Solve the following inequality: |3x|>x+20
Answer:
x>10,x<−5
Step-by-step explanation:
[tex]x > - 5[/tex] or [tex]x < 10[/tex] are the two possible solutions to the given inequality.
What are absolute value functions?
An absolute value function is a function that contains an algebraic expression within absolute value symbols.
What is inequality?A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
According to the given question.
We have an inequality |3x| > x + 20
Solve the above given inequality |3x| > x + 20
⇒ [tex]-(x + 20) < 3x < +( x + 20)[/tex]
⇒ [tex]-x -20 < 3x < x + 20[/tex]
⇒ [tex]3x > -x -20[/tex] or [tex]3x < x + 20[/tex]
⇒ [tex]3x+x > -20[/tex] or [tex]3x - x < 20[/tex]
⇒ [tex]4x > -20[/tex] or [tex]2x < 20[/tex]
⇒[tex]x > -5[/tex] or [tex]x < 10[/tex]
⇒ x ∈ (-∞, -5)∪(10,∞)
Hence, [tex]x > - 5[/tex] or [tex]x < 10[/tex] are the two possible solutions to the given inequality.
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To keep in shape, Vincent exercises at a track near his home. He requires 40 minutes to do 4 laps running and 7 laps walking. In contrast, he requires 18 minutes to do 2 laps running and 3 laps walking. Assuming he maintains a consistent pace while running and while walking, how long does Vincent take to complete a lap at each pace?
Answer:
He completes a lap running in 3 minutes, and walking in 4 minutes.
Step-by-step explanation:
This question can be solved by a system of equations.
I am going to say that:
x is the time needed to complete a lap running.
y is the time needed to complete a lap walking.
He requires 40 minutes to do 4 laps running and 7 laps walking.
This means that:
[tex]4x + 7y = 40[/tex]
[tex]4x = 40 - 7y[/tex]
He requires 18 minutes to do 2 laps running and 3 laps walking.
This means that
[tex]2x + 3y = 18[/tex]
Multipluing everything by 2
[tex]4x + 6y = 36[/tex]
Since [tex]4x = 40 - 7y[/tex]
[tex]40 - 7y + 6y = 36[/tex]
[tex]y = 4[/tex]
And
[tex]4x = 40 - 7y[/tex]
[tex]4x = 40 - 7*4[/tex]
[tex]4x = 12[/tex]
[tex]x = \frac{12}{4}[/tex]
[tex]x = 3[/tex]
He completes a lap running in 3 minutes, and walking in 4 minutes.
Need Trig Help plz Picture attached
if the are 5 buses and the quatation amount is R8,100 how much will each person pay
Answer:
R1620
Step-by-step explanation:
1620 ×1=1620
1620×2=3240
1620×3=4860
1620×4=6480
1620×5=8100
Guys I need help !! X=2 evaluate 5x-2
Answer:
Step-by-step explanation:
Evaluate means to see what value the equation has given x is 2
substitute x for 2 (write instead of x, write 2)
5x-2 will be 5*2-2 , calculate 5*2-2= 10-2 = 8
47. Health care costs per capita Rising health care costs
are a growing concern for everyone in the United
States. Using U.S. Centers for Medicare and
Medicaid Services data from 2006 and projected to
2021, U.S. per capita health care costs can be modeled
by
y = 20.61x? - 116.4x + 7406
where x is the number of years past 2000. Use this
equation to find, to the nearest dollar, the average rate
of change of U.S. per capita health care costs from 2010
to 2015 and from 2015 to 2020.
A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized. where traffic flow in vehicles per hour vehicle speed in miles per hour The following data were collected during rush hour for six highways leading out of the city. Traffic Flow () Vehicle Speed () 1257 36 1329 45 1227 30 1336 50 1349 55 1124 25 a. Use the data to compute the coefficients of this estimated regression equation (to decimals). Enter negative value as negative number. (Create the variable first using Data/Transform
Answer:
ŷ = 0.1286X - 123.2175 ;
R = 0.9465
R² = 0.8958
Step-by-step explanation:
Given the data:
Traffic Flow, X : ()
1257
1329
1227
1336
1349
1124
Vehicle speed, Y () :
36
45
30
50
55
25
The estimated regression equation using a linear regression calculator is given thus:
ŷ = 0.1286X - 123.2175
According to the general linear regression formula :
y = mx + c
Where ; y = predicted variable (vehicle speed)
x = predictor variable (traffic flow)
Slope, m = 0.1286
Intercept, c = 123.2175
The correlation Coefficient, R = 0.9465, This depicts a strong positive relationship between traffic flow and vehicle speed.
The Coefficient of determination, R² = 0.9465² = 0.8958 ; This means about 89.5% of variation in Vehicle speed can be explained by the regression line.
PLS Help While on a strenuous hike, Tara recorded her distance from the peak of the mountain at two different time intervals. The table shows the two pieces of data she collected.
Answer:
Step-by-step explanation:
Equation of a line representing the relation between distance from the peak of the mountain and time is,
h = mt + b
Here, m = Slope of the line
b = y-intercept
Since, slope of the line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
From the table attached,
Slope of the line passing through (2, 2600) and (5, 950) will be,
m = [tex]\frac{2600-950}{2-5}[/tex]
= -550
Therefore, equation of the line will be,
h = -550t + b
Since, point (2, 2600) lies on this line,
2600 = -550(2) + b
b = 2600 + 1100
b = 3700
So, equation of the line will be,
h = -550t + 3700
Input - output values for this line,
t 2 4 6
h 2600 1500 400
Now we can plot these points and get the graph of the line.
PLEASE HELP!!! WILL GIVE BRAINLIEST!!!
Instructions
Search your home for a rectangular prism. Some examples are a cereal box, a CD case, or a coffee table. Measure your prism using appropriate units, such as inches, centimeters, or feet.
Complete the following. Show all work for calculations.
List the dimensions of your box. Be sure to include the units (in, cm, ft, etc.).
Length: 6 inches
Width: 2 and a half inches
Height: 12 inches (1 foot)
Describe the shape of the cross section when the box is cut parallel to the base.
What is the surface area of the box?
What is the surface area of the box if it is scaled up by a factor of 10?
What is the volume of the box?
What is the volume of the box if it is scaled down by a factor of 1/10?
Answer:
I chose a box of cereal-------> rectangular prism
see the attached figure
Part 1)List the dimensions of your box. Be sure to include the units (in, cm, ft, etc.).
Length: 20 cm
Width: 8 cm
Height: 32 cm
Part 2).
Describe the shape of the cross-section when the box is cut parallel to the base
the shape of the cross-section would be a rectangle of dimensions
20 cm x 8 cm
Part 3)
What is the surface area of the box?
surface area=2*area of the base+perimeter of the base*height
area of the base=20*8=160 cm²
perimeter of the base=2*[20+8]-----> 56 cm
height=32 cm
surface area=2*160+56*32------> 2,112 cm²
the answer part 3) is
2,112 cm²
Part 4)
What is the surface area of the box if it is scaled up by a factor of 10?
we know that
surface area of the larger box=[scale factor]²*surface area original box
scale factor=10
surface area original box=2,112 cm²
so
surface area of the larger box=10²*2,112-----> 211,200 cm²
the answer part 4) is
211,200 cm²
Part 5)
What is the volume of the box?
volume of the box=L*W*H-----> 20*8*32------> 5,120 cm³
the answer Part 5) is
5,120 cm³
Part 6)
What is the volume of the box if it is scaled down by a factor of 1/10
we know that
volume of the smaller box=[scale factor]³*volume original box
scale factor=1/10
volume original box=5,120 cm³
so
volume of the smaller box=[1/10]³*5,120-----> 5.12 cm³
the answer part 6) is
5.12 cm³
Step-by-step explanation:
Answer:
541/2 square
Step-by-step explanation:
we know that
the volume of the smaller box=[scale factor]³*volume original box
scale factor=1/10
volume original box=5,120 cm³
so
volume of the smaller box=[1/10]³*5,120-----> 5.12 cm³
the answer part 6) is 541/2 square
A computer laboratory manager was in charge of purchasing new battery packs for her lab of laptop computers. She narrowed her choices to two models that were available for her machines. Since the models cost about the same, she was interested in determining whether there was a difference in the average time the battery packs would function before needing to be recharged. She took two independent samples and computed the following summary information: Battery Pack Model 1 Battery Pack Model 2Sample Size 9 9Sample Mean 5 hours 5.5 hoursStandard Deviation 1.5 hours 1.3 hoursUsing the null and alternate hypothesis:H0:mu1-mu2=0 vs. Ha: mu1-mu2 not equal 0Calculate the test statistic for this test.
Answer:
-0.756
Step-by-step explanation:
N1 = 9
N2 = 9
Sd1 = 1.5 hours
Sd2 = 1.3 hours
X1 = 5 hours
X2 = 5.5 hours
Hypothesis
H0: mu1 - mu2 = 0
H1 : mu1 - mu2 not equal to 0
Test statistic
t = (x1 - x2)/SE
SE is the standard error, which is unknown
SE = √sd1²/n1 + sd2²/n2
= √1.5²/9 + 1.3²/9
= √0.25+0.1878
= √0.4378
= 0.66166
t statistics = (5-5.5)/0.66166
= -0.5/0.66166
= -0.756
four times a number increased by 8 is 54?
Answer:
4x+8=54 this is the correct answer
What is the exact circumference of a circle with a radius of 15 cm?
A. 107 cm
B. 157 cm
C. 307 cm
D. 60 cm
Step-by-step explanation:
Given. radius (r) = 15 cm
Circumference (C)
= 2 π r
= 2 * 3.14 * 15
= 94.2 CM
I Got this answer.....
if the force acting on a body of mass 4kg accelerates it at a constant rate of 4m/s. what would be the acceleration of the mass is doubled?
Answer:
4kg=4m/s
8kg=?
3m/s
Step-by-step explanation:
12kgm/s/4kg
APPLICATIONS
LINE RELATIONSHIPS Think of each segment in the diagram as part of a
line. Fill in the blank with parallel, skew, or perpendicular.
10. DE, AB, and GC
С
DĖ and BE are 2
A А
12. BE and GC
13. Plane GAD and plane CBE are
D
E
are
11.
B В
are
Answer:bb
Step-by-step explanation:
Find set A' n B'
U= {1, 2, 3, 4, 5, 6, 7}
A= {4, 5, 6, 7}
B = {3, 4, 7}
Answer:
its 1 and 2
Step-by-step explanation:
first find A' which is(1,2,3) since these are in the universal set but not in A.
similary B' which is (1,2,5,6)
and since (1,2) are both in A' and B' set A'nB'=(1,2)
Answer:
Step-by-step explanation:
U={1,2,3,4,5,6,7}
A={4,5,6,7}
B={3,4,7}
A'={1,2,3}
B'={1,2,5,6}
A'∩B'={1,2}
Write out the form of the partial fraction decomposition of the function (as in this example). Do not determine the numerical values of the coefficients. (a) x − 20 x2 + x − 20 Incorrect: Your answer is incorrect. (b) x2 x2 + x + 20 Incorrect: Your answer is incorrect.
Answer:
[tex]\frac{x - 20}{ x^2 + x - 20} = \frac{5}{9(x-4)}+\frac{4}{(x+5)}[/tex]
Step-by-step explanation:
Given
[tex]\frac{x - 20}{ x^2 + x - 20}[/tex]
Required
Decompose into partial fraction
Start by factorizing the denominator:
[tex]x^2 + x - 20 =x^2 + 5x -4x- 20[/tex]
[tex]x^2 + x - 20 =x(x + 5)-4(x+5)[/tex]
[tex]x^2 + x - 20 =(x-4)(x+5)[/tex]
So, we have:
[tex]\frac{x - 20}{ x^2 + x - 20} = \frac{A}{x-4}+\frac{B}{x+5}[/tex]
Take LCM
[tex]\frac{x - 20}{ x^2 + x - 20} = \frac{A(x+5)+B(x-4)}{(x-4)(x+5)}[/tex]
Cancel out the denominator
[tex]x - 20 = A(x+5)+B(x-4)}[/tex]
Open brackets
[tex]x - 20 = Ax+5A+Bx-4B[/tex]
Collect Like Terms
[tex]x - 20 = Ax+Bx+5A-4B[/tex]
[tex]x - 20 = (A+B)x+5A-4B[/tex]
By comparison;
[tex](A +B)x = x[/tex] ==>[tex]A + B = 1[/tex]
[tex]5A - 4B = 1[/tex]
Make A the subject in [tex]A + B = 1[/tex]
[tex]A = 1 - B[/tex]
Substitute 1 - B for A in [tex]5A - 4B = 1[/tex]
[tex]5(1-B) -4B = 1[/tex]
[tex]5-5B -4B = 1[/tex]
[tex]5-9B = 1[/tex]
Collect Like Terms
[tex]-9B = 1 - 5[/tex]
[tex]-9B = - 4[/tex]
[tex]B = \frac{4}{9}[/tex]
[tex]A = 1 - B[/tex]
[tex]A = 1 - \frac{4}{9}[/tex]
[tex]A = \frac{9-4}{9}[/tex]
[tex]A = \frac{5}{9}[/tex]
So:
[tex]\frac{x - 20}{ x^2 + x - 20} = \frac{A}{x-4}+\frac{B}{x+5}[/tex]
[tex]\frac{x - 20}{ x^2 + x - 20} = \frac{5}{9(x-4)}+\frac{4}{(x+5)}[/tex]
7+9 x (3+8) Order of operations. Please explain.
Answer:
Not sure if that is "9x" or "9 times" but I will do both. I have attached a picture of me solving and explaining the steps. Hope this helps, thank you !!
HELP!!! in the diagram m ∠ g=96. what is m ∠E
Answer:
M<E
Step-by-step explanation:
It would be m
Answer:
sorry if it’s late, but that would be
B) 84
i just took the test.
Solve for x in the following equation.
X/5=25
X=?
Answer:
125
Step-by-step explanation:
25 × 5 = 125
x/5 = 25 × 5 = 125
x = 125
Why is it important that you put the polynomial in standard form (largest power
to smallest-power)? *
Answer: Polynomials like to be written in standard form. This means they contain no like terms and the exponents are in descending order (largest to smallest).
Step-by-step explanation:
Evaluate
ifr=9 and s = 2.
S
Answer:
(4 × 9) / 2 = 36/2 = 18 gitu yaaa
Answer:
18
Step-by-step explanation:
plug in r and s
4(9)/2
36/2
18
✨6 Grade Math✨ Pls help
Answer:
37Step-by-step explanation:
89 - 4²×4 + 12 = 89 - 16×4 + 12 = 89 - 64 + 12 = 25 + 12 = 37Answer:
[tex]89 - 4 {}^{2} \times 4 + 12 = 89 \\ - 16 \times 4 + 12 \\ \\ = 89 - 64 + 12 \\ \\ = 25 + 12 \\ \\ = 37[/tex]
89-4^2×4+12=89-16×4+12
= 89-64+12
= 25+12
= 37
Mr. Hernandez dilates the triangle shown below by a scale factor of 2 with the origin
as the center to obtain AA'B'C'.
Answer: only student 2
origanal price $60 sale price $45
Answer:
di ko po alam ehh
Step-by-step explanation:
sorry po
Answer:
Step-by-step explanation:
What is the question?
Price reduced by $15
Percentage reduction = 15/60 = 0.25 = 25%
What fractions are the same
Ohhhhhh I get it I thought something else
Answer:
equivalent fractions
Step-by-step explanation:
When fractions have different numbers in them, but have the same value, they are called equivalent fractions. Let's take a look at a simple example of equivalent fractions: the fractions ½ and 2/4. These fractions have the same value, but use different numbers.
Alex scored a 75% on his history test if he correctly answered an 18 question how many questions did Alex answer incorrectly
Answer:
24
Step-by-step explanation:
18 is 75% of 24.
Select the correct answer.
What is the complete factorization of x2 + 2x - 63?
A. (x+ 21)(x-3)
B.
(x-9)(x+7)
C.
(x + 9)(x-7)
D.
(x-21)(x + 3)
Reset
Answer:
the answer of this question is
c
The value of (1-w) (1-w*2) , where w is the cube root of the complex number is?
Answer:
3
Step-by-step explanation:
1+ω+w²=0
ω³=1
(1-ω)(1-ω²)=1-ω²-ω+ω³
=1-ω-ω²+1
=2+1-1-ω-ω²
=3-(1+ω+ω²)
=3-0
=3
This year 0.3 of the x students at Mega Middle School are in 7th grade. There are 294 students in 7th grade.
Answer:
is that even a question ?
Step-by-step explanation:
3/10x=294
x=294*10/3
x=980 students
if you found my answer helpful please mark as brainliest.
estimate 5/8 - 1/10 explain
Answer:
21/40.
Step-by-step explanation:
Find the LCD (Least Common Denominator) of the fractions. The LCD of 5/8 and 1/10 is 40.
Convert both fractions into denominators of 40.
So then we have: 25/40 - 4/40 which is equal to: 21/40.
21/40 is the estimated value of the expression 5/8 -1/10
What is Number system?A number system is defined as a system of writing to express numbers.
The given expression is 5/8 -1/10
The terms in the expression are in the form of fractions, A fraction represents a part of a whole.
To find the value of expression firstly find the LCM of 8 and 10
40 is the LCM
5(5)-1(4)/40
25-4/40
The value of 25 minus 4 is twenty one.
21/40 is the value of the expression 5/8 -1/10
Hence, 21/40 is the estimated value of the expression 5/8 -1/10
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