Step-by-step explanation:
[tex]a + b > 12 \\ [/tex]
but
[tex] \\ a > - 3 \\ [/tex]
if
[tex]a = - 3 \\ then \: \\ a + b > 12 \\ - 3 + b > 12 \\ b > 12 + 3 \\ b > 15[/tex]
Answer:
its -3
Step-by-step explanation:
A Chemist needs to mix a 20% acid solution with a 50% acid solution to obtain 15 liters of a 34% acid solution. How many liters of each acid solution must be used?
8 litres (amount of 20% solution needed) and 7 litres for (amount of 50% solution needed)
Step-by-step explanation:
Let consider ‘x’ for 20% acid solution and (15 – x) for 50% acid solution. And so, the equation would be as below,
20% in x + 50% in (15 – x) = 15 litres of 34%
Convert percentage values, we get
0.20(x) + 0.50 (15 – x) = 15 (0.34)
0.20 x + 7.5 – 0.50 x = 5.1
-0.3 x + 7.5 = 5.1
0.3 x = 7.5 – 5.1
0.3 x = 2.4
[tex]x = \frac{2.4}{0.3} = 8 litres (amount of 20 \% solution needed)[/tex]
Apply ‘x = 8’ value in (15 – x) we get,
15 – 8 = 7 litres
The value of 7 litres for (amount of 50% solution needed)
simplify the expression- 3w+8+1–8
Answer:
Step-by-step explanation:
-3w+9-8
=-3w+1
Nicole’s job pays her salary plus commission. She earns a daily salary of $60 plus 15% commission of her total sales. On Monday, she earned a total of $63.75. What were her total sales?
Answer:
25
Step-by-step explanation:
60 per day 25 in sales 63.75-60=3.75
3.75÷.15=25
If Nicole's earns 15% commission of her total sales, then Nicole's total sale of Monday is 25.
What is percentage?Percentage is a part of the whole number. It is denoted by % sign.
1 %= 1/100.
Given that,
Total salary of Nicole's = $60.
Also,
Nicole gets 15% commission of her total sales,
Total earning on Monday = $63.75
The commission earned on Monday = 63.75 - 60 = 3.75
According to given condition,
15 % = 3.75
1 % = 3.75 / 15
100 % = 3.75 / 15 x 100
100 % = 25
Total sale of Nicole's on Monday is 25.
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The image below shows two dilated figures with lines WX and W'X' drawn. If the larger figure was dilated using a scale factor of 4, what relationship do lines WX and W'X'have?
The relationship between lines WX and W'X' would be that line WX is four times the length of line W'X', and they are parallel.
In a dilation, lines that pass through the center of dilation (the point about which the dilation occurs) remain unchanged.
This means that the line WX and its corresponding line W'X' would be collinear and have the same length if they pass through the center of dilation.
If the larger figure was dilated using a scale factor of 4, it means that every point in the larger figure is four times farther from the center of dilation than its corresponding point in the smaller figure. In this case, line WX would be four times longer than line W'X', and they would be parallel since they maintain the same direction.
So, the relationship between lines WX and W'X' would be that line WX is four times the length of line W'X', and they are parallel.
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What is -10x divided by -11 yall? im tired i have no clue what im doing plz answer quick its for my algebra hw and my teacher is So mean
Answer:
wouldn't it just be [tex]\frac{10}{11} x[/tex]
Step-by-step explanation:
this is also: [tex]\frac{-10*x}{-11}[/tex]
which is why it simplifies to the answer
10 POINTS!! Brainliest.!!!!
For the pair of similar solids, find the scale factor of the solid on the left to the solid on the right. Then find the ratios of the surface areas and the volumes.
Answer:
C
Step-by-step explanation:
Given 2 similar figures with linear ratio = a : b, then
ratio of areas = a² : b² and
ratio of volumes = a³ : b³
Here linear ratio = 42 : 56 ← divide both parts by 14
linear ratio = 3 : 4 ← in simplest form, thus
ratio of areas = 3² : 4² = 9 : 16
ratio of volumes = 3³ : 4³ = 27 : 64
Helppp can someone solve this please
Answer:
[tex]\displaystyle x=-15[/tex]
Step-by-step explanation:
Solution Of A System Of Equations
A system of linear equations is given as
[tex]\displaystyle \left\{\begin{matrix}ax+by=c\\ dx+ey=f\end{matrix}\right.[/tex]
There are many methods to solve them. We will use the method of reduction
The given system is
[tex]\displaystyle \left\{\begin{matrix}2x+3y=45\\ x+y=10\end{matrix}\right.[/tex]
Multiplying the second equation by -3
[tex]\displaystyle \left\{\begin{matrix}2x+3y=45\\ -3x-3y=-30\end{matrix}\right.[/tex]
Adding the resulting equations
[tex]\displaystyle -x=15[/tex]
[tex]\displaystyle x=-15[/tex]
Gary drove to the park at a rate of 50 miles per hour if it took him 2.5 hours to get from his house to the park how far away is the park from his house
Answer:
The distance of the park from the Gary's house is 125 miles.
Step-by-step explanation:
Speed of Gary = 50 miles/hour
Time taken by Gary to reach the park from his house = 2.5 hours
Now, we know that,
Distance travelled = speed × time
So, distance between park and Gary's house = speed × time
= 50 × 2.5
= 125 miles
So, the park is 125 miles away from the Gary's house.
How does graphing linear inequalities differ from graphing linear equations?
Explanation:
When the inequality symbol is replaced by an equal sign, the resulting linear equation is the boundary of the solution space of the inequality. Whether that boundary is included in the solution region or not depends on the inequality symbol.
The boundary line is included if the symbol includes the "or equal to" condition (≤ or ≥). An included boundary line is graphed as a solid line.
When the inequality symbol does not include the "or equal to" condition (< or >), the boundary line is not included in the solution space, and it is graphed as a dashed line.
Once the boundary line is graphed, the half-plane that makes up the solution space is shaded. The shaded half-plane will be to the right or above the boundary line if the inequality can be structured to be of one of these forms:
x > ... or x ≥ ... ⇒ shading is to the right of the boundaryy > ... or y ≥ ... ⇒ shading is above the boundaryOtherwise, the shaded solution space will be below or to the left of the boundary line.
_____
Just as a system of linear equations may have no solution, so that may be the case for inequalities. If the boundary lines are parallel and the solution spaces do not overlap, then there is no solution.
_____
The attached graph shows an example of graphed inequalities. The solutions for this system are in the doubly-shaded area to the left of the point where the lines intersect. We have purposely shown both kinds of inequalities (one "or equal to" and one not) with shading both above and below the boundary lines.
Someone please help! Thank you!
Answer:
The coordinates of point Q will be given by (11,-2)
Step-by-step explanation:
See the attached diagram.
Given that R is the midpoint of PS and Q is the midpoint of RS.
Therefore, the point Q divides the line PS in the ratio 3 : 1.
Now, coordinates of P are (8,10) and that of point S is (12,-6).
Therefore, the coordinates of point Q will be given by
[tex](\frac{3\times 12 + 1 \times 8}{3 + 1}, \frac{3 \times (- 6) + 1 \times 10}{3 + 1})[/tex]
= (11,-2) (Answer)
Jenny goes to the shop.
She buys
• three cups for £1.24 each
three saucers for 95p each
• a teapot for £6.18
Jenny has £20 to spend. She also wants to buy some plates, which are £1.57 each
What is the greatest number of plates Jenny can buy?
Answer:
5
Step-by-step explanation:
1.24 times 3 = 3.72
.95 (the value of pence to a pound in decimal form) = 2.85
6.18 for the teapot
2.72+2.85+6.18=11.75
She now has £8.25 left (20-11.75).
8.25/1.57=the amount of plates she can buy: 5.25477707006, so 5 with some money left
A line passes through the points (–5, 2) and (10, –1). Which is the equation of the line? 025-1. c025-2 y = –5x – 23 y = 5x + 27
Answer:
y=-1/5x+1
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-1-2)/(10-(-5))
m=-3/(10+5)
m=-3/15
m=-1/5
y-y1=m(x-x1)
y-2=-1/5(x-(-5))
y-2=-1/5(x+5)
y=-1/5x-5/5+2
y=-1/5x-1+2
y=-1/5x+1
What is the length of BE given that BD = 18 and figure ABCD is a
parallelogram?
Answer: D. 9
Step-by-step explanation: If BD is 18 then BE is 9
Answer:
can confirm that it is 9
Step-by-step explanation:
slay have a nice day!
Choose the graph which represents -6x - 5y = -10
Answer:
y = 2 + ((-)6/5)x
Step-by-step explanation:
-6x-5y=-10
add 6x to both sides.
-5y = -10 +6x
divide both sides by -5
y = 2 - (6/5)x
Plug in 0 for x to get the y intercept:
f(0) = 2 - (6/5) (0)
y = 2
(0, 2) is the y intercept.
Do the same for values such as -1, -2, 1, and 2, etc.
Then graph it.
To find the correct graph for -6x - 5y = -10, transform it to the slope-intercept form y = 6/5x - 2, which reveals a slope of 6/5 and a y-intercept at -2. Seek a graph with a line that increases 6 units vertically for every 5 units horizontally and intersects the y-axis at -2.
Explanation:To find the graph that represents the equation -6x - 5y = -10,
we first need to manipulate the equation into slope-intercept form,
which is y = mx + b where m is the slope and b is the y-intercept. Starting with the given equation:
-6x - 5y = -10
Let's isolate y by adding 6x to both sides:
-5y = 6x - 10
Now, divide each term by -5 to solve for y:
y = -6x / -5 + 10 / -5
y = 6/5x - 2
The slope-intercept form of the equation is now y = 6/5x - 2. This tells us that the slope (m) of the line is 6/5 and the y-intercept (b) is -2. You will look for the graph with a line that rises 6 units for every 5 units it moves to the right (since the slope is positive) and crosses the y-axis at -2.
ABCD is a parallelogram. If mZCDA = 75, then what is mZDAB?
Answer:
Therefore
m∠ DAB is 105°
Step-by-step explanation:
Given:
ABCD is a parallelogram. The diagram is not drawn to scale.
m∠CDA = 75°,
To FInd
m∠DAB = ?
Solution:
ABCD is a parallelogram.
AB || CD .......{opposite sides of a parallelogram are parallel}
∴∠CDA+∠DAB = 180°{SUM of the interior angles between parallel are supplementary}
substituting the values we get
[tex]75+m\angle DAB=180\\\\m\angle DAB =180-75=105\\\\m\angle DAB =105\°[/tex]
Therefore
m∠ DAB is 105°
Equation of the line that passes through (8,-7) (-6,-7)
Answer:
y = - 7
Step-by-step explanation:
line pass (8, - 7) (- 6, -7)
y = mx + b m: slope b: y intercept
m = difference of y / difference of x
m = (- 7 - (- 7)) / (- 6 - 8) = 0 / (-14) = 0 ... line parallel to x axis
b = y - mx = - 7 - 0*8 = -7
equation : y = -7
Answer:
y = - 7
Step-by-step explanation:
line pass (8, - 7) (- 6, -7)
y = mx + b m: slope b: y intercept
m = difference of y / difference of x
m = (- 7 - (- 7)) / (- 6 - 8) = 0 / (-14) = 0 ... line parallel to x axis
b = y - mx = - 7 - 0*8 = -7
equation : y = -7
1/4÷5 equal what? Djdjjdjdjdjdjdjdjdd
Answer:
1/20
Step-by-step explanation:
A sofa was sold at a price of $270 with a 25% profit. What is the cost of the sofa?
Answer:
The cost of the sofa is $216
Step-by-step explanation:
The sofa was sold at cost plus 25% profit
let the cost of the sofa be = x
therefore x + 25% of x = 270
x + .25x = 270
1.25x = 270
1.25x/1.25 = 270/1.25
x = $216
30 points Asap Recall that Seth's house is 17 miles from school. Which
location should Seth start off at to get to school faster
and how long will it take?
from the bus stop is faster, taking 17 minutes
from the bus stop is faster, taking 24 minutes
from his friend's house is faster, taking 15 minutes
from his friend's house is faster, taking 22.5 minutes
Answer: D
Step-by-step explanation: I just did the quiz
Answer: D
Step-by-step explanation:
Yeah the quiz was like, dud the answers D, so I was like okay it's D
How to solve the following inequality -1 > -2(x - 4) -5(4x - 7)
Answer:
The solution of the inequality is:
[tex]x>2[/tex]
Step-by-step explanation:
Given inequality:
[tex]-1 >-2(x - 4)-5(4x-7)[/tex]
Solving the inequality.
Using distribution.
⇒ [tex]-1 >(-2x) +((- 4)(-2))+(-5\times4x)+((-5)(-7))[/tex]
⇒ [tex]-1 >-2x +8-20x+35[/tex]
Combining like terms
⇒ [tex]-1 >-2x-20x+35+8[/tex]
⇒ [tex]-1 >-22x +43[/tex]
Adding [tex]22x[/tex] both sides.
⇒ [tex]-1+22x >-22x +43+22x[/tex]
⇒ [tex]-1 +22x> 43[/tex]
Adding 1 both sides.
⇒ [tex]-1+1 +22x> 43+1[/tex]
⇒ [tex]22x>44[/tex]
Dividing both sides by 22.
⇒ [tex]\frac{22x}{22}>\frac{44}{22}[/tex]
⇒ [tex]x>2[/tex]
Thus, the solution of the inequality is:
[tex]x>2[/tex]
Consider the expressions:
Expression 1: −9x + 8y
Expression 2: −8x − 2y
Subtract expression 1 from expression 2?
A)
x + 6y
B)
6y − x
C)
10y − x
D)
x − 10y
Answer:
D
Step-by-step explanation:
= −8x − 2y - (−9x + 8y)
Open bracket
= -8x -2y + 9x - 8y
= x - 10y
Final answer:
Subtracting Expression 1 from Expression 2 term by term results in x - 10y, which corresponds to option D).
Explanation:
To subtract Expression 1 from Expression 2, we perform the subtraction operation term by term.
For the x-terms: (-8x) - (-9x) simplifies to x.
For the y-terms: (-2y) - (8y) simplifies to -10y.
Subtracting expression 1 from expression 2:
Expression 2 - Expression 1 = (-8x - 2y) - (-9x + 8y)
Simplify to get: (-8x - 2y) + (9x - 8y)
Combining like terms, the result is x - 10y.
Therefore, subtracting Expression 1 from Expression 2 gives us x - 10y, which matches option D).
20% tip on a bill of 42.26
Answer:
(42.26/100)*120 = $50.712
Step-by-step explanation:
Answer: tip = 8.452
Step-by-step explanation:
1) Members at a yoga school pay $10 per class plus a one-time $100 membership fee. Non-members pay$15 per class. How many classes would a member have to take to save money compared to taking classes as a non-member?
2) Translate the statement into an equation. Then solve the equation. The sum of 8 and 3 times a number is 23.
6) Members at a yoga school pay $7 per class plus a one-time $120 membership fee. Non-members pay $11 per class. How many classes would a member have to take to save money compared to taking classes as a non-member?
Answer all questions please, and if u can show u work, please...
3)A rental car costs $36 for one day plus an additional $0.42 per mile. What is the cost of renting a car for one day and driving it 78 miles?
4) Alice earns 1.5 times her normal hourly rate for each hour she works after 40 hours in a week. She worked 50 hours this week and earned $660. What is her normal hourly rate?
5) Cynthia orders 27 prints of a photograph she took. It costs her a total of $242.73. Which equation can be used to find how much each print cost?
Answer:
Part 1) The number of classes must be greater than 20
Part 2) see the explanation
Part 3) [tex]\$68.76[/tex]
Part 4) [tex]\$12\ per\ hour[/tex]
Part 5) The equation that can be used is [tex]27x=242.73[/tex] and the cost of one print is [tex]\$8.99[/tex]
Part 6) The number of classes must be greater than 30
Step-by-step explanation:
Part 1) we know that
The linear equation in slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope or unit rate
b is the y-intercept or initial value
Let
y ----> the total cost
x ----> the number of classes
we have
Members
The slope is [tex]m=\$10\ per\ class[/tex]
The y-intercept is [tex]b=\$100[/tex]
so
[tex]y=10x+100[/tex] ----> equation A
Non-Members
The slope is [tex]m=\$15\ per\ class[/tex]
so
[tex]y=15x[/tex] ----> equation B
To find out how many classes would a member have to take to save money compared to taking classes as a non-member, solve the following inequality
[tex]10x+100 < 15x[/tex]
Solve for x
subtract 10 x both sides
[tex]100 < 15x-10x[/tex]
[tex]100 < 5x[/tex]
Divide by 5 both sides
[tex]20 < x[/tex]
Rewrite
[tex]x > 20[/tex]
therefore
The number of classes must be greater than 20
Part 2) we have
The sum of 8 and 3 times a number is 23.
Let
x ----> the number
Remember that
3 times a number is the same that multiply 3 by the number ----> 3x
so
The sum of 8 and 3 times a number is 23 is the same that
[tex]8+3x=23[/tex]
solve for x
subtract 8 both sides
[tex]3x=23-8[/tex]
[tex]3x=15[/tex]
Divide by 3 both sides
[tex]x=5[/tex]
Part 3) we know that
The linear equation in slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope or unit rate
b is the y-intercept or initial value
Let
y ----> the total cost of renting a car for one day
x ----> the number of miles
we have
The slope is [tex]m=\$0.42\ per\ mile[/tex]
The y-intercept is [tex]b=\$36[/tex]
so
[tex]y=0.42x+36[/tex]
For x=78 miles
substitute in the linear equation and solve for y
[tex]y=0.42(78)+36[/tex]
[tex]y=\$68.76[/tex]
Part 4) Let
x ----> Alice's normal hourly rate
we know that
40 hours multiplied by her normal hourly rate plus 10 hours (50 h-40 h) multiplied by 1.5 times her normal hourly rate must be equal to $660
so
The linear equation that represent this situation is
[tex]40x+10(1.5x)=660[/tex]
solve for x
[tex]40x+15x=660[/tex]
[tex]55x=660[/tex]
Divide by 55 both sides
[tex]x=\$12\ per\ hour[/tex]
Part 5) Let
x ----> the cost of one print
we know that
The cost of one print multiplied by 27 prints must be equal to $242.73
so
The linear equation is equal to
[tex]27x=242.73[/tex]
solve for x
Divide by 27 both sides
[tex]x=\$8.99[/tex]
Part 6) we know that
The linear equation in slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope or unit rate
b is the y-intercept or initial value
Let
y ----> the total cost
x ----> the number of classes
we have
Members
The slope is [tex]m=\$7\ per\ class[/tex]
The y-intercept is [tex]b=\$120[/tex]
so
[tex]y=7x+120[/tex] ----> equation A
Non-Members
The slope is [tex]m=\$11\ per\ class[/tex]
so
[tex]y=11x[/tex] ----> equation B
To find out how many classes would a member have to take to save money compared to taking classes as a non-member, solve the following inequality
[tex]7x+120 < 11x[/tex]
Solve for x
subtract 7x both sides
[tex]120 < 11x-7x[/tex]
[tex]120 < 4x[/tex]
Divide by 4 both sides
[tex]30 < x[/tex]
Rewrite
[tex]x > 30[/tex]
therefore
The number of classes must be greater than 30
Are u smarter than an 8th grader!?!
Answer:
The function is f(x) = 2x + 3 for x ≥ - 2 and f(x) = - 2x - 5 for, x < - 2.
The vertex of the function is (-2,-1)
Domain of the function is (-∞, +∞)
Range of the function is [-1, +∞).
Step-by-step explanation:
The function has a graph in two parts.
The right side part passes through the points (-2,-1) and (0,3).
So, the equation of this part will be
[tex]\frac{y - 3}{3 - (- 1)} = \frac{x - 0}{0 - (- 2)}[/tex]
⇒ y - 3 = 2x
⇒ y = 2x + 3
Again, the left side part of the graph passes through the points (-2,-1) and (-4,3).
Therefore, the equation of this part will be
[tex]\frac{y - 3}{3 - (- 1)} = \frac{x - (- 4)}{- 4 - (- 2)}[/tex]
⇒ y - 3 = - 2(x + 4)
⇒ y - 3 = - 2x - 8
⇒ y = - 2x - 5
Therefore, the function is f(x) = 2x + 3 for x ≥ - 2 and f(x) = - 2x - 5 for, x < - 2. (Answer)
The vertex of the function is (-2,-1) (Answer)
Domain of the function is (-∞, +∞) (Answer)
Range of the function is [-1, +∞). (Answer)
30 points and brainliest for the correct answers.
Question # 1
Use the points in the diagram to name the figure?
Answer:
Option B is correct. The figure is named as a line 'CD'. The symbol '⟷' is placed UPPER on a line 'CD'.
Explanation:
As we know that a line is a set of points which tend to extend infinitely in two directions. So, in question 1, two points C and D are shown on a line. As a line carries these two points - the infinite line that includes C and D. Double arrow indicates that line is extended infinitely in both directions. While the order of the points does not matter for a line, it is conventional to name the two points in alphabetical order. So, the figure is named as a line 'CD'. So, option B is correct.Note: The symbol '⟷' is placed UPPER on a line 'CD'. Also remember, that the a line is named in alphabetical order.
Question # 2
Which of the following correctly names a line shown in the figure?
Answer:
The option A is correct as the line AP carries the points A and P and extends infinitely in two directions, and the symbol '⟷' is placed UPPER on a line 'AP' which represents the line.
Explanation:
Let us look at some definitions.
Point - has no length, no width, and no height, but it carries a location. Line - a set of points which tend to extend infinitely in two directions. For example line AB.Line Segment - is a piece of line having two end points. For example, segment [tex]{\overline {AB}}[/tex].Ray - a part of line with one end point. For example, Ray [tex]{\overrightarrow {AB}}[/tex]As we have to determine the correct name of a line shown in figure in question 2. So, we need to recall that a line is a set of points which tend to extend infinitely in two directions. Double arrow indicates that line is extended infinitely in both directions.
In question 2, the figure shows that:
[tex]{\overrightarrow {EC}}[/tex] is a ray as it is a part of line with one end point, heading towards infinity in only one direction. Hence, option B is also not a line. [tex]{\overline {NH}}[/tex] is a line segment because it has two end points. Hence, option C is not a line.Option D can not be correct as the symbol ' [tex]{\overline {~~}}[/tex] 'is placed upper on AP. This symbol represents the segment. As we know that a line is a set of points which tend to extend infinitely in two directions. Double arrow indicates that line is extended infinitely in both directions. The symbol '⟷' is placed UPPER on a line 'AP'. Hence, the option A is correct as the line AP carries the points A and P, and the symbol '⟷' is placed UPPER on a line 'AP' which represents the line.So, option A is correct.
Question 3.
Which of the following correctly names a ray shown in the figure?
Answer:
option B is correct. i.e. [tex]{\overrightarrow {EG}}[/tex] correctly names a ray.Explanation:
The option A can not be correct as the symbol ' [tex]{\overline {~~}}[/tex] 'is placed upper on EP. This symbol represents the segment as EP is a line segment. The option C cannot be true as the '⟷' is placed UPPER on 'LG' which represents the line.The option D cannot be true also as it is showing the wrong end point of a ray. As the actual ray would have had E as the end point, and directed towards C, and would have mentioned as [tex]{\overrightarrow {CE}}[/tex]. But, the option D is wrongly mentioning as [tex]{\overrightarrow {EC}}[/tex].As we know that a ray is a part of line with one end point. If we carefully observe the figure, only option B i.e. [tex]{\overrightarrow {EG}}[/tex] is correct. As E is the end point, and directed towards G. So, it becomes [tex]{\overrightarrow {EG}}[/tex]. We cannot call it [tex]{\overrightarrow {GE}}[/tex] as G is not the end point. An array has only one arrow. So, option B is correct.Keywords: ray, segment, line
Learn more about rays, lines, and segments from brainly.com/question/909890
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Rita is hiking along a trail that is 14.3 miles long. So far she has hiked along one-tenth of the trail
How far has Rita hiked?
Rita has hiked miles
Just multiply the total length by the fraction:
14.3 * 1/10 = 1.43 miles
Answer:
1.43
Step-by-step explanation:
NOTE: This is the way I do it , other people may have a other/faster way to do it.
For this question you simpily have to divide 14.3 by 10:
1. Convert 14.3 into a mixed number - 14 3/10
2. Divide 14 by 10 - 1.4
3. Divide 3/10 by 10 - 3/100
4. Convert 3/100 into a decimal- 0.03
5. Add the two decimals - 0.03 + 1.4 = 1.43
Divide using synthetic division. ( x^4-12x^2-9)/(x+3)
Answer:
x^3 - 3x^2 - 3x + 9 + (-36/(x+3))
OR
x^3 - 3x^2 - 3x + 9 - (36/(x+3))
Step-by-step explanation:
First set the divisor equal to 0:
x + 3 = 0
Subtract 3 from both sides
x = -3
This is what you'll divide the dividend by in synthetic division.
Take the coefficents of each term in the dividend. Do not forget the 0 placeholders:
x^4 + 0x^3 - 12x^2 + 0x -9
Coefficents: 1. 0. -12. 0 -9.
Please see the image for the next steps.
The remainder is -36. Put the remainder over the divisor and add it to the polynomial (shown in image)
-36/(x+3)
Divide using synthetic division the remainder is -36. Put the remainder over the divisor and add it to the polynomial -36/(x+3).
First set the divisor equal to 0:
x + 3 = 0
Subtract 3 from both sides
x = -3
This is what you'll divide the dividend by in synthetic division.
Take the coefficents of each term in the dividend. Do not forget the 0 placeholders:
[tex]x^4 + 0x^3 - 12x^2 + 0x -9[/tex]
Coefficents: 1. 0. -12. 0 -9.
The remainder is -36. Put the remainder over the divisor and add it to the polynomial -36/(x+3).
A baker bought 4 gallons oficing to decorate cakes. He uses 4 % cups
of long to completely frost and decorate each cake. What is the
maximum number of cakes he can completely decorate? Explain your
thinking, hint: 16 cups = 1 gallon)
25 cakes can be completely decorated using 4 gallons of icing.
Step-by-step explanation:
Given:
4 gallons of icing
16 cups =1 gallon
No. of icing cups = [tex]4\times16[/tex] cups
=64 cups
No. of cups required to decorate and frost a cake= 4% of total no. of icing cups
= [tex]\frac{(4\times64)}{100}[/tex]
= 2.56
2.56 cups of icing is required to decorate each cake.
Maximum no. of cakes decorated = [tex]\frac{ (64\times1)}{2.56}[/tex]
= 25
25 cakes can be completely decorated using 4 gallons of icing.
West high schools population is 250 students fewer then twice the population of East High school the two schools have a total of 2858 students how many students attend the East high school
Answer:
1036 students
Step-by-step explanation:
Let the number of students at West High be "w" and the number of students at East High be "e"
West High population is 250 FEWER than TWICE of East High, we can write:
w = 2e - 250
Total students in both schools is 2858, so we can write 2nd equation as:
e + w = 2858
We can replace 1st equation in 2nd to get an equation in e, and find "e":
e + w = 2858
e + (2e - 250) = 2858
3e - 250 = 2858
3e = 2858 + 250
3e = 3108
e = 3108/3
e = 1036
Hence,
number of students attending East High School = 1036 students
Can you please help me solve and if you show work I would really appreciate it
You got the equations correct, great job on that!
Let "s" be the variable that represents how many shirts were bought. Let "p" represent the total price/cost.
Equation for the store at Town Center mall:
p = 80 + 3.5s (80 is base cost, and cost increases 3.5 per shirt)
Equation for the store in Arlington:
p = 120 + 2.5s (120 is base cost, and cost increases 2.5 per shirt)
We want to find a point where the systems are equal; thus, we are solving for a system of linear equations, and we already have the equations we need.
p = 80 + 3.5s
p = 120 + 2.5s
We know that variable "p" is equal for both equations; thus, we can combine both equations into:
80 + 3.5s = 120 + 2.5s
Subtract both sides by 2.5s
80 + 3.5s - 2.5s = 120 + 2.5s - 2.5s
80 + s = 120
Subtract both sides by 80
s = 40
Thus, both equations are equal when 40 shirts are bought.
To find the cost, use any of the two equations (or both) to find the total cost, which should be equal.
p = 80 + 3.5(40) = 220
p = 120 + 2.5(40) = 220
Thus, the total price/cost at both stores is $220.
Let me know if you need any clarifications, thanks!