Answers
Problem 1 (on the left)
Answers:[tex]10^2+12^2 = \boldsymbol{244}\\\\14^2 = \boldsymbol{196}\\\\\text{What kind of triangle?} \textbf{ Acute}[/tex]
-------------------------------
Explanation:
The converse of the pythagorean theorem can be used to determine what kind of triangle we're dealing with.
Here are 3 important rules to have in your notes:
[tex]\cdot \text{If } a^2+b^2 > c^2 \text{ then the triangle is } \underline{\text{acute}}\\\\\ \cdot \text{If } a^2+b^2 < c^2 \text{ then the triangle is } \underline{\text{obtuse}}\\\\\cdot \text{If } a^2+b^2 = c^2 \text{ then the triangle is a } \underline{\text{right}} \text{ triangle}\\\\[/tex]
The third rule is probably the most familiar as it's the pythagorean theorem itself.
In this case, we have [tex]a^2+b^2 = 10^2+12^2 = 244[/tex] larger than [tex]c^2 = 14^2 = 196[/tex], which fits the first rule mentioned.
=========================================================
Problem 2 (on the right)
Answers:[tex]8^2+15^2 = \boldsymbol{289}\\\\17^2 = \boldsymbol{289}\\\\\text{What kind of triangle?} \textbf{ Right}[/tex]
-------------------------------
Explanation:
We follow the same idea as problem 1. This time, both [tex]a^2+b^2[/tex] and [tex]c^2[/tex] result in the same value (289). Therefore, [tex]a^2+b^2 = c^2[/tex] is a true equation, and we go for the third rule mentioned earlier. An 8-15-17 right triangle is one of the infinitely many pythagorean triples.
Related Questions
Evaluate 4(2a – b) when a = –1 and b = 5.
–48
–28
–12
32
Answers
4(-2-5)
4(-7)
=-28 (B)
Hey There!
Question:-[tex]\sf \longmapsto \: 4(2a - b)[/tex]
This is a algebraic expression. The values of a and b are given. The values are as follows :-
a = -1
And,
b = +5 .
Solution:-[tex]\sf \longmapsto4(2a - b)[/tex]
Note that a is multiplied with 2 that is :-
[tex]\sf \longmapsto4(2 \times a \: - b)[/tex]
Now, Insert the values that is a = -1 and b = 5 :-
[tex]\sf \longmapsto4(2 \times - 1 - 5)[/tex]
Here,we need to follow BODMAS Rule.
B = Brackets
O = Orders
D = Division
M = Multiplication
A = Addition
S = Subtraction
We need to solve the bracket's calculations first as it is the rule.
So, Firstly Multiply (2 × -1) :-
[tex]\sf \longmapsto4( - 2 - 5)[/tex]
Note that, (-) × (-) equals to (+).
So, it will be 5+2,But as 5 is bigger number than 2, 5 contains a minus sign.So the result will be -7.
[tex]\sf \longmapsto4( 5+ 2)[/tex]
On Simplification:-
[tex]\sf \longmapsto4( - 7)[/tex]
[tex]\sf \longmapsto4 \times (- 7)[/tex]
[tex]\sf \longmapsto \: - 28[/tex]
______________________________________
Henceforth the solution of the algebraic expression is :-
[tex] \bf \:- 28[/tex]
Option B is correct!
______________________________________
I hope this helps!
Please let me know if you have any questions.
~MisterBrian
Write an expression that represents 42 is the product of 6 and y
No explanation needed, just tell me the answer :)
Answers
Answer:
[tex]6y = 42\\y = 7[/tex]
Step-by-step explanation:
the sum of -8 and a number is at least 9 write an inequality and solve each problem
Answers
-8 + x >= 9
Solve for x by adding 8 to both sides:
X >= 17
Mackenzie needed to get her computer fixed. She took it to the repair store. The technician at the store worked on the computer for 3.75 hours and charged her $157 for parts. The total was $400.75. Write and solve an equation which can be used to determine x, the cost of the labor per hour.
Answers
Answer:
x=65
Step-by-step explanation:
Based on the given conditions, formulate: 157+3.75 X x=400.75
Rearrange unknown terms and Calculate the sum:
3.75x = 400.75 - 157
3.75x = 243.75
x=243.75 / 3.75
x=65
The cost of labour per hour is $65.
Given that, the technician at the store worked on the computer for 3.75 hours and charged her $157 for parts. The total was $400.75.
We need to write and solve an equation which can be used to determine x, the cost of the labour per hour.
What is a linear equation?A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.
Now, according to question 157+3.75×x=400.75
⇒3.75x=400.75-157
⇒3.75x=243.75
⇒x=243.75/3.75
⇒x=65
Therefore, the cost of labour per hour is $65.
To learn more about a linear equation visit:
https://brainly.com/question/27664510.
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Heather earns $16
$
16
for each hour she works as a lifeguard.
Choose the equation that models the situation, where ℎ
h
represents the number of hours she works and
m
represents the money she earns.
Answers
Answer:
$128 a day
Step-by-step explanation:
if she works 8 hours a day/ aka full time then its different from what she earns half time/4 hours, most likely she's working fulltime so ure answer would be $128 a day
(I would be happy if u marked me brainiest) thank you
Julio says, "If you subtract 17 from my number and multiply the difference by - 3, the result is
- 39." What is Julio's number?
Julio's number is?
Answers
Answer:
30
Step-by-step explanation:
first, create two equations.
let x = Julio's number and y = answer for Julio's number substrates 17
[tex]x - 17 = y \\ y ( - 3) = - 39 \\ [/tex]
by using substitution method, you will get
[tex]x = 30 \\ y = 13[/tex]
so the answer is 30
6. Which equation has infinite solutions?
A. 6x + 5 - 2x = 4 + 4x - 1
B. - 3+ 12x = - 3( 4x - 1)
C. 5 (x + 3) + 2 = 5x + 17
D. - 5 (x - 5) = - 25 + 5x
Answers
Answer:
C
Step-by-step explanation:
5x+15+2=5x+17
2 Simplify 5x+15+25x+15+2 to 5x+175x+17.
5x+17=5x+17
5x+17=5x+17
3 Since both sides equal, there are infinitely many solutions.
Infinitely Many Solutions
4567 x 1283490 =
I just want to give points : )
Answers
Answer:
5861698830
Step-by-step explanation:
18 POINTS! WHAT IS THE ANSWER TO 1 2 3 AND 4 IN THE SCREENSHOT? PLEASE HURRY! P.S. BRAINLIEST
Answers
Answer:
J, B, A, L
Step-by-step explanation:
The awnser to question one is J, the awnser to questions two is B, the awnser to question three is A and the awnser to question four is L. Hope this helps.
Encuentra las dimensiones de un rectangulo cuyo perímetro es 26 mts y el área es 40m2
Answers
Answer:
Las dimensiones del rectángulo son:
lado corto: 5 cm
lado largo: 8 cm
Step-by-step explanation:
Consideraciones:
El perímetro de un rectángulo se calcula así:
p = 2(lado corto + lado largo)
El área de un rectángulo se calcula así:
a = lado largo * lado largo
Planteamiento:
26 = 2(a+b)
40 = a*b
a = lado largo
b = lado corto
Desarrollo:
de la primer ecuación del planteamiento:
26/2 = a+b
13 = a+b
13-a = b
sustituyendo este último valor en la segunda formula del planteamiento:
40 = a(13-a)
40 = 13*a + a*-a
40 = 13a - a²
-a² + 13a - 40 = 0
a = {-13±√((13²)-(4*-1*-40))} / (2*-1)
a = {-13±√(169-160)} / -2
a = {-13±√9} / -2
a = {-13±3} / -2
a₁ = {-13-3} / -2 = -16 / -2 = 8
a₂ = {-13+3{ / -2 = -10 / -2 = 5
Do it quickly please for brainliest
Answers
Step-by-step explanation:
x/(2x - 4) - (2x - 11)/(x + 2) = 5/8x/(x - 2) - (4x - 22)/(x + 2) = 5/4x(x + 2) - (4x - 22)(x - 2) = 5/4(x + 2)(x - 2)4(x² + 2x - 4x² + 8x + 22x - 44) = 5(x² - 4)4(-3x² + 32x - 44) = 5x² - 20- 12x² + 128x - 176 - 5x² + 20 = 0- 17x² + 128x - 156 = 017x² - 128x + 156 = 0x = (64 ± 38)/17x = 6 or x = 26/17
What is the location of point F, which partitions the directed line segment from D to E into a 5:6 ratio? Negative one-eleventh One-eleventh Two-fifteenths Fifteen-halves.
Answers
The location of point F, which partitions the directed line segment from D to E into a 5:6 ratio is [tex]\frac{1}{11}[/tex].
The given parameters:
Partition of the line segment = 5:6The total segment of the directed line segment from D to E in the given ratio of 5:6 is calculated as follows;
total segment = 5 + 6 = 11
The value of each partition on the directed line segment is calculated as follows;
[tex]partition = \frac{1}{11} \times distance[/tex]
The distance between point D and point E is calculated as follows;
[tex]D = 5 - (-4)\\\\D = 5 + 4\\\\D = 9[/tex]
The partition of the two points (D to E) is calculated as follows;
[tex]partition = \frac{1}{11} \times 9 = 0.82[/tex]
Thus, we can conclude that, the location of point F, which partitions the directed line segment from D to E into a 5:6 ratio is [tex]\frac{1}{11}[/tex].
Learn more about partition of line segments here: https://brainly.com/question/4429522
Answer:
B
Step-by-step explanation:
edge2021
An equivalent expression for16x-8
Answers
Answer:
8(2x-1)
Step-by-step explanation:
16x-8=8(2x-1)
Solve the system of equations
{y= 15x+9
{y= 1/2x–20
What is the solution to the system?
Answers
[tex]y = 15x +9~~~~.....(i)\\\\y = \dfrac 12 x -20~~~ ....(ii)\\\\\\\text{Substitute equation (i) in equation (ii):}\\\\15x +9 = \dfrac 12 x -20\\\\\ \implies 9 +20 = \dfrac x2 - 15 x\\\\\implies 29 = -\dfrac{29 x}2\\\\\ \implies 1 = -\dfrac x 2\\\\\implies x= -2\\\\\text{Substitute}~ x=-2~ \text{in equation (i):}\\\\y = 15(-2) +9 = -30 +9 = -21\\\\\text{Hence}~ (x,y) = (-2,-21)[/tex]
(08.06 MC)
Based on the graph, what is one solution of the equation f(x) = g(x)?
f(x)
(
g(x)
A x=-3.5
b x=-1
c x = 0.25
d x=-2
Answers
Answer:
A: X= -3.5
I just took the test, and I chose -1 and got it wrong and I looked back on the answer and that's what the answer said. Sorry if I was late, but good luck.
NEED HELP ASAP WILL GIVE 100 PTS IN IT HAVE TO BE RIGHT AND I WILL GIVE BRAINIEST
You were helping a friend with their math homework and saw the following work and explanation for one of their answers: (7^0/7^5)^1/5=7^−4/5. They are equivalent because (7/7^5)^1/5=(7^−4)^1/5. You notice their work and explanation are incorrect. Explain why it is wrong and give the correct answer.
Answers
Answer:
Step-by-step explanation:
(7^0/7^5)^1/5
= (1 / 7^5)^ 1/5
= (7^-5)^1/5
= 7^-1
= 1/7 is the correct answer.
what is 1\2 x 1.25
ljl
Answers
Answer:
Step-by-step explanation:
1.25 = 1 1/4
1 1/4 = 5/4
1/2 * 5/4 = 5/8
Write the percent as a fraction or mixed number in simplest form.
31.25%
Please show work!
Answers
i NEED help pleaseee
Answers
May I please receive help?
Answers
Answer:
um
Step-by-step explanation:
Latisha works x hours each day. Demetrius works 1 more hour each day than Latisha.Which expressions both calculate the number of hours Demetrius works in a 5-day work week?
Answers
The expressions that calculate the number of hours that Demetrius works in a week are [tex]5(x+1)\text{ and }5x+5[/tex]
If Latisha works [tex]x[/tex] hours each day
Demetrius works one more hour than Latisha each day. Algebraically, Demetrius works [tex](x+1)[/tex] hours each day
So for a [tex]5[/tex]-day working week, Demetrius will work
[tex](x+1)+(x+1)+(x+1)+(x+1)+(x+1)\\=5\times (x+1)\\=5(x+1)hours[/tex]
If we remove the brackets, we have the equivalent expression
[tex]5(x+1)=5x+5[/tex]
So the expressions that calculate the number of hours that Demetrius works in a week are [tex]5(x+1)\text{ and }5x+5[/tex]
Learn more about word problems here: https://brainly.com/question/17067890
The question is, “ Which fraction is equivalent to 2/6?
A. 3/7
B.3/9
C.3/12
D.3/8”
I think that’s the question she was trying to adk
Answers
Answer:
B .3/9
Step-by-step explanation:
2/6 = 0.333333
3/9=0.333333
2/6=1/3 and 3/9=1/3 as well, making them equal
solutions of the quadratic $x^2 + 7x - 18 = 0.$
Answers
(x^2+7x-18) can be factored into (x+9)(x-2). Set each part equal to zero and solve for x.
x+9=0 => x=-9
x-2=0 => x=2
I’m guessing the dollar signs aren’t supposed to be there.
The solution of the quadratic equation x² + 7x - 18 = 0 will be 2 and negative 9.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.
The quadratic equation is given below.
x² + 7x - 18 = 0
Factorize the quadratic equation, then we have
x² + 7x - 18 = 0
x² + 9x - 2x - 18 = 0
x(x + 9) - 2(x - 9) = 0
(x + 9)(x - 2) = 0
x = 2, -9
The arrangement of the quadratic condition x² + 7x - 18 = 0 will be 2 and negative 9.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
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Latisha works x hours each day. Demetrius works 1 more hour each day than Latisha.
Which expressions both calculate the number of hours Demetrius works in a 5-day work week?
5
x
+
1
and
5
(
x
+
1
)
5 x plus 1 and 5 times open paren x plus 1 close paren
(
x
+
1
)
×
5
and
5
×
x
+
1
open paren x plus 1 close paren times 5 and
5
×
x
+
1
5
(
x
+
1
)
and
5
x
+
5
5 times open paren x plus 1 close paren and 5 x plus 5
(
x
+
1
)
×
5
and
5
+
(
x
×
1
)
open paren x plus 1 close paren times 5and 5 plus open paren x times 1 close paren
Answers
The expressions that can be used to calculate both numbers of hours Demetrius works in 5-day work week is 5(x + 1) and 5x + 5
We are being told that Latisha works x hours each day and Demetrius works 1 more hour each day than Latisha.
So,
Let the amount of works done by Latisha be = xThen, the amount of works done by Demetrius will be = x + 1Thus, the both expression that can determine the number of hours Demetrius works in five days is:
= 5(x + 1) and 5x + 5
This is because if we open the bracket from 5(x+1) and multiply each term in the bracket with 5, we end up having 5x + 5.
5 times open paren x plus 1 close paren and 5 x plus 5 is correct.Learn more about word problems here:
https://brainly.com/question/2610134?referrer=searchResults
What is the number seven hundred thirty-one million, nine hundred thirty-four thousand, thirty written in a stranded form
Answers
Answer:
731,934,030
Step-by-step explanation:
hope this helps you
Answer:
731,934,030
Step-by-step explanation:
Hope it helps
According to the graph, how many students received an 90 for their first semester grade?
A: 0
B: 2
C: 6
D: 15
Answers
20-5+15(25)=b+3+65(23)
Answers
Answer:
-1108
Step-by-step explanation:
Answer:
-b=-1108
Step-by-step explanation:
20-5+375=b+3+1495
-375 -375
20-5=b+3+1420
15=b+1423
-b -b
-b+15=1423
-15 -15
-b=1108
20-5+375=-1108+3+1495
390=390
The original price of a TV is $525. Eddie buys the TV for
14% off the original price. Two weeks later Chuck buys the
same TV for 19% off. How much more money did Eddie
spend than Chuck?
Answers
What type of triangle is AABC? Select all that apply.
Thank u
Answers
Answer:
obtuse and isosceles
Step-by-step explanation:
The local cable company charges $90 per month for basic cable and $12 per month
for each additional premium cable channel. The function c (x) = 90 + 12x represents
the monthly charge (in dollars), where x represents the number of additional premium
channels. How many additional premium channels would you have ordered if your bill
was $114 per month?