Answers
(2y - 1)/ -3 = -5 , prove y = 8: Hence proved
5n - 42 = 12n, prove n = -6: Hence proved
2x + 30 = -4(5x -2), prove x = -1 : Hence proved
18x - 2(3x + 1) = 5x -16, prove x = -2 : Hence proved
What is Algebra?
One of the many different mathematical disciplines is algebra. Algebra, a common thread that runs through nearly all of mathematics, is the study of mathematical symbols and the rules for using them in formulas.
1) (2y - 1)/ -3 = -5
Solving for y
(2y - 1)/ -3 = -5
multiply both side with -3
(2y - 1) x (-3)/(-3) = (-5)(-3)
2y - 1 = 15
adding 1 both side
2y - 1 + 1 = 15 + 1
2y = 16
dividing 2 both side
2y / 2 = 16 / 2
y = 8
Hence Proved
2) 5n - 42 = 12n
Solving for n
5n - 42 = 12n
adding 42 both side
5n - 42 + 42 = 12n + 42
5n = 12n + 42
adding -12n both side
5n - 12n = 12n - 12n + 42
-7n = 42
dividing -7 both side
-7n/-7 = 42/ -7
n = -6
Hence proved
3) 2x + 30 = -4(5x -2)
solving for x
first simplify -4(5x -2)
2x + 30 = -20x + 8
adding 20x both side
2x + 20x + 30 = -20x + 20x + 8
22x + 30 = 8
adding -30 both side
22x + 30 - 30 = 8 - 30
22x = -22
dividing 22 both side
22x / 22 = -22/22
x = -1
Hence proved
4) 18x - 2(3x + 1) = 5x -16
solving for x
first simplify - 2(3x + 1)
18x - 6x - 2 = 5x - 16
adding -5x both side
18x - 5x - 6x - 2 = 5x - 5x - 16
13x - 6x - 2 = -16
7x - 2 = -16
adding 2 both side
7x - 2 + 2 = -16 + 2
7x = -14
dividing 7 both side
7x/ 7 = -14 / 7
x = -2
Hence proved
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Related Questions
What is the exact value of tan 7pi/12? Thank you!
Answers
Remember that
[tex]tan(\frac{7\pi}{12})=tan(105^o)=-tan(75^o)=-tan(45^o+30^o)[/tex]and
[tex]tan(A+B)=\frac{tanA+tanB}{1-tanA*tanB}[/tex]therefore
[tex]tan(45^o+30^o)=\frac{tan45^o+tan30^o}{1-tan45^o*tan30^o}[/tex]substitute given values
[tex]tan(45^o+30^o)=\frac{1+\frac{\sqrt{3}}{3}}{1-(1)(\frac{\sqrt{3}}{3})}=\frac{\frac{3+\sqrt{3}}{3}}{\frac{3-\sqrt{3}}{3}}=\frac{3+\sqrt{3}}{3-\sqrt{3}}*\frac{3+\sqrt{3}}{3+\sqrt{3}}=\frac{9+6\sqrt{3}+3}{6}=\frac{12+6\sqrt{3}}{6}=2+\sqrt{3}[/tex]therefore
The answer is
[tex]tan(\frac{7\pi}{12})=-(2+\sqrt{3})[/tex]The answer is the second option
if y =3x^3 + 2x^2 - 5x + 2, find d^3y/dx^3
Answers
Answer:
18
Step-by-step explanation:
[tex]\frac{dy}{dx}=9x^2 + 4x-5 \\ \\ \frac{d^2 y}{dx^2}=18x+4 \\ \\ \frac{d^3 y}{dx^3}=18[/tex]
Solve for the given variables
Answers
Answer:
7.5?
Step-by-step explanation:
I'm not sure but i think 60=8x so you would do 60÷8 and it's 7.5
66 randomly selected students were asked the number of pairs of shoes they have. Let X representthe number of pairs of shoes. The results are as follows:# of Pairs of Shoes 4Frequency 75 68 9 10 114 11 11 11 2 12 8Round all your answers to 4 decimal places where possible.The mean is:The median is:The sample standard deviation is:The first quartile is:The third quartile is:What percent of the respondents have at least 10 pairs of shoes?9617% of all respondents have fewer than how many pairs of shoes?
Answers
Given data
1. The mean
[tex]\frac{\sum fx}{\sum f}=\frac{505}{66}=7.6515[/tex]2. The median
[tex]\begin{gathered} \text{ Median = (}\frac{\text{N+1}}{2})th \\ =(\frac{66+1}{2})th=(\frac{67}{2})th=33.5th \\ \text{The median is the 33.5th }term\text{ which is between 7 and 8} \\ \text{The median is }\frac{\text{7+8}}{2}=\frac{15}{2}=7.5 \end{gathered}[/tex]3. The sample standard deviation
[tex]\begin{gathered} SD\text{ =}\sqrt[]{\frac{\sum f|x-\bar{x}|}{\sum f}} \\ \bar{x}=7.6515 \\ SD=\sqrt[]{4.8028} \\ SD=2.1915 \end{gathered}[/tex]1) Our baseball team last year had 10 boys. This year there are 15 boys. Find the percent of
change including whether it is an increase and decrease.
Answers
Answer: Hi, the answer would be 150% or in decimal form 1.5 this is an increase. There fore your answere is 1.5 which makes it an increase.
Solve the radical equation. Be sure to check all solutions to eliminate extraneous solutions. 7t+5−−−−−√=7 Enter the exact answers.
Answers
The given equation is
[tex]\sqrt[]{7t+5}=7[/tex]Square both sides to cancel the square root
[tex]\begin{gathered} (\sqrt[]{7t+5})^2=(7)^2 \\ 7t+5=49 \end{gathered}[/tex]Subtract 5 from both sides
[tex]\begin{gathered} 7t+5-5=49-5 \\ 7t=44 \end{gathered}[/tex]Divide both sides by 7
[tex]\begin{gathered} \frac{7t}{7}=\frac{44}{7} \\ t=\frac{44}{7} \\ t=6\frac{2}{7} \end{gathered}[/tex]The solution is t = 44/7 OR t = 6 2/7 (mixed number)
If it is 3:40 p.m. in Denver, what time is it in Miami?
Answers
Answer:
5:40 P.M.
Explanation:
From the time map:
• When the time in Denver is 10.00 AM
,• The time in Miami is 12:00 Noon
This means that Miami is 2 hours ahead of Denver.
Thus, if it is 3:40 p.m. in Denver:
[tex]\begin{gathered} \text{Time in Miami}=3\colon40+2\colon00 \\ =5\colon40p.m\text{.} \end{gathered}[/tex]It is 5:40 P.M. in Miami.
Answer the image below
Answers
The value of the function f'(g(x)) is -10
What is a function?
an expression or rule or law that describes a relationship between one variable and another variable. i.e. between independent variable and dependent variable is known as function.
We are given f(-6)=-3, f'(-6)=-5, g(2)=-6, g'(2)=2
We are asked to find F'(2) where F(x)= f(g(x))
We will use the algebra of function to solve the given problem and find the required value
We have
[tex]F(x)=f(g(x))\\F'(x)= f'(g(x))*g'(x)[/tex]
Substituting x=2 in the above equation we get
[tex]F'(2)=f'(g(2))*g'(2)\\F'(2)=f'(-6)*2\\F'(2)=-5*2\\F'(2)=-10[/tex]
Hence the value of F'(2)= -10 as asked
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Four people ordered total bill for soup and four people ordered stew is $31 .If only 2 people had ordered soup and one person ordered stew ,the bill would have been $12.25 .How much is each order of soup and stew ?
Answers
Let price of 1 soup be "x" and 1 stew be "y".
4 soup and 4 stew is $31, thus we can write:
[tex]4x+4y=31[/tex]Also, given
2 soup and 1 stew costs $12.25, thus we can write:
[tex]2x+y=12.25[/tex]Let' solve this for y and substitute it back to Equation 1. Then we will solve for x. The process is shown below:
[tex]y=12.25-2x[/tex]Substituting,
[tex]\begin{gathered} 4x+4y=31 \\ 4x+4(12.25-2x)=31 \\ 4x+49-8x=31 \\ 49-31=8x-4x \\ 18=4x \\ x=\frac{18}{4} \\ x=4.5 \end{gathered}[/tex]Finding y:
[tex]\begin{gathered} y=12.25-2x \\ y=12.25-2(4.5) \\ y=3.25 \end{gathered}[/tex]Thus,
Answer:
Each order of Soup = $4.50
Each order of Stew = $3.25
21 out of 24 did their edpuzzle what percent did their edpuzzle?
Answers
1) To calculate it, we can set a proportion
24--------100%
21---------x
Cross multiply it
x =2100/24
x=87.5
87.5%
Answer: 87.5% did
Step-by-step explanation:
jeriel leans a 26 foot ladder against a wall so that it forms an angle of 61 with the ground .
Answers
To solve this problem we will use the following diagram:
where d is the distance between the base of the ladder and the wall.
Using the cosine we get:
[tex]\cos 61^{\circ}=\frac{d}{26ft}.[/tex]Multiplying the above equation by 26ft we get:
[tex]\begin{gathered} \cos 61^{\circ}\times26ft=\frac{d}{26ft}\times26ft\text{.} \\ d=26ft\cdot\cos 61^{\circ}\text{.} \end{gathered}[/tex]Then:
[tex]d\approx12.60505013ft\approx12.61ft.[/tex]Answer: 12.61.
Match the coordinate rule with the reflection that produces it.Column AColumn B1.Reflect across the x-axisa. (b, a)2.Reflect across the y-axisb. (a, b)3.Reflect across the originC. (-b, -a)4.Reflect across the line y = xd. (-a, -b)5.Reflect across any horizontal line. Ex: y = -2e. (a, -b)f. (2x-a, b)6.Reflect across any vertical line. Ex: x = 5g. (a, 2y-b)
Answers
4. Reflect across the line y = x ------- (b,a)
for reflection across the line y=x, the value of x and y coordinates are interchanged;
[tex](x,y)\rightarrow(y,x)[/tex]5. Reflect across any horizontal line. Ex: y = -2 ......... (a,2y-b)
for reflection across any horizontal line, the x coordinate remain the same but the y coordinate is subtracted from twice the value of the y coordinate of the line of reflection.
[tex](x,y)\rightarrow(x,2y_1-y)[/tex]6. Reflect across any vertical line. Ex: x = 5 ---------- (2x-a, b)
for reflection across any vertical line, the y coordinate remain the same but the x coordinate is subtracted from twice the value of the x coordinate of the line of reflection.
[tex](x,y)\rightarrow(2x_1-x,y)[/tex]In the diagram below, AB || DEF, AE and BD intersect at C, m2B = 43°, and mZCEF = 152°.
Answers
From the picture, we have the necessary information:
The supplementary angles.
The parallels being intersected by two secant lines. And alternate interior angles are congruent under this condition.
The other angle of the triangle is then:
As a result, the angles vertical angles, therefore
< BAC = 28 (it confirms the alternate interior angle Therefore, we can write all the angles in the following drawing:
ersion with whole number valuesA flower bed has the shape of a rectangle 8 yards long and 3 yards wide. What is its area in square feet?Be sure to include the correct unit in your answer.ft
Answers
Given that length =8 yards and width = 3 yards of the rectangle bed.
Recall the formula for the area of the rectangle is
[tex]A=\text{length }\times width[/tex][tex]\text{Substitute length =8 yards and width=3 yards, we get}[/tex][tex]A=8\text{ yards }\times3\text{ yards}[/tex][tex]A=8\times3yards^2[/tex][tex]A=24yards^2[/tex]We know that one yard=3 feet.
[tex]\text{yards}^2=(3\text{ f}eet)^2[/tex][tex]\text{yards}^2=\text{ 9 f}eet^2[/tex][tex]\text{Substitute }yards^2=9\text{ f}eet^2\text{ in the area of the rectangle as follows.}[/tex][tex]A=24\times9\text{ fe}et^2[/tex][tex]A=216\text{ fe}et^2[/tex]Hence the area of the rectangle flower bed is 216 square feet.
Estimate the point(s) at which the graph of f has a local maximum or a local minimum.
Answers
The graph of f has a local maximum of coordinates at (-2.5, 30) and a local minimum of coordinates at (2.5, -30)
What are Maxima and Minima of a Function?The curve of a function has peaks and troughs called maxima and minima. A function may have any number of maxima and minima. Calculus allows us to determine any function's maximum and lowest values without ever consulting the function's graph.
As per the given graph,
From the given graph it is noticed that the highest point of the function is (-2.5, 30), therefore the local maxima is (-2.5, 30).
From the given graph it is noticed that the lowest point of the function is (2.5, -30), therefore the local maxima is (2.5, -30).
The graph of f has a local maximum of coordinates at (-2.5, 30)
The graph of f has a local minimum of coordinates at (2.5, -30)
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each card in a set of cards has a different number of 1 to 12 written on it a student randomly chooses a car record two numbers shown on the card and replaces the card the table shows the results of the students choosing a card 25 x number of Cars 1 2 3 4 5 6 7 8 9 10 11 12 number of outcomes +23-142-311-2213 space on the data in the table how many of the next 125 cars of the student chooses could be expected to have a number shown on a car that is a multiple of 4
Answers
Given data:
The given table is shown.
The expression for the probability that the number is multiple of 4.
[tex]\begin{gathered} P(4m)=\frac{8}{25} \\ =0.32 \end{gathered}[/tex]When 125 times the cards are chosen then expected number card is multiple of 4 is,
[tex]\begin{gathered} E(4m)=125\times0.32 \\ =40 \end{gathered}[/tex]Thus, the correct option is (A).
Solve for this angle.
X+87° 2x° i have to solve for the angle with the 2 on it
Answers
Answer:
x=31
Step-by-step explanation:
x+87+2x=180(angles on a straight line is equal to 180)
3x+87=180
3x=180-87
3x=93
x=31
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Find the maximum value of the function z = 4x+2y subject to the following constraints.
x≥5
y≥4
4x+3y≤56
Answers
The function at its maximum value will be at point (11,4) and its value is 52 which can be derived keeping in mind the constraints that have been given.
Maximizing a functionThe maximum value of any kind of a function is the place where the said function reaches its highest point, or vertex, on a graph. If your kind of quadratic equation has something as a negative of a term, it will also have a maximum value.
There are a bit of three ways to find that maximum, depending on which form of a quadratic function you have got.
Herein we can find the closed region ABC from the three equations or constraints given
and can mark the points as
A = (5,4)
B = (5, 12)
C = (11, 4)
if we put up the values of the points, we get
at (11, 4), Z = 4 x 11 + 2 x 4
=52 that is the maximum value amongst the three.
Thus, the maximum point of the function can be calculated as (11,4)
How do you extract out the maximum or minimum value of a function?We will at first set out the first derivative of the function to absolute zero and then solve for x to get the exact critical point.
If we then take the second derivative or f’’(x), there in we can find out whether this point will be a maximum or minimum. If the second derivative is seen as positive, it will be a minimum value
What is the maximum value of a function called?The maximum or minimum value that is calculated over the entire function is called an “Absolute” or “Global” maximum or minimum of the function.
There is presence of only one global maximum (and only one global minimum) but there can be several that is more than one local maximum or minimum
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Find 75% of 150. Round to the nearest tenth if necessary.
Answers
Find 75% of 150
First, let's convert 75% to decimal by dividing by 100:
[tex]\frac{75}{100}=0.75[/tex]Now, we will multiply 0.75 with 150 to find out answer:
[tex]\begin{gathered} 0.75\times150 \\ =112.5 \end{gathered}[/tex]Answer112.5I believe that it would be 112.5.
__________________________________________
Convert 75% to a decimal by dividing it by 100:
[tex]\frac{75}{100} = 0.75[/tex]
Next, multiply 0.75 to 150:
[tex]0.75[/tex] × [tex]150 = 112.5[/tex] ← Final Solution
Hope this helps!
what is 2×700 please tell me
Answers
2 multiply by 700 is 1400
An easier trick to multipy numbers with zeros is;
Remove the zeros first, multiply the numbers, then add back the zeros
That is;
2 x 7 = 14
Then add back the zeros
That is;
1400
2x700=1,400
Answer the questions below.
Answers
(a) Daily high temperature
The daily high temperature does not depend on the number of ticket sales.(b) Amount of sleep
The amount of medication influences the amount of sleep.(c) Input U
The independent variable is the input.PLEASE HELP ITS DUE SOON! I DONT GET ANY OF THIS! HELP WOULD BE MUCH APPRECIATED! NEED THIS DONE BEEN STUCK ON THIS FOR WAY TO LONG!
YOU WILL GET 100 POINTS IF YOU HELP! QUESTION DOWN BELOW!!!!!
Answers
ΔMNQ ≅ ΔONP are Congruent triangle.
What do you mean by congruent?
Two figures are considered to be "congruent" if they can be placed perfectly over one another. Both of the bread slices are the same size and shape when positioned one on top of the other. Congruent refers to things that are exactly the same size and shape.1) MN = ON ⇒ Given
2) ∠1 = 2 ⇒ Angles are equal because sides are equal.
3) MN = ON,MP = OQ ⇒ Given
4) ΔNMP and ΔNQO are isosceles trisngle.
5) PN = QN ⇒ Given
6) PQ = QP ⇒ Line segment
7) MP + PO = OQ + QM ⇒ Adding = amount to = line segment
8) ΔMNQ ≅ ΔONP = Congruent
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The diagonal of a rectangular filed 135m long is 157m. What is the Width of the field?
Answers
To solve this exercise let's make a sketch of the rectangular field first:
The length, width, and diagonal of the rectangular field form a right triangle, to determine the width of the rectangle you can apply the Pythagorean theorem.
This theorem states that the square of the hypotenuse is equal to the sum of the square of the legs of the triangle.
[tex]a^2+b^2=c^2[/tex]The diagonal is the hypotenuse of the triangle, the length is one of the legs "a" and the width is the other leg "b".
Write the theorem for b:
[tex]\begin{gathered} a^2-a^2+b^2=c^2-a^2 \\ b^2=c^2-a^2 \\ \sqrt[]{b^2}=\sqrt[]{c^2-a^2} \\ b=\sqrt[]{c^2-a^2} \end{gathered}[/tex]Replace the expression with c=157 and a=135
[tex]\begin{gathered} b=\sqrt[]{157^2-135^2} \\ b=\sqrt[]{24649-18225} \\ b=\sqrt[]{6424} \\ b=80.149\approx80.15 \end{gathered}[/tex]The width of the field is 80.15 meters.
The area of the front yard for question number 1 is 60x^2 + 12x - 21 The grass area of the backyard for question number 2 is 81x^2 - 212x + 68
Answers
Given,
The area of the front yard is 60x^2 + 12x - 21 .
The grass area of the backyard is 81x^2 - 212x + 68.
The total are is the sum of the front yard and the back yard.
So, to obtain the total area adding the area of the front yard and back yard.
[tex]\begin{gathered} \text{Total area= area of front yard+area of back yard} \\ =60x^2+12x-21+81x^2-212x+68 \\ =60x^2+81x^2+12x-212x-21+68 \\ =x^2(60+81)+x(12-212)-21+68 \\ =141x^2-200x+47 \end{gathered}[/tex]Hence, the total area is 141x^2-200x+47.
PLease tell me if its linear exponential quadratic please
Answers
Answer:
Linear
Step-by-step explanation:
X values are increasing equally by 1. Y values are decreasing equally by 2. So, the graph is a linear graph.
In right triangle ABC, CD¯¯¯¯¯ is the altitude to hypotenuse AB¯¯¯¯¯. If AB = 28.3¯ and DB = 12, find CD.
Answers
The side of the right triangle CD is 25.63 units
How to find side of a right triangle?A right triangle is a triangle that has one of its angles as 90 degrees.
Base on the angles, the side of a right triangle can be named as follows:
opposite sidehypotenuse sideadjacent sideTherefore, the side CD of the right triangle can be found as follows:
using Pythagoras theorem,
c² = a² + b²
Hence,
CD = √28.3² - 12²
CD = √800.89 - 144
CD = √656.89
CD = 25.6298653918
Therefore,
CD = 25.63 units
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If the paint costs $1.50 per square meter, how much will she spend to cover the entire wall with paint?
Answers
To find the price to paint the entire wall, we just need to find the area of the wall and multiply by the price per square meter.
The area of a square is given by the product of the side length by itself. Since the measure of the side is 3 meters, the area is
[tex]A=3^2=9[/tex]9 m².
The unitary price per square meter is $1.50. Multiplying this value by the area, we have
[tex]9\times1.5=13.5[/tex]It will cost $13.50 to paint the wall.
Three horse share five bales of hay equally. Five cows share eight bales of hay equally.
How much hay does each horse and each cow get?
Which animal gets more, a horse of a cow? How much more hay do they get?
Answers
How much hay does each horse and each cow get?
(a)The hay shared by 3 horses = 5 bales
So, the hay shared by 1 horse = x
Rewriting the statements ,
3 h = 5 b --(1)
1 h = x -(2)
By applying cross multiplication method to (1) and (2)
3 (x) = 5
x = 5/3
The hay shared by 1 horse = 5/3
(b)The hay shared by 5 cows = 8 bales
So, the hay shared by 1 cow = y
Rewriting the statements ,
5 c = 8 b --(3)
1 c = y -(4)
By applying cross multiplication method to (3) and (4)
5 (y) = 8
x = 8/5
The hay shared by 1 cow = 8/5
Which animal gets more, a horse of a cow?
Comparing the fractions,
The hay shared by 1 horse = 5/3 = 1.7
The hay shared by 1 cow = 8/5 = 1.6
1.7 > 1.6
So, a horse gets more than a cow
How much more hay do they get?
Considering the difference of fractions,
Amount of more hay consumed = Hay shared by a horse - hay shared by a cow.
[tex]=\frac{5}{3} -\frac{8}{5} \\\\=\frac{25-24}{15} \\\\=\frac{1}{15}[/tex]
The horse share [tex]\frac{1}{15}[/tex] more hay than cows
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the base of the triangle prism shown below is a right triangle. What is the lateral surface area of the prism
Answers
Given data:
The given triangular prism.
The expression for lateral surface area is,
[tex]\begin{gathered} LS=(8\operatorname{mm}+\text{ 6mm +}10\text{ mm)}\times12\text{ mm} \\ =288\text{ sq-mm} \end{gathered}[/tex]Thus, the lateral surface area is 288 sq-mm.
Which of the following is the correct mathematical expression for:
Halve a number and then increase it by five
Answers
Answer:
1/2 x + 5
Step-by-step explanation:
Haf of x = 1/2 x
then add 5 : 1/2 x + 5