Answer:
There are 21 ways to choose the first person, 20 ways to choose the second, 19 ways for the third and 18 ways for the fourth so the answer is 21 * 20 * 19 * 18 = 143640.
2 sin(2theta)
_______________
(1 + cos(2theta)) (1 –tan^2theta)
Answer:
For numerator
2sin(2∅)=2(2sin∅cos∅)
For Denominator
(1+cos(2∅))(1+tan²∅)
=(1+cos(2∅))(sec²∅)
=(1+cos²∅-sin²∅)(sec²∅)
Recall. 1-sin²∅=cos²∅
=2cos²∅(sec²∅)
=2.
Answer is...
2(2sin∅cos∅)/2
=2sin∅cos∅ or sin(2∅)
The shortest side of a triangle is 12cm and the area of the triangle is 8 square cm. A similar triangle has an area of 18 square cm. Calculate the shortest side of this triangle
Answer:
27cm
Step-by-step explanation:
Given the following :
Triangle A:
Shortest side = 12cm
Area of triangle = 8cm^2
Triangle B:
shortest side =?
AREA of triangle = 18cm^2
If triangle A and B are similar :.
Area A / Area B = Length A / length B
8cm^2 / 18 = 12 / length B
Cross multiply :
8cm * Length B = 18 × 12
Length B = 216 / 8
Length B = 27
Therefore, the shortest of the other triangle IS 27cm
Answer:
its A C and E hope this helps
Step-by-step explanation:
Hey, can anyone help me out plz?
Answer:
Hey there!
That would be the SAS postulate.
This states that one angle is congruent and between two congruent sides.
Hope this helps :)
figure out if the equation is inverse or direct
Answer:
A. Inverse variation
B. Direct variation
C. Direct variation
D. Inverse variation
Hope this helps you
Marguerite wants to rent a carpet cleaner. Company A rents a carpet cleaner for $15 per day. Company B rents a carpet cleaner for $100 per week, with a one-time fee of $5. The following functions represent the rate structures of the two rental companies: x = the number of weeks Company A f(x) = 15(7x) Company B g(x) = 100x + 5 The function h(x) = f(x) – g(x) represents the difference between the two rate structures. Determine which statements about h(x) and about renting a carpet cleaner are true. Check all that apply. h(x) = 5x – 5 h(x) = 5x + 5
Answer:
If Marguerite rents for 2 weeks, it will cost her less if she rents from Company B
If Marguerite rents for 1 week, it will cost her the same at either company
h(x) = 5x - 5
Step-by-step explanation:
Marguerite wants to rent a carpet cleaner. Company A rents a carpet cleaner for $15 per day. Company B rents a carpet cleaner for $100 per week, with a one-time fee of $5. The following functions represent the rate structures of the two rental companies: x = the number of weeks Company A f(x) = 15(7x) Company B g(x) = 100x + 5 The function h(x) = f(x) – g(x) represents the difference between the two rate structures. Determine which statements about h(x) and about renting a carpet cleaner are true. Check all that apply. If Marguerite rents for 2 weeks, it will cost her more if she rents from Company B. If Marguerite rents for 2 weeks, it will cost her less if she rents from Company B. If Marguerite rents for 1 week, it will cost her the same at either company. If Marguerite rents for 1 week, it will cost her more if she rents from Company A. h(x) = 5x – 5 h(x) = 5x + 5
Answer: Company A rents a carpet cleaner for $15 per day. Company B rents a carpet cleaner for $100 per week, with a one-time fee of $5. In one week there are 7 days, therefore in x weeks the cost of rentals are given below:
For company A: f(x) = 15(7x)
For company B: g(x) = 100x + 5
h(x) = f(x) – g(x) represents the difference between the two rate structures.
h(x) = f(x) - g(x) = 15(7x) - (100x + 5)
h(x) = 105x - 100x - 5
h(x) = 5x - 5
If Marguerite rents for 2 weeks:
The cost for company A = 15(7x) = 15(7 × 2) = $210
The cost for company B = 100x + 5 = 100(2) + 5 = 200 + 5 = $205
If Marguerite rents for 2 weeks, it will cost her less if she rents from Company B
If Marguerite rents for 1 weeks:
The cost for company A = 15(7x) = 15(7 × 1) = $105
The cost for company B = 100x + 5 = 100(1) + 5 = 100 + 5 = $105
If Marguerite rents for 1 week, it will cost her the same at either company
Answer:
If Marguerite rents for 2 weeks, it will cost her less if she rents from Company B.
h(x) = 5x + 5
those are the answers on edge
Step-by-step explanation:
Scarlett bought an ant farm with 80 ants. Frond the following week forward, the ant population tripled every week. Let g(n) be the number on ants in scarletts farm in the nth week since she got it. G is a sequence. What kind is it? Write an explicit formula for the sequence starting with g(n)=? Need help really bad
Answer:
g(n)=80*3^(n-1)
Step-by-step explanation:
Scarlett started with 80 ants
That is, first term (a)=80
The ant population tripled every week.
First week: 80×3=240
Second week=240×3=720
Common ratio=720/240=3
Or
240/80=3
Therefore, r=3
G is a geometric sequence
Geometric sequence is given by
g(n)=a*r^(n-1)
Substitute a=80 and r=3 into the equation
g(n)=a*r^(n-1)
g(n)=80*3^(n-1)
The explicit formula for the sequence is
g(n)=80*3^(n-1)
The canvas of a painting has an area of 64 ft2. What length of frame is needed for the border of the painting?
Answer:
8
Step-by-step explanation:
Assuming, the canvas has the shape of a square. By the square area formula we can derive its side:
[tex]S=l^{2}\\64=l^{2}\\l=\sqrt{64}\\ l=8\: ft[/tex]
Then Each side of the painting measures 8 feet, the length of frame must have 8 feet long, and the width is decided by the framer.
Answer:
The answer is C: 32 ft
Step-by-step explanation:
If you take the square root of the area of 64 ft ^2, you get 8. then it asks what is the length needed for the frame as in the entire frame. So you just have to multiply 8 by 4 which is the number of sides. Also, I got this right on the edg quiz.
pls i want help on this one
Answer:
1808 people
Step-by-step explanation:
Find 1% by dividing by 100.
1600/100=16
Multiply 16 by 13.
208
Add it to 1600.
1808
There are now 1808 people.
Which graph shows the solution to the system of linear inequalities? 2x -3y ≤ 12 y < -3
First solve for y in [tex]2x - 3y \le 12[/tex] to get [tex]y \ge \frac{2}{3}x-4[/tex]. The inequality sign flips because we divided both sides by a negative value.
To graph [tex]y \ge \frac{2}{3}x-4[/tex] we need to graph the boundary line y = (2/3)x - 4. This line has a y intercept of (0,-4) and another point on the line is (6,0).
Draw a solid line through (0,-4) and (6,0). The boundary line is solid because of the "or equal to" part of the inequality sign. The last part is to shade above the boundary line because of the "greater than" sign in [tex]y \ge \frac{2}{3}x-4[/tex].
---------------
As for graphing y < -3, we draw a horizontal dashed line through -3 on the y axis. The line is dashed because there is no "or equal to" here. We do not include boundary points as part of the solution set. Shade below this dashed line due to the "less than" sign.
---------------
After doing both of these things on the same xy grid, you'll get something that looks like choice C. I'm assuming choice C has a dashed line for the red region.
Answer: Choice CThe graph is image 2. (last option)
We first draw the lines 2x - 3y = 12 and y=-3. Image 1.
For 2x - 3y ≤ 12
or, 2x - 12 ≤ 3y
or, 3y ≥ 2x - 12
or, y ≥ (2x - 12)/3
we shade upwards.
For y < - 3 we shade below.
So the graph is image 2.
Learn more: https://brainly.com/question/8806877
Use the drawing tools to form the correct answers on the graph. Plot the vertex and the axis of symmetry of this function: f(x) = (x – 3)2 + 5.
Answer:
Axis of Symmetry: x = 3
Vertex: (3, 5)
Step-by-step explanation:
Use a graphing calc.
Answer:
3
Step-by-step explanation:
Which function is graphed below?
Answer:
The function graphed below is [tex]x = y^{2} - 2[/tex] or [tex]y = \pm \sqrt{x+2}[/tex].
Step-by-step explanation:
The graph represents a second order polynomial function (a parabola), whose axis of symmetry is the x-axis and whose form is presented as follows:
[tex]x - h = C\cdot (y-k)^{2}[/tex]
Where:
[tex]x[/tex], [tex]y[/tex] - Dependent and independent variable, dimensionless.
[tex]h[/tex], [tex]k[/tex] - Horizontal and vertical components of the vertex, dimensionless.
[tex]C[/tex] - Vertex constant, dimensionless. If [tex]C > 0[/tex], then vertex is an absolute minimum, otherwise it is an absolute maximum.
After a quick observation, the following conclusions are done:
1) Vertex is an absolute minimum ([tex]C > 0[/tex]) and located at (-2, 0).
2) Parabola pass through (2, 2).
Then, the value of the vertex constant is obtained after replacing all known values on expression prior algebraic handling: ([tex]x = 2[/tex], [tex]y = 2[/tex], [tex]h = -2[/tex], [tex]k = 0[/tex])
[tex]2+2 = C\cdot (2-0)^{2}[/tex]
[tex]4 = 4\cdot C[/tex]
[tex]C = 1[/tex]
The function is:
[tex]x = -2 + 1\cdot y^{2}[/tex]
[tex]x = y^{2}-2[/tex]
The inverse function of this expression is [tex]y = \pm \sqrt{x+2}[/tex]
The function graphed below is [tex]x = y^{2} - 2[/tex] or [tex]y = \pm \sqrt{x+2}[/tex].
Triangle DEF is the image of triangle ABC after a sequence of transformations. After you reflect ABC in the y-axis, what must you do? Describe a sequence of transformations that proves the triangles congruent.
Answer:
Step-by-step explanation:
After reflection about y-axis, A'B'C' must be translated down 6 units to create image DEF.
ABC and DEF are congruent due to the following common properties of reflections and translations.
1. does not change the nature of geometric elements, i.e. maps a line to a line, a segment to a segment, etc.
2. preserve lenths of segments.
3. preserves angles
By the congruent theorem of SSS, the two triangles are congruent.
The sequence of transformations that proves the triangles congruent is explained in the solution below.
What is transformation?The geometric transformation is a bijection of a set that has a geometric structure by itself or another set. If a shape is transformed, its appearance is changed.
After reflection about y-axis, A'B'C' must be translated down 6 units to create image DEF.
ABC and DEF are congruent due to the following common properties of reflections and translations.
It does not change the nature of geometric elements, i.e. maps a line to a line, a segment to a segment, etc., preserve lengths of segments, and preserves angles.
By the congruent theorem of SSS, the two triangles are congruent.
Learn more about transformation, click;
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Suppose the mean height for adult males in the U.S. is about 70 inches and the standard deviation is about 3 inches. Assume men’s heights follow a normal curve. Using the Empirical Rule, 95% of adult males should fall into what height range?
Question options :
a. They should be between 64 and 76 inches tall.
b. They should be close to the height that is 95% of the mean. That is, 66.5 inches, plus or minus 2 standard deviations.
c. They should be at or below the 95th percentile, which is 74.92 inches.
d. None of the above.
Answer: a. They should be between 64 and 76 inches tall.
Step-by-step explanation:
Given the following :
Assume men's height follow a normal curve ; and :
Mean height = 70 inches
Standard deviation= 3 inches
According to the empirical rule ;
Assuming a normal distribution with x being random variables ;
About 68% of x-values lie between -1 to 1 standard deviation of the mean. With about 95% of the x values lying between - 2 and +2 standard deviation of mean. With 99.7% falling between - 3 to 3 standard deviations from the mean.
Using the empirical rule :
95% will fall between + or - 2 standard deviation of the mean.
Lower limit = - 2(3) = - 6
Upper limit = 2(3) = 6
(-6+mean) and (+6+ mean)
(-6 + 70) and (6+70)
64 and 76
The range of height of adult males in U.S. using the 95% empirical rule is 64 to 76 inches
According to the given data
The mean height for adult males in the U.S. is about 70 inches
The standard deviation of heights is about 3 inches.
Considering the data to be normally distributed
According to the empirical rule for normal distribution we can write that
95.45% of the data lies with in the range of
[tex]\rm \mu - 2\sigma \; to \; \mu +2\sigma\\\\where \\\mu = Mean\\\sigma = Standard \; deviation[/tex]
We have to to determine that using the Empirical Rule 95% of adult males should fall into what height range
According to the given data
[tex]\rm \mu = 70\\\rm \sigma = 3 \\[/tex]
[tex]\rm Lower \; limit \; of \; the\; range \; of\; variation\; of \; height\; range = 70 - 2(3) = 64[/tex]
[tex]\rm Upper \; limit \; of \; the\; range \; of\; variation\; of \; height\; range = 70 +2(3) = 76[/tex]
So we can conclude that the range of height of adult males in U.S. using the 95% empirical rule is 64 to 76 inches
For more information please refer to the link given below
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what describes the transformation of g(x)=3(2)-x from the parent function f(x)=2x
Answer:
Reflect across the y-axis, stretch the graph vertically by a factor of 3
Step-by-step explanation:
The question has certain errors, in fact the functions are the following:
g (x) = 3 * (2) ^ - x
f (x) = 2 ^ x
The transformation that we can do to obtain the translated graph, Are given in 2 steps, which are the following:
1. When x is replaced by -x, then it reflects the graph on the y axis.
2. 3 multiplies with the function, it means that it stretches the main function vertically in 3 units.
So to summarize it would be: Reflect across the y-axis, stretch the graph vertically by a factor of 3
The function d(s) = 0.0056s squared + 0.14s models the stopping distance
of a car, d(s), in metres, and the speed, s, in kilometres per hour. What
is the speed when the stopping distance is 7 m? Use a graph to solve.
Answer:
The car must have a speed of 25 kilometres per hour to stop after moving 7 metres.
Step-by-step explanation:
Let be [tex]d(s) = 0.0056\cdot s^{2} + 0.14\cdot s[/tex], where [tex]d[/tex] is the stopping distance measured in metres and [tex]s[/tex] is the speed measured in kilometres per hour. The second-order polynomial is drawn with the help of a graphing tool and whose outcome is presented below as attachment.
The procedure to find the speed related to the given stopping distance is described below:
1) Construct the graph of [tex]d(s)[/tex].
2) Add the function [tex]d = 7\,m[/tex].
3) The point of intersection between both curves contains the speed related to given stopping distance.
In consequence, the car must have a speed of 25 kilometres per hour to stop after moving 7 metres.
Please answer this in two minutes
Answer:
[tex] csc (R) = \frac{13}{12} [/tex]
Step-by-step explanation:
Formula for any given angle (Ѳ) is given as csc Ѳ = length of hypotenuse side//length of opposite side. It is the inverse of sin Ѳ.
In the right triangle given above, the opposite length = 24, while the length of the hypotenuse = 26
Thus,
[tex] csc (R) = \frac{hypotenuse}{opposite} [/tex]
[tex] csc (R) = \frac{26}{24} [/tex]
[tex] csc (R) = \frac{26}{24} [/tex]
[tex] csc (R) = \frac{13}{12} [/tex]
ASAP!!! THIS WORTH 50 POINTS!
Answer:
90 16-oz cases and 30 20-oz cases will maximize resin and time use120 16-oz cases will maximize profitStep-by-step explanation:
Let x represent the number of cases of 16-oz cups produced.
Let y represent the number of cases of 20-oz cups produced.
The limitation imposed by available production time is ...
x + y ≤ 15·8 = 120 . . . . maximum number of cases produced in a day
The limitation imposed by raw material is ...
14x +18y ≤ 1800 . . . . . maximum amount of resin used in a day
__
The point of intersection of the boundary lines for these inequalities can be found using substitution:
14(120- y)+18y = 1800
4y = 120 . . . . . subtract 1680, simplify
y = 30
x = 120 -30 = 90
This solution represents the point at which production will make maximal use of available resources. It is one boundary point of the "feasible region" of the solution space.
__
The feasible region for the solution is the doubly-shaded area on the graph of these inequalities. It has vertices at ...
(x, y) = (0, 100), (90, 30), (120, 0)
The profit for each of these mixes of product is ...
(0, 100): 25·0 +20·100 = 2000
(90, 30): 25·90 +20·30 = 2850 . . . . uses all available resources
(120, 0): 25·120 +20·0 = 3000 . . . . maximum possible profit
The family can maximize their profit by producing only 16-oz cups at 120 cases per day.
Answer:
90 16-oz cases and 30 20-oz cases will maximize resin and time use
120 16-oz cases will maximize profit
Step-by-step explanation:
Of the books in the Hogwarts Library, 1/4 came from Hermione and 8 came from Luna. Of the rest, 14 were Ron’s, 1/2 were Ginny’s. How many books are there in the library?
Will mark brainlist
Answer:
88
Step-by-step explanation:
The key to this question is combining the two fractional pieces we know about. Namely, Hermione has 1/4 of the books and Ginny has 1/2 of them. This means that between the two of them, they account for 3/4 of the library.
So what does that mean? Well, it means that the books Ron and Hermione have (22 in total) account for the remaining 1/4 of the library. So then the whole library is [tex]4*22=88[/tex].
Can you help me plz
Answer:
[tex]\boxed{\sf y=6}[/tex]
Step-by-step explanation:
There are 5 identical squares.
The area of one square is [tex]\sf s^2[/tex].
[tex]\sf{y^2 } \times \sf{5}[/tex]
[tex]\sf 5y^2[/tex]
The area of the whole shape is 180 cm².
[tex]\sf 5y^2=180[/tex]
Solve for y.
Divide both sides by 5.
[tex]\sf y^2=36[/tex]
Take the square root on both sides.
[tex]\sf y=6[/tex]
On a coordinate plane, a line is drawn from point J to point K. Point J is at (negative 6, negative 2) and point K is at point (8, negative 9). What is the x-coordinate of the point that divides the directed line segment from J to K into a ratio of 2:5? x = (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1 –4 –2 2 4
Answer:
-2
Step-by-step explanation:
The coordinate of a point that divides a line AB in a ratio a:b from A([tex]x_1,y_1[/tex]) to B([tex]x_2,y_2[/tex]) is given by the formula:
[tex](x,y)=(\frac{bx_1+ax_2}{a+b} ,\frac{by_1+ay_2}{a+b} )=(\frac{a}{a+b}(x_2-x_1)+x_1 ,\frac{a}{a+b}(y_2-y_1)+y_1 )[/tex]
Given that a line JK, with Point J is at ( -6, - 2) and point K is at point (8, - 9) into a ratio of 2:5. The x coordinate is given as:
[tex]x=\frac{2}{2+5} (8-(-6))+(-6)=\frac{2}{7}(14) -6=4-6=-2[/tex]
Line segments can be divided into equal or unequal ratios
The x coordinate of the segment is -2
The coordinates of points J and K are given as:
[tex]J = (-6,-2)[/tex]
[tex]K = (8,-9)[/tex]
The ratio is given as:
[tex]m : n =2 : 5[/tex]
The x-coordinate is then calculated using:
[tex]x = (\frac{m}{m + n }) (x_2 - x_1) + x_1[/tex]
So, we have:
[tex]x = (\frac{2}{2 + 5 }) (8 - -6) -6[/tex]
[tex]x = (\frac{2}{7}) (14) -6[/tex]
Expand
[tex]x = (2) (2) -6[/tex]
Open bracket
[tex]x = 4 -6[/tex]
Subtract 6 from 4
[tex]x = -2[/tex]
Hence, the x coordinate of the segment is -2
Read more about line ratios at:.
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Find the value of x for the triangle.
37
37
45°
45°
Answer:
[tex]x=37\,\sqrt{2}[/tex]
Step-by-step explanation:
Notice you are dealing with a right angle triangle, since one of the angles measure [tex]90^o[/tex]. Now, what you are asked to find is the hypotenuse of that triangle, given an angle of [tex]45^o[/tex] and the opposite side: 37 units. Then, we can use for example the sine function which relates opposite, and hypotenuse:
[tex]sin(45^o)=\frac{opposite}{hyp} \\hyp=\frac{opposite}{sin(45^o)} \\hyp=\frac{37}{\sqrt{2}/2}\\hyp=37\,\sqrt{2}[/tex]
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answer:
2.86 seconds
Step-by-step explanation:
A graphing calculator shows the ball hits the ground at t = 2.86 seconds.
_____
You can use the quadratic formula with a=-16, b=45, c=2:
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x=\dfrac{-45\pm\sqrt{45^2-4(-16)(2)}}{2(-16)}=\dfrac{45\pm\sqrt{2153}}{32}\approx\{-0.0438,2.8563\}[/tex]
The ball is in the air for about 2.86 seconds.
What is the equation of the line that passes through (–2, –3) and is perpendicular to 2x – 3y = 6?
Answer:
[tex]y=-\frac{3}{2}x-6[/tex]
Step-by-step explanation:
Since the line needs to be perpendicular to [tex]2x-3y=6[/tex], that means the slope of the line must be the opposite reciprocal. Rearrange the equation [tex]2x-3y=6[/tex] to solve for the value of y, with variable y on the left side.
[tex]-3y=-2x+6\\y=\frac{2}{3} x-2[/tex]
So, the slope of the line given already is [tex]\frac{2}{3}[/tex]. The opposite reciprocal of this is [tex]-\frac{3}{2}[/tex].
From what information we know so far (the slope) about the equation of the line we are trying to find, we can write a basic equation that allows us to solve for the y-intercept. Use the equation [tex]y=mx+b[/tex], where m is the slope (which we already found) and b is the y-intercept.
[tex]y=-\frac{3}{2}x+b[/tex]
Since we are given a set of coordinate points that the line must pass through, we can substitute (-2, -3) in for x and y in the equation above. Then, solve for the value of b, which is our y-intercept.
[tex]-3=-\frac{3}{2}(-2)+b\\ -3=3+b\\b=-6[/tex]
Now we have all the necessary information to create our equation.
[tex]y=-\frac{3}{2}x-6[/tex]
Answer: A.
explanation:just did the test
Lines e and f are parallel. The mAngle9 = 80° and mAngle5 = 55°.
Parallel lines e and f are cut by transversal c and d. All angles are described clockwise, from uppercase left. Where lines e and c intersect, the angles are: 1, 2, 4, 3. Where lines f and c intersect, the angles are 5, 6, 8, 7. Where lines e and d intersect, the angles are 9, 10, 12, 11. Where lines f and d intersect, the angles are 13, 14, 16, 15.
Which angle measures are correct? Select three options.
Answer:
Fist if all u will draw ur Parallel lines e and f are cut by transversal c and d. All angles are described clockwise, from uppercase left. Secondly u will draw ur Parallel lines or angle.
Answer:
a c e
Step-by-step explanation:
x over 4 + 3/5 is equal to 3x over 5 - 2
Answer:
[tex]\huge\boxed{x=\dfrac{52}{7}=7\dfrac{3}{7}}[/tex]
Step-by-step explanation:
[tex]\dfrac{x}{4}+\dfrac{3}{5}=\dfrac{3x}{5}-2\qquad\text{multiply both sides by}\ LCD=20\\\\20\cdot\dfrac{x}{4}+20\cdot\dfrac{3}{5}=20\cdot\dfrac{3x}{5}-20\cdot2\\\\5\cdot x+4\cdot3=4\cdot3x-40\\\\5x+12=12x-40\qquad\text{subtract 12 from both sides}\\\\5x+12-12=12x-40-12\\\\5x=12x-52\qquad\text{subtract}\ 12x\ \text{from both sides}\\\\5x-12x=12x-12x-52\\\\-7x=-52\qquad\text{divide botgh sides by (-7)}\\\\\dfrac{-7x}{-7}=\dfrac{-52}{-7}\\\\x=\dfrac{52}{7}[/tex]
If f(x)=k (square root)2+x, and f^-^1 (-15)=7, what is the value of k
There's a bit of ambiguity in your question...
We know that [tex]f^{-1}(-15)=7[/tex], which means [tex]f(7)=-15[/tex].
I see three possible interpretations:
• If [tex]f(x)=k\sqrt2+x[/tex], then
[tex]f(7)=-15=k\sqrt2+7\implies k\sqrt2=-22\implies k=-\dfrac{22}{\sqrt2}=11\sqrt2[/tex]
• If [tex]f(x)=k\sqrt{2+x}[/tex], then
[tex]f(7)=-15=k\sqrt{2+7}\implies -15=3k\implies k=-5[/tex]
• If [tex]f(x)=\sqrt[k]{2+x}[/tex], then
[tex]f(7)=-15=\sqrt[k]{2+7}\implies-15=9^{1/k}\implies\dfrac1k=\log_9(-15)[/tex]
which has no real-valued solution.
I suspect the second interpretation is what you meant to write.
Which best explains why the orthocenter of an obtuse triangle is outside the triangle?
Answer: All three of the altitudes lie entirely outside the triangle.
Step-by-step explanation:
The orthocenter is the center of the triangle formed by creating all the altitudes of each side.
The altitude of a triangle is formed by creating a line from each vertex that is perpendicular to the opposite side.
In acute traingle , the orthocenter lies inside it.
In right angled triangle, the orthocenter lies on the triangle.
In obtuse triangle , the orthocenter lies outside the triangle because all the three altitudes meet outside .
So, the best explains why the orthocenter of an obtuse triangle is outside the triangle : All three of the altitudes lie entirely outside the triangle.
Answer: It’s A on edge
The Greenpoint factory produced two-fifths of the Consolidated Brick Company’s bricks in 1991. If the Greenpoint factory produced 1,400 tons of bricks in 1991, what was the Consolidated Brick Company’s total output that year, in tons?
Answer:
3500 tons
Step-by-step explanation:
The Greenpoint factory produced 2/5 of the bricks that the Consolidate Brick Company produced in 1991.
Let the amount of bricks produced by the Greenpoint factory be g and the amount of bricks produced by the Consolidated brick company be c.
Therefore:
g = 2/5 * c = 2c/5
That year, the Greenpoint factory produced 1400 tons of bricks. This implies that:
1400 = 2c/5
To find the amount that the Consolidated Brick Company produced, solve for c:
1400 = 2c/5
1400 * 5 = 2c
7000 = 2c
c = 7000 / 2 = 3500 tons
The Consolidated Brick Company had a total production output of 3500 tons in 1991.
. What is half the next number in the pattern 1, 3, 9, 27, 81
A. 234
B. 67
D c. 468
0 0.76
Answer:
A. 243
Step-by-step explanation:
just multiply the next number by 3
81*3= 243
Answer:
[tex]\boxed{243}[/tex]
Step-by-step explanation:
The ratio can be found by dividing a term in the sequence by the previous term.
[tex]\frac{27}{9} =3[/tex]
Each term gets multiplied by 3 to get the next term.
[tex]81 \times 3 = 243[/tex]
What is the y-intercept of the function, represented by the table of values
below?
x
у
-2
16
1
4.
2
0
4
-8
7
-20
Answer:
8
Step-by-step explanation:
The y-intercept (b) of the function is the point at which the line of the graph of the given values of the table above crosses the y-axis, for which x = 0.
To find the y-intercept of the function represented by the tables, recall the equation of a straight line which is given as:
y = mx + b
Where, m is the slope = (y2 - y1)/(x2 - x1)
b = the y-intercept we are to find
y and x could be any values of a point on the graph which is represented in the table of values.
First, let's find the slope (m):
Let's use any 2 given pairs of the values in the table above.
Using,
(1, 4), (2, 0),
y1 = 4,
y2 = 0
x1 = 1
x2 = 2
m = (0 - 4)/(2 - 1)
m = -4/1 = -4
=>Using, y = mx + b, let's find the y-intercept (b), taking any of the coordinate pairs from the table of values given.
Let's use, (1, 4) as our x and y values.
Thus,
4 = -4(1) + b
4 = -4 + b
Add 4 to both sides to solve for b
4 + 4 = -4 + b + 4
8 = b
y-intercept of the function represented by the table of values = 8