Answer: a = 8; b = 15; c = 17
Step-by-step explanation:
c = b + 2 and c = 2a + 1
b = c − 2 and a = [tex]\frac{c-1}{2}[/tex]
c² = b² + a²
[tex]c^{2} = (c-2)^{2} + \frac{c-1}{2}\\[/tex]
[tex]c^{2}= \frac{4 (c-2)^{2}+(c - 1)^{2} }{4}[/tex]
[tex]4c^{2}={4 (c^{2} + 4 -4c)+c ^{2} + 1-2c[/tex]
[tex]4c^{2}={4 c^{2} + 16 -16c)+c ^{2} + 1-2c[/tex]
[tex]c^{2}-18c+17=0[/tex]
[tex]c(c -17)-1(c-17)=0[/tex]
[tex](c -1)(c-17)=0[/tex]
c = 1 or c = 17
If c = 1 then b = 1 - 2 = -1, that's not possible
So x = 17
b = 17 - 2 = 15
a = [tex]\frac{17-1}{2} = 8[/tex]
Length sides of the triangle are 17 cm, 15 cm and 8 cm.
I saw some of this on a site but I want to make sure its correct so we're gonna apply the pythagorean theory and see if its correct.
[tex]a^{2} + b^{2} = c^{2} \\8^{2} + 15^{2} = 17^{2} \\64 + 225 = 289\\289 = 289\\[/tex]
This shows that this is correct.
Hope this helped! Again, some of this was from a site, not from me.
If MNP - TSR and NQ and SU are angle bisectors, find TS.
MN = 2
TS = n + 2
NP = 3
SU = 1
NQ = n + 3
Answer:
TS is 1
Step-by-step explanation:
The given parameters are;
ΔMNP is similar to ΔTSR
[tex]\overline {NQ}[/tex] and [tex]\overline {SU}[/tex] are angle bisectors of ∠MNP and ∠TSR respectively
MN = 2, TS = n + 2, NP = 3, SU = 1, NQ = n + 3
We have;
MN and TS are corresponding sides
[tex]\overline {NQ}[/tex] and [tex]\overline {SU}[/tex] are corresponding sides
Therefore, we have;
MN/TS = [tex]\overline {NQ}[/tex]/[tex]\overline {SU}[/tex] which gives;
2/(n + 2) = (n + 3)/1
(n + 2)·(n + 3) = 2
n² + 3·n + 2·n + 6 = 2
∴ n² + 5·n + 4 = 0, which gives, by factorization;
(n + 1)·(n + 4) = 0
∴ n - 1 or n = -4
TS = n + 2
When n = -1 TS = -1 + 2 = 1
When n = -4, TS = -4 + 1 = -3
Therefore, for a natural number value, we have, n = -1 and TS = 1.
If a,b and c are the sides of a triangle
where a = 6, b = 8 and c = 9
is this a right triangle ?
Answer:
No, it is not a right triangleStep-by-step explanation:
A right triangle consists of hypotenuse, opposite and adjacent. For the sides to be a right angle, the r=square of the longest side (hypotenuse) must be equal to the sum of the square of the other two sides
Given the sides a = 6, b = 8 and c = 9
a²+ b² = c² (This equation must be satisfied)
Taking the sum of the square of a and b
6² + 8²
= 36 + 64
= 100
= 10²
Since the result is not the square of 9 which is the third side, hence the sides is not a right triangle
1) Convert 1/3 to a decimal
using long division
Jason scores 10 points for each question answered
correctly on an exam. Write an algebraic
expression for the total points he will score if he
answers n questions correctly.
Answer:
f(x) = 10n
Step-by-step explanation:
If met with questions like these, the term "for each" means to multiply. simply write an equation that multiplies n and 10. Also "f(x)" can be substituted for "y" if that is what your instructor taught you.
Jerry started sit-ups every day . The first day he did 15 sit up . Everyday he did 2 more sit ups than he did the previous day today jerry did 33 sit-ups
Answer:
2x+15=33
Step-by-step explanation:
Computation of the equation that could be solved to find the number of days Jerry has been doing sit-ups, not counting the first day
Based on the information given the EQUATION will be :
2x+15=33
Where,
x represent Jerry Sit up numbers of days excluding the first day
2x represent the additional 2 more sit ups
2x +15 represent the total number of sit up that was done after the first day
2x+15=33 represent the total 33 sit-ups that jerry did today
Therefore the EQUATION that could be solved to find the number of days Jerry has been doing sit-ups, not counting the first day will be 2x+15=33
I need help ASAP pls help !!
Answer: C plz brainliest
Step-by-step explanation:
Cuz if x is replaced for 646
32.7632(646) + 593.2188 = 21758.246
Since it said approximately it is 21.758
setting 7/3 equal to whuch ratio would result in a valid proportion 9/49 18/42 49/9
Answer:
49/9
Step-by-step explanation:
7/3 = 49/9
What do we multiply to the 7 in the numerator by to get 49?
- Well, 7. So we know the numerators have a factor of 7.
Then what do you multiply to 3 to get 9?
-This is 3.
We notice a pattern of the number multiplying itself, so the first fraction being (7/3)^2 would be 49/9
-2x - 14 =-2
(Solve for x)
Answer:
x = -6
Step-by-step explanation:
Answer:
x=-6
Step-by-step explanation:
-2x - 14 = -2
first, you have to add 14 to both sides
-2x = 12
now you divide -2 from both sides
x = -6
6 - 2 4/7 = ?
answer asap and correct pls.
Answer:
24/7
Step-by-step explanation:
1. Mr. Vasquez went to a restaurant with his family last weekend. He used his bank card and his bank account was debited $45. Represent the amount of money that was debited from his bank account using an integer.
Answer:
-$45
Step-by-step explanation:
INTERGER can said to represent a whole number in which this numbers can either be a positive INTERGER or a negative INTERGER. Therefore Based on the information if after using his bank card, his bank account was debited with the amount of $45 which means that the $45 that was debited will represent a NEGATIVE amount because it has lessen the amount in his bank account.
Therefore to represent the amount of $45 that was debited from his bank account using an INTERGER it will be -$45.
Bodie purchases a rectangular prism ( a box ) to store his dog food in. The prism is LaTeX: \frac{7}{4}7 4 inches long, LaTeX: \frac{9}{4}9 4 inches wide, and 3 inches in height. Bodie's dog food are these cute little cubes that are each LaTeX: \frac{1}{4}1 4 inches long, wide, and high. If Bodie carefully stacks the dog food into the prism, how many little dog food cubes will fit in the prism?
Answer:
84dog cubes
Step-by-step explanation:
First we need to get the volume of the rectangular prism and the little cubes
Volume of the prism = base area × height
Volume f the prism = length × width × height
Given
Length = 7/4in
Width = 9/4in
Height = 3in
Volume of the prism = 7/4×9/4×3
Volume of the prism = 63/48
Volume of the prism= 21/16 in³
Volume of the cube = L³
L is the length of one side of the cube
Volume of the cube =(1/4)³
Volume of tje cube = 1/64in³
Number of dog food cubes that will fit in = 21/16÷1/64
= 21/16×64/1
= 21×4
= 84
Hence 84 dog cubes will fit in
What is the y-value of the solution to the following system of linear equations? Y=x+8
x+2y=1
A.-7
B.-5
C.3
D.13
Answer:
X is -5
y is 3
Step-by-step explanation:
A company has 2.4 times 10 to the 6th power shares of stock and 1.5 times the 10 to the 4th power shareholders. If each shareholder owned the same number of shares, how many shares would each shareholder own? Write your answer in scientific notation
Answer: 1.6 * 10² shares
Step-by-step explanation:
Number of shares company has = 2.4 * 10⁶
Number of shareholders = 1.5 * 10⁴
Number of shares each shareholder owns:
= 2.4 * 10⁶/1.5 * 10⁴
= 2.4/1.5 * 10⁶⁻⁴
= 1.6 * 10²
Buying a car is an example of _____.
a.An immediate goal
b.A long term goal
c.A short term goal
d.A liquid goal
Answer:
C. A short term goal.
Step-by-step explanation:
This is explained to be a goal or target meant and positioned to be hit within short period of time. It is described to be a stepping stone towards a long term goal. Experts has also said that is a bridge that connects the long-term endeavours. This why on a goal standard of living, a car purchase is seen to be a short-term goal. When there are no specific guidelines, the road to your bigger goals becomes murky, this is seen because your compass is wrongly set.
What is 3f + 8f - 8f - 3f simplified?
Answer:
0
Step-by-step explanation:
everything cancels out so the answer is 0
Answer:
0
Step-by-step explanation:
3f + 8f - 8f - 3f
commutative property
(3f - 3f) + (8f - 8f)
3 - 3 = 0
0f + (8f - 8f)
8 - 8 = 0
0f + 0f
combine like terms
0 + 0 = 0
0f, or just 0
Jean is multiplying 6 x 39. She decides to multiply 6 x 30 first, then add on 6 x 9. What property is Jean using to solve the problem? Her procedure would look like this mathematically
Answer:
Jean would add both results to get the final result of the multiplication of 6 x 39.
Step-by-step explanation:
6 x39 = 234
if the 3 in 39 is in the tenth position, then 6 x30 = 180
the number 9 in 39 stands as just 9, so, 6 x 9 = 54
The final multiplication of 6 and 39 = 180 + 54 = 234
please solve this question in mathematics
75*75+4543-8745/3.5
Answer:
7669.42857
Step-by-step explanation:
Please put them in order THANK YOU
32/a = 12.8/5.6
Pls show work for brainest
(Question worth 12 points)
Answer:
a=14
Step-by-step explanation:
32/a=12.8/5.6
a(32/a)=(12.8/5.6)a
32=12.8/5.6a
5.6a(32)=(12.8/5.6a)5.6a
12.8a=179.2 or a = 179.2/12.8
a=14
For which situation is the use of approximate numbers most appropriate?
A. preparing your yearly taxes
B. ordering programs for a high school musical
C. paying a cashier for a meal at a fast food restaurant
D. the maximum number of basketball players on the field
|3x-4| +2=1
Please help!
1.6 !!!!!!!!!! x=1.6 !!!!!
pls
its
due
today
ill
give brainillest
Answer:
m>24
26>m-4
m=24
10.25 divided by -0.5 =
Answer:
20.5 this is the answer 10.25 divided by 0.5
The difference between two numbers is 4. If the larger number is equal to wo more than three times the smaller number. What are the two numbers
Answer:
1 and 5
Step-by-step explanation:
s = smaller number
l = larger number = 2 + 3s
2 + 3s - 1s = 4
2 + 2s = 4
2s = 2
s = 1
l = 2 + 3(1)
l = 5
Please Help Meh I dont Get this
How many solutions exist for the system of equations below?
(3x+y=18
(3x+y=16
none
one
two
infinitely many
Step-by-step explanation:
3x + y = 18 and 3x + y = 16
=> 18 = 3x + y = 16.
However the equality 18 = 16 is false for any real values of x and y. Hence there are no real solutions.
Answer:
A. none
Step-by-step explanation:
What is the image of the point (-9, 1) after a rotation of 90° counterclockwise about
the origin?
Answer:
(- 1, - 9 )
Step-by-step explanation:
Under a counterclockwise rotation about the origin of 90°
a point (x, y ) → (- y, x ) , so
(- 9, 1 ) → (- 1, - 9 )
The image of the point (-9, 1) after a rotation of 90° counterclockwise about the origin is (1, 9).
What is rotation rule of 90°?Here are the rotation rules: 90° clockwise rotation: (x, y) becomes (y, -x) 90° counterclockwise rotation: (x, y) becomes (-y, x) 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y).
The given coordinate point is (-9, 1).
Rule: (x, y)→(y, -x)
The image of the point (-9, 1) is
(-9, 1)→(1, 9)
Therefore, the image of the point (-9, 1) after a rotation of 90° counterclockwise about the origin is (1, 9).
Learn more about the rotation of 90° counterclockwise here:
brainly.com/question/1571997.
#SPJ2
HURRY AND HELP ME PLEASE BRAINLESS
What is (2x - 15 / 48 + 7 =???)
Answer:
2x+107/16
Step-by-step explanation:
Answer:
I think the answer will be 2x + 107 / 16
15.7 is what percent of 785
Answer:
2%
Step-by-step explanation:
15.7 is 2% of 785
Hope this helps :)
A bedroom garbage can weighed 3/4of a pound. A Bathroom garbage can weighed 1/4 of a pound. Which is more?
Answer:
The bedroom garbage
Step-by-step explanation:
since the denominators are same, we can compare the numerators. 3 is larger than 1 so it would be the bedroom garbage
Answer:
3/4 of a pound
Step-by-step explanation:
3/4 of a pound is 1/4 more than half a pound. 1/4 is less then half a pound. Half a pound is 2/4 or 1/2.