One positive number is 8 times another number. Their difference is 70.
Which of the following equations could be used to find the numbers?
Answer:
X equals 10.
8x - x = 70
Step-by-step explanation:
8 x 10 = 80
80 - 10 = 70
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: a = -1[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
For a function f(x) = y,
x represents the value ( x - coordinate ) at which the function has a value y.
[tex]\qquad \tt \rightarrow \: f(x) = a {x}^{2} + 2[/tex]
for point (-1 , 1) to satisfy the equation, we have to calculate the value of a
[tex]\qquad \tt \rightarrow \: f( - 1) = a( - 1) {}^{2} + 2[/tex]
[tex]\qquad \tt \rightarrow \: 1 = a + 2[/tex]
[tex]\qquad \tt \rightarrow \: a = 1 - 2[/tex]
[tex]\qquad \tt \rightarrow \: a = - 1[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Substitute -1 into x
Substitute 1 into y
f(x)= a (-1) ^2+2=1
a=-1
Find an equation for the line that passes through the point P(-5,-3) and is parallel to the line
7x + 4y
10. Use exact values.
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{y = -1.75x - 11.75}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{Goes through (-5, -3) and parallel to 7x + 4y = 10}[/tex]
Find: [tex]\textsf{The equation in slope-intercept form}[/tex]
Solution: We need to first solve for y in the equation that was provided so we can determine the slope. Then we plug in the values into the point-slope form, distribute, simplify, and solve for y to get our final equation.
Subtract 7x from both sides
[tex]\textsf{7x - 7x + 4y = 10 - 7x}[/tex][tex]\textsf{4y = 10 - 7x}[/tex]Divide both sides by 4
[tex]\textsf{4y/4 = (10 - 7x)/4}[/tex][tex]\textsf{y = (10 - 7x)/4}[/tex][tex]\textsf{y = 10/4 - 7x/4}[/tex][tex]\textsf{y = 2.5 - 1.75x}[/tex]Plug in the values
[tex]\textsf{y - y}_1\textsf{ = m(x - x}_1\textsf{)}[/tex][tex]\textsf{y - (-3) = -1.75(x - (-5))}[/tex]Simplify and distribute
[tex]\textsf{y + 3 = -1.75(x + 5)}[/tex][tex]\textsf{y + 3 = (-1.75 * x) + (-1.75 * 5)}[/tex][tex]\textsf{y + 3 = -1.75x - 8.75}[/tex]Subtract 3 from both sides
[tex]\textsf{y + 3 - 3 = -1.75x - 8.75 - 3}[/tex][tex]\textsf{y = -1.75x - 8.75 - 3}[/tex][tex]\textsf{y = -1.75x - 11.75}[/tex]Therefore, the final equation in slope-intercept form that follows the information that was provided is y = -1.75x - 11.75
How many pounds of candy that sells for $0.82 per lb must be mixed with candy that sells for $1.36 per lb to obtain 9 lb of a mixture that should sell for $0.91 per lb?
7.5 pounds of the $0.82 per lb candy must be used in the mixture.
How many pounds of each candy should we use?First, let's define the variables:
x = pounds of the $0.82 candy used.y = pounds of the $1.36 candy used.We want to make 9 lb of mixture, then:
x + y = 9.
And the price of these 9 pounds must be $0.91, then we can write:
x*$0.82 + y*$1.36 = 9*$0.91 = $8.19
Then we have a system of equations:
x + y = 9.
x*$0.82 + y*$1.36 = $8.19
We can isolate y on the first equation so we get:
y = 9 - x
Now we can replace that on the other equation:
x*$0.82 + (9 - x)*$1.36 = $8.19
And now we can solve this for x.
x*($0.82 - $1.36) = $8.19 - 9*$1.36
-x*$0.54 = -$4.05
x = (4.05/0.54) = 7.5
So 7.5 pounds of the $0.82 per lb candy must be used in the mixture.
If you want to learn more about systems of equations:
https://brainly.com/question/13729904
#SPJ1
T(h) = - A - B * cos((pi*h)/12) Where T is the temperature in degrees Fahrenheit and h is the number of hours from midnight (0 <= h <= 24) . a. The initial temperature at midnight was - 15 degrees * F and at Noon of New Year's Day it was 5 degrees * F Find A and B. b. Find the average temperature for the first 10 hours. C. Find an expression for the rate that the temperature is changing with respect to h.
The value of A and B is 5 , 10 ;The average temperature for first ten hours is -7.466 degree F ; an expression for the rate that the temperature is changing with respect to h ; dt/dh = +B sin ((pi*h)/12)
What is a Function ?A function is a mathematical statement used to correlate two variables.
The function given is
T(h) = - A - B * cos((pi*h)/12)
T is the temperature in degrees Fahrenheit and
h is the number of hours from midnight (0 <= h <= 24)
a. The initial temperature at midnight was - 15 degrees * F and
at Noon of New Year's Day it was 5 degrees * F
At midnight h = 0
T(h) = -15 degrees F
-15 = -A-B* cos 0
-15 = -A-B
A+B = 15------------------- (1)
At noon , h = 12 , T(h)= 5
- A - B* cos(pi) = 5
-A - B (-1) = 5
B -A = 5 ----------------------- (2)
Solving equation 1 and 2
2B = 20
B = 10
A = 5
The value of A and B is 5 , 10
The average temperature for first ten hours is -7.466 degree F
Find an expression for the rate that the temperature is changing with respect to h
dt/dh = +B sin ((pi*h)/12)
To know more about Function
https://brainly.com/question/12431044
#SPJ1
Select the correct answer from each drop-down menu.
Consider the function Ax) = 3x+ 1 and the graph of the function g(x) shown below.
Answer:
write three methods of writing set. Give one example of each methods.
What is the simplified form of √ 144x36?
Answer:
12x^18
Step-by-step explanation:
What are m and b in the linear equation y=16+6x
Answer: B=16 and m=6
Step-by-step explanation:
in y=mx+b the number next to x is always the m/slope and the number without a variable is always the b.
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex] \texttt{ \:The absolute maxima of f is f(-8) = 6} [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Absolute maxima is the maximum possible value for a given x, of a function.
and here, the maximum value is at -8, and the maximum value is 6.
[tex]\qquad \tt \rightarrow \: maximum - \: \: f( - 8) = 6[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
What is the value of x in the equation 1/5x - 2/3y=30 when y= 15
Substituting in y=15,
[tex]\frac{1}{5}x-\frac{2}[3}(15)=30\\\\\frac{1}{5}x-10=30\\\\\frac{1}{5}x=40\\\\x=\boxed{200}[/tex]
Which graph shows y=1/2⌈x⌉?
The correct answer is option B which is the graph that represents the equation y = (1/2)x will be the second option in the figure. At every value of y, the value of x is double.
What is a graph?A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
The graph of the equation y =1/2x is represented in the answer below we can see in the graph that at every value of y the value of x is double for example if we put y = 1 then the value of x will be 2.
y = 1/2 x
at x = 2
y = 1/2 x 2
x = 1
Therefore the correct answer is option B which is the graph that represents the equation y = (1/2)x will be the second option in the figure. At every value of y, the value of x is double.
To know more about graphs follow
https://brainly.com/question/25020119
#SPJ1
Which expression can be used to convert 80 US to Australian dollars?
Answer:
0.9668 USD
Step-by-step explanation:
1 USD=1.0343 AUD 1AUD=0.9668 USD.
can someone please help me solve this question step by step not just give me the answer I want to learn lol
find f(x)•g(x)
if f(x)=8x+1 and g(x)=-5+9.
Answer: 32x+4
Step-by-step explanation:
[tex]f(x) \cdot g(x)=(8x+1)(-5+9)=4(8x+1)=\boxed{32x+4}[/tex]
can someone help me asap :)
Answer:
Option 2 - TU is perpendicular to MN and MN is parallel to PQangle M = angle P ( 90°)
so MN is parallel to pq
MN makes 90° with UT so it is perpendicular
Can someone answer this question for me? Thanks!
Answer:
The costco basmati rice
Step-by-step explanation:
Under the label it is given that the bag is 18.14 kg
When converted to lbs= 18.14*2.2~39.91
39.91lbs>10lbs, so it has more quantity of rice: Costco Basmati
Answer:
The Costco bag is a better deal as each pound is $0.65 cheaper
Step-by-step explanation:
Let make the weight of each bag in a common unit
18.14kg = about 40 pounds (formula: multiply the mass value by 2.205)
Now find how much it cost per pound for each bag,
Costco: 49.99 / 40 = $1.25 per pound
Bulkmarket: 18.99 / 10 = $1.90 per pound
1.25 < 1.90
The amount of a pollutant (measured as parts per million) in a local lake can be modeled by the function of A(t)=14(2.71)^-.016*t, where t is the number of years since a government program was began to help clean up the lake. About how long will it take for the amount of pollutant to reach 7 parts per million?
Solving the exponential function, it is found that it will take 43.5 years for the amount of pollutant to reach 7 parts per million.
What is the exponential function for the amount of the substance?It is given by, after t years:
[tex]A(t) = 14(2.71)^{-0.016t}[/tex]
It will reach an amount of 7 parts per million when A(t) = 7, hence:
[tex]A(t) = 14(2.71)^{-0.016t}[/tex]
[tex]7 = 14(2.71)^{-0.016t}[/tex]
[tex](2.71)^{-0.016t} = 0.5[/tex]
[tex]\log{(2.71)^{-0.016t}} = \log{0.5}[/tex]
[tex]-0.016t\log{(2.71)} = \log{0.5}[/tex]
[tex]t = -\frac{\log{0.5}}{0.016\log{2.71}}[/tex]
t = 43.5.
More can be learned about exponential functions at https://brainly.com/question/25537936
#SPJ1
A sells an article to B at profit of 20% and B sells it to C at a profit of 25%. If C buys it for Rs.225, what did A pay for it?
Answer:
A pay 120 for itLet the cost price be X
A Sells to B
profit = 20%
= cost price + 20%
= X + 20/100 of X
= 6x/ 5
B sells to C
profit = 25%
= Cost price + + 25%
= cost price + 25%
= 6x/5 + 25/100*6x/5
= 6x/5.+ 3x/10.
= 3x/2
3x/2 = 225.
3x = 450
x = 150.
sp = C. p + profit
S. p - profit = C. p
X - X/5
4x/5
4(150)/5.
120
What is the value of 6¹?
6° = 1
6 = 6
6 = 36
6 = 216
Answer:
6=6
Step-by-step explanation:
This is because the exponent is multiplying it by one so technically you don't have to do anything but multiply 6*1
Hope this helps
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Fun fact: ANY number powered to the}\\\huge\textbf{1 it automatically that number(just }\\\huge\textbf{regular multiplication).}[/tex]
[tex]\mathsf{6^1}\\\\\\\mathsf{\approx 6\times1}\\\\\\\large\text{So, you're making it 6 ONE TIME}\\\\\mathsf{= \bf 6}\\\\\\\\\\\\\huge\text{Thus, your answer should be: \boxed{\mathsf{Option\ B.\ 6^1 = 6}}}\huge\checkmark[/tex]
[tex]\large\text{Random\ note\ for\ rest\ of\ equations:}\\\\\mathsf{6^0\rightarrow \bf 1}\\\\\mathsf{6^2\rightarrow 6\times 6 \rightarrow \bf 36}\\\\\mathsf{6^3\rightarrow 6\times6\times6\rightarrow 36\times6\rightarrow \bf 216}[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
(7 + 7i)(2 − 2i)
(a) Write the trigonometric forms of the complex numbers. (Let
0 ≤ < 2.)
(7 + 7i) =
(2 − 2i) =
(b) Perform the indicated operation using the trigonometric forms. (Let
0 ≤ < 2.)
(c) Perform the indicated operation using the standard forms, and check your result with that of part (b).
The complex number -7i into trigonometric form is 7 (cos (90) + sin (90) i) and 3 + 3i in trigonometric form is 4.2426 (cos (45) + sin (45) i)
What is a complex number?It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.
We have a complex number shown in the picture:
-7i(3 + 3i)
= -7i
In trigonometric form:
z = 7 (cos (90) + sin (90) i)
= 3 + 3i
z = 4.2426 (cos (45) + sin (45) i)
[tex]\rm 7\:\left(cos\:\left(90\right)\:+\:sin\:\left(90\right)\:i\right)4.2426\:\left(cos\:\left(45\right)\:+\:sin\:\left(45\right)\:i\right)[/tex]
[tex]\rm =7\left(\cos \left(\dfrac{\pi }{2}\right)+\sin \left(\dfrac{\pi }{2}\right)i\right)\cdot \:4.2426\left(\cos \left(\dfrac{\pi }{4}\right)+\sin \left(\dfrac{\pi }{4}\right)i\right)[/tex]
[tex]\rm 7\cdot \dfrac{21213}{5000}e^{i\dfrac{\pi }{2}}e^{i\dfrac{\pi }{4}}[/tex]
[tex]\rm =\dfrac{148491\left(-1\right)^{\dfrac{3}{4}}}{5000}[/tex]
=21-21i
After converting into the exponential form:
[tex]\rm =\dfrac{148491\left(-1\right)^{\dfrac{3}{4}}}{5000}[/tex]
From part (b) and part (c) both results are the same.
Thus, the complex number -7i into trigonometric form is 7 (cos (90) + sin (90) i) and 3 + 3i in trigonometric form is 4.2426 (cos (45) + sin (45) i)
Learn more about the complex number here:
brainly.com/question/10251853
#SPJ1
Need help anyone please!!!
A number is equal to the sum of half a second number and 3. The first number is also equal to the sum of one- quarter of the second number and 5. The situation can be represented by using the graph below, where x represents the second number. 16 NO 8 K 3₂ 5 2 4 st 6 8 10 12 14 16 Which equations represent the situation? Hurry
Need help with the following question
which expression is equivalent to...
Answer:
B
Step-by-step explanation:
|4x + 7| − 4 = 20
Can anyone help me with this
Answer:
x = -31/4 or x = 17/4
Step-by-step explanation:
|4x + 7| − 4 = 20
⇔ |4x + 7| − 4 + 4 = 20 + 4
⇔ |4x + 7| = 24
⇔ 4x + 7 = 24 or 4x + 7 = -24
⇔ 4x = 24 - 7 or 4x = -24 - 7
⇔ 4x = 17 or 4x = -31
⇔ x = 17/4 or x = -31/4
Answer:
x = [tex]\frac{17}{4}[/tex] (17/4 = 4.25)
or x = [tex]-\frac{31}{4}[/tex] (-31/4 = -7.75)
Step-by-step explanation:
| | is notation for absolute value
absolute value - the distance that a number is from 0
> essentially, you can think of absolute value as the "positive version" of whatever is inside of the | |
if we have | x | = 20, we could really have (without the | | ) two versions of x
either | x | = 20 ; or | -x | = 20 {because a negative x inside of the | | has the same value as positive x}
we set this up as two equations:
x = 20 or -x = 20
^ {multiply by -1}
x = 20 or x = -20
now, let's plug our understanding into the equation
|4x + 7| - 4 = 20
first, we should simplify our equation to:
|4x + 7| - 4 = 20
+ 4 + 4
|4x + 7| = 24
now, let's separate this absolute value equation into two separate equations:
4x + 7 = 24:
- 7 - 7 {subtract 7 from both sides to isolate x}
4x = 17
÷4 ÷4 {divide both sides by 4 to get 1x}
x= [tex]\frac{17}{4}[/tex]
or,
4x + 7 = -24:
- 7 -7 {subtract 7 from both sides to isolate x}
4x = -31
÷4 ÷4 {divide both sides by 4 to get 1x}
x = [tex]-\frac{31}{4}[/tex]
so, we know that
x = [tex]\frac{17}{4}[/tex] (17/4 = 4.25)
or x = [tex]-\frac{31}{4}[/tex] (-31/4 = -7.75)
hope this helps!!
Find the area of the trapezoid. TOP 11ft, RIGHT4√3ft , BOTTOM 15ft ,LEFT 8ft
Answer:
[tex]52\sqrt{3} ft^{2}[/tex]
Step-by-step explanation:
Please refer to the attached picture.
First we will find the area of rectangle BCDE.
Area of Rectangle = Length x Breadth = DE x CD
= 11 x [tex]4\sqrt{3}[/tex]
[tex]=44\sqrt{3} ft^{2}[/tex]
Next we will find Area of Triangle ABE.
Area of Triangle = 0.5 x Base x Height
[tex]0.5*4*4\sqrt{3} \\=8\sqrt{3} ft^{2}[/tex]
Area of Trapezoid = Area of Rectangle + Area of Triangle
[tex]=44\sqrt{3} +8\sqrt{3} \\=52\sqrt{3} ft^{2}[/tex]
Answer:
A = 52[tex]\sqrt{3}[/tex] ft² ≈ 90.1 ft²
Step-by-step explanation:
the area (A) of a trapezoid is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )
where h is the perpendicular height and b₁ , b₂ the parallel bases
here h = 4[tex]\sqrt{3}[/tex] , b₁ = 15 , b₂ = 11 , then
A = [tex]\frac{1}{2}[/tex] × 4[tex]\sqrt{3}[/tex] × (15 + 11)
= 2[tex]\sqrt{3}[/tex] × 26
= 52[tex]\sqrt{3}[/tex] ft²
≈ 90.1 ft² ( to the nearest tenth )
It has been estimated that only about 40% of California residents have adequate earthquake supplies suppose you randomly survey 22 California residents we are interested in the number who have adequate earth quake supplies
The answers are as follows:
a) X denotes the number of the california residents that have adequate earthquake insurance
b) x = 1 ,2 ,3 ......
c) P( X=x ) = 0.3(1-0.3) ^ (x-1)
d) P( X=1) + P( X=2) + P( X=3) + P( X=4)
e) 0.49
f)0.42
g)0.33
What is probability?It is a branch of mathematics that deals with the occurrence of a random event.
The complete question is
It has been estimated that only about 30% of California residents have adequate earthquake supplies. Suppose we are interested in the number of California residents we must survey until we find a resident who does not have adequate earthquake supplies. a. In words, define the random variable X. b. List the values that Xmay take on. c. Give the distribution of X.X~ _____(_____,_____) d. WhatistheprobabilitythatwemustsurveyjustoneortworesidentsuntilwefindaCaliforniaresidentwhodoes not have adequate earthquake supplies? e. What is the probability that we must survey at least three California residents until we find a California resident who does not have adequate earthquake supplies? f. HowmanyCaliforniaresidentsdoyouexpecttoneedtosurveyuntilyoufindaCaliforniaresidentwhodoesnot have adequate earthquake supplies? g. How many California residents do you expect to need to survey until you find a California resident who does have adequate earthquake supplies?
given that 30% of California residents have adequate earthquake supplies.
a) variable X denotes the number of the california residents that have adequate earthquake insurance
b) x = 1 ,2 ,3 ......
c) p=0.3
P( X=x ) = 0.3(1-0.3) ^ (x-1)
d) P( X=1) + P( X=2) + P( X=3) + P( X=4)
= 0.3(1-0.3) ^ 0 + 0.3(1-0.3) ^1 + 0.3(1-0.3)^ 2 +...
e) P( X≥ 3) = 1- P(X<3)
= 1- (P(X=1) + (X=2))
= 1- 0.051
= 0.49.
f) E(X)= 1/P
p is the resident who does not have adequate earthquake supplies
p= 1-0.3
p = 0.7
E(X) = 1/0.7
= 0.42
g) E(X) = 1/q
= 1/0.3
= 3.333
Learn more about this concept here:
https://brainly.com/question/15512751
#SPJ1
I need the answer for number 4 please!!
Answer:
-3 - false
0 - true
1 - true
2 - false
4 - true
Step-by-step explanation:
the "zeros" of a function are its x-intercepts
(because that is when the function = zero [0])
So, we can look at the x-intercepts of the graph to find the zeros:
at 0, 1, and 4 the function = 0, meaning that those are zeros of the function
hope this helps!! have a lovely day :)
March 8, 2017, one U.S. dollar was worth 66.79 Indian rupees.
a) On that date, how many dollars was 110.66 rupees worth?
Round your answer to the nearest hundredth of a dollar. I need help with this question.
[tex] \huge \tt \underline {\green{Answer}}[/tex]
If on March 8, 2017 , one U.S. dollar worth 66.79 Indian rupees
ie. $1 = Rs 66.79
$ 1 = 66.79 × 1
$ ? = 110.66
$ = New / old
$ = 110.66 / 66.79
$ = 1.65683485552
or
$1.66 = 110.66
I need help ASAP please
Which statement is true about whether Z and B are independent events?
A: Z and B are independent events because P(Z | B) =P(Z).
B: Z and B are independent events because P(Z | B) = P(B).
C: Z and B are not independent events because P(Z | B) ≠ P(Z).
D: Z and B are not independent events because P(Z | B) ≠ P(B).
Find the value below using your calculator. Round to the nearest hundredth. e³ Find the value below using your calculator . Round to the nearest hundredth . e³
The value of e³ = 20.079.
What is Euler's number , e ?e is an irrational number , It is a numerical constant used in mathematical constant .
The value of e = 2.718
It is asked in the question to determine the value of e³
Therefore
e³ = ( 2.718)³
e³ = 20.079
Therefore the value of e³ = 20.079.
The image of the calculation is attached with the answer.
To know more about Euler's number
https://brainly.com/question/573685
#SPJ1
