Answers
Answer: Option 1
Step-by-step explanation:
[tex]|x+4|=2\\\\x+4=\pm 2\\\\x=-4\pm 2\\\\x=-6, -2[/tex]
Solve Absolute Value.
| x + 4 | = 2
We know either x + 4 = 2 or x + 4 = −2
x + 4 = 2 (Possibility 1)
x + 4 - 4 = 2 - 4 (Subtract 4 from both sides)
x = -2
x + 4 = −2 (Possibility 2)
x + 4 - 4 = - 2 - 4 (Subtract 4 from both sides)
x = -6
Answer: x = - 2 or x = -6
Therefore we conclude that the solution of the exercise | x + 4 | = 2, is the first number line, since both results are negative.
Related Questions
For Exercises 11–16, use inductive reasoning to draw the next shape in each
picture pattern.
Answers
The ways to illustrate the shapes are given.
How to depict the shape?11. In each new figure, one vertex is introduced, and each vertex is joined to each other vertex.
12. In each new figure, 2 rows and 1 column are introduced, and the shading at the corner moves 90 degrees clockwise.
13. In each new figure, one row and one column are introduced, and exactly half of the rectangles are shaded.
14. In each new figure, except at the bottom vertex, two perpendicular lines are introduced at the remaining vertices.
15. In each new figure, one inverted white triangle is inscribed in the orange triangle.
16. The number of squares increases in the pattern. There are blue circles inscribed in one diagonal square and there are yellow circles inscribed in the remaining squares. Also, the blue circles in the diagonal alternate.
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Mathematics word problem
Answers
75 miles per hour is the rate of train.
what is the formula of speed?Formula of speed = distance/time
let,
s1 , speed of A train = s
s2, Speed of B train = s
t1, time of travel for train A = 2.5h
t2, time of travel for train B = 4 h
d1, distance traveled by train A
distance travel by train A = speed*time
= s1*t1
d2, distance traveled by train B
distance travel by train A = speed*time
= s2*t2
Total distance between station A and station B = 562.5 mi
d1+d2=562.5 mi
s1t1+s2t2=562.5
s(2.5)+s(4)=562.5
6.5 s = 562.5
s = 562.5/6.5
s = 86.5 mph
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75 miles per hour is the rate of the train.
what is the rate of the train?Given:
Train A and Train B leave a central station at the same time.They travel at the same speed, but in opposite directions, with train A heading towards station A.Train B heading towards station B.Train A reaches station A after 2 and 1/2 hours.Train B reaches station B after 4 hours.Station A and Station B are 585 mi apart.Find:
Rate of the trains.Solution:
Formula of speed = distance/time
Let us consider
Speed of A train(s1) = s
Speed of B train(s2) = s
Time of travel for train A(t1) = 2.5h
Time of travel for train B(t2) = 4 h
Distance traveled by train A(d1)
= speed*time
= s1*t1
Distance traveled by train B(d2)
= speed*time
= s2*t2
The total distance between station A and station B = 562.5 mi
d1+d2=562.5 mi
s1t1+s2t2=562.5
s(2.5)+s(4)=562.5
6.5 s = 562.5
s = 562.5/6.5
s = 86.5 mph
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Given the drawing, what would the value of x need to be in order
for it to be true that m ||n?
4x + 18
m
7x-21
Be sure to show all calculations and algebraic steps in your re-
sponse.
Hint: What must be true about alternate exterior angles in order
for lines to be parallel?
Answers
[tex]4x + 18 = 7x - 21 \\ 18 + 21 = 7x - 4x \\ 39 = 3x \\ x = \frac{39}{3} = 13 [/tex]
The lifespans of meerkats in a particular zoo are normally distributed. The average
meerkat lives 10.4 years; the standard deviation is 1.9 years.
Use the empirical rule (68 - 95 - 99.7%) to estimate the probability of a meerkat
living less than 16.1 years.
Answers
The probability of a meerkat living smaller than 16.1 years exists at 99.85%.
How to estimate the probability of a meerkat living less than 16.1 years by using empirical rule?
The empirical rule notes that for a normal distribution most of the data lose within three standard deviations (σ) of the mean (µ). That exists 68% of the data lose within the first standard deviation (µ ± σ), 95% loses within the first two standard deviations (µ ± 2σ), and 99.7% declines within the first three standard deviations (µ ± 3σ).
68% declines within (10.4 ± 1.9). 68% declines within 8.5 years to 12.3 years.
95% declines within (10.4 ± 2[tex]*[/tex]1.9). 95% declines within 6.6 years to 14.2 years.
99.7% declines within (10.4 ± 3 [tex]*[/tex]1.9). 68% declines within 4.7 years to 16.1 years.
Probability of a meerkat living less than 16.1 years
= 100% - (100% - 99.7%)/2
= 100% - 0.15%
= 99.85%
Therefore, the probability of a meerkat living less than 16.1 years exists at 99.85%.
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According to the Rational Root Theorem, the following are potential roots of f(x) = 2x2 + 2x – 24.
–4, –3, 2, 3, 4
Which are actual roots of f(x)?
–4 and 3
–4, 2, and 3
–3 and 4
–3, 2, and 4
Answers
The actual roots of f(x) are -4 and 3
How to determine the actual roots?The function is given as:
f(x) = 2x^2 + 2x – 24.
Expand the function
f(x) = 2x^2 + 8x- 6x – 24.
Factorize the function
f(x) = 2x(x + 4) - 6(x + 4)
Factor out x + 4
f(x) = (x + 4)(2x - 6)
Set to 0
(x + 4)(2x - 6) = 0
Solve for x
x = -4 and 2x = 6
This gives
x = -4 and x = 3
Hence, the actual roots of f(x) are -4 and 3
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Answer:
A
Step-by-step explanation:
Got 100 on test
Find the missing side of the triangle. pythagorean 4 A. 337‾‾‾‾√ km B. 5‾√ km C. 193‾‾‾‾√ km D. 112‾√ km
Answers
The missing side in the given triangle is x = √193 km
Pythagoras theoremThe Pythagoras theorem is expressed as;
x^2 = a^2 + b^2
where
x is the longest side
Substitute the given side
x^2 = 12^2 + 7^2
x^2 = 144 + 49
x = √193 km
Hence the missing side in the given triangle is x = √193 km
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The roots of the quadratic function describing the relationship between number of products produced and
overall profit margin are x = 0 and 26. The vertex is (13, -50).
The vertex is a minimum at (13, -50). The company actually loses money on their first few products as it
costs them more to make them, but once they hit 26 items they break even again.
The worst case scenario is that they produce
first root tells us that the profit will be 0 when
Check
items, as they will have a profit of
products are sold.
dollars.
Answers
In Economics, profit can be defined as a measure of the amount of money generated when the selling price is deducted from the cost price of a good or service, which is usually provided by producers.
This ultimately implies that, all producers of any product generally work to maximize their profits and make them as large as possible, in order to enable them break even and successful.
Based on the information provided, we can logically deduce that this function has its roots at x = 0 and x = 26 and its vertex is a minimum. Thus, this quadratic function which describes the relationship between the number of products produced and the overall profit margin is an increasing function:
0 < x < 26, f(x) < 0, which implies a negative profit is generated when between 0 and 26 items are produced.x > 26, f(x) > 0, which implies a positive profit is generated when more than 26 items are produced.x is equal to 26 is the break even point.Therefore, once they hit 26 items they break even again. The worst case scenario is that they produce 13 items, as they will have a profit of -50 dollars because the minimum point is at (18, -35). Also, the first root tells us that the profit will be 0 when 0 products are sold.
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Please help ASAP
What is the measure of YZ?
A.142
B.52
C.128
D.38
Answers
Work Shown:
(arc YZ + arc XU)/2 = angle YVZ
(arc YZ + 38)/2 = 90
arc YZ + 38 = 90*2
arc YZ + 38 = 180
arc YZ = 180 - 38
arc YZ = 142
bryan brought 8/10 gallon of water on a hiking trip.he drank 4/10 gallon of water.how much water is left
Answers
The amount of water left is 4/10 gallons
Difference of fractionsFractions are written as a ratio of two integers
Given the following parameters
Amount of gallon bought = 8/10 gallons
Amount he drank = 4/10
Determine the amount left
Amount left = 8/10 -4/10
Amount left = 4/10 gallons
Hence the amount of water left is 4/10 gallons
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You want to place stone pavers around the edge of your concrete patio. The patio is 12 ft wide by 14 ft long and each stone paver is 14 inches long . How many stone pavers will you need to go around the patio (not counting the side against the house which is 14 ft long)? (round to the nearest whole number )
Answers
The number of stone pavers needed to go round the patio is 3.
What is the number of stone pavers needed to go round the patio?The first step is to determine the perimeter of the concrete patio.
Perimeter : 12 + 12 + 14 = 38 feet
Number of stone pavers needed to go round the patio : perimeter of the patio / length of each stone paver
38 / 14 = 3
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The sum of 12 and one-third of n
Is 1 morethan twice
n. Expres
the statement in the form an equation
Answers
Answer:
(12 + n/3) = 2n + 1
Step-by-step explanation:
(12 + n/3) = 2n + 1
36 + n = 6n + 3
33 = 5n
n = 33/5
A cylinder has a olive of 200mm and a height of 17mm. The volume formula for a cylinder is
Answers
The radius of the given cylinder with a volume of 200 mm³ and a height of 17mm is: 1.93 mm.
How to find the Volume of a Cylinder?The formula for finding the volume of any cylinder is given as: πr²h, where r is the radius and h is the height of the cylinder.
Given the following:
Volume = 200 mm³
Height (h) = 17 mm
Radius (r) = ?
Plug the values into the formula for volume
πr²(17) = 200
r² = 200/17π
r² = 3.74
r = 1.93 mm
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Which equation represents the vertex form of the equation y = x² + 2x - 6?
y = (x + 2)² -
y = (x + 1)2 - 6
y = (x + 2)²-7
y = (x + 1)²-7
Answers
Answer:
Step-by-step explanation:
Steps
1] On the right, put brackets around the 1st 2 terms.
y = (x^2 + 2x) - 6
2] Divide the second term's coefficient by 2 and square the result.
2/2 = 1
3] Square the result
1^2 = 1
4] Add that inside the brackets
y = (x^2 + 2x + 1) - 6
5] Subtract 1 outside the brackets. The original equation is still there.
y = (x^2 + 2x + 1) - 6 - 1
y = (x^2 + 2x + 1) - 7
6] What is inside the brackets is a perfect square.
y = (x + 1)^2 - 7
Answer D
Which inequality can be used to explain why these three segments cannot be used to construct a triangle?
AC + AB > CB
AC + CB < AB
AC + CB > AB
AC + AB < CB
Answers
The answer choice which explains that the three segments cannot be used to construct a triangle is; AC + CB < AB.
Which inequality explains why the three segments cannot be used to construct a triangle?Since, It follows from the triangle inequalities theorem that sum of the side lengths of any two sides of a triangle is greater than the length of the third side.
Hence, since the sum of sides AC + CB is less than AB, it follows that the required inequality is; AC + CB < AB.
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questions 1, 2 and 3 please!
will give brainliest to whoever answers
80 points
Answers
Answer:
a) [tex]f(x) = x + 3[/tex]
b) [tex]f(x) = -x - 5[/tex]
c) [tex]f(x) = 2x + 6[/tex]
Step-by-step explanation:
To determine the equation of a straight line, we need two things:
1. two known points (coordinates) on the line, used to calculate the gradient
2. the y-intercept of the line (the y-coordinate of the point at which the line crosses the y-axis)
Then we can use the equation:
[tex]\boxed {f(x) = ax + q}[/tex]
where a is the gradient and q is the y-intercept, to determine the equation of the line.
a) known points: (0, 3), (-4, -1)
y-intercept: 3
gradient = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
⇒ [tex]\frac{3 - (-1)}{0 - (-4)}[/tex]
⇒ [tex]\bf 1[/tex]
∴ a = 1 , q = 3
∴ equation:
[tex]{f(x) = ax + q}[/tex]
[tex]f(x) = 1x + 3[/tex]
⇒ [tex]\bf f(x) = x + 3[/tex]
b) known points: (-7, 2) , (0, -5)
y-intercept = -5
gradient = [tex]\frac{2 - (-5)}{-7 - 0}[/tex]
⇒ [tex]\bf -1[/tex]
∴ equation:
[tex]f(x) = -1x + (-5)[/tex]
⇒ [tex]\bf f(x) = -x - 5[/tex]
c) known points: (-3, 0), (0, 6)
y-intercept = 6
gradient = [tex]\frac{6 - 0}{0 - (-3)}[/tex]
⇒ [tex]\bf 2[/tex]
∴ equation:
[tex]\bf f(x) = 2x + 6[/tex]
a) A furniture store can sell 40 chairs per week at a price of sh. 80 each. The manager estimates that for each and sh. 5 price reduction, she can sell five more chairs per week. The chairs cost the store sh. 30 each. If x stands for the number of sh. 5 per price reduction, find price of the chairs and the quantity that maximize profit.
Answers
The price of the chairs and the quantity that maximizes profit is to sell 45 chairs at $75 each.
ProfitGiven that a furniture store can sell 40 chairs per week at a price of $80 each, and the manager estimates that for each and $5 price reduction, she can sell five more chairs per week, and the chairs cost the store $30 each, to determine the price of the chairs and the quantity that maximize profit, the following calculation must be made:
40 x (80-30) = 200045 x (75-30) = 202550 x (70-30) = 200055 x (65-30) = 1925Therefore, the price of the chairs and the quantity that maximizes profit is to sell 45 chairs at $75 each.
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Money savers bank offers a savings account that earns 6% interest compounded continuously. If Manuel deposits $2200, how much will he have in the account after three years?
Answers
Answer:
2633.88
Step-by-step explanation:
Pe^rt
2200*e^.06*3
the sum of two numbers is 48.
the second number is seven times the first number
Answers
Answer:
[tex]\huge\boxed{\sf x =6,\ y = 42}[/tex]
Step-by-step explanation:
Let the numbers be x and y
Given condition:x + y = 48 --------(1)
y = 7x -------------(2)
Put Eq. (2) in (1)
x + 7x = 48
8x = 48
Divide 8 to both sides
x = 48/8
x = 6Put x = 6 in Eq. (2)
y = 7 (6)
y = 42[tex]\rule[225]{225}{2}[/tex]
Assume a is the 1st number and b is the 2nd number, a + b = 48
b = 7a (the second number is seven times the first number)
a = a
So, equation: a + 7a = 48
a + 7a = 48
8a = 48
a = 6
To find b = 7 (6) = 42
Hope it helps!
CAN sb HELP MI >_>
what it 0.00000000000000035467 in the scientific notation
Answers
Answer:
3.5467 × 10^-16
For problems 13-19, transcribe the following expressions: (Write it out.)
Example: z + 4 = z plus 4
13. st
14. 6/t - 4
15. 20 + t 2
16. 50 - x
17. x - y 2
18. 24/12 + 12
19. xy - 16
Answers
The transcribe expression is the expression of the equation in words.
How to transcribe expression?The expression can be transcribe as follows;
1. st = s multiply by t
2. 6 / t - 4 = 6 divided by t minus 4
3. 20 + t² = 20 plus t squared.
4. 50 - x = 50 minus x
5. x - y² = x minus y squared.
6. 24 / 12 + 12 = 24 divided by 12 plus 12
7. xy - 16 = x multiply by y minus 16
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At first it decreased by 60 percent and it increased by 80 percent
Answers
The quantity reported an equivalent net percentage change of 28 percent.
How to calculate the net change of a quantity in percentages
In this problem we must determine the simple percentage change equivalent to two consecutive percentual changes. The formula that describes the situation is:
1 + r/100 = (1 - 60/100) · (1 + 80/100)
1 + r/100 = 72/100
r/100 = - 28/100
r = - 28
The quantity reported an equivalent net percentage change of 28 percent.
Remark
The statement is incomplete. Complete form is presented below:
A quantity is changing. At first it descreased by 60 percent and it increased by 80 percent. What is net change of the quantity in percentage?
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We are given a Student's t distribution with d.f. = 11 and t = 1.910. We wish to find an interval containing the corresponding P-value for a two-tailed test. To do this, we will use the Critical values for Student's t Distribution. Below is an excerpt from this table.
one-tail area 0.250 0.125 0.100 0.075 0.050 0.025 0.010 0.005 0.0005
two-tail area 0.500 0.250 0.200 0.150 0.100 0.050 0.020 0.010 0.0010
d.f. \ c 0.500 0.750 0.800 0.850 0.900 0.950 0.980 0.990 0.999
⋮
9 0.703 1.230 1.383 1.574 1.833 2.262 2.821 3.250 4.781
10 0.700 1.221 1.372 1.559 1.812 2.228 2.764 3.169 4.587
11 0.697 1.214 1.363 1.548 1.796 2.201 2.718 3.106 4.437
To determine where the given t-value would fall, we look for the row with heading d.f. =
. In this row, the sample statistic t = 1.910 falls between t = 1.796 and t =
Answers
To determine where the given t-value would fall, we look for the row with heading d.f. =11. In this row, the sample statistic t = 1.910 falls between t = 1.796 and t = 2.201
How to determine the t values?The given parameters are:
Degree of freedom, df = 11Sample statistic, t = 1.910This means that
df = 11 and t = 1.910
To calculate the t value,
We check the row where the heading of the degree of freedom is 11
i.e. df = 11
On this row, the t value 1.910 would be between 1.796 and 2.201
This is because 1.910 is greater than 1.796 and it is less than 2.201
Hence, the complete statement is
To determine where the given t-value would fall, we look for the row with heading d.f. =11. In this row, the sample statistic t = 1.910 falls between t = 1.796 and t = 2.201
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For many years organize crime rent a number game that is now run illegally by minis states government the player select a three digit number from 0 to 999 there are 1000 such members a bet of two dollars is placed on a number say number 115 if the number is selected the player wins $700 if any other number is selected the player wins nothing find the expected value for this game and describe what it means
Answers
Using a discrete distribution, the expected value for this game is of -$1.298, which means that each time he plays, he is expected to lose $1.298.
What is the mean of a discrete distribution?The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.
Considering the situation described in this problem, the distribution for the earnings is given as follows:
P(X = 700) = 1/1000.P(X = -2) = 999/1000.Hence the expected value is given as follows:
[tex]E(X) = 700\frac{1}{1000} - 2\frac{999}{1000} = \frac{700 - 2(999)}{1000} = -1.298[/tex]
The expected value for this game is of -$1.298, which means that each time he plays, he is expected to lose $1.298.
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If x is a real number, what is the smallest possible value of x^2+8 ?
Answers
hi,
smallest value is 8.
x^2 will always be a positive number regardless of the value of x.
the smallest value for a positive number is 0, therefore x^2 +8 will never be smaller than 8
Can anyone help me with this question?:)
Answers
Answer:
ΔABC ≅ ΔEDF
Step-by-step explanation:
Triangle ABC is congruent to triangle EDF because they're the same size.
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
[tex] \sf\triangle ABC \cong \triangle DEF[/tex]
For checking congruency, we need to follow a proper order when choosing the triangle. because each triangle name is unique in itself.
So, According to Triangle ABC, we need to find the triangle with first two letters That resembles AB, that is :
AB = DEand next should be :
BC = EF[tex] \qquad \large \sf {Conclusion} : [/tex]
so, now we got the sense for naming, therefore the answer will be :
[tex] \sf\triangle ABC \cong \triangle DEF[/tex]
John is twice as old as Peter. In 8 years, John's age will be 2 more than the sum of their present ages. How old is John now?
Answers
Answer:12
Step-by-step explanation:
Peter's age = x
John's age = y
y=2x
after 8 years = y+8=y+x+2
=(y-y)+8-2=x
=6=x
y=2(6)=12
What is the price of a two year bond with a 9% annual coupon and a yield to maturity of 8%? 101.78 105.25 102.53 97.51
Answers
The bond price 101.78
What is the price of a bond?
A bond price is the present value of its future cash flows discounted at the yield to maturity which is the appropriate discount rate.
Specifically, the bond price is the present value of annual coupons for 2 two years and the face value discounted at the 8% yield to maturity.
We can determine the bond price using the present value formula of a single cash flow for all cash flows.
PV=FV/(1+r)^N
FV=future cash flow(annual coupons for 2 years and face value)
annual coupon=face value*coupon rate
face value=100
coupon rate=9%
annual coupon=100*9%
annual coupon=9
r=discount rate=8%
N=year of cash flows, 1 for year 1 and 2 for year 2
bond price=9/(1+8%)^1+9/(1+8%)^2+100/(1+8%)^2
bond price= 101.78
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What is the volume of the cylinder?
Answers
The volume of a cylinder with a diameter of 16 feet and height of 10 feet is 2010.62 ft³
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The volume of a cylinder with radius (r) and height (h) is:
Volume = πr²h
Given that h = 10 ft, r = 16/2 = 8 ft
The volume = π * 8² * 10 = 2010.62 ft³
The volume of a cylinder with a diameter of 16 feet and height of 10 feet is 2010.62 ft³
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Can you please help me with this?
Answers
Measure the angle in degrees.
Answers
Answer:
Angle is measured in degrees (°) and radians. It is formed between the two adjacent sides of a polygon. Every polygon has different sides and different numbers of angles. The formula to find the angles in degrees is useful in geometry and trigonometry. It is essential to understand other concepts of mathematics, such as arc, a central angle of the circle, etc.
A full circle = 360°
A straight line = 180°
A semicircle= 180°
A Quarter circle = 90°
exampleGiven: Hypotenuse = 12
Perpendicular = 6
The trigonometry function to calculate the angle is given by:
sinA = 6/12
A = 30°