Answer:
The longest side of the triangle is YZ, the shortest side is ZX, the largest angle is ∠X and the smallest angle is ∠Y.
Step-by-step explanation:
The lengths of the sides of the triangle XYZ are as follows:
XY = n + 4
YZ = 2n
ZX = n - 2
According to the triangle inequality theorem, the sum of two sides of a triangle is always greater than the third side.
Then,
XY < YZ + ZX ⇒ n + 4 < 2n + n - 2 ⇒ n + 4 < 3n - 2 ⇒ 2n > 6 ⇒ n > 3
YZ < XY + ZX ⇒ 2n < n + 4 + n - 2 ⇒ 2n < 2n + 2 ⇒ 0 < 2
ZX < XY + YZ ⇒ n - 2 < n + 4 + 2n ⇒ n - 2 < 3n + 4 ⇒ 2n > -6 ⇒ n > -3
It is provided that n ≥ 5.
Then the sides of the triangle are:
XY = n + 4 ≥ 5 + 4 = 9
YZ = 2n ≥ 2 × 5 = 10
ZX = n - 2 ≥ 5 - 2 = 3
So, the longest side of the triangle is YZ. And the shortest side is ZX.
The largest angle of a triangle is opposite to the longest side.
The angle opposite to YZ would be X. So, the largest angle is ∠X.
The smallest angle of a triangle is opposite to the shortest side.
The angle opposite to ZX would be Y. So, the smallest angle is ∠Y.
Thus, the longest side of the triangle is YZ, the shortest side is ZX, the largest angle is ∠X and the smallest angle is ∠Y.
A B R and P are four points on a circle with centre 0. A O R and C are four points on a different circle. The two circles intersect at the points A and R . CPA CRB and AOB are straight lines. If angle CAB=x prove that angle ABC=x and reason on the Each statement must have a valid reason same line as the statement.
Answer:
x° = ∠OBR = ∠ABC (base angles of a cyclic isosceles trapezoid)
Step-by-step explanation:
APRB form a cyclic trapezoid
∠APO = x° (Base angle of an isosceles triangle)
∠OPR = ∠ORP (Base angle of an isosceles triangle)
∠ORB = ∠OBR (Base angle of an isosceles triangle)
∠APO + ∠OPR + ∠OBR = 180° (Sum of opposite angles in a cyclic quadrilateral)
Similarly;
∠ORB + ∠ORP + x° = 180°
Since ∠APO = x° ∠ORB = ∠OBR and ∠OPR = ∠ORP we put
We also have;
∠OPR = ∠AOP = ∠BOR (Alternate interior angles of parallel lines)
Hence 2·x° + ∠AOP = 180° (Sum of angles in a triangle) = 2·∠OBR + ∠BOR
Therefore, 2·x° = 2·∠OBR, x° = ∠OBR = ∠ABC.
someone please help with this question
Answer:
230
Step-by-step explanation:
9 times 20 = 180
divide by 2 = 90
7 times 20 = 140
140 + 90 = 230
Answer:
A=230 cm2
Step-by-step explanation:
A1= L x W HEIGHT OF TRIANGLE=16-7=9
A1=20 x 7
A1=140 cm2
A2=1/2 x B x H
A2=1/2 x 20 x 9
A2=90 CM 2
1/3 as a percent? Djdjenkeoqkehrwklwjrhr
Answer:
33% or with 10th place decimal 33.3%
Step-by-step explanation:
1/3 has a continuous decimal form of .333333...
So, it is usually rounded to .33
Hope this helps!
Answer: 33.33%
Step-by-step explanation:
Find the volume of a pyramid with a square base, where the perimeter of the base is
15.8 ft and the height of the pyramid is 20.4 ft. Round your answer to the nearest
tenth of a cubic foot.
(It’s on deltamath)
The volume of the given pyramid is 106.1 cubic foot.
To Find the Volume of a pyramid with a square base
Given:
The perimeter of the base is 15.8 feet
The base of the pyramid is square given of side say L .
Thus, from the formula of perimeter of square,
⇒ 4*L = 15.8 feet
∴ L = 3.95 feet
Now the base area of the pyramid is [tex]L^{2}[/tex] as it is a square .
∴ Base area = 3.95*3.95 square feet
= 15.6025 square foot
Now, formula for volume of the pyramid
= 1/3 * base area * height
⇒ Volume = 1/3 * 15.6025 * 20.4 cubic foot
∴ Volume = 106.097 cubic foot
Thus volume of the given pyramid is 106.1 cubic foot rounded off to nearest tenth.
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find the root(s) of f (x) = (x + 5)3(x - 9)2(x + 1). 50 POINTS!!!!!!! -5 with multiplicity 3 5 with multiplicity 3 -9 with multiplicity 2 9 with multiplicity 2 -1 with multiplicity 0 -1 with multiplicity 1 1 with multiplicity 0 1 with multiplicity 1
Answer:
The answer to this question can be described as follows:
-5 with multiplicity 3
9 with multiplicity 2
-1 with multiplicity 1
Step-by-step explanation:
Given:
[tex]\Rightarrow f (x) = (x + 5)^3(x - 9)^2(x + 1)[/tex]
Solve the above equation:
[tex]\Rightarrow f (x) = (x + 5)(x + 5)(x + 5)(x - 9)(x - 9)(x + 1)\\[/tex]
The roots of the polynomial are as follows:
[tex]\Rightarrow (x-x_1)(x-x_2)(x-x_3)......(x-x_n)\\\\\Rightarrow x_1,x_2,x_3.........x_n[/tex]
That's why the roots are:
5 with multiplicity 3
9 with multiplicity 2
-1 with multiplicity 1
Answer:
answer:
a. -5 with multiplicity 3
d. 9 with multiplicity 2
f. -1 with multiplicity 1
Step-by-step explanation:
Solve for x. (1/4)(5x−3) > (1/2)x + (1/3)
Answer:
x >13/9
Step-by-step explanation:
(1/4)(5x−3) > (1/2)x + (1/3)
Distribute
5/4x - 3/4 > 1/2x + 1/3
Multiply each side by 12 to get rid of fractions
12*5/4x -12* 3/4 >12* 1/2x +12* 1/3
15x -9 > 6x +4
Subtract 6x from each side
15x-6x-9 > 6x-6x+4
9x -9> 4
Add 9 to each side
9x-9+9 > 4+9
9x > 13
Divide by 9
9x/9 >13/9
x >13/9
Answer:
3/4
Explanation:
Took the test of K12 and it's right.
Simplify (4+2n3)+(5n3+2). Write the answer in standard form.
Answer:
The answer is 7n3 + 6.
Step-by-step explanation:
To simplify, remove the parentheses and combine like terms.
The standard form of the given expression is 7n³+6.
The given expression is (4+2n³)+(5n³+2).
To add any two expressions group the like terms.
Here, 4+2n³+5n³+2
= (2n³+5n³)+4+2
= 7n³+6
Therefore, the standard form of the given expression is 7n³+6.
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Can someone help me with this problem?
Answer:
(5s + 8) is the missing factor.
Step-by-step explanation:
The given expression is 5s² + 23s + 24
We have to convert the given expression into the factored form.
One factor of the expression has been given as (x + 3)
5s² + 23s + 24 = 5s²+ 15s + 8s + 24
= 5s(s + 3) + 8(s + 3)
= (5s + 8)(s + 3)
So the factors of the expression will be (s + 3) and (5s + 8)
Therefore, the missing factor of the given expression is (5s + 8).
Rob is saving to buy a new MP3 player. For every $12 he earns babysitting, he saves $7. On Saturday, Rob earned $72 babysitting. How much money did he save?
Peter accumulated $7,500 in credit card debt. If the interest rate is 3.5% per year and he does not make any payments for 10 years, how much will he owe on this debt in 10 years by compounding continuously
Answer:
$10579.49
Step-by-step explanation:
The formula for amount gotten after a period of time (in years) on a principal which is compounded continuously is given as:
[tex]A = P(1 + r)^t[/tex]
where P = principal (amount borrowed)
r = interest rate
t = number of years
Peter accumulated $7,500 in credit card debt with interest rate as 3.5% per year and he does not make any payments for 10 years.
Therefore, his debt is:
[tex]A = 7500(1 + \frac{3.5}{100})^{10}\\ \\A = 7500 (1 + 0.035)^{10}\\\\A = 7500(1.035)^{10}\\[/tex]
A = $10579.49
He will owe $10579.49 after 10 years
Answer:
A= $10,643.01
Step-by-step explanation:
if you are rounded to the nearest cent
Identify the values of each variable in the formula. Remember to express the percent as a decimal.
A=?
P= $7,500
r= 0.035
t= 10 years
For compounding continuously, use the formula A=Pert.
Substitute the values in the formula and compute the amount to find
A= 7,500e [tex]x^0.035.10[/tex][tex]x^{0.035.10}[/tex]
A= $10,643.01
what does dependent and independent variables mean
Answer:
independent is the y value or the value that changes at a steady rate no matter what, the dependent variable or x is the variable that is subject to change and is dependent on the y value to find a pattern
Step-by-step explanation:
Answer:
Variables are given a special name that only applies to experimental investigations. One is called the dependent variable and the other the independent variable. The independent variable is the variable the experimenter changes or controls and is assumed to have a direct effect on the dependent variable.
Step-by-step explanation:
please help i will give brainliest answer
Answer:
circumference = 2πr
2×π×6
12πmm
Given:
Radius of circle = 6 mm
Work out :
Workout the circumference of this circle?
Formula used:
Circumference of circle = 2πr
Solution:
According to the question,
Circumference of circle = 2πr
= 2 × π × 6
= 12 π mm
There are 10 marbles in a bag 7 of them are blue and the rest are green If I randomly picked a marble from the bag what is the probability of getting a blue marble
Answer:
7/10
Step-by-step explanation:
10 marbles in a bag 7 of them are blue and the (10-7)=3 green
P( blue) = blue / total
= 7/10
The perimeter of Suzanne's rectangular garden is 40 yards. The length of the garden is 12 yards. What is the area of Suzanne's garden? square yards
Answer:
96 sq yards
Step-by-step explanation:
40-24 is 16, and 16/2 is 8. 8 is the second length, so 8 times 12 is 96 which is the area
What is the cube root of 216?
-6
6
72
-72
Answer:
The cube root for 216 is 6
Step-by-step explanation:
Answer:
the cube root of 216 is 6
Step-by-step explanation:
What information is provided in the second section of the report?
a. Information about overdue accounts
b. Accounts that have been turned over to a credit agency
c. Detailed account information
d. Summarized account information
Answer:
d. Summarized account information
Step-by-step explanation:
At my apartment I have a closet with 250 ft3 worth of space. If each of my spherical cannonballs have a radius of .75 feet, how many can I fit in my closet?
Answer:
141
Step-by-step explanation:
We need to first find the volume of the cannonballs and then, divide the volume of the closet by the volume of the cannonballs.
The radius of the spherical cannonball is 0.75 feet.
The volume of a sphere is:
[tex]V = \frac{4}{3} \pi r^3[/tex]
where r = radius
Therefore, the volume of the cannonballs is:
[tex]V = \frac{4}{3} * \pi * 0.75^3\\\\V = 1.77 ft^3[/tex]
Therefore, the number of cannonballs that can fit the closet is:
250 / 1.77 = 141.24
Since the number is a maximum and it must be a whole number, the number of cannonballs that can fit the closet is 141.
PQRS is a parallelogram. If mQRS = (9x - 20)° and
mSPQ = (4x + 90)°, what is the value of x?
22
8.5
14
10
Answer:
x = 8.5
Step-by-step explanation:
In this question, we are to calculate the value of x.
To calculate this, we shall be utilizing one of the important properties of parallelogram.
This property is that opposite angles of a parallelogram are equal.
This means that mQSR = mSPQ = 4x + 90
Now to finally calculate x, we make use of another important parallelogram property which is that angles of parallelogram which faces each other are supplementary.
This means that they add up to be 180
Since mQSR faces mQRS
This means that;
4x + 90 + 9x -20 = 180
13x + 70 = 180
13x = 110
x = 110/13 which is approximately 8.5
What is the following quotient? 6-3(3 sqrt 6)/3 sqrt 9
Answer:
a. 2(^3 sqrt 3) - ^3 sqrt 18
Step-by-step explanation:
got it right on edge
[tex]\frac{6-3(\sqrt[3]{6})}{\sqrt[3]{9}}[/tex][tex]\frac{6-3(\sqrt[3]{6})}{\sqrt[3]{9}}[/tex][tex]2(\sqrt[3]{3})-\sqrt[3]{18}[/tex] option (A) is Correct.
What is Rationalization?It is a process that finds application in elementary algebra, where it is used to eliminate the irrational number in the denominator.How to Solve the problem ?
The problem can be solved by following steps.
The expression given is [tex]\frac{6-3(\sqrt[3]{6})}{\sqrt[3]{9}}[/tex]
So , The first step we will do is Rationalize the figure
= [tex]\frac{6-3(\sqrt[3]{6})*3 {\sqrt{9^2} }}{\sqrt[3]{9}*\sqrt[3]{9} }[/tex]
The product of radicals with the same index equals the radical of the product:[tex]\frac{6-3(\sqrt[3]{6})*3 {\sqrt{9^2} }} {\sqrt[3]{9*9^2} }[/tex]
Simplify using exponent with same base
[tex]a^{n}*a^{m} = a^{a+m}[/tex]
= [tex]\frac{6-3(\sqrt[3]{6})*3 {\sqrt{9^2} }} {\sqrt[3]{9^1+^2} }[/tex]
Calculate the sum or difference: [tex]\frac{6-3(\sqrt[3]{6})*3 {\sqrt{9^2} }} {\sqrt[3]{9^3} }[/tex]
Simplify the radical expression: [tex]\frac{6-3(\sqrt[3]{6})*3 {\sqrt{9^2} }} {{9} }[/tex]
Calculate the power : [tex]\frac{6-3(\sqrt[3]{6})*3 {\sqrt[3]{3} }} {{9} }[/tex]
Cross out the common factor: [tex]\frac{6-3(\sqrt[3]{6})*3 {\sqrt[3]{3} }} {{3} }[/tex]
Factor Greatest Common Factors : [tex]\frac{3*2\sqrt[3]{3}-\sqrt[3]{18} }{3}[/tex][tex]3*2\sqrt[3]{3}-\sqrt[3]{18}}[/tex]
Reduce the fraction : [tex]2\sqrt[3]{3}-\sqrt[3]{18}}[/tex]
Hence the First option is correct
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name the property used in the following -2/7+0=0+-2/7=-2/7
Answer:
commutative propertyidentity elementStep-by-step explanation:
-2/7+0 = 0+-2/7 . . . . commutative property of addition
The commutative property allows you to swap the order of operands being summed.
0+-2/7 = -2/7 . . . . identity element of addition
The identity element for addition is 0. That is, adding 0 to anything does not change its value.
0.895 95 repeating as a simplified fraction
Answer:
89595/100000
Step-by-step explanation:
A circle is centered at D(-1,3). The point G(-10,1) is on the circle.
Where does the point J(-3, 12) lie?
Answer:on the circle
Step-by-step explanation:
Point J(-3, 12) is lying on the circle whose center is located at point D(-1, 3).
What is a circle?It is defined as the combination of points that and every point has an equal distance from a fixed point ( called the center of a circle).
We have a center of the circle at D(-1, 3)
And point G(-10, 1) is on the circle.
We know the standard equation of the circle when a center is given:
[tex]\rm (x-h)^2+(y-k)^2=r^2[/tex]
Where r is the radius of the circle and (h, k) is the center of the circle.
Here (h, k) ⇒ (-1, 3)
The circle equation becomes:
[tex]\rm (x+1)^2+(y-3)^2=r^2[/tex]
Put the point on the circle equation to get the radius of the circle:
[tex]\rm (-10+1)^2+(1-3)^2=r^2[/tex]
[tex]\rm (-9)^2+(-2)^2= r^2\\\\\rm 81+4 = r^2\\\\ \rm r = \sqrt{85} \ units[/tex]
Equation of circle is:
[tex]\rm (x+1)^2+(y-3)^2=85[/tex]
Now put the point J(-3, 12 ) in the circle equation:
[tex]\rm (-3+1)^2+(12-3)^2=85[/tex]
4+ 81 ⇒ 85
It means point J is lying on the circle.
Thus, point J(-3, 12) is lying on the circle whose center is located at point D(-1, 3).
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Which number is rational?
ΟΟΟ
T
10
16
Answer:
[tex]10[/tex]
[tex]16[/tex]
Explanation:
A rational number is a number that can be expressed as the quotient or fraction of two integers.
the tires of a tractor are 5.25 feet tall. what measure would help to find how many feet the tractor will travel in 1 rotation
and how many feet would it travel
Answer:
16.485 feet
Step-by-step explanation:
Given that tire is 5.25 feet tall
any circular shape is as tall as its diameter.
we can say that diameter of tire is 5.25 feet.
in one rotation tire will start from one point of tire and reach it again.
it is like on a circle moving from on one point and then reaching to same point.
and we know that distance covered on moving on the point of circle is equal to circumference.
Thus, measure of circumference would help to find how many feet the tractor will travel in 1 rotation.
circumference of circle is given by [tex]\pi D[/tex]
where D is the diameter of circle.
we will us 3.14 as value of [tex]\pi[/tex]
thus, circumference of circle is[tex]\pi * 5.25 = 3.14*5.25 = 16.485[/tex]
Hence, tractor would travel 16.485 feet in one rotation.
make x the subject of the formula a=b(1-x)
Answer:
x = -(a - b)/b
Step-by-step explanation:
Solve for x:
a = b (1 - x)
a = b (1 - x) is equivalent to b (1 - x) = a:
b (1 - x) = a
Divide both sides by b:
1 - x = a/b
Subtract 1 from both sides:
-x = (a - b)/b
Multiply both sides by -1:
Answer: x = -(a - b)/b
The scatter plot shows the number of oranges picked, in hundreds, in relation to the number of lemons harvested, in hundreds, by several farmers.The scatter plot shows the number of oranges picked, in hundreds, in relation to the number of lemons harvested, in hundreds, by several farmers.
Complete Question:
The scatter plot shows the number of oranges picked, in hundreds, in relation to the number of lemons harvested, in hundreds, by several farmers. According to the plot, which value is the best estimate of the correlation coefficient of the data?
A.-0.2
B. -0.9
C. 0.9
D. 0.2
*See attachment for the scatter plot
Answer:
C. 0.9
Step-by-step explanation:
If we take a good look at the scatter plot in the attachment showing numbers if oranges picked in relation to number of lemons harvested, we can infer that there's a strong positive correlation between both variables.
Thus, both variables are moving in the same direction. As one variable increases, the other variable increases. Also, the data points represented on the plot seem clustered close to the line rather than farther away.
This will suggest a positive correlation coefficient that is closer to 1.
From the options given above, the best estimate of the correlation coefficient would be 0.9.
The answer is C. 0.9
100 EASY POINTS!!! Please include an explanation :)
Which graph represents functions f and g?
f: initial value of 200 decreasing at a rate of 4%
g: initial value of 40 increasing at a rate of 8%
Answer:
Choice C
Step-by-step explanation:
f: initial value of 200 decreasing at a rate of 4%
g: initial value of 40 increasing at a rate of 8%
f is decreasing so it must go down starting at 200
That eliminates a and d
g is increasing and starts at 40 That eliminates a
We must look at b and c
g is increasing faster than f is decreasing
Choice C
Can anyone help me with this question please
Answer:
7. ∠CBD = 100°
8. ∠CBD = ∠BCE = 100°; ∠CED = ∠BDE = 80°
Step-by-step explanation:
7. We presume the angles at A are congruent, so that each is 180°/9 = 20°.
Then the congruent base angles of isosceles triangle ABC will be ...
∠B = ∠C = (180° -20°)/2 = 80°
The angle of interest, ∠CBD is the supplement of ∠ABC, so is ...
∠CBD = 180° -80°
∠CBD = 100°
__
8. In the isosceles trapezoid, base angles are congruent, and angles on the same end are supplementary:
∠CBD = ∠BCE = 100°
∠CED = ∠BDE = 80°
What is the perimeter P of △DEF to the nearest whole number?
Answer:
Can you please tell me what is the area of the given triangle?
What is the surface area of a right cylinder which has a base with radius 9 units and has a height of 12 units?