Answers
Solution
Given the logarithmic statement below
[tex]\ln7=x[/tex]To change the statement to an exponential statement, we apply an exponent to both sides
[tex]e^{\ln7}=e^x[/tex]Simplifying the expression above gives
[tex]\begin{gathered} 7=e^x \\ e^x=7 \end{gathered}[/tex]Hence, the exponential statement is
[tex]e^x=7[/tex]Related Questions
Pattern A follows the rule "add 2" and Pattern B follows the rule "subtract 2." Pattern A: 1, 3, 5, 7, 9 Pattern B: 10, 8, 6, 4, 2 Which ordered pairs are formed from combining a term in Pattern A with its corresponding term in Pattern B? Select all correct answers. A (1, 3) B (1, 10) C (3, 6) D (5, 4) E (5, 6) F (7, 4) I Need Help Please
Answers
To get the required combining pairs : B, C , D, E , F
B (1, 10) = Pattern A - 1 and pattern B = 10
C (3, 6) = pattern a = 3 and pattern b = 6
D (5, 4)= pattern A = 5 and pattern B = 4
E (5, 6) = Pattern A = 5 and pattern B = 6
F (7, 4) = Pattern A = 7 and pattern B = 4
Given ; Pattern A : 1, 3, 5, 7, 9
Pattern B: 10, 8, 6, 4, 2
To get ; A (1, 3) B (1, 10) C (3, 6) D (5, 4) E (5, 6) F (7, 4)
Thus to get the required pair we have to match it the following way
A ( 1, 3 ) = Pattern A - 1 and pattern B - ? thus not correct
B (1, 10) = Pattern A - 1 and pattern B = 10
C (3, 6) = pattern a = 3 and pattern b = 6
D (5, 4)= pattern A = 5 and pattern B = 4
E (5, 6) = Pattern A = 5 and pattern B = 6
F (7, 4) = Pattern A = 7 and pattern B = 4
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PLEASE HELP!!!!!!!!
Choose the two graphs that preserve congruence.
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The two graphs that reserve congruence are in the option A and option D
What is congruency?Congruent refers to something that is "absolutely equal" in terms of size and shape.
The shapes hold true regardless of how we rotate, flip, or turn them.
Draw two circles with the same radius, for instance, cut them out, and stack them on top of one another. We will see that they will superimpose, or be positioned entirely on top of, one another. This demonstrates the congruence of the two circles.
The images on the graphs in the options A and options D both maintains congruence, The sizes are identical and has a rigid transformation
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There are 25 popular trees currently in the park. Park workers will plant morepopular trees today. When the workers are finished there will be 80popular trees in the park. How many popular trees did the workers plant today?
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Current trees = 25
trees when workers are finished = 80
Subtract the number of current trees (25) to the number of trees that are when the workers are finished:
80-25 = 55
The workers planted 55 trees today
A rectangular patio measures 20 ft by 30 ft. You want to double the patio area by adding the same distance x to the length and width. Write and solve an equation to find a value for x, then find the new dimensions for the patio.
Answers
area = side x side = 20 x 30 =600 ft
we want to double the area, this is 1200 ft, therefore:
[tex]\begin{gathered} \mleft(x+20\mright)\mleft(x+30\mright)=1200 \\ x^2+50x+600=1200 \\ x^2+50x-600=0 \\ \mleft(x+60\mright)\mleft(x-10\mright)=0 \\ x+60=0 \\ x=-60 \end{gathered}[/tex]but, We don't measure in negative numbers, so we disregard this answer. and the other
[tex]\begin{gathered} x-10=0 \\ x=10 \end{gathered}[/tex]therefore, the patio is now 30ft x 40ft
What is the surface area of the prism below2.5 m2 m10 m1.5 m
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The lateral surface area is the total surface area minus the area of the two triangular faces at the top and bottom of the prism. t
5m+3m+ 3 n- m + 6n +8
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The given expression is
5m+3m + 3n - m + 6n + 8
We would simplify the expression by collecting like terms.
The terms containing m are like terms
The terms containing n are like terms
8 is a constant
Thus, we have
5m + 3m - m + 3n + 6n + 8
7m + 9n + 8
The final expression is
7m + 9n + 8
1. Combine like terms
5m + 3m - m = 7m
8 + 3 = 10
6n + n = 7n
Then you put them in an addition sentence
2. 7m + 7n + 10
you have a job wich pays double time when working more than 40 hours a week. last week you worked 55 hours and earned $840. what is your regular pay rate?
Answers
Explanation
The salary with regular pay rate is calculated as:
[tex]S_{\text{regular}}=R\times h[/tex]S is the salary, R is the regular pay rate and h is the number of hours worked.
The salary with over time is:
[tex]S_{\text{overtime}}=2\text{Rxh}_{\text{overtime}}[/tex]Because it pays double after 40 hours.
So the first 40 hours worked you'll get
[tex]S_{\text{regular}}=40R[/tex]The amount of overtime hours is 15 (55-40 = 15), so the overtime salary is:
[tex]S_{\text{overtime}}=2R\times15=30R[/tex]The total Salary is the sum of the regular and the overtime salaries:
[tex]S=S_{\text{overtime}}+S_{\text{regular}}[/tex]If the total salary was $840, then the regular pay rate R is:
[tex]\begin{gathered} 840=30R+40R \\ 840=70R \\ R=\frac{840}{70}=12 \end{gathered}[/tex]Answer
Your regular pay rate is $12 / hour
Given the points (-3,0), (2, 0), (6,0), (0, 12), write the polynomial in factored form.
Answers
what should be the value of k so that the trinomial is a perfect square trinomial ?
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ANSWER:
5
STEP-BY-STEP EXPLANATION:
The perfect square trinomial is given as follows:
[tex](a\pm b)^2=a^2\pm2ab+b^2[/tex]Therefore, in this case would be:
[tex]\begin{gathered} x^2+2kx+25 \\ a=x \\ b=5 \\ (x+5)^2=x^2+2\cdot5x+25 \\ k=5 \end{gathered}[/tex]Therefore the value of k is 5
In the diagram, M is the midpoint of BD and AC. Name two triangles that are congruent.BADABMCX ADMAA ABDACBAA CDM ABMADAB ABCD
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From the question,
The two triangles that are congruent are :
Triangle CDM = Triangle ABM --------- Option C
The following data points represent the number of flying saucers that are owned by each alien on planet nowhere. (a)Arrange the data from the least to greatest 1,4,2,21,8,27(b)Find the median number of flying saucers
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The data that represent the number of flying saucers that are owned by each alien on planet nowhere is given below:
[tex]1,4,2,21,8,27[/tex](a)We sort the data from the least to greatest below.
[tex]1,2,4,8,21,27[/tex](b)The median is the middle number.
In this case, we have two numbers in the middle: 4 and 8
Therefore we find their average:
[tex]\begin{gathered} \text{Median}=\frac{4+8}{2} \\ =\frac{12}{2} \\ =6 \end{gathered}[/tex]Answer:
6 is the correct answer.
Step-by-step explanation:
(1.26 x 10^3) + (1.12 x 10^4)
Work needs to be shown!!!
Answers
Answer:
Step-by-step explanation:
1260+11200=12460
so its, 1.246 x 10^4
∠ACB is a circumscribed angle. Solve for x.Question options:1) 482) 463) 444) 42
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x = 44
Explanations:Note that:
Opposite angles of a cyclic quadrilateral are supplementary
m
mm
(3x + 10) + 38 = 180
3x + 10 + 38 = 180
3x + 48 = 180
3x = 180 - 48
3x = 132
x = 132/3
x = 44
Quinn needs to collect at least 90 toys for a toy drive to earn community service credit. He has already collected 16 toys.
Answers
Let's define the next variable:
t: number of toys that Quinn still needs to collect
The number of toys that he already collected plus the number of toys that Quinn still needs to collect is: 16 + t
Quinn needs to collect at least 90 toys, then 16 + t must be greater than or equal to 90, that is,
16 + t ≥ 90
or
90 ≤ 16 + t
Subtracting 16 at both sides, we get:
90 - 16 ≤ 16 + t - 16
74 ≤ t
The total cost function for a product is given by C(x)=3x3−9x2−243x+1229, where x is the number of units produced and C is the cost in hundreds of dollars. Use factoring by grouping and then find the number of units that will give a total cost of at least $50,000. Verify the conclusion with a graphing utility.
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C(x) = 3x³ − 9x² − 243x + 1229
500 = 3x³ − 9x² − 243x + 1229
Subtract 500 on each side, as follows:
0 = 3x³ − 9x² − 243x + 729
(3x³ − 9x²) - (243x - 729) = 0
3x² (x - 3) - 243 (x - 3) = 0
(x - 3)(3x² - 243) = 0
x = 3, x = 9, x = -9; in the context of this problem, where x is the number
of units produced, negative values of x must be omitted, so x = 3 and x = 9
So we can say that if either 3 units or 9 units are produced the total cost
for the product will be at least $50000
[0, 3] U [9,∞)
evaluate the expression:[tex] \frac{8}{5 - 1} \times (3 + 6) \times 3[/tex]A)102B)-12C)62D)54
Answers
To evaluate the expression:
[tex]\frac{8}{(5-1)}\cdot(3+6)\cdot3[/tex]We can use PEMDAS. We can start from the parenthesis, then, since we have divisions and multiplications, and they have the same precedence, we can start doing the evaluation from the left to the right. Then, we have:
[tex]\frac{8}{(4)}\cdot(9)\cdot3=2\cdot9\cdot3=54[/tex]The answer is 54 (option D).
Number 9 please on this packet, I need it for a class presentation
Answers
9)
Let x represent the amount that she gets for 1/7 of a working day.
From the information given, she gets $35 for 1 working day. Thus, we can set up the equations as follows
35 = 1
x = 1/7
By crossmultiplying, we have
x = 35 x 1/7
x = 5
Ariel will earn $5 for working 1/7 of a day
One number is 9 more than another number. The sum of the numbers is 25. What is one of the numbers?A) 9B) 8C) 16D) 17
Answers
Answer
B) 8 or D) 17
Step-by-step explanation
Let's call x to one unknown number and y to the other number.
If one number is 9 more than another number, then:
[tex]y=x+9\text{ \lparen eq. 1\rparen}[/tex]Given that the sum of the numbers is 25, then:
[tex]x+y=25\text{ \lparen eq. 2\rparen}[/tex]Substituting equation 1 into equation 2 and solving for x:
[tex]\begin{gathered} x+x+9=25 \\ 2x+9=25 \\ 2x+9-9=25-9 \\ 2x=16 \\ \frac{2x}{2}=\frac{16}{2} \\ x=8 \end{gathered}[/tex]Substituting x = 8 into the first equation:
[tex]\begin{gathered} y=8+9 \\ y=17 \end{gathered}[/tex]Then, one of the numbers is 8 and the other one is 17
a recipe requires 7/8 sticks of butter for each 1 1/4 cups of flour. how many cups of flour to sticks of butter
Answers
In order to calculate the rate of cups of flour to stick of butter, just calculate the following quotient:
(1 1/4)/(7/8) = (5/4)/(7/8) = 5·8/7·4 = 40/28 = 20/14 = 10/7
Hence, the required rate is 10/7 or 10:7
that is, 10 cups of flour for 7 sticks of buttter
Construct a system of equations for the word problem. Do not solve. In the space provided, type the answer without any space between the letters, numbers, or symbols.
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Given:
The sum of two numbers is 21, and their difference is 9.
Let x and y be the two numbers.
Equation 1: The sum of two numbers is 21.
[tex]\text{ x + y = 21}[/tex]
Equation 2: Their difference is 9.
[tex]\text{ x - y = 9}[/tex]A plane flew 1225 mi in 5 hr with the wind. It would take 7 hr to travel the same distance against the wind. What is the speed of the plane in still air and the speed of the wind?
Answers
Answer:
wind speed 35 miles per hour
plane speed 210 miles per hour
Explanation:
Let us call p the place speed and w the wind speed.
We know that
p + w = 1225/5 = 245
p - w = 1225/7 = 175
adding the two equations above gives
2p = 245 + 175
2p = 420
dividing both sides by 2 gives
p = 210 miles per hour.
putting in the value of p in p + w = 245 gives
210 + w = 245
w = 245 - 210
w = 35 miles per hour
How many gallons each of 25% alcohol and 10% alcohol should be mixed to obtain 15 gal of 21% alcohol?Gallons ofPure AlcoholGallons ofSolutionХy15Percent(as a decimal)25% = 0.2510% = 0.121% =How many gallons of 25% alcohol should be in the mixture? gal
Answers
Answer
11 gallons of the 25% alcohol is required for the mixture.
4 gallons of the 10% alcohol is required for the mixture.
Explanation
Let the number of gallons of 25% alcohol required be x
Let the number of gallons of 10% alcohol required be y
The total amount of gallons required is 15 gallons. In mathematical terms,
x + y = 15
The alcohol content of the 15 gallons is to be 21%.
21% of 15 gallons = 3.15 gallons
From the first statements,
Let the number of gallons of 25% alcohol required be x
Let the number of gallons of 10% alcohol required be y
25% of x gallons = 0.25x gallons
10% of y gallons = 0.10y gallons
0.25x + 0.10y = 3.15
We can then bring these two equations together to solve simultaneously
x + y = 15
0.25x + 0.10y = 3.15
Solving this simultaneously with the calculator, we obtain
x = 11 gallons
y = 4 gallons
Hope this Helps!!!
find al the solutions for x.9. 8x2+19 = 54 +3x
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8x^2 + 19 = 54 + 3x^2
Solving for x:
8x^2 - 3x^2 = 54 - 19
5x^2 = 35
x^2 = 35/5 = 7
x^2 = 7
x = sqrt(7) = 2.6458
x = -sqrt(7) = -2.6458
Answer:
It has two solutions:
x = 2.6458 and x = -2.6458
PLEASE HELP MEEEEMatch the properties with the steps to solving the following equation(Sz - 6) =2+9Distributive Property4x - 3 = x + 9Subtraction Property ofEquality3x - 3=93x = 12Addition Property ofEqualityDivision Property ofEqualityx = 4Previouse
Answers
apply the distributive property
[tex]4x-3=x+9[/tex]apply the substraction property
Hello, I need some assistance with this homework question, please? This is for my precalculus homework. I submitted the answer x<-14 or x>-14 but it was incorrect Q4
Answers
To find the domain of the rational function we need to equate the denominator to zero and solve the equation, as follows:
[tex]\begin{gathered} x+14=0 \\ x+14-14=-14 \\ x=-14 \end{gathered}[/tex]Then, all the x-values are valid except x = -14, which makes the denominator equal to zero. Therefore, the domain of R(x) is:
[tex]\lbrace x|x\ne-14\rbrace[/tex]What percent of Kenyans are between the ages of 10 and 20 years old?
Answers
In the picture we see that between 10 and 20 years old there are two rectangles . One goes to the 11% aproximately
the other rectangle reach 10% in the Y axis .
So then finally we have to add both percentages to obtain
10% + 11%= 21 %
21 percent are between ages 10 and 20 years old
Determine the value of k for which the inequality $0.5<-4x+k\le12-k$ has the solution set $\left\{x|1.25\le x<2\right\} Need the answer ASAP.
Answers
The value of k for which the inequality has the given solution set is:
k = 8.5.
How to obtain the value of k?The inequality is presented as follows:
0.5 < -4x + k ≤ 12 - k.
Two inequalities compounded, hence the and operation is applied, which means that the solution set is composed by the elements that respect both conditions.
The solution set of the inequality is:
1.25 ≤ x < 2.
The lower bound of the solution is of 1.25, hence:
-4x + k ≤ 12 - k.
-4x + 2k ≤ 12
4x ≥ 2k - 12
x ≥ 0.5k - 3
Hence:
0.5k - 3 = 1.25
0.5k = 4.25
k = 4.25/0.5
k = 8.5.
The upper bound of the solution is of 2, hence:
-4x + k > 0.5
-4x > 0.5 - k
x < -0.125 + 0.25k
Hence:
-0.125 + 0.25k = 2
k = 2.125/0.25
k = 8.5. -> Which confirms the solution.
Missing InformationThe problem is given by the image shown at the end of the answer.
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enter the value of y for which LMNO must be a parallelogram
Answers
In a parallelogram, opposite sides are equal.
ON = LM
OL = NM
OL = y-6
NM= 1/3 x
ON= 5x-8
LM= 9x-26
First, solve for x
ON = LM
5x - 8 = 9x - 26
-8 + 26 = 9x - 5x
18 = 4x
18/4 = x
x = 4.5
Replace x=4.5 on NM, and solve for y:
OL = NM
y-6= 1/3x
y-6 = 1/3 (4.5)
y-6= 1.5
y= 1.5 + 6
y= 7.5 = 15/2
Three volunteers are chosen at random from a group of 20 people to help at a camp. How many unique groups of volunteers are possible?
Answers
In mathematics, a combination is a selection of items from a set that has distinct members
Formula
[tex]^n_{^{}}C_r=\frac{n\text{ !}}{(n-r)!r!}[/tex]Where
n = 20
r =3
[tex]\begin{gathered} ^{20}C_3=\frac{20\text{ !}}{(20-3)!3!} \\ \\ \\ ^{20}C_3=\frac{20\text{ !}}{17!3!} \\ \\ \\ ^{20}C_3=\frac{20\text{ }\times19\times18\times17!}{17!3!} \\ ^{20}C_3=\frac{20\text{ }\times19\times18}{3!} \\ \\ ^{20}C_3=\frac{20\text{ }\times19\times18}{3\times2\times1} \\ ^{20}C_3=\frac{20\text{ }\times19\times18}{6} \\ \\ ^{20}C_3=20\text{ }\times19\times3 \\ \\ \\ ^{20}C_3=1140 \end{gathered}[/tex]The final answer
1140 unique groups of volunteers are possible
1. The graph shown represents the altitude of a hikerduring a period of time. Write a possible situationrepresented by the graph.Altitude (feet)Time (hours)2. Use the vertical line test to determine if the relation represented on the graph
Answers
The vertical line test consists in tracing various vertical lines throughout the function and checking wheter this lines will touch the function more than once.
As we can see none of the lines touch the graph more than once, therefore this graph is a function.