Answer:
[tex] \boxed{ \bold { \huge{ \boxed{ \sf{2x - 14}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{2(3x + 7) - 4(7 + x)}[/tex]
Distribute 2 through the parentheses
⇒[tex] \sf{6x + 14 - 4(7 + x)}[/tex]
Distribute 4 through the parentheses
⇒[tex] \sf{6x + 14 - 28 - 4x}[/tex]
Collect like terms
⇒[tex] \sf{6x - 4x + 14 - 28}[/tex]
⇒[tex] \sf{2x + 14 - 28}[/tex]
Calculate
⇒[tex] \sf{2x - 14}[/tex]
Hope I helped!
Best regards!!
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{2(3x + 7) - 4(7 + x)}}\\\\{\mathsf{= 2(3x) + 2(7) - 4(7) - 4(x)}}\\\\\mathsf{= 6x + 14 - 28 - 4x}\\\\\mathsf{= (6x - 4x) + (14 - 28)}\\\\\mathsf{= 2x - 14}\\\\\huge\textbf{Therefore, your answer is: \boxed{\mathsf{2x - 14}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Which tables display linear functions?Check all that apply
Please help me!!!!!
Answer:
The first one and the last one. A and D.
Step-by-step explanation:
A linear equation is and equation where the line is going up on a graph. In order for that to happen, y must always be bigger than x. The first and last chart all the way to the right is the only one that has that trait. :)
Find the distance that 5,2 is from the origin
Answer:
Step-by-step explanation:feel pleasure to help u.
What value does the 1 represents in the number 4,105.8
Answer:
the 1 represents the value of 100 of one-hundreth place
Step-by-step explanation:
Two rectangles have equal areas. If the base and altitude of one are 12mm and 8mm, and the base of the other is 16mm, what is the altitude of the second rectangle?
Answer:
6mm
Explanation:
since the area of both rectangle is equal, therefore :
Arectangle 1= Arectangle 2
base 1*altitude 1 =base 2*altitude 2
12mm*8mm = 16mm* altitude 2
96mm²= 16mm* altitude 2
96mm²/16mm = altitude 2
6mm = altitude 2
free cus i have 300,000 - 100 = ?
Answer:
Step-by-step explanation:
300,000-100
300,00 + -100
=299900
Answer:
299900
Step-by-step explanation:
you invested $27000 in two account paying 2% and 8% annual interest respectively of the total interest earned for the year was $2100 how much was invested at each rate? the amount invested at 2% is
Answer:2100
Step-by-step explanation:
A party planner is going to use an arch of balloons for a parade of recent graduates. The estimated curve the
balloons will create is modeled by the function given in the table, where x represents the distance in feet along
the ground from the start and f(x) represents the height in feet above the ground.
The planner needs a clearance of 9 feet under the arch. Has the planner met the minimum height?
No, because the width of the arch is 8 feet
Yes, because the width of the arch is 9.6 feet
No, because the maximum height of the arch is 8 feet
Yes, because the maximum height of the arch is 9.6
feet
Answer:
Option (4)
Step-by-step explanation:
Party planner has used an arc of balloons for the parade.
This arc starts from x = 0 along the ground and f(x) defines the height of the arch.
From the table attached, it is clear that at x = 4 maximum height of the arch is 9.6 feet.
Therefore, clearance space below the arc is 9.6 feet which is greater than 9 feet, minimum height required for the clearance of the parade.
Option (4) will be the answer.
Answer:
D. yes, because the maximum height of the arch is 9.6 feet
Step-by-step explanation:
EDGE 2020 :)
What is the area of this triangle?
Answer:
21 units²
Step-by-step explanation:
A=1/2bh
b=6
h=7
1/2(6)(7)=
1/2(42)=
21 units²
consider the geometric sequence: 1, 3, 9, 27, ...
if n is an integer, which of these functions generate the sequence?
a) a(n)=3^n for n greater than or equal to 0
b) b(n)=3(3)^n for n greater than or equal to 0
c) c(n)=3^n for n greater than or equal to 2
d) d(n)=3^n-1 for n greater than or equal to 2
PLS ANSWER ASAPP!!
Answer:
The answer is option DStep-by-step explanation:
Since the sequence is a geometric sequence
For an nth term in a geometric sequence
[tex]A(n) = a ({r})^{n - 1} [/tex]
where
n is the number of terms
a is the first term
r is the common ratio
To find n we must first find the common ratio
To find the common ratio divide the previous term by the next term
That's
r = 3/1 = 3 or r = 9/3 = 3
a = 1
Substitute the values into the above formula
That's
If n is an integer then
[tex]A(n) = 1 ({3})^{n - 1} [/tex]
[tex]A(n) = {3}^{n - 1} [/tex]
where n is greater than or equal to 2
Hope this helps you
The function that describes the sequence is the first one:
a(n) = 3ⁿ fpr n ≥ 0.
Which function generates the sequence?Here we have the following sequence:
1, 3, 9, 27, ...
We can see that all of these are powers of 3, and the function must behave like:
f(0) = 1
f(1) = 3
f(2) = 9
...
And so on, then the function must be:
a(n) = 3ⁿ
when n = 0 we have:
a(0) = 3⁰ = 1
When n = 1
a(1) = 3¹ = 3
And so on.
Then we can see that the correct option is the first one.
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a company needs to refill printing paper. each one of printing paper costs $30 and a delivery fee of $10. write an equation to find the total cost of purchasing x number of boxes of printing paper.
Answer:
Cost in $= x(y(30))+10
Step-by-step explanation:
a company needs to refill printing paper. each one of printing paper costs $30 and a delivery fee of $10.
Let y be the number of paper in a box
Let x be the number of box to be purchased.
So it means for each x box, there are y paper costing $30 and a delivery fee for the box is $10
Cost in $= x(y(30))+10
A 1,000 ohm resistor has a tolerance of 20%. This means that the resistor actual value can be +-20%. What's the acceptable range of values for this resistor
Answer:
[800, 1200]
Step-by-step explanation:
We need to calculate the acceptable range of values for this resistor. The center point would be the nominal resistance: 1000 ohms.
20% above that would be 1.20(1000 ohms) = 1200 ohms, and 20% below would be (0.80)(1000 ohms) = 800 ohms.
Thus, the acceptable resistance range in ohms is [800, 1200]
Please help me with this is important and I’ll give you a brainless if the answer is right
Answer:
She subtracted 5 and got 6 instead of subtracting -5 which is 16
Step-by-step explanation:
11 - (-5)
Subtracting a negative is like adding
11 +5
16
She subtracted 5 and got 6 instead of subtracting -5 which is 16
solve for z? 2x-4y+4z-6w=4 6w-4x+4y-4z=-12 6w+4x-2y+6z=64 4z+2w+6y-4x=56
Answer:
z ≈ 9.22
Step-by-step explanation:
Given the equations
2x-4y+4z-6w=4 ................ 1
6w-4x+4y-4z=-12 ...............2
6w+4x-2y+6z=64 ............... 3
4z+2w+6y-4x=56 ................ 4
We will first need to reduce the equation by cancelling out some variables.
Add equations 1 and 2 will give;
(2x-4x)+(-4y+4y)+(4z-4z)+ (-6w+6w) = 4+12
-2x +0 = 16
-2x = 16
x = -8
Also, equation 2 minus 3
6w-6w+(-4x-4x)+4y+2y+(-4z-6z) = 12-64
-8x+6y-10z = -52
-8(-8)+6y-10z = -52
64+6y-10z = -52
6y-10z = -52-64
6y-10z = -116
3y-5z = -58 ... 5
Equation 3 * 1 and eqn 4 * 3
6w+4x-2y+6z=64 ............... 3
4z+2w+6y-4x=56 ................ 4
6w+4x-2y+6z=64
12z+6w+18y-12x= 168
Subtracting both equations;
16x-20y-6z = -104
8x-10y-3z = -52
8(-8)-10y-3z = -52
-64-10y-3z = -52
-10y-3z = -52+64
-10y-3z = 12 ....... 6
equating 5 and 6 and solving simultaneously;
3y-5z = -58 ... 5 * 10
-10y-3z = 12 ....... 6 * 3
30y-50z = -580
-30y-9z = 36
Add both equations
-50z-9z = -580+36
-59z = -544
z = -544/-59
z = 9.22
Hence z ≈ 9.22
the first three terms of an arithmetic progression is (x + 1), (4 x - 2) and 6 x - 3 if the last term is 18 find the value of x
Answer:
2
Step-by-step explanation:
Since it is AP, the common difference is same for any term:
(4x - 2) - (x + 1) = (6x - 3) - (4x - 2)3x - 3 = 2x -13x - 2x = 3 - 1x= 2The first 3 terms are:
3, 6, 9Since the last term is 18, it means this AP has 6 terms:
{3, 6, 9, 12, 15, 18}Answer: as we need to find the value of x only, it is = 2
Write an algebraic expression for the word expression.
the sum of 9 and a number x
The expression is ___
Answer: 9 + x
The word "sum" indicated that we are adding the two numbers, so we put the number and the variable in an expression that adds them together. There is no indication that there is anything else we need to add to this expression, so this is all you need. (The "x" is a variable, which can represent any number.)
The algebraic expression for the word expression is the sum of 9 and a number x will be 9 + x.
What is an expression?An expression is a combination of some mathematical symbol such that an arithmetic operator and variable such that all are constrained and create an equation.
In other meaning, expression is very useful to determine the end or root value of constraint.
As per the given phrase,
The sum of 9 and the number x.
The sum is an addition and represents by the symbol "+".
Therefore, 9 + x
Hence "The algebraic expression for the word expression is the sum of 9 and a number x will be 9 + x".
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(10+i)^2 = (in form a+bi)
Answer:
99+20i
Step-by-step explanation:
(10+i)^2
➡
(10 + i) × (10 + i) = 100 + 10i + 10i + i^2 add like terms
100 + 20i + i^2 since i^2 = -1 we can write the expression like this
99 + 20i
Over 4 days the temperature was 4, 6, -12, and -5 degrees. What was the average temperature?
Answer:
-1.75
Step-by-step explanation:
add -12 and -5, you get -17, and 4 and 6, get 10, add -17 and 10 to get -7, and divide by 4 and get -1.75
Calculate the expected value of X, E(X), for the given probability distribution. E(X):_________
x 0 1 2 3
P(x) 0.5 0.1 0.1 0.3
Answer:
The expected value of X, E(X), for the given probability distribution is 1.2
Step-by-step explanation:
Mathematical hope (also known as hope, expected value, population means or simply means) expresses the average value of a random phenomenon and is denoted as E(x).
Hope is the sum of the product of the probability of each event and the value of that event. That is, it is the sum of the probability of each possible event multiplied by the frequency of said process, this indicates that if you have a discrete quantitative variable X with "n" possible events x₁, x₂, x₃... xₙ and probabilities P (X = xi) = Pi the mathematical expectation is:
E(x)=x₁*P₁ + x₂*P₂ + x₃*P₃ + ... + xₙ*Pₙ
In this case:
E(x)=x₁*P₁ + x₂*P₂ + x₃*P₃ + x₄*P₄
Being:
x₁: 0 P₁: 0.5x₂: 1P₂:0.1 x₃:2P₃:0.1 x₄: 3P₄: 0.3and replacing:
E(x)= 0* 0.5 + 1* 0.1 + 2*0.1 + 3*0.3
you get:
E(x)= 1.2
The expected value of X, E(X), for the given probability distribution is 1.2
True or false: the coordinate grid below shows the triangle transformed following the rule : (x,y)-> (x-4,y+3)
Answer: True
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
Step 1: Find the Coordinates of the Original Triangle
(2, -2)
(6, -3)
(5, 2)
Step 2: Apply the Transformation to the Coordinates
(2-(4),-2+(3)) -> (-2, 5)
(6-(4),-3+(3)) -> (2, 0)
(5-(4),2+(3)) -> (1, 5)
Step 3: Compare the points on the red triangle with the points you got
(-2, 5) = (-2, 5)
(2, 0) = (2, 0)
(1, 5) = (1, 5)
Because the coordinates are the same we can conclude that the triangle was transformed with the rule: (x,y)-> (x-4,y+3)
On his fishing trip Justin rides on hist 12 km south. The fish aren’t biting so he changes location and goes 4 km west. What is Justin's displacement?
Answer:
Displacement= 12.65 km S 18.44°W
Step-by-step explanation:
Justin rides on hist 12 km south.
He changes location and goes 4 km west.
The displacement from his current location = X
X²= 12²+4²
X²= 144+16
X²= 160
X= √160
X= 4√10
X= 12.649 km
X= 12.65 km
His total distance covered=12+4
His total distance covered= 16 km
Tan ^-1 12/4= angle
71.56° = angle
90-71.56= 18.44°
Displacement= 12.65 km S 18.44°W
Evaluate.
8 x 4 + {15 / [8 - (3 + 2)]}
Answer:
the answer is 37 i believe
37
Step-by-step explanation:
First start with parenthesis 3 + 2=5. Next the brackets
8 - 5=3. Next 15 ÷ 3 = 5. Then Finally, 8 × 4 = 32, and add 5, which 37
Monica Ramirez works at the hospital as a nursing assistant. She works 15 hours per week and earns $8.50 per hour. What is Monica’s straight-time pay for each week? *
1 point
$120.00
$127.00
$127.50
$120.50
Answer:
Answer:
C. She makes $127.50 a week
Step-by-step explanation:
Since we are looking for how much she makes every week, we need to multiply her number of hours by the pay. She makes 8.50 per hour and works 15 hours.
8.5x15=127.5
She makes $127.50 a week
Step-by-step explanation:
The solution is Option C.
The total amount of straight time pay of Monica for the week is $ 127.50
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the total number of hours worked in the week by Monica be = T
The value of T = 15 hours
Let the earnings per hour of Monica be = $ 8.50
Now , the equation will be
Total straight line pay for Monica = number of hours worked in the week by Monica x earnings per hour of Monica
Substituting the values in the equation , we get
Total straight line pay for Monica A = 15 x 8.50
Total straight line pay for Monica A = $ 127.50
Therefore , the value of A is $ 127.50
Hence , The total amount of earnings of Monica for the week is $ 127.50
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30 POINTS! 3 questions! EASY 1. Jason is 22, which is 6 years older than twice his sister Taylor’s age.How old is Taylor? Enter your answer in the box.
2. Each month, Sal must pay for car insurance and fuel to drive a vehicle. Sal's parents agree to pay p percent of his car expenses. The cost of car insurance is the same every month, but the cost of fuel depends on d, the number of miles Sal drives. The expression (1−p)(0.10d+60) represents how much Sal must pay toward his monthly car expenses. Which part of the expression represents the percentage of the monthly expenses that Sal must pay?
A. 0.10d + 60
B. 1−p
C. 60
D. 0.10d
3. Which equation represents this sentence? Twenty-eight is the product of four and a number.
A. 28=4n
B. 28=4+n
C. 28=4n
D. 28=4n
Answer:
question 1: she is 8 years old Question 2: C-60
Step-by-step explanation:
A statistics practitioner would like to estimate a population mean to within 50 units with 99% confidence given that the population standard deviation is 250. What sample size should be used? b. Re-do part (a) changing the standard deviation to 50. c. Re-do part (a) using a 95% confidence leve
Answer:
(a) 167
(b) 7
(c) 97
Step-by-step explanation:
The (1 - α)% confidence interval for the population mean μ is:
[tex]CI=\bar x\pm z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}[/tex]
The margin of error is:
[tex]MOE=z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}[/tex]
Then the formula to estimate the sample size is:
[tex]n=[\frac{z_{\alpha/2}\cdot \sigma }{MOE}]^{2}[/tex]
(a)
For 99% confidence interval the critical value of z is:
z = 2.58.
The standard deviation is, 250.
Compute the sample size as follows:
[tex]n=[\frac{z_{\alpha/2}\cdot \sigma }{MOE}]^{2}[/tex]
[tex]=[\frac{2.58\times 250}{50}]^{2}\\\\=(12.9)^{2}\\\\=166.41\\\\\approx 167[/tex]
The sample size that should be used is 167.
(b)
Now the standard deviation is, 50.
Compute the sample size as follows:
[tex]n=[\frac{z_{\alpha/2}\cdot \sigma }{MOE}]^{2}[/tex]
[tex]=[\frac{2.58\times 50}{50}]^{2}\\\\=(2.58)^{2}\\\\=6.6564\\\\\approx 7[/tex]
The sample size that should be used is 7.
(c)
Now a 95% confidence level is used.
For 95% confidence interval the critical value of z is:
z = 1.96.
Compute the sample size as follows:
[tex]n=[\frac{z_{\alpha/2}\cdot \sigma }{MOE}]^{2}[/tex]
[tex]=[\frac{1.96\times 250}{50}]^{2}\\\\=(9.8)^{2}\\\\=96.04\\\\\approx 97[/tex]
The sample size that should be used is 97.
Find the equation of the line that contains the point (7.9) and is perpendicular to the line 5x + 3y = 4. Write the equation in the form
y = mx + band identify m and b
Answer:
[tex]y = \frac{3}{5} x + \frac{24}{5} [/tex]
m= 3/5
b= 24/5
Show all work to identify the asymptotes and zero of the function f of x equals 5 x over quantity x squared minus 25.
Answer:
asymptotes: x = -5, x = 5zero: x = 0Step-by-step explanation:
The function of interest is ...
[tex]f(x)=\dfrac{5x}{x^2-25}=\dfrac{5x}{(x-5)(x+5)}[/tex]
The asymptotes are found where the denominator is zero. It will be zero when either factor is zero, so at x = 5 and x = -5
__
The zeros are found where the numerator is zero. It will be zero for x = 0.
The asymptotes are x=-5, x=5; the zero is x=0.
Answer:
The asymptotes are x=-5, x=5; the zero is x=0.
Step-by-step explanation:
Jeremy's coach makes him run clockwise around a circular track with radius of 50 meters. Jeremy manages to maintain a constant speed around the track. He takes 48 seconds to finish one lap of the track. From his starting point, it takes him 12 seconds to reach the northernmost point of the track. Answer the following questions below assuming that the center of the track at the origin and the northernmost point is on the y-axis.
a. Give Jeremy's coordinates at his starting point.
b. Give Jeremy's coordinates when he has been running for 4 seconds.
c. Give Jeremy's coordinates when he has been running for 32 seconds.
Answer:
Coordinates of the starting point ( -50 ; 0 )
Coordinates 4 seconds later Q ( - 25*√3 ; 25 )
Coordinates 32 seconds later R ( 25 ; - 25*√3 )
Step-by-step explanation:
a) If Jeremy takes 48 seconds fr a lap then
The length of the lap ( length of the circle ) is:
L = 2*π*r ⇒ L = 100*π
If the time for one lap was 48 seconds at a constant speed, the speed was
v = 100*π / 48 [m/s]
v = 6,54 m/s
12 seconds is 1/4 0f 48 in that time he (she) reach the northernmost point, then he(she) necessarily started on the negative side of the x-axis the coordinates at this point are
( -50 ; 0 )
b) 4 seconds later, at v = 6,54 m/s by rule of three
In 12 seconds 90⁰
In 4 seconds (the third part ) x ??
x = 30⁰
sin 30⁰ = 1/2
cos 30⁰ = (√3)/2
And coordinates for the point are
sin 30⁰ = 1/2 = y/50 ⇒ y = 25
cos 30⁰ = (√3)/2 = x / 50 ⇒ x = 25*√3
coordinates of the point 4 seconds later
Q ( - 25*√3 ; 25 ) she (he) is in the negative part of x-axis
c) 32 seconds later
32 is 12 + 12 + 8
Then she (he) is 8 seconds below the positive side of x-axis
8 is 2/3 of 12 ( negative 60⁰ )
sin 60⁰ = (√3)/2 = y/50 y = 25*√3 negative
cos 60⁰ = 1/2 * 50 = X/50 x = 25
Coordinates of the point R
R ( 25 ; - 25*√3 )
Find the value of (-3)4 +(-2)4 +(-1)4
the value of (-3)4+(-2)4×(-1)4 is -24
Answer:
98
Step-by-step explanation:
-3⁴ = -3*-3*-3*-3 = +81 = 81
-2⁴ = -2*-2*-2*-2 = +16 = 16
-1⁴ = -1*-1*-1*-1 = +1 = 1
Then:
(-3)⁴ + (-2)⁴ + (-1)⁴ = 81 + 16 + 1
= 98
4. A recent poll of 1079 adults finds that 55% of Americans support a more stringent immigration law. Construct a 99% confidence interval of the proportion of the population that will support such a law.
Answer:
0.5306[tex]<\mu<[/tex]0.5694
Step-by-step explanation:
USing the formuls for calculating the confidence interval for the population proportion;
CI = p±Z*√[p(1-p)/n]
p is the percentage proportion of the population 55%
Z is the z-score at 99% confidence interval = 2.576
n is the sample size = 1079
CI = 0.55 ± 2.576*[0.55(1-0.55)/√1079]
CI = 0.55 ± 2.576*[0.55(0.45)/√1079]
CI = 0.55 ± 2.576*[0.2475/√1079]
CI = 0.55 ± 2.576*[0.2475/32.85]
CI = 0.55 ± 2.576*[0.00753]
CI = 0.55 ±0.0194
CI =(0.55-0.0194, 0.55+0.0194)
CI = (0.5306, 0.5694)
Hence, a 99% confidence interval of the proportion of the population that will support such a law is 0.5306[tex]<\mu<[/tex]0.5694
brad walked 2.5 miles in 5/6 of an hour.how fast does he walk per hour
Answer:
Rate or speed=3 Miles per hour
Step-by-step explanation:
Brad walked 2.5 miles in 5/6 of an hour.
Distance covered by Brad = 2.5 miles
Distance covered by Brad= 2 1/2 miles
Distance covered by Brad= 5/2 miles
Time taken to cover the distance = 5/6 of an hour
His rate of walking or how fast he walks is determined by the formula
Rate or speed= distance/time
Rate or speed=( 5/2)/(5/6)
Rate or speed= (5/2)*(6/5)
Rate or speed=6/2
Rate or speed=3 Miles per hour