The perimeter of a rectangle is 2(l+b).
The length and breadth of a rectangle are 31 ft and 19 ft respectively.
How to find the length and breadth of a rectangle?Let the other side of a rectangle = b
And the one side of a rectangle = l = 2b - 7 ft
The perimeter of a rectangle = 2(l+b) = 100 ft.
2(2b - 7+ b) = 100
2(3b - 7) = 100
3b - 7 = 50
3b = 57
b = 57/3ft
b = 19ft
l = 2b - 7
l = 2*19 - 7
l = 38 - 7
l = 31
l = 31ft
Therefore, length = 31 ft. and breadth = 19ft.
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Can you help me find the cube root of .216
Given
0.216
Find
Cube root of the given number
Explanation
Cube root is the value which when multiplying by itself thrice or three times produces the original number
0.216 can be written as the product of
[tex]\begin{gathered} 0.216=\frac{216}{1000} \\ \end{gathered}[/tex]prime factorization of 216 and 1000
prime factorization of 216 =
[tex]\begin{gathered} 2\times2\times2\times3\times3\times3 \\ \end{gathered}[/tex]1000 -
[tex]\begin{gathered} 10\times10\times10 \\ 10 \end{gathered}[/tex]we have to find the cube root so , we make pair of three
so
[tex]\begin{gathered} (2\times2\times2)\times(3\times3\times3) \\ 2\times3 \\ 6 \end{gathered}[/tex]hence
[tex]\begin{gathered} \frac{6}{10} \\ 0.6 \end{gathered}[/tex]so , the cube root of 0.216 is 0.6
Final Answer
Therefore , The cube root of 0.216 is 0.6
In standard notation, 208.06 is written as:
Answer:
[tex]2.0806 * 10^{2}[/tex]
Step-by-step explanation:
Standard notation, also known as scientific notation, is when the whole number can only be [tex]1\leq 0 < 10[/tex]. The rest of the number is behind the decimal point.
which of the following values is the solution to the equation -16 + x equals 30
If we have the equation:
[tex]-16+x=30[/tex]We can solve it as follows:
1. Add 16 to both sides of the equation (addition property of equality):
[tex]-16+16+x=30+16[/tex]Then, we have:
[tex]x=30+16\Rightarrow x=46[/tex]Therefore, the value for x is equal to 46 (x = 46). We can check this as follows:
[tex]-16+46=30\Rightarrow30=30[/tex]We substituted the value, x = 46, in the original equation. This is always TRUE. Therefore, the value for x = 46.
1/8 x 240 please???? Hurry
Answer:
30
Step-by-step explanation:
Question 5 of 6Which exponential expression is equivalent to the one below?(22• (-7))40A. 40 • (22• (-7))O B. (22) • (-7)40C. (22)40 + (-7) 40D. (22)40 . (-7)40+SUBMIT
Okay, here we have this:
Considering the provided expression, we are going to analize which exponential expression is equivalent, so we obtain the following:
As the property of the exponent of a multiplication says that it is equal to the product of each number raised to that power. We have this:
[tex]\begin{gathered} \mleft(22\cdot\mleft(-7\mright)\mright)^{40} \\ =(22)^{40}\cdot(-7)^{40} \end{gathered}[/tex]Finally we obtain that the correct answer is the option D.
Which of these is a point-slope equation of the line that is perpendicular toy-25 = 2(x-10) and passes through (-3,7)?-O A. y+ 7 = 2(x-3)O B. y- 7 = -2(x+3)O C. y-7=-(x+3)O D.y+7=-1(x-3)-
We have to find the equation of the line, in point-slope form, that is perpendicular to y - 25 = 2(x - 10) and passes through (-3,7).
The line y - 25 = 2(x - 10) has a slope m = 2.
Perpendicular lines have slopes that are negative reciprocals, so our line will have a slope that is:
[tex]m=-\frac{1}{m_p}=-\frac{1}{2}[/tex]Then, we have the slope m = -1/2 and the point (-3,7), so we can write the point-slope form of the equation as:
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ y-7=-\frac{1}{2}(x-(-3)) \\ y-7=-\frac{1}{2}(x+3) \end{gathered}[/tex]Answer: y - 7 = -1/2 * (x + 3) [Option C]
255 is 88% of what? Round to the nearest tenth.
Answer:
289.8.
Explanation:
Let the number = x
Then, it implies that:
[tex]88\%\text{ of }x=255[/tex]Next, solve for x:
[tex]\begin{gathered} \frac{88}{100}\times x=255 \\ 88x=25500 \\ x=\frac{25500}{88} \\ x=289.8 \end{gathered}[/tex]The number is 289.8 to the nearest tenth.
Ten light bulbs were in a chandelier. Three-fifths of the bulbs were shining. What fraction of the light bulbs were not shining?
2/5 of bulbs were not shining. It is equal to 4 bulbs.
Step-by-step explanation:
10/10 bulbs equals all 10 bulbs. 3/5 were shining, that is equal to 6/10 of all ten bulbs. (or 60%). 60% of ten is 6 bulbs shining.The number of bulbs that werent shining is 10 - 6=4.
3. John rode is bike 20 kilometers on Monday. How many feet did John ride?
John rode his bike 65616.8 feet on Monday which is determined by converting 20 kilometers into feet.
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.
John rode his bike 20 kilometers on Monday which is given in the question.
To determine the number of feet John rides.
We have to convert 20 kilometers into feets
We know that
one kilometer = 3280.84 feet
Here 20 kilometers into feet will be:
⇒ 20 × 3280.84
Apply the multiplication operation, and we get
⇒ 65616.8 feet
Therefore, John rode his bike 65616.8 feet on Monday
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If the GCF of the nurmerator and the denominator is 1, then the fraction is in __
Recall that a fraction is of the form
[tex]\frac{a}{b}[/tex]where a is the numerator and b is the denominator. The GCF of two numbers is the biggest number that is less than both numbers and that it divides them without any remainder. When the GCF of the numerator and the denominator is 1. This means that we cannot find a common factor for both numbers, so we cannot cancel any more factors. This leads to the fact that the fraction is irreducible or that it is in its simplest form.
A line passes through the point (6, -6) and has a slope of 3/2.
Write an equation in point-slope form for this line.
Answer:
y+6=(3/2)(x-6)
Step-by-step explanation:
Point slope form is: y-y1=m(x-x1)
We know:
x1= 6
y1= -6
m=3/2
Fitness Works charges a $20 monthly fee, plus $5 for each class you take. Gym-tastic charges$100 monthly fee, and offers FREE unlimited classes. How many classes do you have to take forthe cost to be the exact same at both gyms?
Let us assume that the number of classes is x and the total fee is y
In the Fitness works, there is a monthly fee of $20 and $5 per class, then
The total fee y = 20 + 5(x), then
y = 20 + 5x ------ (1)
In the Gym-tastic, there is a monthly fee of $100 for unlimited classes, then
y = 100 ------- (2)
Equate (1) and (2)
20 + 5x = 100
Subtract 20 from both sides
20 - 20 + 5x = 100 - 20
5x = 80
Divide both sides by 5 to find x
x = 16
The number of the classes is 16
I need help with this I have only questions1. Where is y when x is 02. find f(-4)3. what is x when y is 4?4. What is X when f(X)=0? There are two answers put the smaller number in the first answer blank ____ and ____
1) y = 1 2) y =3 3) x = -3 4) y= -7 and y = 1
We are to answer the questions stated using the graph:
1) From the graph, when x = 0:
To understand this, check the point on the line that only lies on y
y = 1
2) f(-4) is the same as what is the value of y when x = -4
This is because f(x) = y
From the graph, when x = -4
y = 3
3) From the graph, when y =4
Trace the value of y=4 on the line to get corresponding x value:
x= -3
4) When f(x) = 0
This means what is the value of x when y = 0. This is because f(x) = y.
From the graph, we have two values of x when y = 0
y = -7
y = 1
To fill the blank spaces starting with the smaller number:
-7 and 1
Stacey's text messaging plan costs $7 for the first 550 messages and 30¢ for each additional text message. If she owes$39.40 for text messaging in the month of May, how many text messages did she send that month?
658 text messages
Explanation:
. Since you already know that for 7$ she gets 550 text messages, we can remove the 7$ from the 39.40$ she spent for the month, which leaves 39.40 - 7 = 32.40$
. Now since we know that for each extra 30 cents she gets to send one addition text,
=> we need to figure out first how many cents there is in the amount of money left she had to pay 32.40 * 100 = 3240 cents { since 1 $ = 100 cents }
=> then we need to figure out how many text does 3,240 cents represent, since 1 text is equivalent to 30 cent it means that in 3,240 / 30 = 108 texts messages is the amount of text she got to send with 32.40$
So in total she sent 550 + 108 = 658 texts messages for 39.40$
5. The function is continuous on the interval [10, 20] with some of its values given in the table above. Estimate the average value of the function with a Right Hand Sum Approximation, using the intervals between those given points. (4 points)x1012151920f(x)-2-5-9-12-16A -9.250B -10.100C-7.550D-6.700
Given the following question:
Kathy and Cheryl are walking in a fundraiser. Kathy completes the course in 3.6 hours and Cheryl completes the course in 6 hours. Kathy walks two miles per hour faster than Cheryl. Find Kathy's speed and Cheryl's speed in miles per hour.
Answer:
Explanation:
Here is what we know;
Both Kathy and Cheryl cover the same distance ( one course).
Kathy completes the course in 3.6 hours.
Kathy's speed is 2 miles/hour faster than Cheryl's
Cheryl completes the course in 6 hours
Cheryl's speed is yet unkown.
Now, the speed v is defined as
[tex]v=\frac{D}{t}[/tex]where D is the distance covered and t is the time taken.
Now, let us say D = distance of one course. Then in Kathy's case, we have
[tex]v_{\text{kathy}}=\frac{D}{3.6hr}[/tex]since Kathy's speed is 2 miles per hour faster than Cheryl's, we have
[tex]v_{\text{kathy}}=\frac{D}{3.6}=2+v_{\text{cheryl}}[/tex]For Cheryl, we know that
[tex]v_{\text{cheryl}}=\frac{D}{6hr}[/tex]or simply
[tex]v_{\text{cheryl}}=\frac{D}{6}[/tex]Putting this into the equation for Kathy's speed gives
[tex]v_{\text{kathy}}=\frac{D}{3.6}=2+v_{\text{cheryl}}\Rightarrow v_{\text{kathy}}=\frac{D}{3.6}=2+\frac{D}{6}[/tex][tex]\Rightarrow\frac{D}{3.6}=2+\frac{D}{6}[/tex]We have to solve for D, the distance of a course.
Subtracting D/6 from both sides gives
[tex]\frac{D}{3.6}-\frac{D}{6}=2[/tex][tex](\frac{1}{3.6}-\frac{1}{6})D=2[/tex][tex]\frac{1}{9}D=2[/tex][tex]D=18\text{miles}[/tex]Hence, the distance of a course is 18 miles.
With the value of D in hand, we can now find the velocity of Kathy and Cheryl.
[tex]v_{\text{cheryl}}=\frac{D}{6hr}=\frac{18\text{miles}}{6hr}[/tex][tex]\Rightarrow\boxed{v_{\text{cheryl}}=3\text{ miles/hr}}[/tex]Hence, Cheryl's speed is 3 miles/hr.
Next, we find Kathy's speed.
[tex]v_{\text{kathy}}=\frac{D}{3.6hr}=\frac{18\text{miles}}{3.6hr}[/tex][tex]\boxed{v_{\text{kathy}}=5\text{miles}/hr\text{.}}[/tex]Hence, Kathy's speed is 5 miles/hr.
Therefore, to summerise,
Kathy's speed = 5 miles/hr
Cheryl's speed = 3 miles/hr
let E b the event where the sun of two rolled dice is greater than or equal to 3. lost the outcomes in E^c
We have the event E defined as:
E: The sum of two rolled dice is greater than or equal to 3
The event E^c is the negation of the event E. Then:
E^c: The sum of two rolled dice is smaller than 3
For two dice, the minimum sum is 2, so this is equal to the event "the sum of two rolled dice is 2". There is only one outcome:
Dice 1: 1
Dice 2: 1
Sum: 2
Then, the only possible outcome for E^c is {1, 1}
The radius of a cylinder is 8cm. it's height is three times it's radius. What is the surface area of the cylinder? No pictures available
Recall that the surface area of the cylinder is
[tex]\begin{gathered} SA=2\pi rh+2\pi r^2 \\ \text{where} \\ r\text{ is the radius} \\ h\text{ is the height} \end{gathered}[/tex]Given the following
radius of 8 cm, and height of 24 cm (3 times the radius), then the surface area of the cylinder is
[tex]\begin{gathered} SA=2\pi rh+2\pi r^2 \\ SA=2\pi(8\text{ cm})(24\text{ cm})+2\pi(8\text{ cm})^2 \\ SA=384\pi\text{ cm}^2+128\pi\text{ cm}^2 \\ SA=512\pi\text{ cm}^2 \\ \; \\ \text{Therefore, the surface area of the cylinder is }512\pi\text{ cm}^2 \end{gathered}[/tex]P(x)=(x+5)(x-5) and q(x)=(x+3)(x-3) where do the graphs of the two intersects
For the equation P(x)=(x+5)(x-5) and q(x)=(x+3)(x-3) the graph of the two equation never intersect each other.
What is a conic section?It is defined as the curve which is the intersection of cone and plane. There are three major conic sections; parabola, hyperbola, and ellipse (a circle is a special type of ellipse).
The given equations are,
P(x)=(x+5)(x-5)
q(x)=(x+3)(x-3)
Parabola is defined as the graph of a quadratic function that has something bowl-shaped.
(x - h)² = 4a(y - k)
(h, k) is the vertex of the parabola:
a = √[(c-h)² + (d-k²]
(c, d) is the focus of the parabola:
The given equation represents a parabola as the equation is graphed we see that the graph of the two never intersects each other.
Thus,for the equation P(x)=(x+5)(x-5) and q(x)=(x+3)(x-3) the graph of the two equation never intersect each other.
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30. Figure A has an area of 18 sq. ft. Figure B has anarea of 98 sq. ft. and one side length is 14 ft. What isthe corresponding side length of Figure A?
Remember that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
In this problem
Figure A and Figure B are similar
so
step 1
Find out the scale factor
scale factor^2=18/98
scale factor=√(18/98)
step 2
To find out the corresponding side length of Figure A, multiply the side length of figure B by the scale factor
so
14*√(18/98)=6
the answer is 6 ftCreate a table to show the relationship of values of X and values of y
We have to complete a table with some points (x,y) from the line that is represented in the graph.
To do that we choose a value of x and wee which value of y corresponds to that value of x in the line.
For example, we can do it for x = 1 as:
Then, we have one point for the table: when x = 1, y = -9.
We can repeat this process for some points of x:
x | y
-------------
-4 | 1
-3 | -1
-2 | -3
-1 | -5
0 | -7
1 | -9
2 | -11
We can see that for each unit increase in x, the value of y decreases by 2. This indicates that the slope is m = -2.
Also, for x = 0, y = -7. Then b = -7 is the y-intercept.
In the unit circle, if the arc length is 1/20 of the circumference, find the area of the sector.
Given:
The length of the arc is (1/12) x circumference of unit circle.
The objective is to find the area of the sector.
Since it is given as a unit cirle, the radius of the circle will be 1 unit.
The circumference of the circle will be,
[tex]\begin{gathered} C=2\cdot\pi\cdot r \\ =2\pi\text{ units.} \end{gathered}[/tex]Then, the length of the arc will be,
[tex]\begin{gathered} l=\frac{1}{12}\times2\pi \\ =\frac{\pi}{6}\text{ units} \end{gathered}[/tex]Now, the formula to find the area of the sector is,
[tex]\begin{gathered} A=\frac{1}{2}r^2\cdot\theta \\ =\frac{1}{2}r^2\cdot\frac{l}{r} \\ =\frac{l\cdot r}{2} \end{gathered}[/tex]On plugging the values in the above relation,
[tex]\begin{gathered} A=\frac{\pi}{6}\times\frac{1}{2} \\ =\frac{\pi}{12} \\ =0.262\text{ sq. units} \end{gathered}[/tex]Hence, the area of the sector is 0.262 square units.
Solve for t: -3 = -t/15t=??[tex] - 3 = - \frac{t}{15} \\ \\ \\ t = [/tex]
Explanation:
[tex]-3=-\frac{t}{15}[/tex]First we can see that there's a minus sign in both sides of the equation, so we can take it out:
[tex]3=\frac{t}{15}[/tex]Now we have to multiply both sides by 15:
[tex]\begin{gathered} 3\cdot15=\frac{t}{15}\cdot15 \\ 45=t \end{gathered}[/tex]Answer:
t = 45
Which sentence is true about an equilateral triangle?
In Equilateral triangle all sides are equal.
HELP PLEASE THIS IS DUE. I been asking for a while but I just get spam answers.
Answer:
y = 12
Step-by-step explanation:
Consider the triangles in the diagram. Triangle QRS (the smaller one on the left) and Triangle PRO (the whole shape)
These two triangles are similar. It helps to write them separately. See image.
You can use a proportion (two ratios equal to each other) to solve this.
There are two good ways to set up an equation.
EITHER:
bottomLeg/sideLeg=bottomLeg/sideLeg
OR
smallbottom/bigbottom=smallside/bigside
see image.
Either way you set it up the answer comes out the same. Pretty much all the work is the same after you crossmultiply.
Solve 9/y = 12/16
OR 9/12 = y/16
see image.
help me pleaseeeeeeeeeeeeeeeeeeeeeeeeeeee
thank you
The domain and range for the relation is [-∞, ∞] and [0,-3], and both of them can be described by interval notation .
Since the graph given to us present a relation or a function, The domain and range of a function are the set of all the inputs and yield a function that can grant separately. The domain and range are vital viewpoints of a function. The domain takes all the conceivable input values from the set of real numbers and the range takes all the yield values of the function. In simple words, the domain is the set of all "x" values and the range is the set of all "y" values in a set of ordered sets and the requested sets are composed as in the form (x, y) or [x,y]
For the given the points are : (0,-3),(1,-3),(2,-3),(3,-3),(4,-3),(5,-3),(-1,-3)(-2,-3),(-3,-3),(-4,-3),(-5,-3)
so the domain set is ={-5,-4,-3,-2,-1,0,1,2,3,4,5}
and the range set is ={0,-3,-4,-5,-6,-7,-8}
so the domain and range is [-∞, ∞] and [0,-3]
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I have no idea how to solve this I have to find the missing terms outside the box
Notice that:
[tex]\begin{gathered} 18x^3=3x\times6x^2, \\ -3x^2=3x\times(-x), \\ 27x=3x\times9. \end{gathered}[/tex]Answer:
what is the solution for 7+k<35
We are given the following inequation:
[tex]7+k<35[/tex]To find the solution we need to subtract 7 to both sides, like this:
[tex]\begin{gathered} 7-7+k<35-7 \\ k<28 \end{gathered}[/tex]Therefore, the solution is the values of "k" smalled than 28.
8. T : R 2 ---+ R 2 first reflects points through the horizontal x 1-
axis and then reflects points through the line x2 = x 1•
Answer:
Thats nice
Step-by-step explanation:
For his phone service, Bob pays a monthly fee of $29, and he pays an additional $0.06 per minute of use. The least he has been charged in a month is $90.44. What are the possible numbers of minutes he has used his phone in a month? Use for the number of minutes and solve your inequality for?
The number of minutes Bob has used his phone in a month is 1024 minutes.
What is meant by the term inequality?In mathematics, an inequality is a link between two expressions as well as values that aren't equal to each other.For the given question;
Monthly phone service paid by Bob = $29.
Additional charges = $0.06 per minute of use.
Total last month charge = $90.44.
Let number of minutes he used be 'm'.
The, the inequality forms is-
90.44 ≤ 29 + 0.06m
Simplifying,
0.06m ≥ 61.44
m ≥ 1024
Thus, the number of minutes Bob has used his phone in a month is 1024 minutes.
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