The value of negative one fifth times the quantity 4 minus 14 times the quantity one fourth squared end quantity is one eighth. Option B is correct.
We are given the following expression:
Negative one fifth times the quantity 4 minus 14 times the quantity one fourth squared end quantity.
Rewrite the given expression properly as:
-1/5 * (4 - 14) * (1/4)^2
Evaluate the difference, we will get;
-1/5 * (-10) * (1/4)^2
Evaluate the exponent, we will get;
-1/5 * (-10) * 1/16
This gives us;
2 * 1/16
Further, evaluation give us;
1/8
So, the value of the given expression is 1/8 or one eighth.
Option B is correct.
Thus, the value of negative one fifth times the quantity 4 minus 14 times the quantity one fourth squared end quantity is one eighth. Option B is correct.
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I need help please!!!
Q2.
I am thinking of two numbers.
The first number is x
The second number is 7.5 more than x.
Write down an expression, in terms of x for the second number.
For the two numbers,
the product is double the sum.
Work out the numbers I could be thinking of.
Give both possible pairs of answers.
Answer:
second number = (x + 7.5)
Since the product of the two numbers is double of their sum,
x(x + 7.5) = 2(x + x + 7.5)
x² + 7.5x = 2(2x + 7.5)
x² + 7.5x = 4x + 15
x² + 7.5x - 4x - 15 = 0
x² + 3.5x - 15 = 0
∴ x = -6 or 2.5
∴ second number
= -6 + 7.5 or 2.5 + 7.5
= 1.5 or 10
∴ The two numbers that I am thinking of are either -6 and 1.5 or 2.5 and 10.
Riley found a receipt for a pair of jeans for $142.95, tax included. If the sales tax rate was 6%, what was the list price of the jeans? Round your answer to the nearest cent.
Answer:
$134.86
Step-by-step explanation:
Let the original price before tax be x.
A whole amount is 100% of the amount, so x is 100% of the original price without tax.
The tax rate is 6%, so the tax on x is 6% of x. Add 6% of x to 100% of x, and you have 106% of x. The item plus tax cost 106% of x.
106% of x = $142.95
106/100 × x = 142.95
1.06x = 142.95
x = 142.95/1.06
x = $134.86
Answer: $134.86
how many distinct 5-letter strings can be created using the letters a, b, c, d, e if repetition is allowed, but the letters a appears at most twice?
2944 distinct 5-letter strings can be created using the letters a, b, c, d, and e if repetition is allowed but the letter a appears at most twice
Given that
form 5-letter distinct strings can be created using the letters a,b,c,d, and e, and repetitions are allowed but the letter a appears at most twice
let's consider that letter a is not there in the string
each letter is repetitive then it is [tex]4^{5}[/tex]
now letter a is considered once
5c1 ×[tex]4^{4}[/tex]
now letter a is repetitive twice
5c2 × [tex]4^{3}[/tex]
[tex]4^{5}[/tex] + 5c1 × [tex]4^{4}[/tex] + 5c2 × [tex]4^{3}[/tex]
1024+ 1280 + 640 = 2944
2944 distinct 5-letter strings can be created using the letters a, b, c, d, and e if repetition is allowed but the letter a appears at most twice
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Expression that equal to p/6+(q+8)
Answer: (p/6 + q) + 8
Step-by-step explanation:
find the perimeter and area
Answer:
perimeter = 22 km and area = 18 km^2
Step-by-step explanation:
First I found and labeled the missing lengths. For the one at the top of the shape, I added 1 + 2 + 3 to get the length, since those are what make up the length.
Afterwards I just added up all the side lengths to get the perimeter. 2+6+2+3+2+3+1=22, so the perimeter is 22 km.
To find the area, I split the shape into two, labeled 1 and 2. (Check the image attached) To find the area you multiply length by width, so i did that for shapes 1 and 2. For shape 1, I did 2 x 6 and got 12, and for shape 2 I did 3 x 2 to get 6. To get the total area of the entire shape, add these two areas. 12 + 6 = 18, so the total area is 18 km^2. (km squared)
let me know if anything is confusing :-))
What is 125 in simplest form?
Answer:
125 in simplest form is 1/8.
Step-by-step explanation:
Jon needs to buy a backpack and several folders for school. If she shops at smart supply, the backpack will cost $45 and folders cost $0.45 each. If she shops at supply Guys, the backpack will cost $50.40 and folders cost 0.15 each. Write and solve an inequality to find the number of folders Jan would need to buy for the Supply Guys to be the cheaper option
Considering the definition of an inequality, the number of folders Jan would need to buy for the Supply Guys to be the cheaper option is more than 18.
Definition of inequalityAn inequality is the existing inequality between two algebraic expressions, connected through the signs:
greater than >.less than <.less than or equal to ≤.greater than or equal to ≥.An inequality contains one or more unknown values in addition to certain known data.
Solving an inequality consists of finding all the values of the unknown for which the inequality is true.
Inequality in this caseIn this case, you know that:
If she shops at smart supply, the backpack will cost $45 and folders cost $0.45 each. If she shops at supply Guys, the backpack will cost $50.40 and folders cost 0.15 each.The Supply Guys is the cheaper option.Being "x" the number of folders, the inequality that expresses the previous relationship is
45 + 0.45x > 50.40 + 0.15x
Solving:
0.45x - 0.15x > 50.40 -45
0.30x> 5.4
x> 5.4÷ 0.3
x> 18
Finally, the number of folders Jan would need to buy is more than 18.
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In this problem we determine the first time after 10 o'clock at which the minute hand and the hour hand of a clock point in the exact same direction ( meaning when they are " on top of" each other). See if you can find the time on your own before reading the following steps. ( Assume that both hands move continously. For example, from 10 o'clock to 11 o'clock, the hour hand smoothly and gradually moves from pointing at the 10 to pointing at the 11.)
a) Let m be the number of mintues after 10 o'clock at which the minuet hand and hour hand are pointing in the same direction. In terms of m, trhough what fraction of hte entire face of the clock has the minute hand traveled during the m minutes after 10 o'clock?
b) In terms of m, what fraction of hte distance from 10 to 11 has the hour hand traveled during the m minutes after 10 o'clock?
c) Trough what farction of the entire clock's face doe sthe hour hand travel during the m minutes after 10 o'clock?
d) At what exact time do the minute hand and hour hand point in the same direction?
( GIVE BRAINLIST IF CORRECT AND ANSWER!! )
Answer:
a) 1:25 b) 2:06 c) 5:00 d) 4:10
Step-by-step explanation:
HELP ASAP GIVING BRAINLIEST
Answer: C
Step-by-step explanation:
Which method and additional information would prove δonp and δmnl similar by the aa similarity postulate? segments om and lp intersect at point n; triangles are formed by points lnm and onp; line k intersects with both triangles at point n. use a rigid transformation to prove that ∠opn ≅ ∠mln. use rigid and nonrigid transformations to prove segment pn over segment mn = segment ln over segment on. use a rigid transformation to prove that ∠npo ≅ ∠lnm. use rigid and nonrigid transformations to prove segment ln over segment on = segment pn over segment mn.
The correct option for the method and additional information that would prove triangle ONP and triangle MNL similar by AA similarity postulate is
option B.
B. Use rigid transformation to prove that angle NPO is congruent to angle NLM.
Angle Angle AA similarity postulate states that two triangles are similar if : two angles in one of the triangles are congruent (equal) to two angles in the other triangle.
The reason for arriving at the above selection is as follows:
The known parameter in triangle ΔONP and ΔMNL are;Lines MO and LP intersect at vertex point N.The angles on opposite side of the point N (either side of the X shape formed by the two lines) which are ∠ONP and ∠LNM are vertically opposite angles or opposite angles.According to vertically opposite angles theorem ∠ONP and ∠LNM, which are vertically opposite angles are congruent, and we can write.
∠ONP ≅ ∠LNM
The required parameters are:
To find the additional information that would prove ΔONP and ΔMNL by
AA (Angle-Angle) similarity postulate.
Given from the drawing,
One (vertex) angle in one triangle is congruent to one (vertex) angle in the other triangle, that is ∠ONP ≅ ∠LNM, it is required to prove that one other angle in triangle ΔONP is congruent to a corresponding angle in triangle ΔMNL.
Prove that:
either ∠NPO or ∠NOP in ΔONP are congruent to ∠NLM or ∠NML respectively in ΔMNL by performing rigid transformations (transformations that does not change shape) on either ΔONP or ΔMNL including:
Rotating triangle ΔONP by 180° with origin at point N, to form the image ΔO'N'P'.
Translating the vertex point P' in the image ΔO'N'P', to the location of the point L in ΔMNL, and verify that the segments LN and LM in ΔMNL coincide with the segments P'N' and P'O' respectively of triangle ΔO'N'P'.
Therefore, the correct option is option B. Use rigid transformation to prove that angle NPO is congruent to angle NLM.
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Answer:
b
Step-by-step explanation:
1.209, 1.9, 3.76, 1.29 order these numbers from least to greatest
Answer:
1.209 < 1.29 < 1.9 < 3.76
Step-by-step explanation:
1. Find the y-intercept of the line paing through the point A (3, -2) and B (-1, 3). (5 pt)
0.96 in fracton form
Answer:
As a fraction in simplest form it SHOULD be 24 over 25.
Step-by-step explanation:
"0.96 as a fraction (simplified form)" MagnetsAndMotors (Dr. B's Other Channel)
Answer:
24/25
Step-by-step explanation:
0.96
By counting the numbers after the decimal point which is two.
so we will write: 96/100, since hundred has to two zero.
Then we will divide 96/100 to it simplest form which is 24/25
643251 to the nearest then thousands
Answer:
64000
Step-by-step explanation:
When you are rounder you must look at the last number to determine if you are rounding up or down.
HELP ME PLEASE, I NEED TO FINISH THIS MATH PROBLEM!
Anna is working two summer jobs, making $9 per hour washing cars and $12 per hour landscaping. Last week Anna worked a total of 7 hours and earned a total of $78. Determine the number of hours Anna worked washing cars last week and the number of hours she worked landscaping last week.
ANSWER: ANNA WORKED _____ HOURS WASHING CARS AND ______ HOURS LANDSCAPING.
Answer: anna worked 4.33repeating hours washing cars and 3.25 hours landscaping
Step-by-step explanation:
i personally used a guess and check method.
i multiplied 9(hourly wage for washing cars) and 4.33repeating(number of hours) = 39
i multiplied 12(hourly wage landscaping) and 3.25(number of hours) = 39
39 + 39 = $78
A square and rectangle are shown below. The width of the rectangle is the same as
the length
of a side of the square, both represented by .x. The length of the rectangle is one
foot more
than twice its width. The perimeter of the rectangle is 26 feet more
than that of the square.
(a) Write an expression for the length of the rectangle in
terms of.x. Label on the drawing.
x
Answer:
Step-by-step explanation:
x=26
help please and thankyou
The value of x will be 24.
What is mean by Triangle?
A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
For a given right triangle, the expression is,
⇒ sin (3x - 7) = cos (x + 1)
Now,
Solve for x as;
The expression is,
⇒ sin (3x - 7) = cos (x + 1)
Since, sin x= cos (90 - x)
So, We get;
⇒ sin (3x - 7) = cos (x + 1)
⇒ cos (90 - (3x - 7)) = cos (x + 1)
⇒ 90 - (3x - 7) = (x + 1)
⇒ 90 - 3x + 7 = x + 1
⇒ 97 - 3x = x + 1
⇒ 97 - 1 = x + 3x
⇒ 96 = 4x
⇒ 4x = 96
⇒ x = 96/4
⇒ x = 24
Thus, The value of x will be 24.
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If a-b=-5 and ab=0 then find a³-b³
What’s the answer?
If a - b = -5 and ab = 0 then the value of the expression a³-b³ is -125.
In the question ,
it is given that ,
the value of a - b = -5 and ab = 0
we need to find the value of the expression (a³-b³) ,
we know the identity that a³-b³ = (a - b)(a² + b² + ab)
we first need the value of a² + b² .
given that a - b = -5
squaring both the sides , we get
(a - b)² = 25
a² + b² - 2ab = 25
given ab = 0, so a² + b² = 25
Substituting a² + b² = 25 in the identity a³-b³ = (a - b)(a² + b² + ab) ,
we get ,
a³-b³ = (-5)(25 + 0)
a³-b³ = -5 × 25
a³-b³ = -125
the answer is -125 .
Therefore , If a - b = -5 and ab=0 then the value of the expression a³-b³ is -125.
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How many minutes are in 1 hour and 3/4? How do you solve it as well?
Answer:
Step-by-step explanation:
105 min
60 min in a hour and then 3/4 of a hour is 45 min.
Total: 105 minutes
A bookstore had 150 copies of a magazine. Yesterday the bookstore sold 2/5 of these copies. How many copies were sold yesterday
Answer:
Hi
Step-by-step explanation:
so the question is asking what is 2/5 of 150
if 150 is able to evenly be split up into 5 even parts we can the add two of those parts to get our answer.
does 150 split up into 5 even parts??
hmmm you probably are thinking, 15 does divide by 5 evenly into 3 parts, so we now know that 150 also splits up into 5 even parts of 30 :)
2 time 30 = 60
so there is how to figure out the answer and , the answer 60 :)
3.6 x 10^7 + 2.1 x 10.7=
a) 14
b) 5.7
c) 3.6
d) none of these
The value of the exponent 3.6 x 10^7 + 2.1 x 10.^7 is D. None of the above.
What is an exponent?The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.
In this case, the value of 3.6 x 10^7 + 2.1 x 10^7 will be:
= 3.6 x 10^7 + 2.1 x 10.^7
= 5.7 × 10^7
Therefore, the correct option is D.
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find the annual salary of a person who is paid $835.50 per week
Answer:
43446
Step-by-step explanation:
52 weeks in an year
835.5 × 52 = 43446
Given the points A(-5,-5) and B(7, 1), find the coordinates of the point P on directed line segment AB that partitions AB in the ratio of 1:5, but not necessary In that order, give two possible coordinates of point P. Graph segment AB and P in the coordinate plane.
The two coordinates on the segment AB due to internal division are (5,0) and (-3,-4).
What is internal division?
When a point P divides the line joining the two points and the potint P lies in between the two coordinates then the division is internal division. If the point lies outside of the given coordinates then the division is known as external division.
The division is internally because point P lies on the line as given in the question.
The formula for the internal division is as follows:
[tex]X=\frac{mx_1+nx_2}{m+n}\\Y=\frac{my_1+ny_2}{m+n}[/tex]
Since points are A(-5,-5) and B(7,1) hence, [tex]x_1=-5,x_2=7,y_1=-5,y_2=1[/tex] and ratio is 1:5 then [tex]m=1,n=5[/tex].
Substute all value to obtain the coordinates.
[tex]X_1=\frac{1(-5)+5(7)}{1+5}\\X_1=5\\Y_1=\frac{1(-5)+5(1)}{1+5}\\Y_1=0[/tex]
Hence, the first cordinate is (5,0).
As given in the question that the ratio in not necessarily in the order of 1:5 so, consider the ratio is 5:1.
Now, m=5 and n=1.
Again substitute all values in to find the new coordinate.
[tex]X_2=\frac{5(-5)+1(7)}{5+1}\\X_2=-3\\Y_2=\frac{5(-5)+1(1)}{5+1}\\Y_2=-4[/tex]
Hence, another coordinate is (-3,-4).
Hence, the two coordinates on the segment AB due to internal division are (5,0) and (-3,-4).
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mario tiene una cinta de 6 m y su amiga beatriz tiene una cinta de 8 m ¿cuantas veces es la longitud de la cinta de mario comparada con la longitud de la cinta de beatriz?
La cinta de Mario tiene una longitud que es 0.75 veces la longitud de la cinta de Beatriz.
¿Como se comparan las longitudes?
Sabemos que la longitud de la cinta de Mario tiene una longitud de 6 metros, mientras que su amiga Beatriz tiene una cinta de longitud de 8 metros.
Para saber cuantas veces es la longitud de la cinta de mario comparada con la longitud de la cinta de beatriz, tenemos que tomar el cociente entre ambas longitudes, obtendremos:
6m/8m = 0.75
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Find the equation of the line passing through the given point and parallel to the given line.
( 1, 9 ), y = 4x + 2
( 5 , 2 ), y = -2x + 7
The line equation passing through the given points and parallel to the given lines are:
Line 1: y=-4x+13...(i)
Line 2: y=2x-12...(ii)
Line 1
The first line is passing through point (1,9) and parallel to the y=4x+2 line.
Since line 1 would be parallel to line y=4x+2, hence both lines would have the same value of slope (m).
Using the standard formula of line equation, we could identify that line y=4x+2 has:
ay = bx + c, m= -b/a
y=4x+2, m=-4
We could use the line equation formula, where:
y-y1 = m (x-x1)
we use the given point (1,9) and the slope value (m=-4) to get the line equation passing through the point:
y-9 = -4(x-1)
y-9=-4x+4
y=-4x+13...(i)
Line 2
The first line is passing through point (5,2) and parallel to the y=-2x+7 line.
Since line 2 would be parallel to line y=-2x+7, hence both lines would have the same value of slope (m).
Using the standard formula of line equation, we could identify that line y=-2x+7 has:
ay = bx + c, m= -b/a
y=-2x+7, m=-2
We could use the line equation formula, where:
y-y2 = m (x-x2)
we use the given point (5,2) and the slope value (m=2) to get the line equation passing through the point:
y-2 = 2(x-5)
y-2 = 2x-10
y=2x-12...(ii)
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What is the sum of (3x + 4) + (9x – 10)?
Answer:
[tex]12x -6[/tex]
Step-by-step explanation:
Take a look at the attachment...
Hope this helps! :)
The graph below shows distance over time.
A student is walking to class. The student increases their speed for 20 seconds for 3 meters. The student then walks a constant speed for 5 seconds and then increases their speed the last 3 meters to class.
Which of these situations could be represented by this graph?
A situation which could be represented by this graph is: A student walks 1.5 km to a friend’s house in 20 minutes. The two students then walk another 1.5 km to school in 40 minutes.
What is a graph?In Mathematics, a graph can be defined as a type of chart that is typically used to graphically represent data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate respectively such as time (min) and distance (km).
In this scenario, the time (in minutes) was plotted on the x-axis of the graph while the distance covered (in kilometers) was plotted on the y-axis of the graph.
By critically observing the graph (see attachment), we can reasonably and logically deduce that the first student walked a distance of 1.5 kilometer to his or her friend’s house in 20 minutes, then, they both walked at a constant speed for 5 seconds before increasing their speed, covering another distance of 1.5 kilometer to their school within 40 minutes (60 - 20 minutes).
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Complete Question:
The graph below shows distance over time. Which of these situations could be represented by this graph?
answer choices
A student walks 1.5 km to a friend’s house in 40 minutes. The two students then walk another 1.5 km to school in 20 minutes.
A student walks 1.5 km to a friend’s house in 20 minutes. The two students then walk another 1.5 km to school in 40 minutes.
A student walks 1.5 km to a friend’s house in 30 minutes. The two students then walk another 1.5 km to school in 30 minutes.
A student walks 1.5 km to a friend’s house in 20 minutes. The two students then walk another 1.5 km to school in 60 minutes.
The tens digit of a two-digit number is twice the ones digit. Its reversed number is 36 less than the original number.
From the calculation, the original number is obtained as 84.
What is the original number?We know that we are told in the question that in the question, we are required to obtain the number and that is what we are going to do below.
Let the tens digit be T and let the units digit be U
We can then write
10U+T = 10T+U-36
Since the reversed number is 36 less than the original number.
Then;
9U = 9T -36
Dividing both sides of the equation by 9
U = T -4
U=2U-4
U=4
T = 8
It then follows that the original number is 84.
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A bank employee notices an abandoned checking account. The bank charges a monthly fee for the account modeled by the function
A(m)=184-8m, where M is in months and A(m) is in dollars.
What is the domain of the function within the context? Use inequality Notation.
The domain of the function A(m) = 184 - 8m representing the bank charges on monthly fees is m ≤ 23
How to find the domain of the functionThe equation is linear equation in the slope intercept form as
y = mx + c
where
m = slope = -8
c = intercept = 184
x = input variables = m
y = output variables = A(m)
The domain refers to all possible values of m, generally the equation has no restriction for m however for the problem being discussed y should not be negative. hence we solve for m when y = 0
0 = 184 - 8m
8m = 184
m = 23
The maximum value of m is 23 hence the domain is m ≤ 23
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