The value of unknown variable [x] is x = 36 x 10⁻⁴
What is the general equation of a Straight line? How it represents a proportional relationship?
The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
y = mx also represents direct proportionality. We can write [m] as -
m = y/x
OR
y₁/x₁ = y₂/x₂
We have a proportional relationship of the form -
y₁/x₁ = y₂/x₂
We can write it as -
x = (5.1 x 10⁴ x 12)/(1.7 x 10⁸)
x = 36 x 10⁻⁴
Therefore, the value of unknown variable [x] is x = 36 x 10⁻⁴
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What is the slope of the line that passes through the points (5, 8) and (11, 5)? Write
your answer in simplest form.
Drag each number to the correct location on the image.
Classify the real numbers below as rational or irrational numbers.
AWNSER GETS BRAIN
Answer:
Step-by-step explanation:
1. Square root of 8 is not a rational number.
2. 1/4 is a rational number.
3. Square root of 90 is not a rational number.
4. 2/3 is a rational number.
5. Square root of 4 is not a rational number.
6. /2 is not a rational number.
7. is not a rational number.
I think these are right, please give me brainliest.
Plssss help!
Geometry A
Brainliest
Answer:
18 ft.
Step-by-step explanation:
SOMEONE PLEASE ANSWER THIS QUESTION!
A store manager paid $44.00 for a shirt. She marked up the price of the shirt by 80% and then sold the shirt what was the selling price of the shirt
Cost price = $44
mark up percent = 80% = 80/100 = 0.8
selling price = ?
The markup formula:
[tex]markup=\text{ }\frac{selling\text{ price - cost price}}{\cos t\text{ price}}[/tex][tex]\begin{gathered} 0.8=\text{ }\frac{selling\text{ price - 4}4}{44} \\ \text{cross multiply:} \\ \text{0.8(44) }=\text{ selling price - 44} \\ \end{gathered}[/tex][tex]\begin{gathered} 35.2\text{ = selling price - 44 } \\ 35.2\text{ + 44 = selling price } \\ \text{selling price = \$79.2} \end{gathered}[/tex]Exercise #99) g(x) = x3 + x f(x) = 2x-3 - 3 Find (gof)(x)
Given two functions f(x) and g(x), its composition will be:
[tex](g\circ f)=g(f(x))[/tex]It is read g compound f or simply said to g we are going to fill it with f. So, you have
[tex]\begin{gathered} (g\circ f)=g(f(x)) \\ (g\circ f)=(2x-3)^3+(2x-3) \end{gathered}[/tex]To expand the binomial, apply the binomial formula to the cube, that is:
[tex](a-b)^3=a^3-3a^2b+3ab^2-b^3[/tex]So, you have
[tex]\begin{gathered} (g\circ f)=(2x-3)^3+(2x-3) \\ (g\circ f)=(2x)^3-3(2x)^2(3)+3(2x)(3)^2-(3)^3+(2x-3) \\ (g\circ f)=2^3x^3-3(2^2x^2)(3)+3(2x)9-27+(2x-3) \\ (g\circ f)=8x^3-3(4x^2)(3)+54x-27+(2x-3) \\ (g\circ f)=8x^3-36x^2+54x-27+2x-3 \end{gathered}[/tex]Finally, operate similar terms
[tex](g\circ f)=8x^3-36x^2+56x-30[/tex]Find the value of x in the triangle shown below
The answer is C, the square root of 65 (8.062).
A writer counted the number of pages she wrote in one year. The graph shows the relationship between the number of short stories written, x, and the number of pages written, y. coordinate plane with the x axis labeled number of short stories and the y axis labeled number of pages with a line that passes through the points 0 comma 1 and 1 comma 3 Part A: Calculate the slope of the linear equation shown in the graph. Show all necessary work. (3 points) Part B: What does the slope mean for the relationship between the number of pages written and the number of short stories written? (3 points) Part C: Interpret the y-intercept in the situation. (3 points) Part D: Write the equation of the line shown on the graph in slope-intercept form. (3 points)
I hope this helps! Good luck! Lmk if you need more help dude.
Step-by-step explanation:
A. Slope formula: y2-y1/x2-x1
(0,1) and (1,3)
3-1/1-0=2
The slope is 2.
B. I think the slope means there are 2 pages for every 1 short story written.
C. y=2x+1
2 is the slope, we see the line crosses through at (0,1) so it is our y-intercept.
A. The slope of the linear equation is 2.
B. The slope indicates that the number of pages written increases by a constant rate of 2 pages.
C. The y-intercept means that the initial number of page is 1.
D. The equation of the line in slope-intercept form is y = 2x + 1.
How to determine the slope and equation of this graph?Part A. First of all, we would determine the slope of the line represented by this graph;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (7 - 3)/(3 - 1)
Slope (m) = 4/2 = 2.
Part B.
The meaning of the slope is that the number of pages written by this writer increases by 2 every year. Therefore, there are two number of pages for every (1) short story that is written by the writer.
Part C.
The y-intercept is located at point (0, 1) and in the context of the situation, it indicates that there is a page when the number of short story is equal to zero (0) or when there are no short stories written.
Part D.
In Mathematics and Geometry, the slope-intercept form of a straight line can be calculated by using the following mathematical equation:
y = mx + b
Where:
x and y represent the points.b is the y-intercept.m represent the slope.By substitution, a linear equation for the line is given by:
y = mx + b
y = 2x + 1
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Caleb wants to buy a pair of shoes that cost $49.95. He also wants to buy a T-shirt, but he cannot spend more than $60. He needs to calculate how much he can spend on a T-shirt. Which inequality models this situation?
Answer:
C) x + 49.95 ≤ 60Step-by-step explanation:
Let the cost of T-shirt is x.
The cost of pair of shoes is $49.95 and the total should be no more than $60.
This can be modeled as:
x + 49.95 ≤ 60The matching choice is C.
Fence A is 1 1/2 yards long but is 1 4/5 inches long on the blueprint. What is the unit rate per yard on this blue print? If fence B is 10 yard king,how long is fence B on the blueprint
The unit rate per yard is 0.03yards per unit
The length of fence B is 0.3yards
What is unit rate?A rate is a ratio that is used for comparing two different kinds of quantities which have different units. On the other hand, the unit rate illustrates how many units of quantity correspond to the single unit of another quantity. We say that when the denominator in rate is 1, it is called unit rate. In fact, unit rate is said to be the amount of something in each unit or per unit.
Fence A which is 1 1/2yards but 1 4/5inches on blueprint. 1 inch = 0.0278 yards
blueorint reading = 9/5×0.0278=0.05=5/100yards
therefore the scale is 3/2 : 5/100 = 3/2÷5/100
= 3/2×100/5= 1:30 = 0.03 :1
therefore the unit rate / yard = 0.03yardperunit
if a fence B is 10yards then on the blueprint it will be 10×0.03= 0.3yards
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Solve the system using the substitution technique:(−6, −3.6)(0.6, 0.8)(6, 4.4)(−0.6, 0)
Given
The system of equations,
[tex]\begin{gathered} -2x+3y=1.2\text{ \_\_\_\_\_}(1) \\ -3x-6y=1.8\text{ \_\_\_\_\_}(2) \end{gathered}[/tex]To find the solution using substitution technique.
Explanation:
It is given that,
[tex]\begin{gathered} -2x+3y=1.2\text{ \_\_\_\_\_}(1) \\ -3x-6y=1.8\text{ \_\_\_\_\_}(2) \end{gathered}[/tex]That implies,
[tex]\begin{gathered} (1)\Rightarrow-2x+3y=1.2 \\ \Rightarrow3y=1.2+2x \end{gathered}[/tex]And,
[tex]\begin{gathered} (2)\Rightarrow-3x-6y=1.8 \\ \Rightarrow-3x-2(3y)=1.8 \end{gathered}[/tex]Substitute 3y=1.2+2x in the above equation.
That implies,
[tex]\begin{gathered} -3x-2(1.2+2x)=1.8 \\ -3x-2.4-4x=1.8 \\ -7x=1.8+2.4 \\ -7x=4.2 \\ x=\frac{4.2}{-7} \\ x=-0.6 \end{gathered}[/tex]And, substitute x=-0.6 in (1).
That implies,
[tex]\begin{gathered} (1)\Rightarrow-2(-0.6)+3y=1.2 \\ \Rightarrow1.2+3y=1.2 \\ \Rightarrow3y=1.2-1.2 \\ \Rightarrow3y=0 \\ \Rightarrow y=0 \end{gathered}[/tex]Hence, the solution is (-0.6,0).
Please help me solve for X, I am including a picture
Answer:
x = 14
Explanation:
To get the value of x, we wll be using the SOH CAH TOA identity
Using sin theta = opposite/hypotenuse
[tex]\begin{gathered} sin45\text{ = }\frac{h}{7\sqrt[]{6}} \\ h\text{ =7}\sqrt[]{6}\text{ sin45} \\ h\text{ = 7}\sqrt[]{6}\times\frac{1}{\sqrt[]{2}} \\ h\text{ = 7}\sqrt[]{3} \end{gathered}[/tex]h is the vertical height of the triangles.
Next is to get the value of x;
Similarly;
[tex]\begin{gathered} \sin \text{ 60 = }\frac{h}{x} \\ \text{ sin60 = }\frac{7\sqrt[]{3}}{x} \\ x\text{ = }\frac{7\sqrt[]{3}}{\sin 60} \\ x\text{ = }\frac{7\sqrt[]{3}}{\frac{\sqrt[]{3}}{2}} \\ x\text{ = 7}\sqrt[]{3}\times\frac{2}{\sqrt[]{3}} \\ x\text{ = 7}\cdot2 \\ x\text{ =14} \end{gathered}[/tex]Hence the value of x required is 14
write an exponential function to model the situation. find the amount after the specified time. $1,000 principal, 3.6% compounded monthly for 10 years
We can model this problem by an exponential growth:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where A is the amount accumulated, P is the principal, r is the interest rate, n is the number of times per year and t is the time. By substituting our given data, we get
[tex]\begin{gathered} A=1000(1+\frac{0.036}{12})^{12t} \\ A=1000(1+0.003)^{12t} \end{gathered}[/tex]therefore, the model is
[tex]A=1000(1.003)^{12t}[/tex]Now, by substituting t=10 years, we have
[tex]A=1000(1.003)^{120}[/tex]then, the amount will be
[tex]A=1432.55\text{ dollars}[/tex]An = -8 - (n-1)2
what’s an equation equivalent
An = -2n-6
An = -2n-10
An = -8n -2
An = -2 - 8(1-n)
What is the volume of a hemisphere with radius 3 ft? What is the volume of a hemisphere with diameter 13 cm?
The volume of a sphere is given by
[tex]V_s=\frac{4}{3}\pi r^3[/tex]Since a hemisphere is half sphere, its volume is given by
[tex]\begin{gathered} V_{}=\frac{4}{6}\pi r^3 \\ \text{which is equivalent to} \\ V_{}=\frac{2}{3}\pi r^3 \end{gathered}[/tex]where r is the radius.
Case a.
In this part r=3 ft, then by substituting this values into our last formula we get
[tex]V=\frac{2}{3}(3.1416)(3^3)[/tex]which gives
[tex]V=56.55ft^3[/tex]Case b.
In this part r=(13/2) cm, then by substituting this values into our last formula we get
[tex]V=\frac{2}{3}(3.1416)(6.5^3)[/tex]which gives
[tex]V=287.59cm^3[/tex]If f(x) = x² +3,then f (x + h) =
The function is f(x) = x² +3,then f (x + h) = [tex]x^2+2xh +h^2+3[/tex].
Given,
In the question:
The function is given as:
f(x) = x² +3
To find the f (x + h) = ?
Now, According to the question:
Substitute x = x + h into f(x) = x² +3
f(x + h) = (x+ h)² +3
Expand the expression using:
[tex](a +b)^2 = a^2 +2ab+b^2[/tex]
f(x + h) = [tex]x^2+2xh +h^2+3[/tex]
Hence, The function is f(x) = x² +3,then f (x + h) = [tex]x^2+2xh +h^2+3[/tex].
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Please help topic is geometry
Image of point O(-2,-1) after two reflections , first across the line y=5 and then across the line x = 2 is (6,11) .
What do you mean by reflection in coordinate plane?
A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another. The reflected picture should have the same size and shape as the original, but it faces the opposite way. Changes in position during contemplation may also result in translation. Pre-image and image are terms used to refer to the same thing in this context.
Given point is O(-2,-1)
It is given that point O has reflected twice,
Firstly point O has reflected across the line y= 5
So, it become ,
(-2,11)
Secondly, it is reflected across the line x = 2
So, it become,
(6,11)
Hence, image of point O(-2,-1) after two reflections , first across the line y=5 and then across the line x = 2 is (6,11) .
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If you know that 84 is 70% of the whole, how can you use proportional reasoning to determine the whole?
70100 shows 70% as a ratio. The ratio 84x compares 84 to the whole, x. Write an equation so that the first ratio is equal to the second ratio. Solve for x : x = 120.
70100 shows 70% as a ratio. The ratio 84x compares 84 to the whole, x. Write an equation so that the first ratio is multiplied by the second ratio. Solve for x : x = 58.8.
70100 shows 70% as a ratio. The ratio x84 compares 84 to the whole, x. Write an equation so that the first ratio is multiplied by the second ratio. Solve for x : x = 120.
70100 shows 70% as a ratio. The ratio x84 compares 84 to the whole, x. Write an equation so that the first ratio is equal to the second ratio. Solve for x : x = 58.8.
The value of x is 120.
70/100 shows 70% as a ratio. The ratio x : 84 compares 84 to the whole, x. Write an equation so that the first ratio is multiplied by the second ratio. Solve for x : x = 120.
Given, that 84 is 70% of the whole.
Let the whole be x,
According to the question,
(70/100) × x = 84
On multiplying both the sides by 100/70, we get
x = 84×100/70
Now, on solving the expression, we get
x = 120
Hence, 70/100 shows 70% as a ratio. The ratio x : 84 compares 84 to the whole, x. Write an equation so that the first ratio is multiplied by the second ratio. Solve for x : x = 120.
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110.4 ÷4 step bye step show me pictures
we ahve
110.4 ÷4
so
110.4/4
Multiply by 10/10 the expression
1104/40
simplify
1104/40=552/20=276/10=27.6
the answer is 27.6
Im an older lady not the best at this type of math please help
We need to first find the intersection between Q and R, which is the common elements between both groups. We have:
[tex]Q\cap R=\mleft\lbrace r,e,x\mright\rbrace[/tex]Now we need to determine the union between them:
[tex]P\cup(Q\cap R)=\mleft\lbrace e,x,a,c,t,r,e,x\mright\rbrace[/tex]A sector with a radius \maroonD{18\,\text{cm}}18cmstart color #ca337c, 18, start text, c, m, end text, end color #ca337c has an area of \goldE{234\pi\,\text{cm}^2}234πcm 2 start color #a75a05, 234, pi, start text, c, m, end text, squared, end color #a75a05.
The formula for the area (A) of the sector is,
[tex]A=\frac{\theta}{360^0}\times\pi r^2[/tex]Given
[tex]\begin{gathered} r=18cm \\ A=234\pi cm^2 \end{gathered}[/tex]Therefore,
[tex]234\pi=\frac{\theta}{360}\times\pi(18)^2[/tex]Solve for θ
[tex]\begin{gathered} \frac{θ}{360}\pi \left(18\right)^2=234\pi \\ \frac{9\pi θ}{10}=234\pi \\ \frac{10\times \:9\pi θ}{10}=10\times \:234\pi \\ 9\pi θ=2340\pi \\ \mathrm{Divide\:both\:sides\:by\:}9\pi \\ \frac{9\pi θ}{9\pi }=\frac{2340\pi }{9\pi } \\ \thereforeθ=260^0 \end{gathered}[/tex]Hence, the answer is
[tex]260^0[/tex]The Associative Property applies to which operations? Check all that apply.
Hello! First, let's remember what is Associative Property:
It is a mathematical rule who says that the order of the factors doesn't change the final result of a calculus.
We have the associative property in two mathematical operations, I'll show you some examples:
If we want to sum three numbers, 5, 10 and 15, how is the right way? We have some ways to do it:
(5+10)+15 = (15)+15 = 30
(5+15)+10 = (20)+10 = 30
5+(10+15) = 5+(25) = 30
So, no matter the order of the numbers, we will always get the same result.
An example with the other operation now:
If we want to multiply three numbers, 2, 3 and 5:
(2*3)*5 = (6)*5 = 30
(2*5)*3 = (10)*3 = 30
2*(3*5) = 2*(15) = 30
Also, no matter the order of the factors, we'll always obtain the same result.
However, in the subtraction and in the division we have to follow the right order, according to the precedence, so we can't use the Associative Property on these operations.
Right answer: C and D.
Subtract 7x minus 8 from 2x^2- minus 1
Expression 2x²-(-1) - [7x-8] is equal to 2x² - 7x +9
Expression is combination of math operations , numbers and unknown variables.
Math operation can be subtraction , addition , multiplication or division.
There are two types of expression : numerical expression and algebraic expression . Expression consists of only numbers are numerical where expression containing numbers and variables are algebraic expression.
Subtract 7x-8 from 2x²-(-1)
2x²-(-1) - [7x-8]
product of two minus is plus
2x²+1 -[7x-8]
open the bracket and change the minus sign
2x²+1 - 7x + 8
there is no x² and x term so,
2x² - 7x +1+8
2x² - 7x +9 is our required expression
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Follow the steps to solve the equation.
Given equation is
[tex] \sqrt[3]{x {}^{2} - 7 } = \sqrt[3]{2x + 1} [/tex]
to solve this equation we first need to cube both the sides . As this would remove the cube root on both the sides ,
[tex]\longrightarrow (\sqrt[3]{x^2-7})^3 = (\sqrt[3]{2x+1})^3[/tex]
This would become ,
[tex]\longrightarrow x^2-7=2x+1 \\[/tex]
[tex]\longrightarrow x^2-2x-7-1=0\\[/tex]
[tex]\longrightarrow x^2-2x-8=0\\[/tex]
[tex]\longrightarrow x^2 -4x +2x -8=0\\[/tex]
[tex]\longrightarrow x(x-4)+2(x-4)=0\\ [/tex]
[tex]\longrightarrow (x+2)(x-4)=0\\[/tex]
[tex]\longrightarrow \underline{\underline{ x = 4,-2}} [/tex]
And we are done!
Answer:
[tex]\textsf{To solve the given equation, $\boxed{\sf cube}$ both sides}.[/tex]
Step-by-step explanation:
Given equation:
[tex]\sqrt[3]{x^2-7} =\sqrt[3]{2x+1}[/tex]
[tex]\textsf{Apply exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:[/tex]
[tex]\implies (x^2-7)^{\frac{1}{3}}=(2x+1)^{\frac{1}{3}}[/tex]
Cube both sides of the equation:
[tex]\implies \left( (x^2-7)^{\frac{1}{3}}\right)^3= \left((2x+1)^{\frac{1}{3}}\right)^3[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies (x^2-7)^{\frac{3}{3}}=(2x+1)^{\frac{3}{3}}[/tex]
[tex]\implies (x^2-7)^{1}=(2x+1)^{1}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^1=a:[/tex]
[tex]\implies x^2-7=2x+1[/tex]
Subtract 2x from both sides:
[tex]\implies x^2-2x-7=1[/tex]
Subtract 1 from both sides:
[tex]\implies x^2-2x-8=0[/tex]
Rewrite -2x as (-4x + 2x):
[tex]\implies x^2-4x+2x-8=0[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(x-4)+2(x-4)=0[/tex]
Therefore:
[tex]\implies (x+2)(x-4)=0[/tex]
Apply the zero-product property:
[tex]x+2=0 \implies x=-2[/tex]
[tex]x-4=0 \implies x=4[/tex]
7. Compare Ann and Barry Lindale's expenses for renting versus owning a home inthe table below.a. Complete each table.b. Is it less expensive for them to buy or rent a home, and what is the difference?
To complete the tables, we multiply the given numbers:
First table:
[tex]\begin{gathered} Rent:\text{ 850}\times12=10200, \\ Phone,\text{ Internet \& Cable TV: }99\times12=1188. \end{gathered}[/tex]Second table:
[tex]Phone,\text{ Internet \& Cable TV: }99\times12=1188.[/tex]Now, to determine which option is less expensive we compute the total annual expenses for each case:
1.-Rental:
[tex]10200+45+180+1560+2400+1188=15,573.[/tex]2.- Homeowner:
[tex]6600+3600+480+1710+2400+1188+570+960+1180=18,688.[/tex]From the above calculations, we can conclude that the cheaper option based on the given annual expenses is to rent.
Answer:Renting is less expensive.
Use the line of best fit to make a
conjecture about the value of
Heather's portfolio at the end of
year 8.
Answer: 25
Step-by-step explanation:
William is 4 years older than three times Alex's age . William is 31 years old . How old is Alex
Answer:
13
Step-by-step explanation:
.
Answer:
Alex is 14 years old.
Step-by-step explanation:
You can take William's age and divide it by 3, because William is 3 times the age of Alex:
31 divided by 3 = 10.33.
So, we will just say 10 for now.
Now, we add 4 to the 10 because WIlliam is 4 years older than three times his age.
So, in conclusion, Alex is 14 years old.
May I have Brainliest please? I am so close to getting my next ranking! I just need 2 more for it! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
Ava ,cole and Zane have a total of 175 stickers.the ratio of the number of stickers Ava has to the number of stickers cole has is 5:3. The ratio of the number of the number of stickers cole has to the number of stickers Zane has in 2:3. How many stickers do Ava have?
Ava has 70 stickers.
Given that the ratio of the number of stickers Ava has to the number of stickers Cole has = 5:3 = 10:6
Also, the ratio of the number of stickers Cole has to the number of stickers Zane has = 2:3 = 6:9
Thus, the compounded ratio of the number of stickers Ava, Cole and Zane has is = 10:6:9
Let the numbers of stickers of Ava has be = 10x
The number of stickers of Cole has, is = 6x
The number of stickers of Zane has, is = 9x
According to question, the total number of stickers they have is 175. So,
10x+6x+9x = 175
25x = 175
x = 175/25
x = 7
Hence Ava has = 10x = 10*7 = 70 stickers.
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Using the counting principle determine the number of elements in the sample space. Two digits are selected without replacement from the digits 1,2,3,4,5 and 6
Consider the experiment of picking one digit first from the initial set (digits from 1 t) 6, and then pgrabbing a second digit without eplace,ment.
As for the first part of the experiment, there are 6 digits to choose from; however, during the second round, there are only 5 digits available. Therefore, according to the counting principle, the sample space has
[tex]6*5=30[/tex]30 elements. he answer is 30 elements in the sampele space.
Write the coefficient of x in the following terms
3. xy
1. 24x
4. x
2. abx
5. 3xy
6. xyz
Answer:
1. 1
2. 24
3. 1
4. 1 [ab]
5. 3
6. 1
Step-by-step explanation:
Every variable or alphabet's coefficient is the number on the left of it.
e. g coefficient of x is 1.
or coefficient of 83x is 83