Answer:
optioc C [tex]10^{2}[/tex]
Step-by-step explanation:
we know that
Hecto (h) is a decimal unit prefix in the metric system denoting a factor of one hundred
so
[tex]h=100=10^{2}[/tex]
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:
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.
More can be learned about association between variables at brainly.com/question/16355498
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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:
I say trapezoidal prism. Am I right! Thanks
The correct answer is:
D=Trapezoidal Prism
Yep! You're right!
It is trapezoidal prism.
Parallelogram abcd has verticals at A(0,0), B(3,6), C(5,5) and D(2,-1) which conclusion can be made ?
Answer:
A.
Step-by-step explanation:
when you plot the vertices;
Side AB is perpendicular to side BC
Side AB is parallel to side DC
Side AC is perpendicular to AB
Side AC is perpendicular to DC
Side AC is parallel to side BC
The conclusion made is that ABCD is a rectangle
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.
The heights of the trees in a forest are normally distributed, with a mean of 25 meters and a standard deviation of 6 meters. What is the probability that a randomly selected tree in the forest has a height greater than or equal to 37 meters? Use the portion of the standard normal table given to help answer the question.
z. Probability
0.00. 0.5000
0.50. 0.6915
1.00. 0.8413
2.00. 0.9772
3.00. 0.9987
0.13%
0.26%
2.3%
4.6%
Answer:
2.3%
Step-by-step explanation:
The formula to convert x into z distribution is
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Where z is the test statistic
x is what we are looking for (in this case 37)
[tex]\mu[/tex] is the mean (in this case, it is 25)
[tex]\sigma[/tex] is the standard deviation (we have 6)
Plugging these into the formula, we get:
[tex]z=\frac{x-\mu}{\sigma}\\z=\frac{37-25}{6}\\z=2[/tex]
Thus we can say we want [tex]P(z\geq 2)[/tex]
Note: [tex]P(z\geq a)=1-P(z\leq a)[/tex]
The table given is for any z where [tex]P(z\leq a)[/tex]
Thus, now we have:
[tex]P(z\geq 2)\\=1-P(z\leq 2)\\=1-0.9772\\=0.0228\\[/tex]
0.0228 into percentage is 0.0228 * 100 = 2.28%
Rounded, we get 2.3%
Third answer choice is right.
Answer:
C fosho
Step-by-step explanation:
GL on tests/exams
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
4 times 10
a . 2
b . 7
c . 40
d .97
Answer:
40
Step-by-step explanation:
10
x 4
=40
Answer:
4*10 = C. 40
Step-by-step explanation:
Add 10 4 times and get 40!!
SIMPLE HOPE IT HEPLS PLEASE MARK BRAINLIST!!
below is the price listed for different sized pizzas
Answer:
the answer is c not sure if right
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]
Help ASAP 2 questions!!!!!!
20 point (10 for each hopefully)
1
2
Answer:
Step-by-step explanation:
1. We aren't worried about the area of the base, so the area is the area of the 4 triangles. Each triangle has an area of half the base times the height.
A = 4 (½ bh)
A = 2 bh
Given b = 6 and h (the height of the triangle, not the pyramid) = 5:
A = 2 (6) (5)
A = 60 ft²
2. This time, we want to include the area of the rectangular base, so:
A = b₁b₂ + 2 (½ b₁h₁) + 2 (½ b₂h₂)
A = b₁b₂ + b₁h₁ + b₂h₂
Given b₁ = 78 m, b₂ = 50 m, h₁ = 52 m, and h₂ = 60 m:
A = (78) (50) + (78) (52) + (50) (60)
A = 10,956 m²
Which expression is 5 times as large as the expression 345+23
Answer:
1840
Step-by-step explanation:
345+23=368*5
Answer: 1840
Step-by-step explanation:
you add 345 + 23 and multiply by 5
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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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 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:
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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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:
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
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]
In the morning, the temperature starts out around 50° F. As the day goes on, the temperature rises first slowly, then more quickly. It stays constant for an hour before dropping slowly. Select the graph that best represents this description
Answer:
Graph A.
Step-by-step explanation:
We will try to understand the graph plotted for the change in temperature for whole day.
In the morning, temperature starts out around 50°F. As the day goes on, the temperature rises first slowly- Slope of the first line will be less.
Then temperature rises more quickly - Slope of the second line will be more than first line.
It stays constant for an hour- third line will be parallel to the x-axis for one hour gap.
Then the temperature dropped down slowly - Last line of the graph will go down.
By the understanding we made for the graph we find graph A is the answer.
Answer:
the top left graph
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.
Solving for matrices
Answer:
D
Step-by-step explanation:
The augmented matrix for the system of three equaitons is
[tex]\left(\begin{array}{ccccc} 3&-4&-5&|&-27\\5&2&-2&|&11\\5&-4&4&|&-7\end{array}\right)[/tex]
Multiply the first row by 5, the second row by -3 and add these two rows:
[tex]\left(\begin{array}{ccccc} 3&-4&-5&|&-27\\0&-26&-19&|&-168\\5&-4&4&|&-7\end{array}\right)[/tex]
Subtract the third row from the second:
[tex]\left(\begin{array}{ccccc} 3&-4&-5&|&-27\\0&-26&-19&|&-168\\0&6&-6&|&18\end{array}\right)[/tex]
Divide the third row by 6:
[tex]\left(\begin{array}{ccccc} 3&-4&-5&|&-27\\0&-26&-19&|&-168\\0&1&-1&|&3\end{array}\right)[/tex]
Now multiply the third equation by 26 and add it to the second row:
[tex]\left(\begin{array}{ccccc} 3&-4&-5&|&-27\\0&-26&-19&|&-168\\0&0&-45&|&-90\end{array}\right)[/tex]
You get the system of three equations:
[tex]\left\{\begin{array}{r}3x-4y-5z=-27\\-26y-19z=-168\\-45z=-90\end{array}\right.[/tex]
From the third equation
[tex]z=\dfrac{90}{45}=2.[/tex]
Substitute z=2 into the second equation:
[tex]-26y-19\cdot 2=-168\\ \\-26y-38=-168\\ \\-26y=-168+38=-130\\ \\y=\dfrac{130}{26}=5.[/tex]
Now substitute z=2 and y=5 into the first equation:
[tex]3x-4\cdot 5-5\cdot 2=-27\\ \\3x-20-10=-27\\ \\3x-30=-27\\ \\3x=-27+30=3\\ \\x=1.[/tex]
The solution is (1,5,2)
The correct answer is option d (1, 5, 2).
To solve the system of equations, let's write the augmented matrix and perform row operations to get it into reduced row-echelon form (RREF). The system of equations is as follows:
3x−4y+5z (1)
5x+2y−2z (2)
5x−4y+4z (3)
The augmented matrix for this system is:
[tex]\left[\begin{array}{ccc}3&-4&5&|27\\5&2&-2&|11\\5&-4&4&|7\end{array}\right][/tex]
Now, let's perform row operations to get the reduced row-echelon form:
Subtract 5 times the first row from the second row:
[tex]\left[\begin{array}{ccc}3&-4&5&|27\\0&22&-27&|-134\\5&-4&4&|7\end{array}\right][/tex]
Subtract 5 times the first row from the third row:
[tex]\left[\begin{array}{ccc}3&-4&5&|27\\0&22&-27&|-134\\0&16&-21&|-118\end{array}\right][/tex]
Multiply the second row by 8/11:
[tex]\left[\begin{array}{ccc}3&-4&5&|27\\0&1&-8/11&|-67/11\\0&16&-21&|-118\end{array}\right][/tex]
Subtract 16 times the second row from the third row:
[tex]\left[\begin{array}{ccc}3&-4&5&|27\\0&1&-8/11&|-67/11\\0&0&5/11&|10/11\end{array}\right][/tex]
Multiply the third row by 11/5:
[tex]\left[\begin{array}{ccc}3&-4&5&|27\\0&1&-8/11&|-67/11\\0&0&1&|2\end{array}\right][/tex]
Add 4/11 times the third row to the second row:
[tex]\left[\begin{array}{ccc}3&-4&5&|27\\0&1&0&|1\\0&0&1&|2\end{array}\right][/tex]
Add 4 times the third row to the first row:
[tex]\left[\begin{array}{ccc}3&-4&0&|35\\0&1&0&|1\\0&0&1&|2\end{array}\right][/tex]
Add 4 times the second row to the first row:
[tex]\left[\begin{array}{ccc}3&0&0&|39\\0&1&0&|1\\0&0&1&|2\end{array}\right][/tex]
Now, we can read off the solutions:
3x=39⇒x=13
y=1
z=2
So, the correct answer is (d) (1,5,2).
Can someone check over my answers? Thanks!
Answer:
Yes, I just checked it. All of it is right!
Step-by-step explanation:
Good Job!!
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:
given x+2<-5 choose the solution set.
Answer:
[tex]\large\boxed{\{x|x\in\mathbb{R},\ x<-7\}}[/tex]
Step-by-step explanation:
[tex]x+2<-5\qquad\text{subtract 2 from both sides}\\\\x+2-2<-5-2\\\\x<-7\to\{x|x\in\mathbb{R},\ x<-7\}[/tex]
Answer:
x < -7; the answer is the first choice.
Step-by-step explanation:
x + 2 < -5
Subtract 2 from both sides.
x < -7
The answer is the first choice.
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 equation represents the graphed function? (0,3) (1,1)
y=-2x+3 in slope-intercept form
3 is the y-intercept and -2 is the slope
Answer:
2x - y + 3 = 0
Step-by-step explanation:
The formula used to find the equation is:
[tex]y-y_1= \frac{(y_2-y_1)}{(x_2-x_1)} (x-x_1)[/tex]
Here, (x₁, y₁) = (0, 3)
and (x₂, y₂) = (1, 1)
Putting all values in above formula,
[tex]y-3= \frac{(1-3}{(1-0)} (x-0)[/tex]
⇒ [tex]y - 3 =\frac{-2}{1}x[/tex]
⇒ y - 3 = 2x
⇒ 2x - y + 3 = 0
which is the requires equation.
What does F equal???
Answer:
F=10
Step-by-step explanation:
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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