Answer:
x = 5 or x = - 2
Step-by-step explanation:
Using the rules of logarithms
log x + log y = log (xy)
log x = log y ⇒ x = y
Given
ln(x- 3) + ln(x + 1) = ln(x + 7) , then
ln (x - 3)(x + 1) = ln (x + 7) , so
(x - 3)(x + 1) = x + 7 ← expand left side using FOIL
x² - 2x - 3 = x + 7 ( subtract x + 7 from both sides )
x² - 3x - 10 = 0 ← in standard form
(x - 5)(x + 2) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5
x + 2 = 0 ⇒ x = - 2
Help help help help help
Answer:
m(∠y) = 64°
Step-by-step explanation:
From the figure attached,
m(∠e) = 90°
m(∠b) + 67° = 180° [Linear pair of angles]
m(∠b) = 180 - 67
= 113°
m(∠c) + 75° = 180° [Linear pair of angles]
m(∠c) = 105°
m(∠a) = m(∠d)
By the property of a polygon,
Sum of the interior angles of a polygon is given by,
Sum of interior angles = (n - 2) × 180°
Here, n = number of sides of the polygon
For n = 5,
Sum of interior angles = (5 - 2)×180°
= 540°
m(∠a) + m(∠b) + m(∠c) + m(∠d) + m(e) = 540°
2m(∠d) + 113° + 105° + 90° = 540°
2m(∠d) + 308 = 540°
2m(∠d) = 540 - 308
m(∠d) = 116°
m(∠d) + m(∠y) = 180°
m(∠y) + 116° = 180° [Linear pair of angles]
m(∠y) = 64°
2 units
5
2 units
2 units
8 units
2 units
2 units
2 units
6 units
The area of the figure is
square units.
Line c has an equation of y=-1/6x+5. Perpendicular to line c is line d, which passes through the point (-3,-8). What is the equation of line d
Answer:
The equation of line d is [tex]y + 8 = 6(x + 3)[/tex]
Step-by-step explanation:
Equation of a line:
The equation of a line, in point-slope form, is given by:
[tex]y - y_0 = m(x - x_0)[/tex]
In which the slope is m and the point is [tex](x_0,y_0)[/tex]
Perpendicular lines:
If two lines are perpendicular, the multiplication of their slopes is -1.
Perpendicular to y=-1/6x+5
Slope of - 1/6, so:
[tex]-\frac{1}{6}m = -1[/tex]
[tex]m = 6[/tex]
So
[tex]y - y_0 = 6(x - x_0)[/tex]
Passes through the point (-3,-8).
This means that [tex]x_0 = -3, y_0 = -8[/tex]. So
[tex]y - y_0 = 6(x - x_0)[/tex]
[tex]y - (-8) = 6(x - (-3))[/tex]
[tex]y + 8 = 6(x + 3)[/tex]
Alix is 10 years older than tamia. Alanna is twice as old as tamia. If the sum of their ages is 74, how old is alanna
Answer:
Alanna is 32 years old
Step-by-step explanation:
Hi there!
We're given that Alix is 10 years older than Tamia and Alanna is twice as old as Tamia.
Since Alix and Alanna's ages are in relation to Tamia's, let's make Tamia's age x
Alix is 10 years older than Tamia, so Alix must be x+10 years old
Alanna is twice as old as Tamia, so she must be 2x years old
We're also given that Alix+Alanna+Tamia=74
When we substitute it with the expressions we have, it becomes:
x+x+10+2x=74
now combine like terms
4x+10=74
subtract 10 from both sides
4x=64
divide both sides by 4
x=16
We found the value of x (Tamia's age)
However, the problem asks for Alanna's age, which we have set as 2x
So Alanna is 2*16, or 32 years old
Hope this helps! :)
Answer:
32 years
Step-by-step explanation:
that is the procedure above
Find the missing term given below.
14,916,2536,?
Which graph shows a dilation
Answer:
show the graphs?
Step-by-step explanation:
How many ounces are equivalent to 9 pounds?(1pound=16 ounces)
Answer: 144
Step-by-step explanation:
If 1 pound is 16 ounces then you have to do 9 X 16
9x16 = 144
Therefore the answer is 144 ounces
Hope this helped!
The quotient of 365.085 and 79.8
Answer:
4.575
Step-by-step explanation:
365.085/79.8=4.575
What are the values of m and 0 in the diagram below?
Answer:The correct answer is m= and θ = 30º.
Step-by-step explanation:First, we must form a triangle whose hypotenuse is the radius r=1, its adjacent leg is m, its opposite leg is and the angle is theta.
First, we calculate the angle with theta's breast:
sin (θ) =
where H is the hypotenuse, in this case, the radio.
θ = ()
θ = 30º
Now, we calculate the adjacent leg, which is equal to the x-coordinate of the point:
cos (θ) =
m = cos 30º * H
m =
m =
Have a nice day!
How long does it take to get more skips
Answer: Just create an account and you have unlimited skips.
What transformation of the parent function f(x) is made to get f(−x)+1
Answer:
It moved one space to the right , so it is a translation.
Step-by-step explanation:
shown below.
Answer:
Handling Data and probability
A scientist is conducting an experiment on two types of bacteria to determine which type will grow faster in a pool. After collecting data for two weeks, she finds that she can model the growth rates as follows:
Bacteria 1: y = 4x
Bacteria 2: y = 4x2
In these models, y represents the number of bacteria colonies and x represents the number of hours.
Based on these models, which type of bacteria is growing faster?
Answer:
bacteria 1
Step-by-step explanation:
i got it right
QUICK PLEASE HELPPPPPPPPPPPP
=====================================================
Explanation:
Set the expression equal to 100 and get everything to one side
[tex]d^2 - 12d + 45 = 100\\\\d^2 - 12d + 45 - 100 = 0\\\\d^2 - 12d - 55 = 0\\\\[/tex]
Now use the quadratic formula. We'll plug in a = 1, b = -12, c = -55.
[tex]\ d = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\ d = \frac{-(-12)\pm\sqrt{(-12)^2-4(1)(-55)}}{2(1)}\\\\\ d = \frac{12\pm\sqrt{364}}{2}\\\\\ d \approx \frac{12\pm19.07878403}{2}\\\\\ d \approx \frac{12+19.07878403}{2}\ \text{ or } \ d \approx \frac{12-19.07878403}{2}\\\\\ d \approx \frac{31.07878403}{2}\ \text{ or } \ d \approx \frac{-7.07878401}{2}\\\\\ d \approx 15.53939201\ \text{ or } \ d \approx -3.53939201\\\\d \approx 15.54 \ \text{ or } \ d \approx -3.54[/tex]
We'll ignore the negative d value as we can't have a negative number of days.
This means d = 15.54 is the only approximate solution we'll consider.
If we plugged in d = 15, then,
d^2 - 12d + 45
(15)^2 - 12(15) + 45
90
This tells us that 90 masks were sold on day d = 15.
Now try d = 16
d^2 - 12d + 45
(16)^2 - 12(16) + 45
109
We see that 109 masks were sold on day d = 16. Somewhere between those days, 100 masks were sold. At the end of the 15th day, we got to 90. So in the middle of day 16 is when we reach the exact 100 mark we're after.
In short, we would round d = 15.54 up to d = 16 so that we clear the hurdle.
In other words, if you rounded d = 15.54 to d = 15, then you'd be 10 masks short of the goal. Besides, 15.54 rounds to 16 when rounding to the nearest whole number.
PLS HELP LAST THING I NEED FOR MATH THIS SCHOOL YEAR
ANSWER WITH STEP BY STEP SOLOUTION/PROCESS = BRAINLIEST ANSWER AND 5* VOTE
TROLLS = WILL GET ALL THEIR ANSWERS AND QUESTIONS REPORTED
PART 2, PART 1 ALREADY POSTED CHECK PROFILE
Answer:
B = 25 because 180-25-130 = 25 and all angles within triangle add to 180 degrees
a = 6 because the triangle is isosceles and we can see symmetry and draw this to prove on two opposite lines, therefore we can now find height easier.
c = 10. 876 because 130/2 = 65 degree and with new central height we can find Right Angle and using 6 x sin (65) = 5. 438 then we multiply by 2 to find c
Then all you have to do is re-write and round to the nearest 10th and check the units and write degree sign where required.
Step-by-step explanation:
Write the word or phrase that best completes each statement or answers the question. Solve the problem.
Two kinds of cargo, A and B, are to be shipped by truck. Each crate of cargo A is 50 cubic feet in volume and weighs 200 pounds, whereas each crate of cargo B is 10 cubic feet in volume and weighs 360 pounds. The shipping company charges $75 per crate for cargo A and $100 per crate for cargo B. The truck has a maximum load limit of 7200 pounds and 1000 cubic feet. How many crates of each cargo should be shipped on each truck in order to satisfy the load limits and yield the greatest charges? What is the greatest charge?
Answer:
z(max) = 2350
x₁ = 18 x₂ = 10
Step-by-step explanation:
Vol (ft³) W (p) Income ($)
Cargo A (x₁) 50 200 75
Cargo B (x₂) 10 360 100
Max load limit 1000 7200
Objective Function
z = 75*x₁ + 100*x₂
Constraints:
Volume constraint:
50*x₁ + 10*x₂ ≤ 1000
Weight constraint:
200*x₁ + 360*x₂ ≤ 7200
Model:
z = 75*x₁ + 100*x₂ to maximize
Subject to:
50*x₁ + 10*x₂ ≤ 1000
200*x₁ + 360*x₂ ≤ 7200
x₁ ≥ 0 x₂ ≥ 0 x₁ and x₂ integers
After 6 iterations with an on-line solver optimal solution is:
z(max) = 2350
x₁ = 18 x₂ = 10
What is the greatest common factor of 35 and 45?
The U.S. Federal Seed Act establishes germination rates for various fruit and vegetable seeds. Watermelon seeds are to meet a 70% germination standard. A skeptical gardener who has not had very good luck planting watermelons believes that the seed company he purchases seeds from is not adhering to the 70% federal mandate. Once a week for 12 weeks, he purchases a pack of 10 watermelon seeds to act as his sample. He plants the seeds in a greenhouse with good soil to maintain a consistent temperature and watering routine. He finds that the germination rate for the company's watermelon seeds is 55%. Compute a 98% confidence interval to estimate the proportion of watermelon seeds that germinate. Be sure to interpret your interval in the context of the problem.
Answer:
The 98% confidence interval to estimate the proportion of watermelon seeds that germinate is (0.4443, 0.6557). This means that we are 98% sure that the true proportion of all watermalong seeds of the company that germinate is between these two values, which means that there is good evidence that the proportion is below the 70% standard.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
Once a week for 12 weeks, he purchases a pack of 10 watermelon seeds to act as his sample. He plants the seeds in a greenhouse with good soil to maintain a consistent temperature and watering routine. He finds that the germination rate for the company's watermelon seeds is 55%.
This means that [tex]n = 12*10 = 120, \pi = 0.55[/tex]
98% confidence level
So [tex]\alpha = 0.02[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.55 - 2.327\sqrt{\frac{0.55*0.45}{120}} = 0.4443[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.55 + 2.327\sqrt{\frac{0.55*0.45}{120}} = 0.6557[/tex]
The 98% confidence interval to estimate the proportion of watermelon seeds that germinate is (0.4443, 0.6557). This means that we are 98% sure that the true proportion of all watermalong seeds of the company that germinate is between these two values, which means that there is good evidence that the proportion is below the 70% standard.
12=x/5 plsss helpppppp
Answer:
The correct answer or value of xis 60
Step-by-step explanation:
12=x/5
or,12×5=x
or,60=x
convert .25 cups to mL?
Answer: 59.14706
Step-by-step explanation:
Answer:
59.14706 mL
Step-by-step explanation:
Formula is
for an approximate result, multiply the volume value by 237
which is 59.25
find all possible values for each expression
9514 1404 393
Answer:
D
Step-by-step explanation:
The sine function is negative only for angles greater than 180°. This eliminates choice B.
The sine function is periodic with a period of 360°, eliminating choices A and C.
The only viable choice is D, which is the correct one.
If you have consistently been exercising during the school year but then take the
summer off, once school starts again your fitness level will be exactly the same as it
was before the summer.
A.
True
B.
False
1
SEE ANSWER⇒
Answer:
Step-by-step explanation:
B
reduce 1/2 × 16/9 is to lowest form
Answer:
The correct answer will be "[tex]\frac{8}{9}[/tex]".
Step-by-step explanation:
The given expression is:
= [tex]\frac{1}{2}\times \frac{16}{9}[/tex]
By applying multiplication, we get
= [tex]\frac{16}{18}[/tex]
= [tex]\frac{8}{9}[/tex]
Thus, the above is the lowest form.
find the equation of the line passing through points A(3,4) and B(1,10)
Answer:
y = -3x + 13
Step-by-step explanation:
First, find the slope:
[tex]m=\frac{y_1-y_2}{x_1-x_2}\\\\m=\frac{4-10}{3-1}\\\\m=\frac{-6}{2}\\\\m=-3[/tex]
Finally, find the equation:
[tex]y-y_1=m(x-x_1)\\\\y-4=-3(x-3)\\\\y-4=-3x+9\\\\y=-3x+13[/tex]
given that abc=def what is the measure of d
Answer:
C. 47 deg
Step-by-step explanation:
m<A = 180 - 94 - 39 = 47
m<D = m<A = 47
Force: F = MA; Solve for m.
mass = force / area
this is second law of motion ( Newton's 2nd law)
[tex]\longrightarrow{\blue{ m = \frac{F}{a} }}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Explanation}}{\red{:}}}}}[/tex]
F = ma
➺ m = [tex]\frac{F}{a} [/tex]
where,
F = Force
m = mass
a = acceleration
"F = ma" is Newton's second law of motion, which states that force is equal to mass times acceleration.
The SI unit of force is newton, symbol N.
[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]
x/2-y/3=3,4x-3y=22
[tex] > < [/tex]
Answer:
x = 10
y = 6
Step-by-step explanation:
x/2 - y/3 = 3 - - - (1)
4x - 3y = 22 - - - (2)
From (1):
x/2 - y/3 = 3
(3x - 2y)/6 = 3
3x - 2y = 18 - - - - (11)
4x - 3y = 22 - - - - (2)
Multiply (11) by 1.5
4.5x - 3y = 27 _____(111)
4x - 3y = 22 - - - (2)
Subtract :
0.5x = 5
x = 5 / 0.5 = 10
From :
4x - 3y = 22
Put x = 10
4(10) - 3y = 22
40 - 3y = 22
-3y = 22 - 40
-3y = - 18
y = 6
Find each event probability
Answer:
Event 4 (0%), Event 2 (45%), Event 3 (80%), Event 1 (100%)
Step-by-step explanation:
Debbie did a survey of how many states the members of her class had visited. The results were: 10, 15, 23, 2, 21, 31, 14, 10,
8.17, 11, 19.8.42.15. 22. 6, 34, 19.3, 24,
What is the five-number summary for this set of data?
Answer:
Step-by-step explanation:
11 22 6 34 19
Can someone please answer quickly <3
Which of the following expressions have a difference of 5? Check all that apply.
VX
0-3-(-8)
-2-3
1-(-4)
07-(-2)
9514 1404 393
Answer:
A, C
Step-by-step explanation:
A: -3 -(-8) = -3 +8 = 5
B: -2 -3 = -5
C: 1 -(-4) = 1 +4 = 5
D: 7 -(-2) = 7 +2 = 9
__
Differences A and C are 5.
Answer: A: -3- (-8)
B:1 -(-4)
Step-by-step explanation:
in A your subtracting them in B your adding them