Answers
Answer:
[tex] {3}^{x} = {9}^{y} - - - eqn(i) \\ 4 ^{xy} = {2}^{x - 2} - - - eqn(ii) \\ from \: (i) \: introduce \: log_{10}\: \: \\ log( {3}^{x} ) = log( {9}^{y} ) \\ x log(3) = y log(9) \\ x log(3) = 2y log(3) \\ x = 2y - - - eqn(iii) \\ substitute \: for \: x \: in \: eqn(ii) \\ {4}^{ {2y}^{2} } = {2}^{2(y - 1)} \\ {4}^{ {2y}^{2} } = {4}^{(y - 1)} \\ from \: indice \: laws \\ {2}^{ {y}^{2} } = y - 1 \\ introduce \: log_{10} \\ {y}^{2} log(2) = log(y) - log(1) \\ log(2) = {y}^{ - 2} log (y \: - \: 1) \\ {y}^{ - 2} (2 - y - 1) = 10 \\ \frac{2}{ {y}^{2} } - \frac{1}{y} - \frac{1}{ {y}^{2} } = 10 \\ 1 - y = 10 {y}^{2} \\ 10 {y}^{2} + y - 1 = 0 \\ [/tex]
hope that step is enough to give you the two values of y, coz I gat no calc here with me.
hint: use the quadratic equation
Related Questions
What is the length of PR?
A: 13.5 inches
B: 7.5 inches
C: 10.5 inches
D: 9.5 inches
Answers
Answer:
The correct option is;
C: 10.5 inches
Step-by-step explanation:
In triangle ΔPQR the given parameters are;
The length of [tex]\overline {QP}[/tex] = 19.5 in.
The length of [tex]\overline {QR}[/tex] = 7.5 in.
In triangle ΔVWX, the given parameters are;
The length of [tex]\overline {WV}[/tex] = 13 in.
The length of [tex]\overline {WX}[/tex] = 5 in.
The length of [tex]\overline {VX}[/tex] = 7 in.
Given that we have;
[tex]\dfrac{\overline {QP}}{\overline {WV}} = \dfrac{19.5}{13} = 1.5 , \ \dfrac{\overline {QR}}{\overline {WX}} = \dfrac{7.5}{5} = 1.5[/tex]
The ratio of the corresponding sides of triangle ΔPQR and triangle ΔVWX are equal, therefore ΔPQR is similar to ΔVWX, from which we have for the corresponding sides, [tex]\overline {PR}[/tex] and [tex]\overline {VX}[/tex];
[tex]\dfrac{\overline {PR}}{\overline {WV}} = \dfrac{\overline {PR}}{\overline {7}} = 1.5[/tex]
∴ [tex]\overline {PR}[/tex] = 7 × 1.5 = 10.5
The length of [tex]\overline {PR}[/tex] = 10.5 inches
helpplsplsplsplsplsplsigiveiraliset
Answers
ANSWER ASAPPPP MARKING BRAINLIEST HELP
Answers
Answer:
A. 30800
B.39600
C. 17600
Step-by-step explanation: 0.12*$35000= 4200 35000-4200 = $30800
$45000*0.12=$5400 $45000-$5400= $39600
$20000*0.12=$2400 $20000-$2400= $17600
write the fraction as a mixed number
31/6
20/10
15/8
13/6
pls answer my dad is gonna hit me
Answers
20/10 will be 2
15/8 will be 1 7/8
13/6 will be 2 1/6
A plant is already 8.75 meters tall, and it will grow 25 centimeters every month. the plants height, H (in meters), after x months is given by the following function H(x)=0.25x+8.75 What is the plants height after 40 months?
Answers
Answer:
18.75 meters
Step-by-step explanation:
8.75 + 0.25(40) = 18.75
One diet uses a ratio of 9:5:4 for carbohydrates, protein, and fat. A nutritionist is developing a diet that provides 450 calories from protein per day. Find the number of calories that should come from carbohydrates
Answers
Answer:
There are 810 calories from carbohydrates
Step-by-step explanation:
carbohydrates: protein: fat
9 :5 :4
We want 450 calories from protein
450 /5 =90
Multiply each term by 90
carbohydrates: protein: fat
9*90 :5*90 :4*90
810 450 360
There are 810 calories from carbohydrates
Answer:
810 calories are carbohydrates
Step-by-step explanation:
We know that the ratio 9:5:4 tells us that 18 equal amounts' of calories make up a meal. Now we know that 450 calories equals 5 of this parts (since protein is made out of 5 of this parts. Now we have to find out the amoung of calories in one of this 18 parts and multiply it by 9. So we do......
450 / 5 = 90
90 x 9 = 810
What is the exact value of tan ( 5 pi/8 )
Answers
===================================================
Explanation:
Make sure your calculator is in radian mode. Use your calculator to find that tan(5pi/8) = -2.41421 which is approximate.
Since the value is negative, this means the answer is between choices C and D. You can use your calculator to compute those expressions given and you should find it matches with choice D.
----------------------
Further explanation:
We can apply the half angle identity for tangent like so
[tex]\tan\left(\frac{x}{2}\right) = \pm \sqrt{\frac{1-\cos(x)}{1+\cos(x)}}\\\\\\\tan\left(\frac{5\pi/4}{2}\right) = -\sqrt{\frac{1-\cos(5\pi/4)}{1+\cos(5\pi/4)}}\\\\\\\tan\left(\frac{5\pi}{8}\right) = -\sqrt{\frac{1-\left(-\frac{\sqrt{2}}{2}\right)}{1+\left(-\frac{\sqrt{2}}{2}\right)}}\\\\\\[/tex]
Simplifying further, we get
[tex]\tan\left(\frac{5\pi}{8}\right) = -\sqrt{\frac{1+\frac{\sqrt{2}}{2}}{1-\frac{\sqrt{2}}{2}}}\\\\\\\tan\left(\frac{5\pi}{8}\right) = -\sqrt{\frac{2+\sqrt{2}}{2-\sqrt{2}}}\\\\\\[/tex]
In the last step, I multiplied top and bottom of the outer fraction by 2 to clear out the denominators of the inner fractions.
Answer:
Answer D
Step-by-step explanation:
on edge 2023
2x - 3x - 18 + -18 + 2x + 5x x= .....? A.X=4.5 B.X=0 C.X=6 D.X=-4.5 :) please help?
Answers
Answer:
-36+7x
Step-by-step explanation:
Answer:
x = 0
Step-by-step explanation:
First, simplify the equation by combining like terms on each side:
2x = 3x - 18 = -18 + 2x + 5x
-x - 18 = -18 + 7x
To solve the equation for x, the variable must be isolated on one side of the equal sign. Use the subtraction property of equality to subtract 7x from both sides. Then use the addition property of equality to add 18 to both sides:
-x - 18 - 7x = -18 + 7x - 7x
-8x - 18 = -18
-8x -18 + 18 = -18 + 18
-8x = 0
Finally, use the division property of equality to divide both sides by -8 and achieve the solution for x:
-8x/-8x = 0/-8
x = 0
Describe what makes 2 lines parallel. Give me a real-world example of a paralell lines.
Answers
Answer:
Step-by-step explanation:
If to lines are parallel then they could go on forever without touching at any given point.
for what value of “x” is the figure the given special parallelogram?
Answers
Answer:
x = 6
Step-by-step explanation:
(In reference to my diagram.... my diagram is similar to the diagram in the question)
We know that diagonals of a square bisect each other at right angles.
In ΔBOC ,
•OB = OC (Diagonals of square bisect each other)
=> ∠OBC = ∠OCB = (7x + 3)° (∵ OB = OC)
• ∠BOC = 90° (Diagonals intersect at right angles)
Using angle sum property of triangle ,
∠OBC + ∠OCB + ∠BOC = 90°
[tex] = > 7x + 3 + 7x + 3 + 90 = 180[/tex]
[tex] = > 14x + 6 = 180 - 90 = 90[/tex]
[tex] = > 14x = 90 - 6 = 84[/tex]
[tex] = > x = \frac{84}{14} = 6[/tex]
An amusement park reduced the admission price to $15.50 per day, but now charges $1.50 per ride. Mark has $26 to spend on admission and rides. Write an algebraic equation to find how many rides Mark can ride in one day.
Answers
Answer:
15.50 + 1.50x ≤ 26
Step-by-step explanation:
Given that:
Total amount to spend = $26
Admission fee = $15.50
Charge per ride = $1.50
Number of rides Mike can take in a day:
Let number of rides can take In a day = x
[Admission fee + (charge per ride * number of rides)] less than equal to total amount
15.50 + 1.50x ≤ total amount
15.50 + 1.50x ≤ 26
1.50x ≤ 26 - 15.50
1.50x ≤ 10.50
Divide both sides by 1.50
x ≤ 10.50 / 1.50
x ≤ 7
Hence, number of rides per day = 7
help me with this
3(2y+4c) use distributive property :)
Answers
Answer:
3(2y+4c) = 3 (x) 2y + 3 (x) 4c
*(x) = Multiplication!!!*
Step-by-step explanation:
PLEASE HURRY!!!!!!
If a=-3x-i and b=3, then find the value of the ab^(2)
in fully simplified form.
Answers
Answer:
Step-by-step explanation:
a= -3x-i
b= 3
[tex]b^{2}[/tex]=9
sooo.. a[tex]b^{2}[/tex] = (-3x-i )(9)
-27x -9i
Caveat : :/ if the i happens to be part of a complex number and the squared part is for the quantity (AB)^2 then it would change this answer ..but... I can't tell if that problem is about complex numbers or not, i'm guessing it's not
Ralph’s current annual income is $32,000. Using the graph shown below, Ralph has calculated that he will have to pay a total of $9,280 in federal taxes this year. Which of the following statements is true?
A circle graph titled Simpson's Annual Expenses. Federal taxes, 24 percent; State/local taxes, 10 percent; Housing and household, 23 percent; Food, 6 percent; Medical care, 8 percent; Transportation, 11 percent; Recreation, 3 percent; Clothing, 5 percent; Other, 10 percent.
a.
Ralph’s calculation is too high, he has only calculated state taxes.
b.
Ralph’s calculation is too high, his calculation includes state taxes.
c.
Ralph’s calculation is correct, he will have to pay $9,280 in federal taxes this year.
d.
Ralph’s calculation is too low, he did not include medical care in his calculation.What is gross pay
Answers
c.
Step-by-step explanation:
Ralph’s calculation is correct, he will have to pay $9,280 in federal taxes this year.
Ralph ’s calculation is too high, as his calculation includes state taxes.
CalculusGiven that Ralph's current annual income is $32,000, and he has calculated that he will have to pay a total of $9,280 in federal taxes this year, knowing that he has to pay 24% in federal taxes, to determine if his calculation is correct you must perform the following calculation:
32000 x 0.24 = X7680=XTherefore, Ralph ’s calculation is too high, as his calculation includes state taxes.
Learn more about calculus in https://brainly.com/question/13204916
please help me I have until Monday to do 82 questions
Answers
Answer and Step-by-step explanation:
We are solving for x.
A)
Multiply each side by 5 to get x by itself.
x = 15
B)
Multiply each side by 2 to get x by itself.
x = 17
#teamtrees #WAP (Water And Plant)
The area of a rectangular warehouse measures 4,288 square feet. The width of the warehouse is 64 feet long. Draw a model to represent the problem, and then solve for the length of the warehouse.
Answers
Answer:
67 feet
Step-by-step explanation:
Step one:
given
The area of a rectangular warehouse measures 4,288 square feet
The width of the warehouse is 64 feet long.
Required:
the length of the warehouse
Step two:
The expression for the area of a rectangle is
A= L*W
so, for the situation
4,288= L*64
solve for L
divide both sides by 64
L= 4,288/64
L=67 feet
Can someone please help me finding x and what is it? I would really appreciate it thank you!
Answers
How do I do this?
also the first part that is answered is wrong
Answers
Answer:
i would say for the second one 2.5 and the first one about 30
Step-by-step explanation:
−k+2(−2k−5) simplify
Answers
Answer:
-k-14
Step-by-step explanation:
Use distributive property and then just carry on and combine like terms.
Answer:
-5k - 10
Step-by-step explanation:
-k + 2 ( -2k - 5 )
= -k - 4k - 10
= -5k - 10
Approximate the percent of values on the box and whisker plot that lie below 68?
50
75
25
49
Answers
Answer:
50
Step-by-step explanation:
Simplify
-d+C-3+7d-8c
given d=2
C= -4
Answers
Answer:
40
Step-by-step explanation:
Ast month when Holiday Creations Inc. Sold $50,000 units, total sales were $200,000. Total variable costs were $120,000 and total fixed costs were $65,000. So, the company's CM ratio will be
Answers
Answer:
40%
Step-by-step explanation:
The first step is to calculate the unit selling price
= total sales/number of units
= 200,000/50,000
= $4
The unit variable expense can be calculated as follows.
= total variable expense/number of units
= 120,000/50,000
= $2.4
The contribution margin per unit can be calculated as follows
=selling price per unit- variable cost.
= $4-$2.4
= $1.6
Therefore the contribution margin ratio can be calculated as follows.
= $1.6/$4
= 0.4×100
= 40%
Melissa had $20 to purchase candy for a party. She purchased 3.6 pounds of candy that cost $2.50 per pound. How much money does Melissa have remaining after this purchase?
Answers
Answer:
1738
Step-by-step explanation:
Melissa has $11 remaining after purchasing 3.6 pounds of candy that cost $2.50 per pound.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Melissa had $20 to purchase candy for a party.
She purchased 3.6 pounds of candy that cost $2.50 per pound
Melissa spent 3.6 x $2.50
= 9 on candy.
Subtracting this amount from her initial $20, we get:
$20 - $9 = $11
Therefore, Melissa has $11 remaining after purchasing 3.6 pounds of candy that cost $2.50 per pound.
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ2
Brandon is playing hide-and-seek with Katy and Tony. Katy is hiding 63 feet south of Brandon, and Tony is hiding due east of Katy. If Brandon is 87 feet from Tony, how far apart are Katy and Tony?
Answers
Answer:
60 feets
Step-by-step explanation:
Given that :
Using Pythagoras rule :
Hypotenus = sqrt(Adjacent^2 + opposite^2)
From the attached picture :
x² = 87^2 - 63^2
x^2 = 7569 - 3969
X^2 = 3600
Take the square root of both sides :
X = sqrt(3600)
X = 60 feets
Hence, Katy and Tony are 60 feets apart
50 POINTS. Select the correct answer from each drop-down menu.
15
In AABC, m B = 90°, COS(I) = 17, and AB = 16 units.
V
V
units.
Based on this information, mzA= v ,mzc=
o, and AC =
Note that the angle measures are rounded to the nearest degree.
Answers
Answer:
m∠C=28°, m∠A=62°, AC=34.1 units
Step-by-step explanation:
Given In ΔABC, m∠B = 90°, , and AB = 16 units. we have to find m∠A, m∠C, and AC.
As,
⇒
By angle sum property of triangle,
m∠A+m∠B+m∠C=180°
⇒ m∠A+90°+28°=180°
⇒ m∠A=62°
Now, we have to find the length of AC
⇒
The length of AC is 34.1 units
Approximate the percent of values on the box and whisker plot that lie below 68?
50
75
25
49
Answers
An expression with only one term is called a
Answers
Answer:
monomial
Step-by-step explanation:
Two shops sell the same phone. In both shops it is £196. One shop increases the price by 17.5%. The other shop increases the price by 22.5%. Calculate the difference between the new prices of the phone in the two shops.
Answers
Step-by-step explanation:
the 1st shop=196-(17.5/100×196)
=196-34.3
=161.7+196
=357.7
the 2nd shop=196-(22.5/100×196)
=196-44.1
=151.9+196
=347.9
so the difference between two shop is
357.7-347.9=9.8
Mega Movies hosted a film premiere on Friday night. They charged $7 for adults and $4 for children. One hundred nine adults and children attended, and $703 was made in ticket sales. How many children and how many adults went to the film premiere?
A.
20 children; 89 adults
B.
17 children; 92 adults
C.
24 children; 85 adults
D.
14 children; 95 adults
Answers
Hope this helps
Have a great day/night
URGENT NEED HELP ILL GIVE YOU BRAINLEST
Answers
Answer:
y = -1/3x +2
Step-by-step explanation:
subtract -1/3x to the side of 2