We can determine the area of the enlarged picture as follows:
*First, we determine the new dimensions, that is:
[tex]5\cdot2.5\text{ = 12.5}[/tex][tex]8\cdot2.5=20[/tex]*Secondly, we find the area using the formula of area for a rectangle, that is:
[tex]A=20\cdot12.5\Rightarrow A=250[/tex]From this, we have that the area of the picture after being enlarged equals 250 in^2.
Solve the quadratic equation by completing
the square: ² - 12r + 31 = 51
Give the equation after completing the
square, but before taking the square root.
Your answer should look like: (ra)² = b
The equation is:
Enter an algebraic equation [more..]
The value of r is 6+ 2[tex]\sqrt{14}[/tex]
What is quadratic equation ?Algebraic equation in x that has a second degree. The quadratic equation in its conventional form is Ax2 + bx + c = 0 where a and b are the coefficients, x is the variable, and c is the constant term. To qualify as a quadratic equation, an equation must contain a non-zero term (a 0) for the coefficient of x2. In order to create a quadratic equation in standard form, the x2 term, the x term, and the constant term must be written first, second, and third, respectively. As opposed to fractions or decimals, integral values are typically used to express the numerical values of letters a, b, and c.
[tex]r^{2}-12r=51-31\\ r^{2}-12r-20=0\\ \frac{b^{2} }{4a} \\ =[/tex]
=36
= do ±36 in equation
=[tex]r^{2}-12r +36 -36 = 20\\ (r-6)^{2}=56[/tex]
=(r-6) = ±[tex]\sqrt{56}[/tex]
r = 6 ±[tex]\sqrt{56}[/tex]
r= 6+ 2[tex]\sqrt{14}[/tex]
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Claire left her home at 11 a.m. travelling along route 1 at 30 miles per hour. At 1 pm,Her counsin Valerie left home and started after her on the same road at 45 miles per hour.At what time did Valerie catch up with Claire ?
(Please give a step by step explanation and answer correctly)
An international company has 28,600 employees in one country. If this represents 29.6% of the company's employees, how many employees does it have in total?
96622 is the total number of employees in the company.
Let x be the total number of employees in the company
we are given that, 28600 employees comprise 29.6% of the company's total employees
Thus,
x * 29.6% = 28600
x * 296/1000 = 28600
x * 296 = 28600 * 1000
x * 296 =28600000
x = 28600000/296
thus x = 96622 employees (approx)
What do you mean by "Percentage"?
"A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100." Hence the percentage refers to parts per hundred.
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What is the value of 7!
As part of your job you spend time each day contacting former customers. During one week, you contacted 15 people on Monday, 12 on Tuesday, 14 on Wednesday, 11 on Thursday, and 13 on Friday. What is the average number of customers contacted each day? Which averaging method did you use?
The average number of customers contacted each day is 13. We used the basic average method which is explained below.
The formula for calculating the average is:
Sum of all the observations ÷ Total number of observations
So, according to the formula
Sum of all the observations = People contacted on (Monday+ tuesday+wednesday+thursday+friday)
= 15+12+14+11+13
= 65
Number of observations = 5
So putting values in the formula, we get
65÷5
= 13
Hence, the average number of customers contacted is 13.
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Please answer please please
Choose the fraction that is equal to 0.81:
A.9/11
B.81/100
C.8/9
D.80/99
Answer: B
Step-by-step explanation:
Answer:
B. 81 / 100
Step-by-step explanation:
9 / 11 = 0.82
81 / 100 = 0.81
8 / 9 = 0.89
80 / 99 = 0.80
Hope this helps! :)
Jim's parents paid for the first three years of his college costs. When
he was a college senior, he was approved for an unsubsidized loan in the
amount of $15,200 at a 4.29% interest rate for 10 years.
a. If he chooses to make interest-only payments until the monthly loan
payments are due, for how long will he be making interest only
payments?
Jim can make interest-only payments until after 1 year and 6 months.
What is the interest-only payment?The interest-only payment enables students to avoid interest capitalization during their school years and during the next six months after graduation.
The six-month period is called the grace period.
Non-capitalization of interest lowers the monthly repayments when payments become due after the grace period.
Amount of student loan = $15,200
Interest rate = 4.29%
Loan period = 10 years
Interest-only period = 1 year and 6 months
Amount of interest per month = $54.34 ($15,200 x 4.29% x 1/12)
Total interest during the interest-only period = $978.12 ($54.34 x 18)
Thus, the interest-only payments last for 18 months.
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Convert the rectangular coordinates (√3, √3) to polar form. Letr>0 and 0 ≤ 0 < 2.
Answer: [tex](r,\theta) = \left(\sqrt{6}, \frac{\pi}{4}\right)[/tex]
In other words, [tex]r = \sqrt{6} \ \text{ and } \ \theta = \frac{\pi}{4}[/tex] where theta is in radians.
=====================================================
Work Shown:
[tex](\text{x},\text{y}) = (\sqrt{3},\sqrt{3})\\\\r = \sqrt{\text{x}^2+\text{y}^2}\\\\r = \sqrt{(\sqrt{3})^2+(\sqrt{3})^2}\\\\r = \sqrt{3+3}\\\\r = \sqrt{6}\\\\[/tex]
and,
[tex]\theta = \tan^{-1}\left(\frac{\text{y}}{\text{x}}\right)\\\\\theta = \tan^{-1}\left(\frac{\sqrt{3}}{\sqrt{3}}\right)\\\\\theta = \tan^{-1}\left(1\right)\\\\\theta = \frac{\pi}{4} \text{ radians}\\\\[/tex]
Use a calculator or the unit circle to arrive at the last step. Keep in mind that (√3, √3) is in the first quadrant where [tex]0 < \theta < \frac{\pi}{2}[/tex] since both x and y are positive.
The angle of elevation to the top of a building changes from 15° to 30° as an observer advances 140 feet toward the building. Find the height of the building, x, to the nearest foot.
pls explain
Answer:
70 ft
Step-by-step explanation:
To find the height of the building, we can use the trigonometric relationship between the angle of elevation, the distance from the object, and the height of the object.
In this case, we have a right triangle formed by the observer, the top of the building, and the base of the building. Therefore, we can use the tangent trigonometric ratio, since the height of the building is the opposite the angle of elevation, and the distance between the observer and the building is the side adjacent the angle.
[tex]\boxed{\begin{minipage}{7 cm}\underline{Tangent trigonometric ratio} \\\\$\sf \tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\end{minipage}}[/tex]
Let "x" be the height of the building.
Let "d" be the initial distance from the observer to the building.
The angle of elevation changes from 15° to 30° as the observer advances 140 feet toward the building.
(See the attachment for a visual representation).
Based on this information, we can set up the following equations:
[tex]\tan 15^{\circ}=\dfrac{x}{d}[/tex]
[tex]\tan 30^{\circ}=\dfrac{x}{d-140}[/tex]
Rearrange both equations to isolate d:
[tex]d=\dfrac{x}{\tan 15^{\circ}}[/tex]
[tex]d=\dfrac{x}{\tan 30^{\circ}}+140[/tex]
Solve this system of equations by the method of substitution.
[tex]\dfrac{x}{\tan 15^{\circ}}=\dfrac{x}{\tan 30^{\circ}}+140[/tex]
[tex]\dfrac{x}{\tan 15^{\circ}}-\dfrac{x}{\tan 30^{\circ}}=140[/tex]
[tex]\dfrac{x\tan 30^{\circ}-x \tan 15^{\circ}}{\tan 30^{\circ}\tan 15^{\circ}}=140[/tex]
[tex]\dfrac{x(\tan 30^{\circ}- \tan 15^{\circ})}{\tan 30^{\circ}\tan 15^{\circ}}=140[/tex]
[tex]x=\dfrac{140\tan 30^{\circ}\tan 15^{\circ}}{\tan 30^{\circ}- \tan 15^{\circ}}[/tex]
[tex]x=\dfrac{140\cdot \frac{\sqrt{3}}{3}(2-\sqrt{3})}{\frac{\sqrt{3}}{3}- (2-\sqrt{3})}[/tex]
[tex]x=\dfrac{\dfrac{140(2\sqrt{3}-3)}{3}}{\dfrac{4\sqrt{3}-6}{3}}[/tex]
[tex]x=\dfrac{140(2\sqrt{3}-3)}{2(2\sqrt{3}-3)}[/tex]
[tex]x=\dfrac{140}{2}[/tex]
[tex]x=70[/tex]
Therefore, the height of the building is exactly 70 feet.
A large cooler contains 16 lemonade 5 sprite 10 cans of coke and 9 cans of root beers you randomly pick two cans one at a time (without replacement) what is the probability you don’t get two cans of
The most appropriate choice for probability will be given by-
Probability of not getting two cans of coke is [tex]\frac{49}{52}[/tex]
What is probability?
Probability of an event is the chance of occurance of that event.
Probability is calculated by Number of favourable outcomes divided by total number of outcomes
Here,
Number of lemonades in a cooler = 16
Number of sprite in a cooler = 5
Number of cans coke in a cooler = 10
Number of cans of root beers in a cooler = 9
Total number of refreshments = 16 + 5 + 10 + 9
= 40
Probability of getting a can of coke in the first draw = [tex]\frac{10}{40}[/tex]
= [tex]\frac{1}{4}[/tex]
Probability of getting a can of coke in the second draw = [tex]\frac{9}{39}[/tex]
= [tex]\frac{3}{13}[/tex]
Probability of getting two cans of coke in the two draws = [tex]\frac{1}{4} \times \frac{3}{13}[/tex]
= [tex]\frac{3}{52}[/tex]
Probabilty of not getting two cans of coke in the two draws = [tex]1-\frac{3}{52}[/tex]
= [tex]\frac{52-3}{52}[/tex]
= [tex]\frac{49}{52}[/tex]
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I can’t find the answer for the application
Value of x is 16/91
How to Find value of x ?
In question
(8/7)/(13/9) = x / (2/9)
Divide the numbers 72/91 =x/(2/9)
Multiply all terms by the same value to eliminate fraction denominators182* (72/91) = 182* (x/(2/9))
Cancel multiplied terms that are in the denominator2 *72 = 819 * x
Multiply the numbers144 = 819 * x
Divide both sides by the same factor(144/819) = 819 *x / 819
SimplifyX = 16/91
The value of x is 16/91
Definition of Fraction :
A fraction represents a part of a whole or, more generally, any number of equal parts.In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator.There are in total six types of fractions such as:
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is y=3x+y=4 y=-1/3x-2 parallel, perpendicular or neither
The equations of the lines that are perpendicular are y = 3x and y = - 1 / 3 x - 2
How to know if an equation of a line is parallel or perpendicular?The equation of a line can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptParallel line have the same slopes.
The products of the slopes of an equation of lines must be equals to negative one for it to be perpendicular.
Therefore,
m₁ m₂ = -1
The equation are as follows:
y = 3x
y = 4
y = - 1 / 3 x - 2
Hence, using m₁ m₂ = -1
3 × - 1 / 3 = -1
Therefore, y = 3x and y = - 1 / 3 x - 2 are perpendicular.
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find the length of arc JM. use 3.14 for pi. round to nearest tenth
hello
to solve this problem, we need the formula of length of an arc
[tex]\begin{gathered} L_{\text{arc}}=\frac{\theta}{360}\times2\pi r \\ \end{gathered}[/tex]t find the value of angle JM, we should take into cognizance that the sum of angles in a circle is equal to 360 degree and angle on a straight line is equal to 180 degree
[tex]\begin{gathered} jk+jm+mk=360 \\ 180+jm+90=360 \\ 270+jm=360 \\ jm=360-270 \\ jm=90 \end{gathered}[/tex]now we know the value of angle jm, let's find the length of the radius
[tex]\begin{gathered} \text{radius}=\frac{\text{diameter}}{2} \\ \text{diameter}=16.4 \\ \text{radius(r)}=\frac{16.4}{2}=8.2\text{miles} \end{gathered}[/tex]with all the necessary informations or data required, we can now proceed to solve for the length of arc jm
[tex]\begin{gathered} L_{\text{arc}}=\frac{\theta}{360}\times2\pi r \\ L_{\text{arc}}=\frac{90}{360}\times2\times3.14\times8.2 \\ L=12.87\text{miles} \end{gathered}[/tex]from the calculations above, the length of the arc is equals to 12.87 miles
Answer:
12.9
Step-by-step explanation:
Find the distance between the points (−1,0) and (7,6).
The distance between the point (-1,0) and (7,6) is 10.
Distance between the points:
Distance between two points is the length of the line segment that connects the two points in a plane.
The formula to find the distance between the two points is usually given by
d=√((x2 – x1)² + (y2 – y1)²).
Given,
(−1,0) and (7,6).
Here we need to find the distance between these points.
Apply the values on the formula , in order to solve it,
d = √(7 - (-1))² + (6 - 0)²
When we simplify it, then we get,
d = √(7 + 1)² + (6)²
d = √(8)² + 36
d = √64 + 36
d = √100
d = 10
Therefore, the distance is 10.
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The pie chart below representsEliana's monthly budget. Whatpercentage of her budget isallocated to savings?
Answer:
percentage = 528/ 3,300*100= 16%
Step-by-step explanation:From the pie chart we can see that saving are 528 dollars, so
now we need to calculate total from the given pie chart, which is
3,300 dollars. So percentage is savings( 528 dollars) divided by total( 3,300 dollars) and then finally multiply by 100
solve similar triangles (advanced) khan academy. solve for x
The length of the unknown side of the triangle using similar triangle ratio concept is; x = 24
How to Solve similar triangles?We want to find the length of the unknown side of the similar triangles.
Similar triangles are defined as triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. Thus, we can say that if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
From the given triangle ADE which is divide into a similar triangle ABC with an unknown side x, we can use the concept of similar triangle ratios to get the unknown value of x as;
6/x = 8/(x + 8)
Cross multiply to get;
6(x + 8) = 8x
6x + 48 = 8x
8x - 6x = 48
2x = 48
x = 48/2
x = 24
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Please help I need this answer immediately
Answer:
Step-by-step explanation:
−2x−y−2z−4x−2y+3z
Combine −2x and −4x to get −6x.
−6x−y−2z−2y+3z
Combine −y and −2y to get −3y.
−6x−3y−2z+3z
Combine −2z and 3z to get z.
−6x−3y+z
DIFFERENTIATE W.R.T. X
−6
A vehicle can cover 80 kilometers in 2 ½ hours. How many kilometers can it cover in 6 hours?
Name the figure below in two different ways.
Answer:
VD; DV
Step-by-step explanation:
you can name the line in two ways
VD or DV
they are the two endpoints of the line
they are the same line
x(x+5)+2x(x-4)
can anyone awnser me this step by step :)
Answer: 3x^2−3x
Step-by-step explanation:
1.) Distribution
2.) Combine like Terms
3.) Combine like Terms.. again
4.) Common Factor
5.) GET UR SOLUTION!!
Becca works for the Humane Society and had to buy food for the dogs. She bought 5 1/2 pounds of dog food. She feeds each dog about one-third of a pound. How many dogs can she feed?
Becca works for the Humane Society and had to buy food for the dogs. She bought 5 1/2 pounds of dog food. She feeds each dog about one-third of a pound. How many dogs can she feed?
_______________________________________________________
Food ÷ amount of food per dog
5 1/2 pounds of dog food ÷ 1/3
5 1/2 ÷ 1/3 = (10/2 +1/2) ÷ 1/3 = 11/2 ÷ 1/3 = 11/2 x 3/1 = 33/ 2
33/ 2 = 16 1/5 = 16.5
_______________________________________
Can you see the updates?
___________________________________
Answer
She can feed 16.5 (16) dogs with 5 1/2 pounds of dog food
_________________________________________
Do you have any questions regarding the solution?
Find the exact area of thetriangle below.
I am going to draw a picture to ilustrate the solution
Now, we are going to use the trigonometric functions for the right triangle on the left to calculate h
[tex]\sin (30)\text{ = }\frac{h}{10\sqrt[]{3}}\Rightarrow\text{ h= sin(30)}\cdot\text{ 10}\sqrt[]{3\text{ }}=\frac{1}{2}\cdot10\sqrt[]{3}=5\sqrt[]{3}[/tex]Now we use the formula for the area of a triangle
[tex]A=\frac{b\cdot h}{2}=\text{ }\frac{20\cdot5\sqrt[]{3}}{2}=50\sqrt[]{3}[/tex]x+12% of x= 3.36 help
Answer:
x = 3
Step-by-step explanation:
x + .12x = 3.36 Combine like terms
1.12x = 3.36 Divide both sides of the equation by 1.12
x = 3
=======================================
Work Shown:
12% = 12/100 = 0.12
x + 12% of x = x + 0.12x = 1.12x = 3.36
1.12x = 3.36
x = 3.36/1.12
x = 3
---------------
Check:
12% of 3 = 0.12*3 = 0.36
x + 12% of x = 3 + 12% of 3 = 3 + 0.36 = 3.36
Or you could say 1.12x = 1.12*3 = 3.36
The answer is confirmed.
Determine the value of x. Use the Pythagorean Theorem. Show your work.
The value of x (hypotenuse) using the Pythagorean Theorem is 5 units.
What is Pythagorean Theorem?The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle, or, in familiar algebraic notation, a² + b², are equal to the c² which is the hypotenuse.So, the formula of the Pythagorean Theorem:
c² = a² + b²Where a (AC) = 4 and b (CB) = 3 as the given figure is symmetric and so line CB will be equal to 3.
Now,
c² = a² + b²c² = 4² + 3²c² = 16 + 9c² = 25c = √25c = 5Therefore, the value of x using the Pythagorean Theorem is 5 units.
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Parallelogram
How divide the figure?
A company produces brake pads for commercial airliners.
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write out the given data for Team A
STEP 2: Find the mean
[tex]\begin{gathered} The\:arithemtic\:mean\:\left(average\right)\:is\:the\:sum\:of\:the\:values\:in\:the\:set\:divided\:by\:the\:number\:of\:elements\:in\:that\:set. \\ \mathrm{If\:our\:data\:set\:contains\:the\:values\:}a_1,\:\ldots \:,\:a_n\mathrm{\:\left(n\:elements\right)\:then\:the\:average}=\frac{1}{n}\sum _{i=1}^na_i\: \\ sum=224250 \\ n=6 \\ mean=\frac{224250}{6}=37375 \end{gathered}[/tex]Hence, the mean of the data for production team A is 37375
Number 12 I don’t get it y’all know ?
Answer:
Approximately $18 each month.
Step-by-step explanation:
This is quite simple. So, we know that there are 12 months in a year. And we know that in a year, the store has given out discounts totaling up to $216. All we have to do is divide the total number by how many months there are in a year.
[tex]216\div12=18[/tex]
This means that the store gives out $18 of discounts per month.
(Also, you don't seem college level)
HELP FOR 100pts
ONLY FOR TWACK
Answer:
3:2
Step-by-step explanation:
Write an expression in factored form for the polynomial of least possible degree graphed below.
y(x)= (blank)
Show your work!
Explain your answers!
No incorrect answers!
No nonsense answers!
No spam answers!
Thanks!
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: {y= -1/6(x⁴ +2x³-7x²-8x+ 12 } [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
The values of x for which curves cuts/touches the x - axis are the roots of that particular polynomial.
And that polynomial can be depicted in form :
[tex]\qquad \tt \rightarrow \: a(x - h1) (x - h2) (x - h3)........ (x - hn) = 0[/tex]
[ where, h1, h2, h3... hn represents roots of that polynomial, and " a " is the stretch of curve]
And by that, we can sort out the roots of given polynomial that are :
x = -3, -2, 1 and 2Since there are four roots, the least degree polynomial formed will have bi - quadratic polynomial.
And it will be represented as :
[tex]\qquad \tt \rightarrow \: y=a(x - ( - 3)) (x - ( - 2))(x - 1)(x - 2) [/tex]
[tex]\qquad \tt \rightarrow \:y=a (x + 3)(x + 2)(x - 2)(x - 1) [/tex]
And it can be further solved to get ~
[tex]\qquad \tt \rightarrow \: y=a(x + 3)( {x}^{2} - 4)(x - 1)[/tex]
[tex]\qquad \tt \rightarrow \:y= a( {x}^{2} - 4)( {x}^{2} + 2x - 3)[/tex]
[tex]\qquad \tt \rightarrow \: y=a( {x}^{4} + 2 {x}^{3} - 3 {x}^{2} - 4 {x }^{2} - 8x + 12)[/tex]
[tex]\qquad \tt \rightarrow \: y=a({x}^{4} + 2 {x}^{3} - 7{x }^{2} - 8x + 12)[/tex]
Now, it's time to evaluate the value of a, for that we can just use a point that satifys the curve ( i.e (0 , -2)
plug in the values :
[tex]\qquad\displaystyle \tt \rightarrow \: {-2= a(0⁴ +2(0)³-7(0)²-8(0) + 12 } [/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: {-2= a(0 +0-0-0 + 12 } [/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: {-2= a( 12 )} [/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: {a= -2 ÷ 12 } [/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: {a= -1/6} [/tex]
Therefore, the required equation is :
[tex]\qquad\displaystyle \tt \rightarrow \: {y= -1/6(x⁴ +2x³-7x²-8x+ 12 } [/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞