Final answer:
To subtract two polynomials, change the sign of the second polynomial and combine like terms. The result of subtracting (5x^2-3x-2) and (-2x^2-x+10) is 7x^2 - 2x - 12.
Explanation:
To subtract the given polynomials, (5x^2−3x−2) and (−2x^2−x+10), we need to change the sign of each term in the second polynomial and then combine like terms with the first polynomial. This is similar to subtracting negative numbers, where subtraction turns into addition when the number being subtracted is negative.
The subtraction process step-by-step is as follows:
Change the signs of the second polynomial: +2x^2 + x - 10
Add the results to the corresponding terms in the first polynomial:
5x^2 + 2x^2 = 7x^2
−3x + 1x = −2x
−2 − 10 = −12
So the answer to the subtraction in standard form is 7x^2 − 2x − 12.
Amber has 4/5-pound bag of colored sand. She uses 1/2 of the bag for the project. How much sand does she use for the project?
Answer:
[tex]\frac{2}{5}[/tex]-pound of sand
Step-by-step explanation:
We have been given that Amber has [tex]\frac{4}{5}[/tex]-pound bag of colored sand. She uses 1/2 of the bag for the project.
We need to find 1/2 'of' the 4/5 as:
[tex]\frac{4}{5}\times \frac{1}{2}[/tex]
[tex]\frac{4\times1}{5\times2}[/tex]
[tex]\frac{2\times1}{5\times1}[/tex]
[tex]\frac{2}{5}[/tex]
Therefore, Amber used [tex]\frac{2}{5}[/tex]-pound of sand for the project.
Solve for c. a(b − c)=d
Find f(x) and g(x) so the function can be expressed as y=f (g (x)).
y=2/x^2 +3
How to draw a grid of area of 12 square centimeters and a perimeter of 16 centimeters?
There were three concerts in Lakeside. The first concert had 935 people in attendance. The second and third concerts each had a full house of 1,100. What was was the average number of people at the three concerts?
How do you solve this ?
width = w
length = w+8
perimieter = 256 feet
formla for perimeter is p=2L+2w
so you have: 256 =2(w+8) +2w =
256 = 2w+16 +2w
256= 4w+16
240=4w
w=240/4 = 60
width is 60 feet
length = 60+8 = 68 feet
8x-5y=-25 -2x-5y=-25
Mason deposited $763.21 in a savings account that earns 1.7% simple interest. What is Mason's account balance after nine years?
a technician charges $25 per hour plus $50 for a house call to repair home computers. Make a table and a graph to show the cost for 1 2 3 and 4 hours of home computer repair service is there a direct variation?
Answer:
Step-by-step explanation:
First, let's formulate an equation. Let the independent variable be x to denote the number of hours. The dependent variable is y to denote the total cost. The equation should be:
y = 25x + 50
The table and graph is shown in the picture. Just use values of x as 1, 2, 3 and 4, find y and plot the points.
A new business receives an invoice for merchandise on August 9. The terms of the sale are 12/10, n/30. If the manager elects to take the cash discount, what is the discount date?
Indication "12/10, n/30" (or "12/10 net 30") on an account represents a cash (sales) discount provided by the seller to the buyer for swift payment.
The term 12/10, n/30 is a classic credit term and means the following:
The discount date begins at August 9 and the last day would be August 19.
The '12/10, n/30' term means a 12% discount is given if payment is made within 10 days of the invoice date, and the entire invoice must be paid within 30 days. As such, the discount date is August 19.
Explanation:The sale terms 12/10, and n/30 in the question denote a sale transaction where the seller is offering the buyer a 12% discount if they pay the invoice within 10 days of the invoice date. The 'n/30' part means that the rest of the invoice amount needs to be paid within 30 days. So, if the manager of the new business opts to take the cash discount, the discount date falls on August 19 (the invoice date - August 9 plus 10 days).
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The function L = 0.8T^2 models the relationship between L, the length in feet of a pendulum, and T, the period in seconds of the pendulum. Which value is closest to the period in seconds for a pendulum that is 30 ft long?
a 5.4s
b 4.9s
c 6.8s
d 6.1s
A certain drug is made from only two ingredients: compound A and compound B. There are 4 millimeters of compound A used for every 7 millimeters of compound B. If a chemist uses 546 millimeters of compound B, how many millimeters of the drug will be made?
The minute hand of a clock is 4 inches long. how far does the tipof the minute hand move in 20 minnutes?
The tip of the minute hand moves approximately (8/3)π inches in 20 minutes, using the circumference of the circular path it follows and the proportion of the path covered in that time.
Explanation:The student is asking about the distance traveled by the tip of the minute hand of a clock over a 20-minute period. To find the distance, we'll consider the movement of the minute hand as part of a circular path, which is described by the arc length of the circle segment.
The length of the minute hand, which is 4 inches, acts as the radius (r) of the circle. The minute hand completes one full rotation around the clock face in 60 minutes, so in 20 minutes, it covers one-third of a full rotation. We can find the arc length of the minute hand's path using the formula for the circumference of a circle (C = 2πr), multiplied by the fraction of the rotation:
Circumference: C = 2π(4 inches) = 8π inches
Arc Length for 20 minutes: (1/3) × 8π inches = (8/3)π inches
Therefore, the tip of the minute hand moves approximately (8/3)π inches in 20 minutes.
Long Division for a quadratic polynomial and binomial, please show your work!
Quadratic polynomial: x^2-x-6=f(x)
Binomial: (x-3)
[tex]\(x^2 - x - 6\)[/tex] can be expressed as the product of [tex]\((x - 3)\) and \((x - 2)\)[/tex]. The long division image is given below.
Long division for polynomials is similar to long division for numbers. We'll divide the quadratic polynomial [tex]\(f(x) = x^2 - x - 6\)[/tex] by the binomial [tex]\((x - 3)\)[/tex].
Here's a step-by-step breakdown of the process:
1. Start by dividing the highest-degree term of the dividend (in this case, [tex]\(x^2\)[/tex]) by the highest-degree term of the divisor (in this case, [tex]\(x\))[/tex]. This gives us [tex]\(x\)[/tex].
2. Multiply the divisor [tex]\((x - 3)\)[/tex] by the result from step 1, which is [tex]\(x\),[/tex] and write the result below the dividend, aligning like terms. So, [tex]\(x \cdot (x - 3) = x^2 - 3x\)[/tex].
3. Subtract the result from step [tex]2 (\(x^2 - 3x\))[/tex] from the dividend ([tex]\(x^2 - x - 6\)[/tex]). This gives us [tex]\(x^2 - x - 6 - (x^2 - 3x)\)[/tex], which simplifies to [tex]\(-x + 3x - 6\),[/tex] resulting in [tex]\(2x - 6\)[/tex].
4. Now, we repeat the process with the new expression [tex]\(2x - 6\)[/tex]. We divide the highest-degree term ([tex]\(2x\)[/tex]) by the highest-degree term of the divisor [tex](\(x\)),[/tex] which gives us [tex]\(2\).[/tex]
5. Multiply the divisor [tex]\((x - 3)\)[/tex] by the result from step 4, which is [tex]\(2\)[/tex], and write the result below the previous result: [tex]\(2 \cdot (x - 3) = 2x - 6\)[/tex].
6. Subtract the result from step [tex]5 (\(2x - 6\))[/tex] from the previous expression [tex](\(2x - 6\))[/tex], which results in [tex]\(0\)[/tex].
Since we have a remainder of [tex]\(0\),[/tex] this means that [tex]\(x^2 - x - 6\)[/tex] is evenly divisible by [tex]\((x - 3)\)[/tex], and the quotient is [tex]\(x - 2\).[/tex] The final result is:
[tex]\[ \frac{x^2 - x - 6}{x - 3} = x - 2 \][/tex]
This tells us that [tex]\(x^2 - x - 6\)[/tex] can be expressed as the product of [tex]\((x - 3)\) and \((x - 2)\)[/tex].
If you only have a 1/3 measuring cup and a recipe calls for 8 2/3 cups of flour, how many 1/3 cups would you need to use?
Item 22 the navy pier ferris wheel in chicago has a circumference that is 56% of the circumference of the first ferris wheel built in 1893. what was the radius of the first ferris wheel?
a) The radius of the navy pier wheel is 70 feet.
b) The radius of the first ferris wheel is 125 feet.
c) The speed of the wheel is 87.2 ft/sec
Given data:
The circumference of circle = 2πr
The area of the circle = πr²
a)
The circumference = 2πr
where π = 3.142
r = radius
Therefore, 2πr = 439.6
(2 * 3.142 * r) = 439.6
6.284r = 439.6
On simplifying the equation:
Radius = 439.6/6.284
Radius = 69.9
≈ 70 feet
b)
The Navy Pier Ferris Wheel in Chicago has a circumference that is 56% of the circumference of the first Ferris wheel.
So, 56% of f = 439.6
0.56f = 439.6
f = 439.6/0.56
f = 785
The circumference of the first wheel is 785 feet.
Now, 2πr = 785
r = 785/2π
r = 785/(2×3.142)
r = 785/6.284
r = 124.9
≈ 125ft
c)
The first ferris wheel took nine minutes to make a complete revolution.
So, the speed of wheel is determined as:
s = 785/9
s = 87.2 ft/sec
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The complete question is attached below:
If the navy pier ferris wheel in chicago has a circumference that is 56% of the circunference of the first ferris wheel built in 1893.
a. What is the radius of the navy pier wheel?
b. what was the radius of the first ferris wheel?
c. The first ferri wheel took nine minutes to make a complete revolution. how fast was the wheel moving?
C=439.6 ft.
How do I do these only need to do 1 I just need to see how to do it!
Lets do the first one(7). Fist change 10x -2y = 3,which is in standard form to point slope form so you can see the slope.
10x - 2y = 3
-2y = -10x + 3
-2y/-2 = -10x / -2 + 3/-2
y = 5x - 3/2
The slope is the m in y = mx + b so our slope is 5x, well it wants you to find the equation of a line that passes through (0,1) that is parallel to the equation this (Parallel) mean has the same slope.The slope is 5. Now that we know the slope is 5 we can find the equation by using the point slope form of an equation of a line.
point slope form = y – y1 = m(x – x1)
Remember m = slope = 5. Now plugin our x and y cord from the point (0,1) and our slope of 5
y - y1 = m(x - x1)
y - 1 = 5(x - 0)
y - 1 = 5x - 0
y - 1+1 = 5x + 1
y= 5x + 1
So the point (0,1) passes through y = 5x + 1
Number 8 is already in slope intercept form so you don't have to do anything to find the slope. You can see that the slope is 7 so just plug your point into y - y1 = m(x - x1) and then put it into slope intercept form.
8)
Point = (5,8)
Slope = 7
y - y1 = m(x - x1)
y - 8 = 7(x - 5)
y = 7x - 27
So for number 8 the point (5,8) passes through y = 7x - 27
(9) For nine they want an equation that is perpendicular, which means to flip the slope. For instance, if you have a slope of 2/5 the perpendicular slope would be 5/2. For 9 we see that the slope is 2/5 so its perpendicular slope would be 5/2. Now just plug your point into the point slope form equation.
Point = (-4, 6)
Slope = 2/5
perpendicular slope = 5/2
y - 6 = 5/2(x - (-4))
y = 5/2 x + 16
So point (-4, 6) passes through y = 5/2 x + 16
(10) Point (4,1) passes through y = 7/5 x - 23/5
Four times the difference of a number and seven is 32
which ordered triple is a solution of this system 2x+y-z=7
-x-2y+4z=-15
x+2y-5z=17
How do you find vertical asymptotes?
Final answer:
To find vertical asymptotes of a function, factor the denominator, set each factor equal to zero, and solve for x.
Explanation:
To find vertical asymptotes of a function, we need to determine the values of x that make the function approach infinity or negative infinity. Vertical asymptotes occur when the function approaches these values but never reaches them.
To find the vertical asymptotes, follow these steps:
Factor the denominator of the function.
Set each factor equal to zero and solve for x.
The values of x obtained in step 2 are the vertical asymptotes.
For example, let's find the vertical asymptotes of the function f(x) = 1/x. The denominator is x, which is already factored. Setting x = 0, we find that x = 0 is the vertical asymptote.
Graph the image of the given triangle after the transformation with the rule (x, y)→(y, x) .
The perimeter of a rectangle is 44 inches, and its area is 105 square inches. find the length and width of the rectangle.
Enter the equation of the line meeting the given conditions. Please put the equation in standard form. Containing A(5, 3) and perpendicular to a line with slope of -2
Answer:
x - 2y = -1
this is correct
Please help with this
The answer to the statement is:
TRUE
Step-by-step explanation:In order for a segment to form a triangle.
The sum of the lengths of any two sides of a triangle must be greater than the length of the remaining third side of the given triangle.
Here we have three segments of length:
7 units, 9 units and 12 units.
Also, for any two pair:
7 and 9 we have:
7+9=16> 12
for 9 and 12 we have:
9+12=21>7
and for 7 and 12 we have:
7+12=19>9
Hence, the segments could form a triangle.
I NEED HELP ASAP
Definition: This is an expression that includes monomials, binomials and more. There is no limit to the number of terms.
Example: 2x+ 3y+ 4xy+ 5xyz What is the term?
A waffle cone for ice cream has a diameter of 8 centimeters and a height of 12 centimeters. What is the volume of the cone, in cubic centimeters?
A. 64π cubic centimeters
B. 32π cubic centimeters
c. 256π cubic centimeters
D. 192π cubic centimeters
Casandra finds a treasure chest packed with metallic coins. The chest has a volume of 0.25 cubic meters. The coins have a combined mass of 4825 kg. Hoping to find gold, she calculates the density to determine the metal of the coins.
What kind of metal are the coins made of?
Bronze (8700 kg per cubic meter)
Silver (10500 kg per cubic meter)
Lead (11300 kg per cubic meter)
Gold (19300 kg per cubic meter)
A cylinder with radius 3 units is shown. Its volume is 86 cubic units.
Find the height of the cylinder.
Use 3.14 for π and round your final answer to the nearest hundredth.
Answer:
A. 64π cubic centimeters
D. Gold (19300 kg per cubic meter)
The height of the cylinder is 3.04 unit
Step-by-step explanation:
A waffle cone for ice cream has a diameter of 8 centimeters and a height of 12 centimeters. What is the volume of the cone, in cubic centimeters?
A. 64π cubic centimeters
B. 32π cubic centimeters
c. 256π cubic centimeters
D. 192π cubic centimeters
EXPLANATION
Volume of a cone is given by the formula V=[tex]\frac{\pi*r^{2}*h }{3}[/tex]
V = [tex]\frac{\pi *4^{2}*12 }{3}[/tex] = 64π
The correction option is A
Casandra finds a treasure chest packed with metallic coins. The chest has a volume of 0.25 cubic meters. The coins have a combined mass of 4825 kg. Hoping to find gold, she calculates the density to determine the metal of the coins.
What kind of metal are the coins made of?
Bronze (8700 kg per cubic meter)
Silver (10500 kg per cubic meter)
Lead (11300 kg per cubic meter)
Gold (19300 kg per cubic meter)
the formula for Density is density = mass/volume
The density of the metal = 4825/0.25 = 19,300kg.
Therefor the coins are made of Gold
The correction option is D
A cylinder with radius 3 units is shown. Its volume is 86 cubic units.
Find the height of the cylinder.
Use 3.14 for π and round your final answer to the nearest hundredth.
The volume of a cylinder is given as V= πr^2h
86 =3.14 * 3^2*h
Make h the subject of the formula h =86/(3.14*9) =86/28.26 =3.04 unit
The height of the cylinder is 3.04 unit
Write and solve an equation to determine how many degrees the temperature TT fell. The temperature at 5 P.M. is 20∘20∘
f. The temperature at 10 P.M. is −5∘−5∘F
To find how much the temperature fell, we created an equation using the given temperatures at 5 P.M. and 10 P.M. We subtracted the temperature at 10 P.M. from the one at 5 P.M. and found the temperature fell by 25 degrees.
Explanation:The subject of this question is Mathematics and this question is for the Middle School grade level.
To solve this problem, we can create an equation using the given information about the temperature at two different times. At 5 P.M., the temperature (let's assume T1) is 20∘F. At 10 P.M., the temperature (let's assume T2) is -5∘F. Therefore, to find how much the temperature fell, we subtract the temperature at 10 P.M. from the temperature at 5 P.M., so the equation would be T1 - T2.
Substitute the temperatures into the equation: 20 - (-5) = 20 + 5 = 25.
Therefore, the temperature fell by 25 degrees.
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PLEASE HELP?!
Both trapezoids are similar. The area of the larger trapezoid is 61 ft2. Which is the best approximation for the area of the smaller trapezoid?
39 ft2
34 ft2
49 ft2
44 ft2
The best approximation for the area of the smaller trapezoid is 39 [tex]ft^2[/tex].
Since the trapezoids are similar, the ratio of their corresponding side lengths is constant. We know the base of the larger trapezoid is 30 ft and the smaller one is 24 ft. Therefore, the ratio of their bases is:
ratio of bases = [tex]\frac{30 ft}{24 ft}[/tex] = [tex]\frac{5}{4}[/tex]
The area of a trapezoid is given by:
Area = [tex]\frac{1}{2}[/tex] * base * height
For similar shapes, the ratio of their areas is proportional to the square of the ratio of their corresponding side lengths. In this case, the ratio of areas will be:
Ratio of areas = [tex](Ratio \ {of \ { bases)^2[/tex] = [tex]({\frac{5}{4} })^2[/tex] = [tex]\frac{25}{16}[/tex]
We know the area of the larger trapezoid is 61 [tex]ft^2[/tex]. Applying the ratio of areas:
Area of smaller trapezoid = (61 [tex]ft^2[/tex]) * [tex]\frac{16}{25}[/tex]
Area of smaller trapezoid ≈ 38.91 [tex]ft^2[/tex] ≈ 39[tex]ft^2[/tex]
An exhibit at Tabu World Square in Japan includes a scale model of the Empire State Building. The model was built using a scale of 1 m : 25 m. The height of the actual Empire State Building is 443.2 meters. What is the height of the model? Round your answer to the nearest thousanths place.
What is the decimal equivalent of this percent? 2691%