To simplify the expression −4(−11+4n)−3(−2n+9), you distribute the multiplication and then combine like terms to get the equivalent expression +17−10n.
Explanation:The student has asked to simplify the expression −4(−11+4n)−3(−2n+9). To simplify this expression, we need to distribute the numbers outside the parentheses across the terms inside the parentheses. We'll do this step by step.
Multiply −4 by −11 to get +44.Multiply −4 by +4n to get −16n.Multiply −3 by −2n to get +6n.Multiply −3 by +9 to get −27.Now combine like terms:
Add +44 and −27 to get +17.Add −16n and +6n to get −10n.So, the simplified equivalent expression is +17−10n.
the simplified and equivalent expression is 17 - 10n.
We need to simplify the expression:
[tex]-4(-11+4n)-3(-2n+9)[/tex]
To do this we need to open the brackets which gives us:
[tex]-4(-11+4n)-3(-2n+9) = 44 -16n + 6n -27[/tex]
Now we can solve the expression as follows:
[tex]-4(-11+4n)-3(-2n+9) = (44 - 27) + (-16n + 6n)\\\\ -4(-11+4n)-3(-2n+9) =17 - 10n[/tex]
So, the simplified and equivalent expression is 17 - 10n.
Need help ASAP !!!!
an ellipse has a center of (3,1), a focus of (8,1) and a directrix of x = 36.8. what is the equation of the ellipse?
hmmm was going to do a quick mockup, but it might be too wide, so let's nevermind that piece.
so let's see, the center of this ellipse is at (3,1), and a focus point is at (8,1), notice, the y-coordinate is the same, meaning the distance between those two points is "c", which is 5, so c = 5.
We also know that the directrix is x = 36.8, well, that's a vertical line, if the line is vertical, that means the ellipse is running perpendicular to that, namely it has a major axis over the x-axis, so is horizontal.
[tex]\bf \textit{ellipse, horizontal major axis} \\\\ \cfrac{(x- h)^2}{ a^2}+\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2- b ^2}\\ eccentricity\quad e=\cfrac{c}{a}\\\\ directrix=h\pm \cfrac{a^2}{c} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf \stackrel{\textit{its directrix}}{x=h\pm\cfrac{a^2}{c}}\implies \stackrel{\textit{using one directrix}}{36.8=h+\cfrac{a^2}{c}}\qquad \begin{cases} h=3\\ k=1\\ c=5 \end{cases}\implies 36.8=3+\cfrac{a^2}{5} \\\\\\ 33.8=\cfrac{a^2}{5}\implies \boxed{169=a^2}\implies 13=a \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \stackrel{\textit{recall that }}{c=\sqrt{a^2-b^2}}\implies 5=\sqrt{169-b^2}\implies 5^2=169-b^2\implies 5^2+b^2=169 \\\\\\ b^2=169-5^2\implies \boxed{b^2=144}\implies b=12 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \cfrac{(x-3)^2}{169}+\cfrac{(y-1)^2}{144}=1~\hfill[/tex]
Answer:
a on edgn btw
Step-by-step explanation:
Please help as soon as possible !! Thanks you
There is a right triangle. One leg is (x+3)ft long, the other leg is (x+5)ft long. The area is 24 sq ft. What does x equal? What is the perimeter? Show your work.
Step-by-step explanation:
[tex]area = \frac{1}{2} (x + 3)(x + 5) = 24 \\ [/tex]
then
[tex](x + 3)(x + 5) = 48[/tex]
[tex] {x}^{2} + 8x + 15 = 48 [/tex]
[tex] {x}^{2} + 8x + 15 - 48 = 0 \\ {x}^{2} + 8x - 33 = 0[/tex]
[tex] {x}^{2} - 3x + 11x - 33 = 0 \\ x(x - 3) + 11(x - 3) = 0 \\ (x - 3)(x + 11) = 0[/tex]
so
[tex]x = 3 \: or \: x = - 11(reject \: because \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x > 0)[/tex]
hence,
[tex]x = 3[/tex]
Thus, one leg is 8 and other leg is 6.
Since it is a right triangle then we have
[tex]hypotenuse = \sqrt{ {8}^{2} + {6}^{2} } = \sqrt{100} = 10[/tex]
Finally,
[tex]perimeter = 8 + 6 + 10 = 24(ft)[/tex]
find the area of this figure
Answer: 125 squared ft
Area of the big rectangle ⬜️, 15ft x 10ft = 150 square ft
Area of the small square(which is spaced), 5ft x 5ft = 25 squared ft
Area of the give figure, 150squared ft- 25squared ft = 125 squared ft
Answer:
The answer is 125ft
Cᴀɴ sᴏᴍᴇᴏɴᴇ ᴇxᴘʟᴀɪɴ ʜᴏᴡ ᴛᴏ ᴅᴏ 1 ᴀɴᴅ 2
Answer:
1.
Experimental : [tex]\frac{14}{25}[/tex] or 56%
Theoretical : [tex]\frac{1}{2}[/tex] or 50%
2.
22 customers
Step-by-step explanation:
Theoretical is how many times you'd expect it to land. So for coin flipping it would be either heads or tails. The probability it would land on heads would be 50% because it's either one or the other.
Experimental is how many times you actually landed it. You flipped a coin and it landed on heads 28 times, so you can put that over 50.
Since [tex]\frac{28}{50}[/tex] can be simplified to [tex]\frac{14}{25}[/tex] or 56%, that is the experimental probability.
For the second variation, we can assume that it is direct variation.
[tex]y=kx[/tex]
When [tex]y[/tex] increases, [tex]x[/tex] increases.
Let's solve for [tex]k[/tex].
[tex]11=50k \\ \\ k=\frac{11}{50}[/tex]
We can plug that in to the second equation since we already know how many customers there will be.
[tex]y=0.22k \\ \\ y=0.22(100) \\ \\ y=22[/tex]
What is the shape of the cross section of the figure that is perpendicular to the rectangular base but does not pass through the top vertex?
A a parallelogram that is not a rectangle
B a rectangle
C a triangle
D a trapezoid
Answer:
I'm pretty sure its a Trapezoid but don't quote me
Step-by-step explanation:
I don't really know
The shape of the cross section of the figure that is perpendicular to the rectangular base but does not pass through the top vertex is a rectangle.
What is a rectangle?A rectangle is a quadrilateral (having four sides and four angles) in which opposite sides are equal and parallel. The diagonals bisect each other, and each angle measures 90 degrees.
The shape of the cross section of the figure that is perpendicular to the rectangular base but does not pass through the top vertex is a rectangle.
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What does F equal???
Answer:
F=10
Step-by-step explanation:
Which odd number have 3 as a factor
Answer: 3, 21, 9, 15, ... any thing you can divide three with
Step-by-step explanation:
Step-by-step explanation:
The odd number whose a factor is the number 3 is a positive odd multiple of 3:
3, 9, 15, 21, 27, 33, 39, 45, 51, 57, ...
An orange juice company sells a can of frozen orange juice that measures 9.4 centimeters in height and 5.2 centimeters in diameter. The company wants to sell a larger can of juice. The height of the can is kept at 9.4 cm, but the diameter is increased to 8.5 cm. About how many times more juice will the new can hold?
Image is the same question w/ a model.
The answer is:
The third option:
2.7 times as much.
Why?To calculate how many more juice will the new can hold, we need to calculate the old can volume to the new can volume.
So, calculating we have:
Old can:
Since the cans have a right cylinder shape, we can calculate their volume using the following formula:
[tex]Volume_{RightCylinder}=Volume_{Can}=\pi r^{2} h[/tex]
Where,
[tex]r=radius=\frac{diameter}{2}\\h=height[/tex]
We are given the old can dimensions:
[tex]radius=\frac{5.2cm}{2}=2.6cm\\\\height=9.4cm[/tex]
So, calculating the volume, we have:
[tex]Volume_{Can}=\pi *2.6cm^{2} *9.4cm=199.7cm^{3}[/tex]
We have that the volume of the old can is:
[tex]Volume_{Can}=199.7cm^{2}[/tex]
New can:
We are given the new can dimensions, the diameter is increased but the height is the same, so:
[tex]radius=\frac{8.5cm}{2}=4.25cm\\\\height=9.4cm[/tex]
Calculating we have:
[tex]Volume_{Can}=\pi *4.25cm^{2} *9.4cm=533.40cm^{3}[/tex]
Now, dividing the volume of the new can by the old can volume to know how many times more juice will the new can hold, we have:
[tex]\frac{533.4cm^{3} }{199.7cm^{3}}=2.67=2.7[/tex]
Hence, we have that the new can hold 2.7 more juice than the old can, so, the answer is the third option:
2.7 times as much.
Have a nice day!
Joshua eat 3/8 of a pizza trevor eats 1/2 of a pizza how much of the pizza did they eat?
Answer:
7/8ths of a pizza.
Step-by-step explanation:
3/8 + 1/2
Find the LCD and then combine.
7/8 in exact form, and 0.875 as a decimal.
In the table below, x represents the miles traveled and y represents the cost to travel by train.
Miles, x
Cost, y
2
8.50
5
15.25
8
22.00
12
31.00
What is the slope of this function?
0.44
0.63
2.25
22.50
Answer:
Third option
m = 2.25
Step-by-step explanation:
The slope of the function is equal to its rate of change between two points.
For example, for a couple of points [tex](x_1, y_1),\ (x_2, y_2)[/tex]
The slope is:
[tex]m =\frac{y_2-y_1}{x_2-x_1}[/tex]
In this problem we have the following points
1.(2, 8.50) , 2. (5, 15.25), 3. (8, 22.00) , 4. (12, 31.00)
We calculate the slope between the first two points
[tex]m =\frac{15.25-8.50}{5-2}=2.25[/tex]
We calculate the slope between the points 3 and 4
[tex]m =\frac{31-22}{8-4}=2.25[/tex]
We calculate the slope between the points 2 and 3
[tex]m =\frac{22-15.25}{8-5}=2.25[/tex]
The slope is always the same. Therefore m is constant and the fution is a line of slope m = 2.25
Answer:it’s C 2.25
Step-by-step explanation:
Plz help me with this
Answer: [tex]\bold{d)\quad y = 3 cos (\dfrac{4}{3}x-2\pi) + 2}[/tex]
Step-by-step explanation:
[tex]\text{Period = }\dfrac{2\pi}{B}\\\\\\\dfrac{1}{2}\text{Period = }\dfrac{1}{2}\cdot \dfrac{2\pi}{B}\quad =\dfrac{2\pi}{2B}\\\\\\\text{In the given equation, B = }\dfrac{2}{3}\implies 2B=\dfrac{2\cdot 2}{3}\quad =\dfrac{4}{3}\\[/tex]
The only option that has B = 4/3 is the last one.
NEED HELP ASAP, WILL GIVE 5 STARS AND BRAINLIEST!!!
Of the boys surveyed, more prefer cats. Of the girls survey, more prefer dogs. The does appear to be an association between gender and animal preference.
How to classify the association between variables?In this problem, we have that boys and girls have different preferences regarding animals, that is, from the table:
More boys prefer cats.More girls prefer dogs.Hence there does appear to be an association between gender and animal preference.
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Which of the following is 6(x+4)(x+3)/24(x-3)(x+4) simplified
Answer:
[tex]\frac{6\left(x+4\right)\left(x+3\right)}{24\left(x-3\right)\left(x+4\right)}=\frac{x+3}{4\left(x-3\right)}[/tex]
[tex]\mathrm{Cancel\:the\:common\:factor:}\:6\\=\frac{\left(x+4\right)\left(x+3\right)}{4\left(x-3\right)\left(x+4\right)}\\\mathrm{Cancel\:the\:common\:factor:}\:x+4[/tex]
Hope this helps!!!
[tex]Sofia[/tex]
What is true about the number 480,516? Check all that apply.
The 8 is in the thousands place.
The 5 is in the hundreds place.
The number is read as "four hundred eight thousand, five hundred sixteen."
480,516 is equivalent to 400,000 + 8,000 + 500 + 10 + 6
480,516 is equivalent to 400,000 + 80,000 + 500 + 10 + 6
It’s the second answer and the last answer :)
Answer:
The 5 is in the hundreds place.
480,516 is equivalent to 400,000 + 80,000 + 500 + 10 + 6
Step-by-step explanation:
Can someone check over my answers? Thanks!
Answer:
Yes, I just checked it. All of it is right!
Step-by-step explanation:
Good Job!!
Order of Operations 4
Use the correct order of operations to evaluate each expression.
choices
-4
-6
1
4
20
21
Answer:
1. 21
2. -4
3. 20
4. 1
5. 4
6. -6
Step-by-step explanation:
if the radius of a circle is 4.25 feet, what is the diameter? and if x= -5 and y=2x^2, then y=
The diameter is 8.5 feet
The Y is 100
What is the area of a triangle with a=2, b=7, and c=8?
Answer:
6.44
Step-by-step explanation:
A=1/ 4 divided by﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4 =1/ 4· divided by﹣24+2·(2·7)2+2·(2·8)2﹣74+2·(7·8)2﹣84 ≈6.4372
Sorry if it's a little complicated but that's how I learned it
Answer:
c.
6.4 units
Step-by-step explanation:
If k is parallel to l find the value of a and the value of b.
Answer:
a = 30
b = 40
C
Step-by-step explanation:
This requires that you use a proportion.
a / (a + 15) = 40 / 60
The small triangle's sides are in proportion to the large triangles sides.
Reduce the right. Divide top and bottom by 20
a/(a + 15) = 40/20 // 60/20
a/(a + 15) = 2/3
Cross multiply
3a = 2(a + 15) Remove the brackets on the right.
3a = 2a + 30
Subtract 2a from both sides
3a-2a = 30
a = 30
Find B
b is done exactly the same way.
b/(b+20) = 2/3
3b = 2b + 40
3b - 2b = 40
b = 40
What is the second term of the sequence defined by the recursive rule f(1)=3,f(n)=f(n-1)+5
Answer:
8
Step-by-step explanation:
To obtain the second term substitute n = 2 into the recursive rule, that is
f(2) = f(2 - 1) + 5 = f(1) + 5 = 3 + 5 = 8
below is the price listed for different sized pizzas
Answer:
the answer is c not sure if right
What is the area of the trapezoid below?
Answer:
684
Step-by-step explanation:
A=a+b
2h=26+46
2·19=684
Answer:
684 m²
Step-by-step explanation:
The area (A) of a trapezoid is calculated using the formula
A = [tex]\frac{1}{2}[/tex] h (a + b)
where h is the perpendicular height and a, b the parallel bases
here h = 19, a = 46 and b = 26
A = [tex]\frac{1}{2}[/tex] × 19 × (46 + 26)
= 9.5 × 72 = 684 m²
Which statements about the graph are true? Check all that apply. The vertices are at (–3, 0) and (1, 0). The distance between the center and each covertex is 2. The distance between the center and each focus is about 2.2 units. The directrices are about 4 units from the center. Both directrices are vertical lines.
Answer:
2, 3, and 4
Step-by-step explanation:
BRAINLIEST + POINTS!
A spring has spring constant 0.3 m/newton. What force is necessary to stretch the spring by 1.5 meters?
If 1 newton pushes it 0.3 meters, it would take 1.5 / 0.3 newtons, or 5 newtons to push it 1.5 meters
Answer: 5 Newton
Step-by-step explanation:
We know that the Hooke's law states that the force 'F' needed to stretch or compress a spring by some distance 'a' is proportional to that distance .
[tex]F=\dfrac{a}{c}[/tex], where c is the spring constant.
Given: A spring has spring constant 0.3 m/newton.
The force is necessary to stretch the spring by 1.5 meters is given by :-
[tex]\Rightarrow\ F=\dfrac{1.5}{0.3}\\\\\Rightarrow\ F=5[/tex]
Hence, the force is necessary to stretch the spring by 1.5 meters = 5 Newton .
Mr. Pham mowed 2\7 of his lawn. his son mowed 1\4 of it. Who mowed the most. How much of his lawn still needs to be mowed.
Answer:
The father did more.
13/28 needs to be mowed which is 0.4643 of the lawn needs to be mowed.
Step-by-step explanation:
The best way to compare the two is to change them to decimals. That will at least answer who mowed the most.
Father: 2/7 = 0.2857
Son: 1/4 = 0.25
Since the father mowed 2/7 of the lawn, he mowed the most.
You can use the decimals to get the second part.
Together they did 0.25 + 0.2857 = 0.5357
The amount of the lawn left is 1 - 0.5357 = 0.4643
================
If you must have this in fractions then
1/4 + 2/7 = 7/28 + 2*4/28 = 7/28 + 8/28 = 15/28
15/28 = 0.5357 which is just what we got above.
Amount left to do = 1- 15/28 = 13/28
13/28 = 0.4643 which is what we got about.
An opaque bag contains 5 green marbles 3 blue marbles and 2 red marbles. What is the probability of randomly picking out a marble and the marble being red?
Answer= .2 probability
Explanation: Since there is a total of 10 marbles, and 2 are red, you would divide the red marbles (2) out of the total marbles (10) which would get u .2. Since it’s asking for probability, we would keep .2 a decimal.
The probability of randomly picking a red marble from the bag is 2 out of 10, or 0.2 when expressed as a decimal, which equates to a 20% chance.
Explanation:The subject of the question you asked is mathematics, specifically probability. In order to calculate the probability of an event happening, you divide the number of successful outcomes by the total number of outcomes. In this case, the successful outcome would be picking a red marble.
The total number of marbles in the bag is 5 (green) + 3 (blue) + 2 (red) = 10. The successful outcomes are 2 (the red marbles). Therefore, the probability of picking a red marble is 2/10 or 0.2.
To put this as a percentage, you multiply by 100, so the probability is 20%. This means that if you pick a marble out at random, there is a 20% chance that it will be red. This is assuming that after each pick, you put the marble back in the bag, also known as picking 'with replacement'.
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determine the domain of the function in the correct set notation. f(x)=1 /2×+6
Answer:
First one.
Step-by-step explanation:
The domain of the function in the correct set notation is {x|x∈R x≠-3}.
What is a domain?The domain of a function is the set of all possible inputs that the function can have.
We can find the domain as follows:The function is given to be f(x)=1 /(2x+6).
Here, we can see that the function would become not be defined if the denominator becomes zero.
Therefore, the domain should not contain the values which make it not defined.
The value of x for which it becomes zero can be determined below:
2x+6=0
2x=-6
x=-3
Therefore, the domain must contain all values of real numbers except -3.
The domain of the function is found. The domain of the function is the set of all real numbers except -3. It can be written as {x|x∈R x≠-3}.
Therefore, we have found the domain of the function in the correct set notation is {x|x∈R x≠-3}.
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The figure below is a net for a triangular prism. Side a = 45 inches, side b = 14 inches, side c = 30 inches, and altitude d = 20 inches. What is the surface area of this figure?
A. 2,370 square inches
B. 1,950 square inches
C. 3,000 square inches
D. 2,790 square inches
The surface area of the triangular prism is 1950 square inches, computed by summing the areas of its constituent triangles and rectangles.
Surface area refers to the measure of the total area that the surface of an object occupies. It is a crucial geometric concept that varies for different shapes and dimensions in geometry, encompassing diverse forms like spheres, cubes, cuboids, cones, and cylinders. Each geometric shape possesses unique formulas for calculating its surface area.
Considering the provided net for a triangular prism with side lengths a, b, and c, and altitude d, the surface area is computed by summing the areas of its constituent shapes – two triangles and three rectangles. The formula for the total surface area is given as:
Total Surface Area = Surface Area of Triangle + Surface Area of Rectangle
Detailed calculations involve substituting the given values for side lengths and altitude into the formulas for the surface area of a triangle and a rectangle. For the triangular prism described, the total surface area is determined as:
Total Surface Area = d * a + b * a + 2 * c * b
Substituting the given values (d = 20, a = 44, b = 14, and c = 30), the calculation yields:
Total Surface Area = (22 * 45) + (12 * 45) + 2 * (30 * 14) = 1950
Therefore, the surface area of the given figure is 1950 square inches.
Final answer:
The surface area of the triangular prism is calculated by adding the areas of the two triangular faces and three rectangular faces. Upon calculation, the areas of two triangles are 600 square inches, and the rectangles are 900 and 280 square inches for sides a and b, respectively. However, none of the provided answer choices match the calculated surface area of 1780 square inches.
Explanation:
To find the surface area of a triangular prism, we need to find the area of all its faces. We have two triangular faces and three rectangular faces. The area of each triangular face is calculated using the formula A = bh/2, where b is the base and h is the height. Since side c is 30 inches and the altitude d is 20 inches, the area of one triangular face is:
A triangle = (c x d) / 2
= (30 inches x 20 inches) / 2
= 600 / 2
= 300 square inches
Since there are two triangular faces, we double this to get 600 square inches for both.
The rectangular faces consist of the sides a, b, and c. Their areas are a x d, b x d and c x d, respectively. So we calculate:
Side a: 45 inches x 20 inches = 900 square inches
Side b: 14 inches x 20 inches = 280 square inches
Side c (already computed as part of triangular faces)
Sum the areas of all these faces to get the total surface area:
Total surface area = (Area of triangles) + (Area of rectangles)
= 600 square inches (triangles) + 900 square inches (side a) + 280 square inches (side b)
= 1780 square inches
The correct answer must include the area of both triangular faces and all three rectangular faces. Since none of the given options match the computed total surface area, it's possible there may have been an error in the provided options or in the dimensions given for the prism.
what is the value of the 7 in the number 2 741 203?
Answer:
700,000
Step-by-step explanation:
2 = million
7 = hundred thousands
4 = ten thousands
1 = thousands
2 = hundreds
0 = tens
3 = ones
I hope I helped!
Let me know if you need anything else!
~ Zoe