Answer:
The solution is [tex]x = \frac{1}{2}[/tex]
Step-by-step explanation:
To solve this exponential equation, we must write both sides as powers of 3.
The equation given is:
[tex]3^{7x + 4} = (\frac{1}{27})^{x-3}[/tex]
Since [tex]3^3 = 27[/tex], we have that [tex]3^{-3} = \frac{1}{3^3} = \frac{1}{27}[/tex], so[tex]\frac{1}{27} = 3^{-3}[/tex]
Then
[tex]3^{7x + 4} = (\frac{1}{27})^{x-3}[/tex]
[tex]3^{7x + 4} = (3^{-3})^{x-3}[/tex]
[tex]3^{7x + 4} = 3^{-3(x-3)}[/tex]
[tex]3^{7x + 4} = 3^{-3x + 9}[/tex]
Since both sides are now powers of 3, we can equal them:
[tex]7x + 4 = -3x + 9[/tex]
[tex]10x = 5[/tex]
[tex]x = \frac{5}{10}[/tex]
[tex]x = \frac{1}{2}[/tex]
The solution is [tex]x = \frac{1}{2}[/tex]
What is the solution of the system of equations? -4x+3y=-12 -2x+3y=-18
*Note: I believe it has no solution, but I would like to make sure. Thank you all for your help.
Answer:
Step-by-step explanation:
I've enclosed a graph to show you that there is one solution.
-4x + 3y = - 12
- 2x + 3y = - 18 Subtract
-2x = 6 Divide by - 2
-2x/-2 = 6/-2
x = - 3
- 4x + 3y = - 12
-4(-3) + 3y = - 12
12 + 3y = - 12
3y = - 12 - 12
3y = - 24
3y/3 = - 24/3
y = - 8
Which is exactly what the graph shows.
You can tell immediately that this has 1 or more solutions just by looking at the number in front of x and y in each each equation.
It's always a good idea to graph a question like this one. Desmos is a pretty good tool to use if you don't have a graphing calculator.
The y's are the same so you are 1/2 way home in saying what you did.
The x's are different so that means you have at least 1 solution.
You claim you are psychic and can predict a coin flip 60% of the time. To test your claim, your friend has you predict a coin flip and then records whether or not you are correct. You do this 200 times and find you are right 135 times. Considering a null hypothesis that you are correctly predict the coin flip 60% of the time, using a hypothesis test, which of the following statements is most accurate?
a. You cannot reject the null at the 10% level of significance.
b. You can reject the null at the 10% level of significance, but cannot reject the null at the 5%, 2%, or 1% level of significance.
c. You can reject the null at the 10% and 5% level of significance, but cannot reject the null at the 2%, or 1% level of significance.
d. You can reject the null at the 10%, 5%, and 2% level of significance, but cannot reject the null at the 1% level of significance.
e. You can reject the null at the 10%, 5%, 2%, and 1% level of significance
Answer:
You can reject the null at the 10% and 5% level of significance, but cannot reject the null at the 2%, or 1% level of significance. ( D )
Step-by-step explanation:
let : P = 0.6
x = 135 , n = 200
p = 135 / 200 = 0.675
H0 : P = 0.6
Ha : P ≠ 0.6
performing the test statistic = ( 0.675 - 0.6 ) / [tex]\sqrt{\frac{0.60(1-0.60)}{200} }[/tex]
= 0.075 / 0.0346 ≈ 2.17
p-value = 2 * P ( Z > - 2.17 ) ( using excel function ; NORMSDIST )
= 2 * 0.015 = 0.03
(2+√2) is
an integer
a rational number
an irrational number
none of these
Answer:
Irrational number
Step-by-step explanation:
√2 is an irrational number.
So, when a integer or rational number is added to irrational number, we will get irrational numbers
2 + √2 is an irrational number.
I am giving brainlest
Which statement best describes the value of 8 ÷ 4 × 7 + (38 – 15)?
a
the product of 4 and 7 divided by 8, plus 38, minus 15
b
the quotient of 8 and 4, times 7, plus the sum of 38 and 15
c
the product of 8 and 4 times 7, plus the difference of 38 and 15
d
the quotient of 8 and 4, times 7, plus the difference of 38 and 15
Answer:
D is the answer
Step-by-step explanation:
Write linear equations in slope intercept form using the graph...
Answer:
Y = - x + 4
Step-by-step explanation:
3. Write the equation of the circle with a center at (-6, 1) and an area of 7n.
A Q(x + 6)^2 + (y - 1)^2 = 14
B (x - 6)^2 + (y + 1)^2 = 49
C (x + 6)^2 + (y - 1)^2 = 49
D (x + 6)^2 + (y - 1)^2 = 7
E (x - 6)^2 + (y + 1)^2 = 7
Answer:
D [tex] (x +6) ^2 +(y-1)^2 =7 [/tex]
Step-by-step explanation:
Center of the circle (h, k) = (-6, 1)
Area of the circle [tex] =\pi r^2 [/tex]
[tex] 7\pi=\pi r^2 [/tex]
[tex] \frac {7\pi}{\pi} =r^2 [/tex]
[tex]r^2=7[/tex]
[tex]r=\sqrt 7[/tex]
Radius [tex] r=\sqrt {7}[/tex]
Equation of circle in center radius form is given as:
[tex] (x - h) ^2 +(y-k) ^2 =r^2 [/tex]
Plugging the values of h, k and r in the above equation, we find:
[tex] [x - (- 6)] ^2 +[y-1 ]^2 =(\sqrt {7})^2 [/tex]
[tex] (x +6) ^2 +(y-1)^2 =7 [/tex]
Which one is the answer
Answer:
x = 30 degrees
Step-by-step explanation:
a triangle's angles should all add up together to 180 degrees. Since a right angle is 90 degrees then you have your 60 degree angle that only leaves 30 degrees left.
Answer: A and C
Step-by-step explanation:
A is right because it’s right triangle since it has a right angle. C is also right, x=30 because we have 60 degrees and 90 degrees. 60 plus 90 is 150 and a triangle is equal to 180 degrees 180-150 is 30
Classify each as a minor arc, major arc, or semicircle!!!!!!!!!!!!
AE:
AEB:
FDE:
FED:
FA:
BDF:
Answer:
Minor Arc: AE, FA
Semicircle: AEB, FDE
Major Arc: FED, BDF
Step-by-step explanation:
Required
Classify base on the type or arc
Keynote
Minor arcs are less than 180 degrees
Semicircle are equal to 180 degrees
Major arcs are less than 180 degrees
Using the above keynote, we have the following observation
AE: Minor
AEB: Semicircle
FDE: Semicircle
FED: Major
FA: Minor
BDF: Major
Determine the slope and y-intercept of each linear function below y=x/3-1
Answer:
Slope= 1/3
y-int: -1
Step-by-step explanation:
PLEASE HELP !!!! ILL GIVE BRAINLIEST !!!
what is the greatest common factor of 36x and -20??
Answer:
6x
Step-by-step explanation:
there's no specific method just follow times table
is 10,26,28 a right triangle
Answer:
No
Step-by-step explanation:
Answer:
No
Step-by-step explanation:
10^2 + 26 ^ 2 = 776
28^2 = 778.
since 776 is less than 778, it is an acute triangle, not right.
find the expression as the cosine of an angle
cos pi/4 cos pi/9 - sin pi/4 sin pi/9
Answer: cos(13pi/36)
Step-by-step explanation: just did the assignment
HELP. photo added. answers are 45, 20 , it 22.5
Answer:
22.5°
Step-by-step explanation:
We know that the measure of straight line is 180° . Therefore the sum of all angles will be 180° .
⇒ 90° + x + 3x = 180°
⇒ 90° + 4x = 180°
⇒ 4x = 90°
⇒ x = 90°/4
⇒ x = 22.5°
Hence the value of x is 22.5°Factorise the expression
it is not possible
that expression is not factorable with rational numbers
rational means - A number that can be expressed as the ratio of two integers.
what is the median to 132, 183, 191, 237, 251, 277, 279, 334, 448, 599?
Answer:
264
Step-by-step explanation:
(251 + 277) / 2 = 264
3. Which of the following could represent the sides of a right triangle?
Hint: use a? + b2 = c2
What is the length of AP?
1) 10
2) 12
3) 17
4) 24
Answer:
4) 24
Step-by-step explanation:
OA = OB = 7 ( radius )
OP = OB + BP
= 7 + 18
OP = 25
In triangle OPB,
By Pythagoras theorem,
( OP )² = ( OA )² + ( AP )²
( AP )² = ( OP )² - ( OA )²
= 25² - 7²
= 625 - 49
( AP )² = 576
AP = 24
Answer:
your answer will be 24
Step-by-step explanation:
∠OAP=90°
OA=OB=7
[tex]OA^{2} +Ap^{2} =OP^{2} \\\\7^{2} +Ap^{2} =(7+18)^{2} \\\\Ap^{2} =25^{2} -7^{2} =576\\\\AP=\sqrt{576} =24\\\\Ap=24[/tex]
hope it helps
have a great day!!
Which angle is coterminal with a 645° angle?
A. An angle measuring 265°
B. An angle measuring 75°
O C. An angle measuring 285°
D. An angle measuring 345º
Answer:
C
Step-by-step explanation:
Coterminal angles are angles that have a common terminal side.
So, given an angle θ, its coterminal angles will always be ±360°. This can be repeated.
We have a 645° angle.
Therefore, all values of the equation:
[tex]645\pm 360n[/tex]
Where n is an integer is coterminal with our original angle.
Letting n = 1 and using the negative case, we acquire:
[tex]\Rightarrow 645-360=285[/tex]
Therefore, an angle measuring 285° is coterminal with a 645° angle.
None of the other options can be reached by adding/subtracting 360.
Therefore, our answer is C.
Help help help help help help
Answer:
18.457
Step-by-step explanation:
Can somebody please help me with this question will give brsinlest
Answer:
Angle #1: 115°
Angle #2: 64°
Angle #3: 90°
Angle #4: 106°
Angle #5: 165°
Step-by-step explanation:
you subtract the ones that give you the exterior angle by 180 because it is a supplementary angle. that means that both angles add up to 180. the little square next to angle three means its a right angle. this means it is exactly 90°. the last angle is a little tricky. you need to add up all the angles you have and then you if you get 540 then your answer is correct because all interior angles of a pentagon must add up to 540.
Hope you have a great day and I hope this helped you out!
<3 :- )
What does the math equation y-2=
Answer:
5
Step-by-step explanation:
your answer is 5 hope it help
Please I need help on Tis question
Answer:
Step-by-step explanation:
The answer is D, the function approaches 1 as x approaches +- infinity. We can divide each term by x^2. We will get the following:
[tex]\frac{1-4/x^2}{1-9/x^2}[/tex]
as x goes to infinity, the -4/x^2 and -9/x^2 go to 0. To the equation just becomes 1/1. So the answer is 1.
Help quick pleaseee.........
Answer:
a) 341
b) 7243
c) 11018
d) 33000
What kind of shape is this? O A. Not a polygon O B. Triangle O c. Quadrilateral O D. Pentagon
Answer:
Add the picture please :) i will go on your page and answer when you add the image. Remember to always double check if you have the image clipped on whenever you ask something that needs an image, thank you.
Trig ratio and finding the missing angle pair.
Hello!
This is a question relating trigonometric ratios and a missing angle.
Here, since we are given all three sides of the triangle, we can use any of the three trigonometric ratios, sine, cosine, or tangent to solve this problem.
I'll be using the sine ratio for this problem.
The sine of an angle is the ratio between the triangle's opposite side and its hypotenuse.
Meaning the following equation could be set up.
[tex]sin(\theta)=\frac{45}{75}[/tex]
Now, we can just solve for theta.
[tex]\theta=sin^{-1}(\frac{45}{75})[/tex]
Make sure you're in degrees when you're solving this problem.
[tex]\theta=36.870[/tex]
Hope this helps!
techwiz Electronics makes a profit of $35 for each MP3 players sold and $18 for each DVD player sold. Last week, techwiz so the combined total of 128 MP3 and DVD players let X be the number of MP3 players techwiz sold last week write an expression of the combined total profit in dollars Tech whiz made from MP3 and DVD player
Answer:
128 = 35x + 18y
Step-by-step explanation:
total = 35(MP3) + 18(DVD)
128 = 35x + 18y
help me!!! HELP ME!!!! ME!!!!!
Answer: 11,921,360
Step-by-step explanation:
Answer:
Gay?
Step-by-step explanation:
write an equivalent expression 8(y-7z+1)
Answer:
8y−56z+8
Step-by-step explanation:
Step by step please
Please
Answer:
137/1000
Step-by-step explanation:
Because we have 3 numbers after 0....
hope it helps