the total length, as said above, is the sum of the length of both semi-circles plus two times the bigger side:
[tex]\begin{gathered} L=2S+2w \\ L=2\cdot\pi r+2\cdot87 \\ L=2\cdot3.14\cdot32+2\cdot87 \\ L=200.96+174 \\ L=374.96 \end{gathered}[/tex]Al the measures used were in meters and length is given in meters to the first power, so the unit of the result is also meters, or just "m".
Thus the answer is 374.96 m.
Geometry question - Given: AB and AC are the legs of isosceles triangle ABC, measure of angle 1 = 5x, measure of angle three = 2x + 12. Find measure of angle 2 (reference picture)
Since triangle, ABC is an isosceles triangle because AB = BC
Then the angles of its base are equal
Since the angles of its bases are <2 and <4, then
[tex]m\angle2=m\angle4[/tex]Since <3 and <4 are vertically opposite angles
Since the vertically opposite angles are equal in measures, then
[tex]m\angle3=m\angle4[/tex]Since measure of <3 = 2x + 12, them
[tex]m\angle4=m\angle2=2x+12[/tex]Since <1 and <2 are linear angles
Since the sum of the measures of the linear angles is 180 degrees, then
[tex]m\angle2+m\angle1=180[/tex]Since m<1 = 5x, then
[tex]\begin{gathered} m\angle1=5x \\ m\angle2=2x+12 \\ 2x+12+5x=180 \end{gathered}[/tex]Add the like terms on the left side
[tex]\begin{gathered} (2x+5x)+12=180 \\ 7x+12=180 \end{gathered}[/tex]Subtract 12 from both sides
[tex]\begin{gathered} 7x+12-12=180-12 \\ 7x=168 \end{gathered}[/tex]Divide both sides by 7
[tex]\begin{gathered} \frac{7x}{7}=\frac{168}{7} \\ x=24 \end{gathered}[/tex]Then substitute x by 24 in the measure of <2
[tex]\begin{gathered} m\angle2=2x+12 \\ m\angle2=2(24)+12 \\ m\angle2=48+12 \\ m\angle2=\mathring{60} \end{gathered}[/tex]The measure of angle 2 is 60 degrees
Factor the given trinomial. If the trinomial cannot be factored, indicate “not factorable” 6v^5-18v^4-168v^3
The polynomial is given below as
[tex]6v^5-18v^4-168v^3[/tex]Step 1: Factor out the highest common factor which is
[tex]6v^3[/tex][tex]\begin{gathered} 6v^5-18v^4-168v^3=6v^3(\frac{6v^5}{6v^3}-\frac{18v^4}{6v^3}-\frac{168v^3}{6v^3}) \\ 6v^5-18v^4-168v^3=6v^3(v^2-3v-28) \end{gathered}[/tex]Step 2: Factorise the quadratic expression
[tex]v^2-3v-28[/tex]To factorize the quadratic expression, we will have to look for two factors that will multiply each other to give a -28, and then the same two factors will add up together to give -3
By try and error, we will have the two factors to be
[tex]\begin{gathered} -7\times+4=-28 \\ -7+4=-3 \end{gathered}[/tex]By replacing the two factors in the equation above, we will have
[tex]\begin{gathered} v^2-3v-28=v^2-7v+4v-28 \\ \text{group the factors to have} \\ (v^2-7v)+(4v-28)=v(v-7)+4(v-7) \\ v^2-3v-28=(v-7)(v+4) \end{gathered}[/tex]Hence,
[tex]6v^5-18v^4-168v^3=6v^3(v-7)(v+4)[/tex]Therefore,
The final answer is 6v³(v - 7)(v + 4)
Need immediate help on 2 questions for my test tomorrow
The data that can be determined from the box plots are
a)
This is because the line in the middle of the box plot is the median of the box plot.
b)
The upper quartile of a box plot is the part of the box plot that is to the right of the line. In this case the median line is at the same location and the upper quartile ends at the same location.
and
The data that can not be determined is
c)
The reason this can not be determined is because the median is the average of the grades. This could mean some students scored in the higher levels and more scored below the median, which in turn drags it down.
d)
Would be following the same reason as C. It can be determined that there was a larger range lower grades in period 5 over period 3, but it can't be determined how many.
Find the area of a circle with a circumferenceof 261 feet.
It is given that Circumference of circle is 26П feet
The expression for the Circumference of circle is 2Пr.
So,
[tex]\begin{gathered} 2\Pi r=26\Pi \\ r=\frac{26\Pi}{2\Pi} \\ r=13 \end{gathered}[/tex]Radius of the circle is 13 feet
The expression for the area of circle is ПRadius²
[tex]\begin{gathered} \text{Area of circle =}\Pi\times r^2^{} \\ \text{Area of circle=3.14}\times13\times13 \\ \text{Area of circle = 530}.93\text{ f}eet^2 \end{gathered}[/tex]Answer: 530.9
A boat sails directly away from a skyscraper located on the edge of a large lake. The skyscraper is 120 meters tall. A photographer on the boat is taking pictures of the skyscraper with a camera that has a 28° viewing lens.
Let's begin by identifying key information given to us:
[tex]\begin{gathered} Height(h)=120m \\ \theta=28^{\circ} \\ d=\text{?} \end{gathered}[/tex]We will use the Trigonometric ratio (SOHCAHTOA) to solve for d. In this case, we will use ''TOA''
[tex]\begin{gathered} TOA\Rightarrow tan\theta=\frac{opposite}{adjacent} \\ tan\theta=\frac{opposite}{adjacent} \\ opposite\Rightarrow height=120m \\ adjacent\Rightarrow d \\ \theta=28^{\circ} \\ tan28^{\circ}=\frac{120}{d} \\ d\cdot tan28^{\circ}=120 \\ d=\frac{120}{tan28^{\circ}}=225.687\approx226 \\ d=226m \end{gathered}[/tex]Amy bought a car in 2009 valued at $32,500. The car is expected to depreciate at a rateof 11.1% annually. In how many years will Amy's vehicle be worth 50% of its originalvalue? Round your answer to the nearest tenth of a year,
ANSWER :
5.9 years
EXPLANATION :
Exponential function can be expressed as :
[tex]y=A(1\pm r)^t[/tex]where A = initial amount
r = (+) growth or (-) decay rate
t = time
y = amount after t years
From the problem, the initial value of the car is A = $32,500
It depreciates at a rate of 11.1% annually, so r = -11.1% or -0.111
The value of the car will be 50% of its original value, so y = 0.50(32,500) = $16,250
Using the formula above :
[tex]\begin{gathered} 16250=32500(1-0.111)^t \\ \frac{16250}{32500}=(0.889)^t \\ \\ 0.5=(0.889)^t \\ \text{ Take the ln of both sides :} \\ \ln(0.5)=\ln(0.889)^t \\ \ln(0.5)=t\ln(0.889) \\ \\ t=\frac{\ln0.5}{\ln0.889}=5.89\sim5.9yrs \end{gathered}[/tex]1.Orange paint uses 3 parts yellow to 2 parts red.The equation y=3/5t can be used to find the cups of yellow paint when given the total cups of paint.Use the equation to complete the table.t. 0 5 10 15 20 25 y _ _ _ _ _ _2.plot the point in the column in the table in problem 1.Then draw a line to represent the equation.3.The equation r=2/5t can be used to find the cups of red paint when given the total cups of paint.Draw a line represent the equation.
we have the equation
y=(3/5)t
so
Find the values of y for different valyes of t
For t=0
y=(3/5)(0)
y=0
For t=5
y=(3/5)(5)
y=3
For t=10
y=(3/5)(10)
y=6
For t=15
y=(3/5)(15)
y=9
For t=20
y=(3/5)(20)
y=12
For t=25
y=(3/5)(25)
y=15
A 76.00 pound flask of mercury costs $150.50. The density of mercury is 13.534 g/cm3.It takes 4.800 in^3 of mercury to make one manometer. Find the price of the mercury used to make 21 manometers by first calculating the cost of mercury for one manometer.What is the price of mercury used to make one manometer?
Price of one pound of mercury is derived as follows;
[tex]\begin{gathered} Price\text{ of 1lb of merc}=\frac{Cost\text{ of flask}}{Pounds\text{ of merc in the flask}} \\ \text{Price of 1 lb}=\frac{150.50}{76} \\ \text{Price of 1 lb}=1.98 \end{gathered}[/tex]This means 1 pound of mercury costs $1.98
1 pound = 453.6 grams
Therefore;
[tex]\begin{gathered} 1lb=453.6gms \\ 76lb=34,473.6gms \end{gathered}[/tex]The price of 1 gram of mercury would be;
[tex]\begin{gathered} Price\text{ of 1 gram}=\frac{Price\text{ per pound}}{\text{grams in 1 lb}} \\ \text{Price of 1 gram}=\frac{1.98}{453.6} \\ \text{Price of 1 gram}=0.004365 \end{gathered}[/tex]This means 1 gram of mercury costs $0.004365
Note that you have 13.534 grams per cubic centimeter of mercury. Therefore, the price of 1 cubic centimeter of mercury shall be calculated as follows;
[tex]\begin{gathered} \text{Price of 1 cubic cm}=grams\text{ per cubic cm x price of 1 gram} \\ \text{price of 1 cubic cm}=13.534\times0.004365 \\ \text{Price of 1 cubic cm}=0.059 \end{gathered}[/tex]This means 1 cubic centimeter of mercury would cost $0.059
Note also that, 1 cubic inch = 16.387 cubic centimeters. Hence,
[tex]\begin{gathered} Price\text{ of 1 cubic inch}=16.387\text{ cubic cm x }price\text{ of 1 cubic cm} \\ \text{Price of 1 cubic inch}=16.387\times0.059 \\ \text{Price of 1 cubic inch}=0.9668 \end{gathered}[/tex]This means 1 cubic inch costs $0.9668
It takes 4.800 cubic inches to make 1 manometer.
Therefore, the cost of 4.800 cubic inches would be;
[tex]\begin{gathered} Price\text{ of 4.800 cubic inches}=Price\text{ of 1 cubic inch x 4.800 cubic inches} \\ Price\text{ of 4.800 cubic inches}=0.9668\times4.800 \\ \text{Price of 4.800 cubic inches}=4.64 \end{gathered}[/tex]If it costs 4.800 cubic inches to make 1 manometer, then the cost of 1 manometer would be $4.64
Therefore, to make 21 manometers, we would have;
[tex]\begin{gathered} 1\text{ manometer}=4.64 \\ 21\text{ manometers}=21\times4.64 \\ 21\text{ manometers}=97.44 \end{gathered}[/tex]ANSWER:
The price of mercury required to make 21 manometers would be $97.44
what do 13% and 0.125 and 1/5 and 10 % have in common
Comparing 13%, 0.125 , 1/ 5 and 10%
1. 13 % = 0.13
2. 0.125 = 0.13 ( 2 decimal places)
3. 1/5 = 0.2
4. 10 % = 0.1
Conclusion : 13% and 0.125 have things in common
rewrite csc(theta) / sec(theta) as a single trig function with no fractions
The given expression is
[tex]\frac{\csc \theta}{\sec \theta}[/tex][tex]\text{ We know that }csc\theta=\frac{1}{\sin x}\text{ and }\sec \theta=\frac{1}{cos\theta}\text{.}[/tex]Using the reciprocal, we get
[tex]\frac{\csc\theta}{\sec\theta}=\frac{\frac{1}{\sin\theta}}{\frac{1}{\cos \theta}}[/tex][tex]\text{ Use }\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a}{b}\times\frac{d}{c}[/tex][tex]\frac{\csc\theta}{\sec\theta}=\frac{1}{\sin\theta}\times\frac{\cos \theta}{1}[/tex][tex]\text{ Use }\frac{\cos\theta}{\sin\theta}=\cot \theta.[/tex][tex]\frac{\csc\theta}{\sec\theta}=\cot \theta[/tex]Hence the answer is
[tex]\cot \theta[/tex]Use the ordered pairs (3,56) and (7,85) to find the equation of a line that approximates the data. Express your answer in slope-intercept form. If necessary round the slope to the nearest hundredth and the y intercept to the nearest whole number
Equation of a line in slope-intercept form:
[tex]\begin{gathered} y=mx+b \\ \\ m\colon\text{slope} \\ b\colon y-\text{intercept} \end{gathered}[/tex]1. Find the slope: Use two ordered pairs (x,y) in the next formula:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ \text{Ordered pairs (3,56) and (7,85)} \\ m=\frac{85-56}{7-3}=\frac{29}{4}=7.25 \end{gathered}[/tex]Slope: m=7.25
2. Find the y-interept: Use one ordered pair and the slope to find b:
[tex]\begin{gathered} \text{ordered pair: (3,56)} \\ x=3 \\ y=56 \\ \\ \text{Slope: m=7.25}_{} \\ \\ y=mx+b \\ 56=7.25(3)+b \\ 56=21.75+b \\ 56-21.75=b \\ \\ b=34.25 \\ \\ b\approx34 \end{gathered}[/tex]y-intercept: b= 34
Then, the equation of the line is:[tex]y=7.25x+34[/tex]Leslie has 3 pounds of peanuts, she uses 1 7/8 pounds to make trail mix. How many pounds does she have left?
What Leslie has is 3 pounds of Peanuts and she has used a fraction of it. That fraction is 1 7/8. To find out how many pounds more she has left, its a matter of subtracting 1 7/8 from 3 whole.
Let the leftover be called x, and you now have;
x = 3 - 1 7/8
Converting the other number to an improper fraction you now have
x = 3 - 15/8
x = 3/1 - 15/8
By using the LCM of both denominators which is 8, the expression now becomes,
x = 24/8 - 15/8
x = 9/8
x = 1 1/8
Les
what is 80% of 685?
548
1) To find what is 80% of 685 we need to rewrite that percentage as a decimal number
[tex]80\%=0.8[/tex]2) So, to find what is 80% we need to multiply 0.8 by 685
[tex]0.8\times685=548[/tex]Thus, 548 is 80% of 685
Given ST is tangent to circle Q, find the value of r
Given the figure of the circle Q
As shown, ST is tangent to circle Q
So, ST is perpendicular to the radius QS
So, the triangle QST is a right-angle triangle
We can apply the Pythagorean theorem where the legs are QS and ST
And the hypotenuse is QT
The side lengths of the triangle are as follows:
QS = r
ST = 48
QT = r + 36
So, we can write the following equation:
[tex]\begin{gathered} QT^2=QS^2+ST^2 \\ (r+36)^2=r^2+48^2 \end{gathered}[/tex]Expand then simplify the last expression:
[tex]\begin{gathered} r^2+2*36r+36^2=r^2+48^2 \\ r^2+72r+1296=r^2+2304 \end{gathered}[/tex]Combine the like terms then solve for (r):
[tex]\begin{gathered} r^2+72r-r^2=2304-1296 \\ 72r=1008 \\ \\ r=\frac{1008}{72}=14 \end{gathered}[/tex]So, the answer will be r = 14
Solve. 15 = 4n- 5solve for nn=
15 = 4n -5
Add 5 to both sides of the equation
15 +5 = 4n -5 + 5
20 = 4n
Divide both sides by 4:
20/4 = 4n /4
5 = n
n= 5
A triangle on a coordinate plane is translated according to the rule T-3,5(X,Y) what is another way to write this ?
Given the translation rule as :
[tex]T_{-3,5}(x,y)[/tex]Solution
Another way of writing this is:
[tex](x,\text{ y) }\rightarrow\text{ (}x\text{ - 3, y + 5)}[/tex]This means that the original coordinates (x,y) would be translated 3 units to the left and 5 units upwards to give the new coordinates.
Answer: Option A
Mr. Smith took a job that the employment agency. The job pays $76k per year. The employment agency is charging a fee of 19% of his first 4 weeks' pay. How much money does Mr. Smith give to the agency.
Answer:
Mr. Smith gave $1110.7 to the agency
Explanation:
Given that the job Mr. Smith took pays $76k per year.
In his first 4 weeks, taking the number of weeks per year to be 52, he is paid:
4 × ($76000)/52
= 4 × $1461.5 (Approximately)
= $5846
He is charged 19% of this earnings:
19% of $5846 is:
0.19 × $5846
= $1110.7
What he has in the end is:
$17000 - $1110.7
= $15889.3
Find the area of the sector of a circle with diameter 30 feet and an angle of 3Pi/5 radians. Round your answer to four decimal places.
half the diameter is the radius, so
[tex]r=15[/tex]now we can calculate the total area of the circle , and then will calculate the area for the angle
[tex]\begin{gathered} A=\pi\times r^2 \\ A=\pi\times15^2 \\ A=225\pi \end{gathered}[/tex]the area of the circle is 225pi, this is the corresponding area for the complete angle of the circle, therefore it is equivalent to 2pi
now we create a relation to find the area corresponding to the indicated angle
if 225pi is equal to 2pi how much is 3pi / 5
[tex]\begin{gathered} 225\pi\longrightarrow2\pi \\ x\longrightarrow\frac{3}{5}\pi \end{gathered}[/tex]where x is the area covered by the angle
we solve ussing cross multiplication, x is equal to: multiply the values that are found diagonally and make them equal
[tex]\begin{gathered} x\times2\pi=\frac{3}{5}\pi\times225\pi \\ \end{gathered}[/tex]and solve for x
[tex]\begin{gathered} x=\frac{\frac{3}{5}\pi\times225\pi}{2\pi} \\ \\ x=\frac{135\pi^2}{2\pi} \\ \\ x=67.5\pi\approx212.0575 \end{gathered}[/tex]The rounded area is 212.0575 square feet
LEO AND OLIVER HAVE TLO CLEAN THIER BEDROOMS. OLIVER CLEANS HIS ROOM IN 3/4 OF AN HOUR.LEO TAKES TWICE AS LONG AS OLIVER. HOW DID IT TAKE LEO TO CLEAN HIS ROOM?
It took 1.5 hour for Leo to clean the room .
In the question ,
it is given that
Leo and Oliver clean their their room
time taken by Oliver to clean the room is = 3/4 of an hour = 0.75 hours .
and also given that Leo takes twice as long as Oliver
which means
time taken by Leo to clean the room = 2*(time taken by Oliver to clean the room )
On substituting the values
we get ,
time taken by Leo to clean the room = 2*(0.75 hours)
= 1.5 hours
Therefore , Leo takes 1.5 hours to clean the room .
Learn more about Equations here
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what is the slope of a line perpendicular to y=-3/4x-1
As given by the question
There are given that the equation
[tex]y=-\frac{3}{4}x-1[/tex]Now,
For find the slope of line perpendicular to given equation
The formula is:
[tex]m_{perpendicular}=-\frac{1}{m}[/tex]Here,
From the equation, the value of m is,
[tex]m=-\frac{3}{4}[/tex]Then,
Put the value of m into the above formula
So,
[tex]\begin{gathered} m_{perpendicular}=-\frac{1}{m} \\ m_{perpendicular}=-\frac{1}{-\frac{3}{4}} \\ m_{perpendicular}=\frac{4}{3} \end{gathered}[/tex]Hence, the correct option is C
20.Dilate Point B by a scale factor of 1/2Va) (1.5,-4)c) (-1,-1.5)b) (-1.5,1)d) (-2,-2)
the coordinate of point B is (-3,2)
In order to dilate the point with a scale factor of 1/2 we need to multiplicate the scale factor by the coordinate-x and the coordinate-y
coordinate x
[tex]-3\cdot\frac{1}{2}=-1.5[/tex]coordinate y
[tex]2\cdot\frac{1}{2}=1[/tex]the coordinate dilate is
B'(-1.5,1)
the correct answer is b
I need help with this. Also, i’m aware you can’t see all the graphs listed so just let me know what coordinates would be appropriate and i’ll choose whichever graph has those coordinates.
Answer: Provided the sunglasses inventory which has the number of sunglasses and days in two columns, we have to find the graph which represents this table.
The table can be modeled by a linear equation:
[tex]\begin{gathered} y(x)=mx+b\Rightarrow(1)\Rightarrow\text{ y glasses as function of days x} \\ \\ \end{gathered}[/tex]Finding the slope and y intercept of this equation (1) leads to the following:
[tex]\begin{gathered} m=\frac{\Delta y}{\Delta x}=\frac{(42-58)}{(10-2)}=\frac{-16}{8}=--2 \\ \\ \\ \\ y(x)=-2x+b \\ \\ 58=-2(2)+b\Rightarrow b=58+4=62 \\ \\ \\ \therefore\Rightarrow \\ \\ y(x)=-2x+62\Rightarrow(2) \end{gathered}[/tex]The answer, therefore, is the plot of equation (2) which is as follows: