The solutions to the exponential equation [tex]12^{x^2 + 5x - 4} = 12^{2x + 6}[/tex] are given as follows:
x = 2 and x = -5.
How to solve the exponential equation?The exponential equation for this problem is defined as follows:
[tex]12^{x^2 + 5x - 4} = 12^{2x + 6}[/tex]
The n^x function is an injective function, which means that if they are equal, and have the same base, than their exponents are equal.
Thus the equation can be simplified as follows:
x² + 5x - 4 = 2x + 6.
x² + 3x - 10 = 0.
The coefficients of the quadratic function are given as follows:
a = 1, b = 3, c = -10.
Hence the discriminant is given as follows:
D = 3² - 4(1)(-10)
D = 49.
The first solution is given as follows:
x = (-3 + 7)/2 = 2.
The second solution is given as follows:
x = (-3 - 7)/2 = -5.
Meaning that the third option is the correct option in the context of this problem.
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Answer:
c
Step-by-step explanation:
A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized. where traffic flow in vehicles per hour vehicle speed in miles per hour The following data were collected during rush hour for six highways leading out of the city. Traffic Flow () Vehicle Speed () 1257 36 1329 45 1227 30 1336 50 1349 55 1124 25 a. Use the data to compute the coefficients of this estimated regression equation (to decimals). Enter negative value as negative number. (Create the variable first using Data/Transform
Answer:
ŷ = 0.1286X - 123.2175 ;
R = 0.9465
R² = 0.8958
Step-by-step explanation:
Given the data:
Traffic Flow, X : ()
1257
1329
1227
1336
1349
1124
Vehicle speed, Y () :
36
45
30
50
55
25
The estimated regression equation using a linear regression calculator is given thus:
ŷ = 0.1286X - 123.2175
According to the general linear regression formula :
y = mx + c
Where ; y = predicted variable (vehicle speed)
x = predictor variable (traffic flow)
Slope, m = 0.1286
Intercept, c = 123.2175
The correlation Coefficient, R = 0.9465, This depicts a strong positive relationship between traffic flow and vehicle speed.
The Coefficient of determination, R² = 0.9465² = 0.8958 ; This means about 89.5% of variation in Vehicle speed can be explained by the regression line.
Alex scored a 75% on his history test if he correctly answered an 18 question how many questions did Alex answer incorrectly
Answer:
24
Step-by-step explanation:
18 is 75% of 24.
What is the exact circumference of a circle with a radius of 15 cm?
A. 107 cm
B. 157 cm
C. 307 cm
D. 60 cm
Step-by-step explanation:
Given. radius (r) = 15 cm
Circumference (C)
= 2 π r
= 2 * 3.14 * 15
= 94.2 CM
I Got this answer.....
The distance from New York City to Riverhead is approximately 150 miles. On a map whose scale is 24mi= 2inch, what is the distance between the two locations in inches?
Answer:
12.5 inches
Step-by-step explanation:
To best find this answer, we should set up a proportion. Our first fraction is practically given to us in the problem, and would look like this:
[tex]\frac{2in}{24mi}[/tex]
Next, we need to set up our second fraction. An important thing to make sure of is that the 150 is on the same side as the 24 since they are both miles. Here is what the final equation should look like:
[tex]\frac{2in}{24mi} = \frac{x}{150mi}[/tex]
To solve, just cross multiply and divide! First, multiply 2 by 150, giving you 300. Next, just divide the 300 by the remaining 24, giving you a final answer of 12.5 inches. Here's what the final calculations look like:
2in X 150mi = 300
300 / 24mi = 12.5in
Answer:
12.5 inches is your answer
estimate 5/8 - 1/10 explain
Answer:
21/40.
Step-by-step explanation:
Find the LCD (Least Common Denominator) of the fractions. The LCD of 5/8 and 1/10 is 40.
Convert both fractions into denominators of 40.
So then we have: 25/40 - 4/40 which is equal to: 21/40.
21/40 is the estimated value of the expression 5/8 -1/10
What is Number system?A number system is defined as a system of writing to express numbers.
The given expression is 5/8 -1/10
The terms in the expression are in the form of fractions, A fraction represents a part of a whole.
To find the value of expression firstly find the LCM of 8 and 10
40 is the LCM
5(5)-1(4)/40
25-4/40
The value of 25 minus 4 is twenty one.
21/40 is the value of the expression 5/8 -1/10
Hence, 21/40 is the estimated value of the expression 5/8 -1/10
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Guys I need help !! X=2 evaluate 5x-2
Answer:
Step-by-step explanation:
Evaluate means to see what value the equation has given x is 2
substitute x for 2 (write instead of x, write 2)
5x-2 will be 5*2-2 , calculate 5*2-2= 10-2 = 8
Sorry if the picture is scuffed. Pls help fast
Answer:
C
Step-by-step explanation:
the domain would be all positive real numbers, including zero
Why is it important that you put the polynomial in standard form (largest power
to smallest-power)? *
Answer: Polynomials like to be written in standard form. This means they contain no like terms and the exponents are in descending order (largest to smallest).
Step-by-step explanation:
✨6 Grade Math✨ Pls help
Answer:
37Step-by-step explanation:
89 - 4²×4 + 12 = 89 - 16×4 + 12 = 89 - 64 + 12 = 25 + 12 = 37Answer:
[tex]89 - 4 {}^{2} \times 4 + 12 = 89 \\ - 16 \times 4 + 12 \\ \\ = 89 - 64 + 12 \\ \\ = 25 + 12 \\ \\ = 37[/tex]
89-4^2×4+12=89-16×4+12
= 89-64+12
= 25+12
= 37
A computer laboratory manager was in charge of purchasing new battery packs for her lab of laptop computers. She narrowed her choices to two models that were available for her machines. Since the models cost about the same, she was interested in determining whether there was a difference in the average time the battery packs would function before needing to be recharged. She took two independent samples and computed the following summary information: Battery Pack Model 1 Battery Pack Model 2Sample Size 9 9Sample Mean 5 hours 5.5 hoursStandard Deviation 1.5 hours 1.3 hoursUsing the null and alternate hypothesis:H0:mu1-mu2=0 vs. Ha: mu1-mu2 not equal 0Calculate the test statistic for this test.
Answer:
-0.756
Step-by-step explanation:
N1 = 9
N2 = 9
Sd1 = 1.5 hours
Sd2 = 1.3 hours
X1 = 5 hours
X2 = 5.5 hours
Hypothesis
H0: mu1 - mu2 = 0
H1 : mu1 - mu2 not equal to 0
Test statistic
t = (x1 - x2)/SE
SE is the standard error, which is unknown
SE = √sd1²/n1 + sd2²/n2
= √1.5²/9 + 1.3²/9
= √0.25+0.1878
= √0.4378
= 0.66166
t statistics = (5-5.5)/0.66166
= -0.5/0.66166
= -0.756
19/20 and 23/25 common denominator
Hello!
The common denominator is 100.
~Sophia
a. Draw a rectangle with an
area of 39 squares, and
perimeter of 32 units.
a
Answer:
It has side lengths of 3 and 13
Step-by-step explanation:
If it has an area of 39, then let the sides be x and y: thus we get the two relationships:
xy=39
2(x+y)=32
From the second equation, you get x+y=16. Now, rearrange to get y=16-x. You can now plug this into the first equation:
x(16-x)=39 -> 16x-x^2=39 -> x^2-16x+39=0 -> (x-3)(x-13)=0
This implies that x=3, or x=13, which further implies that the side lengths must be 3 and 13.
if the are 5 buses and the quatation amount is R8,100 how much will each person pay
Answer:
R1620
Step-by-step explanation:
1620 ×1=1620
1620×2=3240
1620×3=4860
1620×4=6480
1620×5=8100
The local newspaper tells you that ad space costs 40 per column-inch. A "column-inchis space one column wide nch high. You want to buy a space 3 columns wide and 5 inches high. What will it cost you?
A.) $40
B.) $120
C.) $200
D.) $600
Answer:
it should be 600
Step-by-step explanation:
40x3=120x5=600
Find set A' n B'
U= {1, 2, 3, 4, 5, 6, 7}
A= {4, 5, 6, 7}
B = {3, 4, 7}
Answer:
its 1 and 2
Step-by-step explanation:
first find A' which is(1,2,3) since these are in the universal set but not in A.
similary B' which is (1,2,5,6)
and since (1,2) are both in A' and B' set A'nB'=(1,2)
Answer:
Step-by-step explanation:
U={1,2,3,4,5,6,7}
A={4,5,6,7}
B={3,4,7}
A'={1,2,3}
B'={1,2,5,6}
A'∩B'={1,2}
a manager of company plans to produce 3000 units in a day employing 15 workers working 8 hours.How many units can be manufactured when manager employs 18 workers working 6 hours?
Answer:
2,700 units
Step-by-step explanation:
To investigate whether there is a difference in opinion on a certain proposal between two voting districts, A and B, two independent random samples were taken. From district A, 35 of the 50 voters selected were in favor of the proposal, and from district B, 36 of the 60 voters selected were in favor of the proposal. Which of the following is the test statistic for the appropriate test to investigate whether there is a difference in the proportion of voters who are in favor of the proposal between the two districts (district A minus district B)? A. 35-36 A 50 B. 35-36 0.7 0.6 V 50 0 + 60 C. 0.7-0.6 (0..) (.x) (+) 0.7-0.6 D. V(0.7)(0.6) (Hot 50+60 0.7 -0.6 E. (0.7) (0.6) VE 60
Answer:
C: t= x1`-x2`/√p^q^(1/n1 +1/n2)
0.7−0.6/(0.65)(0.35)√(1/50+1/60)
Step-by-step explanation:
The options given are
A
35−36/ 35/√50+3660
B
35−36/0.7/√50+0.660
C
0.7−0.6/(0.65)(0.35)√(1/50+1/60)
D
0.7−0.6/(0.7)(0.6)/√(1/50+1/60)
E
0.7−0.6/(0.7)(0.6)/√150+160
↔↔↔↔↔↔↔↔↔↔↔↔↔↔↔↔↔↔↔↔↔↔↔↔↔↔↔↔↔↔↔↔↔
This is a test hypothesis about difference of means between two proportions.
The test statistic used is
t= x1`-x2`/√p^q^(1/n1 +1/n2)
x1`= 35/50= 0.7
x2`= 36/60= 0.6
so
x1`-x2`
= 35/50-36/60
= 0.7-0.6
p^= 35+36/50+60= 71/110= 0.645= 0.65
q^= 1-p^= 1-0.65= 0.35
p^q^= (0.65) (0.35)
n1= 50 and n2= 60
therefore √1/n1 +1/n2= √1/50+1/60
Now Putting the values in the test statistics we get
t= x1`-x2`/√p^q^(1/n1 +1/n2)
0.7−0.6/√(0.65)(0.35)(1/50+1/60)
Hence C is the correct option
Using the z-distribution, it is found that the test statistic for the appropriate test to investigate whether there is a difference in the proportion of voters who are in favor of the proposal between the two districts is given by:
[tex]z = \frac{0.1 - 0}{0.0906}[/tex]
What are the hypothesis tested?At the null hypothesis, it is tested if there is no difference between the proportions, that is, the subtraction is zero, hence:
[tex]H_0: p_A - p_B = 0[/tex]
At the alternative hypothesis, it is tested if there is a difference between the proportions, that is, the subtraction is not zero, hence:
[tex]H_1: p_A - p_B \neq 0[/tex]
What is the mean and the standard error for the distribution of the difference of proportions?First, we find the mean and the standard error for each proportion:
[tex]p_A = \frac{35}{50} = 0.7[/tex]
[tex]s_A = \sqrt{\frac{0.7(0.3)}{50}} = 0.0648[/tex]
[tex]p_B = \frac{36}{60} = 0.6[/tex]
[tex]s_B = \sqrt{\frac{0.6(0.4)}{60}} = 0.0633[/tex]
Then, for the difference:
[tex]\overline{p} = p_A - p_B = 0.7 - 0.6 = 0.1[/tex]
[tex]s = \sqrt{s_A^2 + s_B^2} = \sqrt{0.0648^2 + 0.0633^2} = 0.0906[/tex]
What is the test statistic?It is given by:
[tex]z = \frac{\overline{p} - \mu}{s}[/tex]
In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.
Hence:
[tex]z = \frac{0.1 - 0}{0.0906}[/tex]
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John roller skates 48km in 3 hours. What is his average speed in kilometers per hour?
Answer:16km/hr
Explanation:
48km/3hr= 16km/hr
47. Health care costs per capita Rising health care costs
are a growing concern for everyone in the United
States. Using U.S. Centers for Medicare and
Medicaid Services data from 2006 and projected to
2021, U.S. per capita health care costs can be modeled
by
y = 20.61x? - 116.4x + 7406
where x is the number of years past 2000. Use this
equation to find, to the nearest dollar, the average rate
of change of U.S. per capita health care costs from 2010
to 2015 and from 2015 to 2020.
This year 0.3 of the x students at Mega Middle School are in 7th grade. There are 294 students in 7th grade.
Answer:
is that even a question ?
Step-by-step explanation:
3/10x=294
x=294*10/3
x=980 students
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What fractions are the same
Ohhhhhh I get it I thought something else
Answer:
equivalent fractions
Step-by-step explanation:
When fractions have different numbers in them, but have the same value, they are called equivalent fractions. Let's take a look at a simple example of equivalent fractions: the fractions ½ and 2/4. These fractions have the same value, but use different numbers.
Mr. Hernandez dilates the triangle shown below by a scale factor of 2 with the origin
as the center to obtain AA'B'C'.
Answer: only student 2
Solve for x in the following equation.
X/5=25
X=?
Answer:
125
Step-by-step explanation:
25 × 5 = 125
x/5 = 25 × 5 = 125
x = 125
Write out the form of the partial fraction decomposition of the function (as in this example). Do not determine the numerical values of the coefficients. (a) x − 20 x2 + x − 20 Incorrect: Your answer is incorrect. (b) x2 x2 + x + 20 Incorrect: Your answer is incorrect.
Answer:
[tex]\frac{x - 20}{ x^2 + x - 20} = \frac{5}{9(x-4)}+\frac{4}{(x+5)}[/tex]
Step-by-step explanation:
Given
[tex]\frac{x - 20}{ x^2 + x - 20}[/tex]
Required
Decompose into partial fraction
Start by factorizing the denominator:
[tex]x^2 + x - 20 =x^2 + 5x -4x- 20[/tex]
[tex]x^2 + x - 20 =x(x + 5)-4(x+5)[/tex]
[tex]x^2 + x - 20 =(x-4)(x+5)[/tex]
So, we have:
[tex]\frac{x - 20}{ x^2 + x - 20} = \frac{A}{x-4}+\frac{B}{x+5}[/tex]
Take LCM
[tex]\frac{x - 20}{ x^2 + x - 20} = \frac{A(x+5)+B(x-4)}{(x-4)(x+5)}[/tex]
Cancel out the denominator
[tex]x - 20 = A(x+5)+B(x-4)}[/tex]
Open brackets
[tex]x - 20 = Ax+5A+Bx-4B[/tex]
Collect Like Terms
[tex]x - 20 = Ax+Bx+5A-4B[/tex]
[tex]x - 20 = (A+B)x+5A-4B[/tex]
By comparison;
[tex](A +B)x = x[/tex] ==>[tex]A + B = 1[/tex]
[tex]5A - 4B = 1[/tex]
Make A the subject in [tex]A + B = 1[/tex]
[tex]A = 1 - B[/tex]
Substitute 1 - B for A in [tex]5A - 4B = 1[/tex]
[tex]5(1-B) -4B = 1[/tex]
[tex]5-5B -4B = 1[/tex]
[tex]5-9B = 1[/tex]
Collect Like Terms
[tex]-9B = 1 - 5[/tex]
[tex]-9B = - 4[/tex]
[tex]B = \frac{4}{9}[/tex]
[tex]A = 1 - B[/tex]
[tex]A = 1 - \frac{4}{9}[/tex]
[tex]A = \frac{9-4}{9}[/tex]
[tex]A = \frac{5}{9}[/tex]
So:
[tex]\frac{x - 20}{ x^2 + x - 20} = \frac{A}{x-4}+\frac{B}{x+5}[/tex]
[tex]\frac{x - 20}{ x^2 + x - 20} = \frac{5}{9(x-4)}+\frac{4}{(x+5)}[/tex]
Solve the following inequality: |3x|>x+20
Answer:
x>10,x<−5
Step-by-step explanation:
[tex]x > - 5[/tex] or [tex]x < 10[/tex] are the two possible solutions to the given inequality.
What are absolute value functions?
An absolute value function is a function that contains an algebraic expression within absolute value symbols.
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.
According to the given question.
We have an inequality |3x| > x + 20
Solve the above given inequality |3x| > x + 20
⇒ [tex]-(x + 20) < 3x < +( x + 20)[/tex]
⇒ [tex]-x -20 < 3x < x + 20[/tex]
⇒ [tex]3x > -x -20[/tex] or [tex]3x < x + 20[/tex]
⇒ [tex]3x+x > -20[/tex] or [tex]3x - x < 20[/tex]
⇒ [tex]4x > -20[/tex] or [tex]2x < 20[/tex]
⇒[tex]x > -5[/tex] or [tex]x < 10[/tex]
⇒ x ∈ (-∞, -5)∪(10,∞)
Hence, [tex]x > - 5[/tex] or [tex]x < 10[/tex] are the two possible solutions to the given inequality.
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Select the correct answer.
What is the complete factorization of x2 + 2x - 63?
A. (x+ 21)(x-3)
B.
(x-9)(x+7)
C.
(x + 9)(x-7)
D.
(x-21)(x + 3)
Reset
Answer:
the answer of this question is
c
HELP!!! in the diagram m ∠ g=96. what is m ∠E
Answer:
M<E
Step-by-step explanation:
It would be m
Answer:
sorry if it’s late, but that would be
B) 84
i just took the test.
The value of (1-w) (1-w*2) , where w is the cube root of the complex number is?
Answer:
3
Step-by-step explanation:
1+ω+w²=0
ω³=1
(1-ω)(1-ω²)=1-ω²-ω+ω³
=1-ω-ω²+1
=2+1-1-ω-ω²
=3-(1+ω+ω²)
=3-0
=3
if the force acting on a body of mass 4kg accelerates it at a constant rate of 4m/s. what would be the acceleration of the mass is doubled?
Answer:
4kg=4m/s
8kg=?
3m/s
Step-by-step explanation:
12kgm/s/4kg
APPLICATIONS
LINE RELATIONSHIPS Think of each segment in the diagram as part of a
line. Fill in the blank with parallel, skew, or perpendicular.
10. DE, AB, and GC
С
DĖ and BE are 2
A А
12. BE and GC
13. Plane GAD and plane CBE are
D
E
are
11.
B В
are
Answer:bb
Step-by-step explanation: