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Explanation:
AB = 10 and BC = 5 are two sides of triangle ABC. The third missing side is AC. We don't have enough information to determine the exact length of AC, but we can narrow things (a bit) to get a range of values.
Through a modified version of the triangle inequality theorem, if we had sides a = 10 and b = 5, then the third side c is restricted like so
a-b < c < a+b
10-5 < c < 10+5
5 < c < 15
This then means that 5 < AC < 15 is the compound inequality that tells us the range of values for side AC. It says that AC is between 5 and 15 units long. Side AC cannot be 5 units exactly, and it can't be 15 units exactly either. I recommend cutting out slips of paper to try this out yourself, and you'll see it's not possible to have something like AC = 15.
So that's why choice D is the answer. Choice A is true, because 10 is between 5 and 15, but it's not the only possible value for AC. There's more to the story. That's why I'm thinking choice D is the better answer. It encapsulates all possible lengths of AC.
The sum of first 'n' terms. Sn of a particular Arithmetic Progression is given by Sn=12n - 2n^2. Find the first term and the common difference
Let a be the first term and d the common difference between consecutive terms. Then the next few terms in the sequence are
a + d
a + 2d
a + 3d
and so on, up to the k-th term
a + (k - 1) d
The sum of the first n terms of this sequence is
[tex]\displaystyle S_n = \sum_{k=1}^n(a+(k-1)d) = 12n-2n^2[/tex]
Expanding the sum, we have
[tex]\displaystyle S_n = \sum_{k=1}^n (a+(k-1)d) \\\\ S_n = \sum_{k=1}^n(a-d+dk) \\\\ S_n = (a-d)\sum_{k=1}^n1+d\sum_{k=1}^nk \\\\ S_n = (a-d)n+\frac{d}2n(n+1) \\\\ S_n = (a-d)n+\frac{d}2(n^2+n) \\\\ S_n = \left(a-\frac{d}2\right)n+\frac{d}2n^2[/tex]
It follows that
a - d/2 = 12
d/2 = -2
Solve these equations for a and d.
d/2 = -2 ==> d = -4
a - d/2 = a + 2 = 12 ==> a = 10
So the sequence is
10, 6, 2, -2, -6, -10, -14, …
Write an equation that expresses the relationship. Then solve the equation for B.
T varies directly as the cube of A and inversely as B.
T= what?
(Use k as the constant of variation.)
Answer:
kkkkkkkllllll
Step-by-step explanation:
llllllllllllllllllllllllll
Write this quadratic equation in standard form.
Answer:
-[tex]x^{2} + 3x -8 = 0[/tex]
Step-by-step explanation:
[tex]x^{2} + x -8 - 2x = 0[/tex] [tex]x^{2} + 3x -8 = 0[/tex]A function does not have any x-intercepts. What
might be true about its domain and range?
The domain exists on all real numbers i.e {x∈R}∈
The range exists all on real numbers except at y = 0
Domains are all input values of a function for which the function exists while ranges are all the output values for which the function exists.
Since the x-intercept of a function exists at where y = 0, this means that the point where a function does not have any x-intercepts are all other points on the graph except at y = 0.
The following statements are therefore true;
The domain exists on all real numbers i.e {x∈R}The range exists all on real numbers except at y = 0Learn more here: https://brainly.com/question/12648810
I’m the triangle shown we can find the angle theta as follows.
Answer:
sin = opp/hyp
cos = adj/hyp
tan = opp/adj
In the accompanying diagram, ΔA′B′C′ is the image of ΔABC. Which type of transformation is shown in the illustration?
A. rotation
B. translation
C. reflection
D. dilation
Answer:
Reflection
Step-by-step explanation:
It is the opposite of the first,...
Find the slope of the line containing the points (-3, 8) and (2, 4).
Answer:
-4/5
Step-by-step explanation:
The slope of the line is m=(4-8)/(2-(-3))=-4/5
A square piece of cardboard of sides 15 cm is folded to make a cube of sides 5 cm.
Is there enough cardboard?
Answer:
Step-by-step explanation:
The 15 cm by 15 cm piece of cardboard area = 225 cm².
A cube has six congruent faces. If each edge is 5 cm, the surface area is 6×5² = 150 cm². So there is enough cardboard to make a cube, but not by folding. You'd have to do some cutting and taping.
V= pi r2h rectangular prism cylinder cone sphere
Answer:
Step-by-step explanation:
rectangular prism=lwh
cylinder=πr²h
cone=1/3 πr²h
sphere=4/3 πr³
Kiara baked 30 oatmeal cookies and 48 chocolate chip cookies to package in plastic containers for her friends at school. She wants to divide the cookies into identical containers so that each container has the same number of each kind of cookies. if she wants each container to have the least number of cookies possible,how many plastic containers does she need?Kiara baked 30 oatmeal cookies and 48 chocolate chip cookies to package in plastic containers for her friends at school. She wants to divide the cookies into identical containers so that each container has the same number of each kind of cookies. if she wants each container to have the least number of cookies possible,how many plastic containers does she need?
Answer:
6
Step-by-step explanation:
If she's looking for the least number per box she wants the greatest common factor of both numbers.
The GCF of 30 and 48 is 6.
Estimate the line of best fit using two points on the line.
.
10
9
8
7
6
5
(6,8)
(9,6)
N
1 2 3 4 5 6
8 9 10
O A. y-2x+12
O B. y--{x+12
O C. y=
O D. y=-3x+12
Answer:
B. y = -2/3x + 12
Step-by-step explanation:
Formula to find the slope when given two points on a line:
y2 - y1
x2 - x1
Substitute the two given points (6, 8) (9, 6):
6 - 8
9 - 6
Slope = -2/3x
We found the slope! And the answer choices already gave us one y-intercept, which is 12. The last thing we do is we form an equation with the information we solved and that was given to us.
y = slope (x) + y-intercept
y = -2/3x + 12
The answer choice that matches this equation is B.
In conclusion, the equation that best estimates the line of best fit shown above is answer choice B.
An equation of a line with given coordinates is y= -2/3 x+12. Therefore, option B is the correct answer.
What is the equation of a line?The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.
From the given graph, the coordinate points are (6, 8) and (9, 6).
We know that, the formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).
Here, slope = (6-8)/(9-6)
= -2/3
Substitute m=-2/3 and (x, y)=(6, 8) in y=mx+c, we get
8=-2/3 (6)+c
8=-4+c
c=12
So, equation of a line is y= -2/3 x+12
Therefore, option B is the correct answer.
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solve for x please help (show work!)
Answer:
x = 1/2 or 0.5
Step-by-step explanation:
8(-2x + 1) = 0
Distribute the 8 by multiplying 8 by what's inside of the parenthesis (-2x and 1)
8 * -2x = -16x
8 * 1 = 8
We now have
-16x + 8 = 0
Subtract 8 from both sides
-16x + 8 - 8 = 0 - 8
-16x = -8
Divide both sides by -16
-16x/-16 = -8/-16
x = 1/2
8( -2x + 1 ) = 0
S O L U T I O N :8( -2x + 1 ) = 0Simplify the left hand side
-16x + 8 = 0Transposing -16x to the other side
8 = 16xCross multiplying we get
x = 8/16x = ½x = 0.5Hence the value of x is 0.5 or ½
Can someone please help me solve the equation?
Subtracting 10 from the original equation will shift the graph down 10 units
The answer is D.
A tortoise is walking in the desert. It walks 7.5 meters in 3 minutes. What is its speed?
Answer:
Step-by-step explanation:
speed is calculated using formula v=d/t
m= 7.5m
t= 3 min
v=?
v= 7.5m/3min
v= 2.5m/min
what term is greater than 50 in the sequence n^2/2
please help
Answer:
296
We start by multiplying 6 times 46, since the first 4 terms are already listed. We then add the product, 276, to the last listed term, 20. This gives us our answer of 296.
Which expression represents the perimeter of the rectangle above? . 6x + 3. 10x + 6. 8x² + 6x. 12x + 6
There is no any image of rectangle
ANSWER ASAP CORRECT ANSWER WILL GET BRAINLIEST PLUS 78 POINTS
9514 1404 393
Answer:
C) 462
Step-by-step explanation:
The presenters can be chosen 11C6 = 462 different ways.
__
If the teacher were concerned about the order of the presentations, the number of possibilities goes up to 11P6 = 332,640 different ways.
What is the area of a circular wading pool with a radius of 50 cm?
A. 157.1 cm2
B. 7854.0 cm2
C. 314.2 cm2
D. 31415.9 cm2
Answer:
B. 7854.0 cm2
The area of a circle is given by A= π [tex]r^{2}[/tex] where r is the radius
So A= π[tex]50^{2}[/tex] = 7854.0 cm2
Bank B pays 5.9% annual percentage rate compound semiannually what is the effective annual yield round to the nearest hundredth
9514 1404 393
Answer:
5.99%
Step-by-step explanation:
The relationship between the effective annual yield (e) and the nominal annual interest rate (r) compounded n times per year is ...
e = (1 +r/n)^n -1
For r = 5.9% and n = 2, the effective rate is ...
e = (1 +0.059/2)^2 -1 = 0.059870 ≈ 5.99%
Margaret drives 188 miles
with 8 gallons of gas. Find the unit rate
The unit rate will be "23.5 miles/gallon". In the below segment, a further solution to the given question is provided.
Given values in the question are:
Total distance,
= 188 miles
Total gas used,
= 8
Now,
⇒ The rate of gas consumption will be:
= [tex]\frac{Total \ distance}{Total \ gas \ used}[/tex]
By putting the given values in the above formula, we get
= [tex]\frac{188}{8}[/tex]
= [tex]23.5 \ miles/gallon[/tex]
Thus the above is the appropriate solution.
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If a= -5 and b= -2,then what is the value of [a-b]2
Step-by-step explanation:
Substitute the values of a and b into [a-b]2
= [-5-(-2)]2
= [-5+2]2
= [-3]2
= -6
Find the slope of the line through the pair of points. (7.-10) and (-6, -3)
Answer:
Fraction form: 7/-13
Decimal form:-0.53846153846154
The point p=(2/5,y) lies on the unit circle below what is the value of y in simplest form
Step-by-step explanation:
distance of (1,0) from the origin is,
√{(1-0)²+(0-0)²}
= √1
= 1
So the radius of the circle is 1,
now for the point (2/5,y) distance from origin should be the same since it's the radius
so,
√{(2/5-0)²+(y-0)²} = 1
or, √(4/25+y²)=1
or, 4/25+y²=1
or, y² = 1-4/25
or, y²=21/25
or, y=√(21/25)
or, y=√21/5
so, the simplest form of y is,
[tex] \frac{ \sqrt{21} }{5} [/tex]
0.003 is 1/10 of
Please help I need this for homework !!!!!!!!!!!!
Answer:
0.03
Step-by-step explanation:
A random number generator is used to create a list of 300 single digit numbers
what is the graph of −36≤2x+4(x−3)
Instructions: The polygons in each pair are similar. Find the
missing side length.
Answer:
45/27=30/18=x/24
x = 30×24/18
or, x = 40
Answer:
? = 40
Step-by-step explanation:
Since the polygons are similar then the corresponding sides are in proportion, that is
[tex]\frac{?}{24}[/tex] = [tex]\frac{?}{24}[/tex] = [tex]\frac{30}{18}[/tex] ( cross- multiply )
18 ? = 720 ( divide both sides by 18 )
? = 40
An angle measures 36° more than the measure of its complementary angle. What is the measure of each angle?
Answer:
Since they are supplementary, they add up to 180 degrees. Since one is 38 degrees more than the other, you can use the equation x + (x+36) = 180 to find both angles
Step-by-step explanation:
ABCD is a rectangle enclosed in a circle with centre at O
and radius of 7cm. AOC is a diameter of the circle. the area of the rectangle is
56 2
. find the height of triangle ADC if the base is AC.
9514 1404 393
Answer:
4 cm
Step-by-step explanation:
The area of the triangle is half the area of the rectangle. The base of the triangle is the diameter of the circle, 14 cm. So the height is found from ...
A = 1/2bh
(56 cm²)/2 = 1/2(14 cm)h
h = (28 cm²)/(7 cm) = 4 cm
The height of triangle ADC is 4 cm.
Find the value of a and YZ if Y is between X and Z. XY = 7a, YZ = 5a, XZ = 6a + 24 = YZ =
[tex]\\ \sf\longmapsto XY+YZ=XZ[/tex]
[tex]\\ \sf\longmapsto 7a+5a=6a+24[/tex]
[tex]\\ \sf\longmapsto 12a=6a+24[/tex]
[tex]\\ \sf\longmapsto 12a-6a=24[/tex]
[tex]\\ \sf\longmapsto 6a=24[/tex]
[tex]\\ \sf\longmapsto a=\dfrac{24}{6}[/tex]
[tex]\\ \sf\longmapsto a=5[/tex]
YZ=5a=5(5)=25Value of a is 4 and value of YZ is 20 units
Step-by-step explanation:
Given:
Y is between point X and Z
Value of line XY = 7a
Value of line YZ = 5a
Value of line XZ = 6a + 24
Find:
Value of "a" and line YZ
Computation:
We know that
XY + YZ = XZ
So,
7a + 5a = 6a + 24
12a = 6a + 24
6a = 24
a = 4
Value of a = 4
So,
Value of line YZ = 5a
By putting value of a
Value of line YZ = 5(4)
Value of line YZ = 20 units
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