Answer:
B. 4 and 6 in
Step-by-step explanation:
The triangle inequality rule states: the length of a side of a triangle is less than the sum of the lengths of the other two sides and greater than the difference of the lengths of the other two sides.
So for the first qualification, we can eliminate A, C, and D. Therefore the answer is B, 4 & 6 in
To check whether the given side-lengths can form a triangle, we have to use the Triangle Inequality Theorem. This theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Let's apply this theorem to each pair of side-lengths given in the options along with the third side of 10 inches:
Option A:
Sides are 3 in, 8 in, and 10 in. According to the Triangle Inequality Theorem, we need to check if:
- 3 + 8 > 10 (which is true, since 11 > 10)
- 3 + 10 > 8 (which is true, since 13 > 8)
- 8 + 10 > 3 (which is true, since 18 > 3)
Since all three conditions are satisfied, option A can form a triangle.
Option B:
Sides are 4 in, 6 in, and 10 in. According to the Triangle Inequality Theorem, we need to check if:
- 4 + 6 > 10 (which is not true, since 10 is not greater than 10)
- 4 + 10 > 6 (which is true, since 14 > 6)
- 6 + 10 > 4 (which is true, since 16 > 4)
Since not all conditions are satisfied (specifically, the sum of the two smaller sides is not greater than the third side), option B cannot form a triangle.
Option C:
Sides are 5 in, 15 in, and 10 in. According to the Triangle Inequality Theorem, we need to check if:
- 5 + 15 > 10 (which is true, since 20 > 10)
- 5 + 10 > 15 (which is not true, since 15 is not greater than 15)
- 15 + 10 > 5 (which is true, since 25 > 5)
Since not all conditions are satisfied, option C cannot form a triangle.
Option D:
Sides are 6 in, 18 in, and 10 in. According to the Triangle Inequality Theorem, we need to check if:
- 6 + 18 > 10 (which is true, since 24 > 10)
- 6 + 10 > 18 (which is not true, since 16 is not greater than 18)
- 18 + 10 > 6 (which is true, since 28 > 6)
Since not all conditions are satisfied, option D cannot form a triangle.
Therefore, the only option that satisfies the Triangle Inequality Theorem and thus can be the measures of the other two sides of the triangle with one side measuring 10 inches is:
Option A: 3 in & 8 in.
Which pattern folds into the triangular prism above?
Answer:
the pattern would be W
Step-by-step explanation:
W should be the answer. Hope I helped you lots please count me brainy
Solve the equation for y
2x+5y=5
***Plz Help me out***
Here is the answer:...
Answer:
- Solve for y
- Subtract 2 x from both sides of the equation then divide by 5 .
-y = 1 − 2 x 5
Step-by-step explanation:
Plz help me with this
Answer: b) -5 ≤ y ≤ 1
Step-by-step explanation:
y = 3 cos (4x) - 2
↓ ↓
amplitude vertical shift
The amplitude is 3 which gives a range of -3 to 3 but there is also a shift down of 2 units so the new range is: -3 - 2 = -5 to 3 - 2 = 1
-5 ≤ y ≤ 1
Divide. Write your answer in simplest form.
8÷7/6
Answer:
4/21
Step-by-step explanation:
In this case, carry out the indicated operations from left to right:
8 1
---- * --- = 4/21
7 6
Please this is urgent !
Answer:
the probability is very high 86% > 14%
Step-by-step explanation:
55+20+11= 86%/100% 100-86=14% chance there will not be any rain or lightning
hope this helps!!
Use Julia’s work and finish finding the areas of the faces what is the surface area of the rectangular pyramid
Answer:
The surface area of the rectangular pyramid is [tex]SA=109.50\ m^{2}[/tex]
Step-by-step explanation:
we know that
The surface area of the rectangular prism is equal to the area of the rectangular base plus the area of the four triangular faces
so
[tex]SA=(8)(5)+2[14.75]+2[\frac{1}{2}(8)(5)][/tex]
[tex]SA=40+29.50+40[/tex]
[tex]SA=109.50\ m^{2}[/tex]
Answer:
109.5
Step-by-step explanation:
The population of a heard of cattle numbered was 5000 to begin with and was 10,000 after 10 years. If the population was growing exponentially, what was the growth rate? show all work
A) r=2
B) r=20
C)r=0.69
D)r=6.9
Answer:
[tex]r=0.0718[/tex]. The closest value from your given choices is C)r=0.69
Step-by-step explanation:
To solve this we are using the standard exponential growth equation:
[tex]f(t)=A(1+r)^t[/tex]
where
[tex]f(t)[/tex] is the final population after [tex]t[/tex] years
[tex]A[/tex] is the initial population
[tex]r[/tex] is the growth rate in decimal form
[tex]t[/tex] is the time in years
We know from our problem that the initial population is 5000, the final population is 10000, and the time is 10 years, so [tex]A=5000[/tex], [tex]f(t)=10000[/tex], and [tex]t=10[/tex].
Let's replace the values and solve for [tex]r[/tex]:
[tex]f(t)=A(1+r)^t[/tex]
[tex]10000=5000(1+r)^{10}[/tex]
Divide both sides by 5000
[tex]\frac{10000}{5000} =(1+r)^{10}[/tex]
[tex]2=(1+r)^{10}[/tex]
Take root of 10 to both sides
[tex]\sqrt[10]{2} =\sqrt[10]{(1+r)^{10}}[/tex]
[tex]\sqrt[10]{2} =1+r[/tex]
Subtract 1 from both sides
[tex]\sqrt[10]{2}-1=r[/tex]
[tex]r=\sqrt[10]{2}-1[/tex]
[tex]r=1.0718-1[/tex]
[tex]r=0.0718[/tex]
We can conclude that the growth rate of our exponential equation is [tex]r=0.0718[/tex]. The closest value from your given choices is C)r=0.69
Can someone help me please
Answer:
L.A. = 60π m² ≈ 188.4 m²S.A. = 85π m² ≈ 266.9 m²Step-by-step explanation:
Lateral Area:
The formula of a Lateral Area of a cone:
[tex]L.A.=\pi rs[/tex]
r - radius
s - slant height
We have r = 5m and s = 12m. Substitute:
[tex]L.A.=\pi(5)(12)=60\pi\ m^2\\\\\pi\approx3.14\to L.A.\approx(6)(3.14)=188.4\ m^2[/tex]Surface Area:
The formula of a Surfaace Area of a cone:
[tex]S.A.=B+L.A.[/tex]
In the base we have the circle with the radius r = 5m.
The formula of an area of a circle"
[tex]A_O=\pi r^2[/tex]
Substiute:
[tex]B=\pi(5^2)=25\pi\ m^2\approx(25)(3.14)=78.5\ m^2[/tex]
[tex]S.A.=60\pi+25\pi=85\pi\ m^2\approx188.4+78.5=266.9\ m^2[/tex]
What is the 25th term of this arithmetic sequence? 3, 9, 15, 21, 27, …
Answer:
147
Step-by-step explanation:
The n th term of an arithmetic sequence is
[tex]a_{n}[/tex] = a + (n - 1)d
where a is the first term and d the common difference
here a = 3 and d = 9 - 3 = 15 - 9 = 6, hence
[tex]a_{25}[/tex] = 3 + (24 × 6) = 3 + 144 = 147
What is the factorization of 729^15+1000?
Answer:
The factorization of [tex]729x^{15} +1000[/tex] is [tex](9x^{5} +10)(81x^{10} -90x^{5} +100)[/tex]
Step-by-step explanation:
This is a case of factorization by sum and difference of cubes, this type of factorization applies only in binomials of the form [tex](a^{3} +b^{3} )[/tex] or [tex](a^{3} -b^{3})[/tex]. It is easy to recognize because the coefficients of the terms are perfect cube numbers (which means numbers that have exact cubic root, such as 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, etc.) and the exponents of the letters a and b are multiples of three (such as 3, 6, 9, 12, 15, 18, etc.).
Let's solve the factorization of [tex]729x^{15} +1000[/tex] by using the sum and difference of cubes factorization.
1.) We calculate the cubic root of each term in the equation [tex]729x^{15} +1000[/tex], and the exponent of the letter x is divided by 3.
[tex]\sqrt[3]{729x^{15}} =9x^{5}[/tex]
[tex]1000=10^{3}[/tex] then [tex]\sqrt[3]{10^{3}} =10[/tex]
So, we got that
[tex]729x^{15} +1000=(9x^{5})^{3} + (10)^{3}[/tex] which has the form of [tex](a^{3} +b^{3} )[/tex] which means is a sum of cubes.
Sum of cubes
[tex](a^{3} +b^{3} )=(a+b)(a^{2} -ab+b^{2})[/tex]
with [tex]a= 9x^{5}[/tex] y [tex]b=10[/tex]
2.) Solving the sum of cubes.
[tex](9x^{5})^{3} + (10)^{3}=(9x^{5} +10)((9x^{5})^{2}-(9x^{5})(10)+10^{2} )[/tex]
[tex](9x^{5})^{3} + (10)^{3}=(9x^{5} +10)(81x^{10}-90x^{5}+100)[/tex]
.
What is the area the of the figure below? A) 26 B) 27 C) 52 D) 54
Answer: B=27
Step-by-step explanation:
10.8 x 5=54/2= 27
Answer:
26in.^2 the first choice
Step-by-step explanation:
Just did the QC
please I need help with all my spring packet
Answer:
Point S coordinates= (-4,5)
Step-by-step explanation:
If you would just move the point 5 PLACES TO THE RIGHT, you would get -4, 5, which is the correct answer.
A drawer contains 3 red marbles 7 green marbles and 10 white marbles if a Marble is drawn from the jar at random what is the probability that the marble is white
Answer:
1/2
Step-by-step explanation:
3+7+10=20
20/2=10=1/2
For a group experiment, your science class measured the fine-particulate concentrations in the air at random places around campus, and estimated a sample average of 22 μg/m3 (micrograms per cubic meter). If 144 readings were taken, and the standard deviation of the sample measurements was 4 μg/m3, you are 99.7% confident that actual concentration of fine particulates at the school is
Answer:
The class interval is from (22.8748 ug/m³ - 21.1252 ug/m³).
Step-by-step explanation:
Given : Sample size(n)= 144
Sample mean [tex]\mu= 22 ug/m^3[/tex]
Standard deviation [tex]\sigma=3.5 ug/m^3[/tex]
To find : 99.7% confident that actual concentration of fine particulates at the school is?
Solution :
The formula for confidence interval is
[tex]CI=\mu \pm z\times\dfrac{\sigma}{\sqrt{n}}[/tex]
Substituting the values in the formula,
[tex]CI=22 \pm 3\times\dfrac{3.5}{\sqrt{144}}[/tex]
[tex]CI=22 \pm 3\times\dfrac{3.5}{12}[/tex]
[tex]CI=22 \pm 3\times 0.2916[/tex]
[tex]CI=22 \pm 0.8748[/tex]
[tex]CI=22+0.8748, 22-0.8748[/tex]
[tex]CI=22.8748, 21.1252[/tex]
Therefore, The class interval is from (22.8748 ug/m³ - 21.1252 ug/m³).
Answer:
21 ug/m^3 - 23 ug/m^3
Step-by-step explanation:
Just got it right
A game has 15 balls for each of the letters B, I, N, G, and O. The table shows the results of drawing balls 1,250 times.
Letter Frequency
B 247
I . 272
N 238
G 241
O 252
For which letter is the experimental probability closest to the theoretical probability?
A. I
B. N
C. G
D. O
Theoretically, each letter should have the same probability of occurring since there are 15 of each. There are 5 letters that can be drawn, so there is a total of 75 balls, and each letter has a probability [tex]\dfrac{15}{75}=\dfrac15[/tex] of being drawn.
This means one would expect a theoretical frequency of [tex]\dfrac{1250}5=250[/tex], i.e. any given letter should get drawn 250 times, which means the answer is D.
Answer:
252 D-O
Step-by-step explanation:
250 and theoretically 252
in 2000 the world's population was 6.08 billion and was increasing at a rate 1.21 each year. use the function to predict the population in the year 2020
Answer:
the population would be 30.28 billion by 2020
Step-by-step explanation:
y=6.08 + 1.21x
y = 6.08 + 1.21(20)
y = 6.08 + 24.2
y = 30.28
Use the graph to write the factorization of x^2+2x-8
Answer:
(x-2)(x+4)
Step-by-step explanation:
So it would be A.
Explanation: The middle number is 2 and the last number is -8.
Factoring means we want something like
(x+_)(x+_)
Which numbers go in the blanks?
We need two numbers that...
Add together to get 2
Multiply together to get -8
Can you think of the two numbers?
Try -2 and 4:
-2+4 = 2
-2*4 = -8
Fill in the blanks in
(x+_)(x+_)
with -2 and 4 to get...
(x-2)(x+4)
Answer:
(x−2)(x+4)
A. (x+4)(x-2). The factorization of the quadratic equation x²+2x-8 given by the graph is (x+4)(x-2).
From the graph shown in the image we can see the parabola's cut points, in the y-axis is -4 and the x-axis is 2, then we write the product changing the signs (x+4)(x-2) = x²+2x-8
What is the difference between a relation
and a function? Is every relation a function? Is every
function a relation? Explain.
Answer:
Not all relationships are functions, but all functions are also relationships
Step-by-step explanation:
A relationship is a correspondence between two sets of values.
A relationship assigns values from an output set called range to a set and input called a domain.
On the other hand, a relation is a function if and only if there is only one value of the output set (Range) assigning to each value of the input set (Domain).
In other words, if an input value [tex]x_1[/tex] is assigned two or more output values [tex]y_1[/tex], [tex]y_2[/tex], [tex]y_3[/tex] .. then the relationship is not a function. This means that not all relationships are functions.
[tex]y=\±\sqrt{x} +3[/tex] is a relation but it is not a function.
because when x = 4 then y = 1 and y = 5.
Not all relationships are functions, but all functions are also relationships
Final answer:
A relation is a set of ordered pairs, while a function is a relation where each input value is associated with only one output value. Not every relation is a function, but every function is a relation.
Explanation:
A relation is a set of ordered pairs where each input value is associated with one or more output values. On the other hand, a function is a relation where each input value is associated with only one output value.
Not every relation is a function. For example, the relation {(1,2), (1,3), (2,4)} is not a function because the input value 1 is associated with two different output values (2 and 3). However, every function is a relation because it establishes a relationship between the input and output values.
Simplify : 2n - 7 + 3(4n - 3)
Answer:
14n-16
Step-by-step explanation:
Given
[tex]2n - 7 + 3(4n - 3)\\[/tex]
Simplification requires the expression to be in its shortest and concise form. The brackets are opened and addition or subtractions are performed
So,
Multiplying 3 inside bracket
[tex]2n - 7 + 12n - 9[/tex]
Combining alike terms:
[tex]2n+12n-7-9[/tex]
Performing addition and subtractions:
[tex]14n-16[/tex]
Hence the simplified form is:
14n-16 ..
-2a(a+b-5)+3(-5a+2b)+b(6a+b-8) the coefficient of the a^2 term is
Answer:
-2
Step-by-step explanation:
the coefficient is the number in front of the variable.
Find the perimeter or cm
Answer:
The perimeter is 22.
Step-by-step explanation:
The perimeter formula (it sometimes varies) is 2(b+h)
b being base (in this example, 6)
h being height (in this example, 5)
So now, with substitution, we are left with:
2(6+5)
Which simplifies down to:
2(11)
22
Simplify ( √ 5)(^3 √ 5) the answer will be a wholenumber and a fraction
[tex]( \sqrt{5)( \sqrt[3]{5} } )[/tex]
Answer:
[tex]\sqrt{5}\cdot\sqrt[3]{5} =\sqrt[6]{5^3} \cdot\sqrt[6]{5^2} =\sqrt[6]{5^5} =5^{(5/6)}[/tex]
Step-by-step explanation:
The rules of exponents apply, even when they are fractional exponents:
[tex]a^b\cdot a^c=a^{b+c}\\\\\sqrt[b]{x^a}=x^{(a/b)}[/tex]
Line AB contains points A (0, 1) and B (1, 5). The slope of line AB is
−4
negative 1 over 4
1 over 4
4
solution here,
slope(m)=(y2-y1)/(x2-x1)
=(5-1)/(1-0)
=4/1 =4
Answer:
The correct answer is D) 4
Step-by-step explanation:
I took the test and this was correct!
Perform the operation and write the answer in simplest form 5 1/7 * 3 1/9
Answer:
16
Step-by-step explanation:
Input it in the calculator
Answer: 16
Step-by-step explanation:
5 1/7 is 36/7=5.142857
3 1/9 is 28/9=3.1
Do 5.142857 times 3.1
And it equals 15.94 but rounds up to 16.
What does that sign mean? What’s the name?
Pie. It’s pie 3.14.... the name of that sign is pie
Answer:
That symbol represents pi.
Step-by-step explanation:
Pi is used by mathematicians to represent the ratio of a circle's circumference to its diameter. It is approximately equal to 3.14159. Hope this helps!
the Johnsons want to cover their backyard with new grass their backyard is rectangular with a length of 3x - 2 feet and a width of 3x + 1 ft however there rectangular swimming pool along with its surrounding patio has dimensions of x + 4 by x + 5 ft what is the area of the region of the yard that they want to cover with new grass
The answer is:
The area that the want to cover with new grass will be:
[tex]Area_{grass}=8x^{2} -12x-22[/tex]
Why?If we want to calculate what is the ara of the region of the backyard that they want to cover with new grass, we need to calculate the area of the backyard, calculate the area of the swimming pool and its patio, and the last step is to subtract the area of the swimming pool and its patio to the total area of the backyard.
So, to calculate the areas, we need to use the following formula:
[tex]Area=Length*Width[/tex]
Also, we need to remember how the distributive property works, since we are going to need it.
We have that:
[tex](a+b)(c+d)=ac+ad+bc+bd[/tex]
We are given the following information:
For the backyard we have:
[tex]Length=3x-2\\Width=3x+1[/tex]
For the swimming pool and its patio:
Since there it's not mentioned, let be the first expression the length, and the second one, the width.
[tex]Length=x+4\\Width=x+5[/tex]
Then, calculating we have:
Backyard:
[tex]Area_{backyard}=(3x-2)*(3x+1)=9x^{2}+3x-6x-2=9x^{2}-3x-2[/tex]
Swimming pool and patio:
[tex]Area_{swimmingpool}=(x+4)*(x+5)=x^{2}+5x+4x+20=x^{2}+9x+20[/tex]
Now, calculating the area that they want to cover with new grass, we have:
[tex]Area_{grass}=Area_{backyard}-Area_{swimmingPool}\\\\Area_{grass}=(9x^{2}-3x-2)-(x^{2}+9x+20)\\\\Area_{grass}=9x^{2} -x^{2} -3x-9x-2-20\\\\Area_{grass}=8x^{2} -12x-22[/tex]
Hence, we have that the area that the want to cover with new grass will be:
[tex]Area_{grass}=8x^{2} -12x-22[/tex]
Have a nice day!
Rewrite sin^4x so that it involves on the first power of cosine
Use the half-angle identities.
[tex]\sin^2x=\dfrac{1-\cos2x}2[/tex]
[tex]\implies\sin^4x=\left(\dfrac{1-\cos2x}2\right)^2=\dfrac{1-2\cos2x+\cos^22x}4[/tex]
[tex]\cos^2x=\dfrac{1+\cos2x}2[/tex]
[tex]\implies\sin^4x=\dfrac{1-2\cos2x+\frac{1+\cos4x}2}4=\dfrac{3-4\cos2x+\cos4x}8[/tex]
sin^4(x) can be expressed in terms of cosine as (1 - cos^2(x))^2.
Rewrite sin^4(x) in terms of cosine by using the Pythagorean identity for trigonometric functions, which relates sin^2(x) and cos^2(x):
sin^2(x) + cos^2(x) = 1
Now, solve for sin^2(x):
sin^2(x) = 1 - cos^2(x)
Now, square sin^2(x) to get sin^4(x):
(sin^2(x))^2 = (1 - cos^2(x))^2
sin^4(x) = (1 - cos^2(x))^2
So, sin^4(x) can be expressed in terms of cosine as (1 - cos^2(x))^2.
for such more question on trigonometric functions
https://brainly.com/question/25618616
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Pls find the answers
Answer:
the number of sheet available is 75, 000
you take the total number of pages available = 8 x 75,000
= 600,000 pages
then each notebooks contains 200 pages
= 600,000 / 200
= 3000 notebooks can be made
Step-by-step explanation:
Answer:
3000 notebooks
Step-by-step explanation:
75,000*8=600000
600000/200=3000
Find the system determinant of the given matrix. -30 -6 6 30
Answer:
- 864
Step-by-step explanation:
In the case of a 2 × 2 matrix the determinant may be defined as:
|A| = [tex]\left[\begin{array}{cc}a&b\\c&d\\\end{array}\right][/tex]= ad-bc
Given in the question a matrix
[tex]\left[\begin{array}{cc}-30&-6\\6&30\\\end{array}\right][/tex]
(-30)(30) - (-6)(6)
-900 + 36
- 864
Answer:
Option A: -30
For Odyssey
**If you are on the pre-test then you might wanna take your time because they can suspect if you are cheating**
how to solve dividing radicals
ANSWER: Multiply out front and multiply under the radicals. "The radical of a product is equal to the product of the radicals of each factor." "The radical of a quotient is equal to the quotient of the radicals of the numerator and denominator."