A number is represented by = n.
We need to write an expression for "an expression for the quantity of four less than the square of this number divided by the quantity five more than four times the number ".
Let us break the statement into smaller parts.
"The quantity of four less than the square of this number(n)".
Square of n is = n^2.
4 less than n^2 = n^2 -4.
"This number(n) divided by the quantity five more than four times the number"
4 times the number n = 4×n = 4n.
Five more than four times the number = 4n +5.
Therefore, we can repharse given statement by an easy way as:
" 4 less than n^2 is divided by (4n+5)."
or (n^2 - 4) ÷ (4n+5).
In fraction form : [tex]\frac{n^2 - 4}{4n+5}[/tex]
Therefore, final expression would be [tex]\frac{n^2 - 4}{4n+5}[/tex].
The expression for the quantity of four less than the square of a number divided by the quantity five more than four times the number is (n^2 - 4) / (4n + 5)
Explanation:To write an expression for the quantity of four less than the square of a number divided by the quantity five more than four times the number, we can represent the number as 'n'.
The square of the number is written as n2.
Four less than the square of the number is (n2 - 4).
Five more than four times the number is (4n + 5).
Therefore, the expression for the given quantity is:
(n2 - 4) / (4n + 5)
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What is the value of f(x) = 3x - 5 when x = 6
Plug in 6 for x in the equation:
f(6) = 3(6) - 5
Remember to follow PEMDAS. First, multiply
f(6) = 3(6) - 5
f(6) = 18 - 5
Finally, subtract
f(6) = 18 - 5
f(6) = 13
f(6) = 13 is your answer
hope this helps
I need help with Math please
the height h increased by 6 inches
"Height h increased by 6" can be displayed as:
h + 6
if axb=0, then a=0 or b=0
3x=0
Answer:
The given equation is
ax b= 0,
As we see that, it is a linear equation in one variable containing two constant.
So , a≠ 0 [then equation has no meaning.If a=0 , then [tex]0 \times x=0[/tex], which is meaningless]. ∴ a=0 is incorrect.
Similarly , b≠ 0 [ Reason same as above]. ∴b=0 is incorrect.
⇒3 x=0
⇒x=0 is the correct response.
Let me explain by this giving an example
⇒5 x=0
⇒ x=0 but 5≠0
So, x=0 or 3 x=0 is correct response.
Antoine has a carnival booth at the school fair where students randomly select a ping pong ball from a can. He wants to place 5 red ping pong balls an n blue ping pong balls in the can. He also wants the probability of randomly choosing a blue ping pong ball to be 3/5.
Part A:
Write an equation that can be used to model this situation.
Part B:
Solve the equation and interpret the solution in terms of the context, determining if the solution is viable.
Answer:
(a)[tex]5n=3n+15[/tex]
(b)[tex]n=7.5[/tex]
Solution is not viable
Step-by-step explanation:
(a)
Total number of red ping pong balls[tex]=5[/tex]
Total number of red ping pong balls[tex]=n[/tex]
Now, probability of an event [tex]=\frac{Number of favourable events}{Total number of events}[/tex]
Then, theprobability of randomly choosing a blue ping pong ball is
[tex]=\frac{n}{n+5}[/tex]
Given that this probability is[tex]=\frac{3}{5}[/tex]
Thus, we have that,
[tex]\frac{n}{n+5}= \frac{3}{5}\\ 5n=3(n+5)\\5n=3n+15[/tex]
(b)
Solving, the above equation,
[tex]5n=3n+15\\2n=15\\n=7.5[/tex]
This solution is not viable as, number of ping pong ball must be an integer and not a decimal number.
Examine the worked problem and solve the equation.
The solution is x =
Answer:
x = 7
Step-by-step explanation:
Edginuity, got le question correct humans
Based on the expression given, the for x will be 7.
From the diagram given, we can see that the last expression that's given is 4x/3 = 28/3. The next thing that will be done in this case is to cross multiply and this will be:
4x/3 = 28/3.
Cross multiply
4x × 3 = 28 × 3
12x = 84
x = 84/12.
x = 7
Therefore, the value of x will be 7.
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I need help please!!!!!!!
Jeremy surveyed students in his class about their spending habits in the school cafeteria. He used the data to create a scatterplot.
Answer:
Step-by-step explanation:
From the graph, you can first see that there is a positive slope, and a negative y intercept. That should automatically rule out the first option.next, find the slop...
To do this take the two points that are given (2,5.5) and (5,15.25) and do rise over run. This would be (15.25-5.5)/(5-2). I just put this in a calculator and found the slope to be 3.25. You automatically know the answer because the only equation with the slope 3.25 is the third one.
The scatterplot shows the distribution of the students' spending habit
The equation of the trend line is: [tex]\mathbf{y = 3.25x -1}[/tex]
From the scatter plot (see attachment), we have the following points:
[tex]\mathbf{(x,y) = (2,5.5)\ (5,15.25)}[/tex]
So, the slope (m) of the trend line is:
[tex]\mathbf{m = \frac{y_2 - y_1}{x_2 - x_1}}[/tex]
This gives
[tex]\mathbf{m = \frac{15.25 - 5.5}{5- 2}}[/tex]
[tex]\mathbf{m = \frac{9.75}{3}}[/tex]
[tex]\mathbf{m = 3.25}[/tex]
The equation of the trend line is then calculated as:
[tex]\mathbf{y = m(x - x_1) + y_1}[/tex]
This gives
[tex]\mathbf{y = 3.25(x - 2) + 5.5}[/tex]
[tex]\mathbf{y = 3.25x - 6.5 + 5.5}[/tex]
[tex]\mathbf{y = 3.25x -1}[/tex]
Hence, the equation of the trend line is: [tex]\mathbf{y = 3.25x -1}[/tex]
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What is the approximate value of 200,000 x 200
it would be 40000000 because there there are 7 zeroes and then you and then you multiply the two twos together and then put it in the front.
Answer:
the approximate value of 200,000 x 200 is 40,000,000
Step-by-step explanation:
the approximate value of 200,000 x 200
To find the approximate value we multiply 200,000 times 200
WE have two zeros in 200. so when we multiply we add two zeros
now we multiply the numbers
2 times 2 gives us 4
[tex]200,000 \ times \ 200= 40,000,000[/tex]
So the approximate value of 200,000 x 200 is 40,000,000
can someone plz answer this . its due tomorrow
Circumference of Earth = Pi* Diameter= 3.1415926536X7926Miles=24,900.3Miles
Monday's dog Rex. Weighed 80 pounds a year ago now he weighs 92 pounds what us the percent increase in his weight
First we find increase in weight
Increase in weight is =92-80 = 12
To find percentage increase in weight we use formula =( increase / actual) ×100
Percentage increase =( 12÷80)×100= 15 %
The answer is about 4%
which expression correctly shows the sum of 20 and 8minus the product of 3 and 5
It would be 20+8-(3x5).
Three girls made necklaces using beads. Jamie used 5 times as many beads as Carmen did. Allison used 8 more than 3 times as many beads as Carmen did. The total number of beads used by the three girls was 143. Which equation can be solved to find the number of beads (n) that Carmen used to make her necklace?
what are 3 equivalent ratios for 14/2
The answer is:
28/4
42/6
56/8
How are the absolute values of opposite intergers related ?? Help me 16 points give me a good answer plz and THX
Opposite integers are pairs of opposite sign, so the opposite integer to 2 is -2, 3 is opposite to -3, and so on.
Absolute value make any integer non-negative by removing its negative sign if there is any.
Absolute values of opposite integers are related in that they are *identical*
Any pair of opposite integers shares the same absolute value.
Lmk if you have questions.
the product of two rational number is 19/27. if one of the number be 38/9 ,find the other
[tex]\frac{38}{9} x = \frac{19}{27}[/tex]
[tex](27)\frac{38}{9} x = \frac{19}{27}(27)[/tex]
3(38)x = 19
[tex]x = \frac{19}{3(38)}[/tex]
[tex]x = \frac{1}{3(2)}[/tex]
[tex]x = \frac{1}{6}[/tex]
Answer: [tex]x = \frac{1}{6}[/tex]
(w+14)/(4w+6)=(3)/(4) show work plz
Answer:
w = -1.44 and w = -14.06
Step-by-step explanation:
That "(3) / (4)" in (w+14)/(4w+6)=(3)/(4) looks fishy. Assuming that you really meant 3/4, then we have (w+14)/(4w+6)=3/4.
Mult. both sides by 4 to remove the fraction: 4(w+14)/(4w+6) = 3.
Multiply out (w+14)/(4w+6): 4w^2 + 6w + 56w + 84. Combine the w terms, obtaining 4w^2 + 62w + 84. Then the original equation becomes:
4w^2 + 62w + 84 = 3, or 4w^2 + 62w + 81 = 0.
This is a quadratic equation, with a = 4, b = 62 and c = 81. The two roots (values of
w) are as follows:
-62 plus or minus √(62^2-4(4)(81)
----------------------------------------------------------
8
-62 plus or minus √(2548) -62 plus or minus 50.48
w = ------------------------------------------- = ---------------------------------------
8 8
Simplifying, we get w = -1.44 and w = -14.06
To solve the algebraic equation (w+14)/(4w+6) = 3/4, we clear the fractions, combine like terms, and isolate the variable w, which gives us the solution w = 4.75.
To solve the equation (w+14)/(4w+6) = 3/4, we first clear the fractions by multiplying both sides by the least common denominator, which is 4(4w+6). This eliminates the denominators and gives us:
4(w + 14) = 3(4w + 6)
Distribute the 4 on the left side and the 3 on the right side:
4w + 56 = 12w + 18
Next, we want to get all the terms with w on one side and the constant terms on the other. Subtract 4w and 18 from both sides:
4w + 56 - 4w - 18 = 12w + 18 - 4w - 18
This simplifies to:
38 = 8w
Divide both sides by 8 to isolate w:
w = 38 / 8
Finally, simplify the fraction to find the value of w:
w = 4.75
You are packaging expansion packs for the game of checkers. The table below lists the number of each part needed per expansion pack, as well as the number of each part that you have available.
Part Number in each pack Number available
People marker 6 287
6-sided die 3 143
Teleporter marker 7 341
You make as many expansion packs as you can. With the parts remaining, you could make 1 more expansion pack if you had:
A) 1 more people marker and 1 more die.
B) 1 more die and 1 more teleporter marker.
C) 1 more teleporter marker and 1 more people marker.
D) 2 more people markers.
E) 2 more teleporter markers
Answer: Option (A)1 more people marker and 1 more die.
Step-by-step explanation:
We have to pack expansion packs for the game of checkers in such a way such that there should be enough cards as per requirement.
So for that we have to find packs of each item by dividing each pack by part numbers and what is left after as remainder.
People marker =287 =6(47) + 5 ( as each pack of people marker contains 6 items)
6-sided die =143 = 3(47) + 2 (as each pack of 6- sided die contains 3 items)
Teleport-er marker=341 = 7(48) + 5 (as each pack contains 7 teleport-er marker)
So we can see that for 48th pack we have enough Teleport-er marker just we need one People marker and one 6-sided die. which is option A.
Given the quantities of game components available, we can form 47 complete expansion packs. We can form another pack if we had 1 more 6-sided die and 1 more people marker. Thus, the correct answer is option A.
Explanation:To answer the question, we first need to calculate how many complete expansion packs can be made with the available components:
People marker: We would divide the total number of available markers (287) by the number needed for each pack (6). Thus, a total of 47 full packs can be made with an extra 5 markers left over. 6-sided die: Dividing the total number of dice available (143) by the number needed for each pack (3), we get 47 full packs with 2 dice left over. Teleporter marker: Divided by 7 (the amount needed per pack), the 341 available teleporter markers would result in 48 full packs with 5 markers left over.
Given the available quantities, we can make a total of 47 complete packs. However, we'd have enough components to complete one more pack if we had 1 more die and 1 more people marker. Therefore, the correct answer is option A.
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Graph the image of this figure after a dilation with a scale factor of 2 centered at (2, 2) .
Use the polygon tool to graph the dilated figure.
Answer:
The points of the dilated figure would be at (-2, 10), (2, 6), and (-8, 4); an image of the figure is attached.
Step-by-step explanation:
First we translate the center of dilation and figure so the origin becomes the center of dilation.
Since the point (2, 2) is our center of dilation, we must translate it left 2 and down 2 to make the origin the center; this means we map every point
(x, y)→(x-2, y-2)
The scale factor of 2 means that each point will be multiplied by 2; this gives us the rule
(x, y)→(2x-4, 2y-4)
Lastly we will translate the figure right 2 and up 2 to move it back to its original position; this gives us the rule
(x,y)→(2x-4+2, 2y-4+2) = (2x-2, 2y-2)
The first point in the original figure, at the top, is (0, 6). Applying the transformation gives us
(0, 6)→(2*0-2, 2*6-2) = (0-2, 12-2) = (-2, 10)
The point on the right of the pre-image is (2, 4). Applying the transformation rule gives us
(2, 4)→(2*2-2, 2*4-2) = (4-2, 8-2) = (2, 6)
The point on the left of the pre-image is at (-3, 3). Applying the transformation rule, we have
(-3, 3)→(-3*2-2, 3*2-2) = (-6-2, 6-2) = (-8, 4)
Answer:
Here is the correct answer
Step-by-step explanation:
I hope this helps!
twelve is the same as two-thirds a number diminished by two.
12 = 2/3(x - 3)
Distributive property.
12 = 2/3x - 2
Add 2 to both sides.
14 = 2/3x
Multiply both sides by 3.
42 = 2x
Divide both sides by 2.
21 = x
The value of x is equal to 21.
The equation, twelve is the same as two-thirds a number diminished by two - True
Explanation:To determine if twelve is the same as two-thirds of a number diminished by two, we can set up an equation. Let's represent the number as 'x.' According to the statement, twelve is equal to two-thirds of x diminished by two. Mathematically, this can be written as:
12 = (2/3)x - 2
To solve for x, we need to isolate it on one side of the equation. First, we can add 2 to both sides:
14 = (2/3)x
Next, we can multiply both sides by 3/2 to eliminate the fraction:
14 * (3/2) = x
21 = x
Therefore, the number in question is 21. To confirm, we can substitute x back into the original equation:
12 = (2/3)(21) - 2
12 = 14 - 2
12 = 12
Since the equation is true, we can conclude that the statement is True.
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Complete Question:
Twelve is the same as two-thirds a number diminished by two. True or False ?
Triangle ABC has these side measurements: AB = 17 BC = 18 AC = 21 Order the angles of the triangle from largest measure to smallest measure.
Answer:
B, A, C
Step-by-step explanation:
B has the largest angle of 73.677, A has the second largest of 55.345, and C has the smallest angle of 50.977
The order of the angles of the triangle from largest measure to smallest measure. will be ∠B, ∠A, and ∠C.
What is angle measurement?An angle measure is the measurement of the angle created by two rays or arms at a shared vertex in geometry. A protractor is used to measure angles in degrees (°).
Angle obtained from the triangle are;
∠B=73.6°
∠A= 55.345°
∠C =50.977°
As a result, the arrangement of the triangle's angles is from biggest to smallest measure. ∠B, ∠A, and ∠C will be the results.
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Audrey is trying to find the equation of a line parallel to y = 2 over 3 x −5 in slope-intercept form that passes through the point (−6, −1). Which of the following equations will she use
Final answer:
To find the parallel line's equation, Audrey used the slope of 2/3 from the given line and the point (-6, -1) to write the equation in point-slope form, eventually simplifying it to y = 2/3x + 3.
Explanation:
Audrey is looking to find the equation of a line that is parallel to the line with the equation y = 2/3x - 5 and that passes through the point (-6, -1). Since parallel lines have the same slope, our new line will keep the slope of 2/3. Using the point-slope form of the equation of a line, we set up y - y1 = m(x - x1). Plugging in the known slope m and point (x1, y1), we get y - (-1) = 2/3(x - (-6)). After simplifying, we have y + 1 = 2/3x + 4. Finally, we solve for y by subtracting 1 from both sides, yielding the equation y = 2/3x + 3 as the line that is parallel to the original line and passes through the given point.
how do write 3 to 4 2 other ways?
The ratio "3 to 4" can also be written as "3:4". Typically, though, we write it as "3/4" like a fraction. Those are the three main ways to write out ratios ( a to b, a:b, or a/b).
Complete the mapping of the vertices of ΔDEF. D(2, –4) → D' E(1, –1) → E' F(5, 1) → F' What is the rule that describes a reflection across the line y = x? rx = y(x, y) →
D(2, –4) → D' = (-4, 2)
E(1, –1) → E'= (-1, 1)
F(5, 1) → F'=(1, 5)
What is the rule that describes a reflection across the line y = x?
rx = y(x, y)= (y, x)
The rule which describes a reflection across the line is y(x, y) --> (y, x) and the mapping of the vertices of ΔDEF is (-4, 2)D', (-1, 1)E' , (1, 5)F'.
What is reflection?The reflection of a plane or shape is flipping the original figure with respect to a reference line.
The following steps are used to for reflecting a shape-
Select the shape which has to be reflected.Select a base line or reference line over which the shape has to be reflected.Mark the corners of the shape at the equidistant from the reference line as the original shape has, but in the opposite direction.The reflected shape is now is facing the opposite direction.The rule that describes a reflection across the line says that when your reflect a point across the line say y=x. Then the coordinates of x and y are interchanged as,
y(x, y) → (y, x)
Now let's complete the mapping of the vertices of ΔDEF using the above rule. For this, change the places of x and y coordinate as,
D(2, –4) → (-4, 2)D'
E(1, –1) → (-1, 1)E'
F(5, 1) → (1, 5)F'
Thus, the rule which describes a reflection across the line is y(x, y) --> (y, x) and the mapping of the vertices of ΔDEF is (-4, 2)D', (-1, 1)E' , (1, 5)F'.
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What is the graph of the inequality
The inequality "x ≤ 5" means that the value of x is going to be less than or equal to the quantity 5.
Because of this, the correct answer on the graph would be a filled in dot (meaning starting at that quantity, rather than one less or one more than), and an arrow pointing to the left.
The value of x could be 5, 4, 3, and so on. Any quantity lower than, and including, 5 is a possible answer for the value of x.
The correct answer is the 2nd option.
Answer:
Graph represented by option B is the correct choice.
Step-by-step explanation:
We have been given an inequality [tex]x\leq 5[/tex]. We are asked to find the graph of the given inequality.
Our given inequality tells that solution is any value of x less than or equal to 5.
Since our given inequality has less than or equal to sign, then the number line will have a solid dot at [tex]x=5[/tex].
Since the values of x are less than or equal to 5, so the solution of the inequality will be numbers less than 5.
Since the numbers on the left side of a number line are less than number on right side, therefore, the graph represented by option B is the correct choice.
Is -6.809 more or less than -6.812
it is more because of the negative.
In mathematics, when dealing with negative numbers, the number closer to zero is greater. Thus, -6.809 is greater than -6.812 because it's closer to zero.
Explanation:In the field of mathematics, when you're dealing with negative numbers, the number that is closer to zero is always greater. Here, we have the numbers -6.809 and -6.812. Looking carefully, -6.809 is closer to zero than -6.812. Hence, -6.809 is greater than -6.812.
Let's understand it with a simpler example. If we have -3 and -5, even though 5 is greater than 3, -5 is lesser than -3 because it's further away from zero.
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Ten years ago in Louisiana, schools average 182 pupils for every 10 teachers what is the ratio?
I think the ratio is 182:10
182/10 so every teacher will have about 18 students.
Hope this helps,im very sorry if it dont!!
Plz help me I don’t get is show your work
Is the equations true, false, open or none of the above?
10x + 5 = 8x + 2
10x + 5 = 8x + 2
Subtract 5 from both sides.
10x = 8x - 3
Subtract 8x from both sides.
2x = -3
Subtract both sides by 2.
x = -1.5
Because we are able to get a value for x, we know that the equation is true, as we can plug the value of x back into the original equation to verify.
10(-1.5) + 5 = 8(-1.5) + 2
-15 + 5 = -12 + 2
-10 = -10 √ this equation is true.
For the equation 10x + 5 = 8x + 2, the statement is true.
The given equation is 10x + 5 = 8x + 2.
The first thing to do is to subtract 5 from both sides.
10x + 5 - 5 = 8x + 2 - 5
10x = 8x - 3
Then, we'll subtract 8x and this will be:
10x - 8x = -3
2x = -3
Divide both side by 2
2x/2 = -3/2
x = -1.5
10x + 5 = 8x + 2,
10(-1.5) + 5 = 8(-1.5) + 2
-15 + 5 = -12 + 2
10 = 10
Therefore, the statement is true
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One of the stamps in Evelyn's stamp collection is 19.51 mm wide and 24.4 mm long. How much longer is the length of the stamp than the width of the stamp? Enter your answer in the box.
24.4-19.51= 4.89
Answer: 4.89 mm