The correct answers are:
1. The equation |-x -4| = 8 will have two solutions. (True)
5. The equation |0.5x – 0.75| + 4.6 = 0.25 will have no solutions. (True)
What is Equation?
An equation is a mathematical statement with an 'equal to =' symbol between two expressions that have equal values.
1. The equation |-x -4| = 8 will have two solutions. (True)
|-x - 4| = 8
-x -4 = ±8
-x -4 = 8 and -x -4 = -8
-x = 8 + 4 and -x = -8 + 4
-x = 12 and -x = -4
x = -12 and x = 4
Therefore, it has two solutions x ∈ {-12, 4}
2. The equation 3.4|0.5x - 42.1| = -20.6 will have one solution. (False)
Since the right side of the equation has a negative value therefore, according to rules of absolute value equations, it has no solution.
3. The equation |1/2x - 3/4| = 0 will have no solutions. (False)
|(1/2)x - 3/4| = 0
(1/2)x - 3/4 = ±0
Since ±0 is the same
(1/2)x = 3/4
x = 2X3/4
x = 3/2
Therefore, it has one solution x = 3/2
4. The equation |2x – 10| = –20 will have two solutions. (False)
Since the right side of the equation has a negative value therefore, according to rules of absolute value equations, it has no solution.
5. The equation |0.5x – 0.75| + 4.6 = 0.25 will have no solutions. (True)
|0.5x – 0.75| + 4.6 = 0.25
|0.5x – 0.75| = 0.25 - 4.6
|0.5x – 0.75| = -4.35
Since the right side of the equation has a negative value therefore, according to rules of absolute value equations, it has no solution.
6. The equation |(1/8)x - 1| = 5 will have infinitely many solutions. (False)
|(1/8)x - 1| = 5
(1/8)x - 1 = ±5
(1/8)x - 1 = 5 and (1/8)x - 1 = -5
(1/8)x = 5 + 1 and (1/8)x = -5 + 1
(1/8)x = 6 and (1/8)x = -4
x = 6X8 and x = -4X8
x = 48 and x = -32
Thus, it has two solutions x ∈ {48, -32}
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At the beginning of the school year, Jamie had $500 in her savings account. She wants to have at least $200 left in the account at the end of the school year. Each week, she withdraws $30 for spending money. To determine how many weeks she can spend $30, Jamie wrote and solved this inequality.
The mistake she had done is she should have reversed the inequality as per the division property of inequality.
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.
The inequality is:
500 − 30x ≥ 200 −500 −500 −30x ≥ −300 x ≥ 10
Given:
Jamie had $500 in her savings account.
She wants to have at least $200 left in the account at the end of the school year.
The inequality she had done is
500 − 30x ≥ 200 −500 −500 −30x ≥ −300 x ≥ 10
But when she was dividing she should have reversed the inequality as per the division property of inequality.
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Simply the function f(x)=7(3Square root 54^x)
Answer:
54 = 2 × 3 × 3 × 3 = 2 × 3³
[tex] f(x) = 7(\sqrt[3]{54})^x [/tex]
[tex] f(x) = 7(\sqrt[3]{3^3 \times 2})^x [/tex]
[tex] f(x) = 7(3\sqrt[3]{2})^x [/tex]
Initial value: x = 0
[tex] f(0) = 7(3\sqrt[3]{2})^0 [/tex]
[tex] f(0) = 7(1) [/tex]
[tex] f(0) = 7 [/tex]
The initial value is 7.
The domain is all real numbers.
The range is all real numbers greater than zero.
The following two way table shows the number of students of a school who have a cell phone and or have a part-time job.
Answer:
the answer is b.40 that the kids that are working and have phone b
21. What is the perimeter of the triangle?
18.2 units
18.3 units
9 units
15.5 units
(1,6)
(3, 1)
(6, 1)
Answer:
C) 15.5 units
Step-by-step explanation:
(5x-1) -(2-8x) for x = 0.75
Common types of data patterns that can be identified when examining a time series plot include all of the following except ______.
Answer:
Vertical is the answer
A bakery makes and sells designer cakes. The function d (x) = 125€ represents
the income, in dollars, from selling a cakes. The function p (y) = y - 1620
represents the monthly profit, in dollars, if the bakery makes y dollars in income for
the month. What is the profit from selling 30 designer cakes in a single month?
The profit from selling 30 designer cakes in a single month is; $2130.
What is the profit for selling 30 cakes in a month?It follows from the task content that the income function as given is; d(x) = 125 × a.
Hence, when 30 designer cakes are sold, thee income is; 125 × 30 = 3750$.
The profit which is a function of the income y is given as; p (y) = y - 1620.
On this note, if follows that the profit is; p (y) = 3750 - 1620 = $2130.
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Exit A bag contains 4 blue balls, 7 yellow balls and 4 white balls. Event A is defined as drawing a blue ball on the first draw and event B is defined as drawing a white ball on the second draw. If two balls are drawn from the bag, one after the other and not replaced, what is P(B|A) expressed in simplest form?
A. 2/7
B. 3/14
C. 4/15
D. 4/11
please hurry
P(B|A) expressed in simplest form is 4/15. Option C is correct answer.
What is Probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
Here, probability of event A = 4/15
probability of event B = 4/15
P(B|A) = P(A ∩ B)/P(B)
P(A ∩ B) = P(A) X P(B)
= (4/15)(4/15)
= 16/225
Now, conditional probability;
P(B|A) = (16/225) / (4/15)
= (16/225)(15/4)
= (16 X 15) / (225 X 4)
= 4/15
Thus, P(B|A) expressed in simplest form is 4/15. Option C is correct answer.
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Evaluate − 5 x 2 + 4 y 3 when x = − 2 and y = 2
Answer:
hope this is helpful.
putting values of X and y in the equation
Answer is 12
Answer:
answer is 39
Step-by-step explanation:
So, we start with the original problem:
3
x
2
−
4
y
2
Then we substitute the given
x
and
y
values into the expression:
3
(
5
)
2
−
4
(
3
)
2
Now, according to the order of operations, we simplify the exponential powers first, thus, reducing the expression to this:
3
(
25
)
−
4
(
9
)
Then, we use the order of operations again and do the multiplication next:
75
−
36
We then use the order of operations a final time and finish off the expression with subtraction:
39
The graphs below have the same shape. What is the equation of the red
graph?
Answer:
g(x) = x^2+4
Step-by-step explanation:
The graph of f(x) = x^2 is translated up 4 units to become g(x) = x^2+4
i need help asappppppppppppp
Answer: Choice [D] - "power of a power" ✅
Step-by-step explanation:
Hii, do you need to know which law you should use to simplify [tex]\sf\bigg(x^4\bigg)^9[/tex]?
No problem!
The law we will use here is "power of a power".
What "power of powers" means is we raise a power to a power, which is exactly what we do here: We raise x^4 to the power of 9. To simplify our expression, we multiply the powers. ([tex]\boldsymbol{4\cdot9}[/tex])
So the right answer is: Choice [D] - "Power of a power"
The simplified answer is [tex]\LARGE\boldsymbol{x^{4\cdot9}=x^{36}}[/tex]
Voila! There's our answer, cheers!
--
Hope that this helped! Best wishes.
[tex]\it Reach\;far.\;Aim\;high.\;Dream\;big.}[/tex]
--
In the year 2008, a person bought a new car for $23500. For each consecutive year after that, the value of the car depreciated by 10%. How much would the car be worth in the year 2011, to the nearest hundred dollars?
Answer:
$17131.50
Step-by-step explanation:
23500 decrease 10% =
23500 × (1 - 10%) = 23500 × (1 - 0.1) = 21150
21150 decrease 10% =
21150 × (1 - 10%) = 21150 × (1 - 0.1) = 19035
19035 decrease 10% =
19035 × (1 - 10%) = 19035 × (1 - 0.1) = 17131.5
In a basket, there are 52 apples or pears. The number of apples is 8 more than the number of
pears. How many numbers of apples and pears in the box?
Answer:
44 pears and 52 apples
Step-by-step explanation:
pears are 8 more than apple so 52-8 = 44
Number of apples and pears in a box is equals to [tex]30[/tex] and [tex]22[/tex] respectively.
What is number?" Number is defined as the count of any given quantity as per given condition."
According to the question,
Given,
Total number of apples [tex]= 52[/tex]
[tex]'x'[/tex] represents the number of pears
[tex]'x+ 8'[/tex] represents the number of apples
As per the given condition required equation we get,
[tex]x + x + 8 = 52\\\\\implies 2x = 52-8\\\\\implies x = \frac{44}{2} \\\\\implies x = 22[/tex]
number of pears [tex]= 22[/tex]
number of apples [tex]= 22+8[/tex]
[tex]=30[/tex]
Hence, number of apples and pears in a box is equals to [tex]30[/tex] and [tex]22[/tex] respectively.
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write these recurring decimals as fractions:
1. 0.7 recurring
2. 0.7235 [the 3 and 5 are recurring]
Answer:
[tex]\frac{7}{9}[/tex] and [tex]\frac{7163}{9900}[/tex]
Step-by-step explanation:
we require 2 equations with the repeating digits placed after the decimal point.
(1)
let x = 0.777... (1) ← multiply both sides by 10
10x = 7.777... (2)
subtract (1) from (2) thus eliminating the repeating digits
9x = 7 ( divide both sides by 9 )
x = [tex]\frac{7}{9}[/tex]
(2)
let x = 0.723535.. ( multiply both sides by 100 and 10,000 )
100x = 72.3535.... (1)
10,000x = 7235.3535..... (2)
subtract (1) from (2) thus eliminating the repeating digits
9900x = 7163 ( divide both sides by 9900 )
x = [tex]\frac{7163}{9900}[/tex]
What is the inverse of f(x)=5x/3+5
Answer:
f^-1(x)=8x/5
Step-by-step explanation:
The inverse of f(x)=5x/3+5 is 8x/5
The inverse function of f(x)=5x/3+5 is f-1(x) = 3x/5 - 15
How to determine the inverse?We have:
f(x)=5x/3+5
Rewrite as:
y=5x/3+5
Swap x and y
x = 5y/3 + 5
Subtract 5 from both sides
5y/3 = x - 5
Multiply through by 3
5y = 3x - 15
Divide through by 5
y = 3x/5 - 15
Rewrite as:
f-1(x) = 3x/5 - 15
Hence, the inverse function of f(x)=5x/3+5 is f-1(x) = 3x/5 - 15
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Select the correct answer from each drop-down menu. polygon abcde has the vertices a(2, 8), b(4, 12), c(10, 12), d(8, 8), and e(6, 6). polygon mnopq has the vertices m(-2, 8), n(-4, 12), o(-10, 12), p(-8, 8), and q(-6, 6). a transformation or sequence of transformations that can be performed on polygon abcde to show that it is congruent to polygon mnopq is a . if polygon mnopq is translated 3 units right and 5 units down, it will coincide with a congruent polygon, vwxyz, with its vertices at
1). Option C
2). Option A
What is Polygon?Polygon is given as a closed two-dimensional figure with three or more straight lines.
The given vertices of polygon ABCDE are A(2, 8), B(4, 12), C(10, 12), D(8, 8) and E(6, 6)
After reflection new polygon formed MNOPQ has the vertices M(-2, 8), N(-4, 12), O(-10, 12), P(-8, 8) and Q(-6, 6).
By comparing the vertices we find the x-coordinates of polygon ABCDE have been changed to MNOPQ by negative notation only. Y- coordinates are same.
Therefore, polygon ABCDE has been reflected across the y-axis.
Option C. is the answer.
If polygon MNOPQ is translated 3 units right and 5 units down then the new vertices of congruent polygon VWXYZ will be
M(-2, 8) = [(-2 - 3), (8 + 5)] = (-5, 13)
N(-4, 12) = [(-4 - 3), (12 + 5)] = (-7, 17)
O(-10, 12) = [(-10 - 3),(12 + 5)] = (-13, 17)
P(-8, 8) = [(-8 - 3), (8 + 5)] = (-11, 13)
Q(-6, 6) = [(-6 -3),(6 + 5)] = (-9, 11)
Thus, Option A. is the correct option.
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Answer:
Step-by-step explanation:
the
A website sells a dress at £50 and shoes at £43.
The website has an offer:
Buy a dress and shoes together and get
1
3
off the price.
There is also a shipping and handling charge of £7 added at the end, after any discount.
If Ruth buys both a dress and shoes, how much will she actually pay?
Answer:
£69
Step-by-step explanation:
Given information:
Cost of dress = £50Cost of shoes = £43Discount offer: Buy a dress and shoes together and get 1/3 off the price.Shipping & handling charge = £7 (added after the discount is applied)Cost of buying a dress and shoes:
⇒ £50 + £43 = £93
Discount:
⇒ 1/3 of £93 = 1/3 × 93 = £31
Cost of goods after discount is applied:
⇒ £93 - £31 = £62
Addition of shipping and handling:
⇒ £62 + £7 = £69
Therefore, Ruth will pay £69 if she buys a dress and shoes.
(06.06)
Which of the following demonstrates the Commutative Property of Multiplication?
5(2a − 3) = 10a − 15
10a − 15 = (2a − 3) ⋅ 5
5(2a − 3) = (2a − 3) ⋅ 5
(5 ⋅ 2a) − 3 = 5(2a − 3)
The correct answer is option C which is 5(2a − 3) = (2a − 3) ⋅ 5 showing commutative property.
What is commutative property?If altering the operands' order has no effect on the outcome, the binary operation is commutative in mathematics.
a x b = b x a
So for the expression 5(2a − 3) = (2a − 3) ⋅ 5 suppose 5 is a and ( 2a - 3 ) is b so.
a x b = b x a
5(2a − 3) = (2a − 3) ⋅ 5
Therefore the correct answer is option C which is 5(2a − 3) = (2a − 3) ⋅ 5 showing commutative property.
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Menna is traveling in a country that measures its temperature in degrees Celsius. If the high temperature for tomorrow will be 25
∘
C, what is the equivalent temperature in
∘
F?
a. 102.6∘
F
b. 57∘
F
c. 77∘
F
d. 45.9∘
F
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: Temp = 77° F[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: f = \bigg (c \sdot \cfrac{9}{5} \bigg) + 32[/tex]
[ convert 25° C to °F ]
[tex]\qquad \tt \rightarrow \: \bigg (25 \sdot \cfrac{9}{5} \bigg) + 32[/tex]
[tex]\qquad \tt \rightarrow \: (5 \sdot9) + 32[/tex]
[tex]\qquad \tt \rightarrow \: 45 + 32[/tex]
[tex]\qquad \tt \rightarrow \: 77 \degree \: \: f[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Answer:
77
Step-by-step explanation:
took the quiz
Which is true about the solution to the systems of inequalities shown?
Answer:
There are no solutions
Step-by-step explanation:
If y is greater or equal to 3x+1 it can not be less than 3x-3 since 3x-3 is 4 less than 3x+1. Therefore, there can not be any solutions for the system of inequalities.
Solve |2x + 2| = 10
Answer:
x = - 6 , x = 4
Step-by-step explanation:
the absolute value function always gives a positive value but the expression inside can be positive or negative , that is
2x + 2 = 10 or - (2x + 2) = 10
solving both
2x + 2 = 10 ( subtract 2 from both sides )
2x = 8 ( divide both sides by 2 )
x = 4
or
- (2x + 2) = 10
- 2x - 2 = 10 ( add 2 to both sides )
- 2x = 12 ( divide both sides by - 2 )
x = - 6
Indira makes a box-and-whisker plot of her data. she finds that the distance from the minimum value to the first quartile is greater than the distance between the third quartile and the maximum value. which is most likely true?
The statement that is most likely true is , The mean is less than the median because the data is skewed to the left.
Option E is the correct answer.
What is a Box and Whisker Plot ?The method of representing the variation in a data set is called a Box and Whisker Plot .
A data distribution in which the data is skewed to the left
the mean is less than the median.
A data distribution in which the data is skewed to the right
the mean of the data is greater than the median.
It is given in the question that
The distance from the minimum value to the first quartile is greater than the distance between the third quartile and the maximum value.
this means data is skewed to the left,
Therefore, the statement that is most likely true is , The mean is less than the median because the data is skewed to the left.
Option E is the correct answer.
The complete question is
Indira makes a box-and-whisker plot of her data. She finds that the distance from the minimum value to the first
quartile is greater than the distance between the third quartile and the maximum value. Which is most likely true?
The mean is greater than the median because the data is skewed to the right.
The mean is greater than the median because the data is skewed to the left.
The mean is less than the median because the data is skewed to the right
The mean is less than the median because the data is skewed to the left.
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a= help me please thank u
Step-by-step explanation:
the circumference of a whole circle is
2×pi×r
with r being the radius. which is in our case a.
so,
2×pi×a
the part arc of just a sector of the circle is just the angle/360 part (as the whole circle is 360°).
we therefore know
27×pi = 2×pi×a × 60/360 = 2×pi×a × 1/6 = pi×a × 1/3
3×27×pi = pi×a
81×pi = pi×a
a = 81
Solve
P =
Check
P-2w
2
= 1 for P.
Answer:
P= 2l + 2W
Step-by-step explanation:
(P-2W)/2= l
(P-2W)= 2l
P-2W= 2l
P= 2l + 2W
state the domain and range for the function (f)x = 2csc (x/2))
Step-by-step explanation:
domain XER\{2kπ},kE
What is 8 Divided by 231 to the nearest thousandth
Answer:
0.346
Step-by-step explanation:
brainiest pls ty
Answer:
.,..
Step-by-step explanation:
0.346 ............ I'm..............
I need help with this please. Brainliest to person who answers first. Its worth 12 points.
Question is in attachment.
Answer:
54x + 36
Step-by-step explanation:
Simplify:
First open the brackets by multiplying each term by 7.
5x - 6 + 7(7x + 6) = 5x - 6 + 7*7x + 7*6
= 5x - 6 + 49x + 42
= 5x + 49x - 6 + 42
Combine like terms. Like terms have same variable with same power. Here 5x and 49x are like terms & (-6) and 42 are like terms (Constants)
= 54x + 36
Answer:
54x +36
Step-by-step explanation:
5x - 6 + 7(7x+6) multiply
5x -6 +49x+42 add like terms
54x + 36 that's the answer
how did the temperature change if at first it changed by 5 percent then it changed by 20
CAN SOMEONE HELP ILL GIVE 70 POINTS PLSSSSSSS
Answer:
26% increase
Step-by-step explanation:
Initial temperature= t
5% increase= t+ 5%= 1.05t
20% increase= 1.05t +20%= 1.05t*1.2= 1.26t
1.26 t= t + 26%
So temperature increased by 26%
Jamie is interested in taking dance lessons, but she would have to pay $35 for balet shoes and also pay $20 per hour. write an ssion that represents jamies total cost in terms of h
An investment group compares returns on an account against the function represented in the table, where x is the time in years and f(x) is the total return on investment.
Which describes the function over the interval given in the table?
a decreasing quadratic function
an increasing quadratic function
a decreasing exponential function
The function over the interval is an increasing exponential function.
What is quadratic function?A quadratic function is" a polynomial function with one or more variables in which highest exponent of variable is 2".
The complete question is
An investment group compares returns on an account
against the function represented in the table, where x is the
time in years and f(x) is the total return on investment.
Which describes the function over the interval given in the
table?
х
a decreasing quadratic function
an increasing quadratic function
a decreasing exponential function
an increasing exponential function
0
5
f(x)
10,000
12,201.90
14,888.64
22,167.15
10
20
A decreasing quadratic function is the vertex of the parabola lies on the axis parabola. So, time in years change does not give maximum total return on investment.
For increasing quadratic equation, the graph increasing at one side of the axis and decreases at other side.
For, Exponential function
When the exponential function then it shows total return on investment is not maximum.
When the exponential function is increasing it shows time goes, total return on investment is maximum.
Hence, the exponential function is increasing.
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