Answer:
speed = (3/8 mi)/(3/5 h)
Step-by-step explanation:
... speed = distance/time
Fill in the given values:
... speed = (3/8 mi)/(3/5 h)
_____
Comment on units
You can use the units to provide both guidance and assurance. You know speed is generally expressed in miles per hour. If you consider "per" to mean "divided by", this expression of units tells you speed is calculated by dividing miles by hours.
If you leave the units with the numbers, as we have above, they enter into the calculation the same way any variable might. You can do the arithemetic with the numbers, and you can indicate the arithmetic with the units (just as you would with any variables). Here, the result of evaluating the equation would be ...
[tex]\displaystyle\frac{\frac{3}{8}\,\text{mi}}{\frac{3}{5}\,\text{h}}=\frac{\frac{3}{8}}{\frac{3}{5}}\,\frac{\text{mi}}{\text{h}}=\frac{5}{8}\,\text{mi/h}[/tex]
The fact that the units come out mi/h (the units of speed) provides assurance that you probably did the math correctly.
Answer:
three eighths over three fifths = five eighths mile per hour
Step-by-step explanation:
Which rectangular prism has the greatest volume?
Answer: First prism has the greatest volume.
Step-by-step explanation:
Since we have given that
Volume of prism = Length × Breadth × Height
So, we need to find the greatest volume, for which we find volumes of all figures:
1) Volume of prism would be
[tex]5\times 7\times 5\\\\=175\ cm^3[/tex]
2) Volume of prism would be
[tex]10\times 3\times 4\\\\=120\ cm^3[/tex]
3) volume of prism would be
[tex]7\times 7\times 3\\\\=147\ cm^3[/tex]
4) Volume of prism would be
[tex]5\times 3\times 7\\\\=105\ cm^3[/tex]
Hence, first prism has the greatest volume.
The volume of the prism with the Greatest volume is 250cm³
The volume of a prism is calculated by multiplying the prism's base area by its height. Mathematically expressed as
V = Base Area×Height
, it represents the space enclosed within the prism.
Since the prism is a cuboid, then
V = l × w × h
Where h is the height , l is the length and w is the width.
V = 5 × 5 × 10
V = 250 cm³
The volume of the prism is 250cm³
Stella initially put $5 into a piggy bank. Over the next few years she continued to put all of her coins in the piggy bank, such that each year the amount of money in the piggy bank doubled. Determine the equation that represents this situation and use it to decide which of the following graphs represents the amount of money, A(x), in Stella's piggy bank after x years.
Answer: Z.
Step-by-step explanation:
They want you to figure formula then find right graph, but do it fastest way. If it doubles each year, graph can't be straight line, eliminate Y.
A(0) has to be $5, eliminate W. A(1) has to be double A(0), eliminate X. Check: Z shows A(1) is 10, A(2) is 20.
Answer:
The equation is A(x) = 5(2)ˣ and the graph is Graph Z.
Step-by-step explanation:
Equations on compounding interest (which this essentially is) are of the form
A(x) = p(1+r)ˣ, where p is the amount of principal, r is the interest rate and x is the amount of time.
Since Stella begins with $5, the principal is 5.
Since the amount of money doubles each year, this means we add an extra 100%; this makes r equal to 1.
This gives us the equation
A(x) = 5(1+1)ˣ = 5(2)ˣ
This graph will not be linear, as there is not a constant rate of change (there are different amounts added every year).
She begins with $5. This means the y-intercept of the graph will be 5.
After 1 year, the amount of money doubles; this makes it 10. The only graph that is not linear and goes through (0, 5) and (1, 10) is graph Z.
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19. Graham's class raise $200 in a coin drop for a school fundraiser. The total for the entire school campus was 4.8 * 10^3 how many times greater was the total amount raised by the school compared to grahams class? Express your answer in scientific notation.
Answer:
2.4 * 10^1
Step-by-step explanation:
Divide the two numbers. 4.8 * 10^3 = 4800
4800/200 = 24
Put into scientific notation
24 = 2.4 * 10^1
4.8 * 10^3 is 24 (2.4*10^1) times greater than 200
The total amount raised by the school is 24 times greater than the amount raised by Graham's class.
Explanation:The amount raised by Graham's class is $200.
The total amount raised by the school is [tex]4.8 * 10^3.[/tex]
To find the number of times greater the total amount raised by the school is compared to Graham's class, we need to divide the total amount raised by the school by the amount raised by Graham's class.
So, we divide 4.8 * 10^3 by 200 to find the number of times greater the total amount raised by the school is compared to Graham's class.
Therefore,
[tex]= 4.8 * 10^3/ 200[/tex]
[tex]= 2.4 * 10^1.[/tex]
Therefore, the total amount raised by the school is 24 times greater than the amount raised by Graham's class.
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Use the graph below to write 5 conic section equations that create it. Use Desmos to check if your equations produce this picture. Hint: 3 circles, 1 ellipse and 1 parabola
1.The head(red circle)
2. The Left Eye (Blue Circle)
3. The Right Eye (Green Circle)
4. The Mouth (Purple Ellipse)
5. The Body (Black Parabola)
Answer:
See below for the graph.
Step-by-step explanation:
A circle or ellipse can be defined using the same sort of equation. Here, we have chosen to use the formulation ...
... ((x -a)/p)^2 +((y -b)/q)^2 -1 = 0
This will be the general form of the equation for an ellipse with center (a, b) and semi-axes p and q, in the x- and y-directions, respectively. When the axes are the same length, the ellipse is a circle.
By defining the function ...
... c(a, b, p, q, x, y) = ((x -a)/p)^2 +((y -b)/q)^2 -1
we can use the same function for all of the circles/ellipses in the figure. The parabola has vertex (0, -6) and a vertical scale factor of -1, so it can be formulated using the vertex form:
... y = k(x -a)^2 +b . . . . . for vertex (a, b) and vertical scale factor k.
_____
The equations
(x/6)² +(y/6) -1 = 0(x+2)² +(y-2)² -1 = 0(x-2)² +(y-2)² -1 = 0(x/3)² +(y+2)² -1 = 0y = -x² -6Parabola is a plane curve. The iconic character can be made with the following equation as given below,
[tex](x-0)^{2}+(y-0)^{2}=6^{2}[/tex][tex](x+2)^{2}+(y-2)^{2}=1^{2}[/tex][tex](x-2)^{2}+(y-2)^{2}=1^{2}[/tex][tex](\dfrac{x}{3})^{2}+(y+2)^{2}-1=0[/tex][tex]y=-(x-0)^{2}-6[/tex]
We need to draw 3 circles, an ellipse and a parabola, in order to get the desired digram.
For a circle, we only need to know the radius of the circle and the center of the circle,
1. The head(red circle)
The head of the circle is drawn from the origin of the coordinate, while the radius can be found by dividing the length between the points where the circle cuts the x-axis.
[tex]Radius =\dfrac{6-(-6)}{2} = 6[/tex]
Equation of the circle face,
[tex]\text{Equation of the circle face} => {(x-0)^2+(y-0)^2} = 6^2[/tex]
2. The Left Eye (Blue Circle)
3. The Right Eye (Green Circle)
Similarly for the eyes of the diagram,
The right eye = [tex](x-2)^{2}+(y-2)^{2}=1^{2}[/tex]
The left eye = [tex](x+2)^{2}+(y-2)^{2}=1^{2}[/tex]
4. The Mouth (Purple Ellipse)
The equation of the parabola can be written as,
(x/3)² +(y+2)² -1 = 0
5. The Body (Black Parabola)
The parabola can be made using the equation,
Equation of a parabola
y = a(x-h)² + k
where,
(h, k) are the coordinates of the vertex of the parabola in form (x, y);
a defines how narrower is the parabola, and the "-" or "+" that the parabola will open up or down.
Therefore, the equation for the body,
Equation of the parabola = [tex]y = -(x-0)^2 -6[/tex]
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Which graph represents the inequality:
-6 x 2
Attachment
QUESTION 32
4 is a solution of x < -5
True
False
QUESTION 33
Solve for x: x + 3 > 5
x > 2
x > 8
x > 1
x > 3
Answer:
31) Second number line
32) False
33) x>2
Step-by-step explanation:
31) Since -6<x has only < sign but no = sign, it will be an open dot on top of -6.
Since x≤2 has = sign, it will be a closed dot on top of 2.
So, second number line is the correct option.
32) x < -5 represents all the numbers to the left of -5 on a number line like -6,-7,-8,-9 etc.
Since 4 is on the right side of -5 on the number line, it won't be a solution of the inequality x < -5.
33) x+3 > 5
Subtracting 3 from both the sides of the inequality, we have
x + 3 -3 > 5 - 3
Cancelling out the +3 and -3 from the left side, we have
x > 2
1. The 2nd number line represents the inequality.
Explanation:
In words, the inequality reads "negative six is less than x, which is less than or equal to two". On the number line, the open circle at negative six means that -6 is not a solution to the inequality: -6 < x. The point at positive two means that positive two is a solution to the inequality: x ≤ 2. Therefore, all numbers greater than -6 and less than or equal to +2 are solutions to the inequality. This is shown on the second number line.
2. False
Explanation:
In words, the inequality reads "x is less than negative five". This means that all numbers less than -5 are solutions to the inequality. Positive four is not less than negative five, so it is not a solution to the inequality.
3. x > 2
Explanation:
To solve the inequality, we have to move all the terms that do not contain x to one side. This inequality is simple because it only requires one step: subtraction.
Solve for x: x + 3 > 5
1. Subtract 3 from both sides to get x by itself:
x + 3 - 3 > 5 - 3
2. Simplify
x > 2
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Find the constant of proportionality for the table and write in the form y = kx.
A) y = 1
15
x
B) y = 10x
C) y = 15x
D) y = 150x
Divide y by x:
150/10 = 15
135/9 = 15
30 /2 = 15
They all equal 15
This means the constant of proportionality would be y = 15x
The answer is C.
Answer:
Option C is correct
y = 15x
Step-by-step explanation:
Direct variation states that:
[tex]y \propto x[/tex] ......[1]
then, the equation is in the form of:
[tex]y=kx[/tex], where k is the constant of variation.
From the given table :
consider any points;
x = 9 and y = 135
Substitute these in [1] we have;
[tex]135 = 9k[/tex]
Divide both sides by 9 we have;
15 = k
or
k = 15
then, the equation we have; y = 15x
Therefore, the constant of proportionality for the table and write in the form y = kx is, y = 15x
Analyze the diagram below and complete the instructions that follow.
Find m < 0
A.
49
B.
59
C.
63
D.
78
Answer:
A. 49°
Step-by-step explanation:
∠O is the other base angle (along with ∠Q) of the isosceles triangle OPQ. Base angles of an isosceles triangle have the same measure.
((− 1/2 )y^4)^3·(–16y^2)
one half of y to the power of four to the power of three times sixteen y squared
Answer:
2y^14
Step-by-step explanation:
= (-1/2)^3 · (y^4)^3 · (-16) · y^2
= (-1/8)·(-16) · (y^(4·3) · y^2) . . . . . simplify some
= 2 · y^(12 +2) . . . . . simplify more
= 2y^14
#2. Find the missing side. Round to the nearest tenth.
5.3
Step-by-step explanation:The mnemoic SOH CAH TOA reminds you that ...
... Tan = Opposite/Adjacent
... tan(24°) = x/12
Then multiplying by 12 gives ...
... 12·tan(24°) = x = 5.34274 ≈ 5.3
The table below shows Britney's distance, in miles, from her destination after different time intervals in hours: Time (hours) (x) 2 4 1 3 6 5 7 Distance from destination (miles) (y) 1,000 880 1,060 940 760 820 690 What is the correlation coefficient for the data, and what does it represent? 0; it represents no correlation between x and y 0.999; it represents a linear positive correlation between x and y −0.999; it represents a linear negative correlation between x and y 0.999; it represents a linear negative correlation between x and y
Answer:
r = -0.9997
Step-by-step explanation:
A statistics calculator gives the value
r = -0.9997
You can see in the graph below that it represents an excellent negative correlation between x and y.
Every point appears to be exactly on the regression line .
It represents a linear positive correlation between x and y −0. 999.
Given
The table shows Britney's distance, in miles, from her destination after different time intervals in hours:
Time (hours) (x) 2 4 1 3 6 5 7
Distance from destination (miles) (y) 1,000 880 1,060 940 760 820 690
What is the correlation coefficient?A number between +1 and −1 is calculated so as to represent the linear interdependence of two variables or sets of data.
Then,
The correlation coefficient for the data, and what does it represent is;
It represents no correlation between x and y.
0.999; Represents a linear positive correlation between x and y.-0.999; represents a negative correlation between x and y.0.999; it represents a negative correlation between x and y.Hence, it represents a linear positive correlation between x and y −0. 999.
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The beginning checkbook balance of Gregory Co. was $3,045.58. Their bank statement indicated a balance of $4,262.92. The bookkeeper of Gregory Co. discovered a $220.05 deposit not reflected on the statement and checks numbered 478 and 492 in the amounts of $325.50 and $497.65 still outstanding. The bank credited Gregory’s account for $651.84 for a note that they had collected. The bank charged their account $37.60 for printed checks. Their reconciled balance was (Remember: To reconcile the bank balance with the checkbook balance means to compare the two, make the necessary adjustments (debits and credits) and ensure that the two amounts are equal.)
$3,569.82. $3,659.28. $3,659.82. $6,359.82.
Answer:
$3,659.82
Step-by-step explanation:
Adding to the checkbook those debits and credits not already there brings its balance to ...
... $3045.58 +651.84 -37.60 = $3659.82
Adjusting the bank's balance by the deposits and checks not already there brings its balance to ...
... $4262.92 +220.05 -325.50 -497.65 = $3659.82
Thus, the reconciled accounts will agree on the balance $3659.82.
The reconciled balance for Gregory Co. was $3,659.82 after accounting for all transactions including deposits, outstanding checks, credited note, and bank charges.
The question involves reconciling the checkbook balance with the bank statement balance for Gregory Co. To reconcile the bank balance with the checkbook balance, we need to account for any transactions that have not been reflected in one or the other. We start with the bank statement balance and adjust it for outstanding checks and deposits not reflected on the statement.
Starting balance: $3,045.58Add outstanding deposit: $220.05Subtract outstanding checks: $325.50 + $497.65Add credited note: $651.84Subtract bank charges: $37.60Reconciled balance calculation: $3,045.58 + $220.05 - $325.50 - $497.65 + $651.84 - $37.60 = $3,659.82Simplify 4 square root of 2 end root plus 7 square root of 2 end root minus 3 square root of 2
2 square root of 8
8 square root of 2
8 square root of 6
6 square root of 8
Answer:
8√2
Step-by-step explanation:
4√2 + 7√2 - 3√2 = (√2)(4 + 7 - 3) = 8√2
Recognize that √2 is a common factor and simply add its coefficients.
[tex]4\sqrt2+7\sqrt2-3\sqrt2=(4+7-3)\sqrt2=\boxed{8\sqrt2}\\\\Answer:\ \boxed{\text{8\ square root of 2}}[/tex]
Whic number is divisible by 3?
A. 35
B. 133
C. 103
D. 153
Answer:
D
Step-by-step explanation: 153 divided by 3 = 51
Answer:
D. 153
Step-by-step explanation:
Which number is divisible by 3?
A number is divisible by 3 if you add all the digits and it is divisible by e.
A. 35
3+5 = 8
8/3 has a remainder so it is not divisible by 3
B. 133
1+3+3 = 7
7/3 has a remainder so it is not divisible by 3
C. 103
1+0+3 =4
4/3 has a remainder so it is not divisible by 3
D. 153
1+5+3 =9
9/3 =3 153 is divisible by 3
Nicole will spend more than $30 on gifts. So far, she has spent $17 . What are the possible additional amounts she will spend? Use c for the additional amount (in dollars) Nicole will spend. Write your answer as an inequality solved for c
Nicole has already spent 17 dollars, and will spend c more dollars, for a total of [tex] 17+c [/tex] dollars.
We want this total to be more than 30, so we have
[tex] 17+c>30 [/tex]
Solving this inequality for c yields
[tex] c > 13 [/tex]
The question asks about the additional amount Nicole will need to spend to exceed a total of $30. Given she has already spent $17, the inequality c > 13 represents the additional amount, in dollars, Nicole must spend to meet this requirement. Therefore, Nicole must spend more than $13.
Explanation:The question is about calculating the possible additional spending of Nicole in order to ensure her total spent will exceed $30. Nicole has already spent $17. As per the condition, set up the inequality which indicates that Nicole will spend more than $30. It's mentioned that we can use c for the additional amount Nicole will spend. Therefore:
17 + c > 30
This inequality can be solved for c by subtracting 17 from both sides:
c > 30 - 17
So,
c > 13
This means Nicole will have to spend more than $13 additionally to ensure her total spending is more than $30.
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classify each triangle by its angles and its sides
Answer:
Acute
Step-by-step explanation:
The last angle is 71 which is less than 90
Answer:
acute triangle
Step-by-step explanation:
The sum of the two angles given is more than 90°, so the remaining angle is less than 90°. All angles are acute angles, so the triangle is an acute triangle.
Why is -0.45, 5/12, 0, 247 rational or an irrational number.
All are rational.
Step-by-step explanation:Any number you can write exactly and completely, or any repeating decimal is a rational number. Any number that can only be written exactly using a symbol, such as π or √2, is an irrational number. Something like √6.25 is rational, because it can be written exactly as 2.5, without the symbol.
The idea of "rational" means the number can be expressed as the ratio of two integers. Any integer can be expressed as the ratio of itself and 1.
All of your numbers can be expressed as the ratio of integers:
... -0.45 = -45/100 . . . . any terminating decimal can be expressed as a ratio of integers by making use of the place value multipliers
... 5/12 . . . . is the ratio of integers
... 0 = 0/1
... 247 = 247/1
Which of the following ordered pairs is a solution to y = 2^x?
(3, 8)
(3, 9)
(3,27)
Answer:
(3, 8)
Step-by-step explanation:
For x = 3,
. . . y = 2^x
. . . y = 2^3 = 2·2·2 = 8
This is represented by the ordered pair (x, y) = (3, 8).
Answer:
(3,8)
Step-by-step explanation:
Since the answer choices are given we can plug the "x" value and see if it returns the y-value given in the ordered pair (x,y) and so:
[tex]y=2^x[/tex]
Let's use the ordered pair (3,8) meaning that when x=3 y =8 and so:
[tex]y=2^3=2\times2\times2=8[/tex]
[tex]y=8[/tex]
This is correct and so this is a solution, since the solution is unique when x=3 y is always going to return an 8.
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1. Work out the expression -2.5(1 - 2n) - 1.5n using both the Distributive Property and Combining Like Terms
2. Can we subtract -2.5 - 3.5n?
3. Can we add -2.5 + 3.5n?
4. Can we subtract -2.5 - 6.5n?
The graph shown represents an inequality. The solid line that forms the boundary tells you that ______.
The graph is correct.
The inequality is correct.
The inequality has no equal sign in it.
The inequality has an equal sign in it.
Answer:
D. The inequality has an equal sign it
Step-by-step explanation:
We use solid lines whenever the inequality contains [tex]\leq[/tex] or [tex]\geq[/tex]. That means it contains an equal sign which means the boundary line is inclusive.
On the other hand when the inequality does not have an equal sign in it we use a dashed line to indicate that all values on the boundary line are not inclusive.
That is we use a dashed or broken line for the boundary line of an inequality whenever it contains [tex]\:<\: or \:>\:[/tex].
The correct answer is D
1.) (7.RP.3) Tracy started a savings account that is set up so that the simple interest earned on the investment is moved into a separate account at the end of each year. Tracy invests $5,000 at 4.5%, what is the total simple interest accumulated in the checking account after 2 years? Show your work. *
$4.50
$45
$450
$4,500
$45,000
2. (7.RP.3) Sylvia bought a 6-month $1900 certificate of deposit. At the end of 6 months, she received a $209 simple interest. What rate of interest did the certificate pay? *
$450
Step-by-step explanation:Each year, the amount of interest earned is ...
... 4.5% × $5000 = $225
After 2 years, a total of ...
... $225 × 2 = $450
has been transferred.
_____
Comment on percentages
Of course, you know that 4.5% = 4.5/100 = 45/1000 = 0.045.
You can think of the % symbol as a fancy (shorthand) way to write /100. (Likewise, the ‰ symbol means /1000.)
At a farm, there are two huge pits for storing hay. 90 tons of hay is stored in the first pit, 75 tons in the second pit. Then, three times as much hay was removed from the first pit as was removed from the second pit. After that, there was half as much hay in the first pit as there was now in the second pit. How many tons of hay was taken from the first pit?
Answer:
63 tons
Step-by-step explanation:
The problem statement asks for the tons of hay removed from the first pit. It is convenient to let a variable (x) represent that amount. This is said to be 3 times the amount removed from the second pit, so that amount must be x/3.
The amount remaining in the first pit is 90-x.
The amount remaining in the second pit is 75 -x/3.
Since the first pit remaining amount is half the second pit remaining amount, we can write the equation ...
... 90 -x = (1/2)(75 -x/3)
... 180 -2x = 75 -x/3 . . . . multiply by 2
... 105 - 2x = -x/3 . . . . . . subtract 75
... 315 -6x = -x . . . . . . . . multiply by 3
... 315 = 5x . . . . . . . . . . . add 6x
... 63 = x . . . . . . . . . . . . . divide by 5
63 tons of hay were taken from the first pit.
_____
Check
After removing 63 tons from the first pit, there are 27 tons remaining. After removing 63/3 = 21 tons from the second pit, there are 54 tons remaining. 27 is half of 54, so the answer checks OK.
What is the measure of ∠BCD? Enter your answer in the box. ° quadrilateral A B C D with side A B parallel to side D C and side A D paralell to side B C. angle B is 103 degrees.
Answer:
77°
Step-by-step explanation:
Angles B and C are adjacent angles of a parallelogram, so are supplementary.
... ∠C = 180° -∠B = 180° -103° = 77°
The measure of ∠BCD in a parallelogram with ∠B given as 103° is also 103° because opposite angles in a parallelogram are equal.
Explanation:The measure of ∠BCD in a parallelogram can be found by using the property that opposite angles in a parallelogram are equal.
To find the measure of angle BCD, we can use the fact that angles in a quadrilateral sum up to 360 degrees.
We know that angle B is 103 degrees.
Since quadrilateral ABCD has sides AB and DC parallel, as well as sides AD and BC parallel, it is a parallelogram.
Given that ∠B is 103°, the measure of ∠BCD is also 103° because it is the angle opposite ∠B.
Last August we had 729 7th grade students. This august we started with 1084 7th grade students. what was the percent increase in 7th grade enrollment from august 2017 to august 2018?
Answer:
The percent increase was 48.7.
Step-by-step explanation:
The absolute increase in enrollment is 1084 - 729 = 355. This corresponds to a relative increase of 355/729=0.487 (relative to Aug 2017). The proportion 0.487, expressed in percent: 48.7%
Depending on your current method to exercise, you could solve this using the proportionality method: 355/729 = x/100, then cross-multiply and solve for x. Same thing.
The price of a gallon of gasoline has increase, on average from $2.50 in 2006 to $4.00 in 2008. What is the percentage of increase?
Answer:
60% increase
Step-by-step explanation:
Percentage increase = (new - old)/ old * 100
We know the new = 4.00
old = 2.50
Lets substitute the values in
Percentage increase = (4-2.5)/2.5 *100
= 1.5/2.5 * 100
=.6*100
=60%
Amelia had 26 sea shells. Then, she collected 11 more sea shells. After that, she gave S sea shells to her little sister. Which of the following shows how many sea shells she has currently? A. 26 + S + 11 B. 26 - 11 - S C. 26 + 11 - S D. 26 + S - 11
Answer:
C. 26 + 11 - S
Step-by-step explanation:
She had 26 shells
She collected 11 more shells ( that is addition)
26 + 11
Then she gave S shells away ( that is subtraction)
26+11-S
She has 26+11-S
Answer:
C. 26 + 11 - S
Step-by-step explanation:
Ana took Ali out for lunch. Their lunches cost $13.28 and $14.25, including tax and tip. Ana paid with two $20 bills. How much change did Ana receive?
Answer:
$12.47
Step-by-step explanation:
The total charge was ...
... $13.28 +14.25 = $27.53
The change from 2 $20 bills is ...
... 2 × $20 - 27.53 = $40.00 -27.53 = $12.47
The total cost of lunch is $27.53. Ana paid with two $20 bills, which equals $40.00. After Ana gave the two $20 bills, she received $12.47 in change.
Explanation:The subject area of this question is mathematics, specifically arithmetic involving decimal numbers. To solve this, we first add together the costs of the two lunches, which are $14.25 and $13.28, that result in $27.53. Ana initially pays with two $20 bills, which sums up to $40.00. Now, we subtract the total cost of the lunches from the amount Ana paid with. So, $40.00 - $27.53 gives us $12.47. This tells us that Ana received $12.47 in change back after paying for lunch.
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Solve each system by substitution. Tell whether the system has one solution, infinitely many solutions, or no solution.
3x+6y=18
3y=-3/2x+9
What would be the answers for the three boxes please help
Look at the prime factorization. If all the factors have powers that are multiples of 6, then the number is a square and a cube. If they are multiples of 3, then a cube; if multiples of 2, then a square.
1000 = 2³·5³ . . . . a perfect cube
4 = 2² . . . . a perfect square
120 = 2³·3·5 . . . . none of the above (not a square or a cube)
36 = 2²·3² . . . . a perfect square
100 = 2²·5² . . . . a perfect square
49 = 7² . . . . a perfect square
125 = 5³ . . . . a perfect cube
25 = 5² . . . . a perfect square
please help with this and show work
9. AM ≅ AT
10. x=3, y=5
AH being the perpendicular bisector of MT means MH ≅ TH. Then ΔAHM ≅ ΔAHT by SAS, and by CPCTC.
... SAS — side-angle-side: if two adjacent sides and the included angle of a triangle are congruent to their corresponding sides and angles in another triangle, the two triangles are congruent.
... CPCTC — Corresponding Parts of Congruent Triangles are Congruent
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Using the result of problem 9 as a guide, you can say that ...
... 2x = x+3 ⇒ . . . . (subtract x from both sides)
... y +4 = 2y -1 ⇒ . . . . (add 1-y to both sides)
Using a logarithm, solve the following equation 500=(2)(10^5x) enter the value for x rounded to the nearest hundredth
Answer:
0.48
Step-by-step explanation:
The problem at hand
[tex]500 = (2)(10^{5x})[/tex]
First divide out 2 on both side of the = sign
[tex]500 = (2)(10^{5x})[/tex]
[tex]\frac{500}{2} = \frac{(2)(10^{5x})}{2}[/tex]
[tex]250 = 10^{5x}[/tex]
Now take the base 10 log on each side of the = sign
[tex]\log_{10} (250) = \log_{10} (10^{5x})[/tex]
Now move the exponent to the left like so
[tex]\log_{10} (250) = 5x \log_{10} (10)[/tex]
Rule you need to know. [tex]\log_a (a) = 1[/tex]
[tex]\log_{10} (250) = 5x (\log_{10} (10))[/tex]
[tex]\log_{10} (250) = 5x(1)[/tex]
[tex]\log_{10} (250) = 5x[/tex]
Now divide 5 from both sides of the equation
[tex]\frac{\log_{10} (250)}{5} = \frac{5x}{5}[/tex]
[tex]\frac{\log_{10} (250)}{5} = x[/tex]
[tex]x = \frac{\log_{10} (250)}{5}[/tex]
[tex]x = 0.4795880017[/tex]
Round to nearest hundredths
[tex]x = 0.48[/tex]
Side Note:
You could approach this problem in a different manner.
For instance, we could have done the following
[tex]x = \frac{\log_{10} (250)}{5(\log_{10} (10))}[/tex]
Also, you did not have to use log with a base 10. You could have used the natural log, which is [tex]\ln_e (x)[/tex]
[tex]x = \frac{\ln_{e} (250)}{5(\ln_{e} (10))}[/tex]
Solving the equation gives 0.48 when rounded to the nearest hundredth.
To solve the equation [tex]500 = (2)(105x)[/tex] , we will first isolate the exponential term. The steps are as follows:
Divide both sides of the equation by 2 to get 250 = 105x.
Take the common logarithm (log) of both sides of the equation to get [tex]log(250) = log(105x).[/tex]
Using logarithmic properties, we have log(250) = 5x log(10)
Now we simplify further since log(10) is 1, so log(250) = 5x.
Divide both sides by 5 to solve for x, which gives [tex]x = log(250) / 5.[/tex]
Using a calculator with a LOG button, we find log(250) approximately equals 2.39794 and, therefore, x is approximately 0.47959 when rounded to five decimal places.
However, we are asked to round x to the nearest hundredth, so the final answer is x = 0.48.