Answer: assuming that this was your equation;
[tex]\frac{1}{16} =64^{4x-3}[/tex]
You answer is x= 7/12
Step-by-step explanation:
First, rewrite 1/16 as 2^-4 and 64^4x-3 as 2^24x-18
This will leave you with;[tex]2^{-4} =2^{24x-18}[/tex]
Since bases are the same, set the exponents equal (eliminate the 2’s);
-4=24x-18
Move 24x to the left to get; -24x-4=-18
Move constant to the right to get -24x=-18+4
Add 4 to -18 to get; -24x=-14
Divide both sides by -24 to get you final answer for x which is 7/12
Hope this helps. Please rate and hit that thanks button. Cheers!
The required value of exponential equation is x = [tex]\frac{7}{12}[/tex].
Given that,
Exponential equation; [tex]\frac{1}{16} = 64^{4x-3}[/tex]
We have to determine,
The value of x.
According to the question,
To obtain the value of x by solving the exponential equation follow all the steps given below.
Exponential equation;
[tex]\dfrac{1}{16} = 64^{4x-3}[/tex]
Then,
[tex]\dfrac{1}{16} = 64^{4x-3}\\\\\dfrac{1}{2^{4}} = 2^{6(4x-3)}\\\\2^{-4} = 2^{24x-18}\\\\[/tex]
Since, bases are the same, set the exponents equation,
Then,
Equating the power of exponential equation,
[tex]-4 = 24x-18\\\\24x = -4+18\\\\24x = 14\\\\x = \dfrac{14}{24}\\\\x = \dfrac{7}{12}[/tex]
Hence, The required value of exponential equation is [tex]\frac{7}{12}[/tex].
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Please help: Quadratic Formula Question
Answer:
1. b=-7
2. c= -10
Step-by-step explanation:
The standard form for the quadratic function is
ax^2 +bx+c
so we need to rewrite the function to be in this form
2x^2 -10 = 7x
Subtract 7x from each side
2x^2 -7x-10 = 7x-7x
2x^2 -7x-10 = 0
a =2, b= -7 c=-10
Dan paid $34.30 for a sweater the price included a 40% markup what is the cost of the sweater before the markup
Answer:
$24.5
Step-by-step explanation:
Let x be the cost of sweater before markup.
We are told that Dan paid $34.30 for a sweater the price included a 40% markup. This means x plus 40% of x equals 34.30.
We can represent this information as:
[tex]x+\frac{40}{100}x=34.30[/tex]
[tex]x+0.40x=34.30[/tex]
[tex]1.40x=34.30[/tex]
[tex]x=\frac{34.30}{1.40}[/tex]
[tex]x=24.5[/tex]
Therefore, the cost of sweater before the markup was $24.5.
The length of a base of a rectangular prism is 8 inches. The width of the prism is 4 and a half inches, and the height is 3 and a half inches. What is the volume of the prism?
A hotel has 150 rooms. The charges for a double room are $270 per night and $150 per night for a single room. On a night when the hotel was completely occupied. Revenues were $33,300. Which pair of equation can be used to determine the number of double room, d and the number of single room,s,in the hotel?
Step-by-step explanation:
Let s be charges for a single room and d be charges for a double room per night.
We are told that a hotel has 150 rooms. We can represent this information as:
[tex]s+d=150...(1)[/tex]
The charges for a double room are $270 per night and $150 per night for a single room. So the charges for s single rooms will be 150s and charges for d double rooms will be 270d.
On a night when the hotel was completely occupied. Revenues were $33,300.
We can represent this information as:
[tex]150s+270d=33,300...(2)[/tex]
Therefore, our desired pair of equations will be:
[tex]s+d=150...(1)[/tex]
[tex]150s+270d=33,300...(2)[/tex]
Answer: First equation: s+d=150; second equation: 150s+270d=33300
Step-by-step explanation: To solve the given problem we need to write two equations, the first one will express that the total number of rooms is the sum of the single rooms an the double rooms. The second equation will include the sum of the total earnings for the single and double rooms:
First equation:
s+d=150 (the single rooms and the double rooms equal 150 rooms)
second equation:
150s+270d=33300 (the sum of the single and double rooms each one of them multiplied by their prices, equals the total revenue)
To solve the equation we isolate s from the first equation:
s=150-d
and we replace it in the second one:
150(150-d)+270d=33300
solving for d:
22500-150d+270d=33300
120d=33300-22500
120d=10800
d=10800/120
d=90.
now we calculate s from the first equation:
s=150-d
s=150-90
s=60.
There are 60 single rooms and 90 double rooms.
A cone shaped cup has a radius of 3 inches and a height of 7 inches. What is the volume in cubic inches for the cup? Use 3.14 for π.
Answer:
65.94 cubic inches
Step-by-step explanation:
We are given that a cone shaped cup has a radius of 3 inches and a height of 7 inches and we are to find the volume of this cone shaped cup.
We know the formula for the volume of a cone:
Volume of a cone = [tex]\pi r^2\frac{h}{3}[/tex]
So substituting the given values in the above formula to get:
Volume of the cone shaped cup = [tex]3.14*3^3*\frac{7}{3} =65.94[/tex]
Therefore, the volume of the cone shaped cup is equal to 65.94 cubic inches.
Answer:
65.94 inches^3
Step-by-step explanation:
hope this helps
If you break up the number under the radical in the square root of 36 into two factors that are perfect squares, what are the two factors?
Answer:
6
Step-by-step explanation:
sqrt (36)
Lets break this into parts
sqrt(4 * 9)
sqrt(4) * sqrt(9)
2 * 3
6
Can someone help with these? 17 PT + BRainliest
29. e = D/(3f²)
30. k=-4, x=41 . . . . matches the 2nd selection
Step-by-step explanation:29. Multiply by the inverse of the coefficient of e. That coefficient is 3f², so you divide by that quantity.
... D = e(3f²)
... D/(3f²) = e . . . . . matches the first choice
___
30. You want to solve for k and use it with a different y-value.
... y = kx
... -96 = k·24
... -96/24 = k = -4
For y = -164, you have
... -164 = -4·x
... -164/-4 = x = 41
The coefficient of variation is -4, x is 41.
Solve for x.
−3x + 4b > 9
1.) x > The quantity 4 times b minus 9 all over 3 <-- My answer
2.) x < the quantity 9 minus 4 times b all over 3
3.) x < the quantity negative 4 times b plus 9 all over negative 3
4.) x > the quantity 4 times b plus 9 all over negative 3
Answer: [tex]\bold{x < \dfrac{4b-9}{3}}[/tex]
Step-by-step explanation:
-3x + 4b > 9
-4b -4b
-3x > -4b + 9
÷-3 ↓ ÷-3
x [tex]<\dfrac{-4b+9}{-3}[/tex]
x [tex]<\dfrac{-1(4b-9)}{-1(3)}[/tex]
x [tex]<\dfrac{4b-9}{3}[/tex]
Answer:
A
Step-by-step explanation:
A
Mr. Vargas is buying used computer equipment. He buys 3 keyboards and 4 mice. He spends $42. If the items are all the same price, how much does each item cost?
Answer:
Hello.
The answer is $6 each item.
Step-by-step explanation:
If all of the items are the same price, then we have a total of 7 items ( 3 keyboards + 4 mic = 7 items).
So at the end is: 7 items ÷ $42 = $6.
The cost of each item is $6.
What is Division?A division is a process of splitting a specific amount into equal parts.
Given that Mr. Vargas is buying used computer equipment. He buys 3 keyboards and 4 mice. He spends $42.
Since, cost of each item is same, therefore total item = (3 + 4) = 7
Let the cost of each item be c,
7c = 42
c = 6
Hence, The cost of each item is $6.
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Which is the equation of the given line?
y=-2
Find the slope of the line between
Answer:
y = -2
Step-by-step explanation:
The y values remain constant through the whole line. It pass through the point where y = -2 so it's equation is:
y = -2
please help me out!!!!!!
1) The question is specifically asking about graduates. The total number of graduates is 2,610.
2) The total number of graduates on financial aid is 1,879.
3) So I think what you need to do is divide 2,610 (the total number of graduates) by the total of graduates on financial aid.
4) Using a calculator, I got 1.3.
Edit: I think MrBillDoesMath got it correct. But I appreciate you thanking me, despite my answer not being right.
Hello from MrBillDoesMath!
Answer:
.72
Discussion:
From the table, 1879 graduates students are receiving financial aid. Also from the table the total number of grad students is 2610. Hence the probability of a grad student receiving financial aid is 1879 /2610 = .72
Regards,
MrB
Given that SU≅UT and SV>VT, identify a two-column proof that proves m∠SUV>m∠TUV.
Answer: Choice B
We start with SU = UT being given, and so is SV > VT.
The second line is UV = UV by the reflexive property to help us use the converse of the hinge theorem next.
The hinge theorem basically says that the more open an angle is, the larger the opposite side will be (the side opposite from the angle that varies). Imagine a door opening and closing. The further open it gets, the longer the rope will be that connects the door handle to the frame. Going in reverse, the converse says that if the opposite side of the angle gets bigger, then the angle itself gets bigger as well. The hinge theorem is handy to help compare two sides even if we don't know their exact lengths (we can figure out which side is larger than the other)
The conditions given that SU is congruent to UT and SV is greater than VT create a scenario where we can prove that the measure of angle SUV is greater than the measure of angle TUV.
Explanation:Given that SU≅UT means that segment SU is congruent to segment UT, and SV>VT meaning that segment SV is greater than segment VT, this sets up two important conditions for the triangle SUV. First, as SU is congruent to UT, this implies that ∠SUV is congruent to ∠TUV due to the Base Angles Theorem (If two sides of a triangle are congruent (equal), then angles opposite these sides are congruent). However, SV>VT creates an inequality which contradicts this, pointing towards the fact that ∠SUV is greater than ∠TUV.
Proof:
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What is the range of the data represented by the box plot?
Answer:
The range is 12
Step-by-step explanation:
The range of the data is the largest number minus the smallest number.
The largest number is 17
The smallest number is 5
17-5
12
The range is 12
From the table below, determine whether the data shows an exponential function. Explain why or why not.
Answer:
B
Step-by-step explanation:
Which of the following terms best describes three points that all lie in a straight line?A. CollinearB. CongruentC. EqualD. Midpoint
I would appreciate a description of this as well.
*Take math seriously or you gone have to retake this subject*
Answer:
A. Collinear
Step-by-step explanation:
three points that all lie in a straight line
A. Collinear- means along the same line
B. Congruent - means the same
C. Equal = means the same
D. Midpoint= means the middle
Answer by YourHope:
Hi! :)
Which of the following terms best describes three points that all lie in a straight line?
I would say A. Collinear!
:)
6>d-1 graph it please
Answer:
Step-by-step explanation:
6>d-1
Add 1 to each side
6+1 > d-1+1
7>d
Hi there!
Answer:
D>7
*The answer must have a positive sign and greater than symbol.*
Step-by-step explanation:
First, you switch sides of an equation.
[tex]d-1>6[/tex]
Then, you add by 1 from both sides of an equation.
[tex]d-1+1>6+1[/tex]
And finally, you add by the numbers from left too right.
[tex]6+1=7[/tex]
Final answer is d>7
I hope this helps you!
Have a nice day! :)
-Charlie
:D
Please answer this question! Brainliest and thirty points!
Answer:
option c
Step-by-step explanation:
x + 9 - 4x =3 - 2x + 4
=>x + 2x - 4x =7 - 9
=>3x - 4x = -2
=>-x = -2
=>x = 2
Answer:
x=2
Step-by-step explanation:
x+9 -4x = 3-2x+4
The first step is to combine like terms
-3x+9 = -2x+7
Add 3x to each side
-3x+3x+9 = -2x+3x+7
9 = x+7
Subtract 7 from each side
9-7 = x+7-7
2 =x
Kareem lives 4/10 of a mile from the mall. Wright to equivalent fractions that show what fration of a mile Kareem lives from the mall
Answer:
8/20 and 12/30 are equivalent to 4/10.
Step-by-step explanation:
You just have to multiply the numerator and denominator by the same number.
Luke's turkey chili recipe calls for 1.5 pounds of ground turkey for every 6 servings. How many servings can he make if he has 5 pounds of ground turkey? Show your work.
Final answer:
Luke can make 20 servings with 5 pounds of ground turkey.
Explanation:
To determine the number of servings Luke can make with 5 pounds of ground turkey, we need to set up a proportion. The recipe calls for 1.5 pounds of ground turkey for every 6 servings. So, we can set up the proportion: 1.5 pounds / 6 servings = 5 pounds / x servings, where x represents the unknown number of servings. To solve for x, we cross multiply: 1.5 pounds * x servings = 5 pounds * 6 servings. Simplifying the equation, we get: 1.5x = 30. Dividing both sides by 1.5, we find that x = 20. Therefore, Luke can make 20 servings with 5 pounds of ground turkey.
If sin x=−1/2, and 270°
*
If 180°<θ<270°, and sinθ=−3/4, what is the value of sin(−θ)?
Answer:
For each of the three basic trig functions, (sin, cos, tan) there are three more which act as their reciprocals. (csc, sec, and cot respectively)
Reciprocals, of course, are flipped fractions. If you have some number x, the reciprocal can be expressed as .
An important property of reciprocals is that if you mutliply them together they will cancel out--take for example.
Since secӨ is literally defined as the reciprocal of cosӨ, it is evident that
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Step-by-step explanation:
Select the correct answer. Given: AD = CF BC = DE Prove: AB = EF Statement Reason 1. AD = CF given 2. AD = AB + BC + CD CF = CD + DE + EF segment addition 3. AB + BC + CD = CD + DE + EF Transitive Property of Equality 4. AB + BC = DE + EF 5. BC = DE given 6. AB = EF Subtraction Property of Equality What is the reason for the fourth statement in this proof? A. definition of collinear points B. segment addition C. Subtraction Property of Equality D. Substitution Property of Equality
Answer:
Step-by-step explanation: The answer is D- Substitution Property of Equality. I just did the test and it was right.
Answer:
C. Subtraction property of equality.
Step-by-step explanation:
Given AD= CF
And BC=DE
To prove that AB=EF
Proof:
1.Statement: AD=CF
Reason: Given in question.
2. Statement: AD= AB+BC+ CD, CF= CD+DE+EF
Reason: Segment addition property because AB,BC,and CD are the segments of AB and CD,DE and DE are segments of CF.
3. Statement: AB+BC+CD=CD+DE+EF
Reason: Transitive property of equality
Transitive property: If ab=bc and bc=ca
Then , ab=ca
4.Statement: AB+BC= DE+EF
Reason: By using subtraction property of equality.
5. Statement:BC=DE
Reason: Given in question.
6. Statement: AB=EF
Reason: when we put BC=DE . Then we get AB+DE=DE+EF. By using subtraction property of equality .
Hence proved .
A television normally costs $1,420. Due to a store sale, the televison is now $1,022.40. What was the percentage taken off the television?
Answer: 28%
Step-by-step explanation:
[tex]\dfrac{new-original}{original}[/tex]
[tex]=\dfrac{1022.40-1420}{1420}[/tex]
[tex]=\dfrac{-397.60}{1420}[/tex]
= -0.28
= -28%
NOTE: negative sign represents decrease
The perimeter of a rectangle is 84m. The length is two and a half times the width. Find the dimensions of the rectangle. Question 5 options: Length = 30m; Width = 12m Length = 28m; Width = 70m Length = 12m; Width = 30m Length = 70m; Width = 28m
w - width
2.5w - length
84m - perimeter
w + w + 2.5w + 2.5w = 7w - perimeter
The equation:
7w = 84 divide both sides by 7
w = 12 m
length = 2.5w → 2.5w = 2.5(12) = 30 m
Answer: length = 30m; width = 12mI need help. I have tried doing this question and none of the answers were right. Please help me.
Which ordered pairs lie on the graph of the exponential function f(x)=− 3 (x−1) +2 ? Select each correct answer.
A. (4,−25)
B. (1, 1)
C. (−1, 2)
D. (0, 0)
Answer:
A and B
Step-by-step explanation:
assuming the function should be
- [tex]3^{x-1}[/tex] + 2, then
A
substitute the x value into f(x) and check the validity of the y- value
f(4) = - [tex]3^{3}[/tex] + 2 = - 27 + 2 = - 25 ← agrees with y value
(4, - 25) lies on the graph
B f(1) = - [tex]3^{0}[/tex] + 2 = - 1 + 2 = 1 ← agrees with y value
(1, 1) lies on the graph
C
f(- 1) = - [tex]3^{-2}[/tex] + 2 = - [tex]\frac{1}{9}[/tex] + 2 ≠ 2
(- 1, 2) does not lie on the graph
D
f(0) = [tex]3^{-1}[/tex] + 2 = - [tex]\frac{1}{3}[/tex] + 2 ≠ 0
(0, 0) does not lie on the graph
Natalie makes 2000 per month she spends 100 on credit card payments and 250 on an auto loan what is her debt to income ratio
After a birthday party 1/3 of the cake was left if the cake was shared equally between 4 people what fraction did each person revive
Triangle QRS is dilated about the origin by a scale factor of 2/3 to create triangle ABC . Are the two triangles congruent?
Answer:
No
Step-by-step explanation:
In a dilation, size is not preserved. Triangles must have the same shape and size in order to be congruent. If it is dilated by 2/3, then it gets smaller, and is therefore not the same size.
Final answer:
Triangle QRS is not congruent to triangle ABC after a dilation of [tex]\frac{2}{3}[/tex], but the two triangles are similar because their corresponding angles are equal and sides are proportional.
Explanation:
The question concerns the concept of congruent and similar triangles in geometry. When triangle QRS is dilated about the origin by a scale factor of [tex]\frac{2}{3}[/tex] to create triangle ABC, the two resulting triangles are not congruent because their corresponding sides are not equal in length. However, they are similar since the angles remain the same and the sides are proportional. Congruent triangles are identical in both shape and size, but similar triangles maintain the same shape while the size can vary in proportion.
Postal carrier can deliver 130 houses and 2.5 hour. At this rate how many hours will it take to deliver 312 at houses
First, you much find out how many houses are deliverd in 1 hour.
130/2.5=52
So 52 houses are delivered in 1 hour. Now, divide that by 312.
312/52=6
It would take 6 hours to deliver 312 houses.
Alice paid $21.75 for some packs of rice crackers. If each pack costs $1.75, how many packs did she buy?
We have dollars and dollars per pack, so we divide to get how many packs.
[tex] \dfrac{21.75}{1.75} = \dfrac{2175}{175} = \dfrac{87(25)}{7(25)} = \dfrac{87}{7} \approx 12.4[/tex]
Odd that it's not a whole number of packs; please check the question carefully. Let's say she bought 12 and got some change.
My guess is the question really says Alice spent $22.75, so she bought 13 packs. Again check the question carefully. You don't need us to divide two numbers.
Brandon buys a basket of flowers for $7 before tax. The sales tax is 4%. What is the total price Brandon pays for the basket of flowers?
Answer:
$7.28
Step-by-step explanation:
We have been given that Brandon buys a basket of flowers for $7 before tax. The sales tax is 4%.
The total price that Brandon paid for the basket of flowers will be equal to 7 plus 4% of 7.
We can represent this information in an equation as:
[tex]\text{The total price that Brandon paid for the basket of flowers}=7+(\frac{4}{100}\times 7)[/tex]
[tex]\text{The total price that Brandon paid for the basket of flowers}=7+(0.04\times 7)[/tex]
[tex]\text{The total price that Brandon paid for the basket of flowers}=7+0.28[/tex]
[tex]\text{The total price that Brandon paid for the basket of flowers}=7.28[/tex]
Therefore, the total price paid by Brandon for the basket of flowers was $7.28.
Answer:
Total price Brandon pays for the basket of flowers is, $7.28
Step-by-step explanation:
As per the given statement: Brandon buys a basket of flowers for $7 before tax.
Convert this $7 into cents.
1 dollars = 100 cents.
$7 = 700 cents.
It is also given that the sales tax is 4%.
then;
Sales tax = [tex]4\% \times 700 = \frac{4}{100} \times 700 = 4 \times 7 =28 cents[/tex]
Total price Brandon pays = Price of Brandon buys a flower before tax + sales tax price
= 700 + 28 = 728 cents = $7.28
Therefore, the total price Brandon pays for the basket of flowers is, $7.28