Answer:
[tex] x = \dfrac{\log 5}{\log 7} [/tex]
Step-by-step explanation:
[tex] 7^{2x} - 4 \times 7^x = 5 [/tex]
[tex] 7^{2x} - 4 \times 7^x - 5 = 0 [/tex]
[tex] (7^x)^2 - 4(7^x) - 5 = 0 [/tex]
This is a quadratic equation in 7^x.
Let u = 7^x.
Substitute u for 7^x to see the quadratic equation more clearly.
[tex] u^2 - 4u - 5 = 0 [/tex]
Now we have a factorable quadratic equation in u.
[tex] (u - 5)(u + 1) = 0 [/tex]
[tex] u - 5 = 0 [/tex] or [tex] u + 1 = 0 [/tex]
[tex] u = 5 [/tex] or [tex] u = -1 [/tex]
Now substitute back 7^x for u.
[tex] 7^x = 5 [/tex] or [tex] 7^x = -1 [/tex]
[tex] 7^x = -1 [/tex] does not have a real solution.
Continue solving [tex] 7^x = 5 [/tex] for x.
Take log of both sides.
[tex] \log 7^x = \log 5 [/tex]
[tex] x \log 7 = \log 5 [/tex]
[tex] x = \dfrac{\log 5}{\log 7} [/tex]
Answer:
[tex]x=\log_75[/tex]
Step-by-step explanation:
Given equation:
[tex]7^{2x}-4 \cdot 7^x=5[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c:[/tex]
[tex]\implies (7^x)^2-4 \cdot 7^x=5[/tex]
Subtract 5 from both sides:
[tex]\implies (7^x)^2-4 \cdot 7^x-5=0[/tex]
[tex]\textsf{Let \; $u = 7^x$}:[/tex]
[tex]\implies u^2-4u-5=0[/tex]
Factor the quadratic:
[tex]\implies u^2+u-5u-5=0[/tex]
[tex]\implies u(u+1)-5(u+1)=0[/tex]
[tex]\implies (u-5)(u+1)=0[/tex]
Apply the zero-product property:
[tex]\implies u-5=0 \implies u=5[/tex]
[tex]\implies u+1=0 \implies u=-1[/tex]
[tex]\textsf{Substitute back in \; $u = 7^x$}:[/tex]
[tex]\implies 7^x=5[/tex]
[tex]\implies 7^x=-1 \quad \textsf{is not valid as $7^x > 0$}.[/tex]
Therefore, the only valid solution is:
[tex]\implies 7^x=5[/tex]
[tex]\textsf{Apply log law}: \quad a^c=b \iff \log_ab=c[/tex]
[tex]\implies \log_75=x[/tex]
[tex]\implies x=\log_75[/tex]
solve this equation 3/5x - 1/10x
Answer:
[tex]\frac{1}{2}[/tex]x
Step-by-step explanation:
3/5 is the same as 6/10
[tex]\frac{6}{10}[/tex] x - [tex]\frac{1}{10}[/tex]x
[tex]\frac{5}{10}[/tex]x = [tex]\frac{1}{2}[/tex]x
Find the measure of the marked angles.
(11x + 17) = ____.
(13x - 1) = ____.
Answer:
(11x + 17) = 116°
(13x - 1) = 116°
Step-by-step explanation:
(11x + 17) and (13x - 1) are equal because they are vertically opposite angles.
11x + 17 = 13x - 1
2x = 18
x = 9
Substitute x = 9 into angle measures.
11(9) + 17 = 116°
Since both angles are equal, (13x - 1) is also 116°.
Factor Completely
6p² +90p + 300
Answer:
6(p + 5)(p + 10)
Step-by-step explanation:
6p² + 90p + 300 ← factor out 6 from each term
= 6(p² + 15p + 50) ← factor the quadratic
consider the factors of the constant term (+ 50) which sum to give the coefficient of the p- term (+ 15)
the factors are + 5 and + 10 , then
p² + 15p + 50 = (p + 5)(p + 10)
and
6p² + 90p + 300
= 6(p + 5)(p + 10)
A one year
membership to
your local gym costs $539
There is an initial sign up fee
of $55 Write an equation you
can use to find out how much
you pay per month
The local gym per month fees is $44.92
Define Division
Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
What do you mean by Cost ?
The amount or equivalent paid or charged for something.Monthly Cost means the Annual Cost divided by twelve (12).It's given that,
One year membership cost is = $539
So, per month cost will be = 539 / 12
= 44.91666 or 44.92
Hence, the local gym per month fees is $44.92
To read more about Cost.
https://brainly.com/question/2021001
#SPJ9
In triangle def, m∠d = (3x 27)°, m∠e = (4x 22)°, and m∠f = 68°. determine the degree measure of the exterior angle to ∠d. 54° 58° 122° 126°
Answer:
It is known that the sum of all three angles inside a triangle will be 180°.
So, m∠D + m∠E + m∠F = 180°
(3x + 27) + (4x + 22) + 68 = 180
7x + 49 + 68 = 180
7x = 63
x = 9
So, m∠D = (3(9) + 27)° = 54°.
The exterior angle of D = 180- 54 = 126°.
Hence "The sum of all interior angles of a triangle is 180° thus the measure of the exterior angle to ∠D is 126°".
Can someone help me really quick
(Please Explain how you know this is correct.)
7.53 one-hour carbon monoxide concentrations in air samples from a large city average 12 ppm (parts per million) with standard deviation 9 ppm. a do you think that carbon monoxide concentrations in air samples from this city are normally distributed? why or why not? b find the probabili
The probability is 0.0132.
Here we have mean and standard deviations for air samples from large cities.
According to large samples, the law sample average calculated from large samples is approximately equal to the population average.
As here sample is taken from a large city, the sample is considered a large sample. Hence mean is approximately equal to the population mean. Also, it is considered a random sample is representative of the population and the sample standard deviation is approximate to the population standard deviation. Hence we can say that carbon monoxide concentrations in air samples from this city are normally distributed.
So here we have
μ = 12
σ = 9 , n = 100
Hence here we need to find,
= p (x > 14)
= p((x-μ /(σ/√n)) > 14-12/9/√100)
= p ( z > 2.22 )
= 1 - p ( z < 2.22 )
= 1 - 0.9868 (using excel formula = norm.s.dist(2.22,1))
= 0.0132
To learn more about standard deviation, and probability,
https://brainly.com/question/13905583
#SPJ4
suppose that a line chart includes several lines. which chart element will tell you the category of data that each line represents?
The legend chart element will tells the category of data that each line represents the lines.
Lines:
Lines refers a one-dimensional figure, which has length but no width.
Given,
suppose that a line chart includes several lines.
Here we need to identify the chart element will tell you the category of data that each line represents.
Basically, chart is a visual representation of numeric data in a worksheet. And it helps you to identify trends, make comparisons, and recognize patterns in the numbers.
In order to get the clear information that appears in your chart, you can add a chart title, axis titles, and data labels.
The element legend or data table is used to represents the category of the data.
To know more about Lines here.
https://brainly.com/question/17188072
#SPJ1
Nilo wants to save a total of $500,000 for retirement. How much should they deposit monthly into an account that pays 3.7% interest, compounded monthly, to meet their goal in 22 years? What is their monthly deposit?
The monthly deposit for the amount to compound monthly would be $1515.15.
What is compounding?
Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit. It is considered to be the 8th wonder of the world as it has great power in terms of money.
Main Body:
formula for compound interest monthly(C.I.) =[tex]P(1+\frac{R}{12})^{12t} -P[/tex]
Here R- 3.7% = 0.037 , T=22 years , C.I. = 500000 P=?
Calculating ,
500000 = P(1+[tex]\frac{0.037}{12}^{12*22}[/tex]) -P
500000 = P(1.25)
P= 400000 but it is for all time period.
so monthly deposit = P/12*22
= 400000/264
= 1515.15
Hence the answer is $1515.15.
to learn more about compounding click on the link below.
https://brainly.com/question/24924853
#SPJ13
3. repeated-measures and matched-subjects experiments repeated-measures experiments measure the same set of research participants two or more times, while matched-subjects experiments study participants who are matched on one or more characteristics. which of the following are true for both a repeated-measures experiment and a matched-subjects experiment when used to compare two treatment conditions? check all that apply. the researcher computes difference scores to compute a t statistic. participants in both types of experiments are all measured the same number of times. the researcher must compute an estimated standard error for the mean difference score to compute a t statistic. if the researcher has n number of participants to use in the experiment, then the degrees of freedom will be the same in a repeated-measures experiment or in a matched-subjects experiment. for a repeated-measures experiment comparing two treatment conditions, the t statistic has a df of 31. how many subjects participated in this study? 64 31 32 62 a matched-subjects experiment produced a t statistic with a df of 13. how many subjects participated in this study? 26 13 14 28
Answer: A. The researcher computes difference scores to compute a t statistic
B. If the researcher has n number of participants to use in the experiment, then the degrees of freedom will be the same in a repeated-measures experiment or in a matched-subjects experiment
C. The researcher must compute an estimated standard error for the mean difference score to compute a t statistic.
D. Participants in both types of experiments are all measured the same number of times
A matched-subjects experiment produced a t statistic with a df of 9. How many subjects participated in this study?
A. 20
B. 10
C. 18
D. 9
For a repeated-measures experiment comparing two treatment conditions, the t statistic has a df of 11. How many subjects participated in this study?
A. 12
B. 22
C. 24
D. 11
Step-by-step explanation:
Sia designs a board game in which a card is drawn on each turn.
A blue card means move forward 4 squares.
A red card means move back 6 squares.
Liam suggests adding some other cards to Sia's game
Part A
Liam explains that drawing a yellow card is equivalent to drawing a blue card followed by a red card. How many spaces forward or backward does a player move after drawing a
yellow card? Justify your answer.l
By using addition of integers, it has been calculated that
On drawing a yellow card, the player has to move 2 block backward
What is addition of integers?
At first it is important to know about integers
To find the sum total of two or more integers, addition operator is used on the integers
Here addition operator will be required
Let going forward be denoted by a positive sign and going backward be denoted by a negative sign
A blue card means move forward 4 squares.
A red card means move back 6 squares.
So we assign +4 to blue card and we assign -6 to red card
Now, drawing a yellow card is equivalent to drawing a blue card followed by a red card
Number of spaces moved by a player = (+4) + (-6)
= 4 - 6
= -2
So on drawing a yellow card, the player has to move 2 block backward
To learn more about integers, refer to the link-
https://brainly.com/question/17695139
#SPJ9
A parking lot has a length of 32 meters and a width of 24 meters. Madison made a scale drawing of the parking lot using a scale of
2
1
inch = 4 meters.
Label the dimensions of the scale drawing.
The dimensions of the scale drawing is length = 168 inches and width = 126 inches
How useful is a scale drawing?Scale drawing helps to represent surfaces on earth in a paper by either enlarging its dimension, reducing its dimension by a constant factor called the scale factor.
The conversion or scale factor is 21 inches = 4 meters
If 21 inches = 4 meters,
then 1 meter = 21/4 inches
32 meters inches = 32 x 21/4 = 168 inches
24 meters = 24 x 21/4 = 126 inches.
In conclusion, length of the scale drawing is 168 inches and width of the scale drawing iss 126 inches
Learn more about scale factor: https://brainly.com/question/26855848
#SPJ1
If g(x) = x²-x, then g(t-1) =
Answer:
g(t - 1) = t² - 3t + 2
Step-by-step explanation:
substitute x = t - 1 into g(x) , that is
g(t - 1)
= (t - 1)² - (t - 1) ← expand squared factor using FOIL
= t² - 2t + 1 - t + 1 ← collect like terms
= t² - 3t + 2
ade's gem shop is having its annual spring sale, when every item in the store gets marked down. during the sale, charm bracelets sell for $4 less than full price. kristen purchases 5 identical charm bracelets: one for each of her friends. she pays a total of $45. which equation can kristen use to find how much money, c, each charm bracelet costs at full price?
Based on the information provided, the equation that can be used to find how much money, c, each charm bracelet cost at full price is 5(c – 4) = 45.
An equation is its simplest form in algebra, refers to a mathematical statement that represents that two mathematical expressions are equal. For example, 2x + 6 = 14 is an equation, where 2x + 6 and 14 are two expressions that are separated by an equal sign. In the given case, as each bracelet cost is reduced by $4 from the full price, and the total cost of 5 identical charm bracelets is $45, the equation that can be used is given by:
5(c – 4) = 45
Solving the equation,
5(c – 4) = 45
c – 4 = 9
c = 9 + 4 = $13
Learn more about Equation:
https://brainly.com/question/24334139
#SPJ4
(8x-12)=64
Solve for x
Answer:
-4
Step-by-step explanation:
Simplifying
8(x + 12) = 64
Reorder the terms:
8(12 + x) = 64 (12 * 8 + x * 8) = 64 (96 + 8x) = 64
Solving
96 + 8x = 64
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-96' to each side of the equation.
96 + -96 + 8x = 64 + -96
Combine like terms: 96 + -96 = 0
0 + 8x = 64 + -96
8x = 64 + -96
Combine like terms:
64 + -96 = -32
8x = -32
Divide each side by '8'.
x = -4
Simplifying
x = -4
Answer:
x = 19/2 (or) 9.5
Step-by-step explanation:
The equation is,
→ (8x - 12) = 64
Now the value of x will be,
→ (8x - 12) = 64
→ 8x = 64 + 12
→ x = 76/8
→ x = 19/2
→ [ x = 9.5 ]
Hence, the value of x is 9.5.
Find the missing length indicated.
Answer:
28 unitsStep-by-step explanation:
Let the missing part be x.
According to triangle proportionality theorem we have:
x/(35 - x) = 12/3x / (35 - x) = 4x = 4(35 - x)x = 140 - 4xx + 4x = 1405x = 140x = 140/5x = 28The required side is 28.
What is similarity?Similarity of a triangle is the ratio of their corresponding sides or angles which are equal .
Given that AB=35, AE=12 and CE=3.
Let BD=x ⇒ AD = 35-x
Triangle ΔABC and ΔADE are similar,
By using property of similarity,
AB/AC=AD/AE
35/15=35-x/3
x=28
value of side x=28.
To learn more on Similarity:
https://brainly.com/question/16919171
#SPJ1
replacement times for cd players are normally distributed with a mean of 7.1 years and a standard deviation of 1.4 years (data from consumer reports). (a) what is the probability that a randomly-selected cd player will have to be replaced in 8 years or less?
The probability that a randomly selected CD player will have a replacement time of fewer than 8.0 years is 0.7389
P(X<8) = P((X-mean)/s <(8-7.1)/1.4)
= P(Z<0.64) = 0.7389 (from standard normal table)
= P(X>c)=0.02
= P(Z<(c-7.1)/1.4) = 1-0.02 = 0.98
= (c-7.1)/1.4 =2.05 (from the standard normal table)
= c = 7.1+2.05*1.4 = 9.97
Probability sampling alludes to the choice of an example from a populace when this determination depends on the rule of randomization, that is to say, irregular determination or possibility. Probability sampling is more intricate, additional tedious, and normally more exorbitant than non-probability sampling.
While picking a probability test plan, the objective is to limit the inspecting blunder of the evaluations for the main study factors, while at the same time limiting the time and cost of leading the review. A few functional limitations can likewise affect that decision, for example, the qualities of the survey frame.
To learn more about probability and its theorem,
https://brainly.com/question/9793303
#SPJ4
if f(x) =-2^2+6 find f(2)
The value of f(2) when f(x) = [tex]-x^{2} +6[/tex] will be 2.
According to the question,
We have the following expression:
f(x) = [tex]-x^{2} +6[/tex]
Now, we can easily find the value of f(2) by putting the value of x in the given expression as 2.
So, we will have the following expression:
f(2) = [tex]-(2)^{2} +6[/tex]
f(2) = -4+6
(More to know: the two integers with different signs are subtracted but the sign in the final result remains that of the larger integer. So, in this case, the sign will be positive in the final result.)
f(2) = 2
Hence, the value of f(2) when f(x) = [tex]-x^{2} +6[/tex] will be 2.
To know more about value here
https://brainly.com/question/13527898
#SPJ9
5(m - 6) = 10 - 4[2(m - 7) - 5m]
Answer:
m = -96/7
Step-by-step explanation:
5(m - 6) = 10 - 4[2(m - 7) - 5m]
5m - 30 = 10 - 4[2m - 14 - 5m]
5m - 30 = 10 - 4(-3m - 14)
5m - 30 = 10 + 12m + 56
-7m = 96
m = -96/7
Is 13 72/99 rational or irrational
13 72/99 is rational number.
A rational number is a number that can represented in the form p/q where p, q are integers and q ≠ 0. E.g. 3/1, 5/12.
An irrational number is the opposite of a rational number that cannot be represented in the form p/q where p, q are integers and q ≠ 0. E.g. √2
Given, number = 13 72/99
It is a mixed fraction. It can be converted into proper fraction :
(13×99 + 72)/99 = 1359/99
1359/99 is a rational number since numerator and the denominator are both integers.
To know more about rational:
https://brainly.com/question/10894434
#SPJ1
fill in the value for a to make the equation below an infinite solutions 2(x+3) = [a]+6
The value of "a" for which the given equation has an infinite number of solutions is 2x.
We are given an equation. The equation is linear in nature. An equation is a mathematical statement that includes the sign "equal to" between two expressions with equal values. We need to find the value of the variable "a" such that the equation has infinite solutions. A variable is a quantity that can change in the context of a mathematical problem or experiment. The equation is : 2(x + 3) = a + 6. If an equation has infinite solutions, then the equation is called an identity. Identity is an equation that is true regardless of the values used.
2(x + 3) = a + 6
2x + 6 = a + 6
a = 2x
To learn more about equations, visit :
https://brainly.com/question/10413253
#SPJ1
A piece of notebook paper measures 8 1/2 inches by 11 inches. Which of the following metric approximations is the same?
2 m x 2.8 m
3 cm x 4 cm
22 cm x 28 cm
30 m x 40 m
Calculate the length of AC in ABAC to 1 decimal place.
The length of AC in triangle BAC is equal 10.7 units
Cosine RuleIn trigonometry, the cosine rule says that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.
The formula is given as
AC² = AB² + BC² - 2(AB)(BC) cos AC
AC² = 6² + 7² - 2(6)(7)cos110
AC = 10.7
Using cosine rule, the length of AC is 10.7 unit.
Learn more on cosine rule here;
https://brainly.com/question/28716982
#SPJ1
Assume that a constant rate of change exists for the model formed. The table lists data regarding the average salaries of
several professional athletes in the years 1991 and 2001.
a) Use the two data points to find a linear function that fits the data. Let x = the number of years after 1990 and S(x) = the
average salary.
b) Use the function of part (a) to estimate the average salary in 2005. Predict the average salary in 2010.
The average salary is s(x) = 117400 x + 138600
The average salary in 2005 is $1899600
The average salary in 2010 is $2486600
What is average salary ?
The mean wage earned by a country's working population is known as the national average salary (or national average wage). It is computed by adding together the yearly wages of everyone who is employed and dividing the total by the number of employees.
Let s(x) = mx + b →Linear model in slope-intercept form
at s(1) = $256,000
s(11) = $1430000
slope [tex]m = \frac{s(11) - s(1)}{11-1}[/tex]
= (1430000-256000) / 10
= 117400
To find b we can write
s(1) = 117400 (1) +b
256000 = 117400 + b
b = 256000 - 117400
= 138600
s(x) = 117400 x + 138600
(b) s(15) = 117400 (15) + 138600
= $1899600
(c) s(20) = 117400 (20) + 138600
= $2486600
To learn more about average salary from the given link
https://brainly.com/question/1286047
#SPJ1
air quality measurements were collected in a random sample of 25 country capitals in 2013 and then again in the same cities in 2014. we would like to use these data to compare average air quality between the two years. should we use a paired or unpaired test? explain your reasoning
Use of the two-tailed test is advised. In order to compare the average across two years,
A random sample of 25 national capitals had their air quality measured in 2013, and the same cities had been visited again in 2014. We want to compare the average air quality between the two years using this data.
A one-sided or two-sided test should be used, right? Describe your thinking.
The two-tailed test should be used. We want to contrast the average across two years. If the test parameter calculated for the two years differs, it would be interesting to know. (There is no exact comparison to show if one year is better or worse than the other.)
To learn more about test parameters click here:
brainly.com/question/13978790
#SPJ4
The distribution of heights in a population of women is approximately normal. Sixteen percent of the women have heights less than 62 inches. About 97.5% of the women have heights less than 71 inches. Use the empirical rule to estimate the mean and standard deviation of the heights in this population. Mean: K inches Standard Deviation: inches
The mean is 65 inches and the standard deviation is 3 inches.
Given,
In a group of women, the distribution of heights is roughly normal. Women who are shorter than 62 inches in height make up 16% of the population.
The empirical rule, less than μ - σ of 16% of the data is accurate.
P (x < μ - σ) = 16%
μ - σ = 62 → (I)
Approximately 97.5% of the women are under 71 inches in height,
P (x < μ + 2σ) = 97.5%
μ + 2σ = 71 → (II)
By solving (I) & (II);
μ - σ = 62
μ + 2σ = 71
3σ = 9
σ = 3
From (I);
μ - σ = 62
μ - 3 = 62
μ = 65
Hence, Mean = 65 inches
Standard deviation = 3 inches
To learn more about Mean click here:
brainly.com/question/23631778
#SPJ4
−50÷(−10)
solve and show how you solved
What are the vertex and range of y = |2x + 4| + 5?
(0, 5); −∞ < y < ∞
(0, 5); 5 ≤ y < ∞
(−2, 5); −∞ < y < ∞
(−2, 5); 5 ≤ y < ∞
The vertex is (-2, 5) and The range is [5, ∞)
The correct option is (D) i.e., (−2, 5); 5 ≤ y < ∞
Given:
The Function is :
y = |2x + 4| + 5
To find the vertex and range of the function.
What is vertex and range ?
The vertex is given by the coordinates (h, k), so all we need to consider is the k. For example, consider the function f(x)=3(x+4)2−6. a is positive and the vertex is at (−4,−6), so the range is all real numbers greater than or equal to −6.
Now, According to the question:
The function is given as:
y = |2x + 4| + 5
So, According to the above statement is:
The vertex in y = |2x + 4| + 5
The vertex is (-2, 5)
The range in y = |2x + 4| + 5
The range is all real numbers
The range is [5, ∞)
Hence, The vertex is (-2, 5) and The range is [5, ∞)
The correct option is (D) i.e., (−2, 5); 5 ≤ y < ∞
Learn more about Vertex and Range at:
https://brainly.com/question/1689812
#SPJ1
(D) - (−2, 5); 5 ≤ y < ∞
*45 Points* Manuel completed the right column of the table to help him find the difference of 5/8 and 1/4 .
Answer:
Step 2
Step-by-step explanation:
He messed up because while changing the denominator (number on the bottom), he forgot to change the numerator (number on top).
It should be 2/8 instead of 1/8.
f ( x) = 4/x - 5
plss helppp
