75 x = 87
x = 87/75
x = 1.16
1.16 x 100 = 116%
116 -100 = 16%
It increased 16%
identify the perpendicular lines in the diagram below. select all that apply
The answer is
[tex]m\perp k[/tex]and
[tex]n\perp k[/tex]PLEASE HELP TODAY ASAPPP !!!!! What is the prime factor of 18
The prime of factor of 18 would be the following:
Prime factor of 18=2*3*3=18
2 and 3 are both the prime numbers.
So, 2*3*3=18 would be the prime factor.
I need help figuring out statements in algebra 2 please
Solution:
The equations are given below as
[tex]\begin{gathered} 2x+3y-46=22\ldots..(1) \\ 10-3y+6x=20\ldots..(2) \end{gathered}[/tex]Step 1:
From equation (1), add 46 to both sides
[tex]\begin{gathered} 2x+3y-46+46=22+46 \\ 2x+3y=68\ldots\text{.}(3) \end{gathered}[/tex]Step 2:
From equation (2),substract 10 from both sides
[tex]\begin{gathered} 10-10-3y+6x=20-10 \\ 6x-3y=10\ldots\text{.}(4) \end{gathered}[/tex]Step 3:
Multiply equation (3) by 3
[tex]\begin{gathered} 3(_{}2x+3y)=68\times3 \\ 6x+9y=204\ldots\text{.}(5) \end{gathered}[/tex]Step 4:
Substract equation (4) from equation (5)
[tex]\begin{gathered} 6x+9y-(6x-3y)=204-10 \\ 6x-6x+9y+3y=194 \\ 12y=196 \\ \frac{12y}{12}=\frac{194}{12} \\ y=\frac{97}{6} \end{gathered}[/tex]Step 5:
Substitute y= 97/6 in equation (4)
[tex]\begin{gathered} 6x-3y=10 \\ 6x-3(\frac{97}{6})=10 \\ 6x-\frac{97}{2}=10 \\ 6x=10+\frac{97}{2} \\ 6x=\frac{20+97}{2} \\ 6x=\frac{117}{2} \\ 12x=117 \\ \frac{12x}{12}=\frac{117}{12} \\ x=\frac{39}{4} \end{gathered}[/tex]Hence,
The value of x=39/4 and y= 97/6
The solution system of equations has exactly one point
A physical therapy facility is building a new pool that is 60 feet long and 6 feet deep. They have ordered enough tile for a 160-foot-long border around the edge. How wide should the pool be to ensure that all tiles are used?
20 feet wide
1) Let's sketch out this pool:
2) This is a problem that deals with perimeter, so we can write out:
2p = 60 + 60 + x +x Since we have 160 foot as the perimeter
160 = 60 +60 +2x
160 = 120 + 2x Subtract 120 from both sides
160 -120 = 2x
40 = 2x Divide both sides by 2
x = 20
3) Hence, the pool must be 20 feet wide
Rectangle ABCD has vertex coordinates A(-1, -1), B(-1, -3),C(-4,-3), and D(-4, -1). It is translated 4 units to the rightand reflected across the line y = x. What are the coordinatesof A"B"C"D'?A. 443,1), 33,3),C^0,3),0 0,1)B. AY-13),B"-3,3).C'(-3,0), 0"(-1,0)C. AM-1,-1),B"(-3,-1),CY-3.-4), D'(-1,-4)D. 413,-1).B'(3.-3).C'(0,-3), O'(0 - 1)
Solution
For this case we have the following coordinates:
A= (-1, -1)
B= (-1, -3)
C= (-4, -3)
D= (-4, -1)
If we move the rectangle 4 units to the right we have these new coordinates
A' = (3, -1)
B' =(3, -3)
C' = (0,-3)
D'= (0, -1)
And now after a reflection thorugh the line y= x we got:
A'' = (-1, 3), B'' = ( -3, 3), C'' = (-3, 0), D'' = (-1, 0)
Select all the expressions that equivalent to 4(t - 4)
Equivalent expressions are
(-4 + t) 4
That is all
Find the slope of the line. 2 5 -9 The slope is
To calculate the slope of a line we need to find at least two points of the line.
For example, for this line, points (0,0) and (1,-3).
We can calculate the slope as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{-3-0}{1-0}=\frac{-3}{1}=-3[/tex]Answer: the slope is m=-3.
Juan's mother gave him a recipe for trail mix. 5 cup almonds 6 2 cup peanuts 3 1 cup cereal 1 2. cup raisins Order the ingredients used in the recipe from least to greatest.
Given that on trial mix, Juan's mother uses 5/6 cup almonds. 2/3 cup peanuts, 1/4 cup cereal and 1/2 cup raisins.
Make the denominator of all equal to lcm(6,3,4,2) = 12.
Theb:
[tex]\begin{gathered} \frac{5}{6}=\frac{10}{12} \\ \frac{2}{3}=\frac{8}{12} \\ \frac{1}{4}=\frac{3}{12} \\ \frac{1}{2}=\frac{6}{12} \end{gathered}[/tex]Now, just check the value in the numerator.
[tex]\begin{gathered} 3<6<8<10 \\ \frac{3}{12}<\frac{6}{12}<\frac{8}{12}<\frac{10}{12} \\ \text{Cereal < Raisins }<\text{Peanuts}<\text{Almonds} \end{gathered}[/tex]bob wants to buy 150 dL of soda if 7.65 L cost $9.40 then how much will he pay for 150 dL
In order to determine the cost of 150 dL, first convert this quantity to L, as follow:
[tex]150dL\cdot\frac{1L}{10dL}=15L[/tex]where we have use the equivalence 1L = 10dL.
Next, if 7.65L cost $9.40, then, by using rule of three you can write:
[tex]\frac{x}{15L}=\frac{9.40}{7.65L}[/tex]where x is the cost of 15L. Then, by solving for x and by simplifying we obtain:
[tex]\begin{gathered} x=\frac{9.40}{7.65}\cdot15L \\ x\approx14.4 \end{gathered}[/tex]Hence, 150dL cost approximately $14.4
3. Which value is not rational?4. WfuA.1217B. 2012)C. 0.583D.1353
Rational numbers are numbers that can be expressed as a fraction such that the numerator and denominator is an integer(whole numbers).
We would consider the given options
A. The square root of 121 is 11. This means that the number would be
- 11/7
The numerator and denominator are integers. thus, it is a rational number
B. It can be written as 2 root 2 divided by 1. But root 2 is not an integer. This means that the numerator is not an integer. Thus, the number is not rational.
C. The number is a repeating decimal. This means that it can be expressed as a fraction of two
A rectangular piece of metal is 15 in longer than it is wide. Squares with sides 3 in long are cut from the four comers and the flaps are folded upward to form an open box. If the volume of the box is 1218 in³ what were the originaldimensions of the piece of metal?What is the original width? in
Let's make a wuick sketch of the metal. Let x be its width. Since the length is 15 in longer, the legnth is x + 15:
As we can see, both the length and the width will lose 3 in on each side, so each will be 6 in smaller on the final box.
The height of the box will be just the dimension of the square that was cut off.
So, the final box will have a length of x + 15 - 6 in and a width of x - 6 in, and its height is 3 in.
The volume of a rectangular box like this is the products of its three dimensions, so:
[tex]\begin{gathered} V=(x+15-6)(x-6)3 \\ V=3(x+9)(x-6) \end{gathered}[/tex]We know the volume is 1218 in³, so:
[tex]3(x+9)(x-6)=1218[/tex]To solve x, we will first need to distribute the parenthesis, but before that we can simplify the equation by dividing both sides by three:
[tex]\begin{gathered} (x+9)(x-6)=\frac{1218}{3} \\ (x+9)(x-6)=406 \\ x^2-6x+9x-54=406 \\ x^2-6x+9x-54-406=0 \\ x^2+3x-460=0 \end{gathered}[/tex]Now, we have a quadratic equation, so we can use the quadratic formula to solve for x:
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}=\frac{-3\pm\sqrt[]{3^2-4(1)(-460)}}{2(1)} \\ x=\frac{-3\pm\sqrt[]{9^{}+1840}}{2}=\frac{-3\pm\sqrt[]{1849}}{2}=\frac{-3\pm43}{2} \\ x_1=\frac{-3+43}{2}=\frac{40}{2}=20 \\ x_2=\frac{-3-43}{2}=\frac{-46}{2}=-23 \end{gathered}[/tex]Since x is the original width of the box, it can't be a negative value, so the second solution is invalid in this case.
This means that the only possible solutions is 20, and its units is in inches, so 20 in.
So, the original width was 20 in, which makes the original length equal to 35 in.
How do you find the equation of the line. write the equation in standard form. through (7,-5); parallel to the line 2x+9y=8
First, we need to clear y in the line given
[tex]\begin{gathered} 2x+9y=8 \\ 9y=-2x+8 \\ y=-\frac{2}{9}x+\frac{8}{9} \end{gathered}[/tex]because we need to have the slope-intercept form
[tex]y=mx+b[/tex]where m is the slope
if the line is parallel that have the same slope so the slope of the line that passes through (7,-5) is
m=-2/9
(7,-5)=(x1,y1)
In order to obtain the equation of the line
[tex]y-y_1=m(x-x_1)[/tex]then we substitute the values
[tex]\begin{gathered} y+5=-\frac{2}{9}(x-7) \\ y+5=-\frac{2}{9}x+\frac{14}{9} \\ y=-\frac{2}{9}x-\frac{31}{9} \end{gathered}[/tex]the equation of the line is
[tex]y=-\frac{2}{9}x-\frac{31}{9}[/tex]solve the inequality - 8u <= 96and - 9c < 126
Answer:
[tex]\begin{gathered} u\ge-12 \\ \text{and} \\ c>-14 \end{gathered}[/tex]Explanation:
Given the inequalities:
[tex]\begin{gathered} -8u\leq96 \\ \\ -9c<126 \end{gathered}[/tex]To solve these, first of all note that: Dividing both sides of an inequality by a negative number changes the inequality sign to the opposite.
For
[tex]-8u\leq96[/tex]Divide both sides of the inequality by -8
[tex]\frac{-8u}{-8}\ge\frac{96}{-8}[/tex]Therefore
[tex]u\ge-12[/tex]For
[tex]-9c<126[/tex]Divide both sides of the inequality by -9
[tex]\begin{gathered} \frac{-9c}{-9}>\frac{126}{-9} \\ \\ c>-14 \end{gathered}[/tex]Please I would like the answer for number 10?Thank you
SOLUTION:
If we know the LCM of 4 and 5, which is 20, then to find the LCM of 40 and 50 that will be the LCM of 4 and 5 multiplied by 10 (i.e. 20 x 10 = 200) because both 4 and 5 are multiplied by 10 to get 40 and 50, so the LCM of of 4 and 5 must be multiplied by 10 for us to get the LCM of 40 and 50.
In conclusion;
LCM of 4 and 5 = 20
LCM of 40 (i.e. 4 x 10) and 50 (i.e. 5 x 10) = 200 (i.e. 20 x 10).
scare Drawings Wendell is designing the layout of the backyard behind his new home. He wants to build a dog house and add some flower gardens. In the following tasks, you will help Wendell create a scale drawing of his backyard to he him plan the location and size of the dog house and gardens. The provided sketch is not drawn to scale, but it does give the actual dimensions of the lawn in feet. The backyard is a trapezoid-the west side is perpendicula to both the north and south sides, and the deck is a rectangle. The scale factor of the drawing is 1 inch to 10 feetpart Bin the scale drawing, what will the length of the east side of the backyard be?part C in the scale drawing, what will the length of the south side of the backyard be?part Din the scale drawing, what will the length of the west side of the backyard be?part Ein the scale drawing, what will the length of the north side of the backyard be?part Ftwo corners of the backyard are right angles. the third corner forms an obtuse angle measuring 127°, the fourth corner forms an acute angle measuring 53°, when transferring these angle measurements from the real world to the scale drawing, will their measures increase, decrease, or stay the same?part G in the scale drawing, what is the area of the lawn (that is, the area of the whole backyard, except for the deck)?
Part B
scale factor is given as 1 inch to 10 feet
In the diagram, the actual length of the east side is 35 feet,
the length of the east side on the scale drawing will be 35/10 = 3.5 inches
Part C
In the diagram, the actual length of the south side is 71 feet,
the length of the south side on the scale drawing will be 71/10 = 7.1 inches
Part D
In the diagram, the actual length of the west side is 28 feet,
the length of the west side on the scale drawing will be 28/10 = 2.8 inches
Part E
In the diagram, the actual length of the north side is 50 feet,
the length of the north side on the scale drawing will be 50/10 = 5 inches
Part F
The measurement of the angles will stay the same on the scale drawing
Part G
The whole backyard is a trapezoid while the deck is a rectangle
so,
area of the lawn = Area of Backyard (trapezoid) - area of lawn (rectangle)
Area of backyard =
[tex]\begin{gathered} \frac{1}{2}(a\text{ + b)h} \\ =\frac{1}{2}(5\text{ + 7.1)2.8} \\ =\frac{1}{2}(12.1)2.8=16.94inch^2\text{ } \end{gathered}[/tex]Area of deck = length x breadth
[tex]1\times0.5=0.5inch^2[/tex]Area of the lawn =
[tex]16.94inch^2-0.5inch^2=16.44inch^2[/tex]Angles L3 and L2 are alternate anglesinterior anglescorresponding anglesthese are not angles
ANSWER
Interior angles
EXPLANATION
Angles L3 and L2 are between the two parallel lines. Therefore, they are interior angles - specifically same side interior angles, because they are on the same side of the transversal.
A random variable is a numerical valued function defined on a ____________.sample spacesample pointsample theorydistribution
The Solution:
A random variable is a numerical valued function defined on a Sample Space.
Thus, the correct answer is [option 1]
when m angle 1 = m angle 6
We cannot deduce if the lines are parallel by only knowing m<1=m<6 .The answer is none.
Find the final amount of money in an account if $4,400 is deposited at 5 % interest compoundedquarterly (every 3 months) and the money is left for 10 years.The final amount is $Round answer to 2 decimal placesSubmit Question
Based on the problem, here are the data given:
Principal (P) = $4, 400
rate (r) = 5%
number of conversions per year (m) = 4 (quarterly)
time (t) = 10 years
To be able to solve for the final or future value, we have the following formula below:
[tex]F=P(1+\frac{r}{m})^{mt}[/tex]Let's use the given data and substitute it to the formula above.
[tex]\begin{gathered} F=4400(1+\frac{0.05}{4})^{4\times10} \\ F=4400(1+0.0125)^{40} \\ F=4400(1.0125)^{40} \\ F=4400(1.643619463) \\ F\approx7,231.93 \end{gathered}[/tex]The final amount of the money after 10 years is $7,231.93.
I want to find step by step answers for these questions pls
Answers:
a) midpoint: (1, 4)
b) slope of PQ: 1/3
c) length of PQ: √40
d) equation of perpendicular bisector of PQ:
Explanation:
The given points are P(4, 5) and Q(-2, 3)
Part a)
The midpoint of two points (x1, y1) and (x2, y2) can be calculated as
[tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]So, replacing (x1, y1) = P(4, 5) and (x2, y2) = Q(-2, 3), we get:
[tex](\frac{4+(-2)}{2},\frac{5+3}{2})=(\frac{2}{2},\frac{8}{2})=(1,4)[/tex]Then, the midpoint of PQ is (1, 4)
Part b)
The slope of a segment that passes through points (x1, y1) and (x2, y2) can be calculated as
[tex]\text{slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]Replacing (x1, y1) = P(4, 5) and (x2, y2) = Q(-2, 3), we get:
[tex]\text{slope}=\frac{3-5}{-2-4}=\frac{-2}{-6}=\frac{1}{3}[/tex]So, the slope is 1/3
Part c)
The length of a segment that goes from (x1, y1) to (x2, y2) is calculated as
[tex]\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Replacing (x1, y1) = P(4, 5) and (x2, y2) = Q(-2, 3), we get:
[tex]\begin{gathered} \sqrt[]{(-2-4)^2+(3-5)^2} \\ \sqrt[]{(-6_{})^2+(-2)^2} \\ \sqrt[]{36+4} \\ \sqrt[]{40} \end{gathered}[/tex]Therefore, the length of PQ is √40.
Part d)
The perpendicular bisector of PQ is a line that divides the segment into two equal and forms a 90 degrees angle with the segment.
First, we need to calculate the slope of the line. Taking into account that the slope of perpendicular lines multiply to -1, we get that the slope of the perpendicular bisector is
[tex]\begin{gathered} m\cdot\frac{1}{3}=-1 \\ m\cdot\frac{1}{3}\cdot3=-1\cdot3 \\ m=-3 \end{gathered}[/tex]Additionally, the perpendicular bisector will pass through the midpoint of PQ, so it will pass through (1, 4).
Now, the equation of a line with slope m= -3 that passes through the point (x1, y1) = (1, 4) is
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-4=-3(x-1) \\ y-4=-3x-3(-1) \\ y-4=-3x+3 \\ y-4+4--3x_{}+3+4 \\ y=-3x+7 \end{gathered}[/tex]Therefore, the equation of the perpendicular bisector is y = -3x + 7.
Write the equation of the line that passes through the given points in slope-intercept form.(-1, 5) and (-4, 2)m =b =equation
1. Darla's piggy bank is full, so she plans to empty out all of the coins, roll asmany as possible to deposit into her savings account, and put the remainingcoins back into the piggy bank. Rolls of pennies and dimes consist of 50 coinseach, while rolls of nickels and quarters consist of 40 coins each.(9 points: Part 1 - 2 points; Part II - 2.5 points; Part III - 2 points; Part IV - 2.5points)Part : After emptying out all of the coins, Darla counted 472 pennies, 319 nickels,436 dimes, and 271 quarters. How many rolls of pennies, nickels, dimes, andquarters will she have?
The given information are:
• Rolls of pennies = 50 coins
,• Rolls of dimes = 50 coins
,• Rolls of nickels = 40 coins
,• Rolls of quarters = 40 coins
The problem is to determine how many rolls of pennies, nickels, dimes, and quarters are in:
• 472 pennies
,• 319 nickels
,• 436 dimes
,• 271 quarters
What we do - is divide each of the number of pennies, nickels, dimes, and quarters she has by the corresponding number of coins that make a roll.
FOR PENNIES
[tex]\frac{472}{50}=9.44\text{ rolls of pennies}[/tex]FOR NICKELS
[tex]undefined[/tex]Choose both the multiple of 10 that can be used to remove the decimals and the equation and the value of y
The multiple of 10 that can be used to multiply the equation is 100, because of the figures in their hundredth,
Multiplying the equation by 100,
[tex]\begin{gathered} \text{Multiply both sides by 100} \\ 100(1.2y+6.5+(-3.25y))=100(0.14-4.29+(-2y)) \\ \end{gathered}[/tex]Open the brackets,
[tex]120y+650+(-325y)=14-429+(-200y)_{}[/tex]Collect like terms,
[tex]\begin{gathered} 120y+650-325y=14-429-200y \\ 650-14+429=325y-120y-200y \\ 1065=15y \\ \text{Divide both sides by 15} \\ \frac{1065}{15}=\frac{15y}{15} \\ 71=y \\ y=71 \end{gathered}[/tex]Hence, the multiple of 10 that can remove all the decimals is 100 and the best option is B.
Find the value of X and each arc measurex =mDE =mEF = mDFG =
Arc EF + arc FG = 180 ( Reason: GE is a straight line)
[tex]\begin{gathered} x-3+12x-25=180 \\ 13x-28=180 \\ 13x=180\text{ + 28} \\ 13x=208 \\ \text{Divide both sides by 13},\text{ we get,} \\ x\text{ =}\frac{208}{13}=16 \end{gathered}[/tex]Arc DE = Arc GF = 12x - 25 = 12(16) - 25 = 192 - 25 = 167 degrees
Arc EF = x -3 = 16 - 3 = 13 degrees
Arc DFG = arc DE + arc EF + arc FG = 167 + 13 + 167 = 347 degrees
Evaluate 715when r3 and 3 = 5.Stuck? Watch a video or use a hint.7r-15/s when r=3 and s=5
To evaluate this expression 7r - 15/s
r = 3 and s = 5
Substitute the values of r and s in the expression:
7*(3) - 15/5
21 - 15/5
6/5.
So, the answer is 6/5.
If point P(3,10) is reflected across the line y=1, what are the coordinates of its reflection image?
A) 3, -10
B) -1, 10
C) 3, -8
D) 10, 3
Answer:
C.
Step-by-step explanation:
I need help working through a few math problems on trig.. What is EF?
Given the figure, we can deduce the following information:
1. m2. DF = 4.5
To determine EF, we use the formula:
To determine the sides, we follow the figure shown below:
Based on the given triangle DEF, the hypotenuse side is 4.5 while EF is the opposite side. We plug in what we know:
[tex]\begin{gathered} \text{ Sin}\theta=\frac{EF}{4.5} \\ \text{ Sin}26=\frac{EF}{4.5} \\ 0.44=\frac{EF}{4.5} \\ \text{Simplify and rearrange} \\ EF=(0.44)(4.5) \\ EF=1.98 \end{gathered}[/tex]Therefore, the answer is EF= 1.98.
Sweatest Graphing Linear Inequalities Sketch the rupt of each timear inequality Name Semana Daxe 1-2-2
Answer:
Step by step solution:
[tex]x\ge-2[/tex]This inequality encompasses all the real numbers greater equal than -2.
We make a solid line at x = -2, because x=-2 is included and shade the right region.
Find the length of AB.AÁB = [ ? ]m140°8 mB.Round your answer to the nearest hundredth.
STEP 1:
Write out the formula
The length AB represents an arc
[tex]\text{Length of arc (AB)=}\frac{\theta}{360}\times2\pi r[/tex]The given values are angle=140 degree and radius = 8metres
STEP 2:
Substitute the given values into the formula.
[tex]\begin{gathered} AB=\frac{\theta}{360}\times2\pi r \\ =\frac{140}{360}\times2\times\frac{22}{7}\times8 \\ =\frac{140\times2\times22\times8}{360\times7} \\ =\frac{49280}{2520} \\ =19.56m \end{gathered}[/tex]Write an equation in slope-intercept form for the line described below:
Answer:
y=-2x+8
Explanation:
Given the line:
[tex]y=\frac{1}{2}x-1[/tex]We want to find a line that is perpendicular to the line with an x-intercept of 4.
Note: Two lines are perpendicular if the product of their slopes is -1.
Comparing y=½x-1 to the slope-intercept form y=mx+b, its slope =1/2.
Therefore, the slope of the line perpendicular to it = -2.
Since the x-intercept is 4, we have the point (4,0) on the line.
Using the point slope form:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-0=-2(x-4) \\ y=-2x+8 \end{gathered}[/tex]Therefore, the required line is: y=-2x+8
