Answer:
80 in.
Step-by-step explanation:
The dimensions of the dilated picture are ...
4·4 in = 16 in . . . by . . . 4·6 in = 24 in
Then the perimeter of the painting is the sum of the lengths of its sides ...
16 in + 24 in + 16 in + 24 in = 80 in
Answer:
80in
Step-by-step explanation:
The scale factor of the dilation is 4, so a 1 inch by 1 inch square on the photograph represents a 4 inch by 4
inch square on the painting.
The height of the image is the product of the height of the preimage and the scale factor.
w=4(6)=24
in
.
The width of the image is the product of the width of the preimage and the scale factor.
h=4(4)=16
in
.
So, the perimeter is
P=2(16)+2(24)=80
in
.
The figure shows two rectangles. The larger rectangle is 16 inches long and 24 inches wide. The smaller rectangle is 4 inches long and 6 inches wide. The sides of the larger rectangle are parallel to the corresponding sides of the smaller one, respectively.
Therefore, the perimeter of the painting is 80
inches.
Shylah is purchasing 4 patio chairs that are each 25% off the original price p.
Which expressions can she use to find the total cost of all 4 chairs?
Select each correct answer.
0.75p
4(p−0.25p)
3p
4p−0.25p
Answer: Second option is correct.
Step-by-step explanation:
Let the original price of chair be 'p'.
Number of chairs = 4
Discount rate = 25%
So, Amount of discount would be
[tex]\dfrac{25}{100}p\\\\=0.25p[/tex]
So, Cost of each chair after discount would be
[tex]p-0.25p[/tex]
So, Cost of all 4 chairs would be
[tex]4(p-0.25p)[/tex]
Hence, Second option is correct.
Answer:
25% is being taken off the original price, p, of each patio chairs.
That means the price of each patio chair is the full price, p, minus 25% of the original price.
1) To find 25% of the original price, multiply p (original price) by the decimal form of 25%, or 0.25. That means 25% off original price = 0.25p.
2) Now subtract 0.25p from the original price of the chairs to find the price of each (1) chair. p - 0.25p
Shylah is buying 4 chairs at that discounted price. That means you need to multiply the discounted price, p - 0.25p, by 4. Shylah is paying 4(p-0.25p) total for the 4 chairs, which is answer choice B.
Since you can choose more than one choice, you can simplify 4(p-0.25p) by subtracting what is in the parathesis, then multiplying, following the order of operations:
4(p-0.25p)
= 4(0.75p)
= 3p
That is answer choice A.
--------
Answer: Choices A and B, 3p and 4(p−0.25p).
Step-by-step explanation:
Choices A and B, 3p and 4(p−0.25p).
Consider the following sequence of numbers.
The common ratio of the sequence is =?
The sum of the first five terms of the sequence is=?
Blank 1 options: -1/3,-3,1/3,3
Blank 2 options: -303,183,-60,363
Answer:
Blank 1 is -3
Blank 2 is 183
Step-by-step explanation:
Let r be common ratio
[tex]r = \frac{ - 9}{3} \\ r = - 3[/tex]
Sum of first 5 terms
[tex]s = \frac{a( {r}^{n} - 1)}{r - 1} \\ s = \frac{ 3( {( - 3)}^{5} - 1) }{ - 3 - 1} \\ s = 183[/tex]
Answer:
1) Second option: -3
2) Second option: 183
Step-by-step explanation:
1) You can use any two consecutive terms to find the common ratio. This is given by:
[tex]r=\frac{a_n}{a_{n-1}}[/tex]
You can choose these consecutive terms:
[tex]a_n=-9\\a_{n-1}=3[/tex]
Then the common ratio "r" is:
[tex]r=\frac{-9}{3}=-3[/tex]
2) The sum of the first "n" terms can be found with this formula:
[tex]S_n=\frac{a_1(r^n-1)}{r-1}[/tex]
Since ther first term is 3 and you need to find the sum of the first 5 terms, then:
[tex]a_1=3\\n=5[/tex]
Substituting into [tex]Sn=\frac{a_1(r^n-1)}{r-1}[/tex], you get:
[tex]S_{(5)}=\frac{3((-3)^5-1)}{-3-1}=183[/tex]
Mike is a salesperson in a retail carpet store. He is paid $500 base salary per month plus 5% commission on sales over $10,000. His sales this month were $23,750. His total deductions were $152.75. What is Mike’s net pay?
Answer:
$1034.75
Step-by-step explanation:
Mike's net pay is ...
base pay + commission - deductions
= $500 + 5%(23750 -10000) -152.75
= 347.25 + 0.05×13750
= $1034.75
Answer:
$1034.75
Step-by-step explanation:
Here we are given that the base salary of Mike is $500. He is also rewarded with some commission depending on sales. Hence we can bifurcate his gross pay as
Gross Pay = Base Pay + Commission
Commission = 5% of Sales over $10000
= 5% of (23750-10000)
= 5% of 13750
= 0.05*13750
= 687.50
Hence Gross pay = 500 + 687.50
= 1187.50
Also given that he has some deductions also i.e. $152.75 .
Therefor Net pay = Gross pay - Deductions
= 1187.50-152.75
= 1034.75
Hence Net Pay = $1034.75
Identify m∠MNP. PLEASE HELP!!!!
The measure of angle MNP also means the measure of angle N.
N = (1/2)(arc MP)
N = (1/2)(180°)
N = 90°
The measure of angle MNP is 90°.
The measure of ∠MNP is 90.
What is arc angle?An arc of a circle is any part of the circumference. The angle subtended by an arc at any point is the angle formed between the two line segments joining that point to the end-points of the arc.
As, the degree of the arc of a circle is usually 2 times the measure of the corresponding angle.
The measure of angle MNP
MNP = (1/2)(arc MP)
MNP = (1/2)(180°)
MNP = 90°
Hence, the measure of angle MNP is 90°.
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if f(x)=3x+2,find f(f^-1(14)).
Answer: 14
Step-by-step explanation:
f(x) = 3x + 2
To find f⁻¹, swap the x's and y's and solve for y --> Note: f(x) is y
x = 3y + 2
x - 2 = 3y
[tex]\dfrac{x-2}{3}=y[/tex]
[tex]\implies f^{-1}(x)=\dfrac{x-2}{3}[/tex]
[tex]\implies f^{-1}(14)=\dfrac{14-2}{3}[/tex]
[tex]\implies f^{-1}(14)=\dfrac{12}{3}[/tex]
[tex]\implies f^{-1}(14)=4[/tex]
f(f⁻¹(14)) = f(4)
f(4) = 3(4) + 2
= 12 + 2
= 14
NOTE: the simplified version is .... f and f⁻¹ cancel out, leaving you with 14
What would the coordinates of the new image be? (View Picture)
Answer:
T(1, 5), R(7, 7), A(7, 1), M(4, 5)
Step-by-step explanation:
The mapping for -90° rotation is (x, y) ⇒ (y, -x).
for example, T(-5, 1) ⇒ T'(1, 5)
__
If you're doing this with pencil and paper, you can draw the image and axes the way it is, then rotate your drawing 90° clockwise (so the axes line up) and copy it into the first quadrant.
describe how you would simplify the given expression. (20x^5y^2/5x^-3y^7)-3
[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\[/tex]
[tex]\bf \left( \cfrac{20x^5y^2}{5x^{-3}y^7} \right)^{-3}\implies \left( \cfrac{5x^{-3}y^7}{20x^5y^2} \right)^3\implies \left( \cfrac{5^3x^{-3\cdot 3}y^{7\cdot 3}}{20^3x^{5\cdot 3}y^{2\cdot 3}} \right)\implies \cfrac{5^3}{20^3}\cdot \cfrac{x^{-9}y^{21}}{x^{15}y^6} \\\\\\ \cfrac{1}{64}\cdot \cfrac{y^{21}\cdot y^{-6}}{x^{15}\cdot x^9}\implies \cfrac{1}{64}\cdot \cfrac{y^{21-6}}{x^{15+9}}\implies \cfrac{y^{15}}{64x^{24}}[/tex]
Answer:
Simplify inside the parentheses by dividing coefficients, subtracting the exponents on like bases, and raising the resulting expression to the –3 power. Then, write bases with positive exponents.
Raise the numerator and denominator to the –3 power. Then, using the power of a power property, multiply the exponents. Divide the coefficients and subtract the exponents on like bases, then write with positive exponents.
Step-by-step explanation:
Find an equation for the nth term of the arithmetic sequence.
-3, -5, -7, -9, ...
Answer:
a(n) = -3 - 2(n-1)
Step-by-step explanation:
The most general formula for the nth term of an arithmetic sequence (such as this sequence is) is
a(n) = a(1) + c(n-1), where c is the common difference.
Here a(1) = -3 and c = -2.
Thus,
a(n) = -3 - 2(n-1).
Solve the equation 32 – 5y = 87.
A. 11
B. –23.8
C. –11
D. 23.8
Answer:
C. :)
Step-by-step explanation:
Move all terms not containing
y
y
to the right side of the equation.
−
5
y
=
55
-5y=55
Divide each term by
−
5
-5
and simplify.
y
=
−
11
y=-11
Answer: the answer is - A. -11
Step-by-step explanation:
Determine all positive number replacements (less than the modulus) for the question mark that make the statement true.
3 x ? = 1 (mod 6)
Answer:
There are none.
Step-by-step explanation:
3 is a divisor of the modulus, so the product mod 6 will be either 3 or 0.
In the modular arithmetic problem 3 x ? = 1 (mod 6), the correct positive number replacement for the question mark is 3.
The problem given is a modular arithmetic equation: 3 x ? = 1 (mod 6). To solve for the question mark (?), we need to find a number that when multiplied by 3 and divided by 6, leaves a remainder of 1. Since we are working with mod 6, the potential replacements for the question mark can only be positive numbers less than 6.
The steps to find the solution are as follows:
Try each positive number less than 6 to see which, when multiplied by 3, yields a remainder of 1 when divided by 6.
By testing, we find that 3 x 5 = 15, and 15 mod 6 = 3 x 6 + 1 (15 = 2*6 + 3).
Since we need a remainder of 1, and not 3, we should keep looking.
Next, 3 x 3 = 9, and 9 mod 6 = 1 since 9 = 1*6 + 3 = 3 x 3.
Thus, the number that satisfies the equation is 3 since it makes the modular equation true: 3 x 3 = 9, and 9 mod 6 = 3 x 6 + 3, which gives us a remainder of 1.
The correct positive number replacement for the question mark making the statement true is 3.
8.06
A study was completed in Florida. In southern Florida, the study involved 3,000 patients; 54% of them experienced flulike symptoms during the same month. The study had a margin of error of 1.8%. What does that mean for the study?
Answer:
The confidence interval is between 52.2% and 55.8%
Step-by-step explanation:
Since the study showed that 54% of the people involved in the study had experienced flu-like symptoms, and the margin of error is 1.8%, which is relatively small margin of error, we can easily come to the confidence interval. Since the margin of error goes both ways, above and below the official percentage, in order to get to the confidence interval we need to deduct the margin of error from the percentage, and also, separately, to add the margin of error to the percentage.
54 - 1.8 = 52.2
So the low border of the confidence level is 52.2%.
54 + 1.8 = 55.8
So the high border of the confidence level is 55.8%.
Answer:
the interval is between 52.8% and 55.8%
Step-by-step explanation:
Molly shared a spool of ribbon with 12 people. Each person received 3 feet of ribbon. Which equation can she use to find r, the number of feet of ribbon that her spool originally had?
For this case we have that if Molly spent all the spool ribbon with 12 people, then "r" would be given by the product of 12 for the amount of ribbon that each person received, that is:
[tex]r = 12 * 3\\r = 36 \ft[/tex]
Thus, the spool initially had 36 feet of ribbon.
If Molly also keeps 3 feet of ribbon, then the value of "r" is given by:
[tex]r = 13 * 3\\r = 39 \ ft[/tex]
In this case, the ribbon spool initially had 39 feet of ribbon.
Answer:
[tex]r = 36 \ ft[/tex]shared between 12 people
[tex]r = 39 \ ft[/tex]shared between 12 people and Molly
Answer:
It is C. aka 3r = 12.
Step-by-step explanation:
If θ is an angle in standard position that terminates in Quadrant III such that tanθ = 5/12, then sinθ/2 = _____
Answer:
sin θ/2=5√26/26=0.196
Step-by-step explanation:
θ ∈(π,3π/2)
such that
θ/2 ∈(π/2,3π/4)
As a result,
0<sin θ/2<1, and
-1<cos θ/2<0
tan θ/2=sin θ/2/cos θ/2
such that
tan θ/2<0
Let
t=tan θ/2
t<0
By the double angle identity for tangents
2 tan θ/2/1-(tanθ /2)^2 = tanθ
2t/1-t^2=5/12
24t=5 - 5t^2
Solve this quadratic equation for t :
t1=1/5 and
t2= -5
Discard t1 because t is not smaller than 0
Let s= sin θ/2
0<s<1.
By the definition of tangents.
tan θ/2= sin θ/2/ cos θ/2
Apply the Pythagorean Algorithm to express the cosine of θ/2 in terms of s. Note the cos θ/2 is expected to be smaller than zero.
cos θ/2 = -√1-(sin θ/2)^2 = - √1-s^2
Solve for s.
s/-√1-s^2 = -5
s^2=25(1-s^2)
s=√25/26 = 5√26/26
Therefore
sin θ/2=5√26/26=0.196....
Shay works each day and earns more money per hour the longer she works. Write a function to represent a starting pay of $20 with an increase each hour by 4%. Determine the range of the amount Shay makes each hour if she can only work a total of 8 hours.
A.20 ≤ x ≤ 22.51
B.20 ≤ x ≤ 25.30
C.20 ≤ x ≤ 26.32
D.20 ≤ x ≤ 27.37
Answer:
Function: [tex]p(x)=20(1.04)^x[/tex]Range: option D. 20 ≤ x ≤ 27.37Explanation:
The function must meet the rule that the pay starts at $20 and it increases each hour by 4%.
A table will help you to visualize the rule or pattern that defines the function:
x (# hours) pay ($) = p(x)
0 20 . . . . . . . . [starting pay]
1 20 × 1.04 . . . [ increase of 4%]
2 20 × 1.04² . . . [increase of 4% over the previous pay]
x 20 × 1.04ˣ
Hence, the function is: [tex]p(x)=20(1.04)^x[/tex]
The range is the set of possible outputs of the function. To find the range, take into account that this is a growing exponential function, meaning that the least output is the starting point, and from there the output will incrase.
The choices name x this output. Hence, the starting point is x = 20 and the upper bound is when the number of hours is 8: 20(1.04)⁸ = 27.37.
Then the range is from 20 to 27.37 (dollars), which is represented by 20 ≤ x ≤ 27.37 (option D from the choices).
Answer:
its D for shure
Step-by-step explanation:
30p question
Calculate the missing values.
For the six month period given, Fred wants to calculate the monthly deviation from the average.
Month Sales Average Deviation
July $1,250 1,412.50 -162.50
Aug. $1,700 1,412.50 ( )
Sept. $1,125 1,412.50 ( )
Oct. $1,850 1,412.50 ( )
Nov. $1,500 1,412.50 ( )
Dec. $1,050 1,412.50 ( )
Subtract the average from the sales to get the deviation.
Aug. 1700 - 1412.50 = 287.50
Sept. 1125 - 1412.50 = -287.50
Oct. 1850 - 1412.50 = 437.50
Nov. 1500 - 1412.50 = 87.50
Dec. 1050 - 1412.50 = -362.50
The monthly deviation from the average exists at 287.50, -287.50, 437.50, 87.50, and -362.50.
Monthly deviation from the averageEstimating the mean average enables you to specify the deviation from the mean by computing the difference between the mean and each value.
Subtract the average from the sales to acquire the deviation.
Aug. 1700 - 1412.50 = 287.50
Sept. 1125 - 1412.50 = -287.50
Oct. 1850 - 1412.50 = 437.50
Nov. 1500 - 1412.50 = 87.50
Dec. 1050 - 1412.50 = -362.50
The monthly deviation from the average exists at 287.50, -287.50, 437.50, 87.50, and -362.50.
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What is the result of
? Use the model to find the answer is c 16.
Answer:
c
Step-by-step explanation:
c
The question related to a mathematical model is not completely clear. It seems to reference an algebraic variable 'c' with a value of 16, but without more context, a more specific answer cannot be provided.
Explanation:Unfortunately, the question you asked is not fully clear. It seems like there is a part missing from the formula you're asking about. However, if you've mentioned that the answer is c 16, it suggests you are referring to a Model which is not clearly described in the question.
If you're referring to an algebraic problem or a model related to algebra, then c could be a variable and 16 its corresponding value. Without more information, I'm afraid I can't provide a more precise answer. Please provide additional details for better understanding of your question.
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Last year, a construction worker had a gross income of $29,700, of which he contributed 7% to his 401(k) plan. If he got paid monthly, how much was deducted from each paycheck for his 401 (k) plan?
Answer:
$173.25
Step-by-step explanation:
His annual contribution is ...
0.07 × $29,700 = $2079
If 1/12 of that is contributed each month, the monthly contribution is ...
$2079/12 = $173.25
Which expression is equivalent?
Answer:
Third choice from the top is the one you want
Step-by-step explanation:
This whole concept relies on the fact that if the index of a radical exactly matches the power under the radical, both the radical and the power cancel each other out. For example:
[tex]\sqrt[6]{x^6} =x[/tex] and another example:
[tex]\sqrt[12]{2^{12}}=2[/tex]
Let's take this step by step. First we will rewrite both the numerator and the denominator in rational exponential equivalencies:
[tex]\frac{\sqrt[4]{6} }{\sqrt[3]{2} }=\frac{6^{\frac{1}{4} }}{2^{\frac{1}{3} }}[/tex]
In order to do anything with this, we need to make the index (ie. the denominators of each of those rational exponents) the same number. The LCM of 3 and 4 is 12. So we rewrite as
[tex]\frac{6^{\frac{3}{12} }}{2^{\frac{4}{12} }}[/tex]
Now we will put it back into radical form so we can rationalize the denominator:
[tex]\frac{\sqrt[12]{6^3} }{\sqrt[12]{2^4} }[/tex]
In order to rationalize the denominator, we need the power on the 2 to be a 12. Right now it's a 4, so we are "missing" 8. The rule for multiplying like bases is that you add the exponents. Therefore,
[tex]2^4*2^8=2^{12}[/tex]
We will rationalize by multiplying in a unit multiplier equal to 1 in the form of
[tex]\frac{\sqrt[12]{2^8} }{\sqrt[12]{2^8} }[/tex]
That looks like this:
[tex]\frac{\sqrt[12]{6^3} }{\sqrt[12]{2^4} }*\frac{\sqrt[12]{2^8} }{\sqrt[12]{2^8} }[/tex]
This simplifies down to
[tex]\frac{\sqrt[12]{216*256} }{\sqrt[12]{2^{12}} }[/tex]
Since the index and the power on the 2 are both 12, they cancel each other out leaving us with just a 2! Doing the multiplication of those 2 numbers in the numerator gives us, as a final answer:
[tex]\frac{\sqrt[12]{55296} }{2}[/tex]
Phew!!!
Which statement is true about a skewed distribution?
A.) the mean lies to the right of the median for a positively skewed distribution.
B.) the mean lies to the left of the median for a positively skewed distribution.
C.) the mean lies to the left of the median for a symmetric distribution
D.) a distribution skewed to the left is said to be negatively skewed.
E.) a distribution skewed to the right is said to be positively skewed.
Answer:
B.) the mean lies to the left of the median for a positively skewed distribution.
Step-by-step explanation:
brainliest please help me asap
Nemo's aquarium is filled with 24 cubic centimeters of water. The base of the aquarium is 20 cm long and 12 cm wide.
What is the height of the water in Nemo's aquarium? in centimeters
Answer:
0.1 cm
Step-by-step explanation:
given : volume = 24 cm³, length = 20 cm, width = 12 cm
Use formula :
Volume = Length x width x height
height = Volume / (length x width) = 24 / (20 x 12) = 0.1 cm
If two polynomial equations have real solutions, then will the equation that is the result of adding, subtracting, or multiplying the two polynomial equations also have real solutions?
No, there are polynomials that have real solutions but when combined would be possible to have no real solutions.
Answer:
No.
Step-by-step explanation:
No, one easy way to see it is with quadratic formulas. There exists quadratic polynomials with no real solutions, then if you add, subtract or multiply two polynomials and obtain a quadratic formula, possibly this polynomial won't have real solutions.
I am going to give one counterexample:
We have the two polynomials [tex]p(x) = x^2+2x+3[/tex] and [tex]q(x)= 2x^2+3x+4[/tex], then is we subtract q(x)-p(x) we obtain
[tex]2x^2+3x+4-(x^2+2x+3) = 2x^2+3x+4-x^2-2x-3 = x^2+x+1.[/tex]
The resulting polynomial is a quadratic polynomial of the form [tex]ax^2+bx+c[/tex] with a=1, b=1 and c=1. This polynomial has no real solutions, you can check it with the discriminating [tex]b^2-4ac = 1^2-4(1)(1) = 1-4 = -3.[/tex] As the discriminating is negative, the polynomial has no real solutions.
Your fish tank holds 35 liters of water. How much is that in milliliter
Answer:
1 litre = 1000 millilitres (ml)
35 litres = 35×1000 => 35000 ml
So your fish tank holds 35000 ml of water
Pls answer fast
Cos65=x/18
Answer:
7.61
Step-by-step explanation:
[tex]cos65=\frac{x}{18}\\x=18cos65\\x=7.61[/tex]
Note: I assumed that all angles were in degrees
For the functions f(x) = 2x^2- 5x + 2 and g(x) = x– 2, find (f/g)(x) and (f/g)(4)
Answer:
[tex]\frac{f}{g}(x)=2x-1\\\\\frac{f}{g}(4)=7[/tex]
Step-by-step explanation:
[tex]\frac{f}{g}(x)=\dfrac{2x^2-5x+2}{x-2}=\dfrac{(x-2)(2x-1)}{(x-2)} =2x-1 \quad\text{x$\ne$2}\\\\\frac{f}{g}(4)=2\cdot 4-1=7 \qquad\text{fill in 4 for x and do the arithmetic}[/tex]
[tex]\left(\dfrac{f}{g}\right)(x)=\dfrac{2x^2-5x+2}{x-2}\\\\\left(\dfrac{f}{g}\right)(4)=\dfrac{2\cdot 4^2-5\cdot 4+2}{4-2}=\dfrac{32-20+2}{2}=7[/tex]
Find the circumference
[tex]\bf \textit{arc's length}\\\\ s=\cfrac{\pi \theta r}{180}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ \cline{1-1} \theta =87\\ s=14 \end{cases}\implies 14=\cfrac{\pi (87)r}{180} \\\\\\ 2520=87\pi r \implies \cfrac{2520}{87\pi }=\boxed{r} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \textit{circumference of a circle}\\\\ C=2\pi r\qquad \qquad \implies C=2~~\begin{matrix} \pi \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ \left(\boxed{\cfrac{2520}{87~~\begin{matrix} \pi \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}} \right)\implies C = \cfrac{5040}{87} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill C\approx 57.93~\hfill[/tex]
Factor the polynomial.
b^2 + 4b + 4
Answer:
(b + 2)^2
Step-by-step explanation:
b^2 + 4b + 4
It's perfect square: a^2 + 2ab + b^2 = (a + b)^2
So
b^2 + 4b + 4 = (b + 2)^2
Answer:
(b + 2)(b + 2)
Step-by-step explanation:
Factor the polynomial.
b^2 + 4b + 4
Sum of 4 which product is 4
Sum: 1 + 3 = 4
2 + 2 = 4
Product: 1 × 4 = 4
2 × 2 = 4
We use 2 × 2 because it sum is the same as the product of 4. Because 2 and 4 are perfect square so we have:
b² + 4b + 4 splitted as
(b + 2)(b + 2) or (b + 2)²
Graph the functions and approximate an x-value in which the exponential function surpasses the polynomial function.
f(x) = 4x
g(x) = 4x2
The 2 in the 2nd equation is supposed to be an exponent btw
Answer:
Hi,
The answer is (-0.383,1) and (2,∞).
Step-by-step explanation:
See the attachment.
g(x) is a parabolic function, and the Image is always ≥ 0.
f(x) is a exponential function, and the Image is always ≥ 0.
At x = -0.383 , g(x) = 0.588 and f(x) = 0.588.
For x=(-0.383, 1), g(x) is greater than f(x).
At x = 1, g(x) = 1 and f(x) = 1.
For x=(1, 2), f(x) is greater than g(x).
At x= 2, g(x) = 16 and f(x) = 16
For x=(2,∞), g(x) is greater than f(x)
What should be done to solve the equation? x+14=21 Add 14 to both sides of the equation. Subtract 14 from the left side of the equation. Add 14 to the left side and subtract 14 from the right side of the equation. Subtract 14 from both sides of the equation.
Answer:
Subtract 14 from both sides of the equation.
Step-by-step explanation:
The subtraction property of equality tells you the equal sign only remains valid if you subtract the same value from both sides of the equation.
Here, we want the 14 on the left side to be replaced by 0. Thus we must add its opposite. Since we must do the same thing to both sides of the equation, we must subtract 14 from both sides of the equation.
Answer:
Last option: Subtract 14 from both sides of the equation.
Step-by-step explanation:
To solve the equation [tex]x+14=21[/tex] you must solve for the variable "x".
To calculate the value of the variable "x" it is important to remember the Subtraction property of equality. This states that:
[tex]If\ a=b\ then\ a-c=b-c[/tex]
Therefore, applying this property, you should subtract 14 from both sides of the equation to find the value of the variable "x". Then:
[tex]x+14-(14)=21-(14)\\\\x=7[/tex]
Match each item in Column A to an answer in Column B. 2. What is the distance between the two points on a number line? Column A Column B 1. X = –6, Y = 11 2. P = 8, Q = –15 3. U = –3, V = –20 4. J = 16, K = 7 A. 9 B. 17 C. 23
Answer:
17 (B)23 (C)17 (B)9 (A)Step-by-step explanation:
The distance between two points on a number line is the difference between the rightmost point and the leftmost point.
1. 11 -(-6) = 11+6 = 17
2. 8 -(-15) = 8+15 = 23
3. -3 -(-20) = -3+20 = 17
4. 16 -7 = 9
y/3 + 8 = -2 solve for y
a. -30
b. -18
c. 18
d. 30
Answer:
[tex]\large\boxed{a.\ -30}[/tex]
Step-by-step explanation:
[tex]\dfrac{y}{3}+8=-2\qquad\text{subtract 8 from both sides}\\\\\dfrac{y}{3}+8-8=-2-8\\\\\dfrac{y}{3}=-10\qquad\text{multiply both sides by 3}\\\\3\!\!\!\!\diagup^1\cdot\dfrac{y}{3\!\!\!\!\diagup_1}=(3)(-10)\\\\y=-30[/tex]