Answer:
5, 12, 13
Step-by-step explanation:
let x be the longer leg then x + 1 is the hypotenuse and x - 7 the shorter leg
Using Pythagoras' identity in the right triangle
x² + (x - 7)² = (x + 1)² ← expand using FOIL
x² + x² - 14x + 49 = x² + 2x + 1
2x² - 14x + 49 = x² + 2x + 1 ( subtract x² + 2x + 1 from both sides )
x² - 16x + 48 = 0 ← in standard form
(x - 4)(x - 12) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 4 = 0 ⇒ x = 4
x - 12 = 0 ⇒ x = 12
x = 4 , then x - 7 = 4 - 7 = - 3 ← not possible
x = 12, then x - 7 = 12 - 7 = 5 and x + 1 = 12 + 1 = 13
The lengths of the 3 sides are
longer leg = 12 m , shorter leg = 5 m and hypotenuse = 13 m
Whose perfect square should be added to the sum of the greatest three digit prime number and the smallest two-digit prime number, so that the resultant number is perfect square of 32? pls give me ans pls pls pls
Answer:
Step-by-step explanation:
Let y is the required number.
a/c to question,
y² + greatest three digit prime number + smallest two digit prime number = 32²
we know, greatest three digit prime number = 997
smallest two digit prime number = 11
now, y² + 997 + 11 = 32²
or, y² + 1008 = 1024
or, y² = 1024 - 1008
or, y² = 16
or, y = 4
hence, required number number is one digit even number e.g., y = 4
Hope this answer helps you :)
Have a great day
Mark brainliest
I cant think of this question
Answer:
abcdsStep-by-step explanation:
NEED HELP BEFORE I FAIL PLS :( ITS PYTHAGOREAN THEOREM
Answer:
[tex] \bf \: {c}^{2} = {(56)}^{2} + ( {33)}^{2} \\ = > {c}^{2} = 3136 + 1089 \\ = > {c}^{2} = 4225 \\ = > c = \sqrt{4225} \\ = > c = 65 \: yards[/tex]
Answer:
65..
Step-by-step explanation:
[tex] \sqrt{(56) {}^{2} } + (33) {}^{2} \\ = 65[/tex]
[tex]3x + 9 = 12[/tex]
Solve for x
Answer:
x=1
Step-by-step explanation:
3x+9 = 12
Subtract 9 from each side
3x+9-9=12-9
3x = 3
Divide by 3
3x/3 = 3/3
x=1
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]x = 1[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Calculating the answer...}}\\\\3x + 9 = 12\\-------------\\\rightarrow 3x + 9 - 9 = 12 - 9\\\\\rightarrow 3x = 3\\\\\rightarrow \frac{3x=3}{3}\\\\\rightarrow \boxed{x=1}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Determine the coefficient of x^3 in the expansion of (1 – x)^5(1 + 1/x)^5
Notice that
(1 - x)⁵ (1 + 1/x)⁵ = ((1 - x) (1 + 1/x))⁵ = (1 - x + 1/x - 1)⁵ = (1/x - x)⁵
Recall the binomial theorem:
[tex]\displaystyle(a+b)^n = \sum_{k=0}^n\binom nk a^{n-k}b^k[/tex]
Let a = 1/x, b = -x, and n = 5. Then
[tex]\displaystyle\left(\frac1x-x\right)^5 = \sum_{k=0}^5\binom5k\left(\frac1x\right)^{5-k}(-x)^k = \sum_{k=0}^5 (-1)^k\binom5k x^{2k-5}[/tex]
We get an x ³ term for
2k - 5 = 3 ==> 2k = 8 ==> k = 4
so that the coefficient would be
[tex](-1)^4\dbinom54 = \boxed{5}[/tex]
cho tam giác ABC có A(3;4), B(2;1), C(-1;-2). tìm điểm M nằm trên đường thẳng BC sao cho S ABC=3S ABM
Answer:
Step-by-step explanation:
BRAINLIEST ANSWER TO WHOEVER ANSWERS FIRST... What is the volume of the sphere in terms of *pi ? in
Formula for the volume of a sphere: V = 4/3 x pi x r^3
V = 4/3 x pi x 6^3
V = 4/3 x pi x 216
V = 288 pi in^3
Hope this helps!
Answer:
288 pi in ^3
Step-by-step explanation:
The volume of a sphere is given by
V = 4/3 pi r^3 where r is the radius
V = 4/3 pi *( 6)^3
V = 4/3 pi (216)
V = 288 pi in ^3
What is the circumference of a circle with a diameter of 9 feet? Use 3.14 for
TL
d = 9ft
O A. 28.26 ft
PREVIOU
the formula for calculating the circumference is [tex]\pi[/tex] x diameter
so, 3.14 x 9 = 28.26ft (a)
Answer:
C = 28.26 ft
Step-by-step explanation:
The circumference of a circle is given by
C = pi *d
C = 3.14 *9
C = 28.26 ft
cherly gets paid $8 per hour at her job at the record store. she made a total of $96 last week .write a multiplication equation to show how many hours she worked last week
Answer:
8(h)=96
Step-by-step explanation:
Remember when you are writing a multiplication equation, it's a division backwards.
96/8=h
h×8=96
hope this helps you
goodluck
Answer: 8x=96
Step-by-step explanation:
8X = 96
X = 96/8
X = 12 hours
PLEASE HELP ASAP!!! I dont understand
Answer:
15
Step-by-step explanation:
(3x-1+2x+1)(3) -> 3 is the plug-in for x
3x-1+2x+1=5x
5*3=15
15
Answer:
15
Step-by-step explanation:
f(x) = 3x -1
g(x) = 2x+1
(f+g)(3)
find g(3) = 2(3)+1 = 6+1 = 7
Then find f(3) = 3(3) -1 = 8
f(3) + g(3) = 7+8 = 15
13 + {16 + 2 -[25 + 45) x 3] + 9}
Answer: -170
Concept:
When encountering questions that require multiple steps of the calculation, it is suggested to follow the PEMDAS.
ParenthesisExponentsMultiplicationDivisionAdditionSubtractionSolve:
**Disclaimer** I assume that it is supposed to be (25 + 45). If it was, then you may refer to my answer. If the ")" after 45 is just a typo, you may point it out and I will redo it.
Given expression
13 + {16 + 2 - [(25 + 45) × 3] + 9}
Do the parenthesis of the inner most
=13 + {16 + 2 - [70 × 3] + 9}
=13 + {16 + 2 - 210 + 9}
Do addition first, then subtraction
=13 + {18 - 210 + 9}
=13 + {27 - 210}
=13 - 183
=-170
Hope this helps!! :)
Please let me know if you have any questions
50 POINTS. For what value of the variable is the value of the expression is -3(2x+1) is 20 greater than the expression 8x+5? Please answer correctly, don't show your work, just give the correct answer.
Answer:
my x is ;
x= -0.6205
this is because for the first equation to be equal to the second equation we need to multiply the second equation with 20
Find the missing side lengths
Answer:
Download gauthmath it will help
Jesus loves u
Can someone please help me with this
Answer:
8.5 km
Step-by-step explanation:
The distance is given by sqrt(8^2+3^2)=sqrt(64+9)=sqrt(73)=8.5 km
Select the correct answer. Which line has a y-intercept of 2 and an x-intercept of -3? W. X. Y. Z. A. W B. X C. Y D. Z
Answer:
[tex]y = -\frac{2}{3}x + 2[/tex]
Step-by-step explanation:
The question is incomplete, as the graphs or equations of the lines are not given.
However, I will give a general explanation of calculating both intercepts
A linear equation is of the form:
[tex]y = mx + b[/tex]
Where:
[tex]b \to[/tex] y intercept
So, the equation
[tex]y = -\frac{2}{3}x + 2[/tex]
has 2 as its y-intercept
Set y to 0, to calculate the x-intercept
[tex]0 = -\frac{2}{3}x + 2[/tex]
Collect like terms
[tex]\frac{2}{3}x = 2[/tex]
Multiply by 3/2
[tex]x = 2 * \frac{3}{2}[/tex]
[tex]x = 3[/tex]
So, the equation with the required criteria is:
[tex]y = -\frac{2}{3}x + 2[/tex]
What is the value of x in the figure below? In this diagram, AABD ~ ACAD.
15
B
х
20
Answer:
E
Step-by-step explanation:
(leg of big triangle)² = (part of hypotenuse below it) × (whole hypotenuse)
15² = x × 20
225 = 20x ( divide both sides by 20 )
[tex]\frac{225}{20}[/tex] = x , that is
x = [tex]\frac{45}{4}[/tex] → E
The value of the x in the given triangle is 45/4.
What are similar triangles?Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.
Given is right triangle ABC, divided into two more right triangles, ADC and ADB, also, triangle ABD ~ triangle CAD.
Therefore, according to the definition of similar triangles, the corresponding sides are in proportion.
we have,
CA / CB = CD / CA
15/20 = x/15
x = 15²/20
x = 225/20
x = 45/4
Hence, the value of the x in the given triangle is 45/4.
Learn more about similar triangles click;
https://brainly.com/question/14926756
#SPJ7
A farmer uses 1/3 of his land to grow corn and 1/4 to grow yams . What fraction of the land is left?
Answer:
7/12
Step-by-step explanation:
3*4=12. 4/12+3/12=7/12.
Answer:
5/12
Step-by-step explanation:
you find the common factor of 12, divide 12 by the denominator, multiply the numerator by that, add the new numerators, put it on the denominator of 12, subtract it from 12/12
what is the domain of the function in the graph?
Answer:
6AJNSDJN
Step-by-step explanation:
PLEASE ANSWER AS SOON AS POSSIBLE
The trinomial x²−4x+4 is a perfect square. By factoring and finding the square roots, what values of x make the equation x2−4x+4=1 true?
Answer:
x²−4x+4 = (x-2)²
x²−4x+4 = 1
(x-2)² = 1
x-2 = ±√1
x = 1+2 or =-1+2
= 3 or = 1
2/5 divided by 8/5 .......
Answer:
1/4
Step-by-step explanation:
2/5 divided by 8/5 is the same as 2/5 * 5/8. we cross out the same 5's to get 2/8. We simplify that to 1/4.
1/4 is our answer.
Function g is the result of these transformations on the parent sine function:
-vertical stretch by a factor of 3
-horizontal shift left pi/2
-units vertical shift down 4 units
Below is the question from the Edmentum test :)
Answer:
g(x) = 3·sin(x + π/2) - 4
Step-by-step explanation:
The given (general form of a) sin function is g(x) = A·sin(x + C) + D
Where;
A = The amplitude (the vertical stretch) = 3
C = The phase shift, left = π/2
D = The vertical shift = 4 units down = -4
Therefore, given that in the parent function, we have f(x) = sin(x), by substituting the values of A, C, and D to complete the equation modeling the function g, we get;
g(x) = 3·sin(x + π/2) - 4
Simplify
(+8)-(-4)+(-5)
Answer:
17
Step-by-step explanation:
8+4+5=17
Answer:
7
Step-by-step explanation:
(+8)-(-4)+(-5)
=8+4-5
=12-5
=7
Un litro de leche de búfala equivale a 1.7 litros de leche de vaca. ¿si tengo 27 litros de leche de búfalo, a cuantos litros de leche de vaca equivaldría?
Answer:
Equivaldría a 45.9 litros de leche de vaca.
Step-by-step explanation:
Esta pregunta se resuelve por proporciones, usando una regla de tres.
Un litro de leche de búfala equivale a 1.7 litros de leche de vaca.
27 litros de leche de buffalo - x litros de leche de cava
1 - 1.7
Aplicando multiplicación cruzada :
[tex]x = 27*1.7 = 45.9[/tex]
Equivaldría a 45.9 litros de leche de vaca.
find the interior angle sum for the following polygon.
We know that the interior angle sum of a polygon is (n − 2) × 180°, where n is the number of sides.
Here, number of sides (n) = 12
So, interior angle sum = (n − 2) × 180°
=> interior angle sum = (12 - 2) × 180°
=> interior angle sum = 10 × 180°
=> interior angle sum = 1800°
So, the interior angle sum of this polygon is 1800°.
f(x) = -4(x+3)+6(x+4)
Answer:
zero of the function occurs at x = -6
Step-by-step explanation:
Given f(x) = -4(x+3)+6(x+4)
Since the question is incomplete, we can as well find the zero of the given function. The zero exists when f(x) = 0
Hence;
-4(x+3)+6(x+4) = 0
Expand
-4x - 12 + 6x + 24 = 0
Collect the like terms
-4x + 6x - 12 +24 = 0
2x + 12 = 0
2x = -12
x = -12/2
x = -6
Hence the zero of the function occurs at x = -6
use the ratio of a 45-45-99 triangle to solve for the variables.
Answers:
[tex]a = 18\sqrt{2}[/tex]
[tex]b = 18[/tex]
==============================================================
Explanation:
For any 45-45-90 triangle, the two legs are the same length. We consider triangles like this to be isosceles. So we have b = 18 as the vertical leg because the horizontal leg is also 18 units long.
The hypotenuse of these types of triangles is always [tex]\sqrt{2}[/tex] times longer compared to the leg length. So the hypotenuse is [tex]a = 18\sqrt{2}[/tex]
As an alternative, you can use the pythagorean theorem to find the hypotenuse.
Eliana claims she has discovered a method for determining the general form equation of a line
The line Ax + By + C = 0 will always be perpendicular to the line Bx - Ay + C = 0.
Is Eliana's method reasonable? Explain why or why not?
Answer:
The answer is below
Step-by-step explanation:
The general form of a line is given by:
Ax + By + C = 0
The slope intercept form of a line is give by:
y = mx + b;
where m is the slope and b is the y intercept
Given a line with equation Ax + By + C = 0; the slope of the line can be gotten by representing in slope intercept form, hence it becomes:
By = -Ax - C
y = (-A/B)x - C/B
The slope is -A/B
For a line with equation Bx - Ay + C = 0:
Ay = Bx + C
y = (B/A)x + C/A
the slope is B/A
Two lines are said to be perpendicular if the product of the slopes is -1. Hence:
-A/B * B/A = -1; hence the two lines are perpendicular
Deandra is doing her math homework. She completed the first 6 problems in 2 hours and the last 12 problems in 3 hours.
Which best describes Deandra’s rate for completing her homework?
Deandra completed the first 6 problems at a rate of 6 problems per hour and the last 12 at a rate of 2 problems per hour.
Deandra completed the first 6 problems at a rate of 3 problems per hour and the last 12 at a rate of 4 problems per hour.
Deandra completed the first 6 problems at a rate of 2 problems per hour and the last 12 at a rate of 6 problems per hour.
Deandra completed the first 6 problems at a rate of 4 problems per hour and the last 12 at a rate of 3 problems per hour.
Answer:
Deandra completed the first 6 problems at a rate of 3 problems per hour and the last 12 at a rate of 4 problems per hour.
Step-by-step explanation:
6 problems ÷ 2 hours = 3 problems per hour
12 problems ÷ 3 hours = 4 problems per hour
Answer B is the answer
Name and describe two theorems that you can use to prove two triangles are congruent?
Answer:
The Angle-Side-Angle Theorem (ASA) states that if two angles and their included side are congruent to two angles and their included side to another triangle, then these two triangles are congruent.
Step-by-step explanation:
found this on varsitytutors.com
Choose the complete predicate for the sentence below. My friend from school is going to a football game tomorrow. My friend My friend from school going to a football game tomorrow is going to a football game tomorrow
Answer:
The complete predicate is the following: "is going to a football game tomorrow."
Step-by-step explanation:
A sentence is spit into two main parts, the subject and the predicate. The subject is what the sentence is about and it typically occurs before the verb. Everything before the verb in this case would be the complete subject. What is left is the complete predicate. The complete predicate includes the verb and everything after it until the end of the sentence.
Answer:
The complete predicate is the following: "is going to a football game tomorrow."
Step-by-step explanation:
A sentence is spit into two main parts, the subject and the predicate. The subject is what the sentence is about and it typically occurs before the verb. Everything before the verb in this case would be the complete subject. What is left is the complete predicate. The complete predicate includes the verb and everything after it until the end of the sentence.
