Answer:
x = 35.5
Step-by-step explanation:
cos 65° = 15/x
cos 65° · x = 15
x = 15/cos 65°
x = 35.5
log subscript-4 (m^2)=log subscript-4 (18-7m)?
Answer:
m = {-9, 2}Step-by-step explanation:
log₄ (m²) = log₄ (18 - 7m)18 - 7m > 0 ⇒ 7m < 18 ⇒ m < 18/7
m² = 18 - 7mm² + 7m - 18 = 0m² + 2*3.5m + 12.25 = 30.25(m + 3.5)² = 5.5²m = - 3.5 ± 5.5m = 2 m = -9Answer:
[tex] \displaystyle m_{1} = 2 \quad \text{and} \quad \displaystyle m _{2} = - 9[/tex]
Step-by-step explanation:
we are given a logarithm equation
[tex] \displaystyle \log_{4}( {m}^{2} ) = \log_{4}(18 - 7m) [/tex]
notice that, we have [tex]\log_4[/tex] both sides therefore we can get rid of it
[tex] \displaystyle {m}^{2} = 18 - 7m[/tex]
in order to solve it we should make it standard form we know that
[tex] \displaystyle a {x}^{2} + bx + c = 0[/tex]
so right hand side expression to left hand side and change its sign:
[tex] \displaystyle {m}^{2} + 7m- 18=0[/tex]
now we can solve it by using factoring method
to do so rewrite the middle term as sum or subtraction of two different terms
in that case -2m+9m is good to use
[tex] \displaystyle {m}^{2} - 2m + 9m - 18 = 0[/tex]
factor out m:
[tex] \displaystyle m({m}^{} - 2 )+ 9m - 18 = 0[/tex]
factor out 9:
[tex] \displaystyle m({m}^{} - 2 )+ 9(m - 2)= 0[/tex]
group:
[tex] \displaystyle (m - 2)(m + 9) = 0[/tex]
hence,
[tex] \displaystyle m_{1} = 2 \quad \text{and} \quad \displaystyle m _{2} = - 9[/tex]
remember that,
when we deal with logarithm equation we should always check the roots
let's check the root 1:
[tex] \displaystyle \log_{4}( {2}^{2} ) \stackrel{?}{=} \log_{4}(18 - 7.2) [/tex]
simplify square:
[tex] \displaystyle \log_{4}( 4) \stackrel{?}{=} \log_{4}(18 - 7.2) [/tex]
simplify multiplication:
[tex] \displaystyle \log_{4}( 4) \stackrel{?}{=} \log_{4}(18 - 14) [/tex]
simplify substraction:
[tex] \displaystyle \log_{4}( 4) \stackrel{?}{=} \log_{4}(4) [/tex]
simplify logarithm:
[tex] \displaystyle 1 \stackrel{ \checkmark}{=} 1[/tex]
let's check root 2:
[tex] \displaystyle \rm \log_{4}( { - 9}^{2} ) \stackrel{?}{=} \log_{4}(18 - 7.( - 9)) [/tex]
simplify square:
[tex] \displaystyle \rm \log_{4}( 81 ) \stackrel{?}{=} \log_{4}(18 + 63) [/tex]
simplify addition:
[tex] \displaystyle \rm \log_{4}( 81 ) \stackrel{ \checkmark}{=} \log_{4}(81) [/tex]
therefore,
[tex] \displaystyle m_{1} = 2 \quad \text{and} \quad \displaystyle m _{2} = - 9[/tex]
What is the y-intercept of this line?
12, 8, 4, 0
Step-by-step explanation:
Thank Me. Super.
Is 40/1000 and 40% an equivalent pair
Answer:
No
Step-by-step explanation:
40/1000 is 4%
Answer:
no, it would be equivalent if it was 4%
Step-by-step explanation:
In a tennis club the ratio number of junior members : number of senior members is
7 : 10. There are 18 more senior members than junior members. Find the total amount of club members.
Answer:
35 members
Step-by-step explanation:
In a tennis club the ratio number of junior members : number of senior members is 7 : 10
From the above ratio
Number of junior member = 7
Number of senior members = 10
There are 18 more senior members than junior members.
S = 18 + j
10 + 18 = 28 senior members
Hence,
Total number of members = 28 senior members + 7 junior members
= 35 members
what is the slope of the line
Answer:
The slope equals the rise divided by the run: . You can determine the slope of a line from its graph by looking at the rise and run. One characteristic of a line is that its slope is constant all the way along it.
Answer:
the slope of the line is 1
Step-by-step explanation:
The line goes 1 up, 1 right, 1 up 1 right ........
1 divided into 1 = 1
Which expression is equivalent to sqrt10/4sqrt8
Answer:
i think it is the third one.
Step-by-step explanation:
Answer:
first choice: ⁴√200 / 2
Step-by-step explanation:
√10 / ⁴√8 = ((√10)*(⁴√2)) / ((⁴√2³)*(⁴√2))
= (⁴√100 * ⁴√2) / (⁴√2⁴)
= ⁴√200 / 2
what is this ecspression in simplified form
(-7 square root 3)(11 square root 10)
Answer:
-77·√30
Step-by-step explanation:
(-7)·√3·11·√10 = (-77)·√3·10 = -77·√30
What are the x-intercepts of y = x^2 + 5x - 1?
Answer:
hope this helps:) have a good day
prove triangle AOC is congruent to triangle BOD
Step-by-step explanation:
We are given two Triangles and we need to prove them congruent . In ∆AOC and ∆BOD , we have
[tex]\to AC = BD ( given ) \\\\\to OD = OA \\\\\to \angle CAO =\angle BDO (Since\ BD || AC ) [/tex]
Therefore by AAS congruent condition we can say that ,
[tex]\implies\red{ \triangle AOC \cong \triangle BOD }[/tex]
Hence Proved!
find the amount of sap maple syrup producer would have cod from each tree if the total amount (5gallons) was redistributed equally among the trees
Answer: hi
Step-by-step explanation:
Answer:
1/4
Step-by-step explanation:
hope is helps <3
I need help on one question. Please someone help me. Don’t put a link. I only need help on 22.
Answer:
Supplementary
Step-by-step explanation:
Write an equation of the line that passes through point P and is parallel to the line with the given equation: P(2,5) Y-1=4x
Given:
The equation of a line is:
[tex]y-1=4x[/tex]
A line parallel to the above line passes through the point P(2,5).
To find:
The equation of the parallel line.
Solution:
The slope intercept form of a line is:
[tex]y=mx+b[/tex] ...(i)
Where, m is the slope and b is the y-intercept.
The given equation is:
[tex]y-1=4x[/tex]
It can be rewritten as
[tex]y=4x+1[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]m=4[/tex]
It means the slope of the given line is 4.
We know that the slopes of two perpendicular lines are equal. So, the slope of the required parallel line is also 4.
The parallel line passes through the point P(2,5) with slope 4, thus the equation of the parallel line is
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-5=4(x-2)[/tex]
[tex]y-5=4x-8[/tex]
[tex]y=4x-8+5[/tex]
[tex]y=4x-3[/tex]
Therefore, the equation of the required parallel line is [tex]y=4x-3[/tex].
The cost C in dollars of manufacturing x bicycles at a production plant is given by the function shown below.
C(x) = 3x^2- 600x + 43,500
a. Find the number of bicycles that must be manufactured to minimize the cost.
b. Find the minimum cost.
Answer:
Minimum 100 bicyclesMinimum cost is 13500Step-by-step explanation:
Given function:
C(x) = 3x^2- 600x + 43500a.
Minimum cost is obtained at vertex.
Vertex is determined by formula x = -b/2a, in standard form of
f(x) = ax^2 + bx + c
Vertex of the given function is:
x = -(-600)/(2*3) = 100b.
Cost at vertex is:
C(100) = 3*100^2 - 600*100 + 43500 = 13500couldn't write it out so i took a pic of it
Answer:
4th is the answer
Step-by-step explanation:
Answer:
the measure of <ABD = 1/2 the measure of <ABC is the answer :)
Step-by-step explanation:
Which statement is best supported by the information in the box plots?
Answer: A
Step-by-step explanation:
Answer:
It is A
Step-by-step explanation:
help please thank you sm!!!
Answer:i think it is 54 degree
Step-by-step explanation:
Answer:
36
Step-by-step explanation:
An angle inscribed in a semi circle measures 90. So that means the third angle measures 36.
Yoko can type 36 words in 6 minutes what is her rate in the words per minute
Answer:
6 words per minute
Step-by-step explanation:
Divide 36 by 6 minutes to find how many words per minute
Answer:
6 words per minute
Step-by-step explanation:
36 words/ 6 minutes = 6 words per minute
Help! I don't get it!
What is the circumference of the pancake?
Use the Pythagorean theorem to find the unknown side of the right triangle.
Hypotenuse length_____
Answer: If you use a^2+b^2=c^2 formula you should get your answer of 39
Step-by-step explanation:
The number 40 is 5 percent of what number?
A) 80 B) 8 C) 200 D) 2 E) 800
Answer:
800
Step-by-step explanation:
Is means equals and of means multiply
40 = 5% *N
Change to decimal form
40 = .05N
Divide each side by .05
40/.05 =.05N/.05
800 = N
Plz help so I can pass
Answer: 36.2
Step-by-step explanation:
divide 30 by two (15)
use the pythagorean theorem (a^2+b^2=c^2)
15^2+33^2=x^2
225+1089=x^2
1314=x^2
36.249137... = x
You can send 34 text messages in 12 minutes. How many minutes does it take you to send 68 messages?
Answer:
24
Step-by-step explanation:
34 messages per 12 minutes
68 is just 34 mulitplied by 2.
it would take you twice as long because there are twice as many messages.
12 minuted multipled by 2 is 24.
It would take you 24 minutes to send 34 messages.
Answer:
24 minutes
Step-by-step explanation:
34/12
68/x
34*2=68
12*2=24
Find area of parallelogram plz
Answer:
A)
Step-by-step explanation:
The answer is A) because the formula to solving the area of a parrellogram is b x h
Find the value of c that makes x2 + 6x + c a perfect square. Then write the trinomial as a perfect square.
Hi there!
[tex]\large\boxed{c = 9, (x +3)^2}[/tex]
To find the value of c, we can say:
ax² + bx + c
(b/2)² = c
Therefore:
(6/2)² = 3² = 9
Rewrite the trinomial:
x² + 6x + 9
To write as a binomial, take the square root of c:
√9 = 3
Thus:
(x + 3)² = x² + 6x + 9
The measure of two sides of a triangle are given. If the perimeter is 11x^2 - 29x + 10, find the measure of the third side.
Answer:
I would say use photomath if you cant find your answer.
Step-by-step explanation:
What is the solution to the system of linear equations graphed here?
A (2,-1)
B (-1,2)
C (2,1)
D) No Solution
Answer:
One solution, A) (2 , -1)
Step-by-step explanation:
The solution is where the two lines intersect. If the lines do not intersect, it is no solution. If the line intersects once (like in the picture), it has one solution. If it intersects more than once (x), then it will have x amount of solutions.
In this case, the intersection is at (2 , -1), therefore, A) (2 , -1) is your answer.
~
Whoever answers correctly gets brainliest.
Answer:
C. r+r+r+t+t = 3r + 2t
Step-by-step explanation:
because we cant add numbers with different variables
What is the mead absolute deviation of this data set?
A) 1.56
B) 143
C) 14.3
D) 15.6
Gretta wrapped 15 presents every 20 hours. At that rate, how long, in hours, will it take to wrap 18 presents? label optional
Answer:
[tex]15 \: presents = 20 \: hours \\ 18 \: presents = ( \frac{18}{15} \times 20) \: hours \\ = 24 \: hours[/tex]
Time required to wrap 1 present
20/154/3hTkme to wrap 18 present
18(4/3)6(4)24h