The equations that have the same solution as 2X -5 equals 15 is option B and option D.
Given equation:
2x -5 = 15
solve for value of x
2x = 15 + 5
2x = 20
divide by 2 on both sides
x = 20/2
x = 10
A. 2x =10
x = 10/2
x = 5
B. 2x = 20
x = 20/2
x = 10
C. 2(x -5) = 15
2x -10 = 15
2x =25
x = 25/2
x = 12.5
D. 2x - 20 = 0
2x = 20
x = 20/2
x = 10
E. 15 = 5 - 2x
2x = 5 - 15
2x = -10
x = -5
From the option A,B,C,D,E we observe that only options B , D x value matches with the given equation x value so option B and option D is correct.
Therefore he equations that have the same solution as 2X -5 equals 15 is option B and option D.
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Simplify the following expressions. Make sure it is simplified completely when selecting your answer. Choose the correct answer below.
The correct option is option number 2.
AlusTranslate the triangle.Then enter the new coordinates.A (3,0)A' ([?], [])B'([],[ ]C'([ ]:[]).B(4,-2)(1-3)<-5.3Enter
Triangle ABC is shown. Select all the triangles that are scale drawings of triangle ABC.
Athe the triangles are similar to triangle ABC.
If W (-10,4),X(-3,-1)and Y (-5,11) classify angle WXY by its sides
So,
Let me graph the three points here below:
To classify this triangle by its sides, the first thing we need to do is to find the measure of each segment. For this, we could use the formula for the distance between two points for each one.
Let's start with segment WX.
[tex]\begin{gathered} WX=\sqrt[]{(4-(-1))^2+(-10-(-3))^2} \\ WX=\sqrt[]{(5^2)+(-7)^2} \\ WX=\sqrt[]{25+49} \\ WX=\sqrt[]{74} \end{gathered}[/tex]Now, continue with XY:
[tex]\begin{gathered} XY=\sqrt[]{(11-(-1))^2+(-5-(-3))^2} \\ XY=\sqrt[]{12^2+(-2)^2} \\ XY=\sqrt[]{148} \end{gathered}[/tex]And finally, WY:
[tex]\begin{gathered} WY=\sqrt[]{(11-4)^2+(-5-(-10))^2} \\ WY=\sqrt[]{7^2+5^2} \\ WY=\sqrt[]{74} \end{gathered}[/tex]As you can see, sides WY and WX are equal. So, the triangle has two equal sides and one different.
For this reason, the triangle is an isosceles triangle.
Mr adams shares out 24 pencils between niamh and jack in the ratio 3:5
The number of pencils taken by Niamh is 9 and by jack is 15.
\What are ratios and proportions?An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.
Given that Mr Adams shares out 24 pencils between Niamh and Jack in a ratio of 3:5.
Let the common factor between the sharing be x. Form an equation and solve.
Niamh's share = 3x
Jack's share = 5x
3x+ 5x = 24
8x = 24
x = 3
Niamh's share = 3x = 3 x 3 = 9 Pencils
Jack's share = 5x = 5 x 3 = 15 Pencils
Therefore, the number of pencils taken by Niamh is 9 and by jack is 15.
The complete question is given below.
Mr Adams shares out 24 pencils between Niamh and jack in a ratio 3:5. Find the number of pencils taken by Niamh and Jack.
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The table shows the number of gallons of paint Mrs. Brown used to paint the of rooms in her house. Find the slope of the line
Answer:
The slope is [tex]\frac{3}{2}[/tex] or [tex]1.5[/tex]
Step-by-step explanation:
The slope formula: [tex]\frac{y2-y1}{x2-x1}[/tex]
Now, in this case, when you get tables, you could choose two coordinates.
So, for instance, you chose the coordinates: (2,3) and (6,9)
Since we have the two coordinates, we now could solve for the slope.
-
Substituting and finding the slope:
1) [tex]m =\frac{9-3}{6-2} \\[/tex]
2) [tex]m = \frac{6}{4} = \frac{3}{2}[/tex]
3) [tex]m = \frac{3}{2}[/tex] or [tex]1.5[/tex]
connie wants to buy 10 identical items for birthday party favors, and she wants them to be delivered to her home. She has $55 to spend, but the store adds a mandatory $5 tax for delivery items. How much can each favor cost in order to spend all of her $55?
Let x represent the cost of each items for birthday party favors.
Given that she wants to by 10 items,
cost of 10 items = 10 * x = 10x
From the information given,
cost of delivery of the items = 5
Total cost of items = cost of 10 items + cost of delivery = 10x + 5
Given that she has $55 to spend and she can spend all of it,
the linear equation representing this scenario is
10x + 5 = 55
Subtract 5 from both
10x + 5 - 5 = 55 - 5
10x = 50
Diviiding both sides by 10,
10x/10 = 50/10
x = 5
Each favor can cost $5 in order to spend all of her $55
#3 iFind the volume of the sphere. Round your answer to the nearest hundredth.4 ftThe volume is aboutcubic feet.
Given: A sphere with a radius of 4 ft.
Required: To determine the volume of the sphere.
Explanation: The volume of a sphere is given by the formula-
[tex]V=\frac{4}{3}\pi r^3[/tex]Substituting the value of the radius, r=4 into the formula as-
[tex]V=\frac{4}{3}\times3.14\times4^3[/tex]Further solving-
[tex]\begin{gathered} V=267.946\text{ ft}^3 \\ \approx267.95\text{ ft}^3 \end{gathered}[/tex]Final Answer: The volume is about 267.95 cubic feet.
Kiara sets up a passcode on her tablet, which allows only four digit codes. She has heard that it’s more secure if a digit is repeated in the passcode. A spy sneaks at Kiara’s tablet and sees her fingerprints on the screen over three numbers. what is the probability the spy is able to unlock the tablet on his first try? express your answer as a fraction.
Let:
A = Unlock the table on the first try
a = Number of Possible right digits
N = Total number of possible digits
the probability the spy is able to unlock the tablet on his first try is:
[tex]\begin{gathered} P(A)=\frac{a}{N} \\ P(A)=\frac{1}{10} \end{gathered}[/tex]a theater has 22 rows of seats. If there are 27 seats in the 1st row, 30 in the 2nd, 33 in the 3rd and so on how many seats are there in all. PLEASE HELP ASAP
The total number of seats in the theatre are 1287.
Given that:-
Number of rows in the theatre = 22
Seats in 1st row = 27
Seats in 2nd row = 30
Seats in 3rd row = 33
and so on.
This is a question of Arithmetic Progression (AP).
Here,
First element = 27
Common difference = 3
Number of terms = 22
First we will find the number of seats in 22nd row.
Number of seats in 22nd row = 27 + (22-1)*3 = 27 + 21*3 = 27 + 63 = 90.
Now, we have to find,
27 + 30 + 33 + 36 + .... + 90
Hence, sum of the number of seats in all the rows = (22/2)(2*27 + (22-1)*3) = 11(54 + 21*3) = 11(54+63) = 11(117) = 1287.
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Hong Tang's gross weekly salary is $615. His weekly federal withholding is $55. The Social Security tax is 6.2 percent of the first $90,000. The Medicare tax is 1.45 percent of gross pay. The state tax is 1.5 percent of gross pay. Each week he pays $22.40 for medical insurance. How much is deducted from Tang's weekly wages for state tax and Medicare tax combined?
We have that the Medicare tax is 1.45% of gross pay, and the state tax is 1.5%. Then, if Hong Tang's gross weekly salary is $615, then::
[tex]\begin{gathered} (615)(0.0145)=8.92 \\ (615)(0.015)=9.22 \\ \Rightarrow8.92+9.22=18.14 \end{gathered}[/tex]therefore, from state tax and Medicare tax combined, Hong Tang gets deducted $18.14
You hang two strands of decorative lights.
a strand of red and blue decorative lights a strand of yellow and green decorative lights
Strand 1: changes color every 16 seconds Strand 2: changes color every 28 seconds
Both strands just changed color. After how many seconds will the strands change color at the same time again?
The strands will change color at the same time again after
seconds.
Both the decorative light strands will change change the colors at the same time again after 448 seconds
In the above question, it is given that,
Two strands of decorative lights, red and blue is one strand and green and yellow is another are hanged
Strand one changes colors in = 16 seconds
Strand two changes colors in = 28 seconds
We need to find, after how many seconds will the strands change color at the same time again
To find this, we will take the LCM(Lowest Common Multiple) of both strands time
Factors of 16 = 2 x 2 x 2 x 2
Factors of 28 = 2 x 2 x 7
LCM( 16 and 28) = 2 x 2 x 2 x 2 x 2 x 2 x 7 = 448
Therefore, It can be concluded that, both the decorative light strands will change change the colors at the same time again after 448 seconds
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Solve each system by substitution.y - 4x = 3 2x - 3y = 211. Rewrite the first equation in terms of . y=2. Substitute the value of into the second equation. 2x - 3 = 213. Solve for X .4. Substitute the value of in one of the original equations. Solve for y .5. Write your answer as an ordered pair (x,y) .Solution: ( , )
We have to solve this system by substitution.
This method let us define a varaible in function of the other (or others, if they are more than two) and then replace it in the other equations by this relation.
The system is:
[tex]\begin{gathered} y-4x=3 \\ 2x-3y=21 \end{gathered}[/tex]1. From the first equation, we can easily define y in function as x:
[tex]\begin{gathered} y-4x=3 \\ y=4x+3 \end{gathered}[/tex]2. Now, we substitute y in the second equation:
[tex]\begin{gathered} 2x-3y=21 \\ 2x-3(4x+3)=21 \end{gathered}[/tex]3. We got an equation that is expressed only in function of x, so we can solve it as:
[tex]\begin{gathered} 2x-3(4x+3)=21 \\ 2x-3\cdot4x-3\cdot3=21 \\ 2x-12x-9=21 \\ -10x=21+9 \\ -10x=30 \\ x=\frac{30}{-10} \\ x=-3 \end{gathered}[/tex]4. If we replace x in the equation for y, we get:
[tex]\begin{gathered} y=4x+3 \\ y=4(-3)+3 \\ y=-12+3 \\ y=-9 \end{gathered}[/tex]5. Then, we can write the answer a s a pair (x,y) = (-3,-9)
Please explain how Pascals triangle works?
Pascals triangle or Pascal's triangle is a special triangle that is named after Blaise Pascal, in this triangle, we start with 1 at the top, then 1s at both sides of the triangle until the end. The middle numbers are so filled that each number is the sum of the two numbers just above it.
Generally, we can use Pascals' triangle to find the coefficients of binomial expansion
For example, we want to expand
[tex](x\text{ + y\rparen}^2[/tex]Using Pascal's triangle, we can get the coefficients of the expansion:
[tex](x\text{ + y\rparen}^2\text{ = 1x}^2\text{ + 2xy + 1y}^2[/tex]Ryan's motorcycle is now worth $2500. Ithas depreciated 12% each year since itwas purchased. If he bought it four yearsago, what did it cost brand new? Roundto the nearest dollar
Given a principal of P and a depreciation rate of r %,
after n years the new amount A is given by
[tex]A=P(1-r^{})^n[/tex]In this case,
[tex]A=\text{ \$2500 r = 12\% n = 4years}[/tex]Then, we have
[tex]\begin{gathered} 2500=P(1-0.12^4) \\ \text{ Which implies that } \\ P=\frac{2500}{(1-0.12)^4}=\frac{2500}{0.88^4}=\frac{2500}{0.5997}=\text{ \$4169} \end{gathered}[/tex]Hence the cost brand new is $4169
1. In the Gizmo, plot the points (1.3) and (4, 6).A. What is the equation of this line?
Let's plot the points (1,3) and (4, 6), as follows:
As you can see, we have:
x = 1, y = 3 as the first point we know.
x = 4, y = 6 as the second point we know.
We can replace y, with x + 2 (3 - 1 or 6 - 4),, therefore the equation of this line is:
x + 2 = y or x = y - 2 Any of these equations will solve the question A.
State the equation for: The sum of two numbers is 21. One number is one more than the other.
So,
Let "x" and "y" be the numbers that we're asking for.
As we know, one number is one more than the other, so we could write:
[tex]x+y=21[/tex]And,
[tex]y=x+1[/tex]Now, the equation that we could state is:
[tex]x+x+1=21[/tex]8. The cone shown below has a circular base with a diameter of 8 feet. 8 feet 5 feet What is the volume of the cone? Use 3.14 for n.
Answer:
The volume of the cone is;
[tex]83.73ft^3[/tex]Explanation:
Given the cone with diameter 8 feet and height 5 feet;
[tex]\begin{gathered} d=8\text{ f}eet \\ h=5\text{ f}eet \end{gathered}[/tex]The volume of cone can be calculated using the formula;
[tex]\begin{gathered} V=\frac{1}{3}\pi r^2h \\ V=\frac{1}{3}\pi(\frac{d}{2})^2h \\ V=\frac{1}{3}\pi(\frac{d^2}{4})h \\ V=\frac{1}{12}\pi d^2h \end{gathered}[/tex]Substituting the given values;
[tex]\begin{gathered} V=\frac{1}{12}\pi d^2h \\ V=\frac{1}{12}\times(3.14)\times(8)^2\times5 \\ V=83.73ft^3 \end{gathered}[/tex]Therefore, the volume of the cone is;
[tex]83.73ft^3[/tex]Use the properties of logarithms to write the logarithm in terms of log7^(2) and log7^(5)
The given logarithm expression is:
[tex]log_750[/tex]This can be re-written as:
[tex]\begin{gathered} \log_750=\log_7(2\times25) \\ \\ \log_750=\log_72\frac{}{}+\log_725 \\ \\ \log_750=\log_72+\log_75^2 \\ \\ \operatorname{\log}_750=\operatorname{\log}_72+2\operatorname{\log}_75 \end{gathered}[/tex]9. Simplify, write the final answer as positive
exponent.
34
39
We apply the formula : a^m : a^n = a^(m-n)
-> 3^4 : 3^9 = 3^(4-9) = 3^-5
Since we need the final answer with a positive exponent, 3^5.
Identifying Trig Ratios (Diagram), Level 1Jun 04, 3:20:20 PMExpress cos N as a fraction in simplest terms.L28M MZ21
1. Use a calculator to find each angle measure to the nearest degree.a) sin A = 0.4848b) cos Y = 0.7431c) cos X = 0.4226d) tan B = 19.0811
Given
a) sin A = 0.4848
b) cos Y = 0.7431
c) cos X = 0.4226
d) tan B = 19.0811
To find:
Each angle measure to the nearest degree.
Explanation:
It is given that,
a) sin A = 0.4848
b) cos Y = 0.7431
c) cos X = 0.4226
d) tan B = 19.0811
That implies,
a) sin A = 0.4848.
Then,
[tex]\begin{gathered} A=\sin^{-1}(0.4848) \\ =28.99\degree \\ =30\degree \end{gathered}[/tex]b) cos Y = 0.7431.
Then,
[tex]\begin{gathered} Y=\cos^{-1}(0.7431) \\ =42.0038\degree \\ =42\degree \end{gathered}[/tex]c) cos X = 0.4226.
Then,
[tex]\begin{gathered} X=\cos^{-1}(0.4226) \\ =65.001\degree \\ =65\degree \end{gathered}[/tex]d) tan B = 19.0811.
Then,
[tex]\begin{gathered} B=\tan^{-1}(19.0811) \\ =86.99\degree \\ =87\degree \end{gathered}[/tex]Hence, the measure of each angle is,
a) A = 30°.
b) Y = 42°.
c) X = 65°.
d) B=87°.
15. What is missing in the problem, 48 is ____ % of 120? A. base B. percentage C. rateD. time
The following equation-definition will be consider to solve the problem:
[tex]Base*Rate=Part[/tex]Where the base in this case is 120.
The rate is the porcentage, which is the missing part in the problem.
And 48 is the part. Hence, the solution is:
The solution is C. rate
the diagram below is a picture of a broken post. determine the height of the post before it was broken.
step 1
Find the hypotenuse of the right triangle
Applying Pythagorean Theorem
c^2=7^2+24^2
c^2=625
c=25 ft
therefore
the height is equal to
h=25+24=49 ft
answer is 49 ftF=9/5C + 32 solve for C
To solve for C let us do these steps
1. Put the term of C on one side and the other terms on the other side
Subtract 32 from both sides to move the term 32 to the other side
[tex]\begin{gathered} F-32=\frac{9}{5}C+32-32 \\ F-32=\frac{9}{5}C \end{gathered}[/tex]2. Make the coefficient of C = 1
Divide both sides by 9/5
[tex]\begin{gathered} \frac{F-32}{\frac{9}{5}}=\frac{\frac{9}{5}C}{\frac{9}{5}} \\ \frac{5}{9}(F-32)=C \\ C=\frac{5}{9}(F-32) \end{gathered}[/tex]You can Multiply the bracket (F- 32) by 5/9
[tex]C=\frac{5}{9}F-\frac{160}{9}[/tex]Which linear equation describes the line passing through point (10, 3) and has a y-intercept at (0, -1)?10y = -3x +y = -x +y=2- 1= 5*-y=31-x-13*-52
Answer: y = 2x/5 - 1
Explanation:
The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m represents slope
c represents y intercept
The formula for calculating slope is expressed as
m = (y2 - y1)/(x2 - x1)
The given points are (0, -1) and (10, 3). thus,
x1 = 0, y1 = - 1
x2 = 10, y2 = 3
m = (3 - - 1)/(10 - 0) = (3 + 1)/10 = 4/10 = 2/5
By substituting m = 2/5 and c = - 1 into the slope intercept equation, the equation of the line is
y = 2x/5 - 1
I need so help with my math
We have to change the oz to lb. So we get that
[tex]\begin{gathered} 5oz=0.3125lb \\ 10oz=0.625lb \end{gathered}[/tex]so the problem goes as
[tex]9.3125-6.625=2.6875lb[/tex]and that is
[tex]2lb11oz[/tex]Hey I got the the idea! But it looks like the answer doesn’t have the other number? Which kinda makes me think it if we even did this lol!
The area of a right triangle can be calculated as half the product of each leg length.
So, if the legs measure 4 cm and 3 cm, we have:
[tex]\begin{gathered} A=\frac{4\cdot3}{2} \\ A=2\cdot3 \\ A=6\text{ cm}^2 \end{gathered}[/tex]Therefore the triangle area is 6 cm².
Find the product (-10) (-2)
Remember that in a multiplication between two negative numbers the result always will be positive
(-10)(-2)=20
The result is 20
Answer:
20
Step-by-step explanation:
the product just means to multiply, so you do:
-10 x -2 = 20
the mean value of land and buildings per acre from a sample of farms is $1500, with a standard deviation of $100. the data set has a bell shaped distribution. assume the number of farms if the sample is 70. use the empirical rule to estimate the number of farms whose land and building values per acre are between $1400 and $1600
The sample mean is X[bar]=$1500
The sample standard deviation is S=$100
The sample size is n=70
The data set has a bell shaped distribution
The empirical rule states that
The values $1400 and $1600 are within one standard deviation away from the mean:
X[bar]+S=$1500+$100=$1600
X[bar]-S=$1500-$100=$1400
Following the rule you can expect 68% of the sample to be between them.
Whats left to do is to calculate the 68% of the sample
[tex]70\cdot0.68=47.6[/tex]Around 47.6 of the farms have values per acre are between $1400 and $1600