Answers
[tex]\bf 3^{5x-9}=\left( \cfrac{1}{27} \right)^{2x-8}\qquad \boxed{27=3^3}\qquad 3^{5x-9}=\left( \cfrac{1}{3^3} \right)^{2x-8} \\\\\\ 3^{5x-9}=\left( 3^{-3} \right)^{2x-8}\implies 3^{5x-9}= 3^{-3(2x-8)} \\\\\\ 3^{5x-9}= 3^{-6x+24}\impliedby \begin{array}{llll} \textit{the bases are the same, then}\\ \textit{the exponents must be the same} \end{array} \\\\\\ 5x-9=-6x+24\implies 11x=33\implies x=\cfrac{33}{11}\implies x=3[/tex]
Related Questions
Which property justifies this statement?If x=−2, then 5x=−10.
A.Multiplication Property of Equality
B.Transitive Property of Equality
C.Symmetric Property of Equality
D.Subtraction Property of Equality
Answers
Answer:
Correct option is:
A.Multiplication Property of Equality
Step-by-step explanation:
The Multiplication Property of Equality states that if you multiply both sides of an equation by the same number, the sides remain equal (i.e. equality is preserved).
Here, we are given a equality:
x= -2
Now, on multiplying both sides by 5, the equality will be preserved
i.e. 5x= -2×5
i.e. 5x= -10
Hence, Correct option is:
A.Multiplication Property of Equality
The property of equality that justifies the given statement is the Multiplication Property of Equality
The correct option is A.Multiplication Property of Equality
From the question, we have that
If x=−2, then 5x=−10
The property of equality that justifies this statement is the Multiplication Property of Equality.
This is because, when both sides of the first equation is multiplied by 5, the result gives the other equation.
That is,
[tex]5 \times x = -2 \times 5[/tex], yields
5x=−10.
Hence, the property of equality that justifies this statement is the Multiplication Property of Equality
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RULES:
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1) How many moles are there in 24.5 grams of CoF3?
2) How many molecules are there in 150.00 grams of Na2SO4?
3) How many moles are there in 2.3 x 1024 atoms of sulfur?
4) How many grams are there in 7.40 x 1023 molecules of PH3?
5) How many moles are there in 7.5 x 1023 molecules of H2SO4?
6) How many molecules are there in 55.5 grams of Cu(ClO¬3)2?
7) How many grams are there in 8.20 x 1025 molecules of water?
8) How many molecules are there in 238.05 grams of CO2?
9) How many molecules are there in 2.35 grams of NH4F?
10) How many grams are there in 1.50 x 1023 molecules of N2H6?
11) How many molecules are there in 20.40 grams of SiCl4?
12) How many grams are there in 3.50 moles of AlCl3?
13) How many moles are there in 4.50 x 1022 molecules of CH4?
14) How many molecules are there in 9.34 grams of NO?
15) How many grams does 4.00 moles of UF6 weigh?
16) How many moles are there in 230.0 grams of NH4OH?
Answers
2.
Na = 23
S= 32
O= 16
3. 2355.2
4. 7570.2
5. 8.08 g/mol * 1.2 mol = 120 g
6. 0.024083482462885
7. 455176242.02054
srry this is all i can answer
The student's questions involve calculations of moles, mass, and molecule amounts in various chemical compounds based on stoichiometric principles. The answers are given as a sorted list. Values should be verified with available molar masses.
Explanation:This student's questions relate to moles, mass, and molecule amounts in different chemical compounds, following the principles of
stoichiometry
. Here are the answers, calculated using the appropriate molar mass for each substance:
24.5 grams of CoF3 is approximately 0.294 moles.150.00 grams of Na2SO4 equates to about 1.12 x 1024 molecules.2.3 x 1024 atoms of sulfur is around 38.18 moles.7.40 x 1023 molecules of PH3 is about 61.12 grams.7.5 x 1023 molecules of H2SO4 is around 49.89 moles.As chemistry problems can be complex, please double-check these answers using your own molar masses.
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Which number sentence best represents this story problem? Carol picks 42 apples. She puts an equal number of apples in each of 6 bags. How many apples are in each bag? A. 42 × 6 = ? B. 42 ÷ 6 = ? C. 42 + 6 = ? D. 42 – 6 = ?
Answers
The correct answer is B. 42 / 6.
This is because we are trying to find the amount of apples per bag and therefore we have to divide the total number of apples by the number of bags.
Hope This Helps You!
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- Hannah ❤
The vector has components +5 and +7 along the x- and y-axes respectively. along a set of axes rotated 90 degrees counterclockwise relative to the original axes, the vector's components are
Answers
After rotating 90 degrees counterclockwise,
Now, Vector components are +7 in x-axis & +5 in y-axis.
Let the coordinates of the rotated vector be (a,b).
From the Pythagorean theorem,
d = √(5² + 7²) = 8.6023
The angle θ is given by
tan θ = 7/5 = 1.4
θ = tan⁻¹ 1.4 = 54.46°
φ = 180 - (90 + 54.46) = 35.54°
The coordinates of the rotated vector are
a = - d cos φ = - 8.6023*cos(35.54) = 7
b = d sin φ = 8.6023*sin(35.54) = 5
Answer: (-7, 5)
Write the complete balanced equation for the reaction between barium oxide (BaO) and water (H2O). You do not need to make the subscripts smaller; just write them out as regular numbers. For example: H2O.
Answers
Answer:
The balanced chemical equation is ;
[tex]BaO(s)+H_2O(l)\rightarrow Ba(OH)_2(aq)[/tex]
Step-by-step explanation:
When barium hydroxide react with water it gives an alkaline solution of barium hydroxide.
The balanced chemical equation is given as:
[tex]BaO(s)+H_2O(l)\rightarrow Ba(OH)_2(aq)[/tex]
according to stoichiometry,when 1 mole of barium oxide reacts with 1 mole of water it gives 1 mole of barium hydroxide.
What is the value of the function at x=−3?
Answers
If so it would be 4
Answer:
correct answer is 4
Step-by-step explanation:
Lori sold 3 times as many raffle tickets as tony. lori sold 24 tickets. how many more raffle tickets did lori sell than tony?
Answers
Answer:
Your Answer is C) 16
Step-by-step explanation:
Step 1: Find the number Tony sold.
24 ÷ 3 = 8
Step 2: Find how many more tickets were sold by Lori than Tony.
24 - 8 = 16
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I need help with this. 20 points!
If f(x) = 5x - 4, then what is the value of f(7)?
Answers
f(7) = 35 - 4
f(7) = 31
Hope this helps in your understanding this problem!!
name the property of equality or congruence that justifies going from the first statement to the second statement.
ST=QR
QR=ST
a) reflexive property of congruence
b) symmetric property of congruence
c) transitive property of congruence
d) substitution property of congruence
Answers
What is the area of The shaded sector of the circle
Answers
1/3 of circle = 81pi / 3 = 27 pi units^2
answer
B. 27 pi units^2
Answer: 27[tex]\pi[/tex] [tex]unit^{2}[/tex]
Step-by-step explanation: area of circle =[tex]\pi r^{2}[/tex]
where r is the radius of circle
here r=9
to find the area of circle we cover an angle of 360° but here we have to cover only 120°=360°÷3
so area of shaded region =area of circle÷3
=[tex]\pi[/tex]×9×9÷3
=27[tex]\pi[/tex] [tex]unit^{2}[/tex]
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Answers
In an isometric transformation, the preimage and image must not __________. A. change size B. rotate C. preserve angle measures D. reflect across the x axis Please select the best answer from the choices provided A B C D
Answers
violet chewed 5 times as many pieces of bubble gum in one week as her friend if her friend chewed 12 pieces of bubble gum.how many did violet chew
Answers
so I would say it's 5 (12)=60 so I think Violet chewed chewed 60
and if it was asking how many pieces of bubble gum Violet chewed more than her friend it would be 60-12=48
Violet chewed 60 pieces of bubble gum in one week.
Explanation:To find out how many pieces of bubble gum Violet chewed, we need to multiply the number of pieces that her friend chewed by 5. Her friend chewed 12 pieces of bubble gum, so we can multiply 12 by 5.
12 x 5 = 60
Therefore, Violet chewed 60 pieces of bubble gum in one week.
What is the answer to John bought a video game on sale for $35. The original price of the game was 3 times that amount. John also bought video game controllers on sale for $28. The original price of the game controllers are 5 times that amount. Together how much money did the video game and controllers cost before they went on sale?
Answers
Video game: $35
Controller: $28
~~~~~~~~~~~~~~~~~~~~~~~~~
Video game:
35 x 3 = 105
Controller:
28 x 5 = 140
140 + 105 = 245
Total: $245
Why are two lines with the same y intercept are perpendicular?
Answers
If you want to know why 2 lines are perpendicular or parallel you have to look @ the slope
Perpendicular: The slope is the negative reciprocal of the slope of the original equation (other line slope) what this means it that you flip the numerator and denominator and make it negative (or positive, depending if it's already negative)
Parallel: The slope is the same (see 2nd picture as an EX).
Two lines with the same y-intercept are perpendicular because they are only perpendicular if their slopes are the reciprocals of each other's negative values.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The standard form of the lines are:
y = mx + c
Here m is the slope and c is the y-intercept of the line
mM = -1
The M is the slope of the second line which is perpendicular to the first one.
y = Mx + c (with the same y-intercept)
Thus, two lines with the same y-intercept are perpendicular because they are only perpendicular if their slopes are the reciprocals of each other's negative values.
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A card is drawn from a standard deck of 52 cards. find p(drawing an ace and 9)
Answers
possibility of drawing any one card would be proportion
52(cards in deck) : 100%(full deck has 100%)=1(this is any one card in deck) : X(possibility you are looking for)
X=100/52=about 1.9% of geting Ace 9
Which graph describes the open sentence –1 ≤ n + 2 ≤ 6?
A. Number line showing range from negative four to four. There are two rays on the graph. The first has a right end point with a closed dot at negative two with a ray pointing left past negative four. The second has a left end point with an open circle at three with a ray pointing right past four.
B. Number line -5 to +5 in single-integer increments - assessment graphic
C. Number line showing range from negative three to three The left end point is an open circle halfway between negative one and zero. There is a closed dot at three, and a ray points past three.
D. Number line showing range from negative eight to eight. There are two rays on the graph. The first has a right end point with an open circle halfway between negative six and negative four with a ray pointing left past negative eight. The second has a left end point with an open circle at four with a ray pointing right past eight.
Answers
The value of n≥-3 and n≤4 describes the open sentence -1≤n+2≤6
What will be the range of n for -1 ≤ n+2 ≤ 6 ?If we follow the above condition for the different values of n
At value of n=-3 we will get n+2=-3+2=-1
similarly at n=-2 we will get n+2=-2+2=0
and at n=-1 we will get n+2=-1+2=1
all three (-1,0,1) follow the condition -1 ≤ n+2
Similarly at n=(0,1,2,3,4) condition n+2 ≤ 6 is followed
Hence value of n≥-3 and n≤4 describes the open sentence -1≤n+2≤6
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The correct graph is option C.
Sure, let's break down the steps to understand why option C is the correct graph for the open sentence [tex]\(-1 \leq n + 2 \leq 6\)[/tex]:
1. Identify the Middle Term: The middle term in the open sentence is [tex]\(n + 2\)[/tex]. This means our focus is on the expression [tex]\(n + 2\)[/tex].
2. Understand the Inequality: The inequality [tex]\( -1 \leq n + 2 \leq 6\)[/tex] can be understood as "n + 2 is greater than or equal to -1 and less than or equal to 6".
3. Subtract 2 from Each Part: To isolate [tex]\(n\)[/tex], subtract 2 from each part of the inequality:
[tex]\[ -1 - 2 \leq n + 2 - 2 \leq 6 - 2 \][/tex]
Which simplifies to:
[tex]\[ -3 \leq n \leq 4 \][/tex]
4. Draw the Number Line: Draw a number line ranging from -3 to 4, inclusive.
5. Plot the Endpoints: On the number line, mark endpoints at -3 and 4.
6. Determine the Endpoints: Since the inequality includes "equal to" signs, the endpoints should be marked with closed dots (indicating inclusion).
7. Determine the Direction of the Ray: Since the inequality does not include strict inequality signs (< or >), the rays should extend in both directions from the endpoints.
8. Indicate the Rays: Draw rays to the left of -3 and to the right of 4, indicating the range extends indefinitely in both directions.
9. Mark the Open Circle: Since the inequality involves strict inequality at -1 and 6, mark an open circle at the points halfway between -1 and -3, and 6 and 4, respectively.
10. Verify the Result: The resulting graph should have closed dots at -3 and 4, indicating the range includes those values, and open circles at -1 and 6, indicating exclusion.
Option C correctly represents these steps, making it the correct graph.
The graph is given below:
From long experience, it is known that the time it takes to do an oil change and lubrication job on a vehicle has a normal distribution with a mean of 17.8 minutes and a standard deviation of 5.2 minutes. An auto service shop will give a free lube and oil change service to any customer who must wait beyond the guaranteed time to complete the work. If the shop does not want to give more than 1% of its customers a free lube and oil change service, how long should the guarantee be? Round appropriately to the minute.
Answers
To find the guarantee time for an oil change and lubrication job, calculate the z-score for the 1% percentile of a standard normal distribution and use the formula z = (x - μ) / σ to solve for x. Round x to the nearest whole number.
Explanation:The question is asking for the guarantee time that an auto service shop should offer for an oil change and lubrication job. To find this, we need to calculate the z-score that corresponds to the 1% percentile of a standard normal distribution. The z-score can be found using a z-table or calculator, and then we can use the formula z = (x - μ) / σ to solve for x. Round x to the nearest whole number to get the guarantee time.
the product of two consecutive odd integers is one less than four times their sum. Find the two integers.
Answers
x^2 + 2x = 8x + 8 - 1
x^2 - 6x - 7 = 0
(x-7)(x+1) = 0
x = 7 and x = -1
the two integers are 7 and 9
or
two integers are - 1 and 1
Which of the following disjunctions is false ?
A. 4 - 3 = 2 or 6 · 3 = 9
B. 5 · 6 = 30 or 3 + 4 = 7
C. 8 + 3 = 11 or 5 · 4 = 23
D. 7 + 6 = 13 or 5 · 2 = 10
Answers
----------------------------------------------
Choice A
4-3=2 is false
6*3=9 is false
both parts are false, so overall the entire disjunction is false
----------------------------------------------
Choice B
5*6=30 is true
3+4=7 is true
Neither part is false, so overall the entire thing is true
----------------------------------------------
Choice C
8+3=11 is true
5*4=23 is false
While second piece is false, the overall disjunction is true. The first part (true) makes the whole thing true.
----------------------------------------------
Choice D
7+6=13 is true
5*2=10 is true
Neither part is false, so overall the entire thing is true
----------------------------------------------
----------------------------------------------
In summary, we have
A. False
B. True
C. True
D. True
Making choice A the only answer that is false. So choice A is the final answer
Both 4 – 3 = 2 and 6 · 3 = 9 parts are false, so overall the entire disjunction is false.
What is a disjunction?A logical relation called a disjunction states that either one or more of the stated choices are correct.
A. 4 – 3 = 2, is false
6 · 3 = 9, is false
Both parts are false, so overall the entire disjunction is false
B. 5 · 6 = 30, is true
3 + 4 = 7, is true
Neither part is false, so overall the entire thing is true
C. 8 + 3 = 11, is true
5 · 4 = 23, is false
While second piece is false, the overall disjunction is true. The first part (true) makes the whole thing true.
D. 7 + 6 = 13, is true
5 · 2 = 10, is true
Neither part is false, so overall the entire thing is true
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The square root of 31 is between what two integers
Answers
6^2 = 36
NOTE: There must be math program you get to learn for this. Please do
The perimeter of a rectangle is 78 cm and the basis measures 27 cm. Calculates the perimeter of the square equivalent to the rectangle.
Answers
27*12=324 cm² (A rectangle)
4*√324=
4*18=
72 cm (perimeter of the square)
Given that f(x) = 2x −5, find the value of x that makes f(x) = 15. (5 points)
5
10
20
25
Answers
15 = 2x - 5
Now you must solve like a normal equation:
15 = 2x - 5 )+5
20 = 2*x ):2
10 = x
ANSWER: The value of x is 10
The cost c ( x ) c(x), where x x is the number of miles driven, of renting a car for a day is $49 plus $0.55 per mile.
Answers
To calculate the cost c(x) of renting a car for a day based on the number of miles driven, use the formula c(x) = $49 + $0.55 imes x, where x represents miles driven.
Explanation:The student's question involves calculating the cost of renting a car for a day based on the number of miles driven. The function c(x) represents the total cost, which includes a fixed charge and a variable charge per mile. The fixed charge is $49, and the variable charge is $0.55 per mile. The total cost can be expressed as c(x) = $49 + $0.55 imes x, where x is the number of miles driven.
To calculate the cost for a given number of miles, simply multiply the number of miles by $0.55 and add the base charge of $49. For example, if a student drives 20 miles, the cost would be calculated as follows: c(20) = $49 + ($0.55 imes 20) = $49 + $11 = $60.
If a microscope has a series of three lenses that magnify individually 5x, 5x, and 7x, what is the total magnification of the microscope
Answers
Hope this helps!
The total magnification of the microscope is 175x.
Given that,
If a microscope has a series of three lenses that magnify individually 5x, 5x, and 7x.Based on the above information, the calculation is as follows:
[tex]= 5 \times 5 \times 7[/tex]
= 175x
Therefore we can conclude The total magnification of the microscope is 175x.
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Write an equation in point-slope form of the line through point J(-8,10) with slope -5.
A. y + 10 = -5(x + 8)
B. y - 10 = 5(x + 8)
C. y - 10 = -5(x + 8)
D. y - 10 = -5(x - 8)
Answers
Hope this helps! :)
REVISE: I accidently put y instead of x in the -5(x + 8) part. It's fixed now.
Solving systems of three equations w/ elimination
Answers
Solve x2 + 4x − 4 = 0.
Answers
The solution to the given quadratic equation is: x = - 2 ± 2√2
What is the solution to the quadratic equation?The general form of a quadratic equation is expressed as;
y = ax ² + bx + c
The quadratic equation is given as;
x² + 4x - 4 = 0
We can solve either by quadratic formula or by factorization
We will use quadratic formula as;
x = [-b ± √(b² - 4ac)]/2a
Thus:
x = [-4 ± √(4² - 4(1 * - 4))]/2(1)
x = (-4 ± √32)/2
x = - 2 ± 2√2
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To solve the quadratic equation x^2 + 4x - 4 = 0, identify the coefficients, apply the quadratic formula, and find the solutions.
To solve the quadratic equation x2 + 4x - 4 = 0:
Identify the coefficients a = 1, b = 4, and c = -4.Substitute the values into the quadratic formula: x = (-b ± √(b2 - 4ac)) / 2a.Solve for x to find the two possible solutions.a right rectangular pyramid is shown. the height of the pyramid is 12 units the length are the width are 6 units and 8 units
Answers
Answer:
The answers are 10, 13, and 12.37
Step-by-step explanation:
Identify the degree of the polynomial 6xy2 − xy + 8 + 12y.