Answer:
The value of x is 6.
Step-by-step explanation:
You have to use Pythagorean Theorem, a² + b² = c². Make (4x+1)cm as the hypotenuse because any values substitute into x will give the highest length among these 3 expressions of length :
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
Let a = side = (x+1)cm,
Let b = side = 4x cm,
Let c = hypotenuse = (4x+1)cm,
[tex] {(x + 1)}^{2} + {(4x)}^{2} = {(4x + 1)}^{2} [/tex]
[tex] {x}^{2} + 2x + 1 + 16 {x}^{2} = 16 {x}^{2} + 8x + 1[/tex]
Then you have to simplify :
[tex]17 {x}^{2} + 2x + 1 = 16 {x}^{2} + 8x + 1[/tex]
[tex]17{x}^{2} + 2x + 1 - 16 {x}^{2} - 8x - 1 = 0[/tex]
[tex] {x}^{2} - 6x = 0[/tex]
Next you have to solve it :
[tex] {x}^{2} - 6x = 0[/tex]
[tex]x(x - 6) = 0[/tex]
[tex]x = 0 \: (rejected)[/tex]
[tex]x - 6 = 0[/tex]
[tex]x = 6cm[/tex]
The value of x in the right triangle is 6 cm.
What is the Pythagorean theorem?Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We have,
Right triangle:
The three sides are:
x + 1, 4x and 4x + 1
Applying the Pythagorean theorem.
(x + 1)² + (4x)² = (4x + 1)²
x² + 2x + 1 + 16x² = 16x² + 8x + 1
17x² + 2x + 1 = 16x² + 8x + 1
17x² - 16x² = 8x - 2x
x² = 6x
x gets canceled.
x = 6
Thus,
The value of x is 6.
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suppose f(x)=x^2. what is the graph of g(x)=f(3x)?
Answer:
Option A is correct
g(x) = 9x^2
Step-by-step explanation:
f(x) = x^2
g(x) = f(3x) = (3x)^2 = 9x^2
Let's consider the function: g(x) = 9x^2. This function is always greater or equal to 0 (because x^2 is always greater or equal to 0)
=> Option B and C are incorrect (the value of y is smaller than 0)
Let's continuously see the option D. The graph shows that when x is equal to 3, y is approximately 5. This is incorrect because if we substitute x = 3 into g(x), the y value should be y = 9 x 3^2 = 9 x 9 = 81, much greater than 5.
=> Option D is incorrect
=> Only option A is correct
Hope this helps!
Option A is correct
g(x) = 9x^2
f(x) = x^2
g(x) = f(3x) = (3x)^2 = 9x^2
Let's consider the function: g(x) = 9x^2. This function is always greater or equal to 0 (because x^2 is always greater or equal to 0)
B and C are incorrect (the value of y is smaller than 0)
Let's continuously see option D. The graph shows that when x is equal to 3, y is approximately 5.
This is incorrect because if we substitute x = 3 into g(x), the y value should be y = 9 x 3^2 = 9 x 9 = 81, much greater than 5.
Option D is incorrect
Only option A is correct
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Which side of AABC is the longest?
Answer:
B
Step-by-step explanation:
The side opposite the largest angle is the longest side.
Hope this helps
Carrie took a 24-hour train ride from Colorado to Illinois. If she arrived in Illinois at 2:45pm CST on Wednesday, when she did she leave Colorado?
Answer:
Carrie left Colorado at 2:45pm CST on Tuesday.
Step-by-step explanation:
The train travels a total of 24 hours to get from Colorado to Illinois, that is, it takes one complete day of travel to get from one city to the other.
So, if Carrie arrives Illinois at 2:45pm CST on Wednesday, she left Colorado exactly one day before that, in the same hour, so she left Colorado at 2:45pm CST on Tuesday.
Please answer correctly !!!!! Will mark brainliest !!!!!!!!!!!!!
Answer:
10 and 8
Step-by-step explanation:
1. An endpoint of a line segment is (4,5) and the midpoint of the line segment is (3,−2). Find the other endpoint.
______
2. An endpoint of a line segment is (−10,−2) and the midpoint of the line segment is (0,4). Find the other endpoint.
______
Answer:
1. (2, -9) 2. (10, 10)
Step-by-step explanation:
100 POINTS WILL MARK BRAINLIEST x^2 − 8x + 13 = 0 Which of the following is the first correct step to write the above equation in the form (x − p)^2 = q, where p and q are integers? Subtract 5 from both sides of the equation Add 3 to both sides of the equation Add 5 to both sides of the equation Subtract 3 from both sides of the equation
Answer:
We will add 3 to each side of the equation
Step-by-step explanation:
x^2 − 8x + 13 = 0
We want to complete the square
We will subtract 13 from each side of the equation
x^2 -8x +13 -13 = 0 -13
x^2 -8x = -13
Then take the coefficient of x
-8
Divide by 2
-8/2 = -4
Square it
(-4)^2 = 16
Add this to each side
x^2 -8x +16 = -13+16
( x-4) ^2 = 3
The sum of subtracting 13 and adding 16 is adding 3
Answer:
It is Subtract 3 from both sides of the equation
Step-by-step explanation:
A triangle has two sides of 8 and 15. What is the largest possible whole number length for the third side?
Answer:
Largest possible value for the 3rd side can be 22.
Step-by-step explanation:
Property of sides of a triangle:
If two sides of a triangle are [tex]a[/tex] and [tex]b[/tex] long, then the length of third side [tex]c[/tex] must be:
[tex](a+b) > c[/tex]
i.e. the sum of two sides [tex]a[/tex] and [tex]b[/tex] must be greater than the third side [tex]c[/tex].
So, to find the largest possible value:
[tex]a = 8\\b= 15[/tex]
[tex]a+b=23[/tex]
Largest possible value of [tex]c[/tex] can be lesser than 23.
i.e. 22 can be the largest possible value of the third side.
One vertex of a triangle is located at (0,5) on a coordinate
grid. After a transformation, the vertex is located at (5,0).
Which transformations could have taken place? Select
two options.
Ro, 90°
Ro, 180°
Ro, 270°
U
Ro -90°
Ro -180°
Answer: Ro, 270° and Ro -90°
Step-by-step explanation: If the vertex is at 5 on the y-axis at (0,5) and the transformation has moved the vertex to (5,0) it is now at +5 on the x-axis. This is a rotation around the origin, Rotation notation Ro.
This is fairly easy to visualize: like the hand of an analog clock moving from 12 o'clock to 3 o'clock.
In geometry, rotations are given in degrees, moving counter-clockwise. There are 360° in a circle.
Moving 3/4 of the way around the circle counterclockwise.
Multiply(3/4)(360) = 270. This is a positive rotation, counter-clockwise
Clockwise, it is 1/4 of the circle, so Multiply (1/4)(360)= 90 But remember to add the negative sign because clockwise is considered a negative rotation.
Ro, -90°
The transformations that could have taken place are Ro, 270° and Ro -90°
How to determine the transformationsThe vertex of the triangle is given as: (0,5)
After transformation, the vertex of the image is given as: (5,0)
The transformation follows the rule:
[tex](x,y) \to (y,x)[/tex]
The above rule represent:
90 degrees counterclockwise rotation270 degrees clockwise rotationHence, the true statements are Ro, 270° and Ro -90°
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p + 0.20p as an equivalent expression
Answer:
An equivalent expression to p - 0.20p is 0.8p Hope this helps :)
There are 2 1/2 pizzas if each gets an eighth of a pizza how many people get a slice
Answer:
20.
Step-by-step explanation:
That would be 2 1/2 divided by 1/8
= 5/2 / 1/8
= 5/2 * 8
= 40/2
= 20.
Which of the following is an example of a quadratic equation?
O A. y = 4x +6
O B. x2 - 64 = 0
O C. X+ 10 = 33
O D. y=1/x2+6
Answer:
[tex]x^{2} -64 = 0\\[/tex]
Step-by-step explanation:
According to Wikipedia In algebra, a quadratic equation is any equation that can be rearranged in standard form as where x represents an unknown, and a, b, and c represent known numbers, where a ≠ 0. If a = 0, then the equation is linear, not quadratic, as there is no term.
Carmen has a sign with dimensions 5 ft × 7.5 ft. She wants to reduce it to make a postcard. Postcard sizes are 3.5 in. × 5 in., 4 in. × 6 in., and 4.25 in. × 6 in. Which size postcard should she use? Explain.
Answer:
The size of the post card she should use is 4 in. × 6 in.
Step-by-step explanation:
The parameters given are;
Dimensions of sign = 5 ft. × 7.5 ft
Hence, the ratio of the side sizes are;
5:7.5 which is the same as 2:3, therefore, to obtain the most accurate design of the sign on the post card, the size of the post card must be in direct proportion to the size of the sign which gives;
Side length ratio of post card = 2:3 = 4:6 = 4 in. × 6 in.
The size of the post card she should use is therefore = 4 in. × 6 in.
can someone please help and explain
Answer:
2
Step-by-step explanation:
2 4/5 * 5/7
Change to an improper fraction
(5*2+4)/5 * 5/7
14/5 * 5/7
Canceling the 5's
14/7
2
Answer:
2
Step-by-step explanation:
[tex]2\dfrac{4}{5}\times \dfrac{5}{7}= \\\\\\\dfrac{14}{5}\times \dfrac{5}{7}=\\\\\\\dfrac{14\times 5}{5\times 7}=\\\\\\\dfrac{14}{7}=\\\\\\2[/tex]
Hope this helps!
algebraic fractions and formulae
(help me find Z)
thank you ❤❤
Answer:
Step-by-step explanation:
z= y( z-y)/x
z = yz - y^2 /x
zx = yz -y^2
y^2 = yz - zx
y^2 = ( y- x)z
therefore z = y^2/(y-x)
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Angel entered a triathlon (a three-part race). He swam 1 mile, rode his bike 30 miles, and ran 10 miles. How far did he go altogether?
Answer:
41 miles
Step-by-step explanation:
30+10+1=41
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Does anyone know the answer?
Answer:
i think it the 2 one
Step-by-step explanation:
Find the range of the following data:
(a) The weights (in kg) of 10 persons are:
22, 27, 29, 31, 33, 36, 37, 39, 41, 43.
Answer:
range = 21 Kg
Step-by-step explanation:
The range is the difference between the largest and smallest values in the data set
largest value = 43 Kg and smallest value = 22 Kg, thus
range = 43 - 22 = 21 Kg
[tex]answer =21 \\ solution \\ given \: data = 22 ,27,29,31,33,36,37,39,41,43 \\ range = highest \: score - lowest \: score \\ \: \: \: \: \: \: \: \: \: \: = 43 - 22 \\ \: \: \: \: \: \: \: \: = 21 \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]
What is \redD{\text{A}}Astart color #e84d39, start text, A, end text, end color #e84d39 rounded to the nearest ten? What is \redD{\text{A}}Astart color #e84d39, start text, A, end text, end color #e84d39 rounded to the nearest hundred?
Answer:
What? Retype the question below and ill answer it, but this isnt answerable.
Step-by-step explanation:
What is \redD{\text{A}}Astart color #e84d39, start text, A, end text, end color #e84d39 rounded to the nearest ten? What is \redD{\text{A}}Astart color #e84d39, start text, A, end text, end color #e84d39 rounded to the nearest hundred?
Like what kind of language is this ;--;
What are the domain and range of the function
Answer:
Step-by-step explanation:
I don't say u must have to mark my ans as brainliest but if it has really helped u plz don't forget to thank me my frnd..
__________________________________
Hey!!!!!!
Domain and RangeLet R be a relation from A to B.
Then, the set of first components or the set of elements of A are called domain and the set of second components or the set of elements of B are called the Range.
For example:
If R:(A,B)={(1,1), (2,4), (3,9)} then,
Domain={1,2,3}
Range={1,4,9}
Hope it helps...Good luck on your assignment.........
Stay Safe......__________________________________
The sum of two numbers which are in the ratio 5:7 is 48. Find the smaller number
Step-by-step explanation:
5+7=12
5/12×48 7/12×48
=20 =28
I don't say you have to mark my ans as brainliest but if my ans has really helped u pz dpn't forget to thank me....
A circle is cut from a square piece of cloth, as shown: How many square inches of cloth are cut from the square? (π = 3.14)
A.) 1,061.32 in2
B.) 2,122.64 in2
C.) 2,704.00 in2
D.) 3,622.31 in2
Answer:
2122.64 in^2
Step-by-step explanation:
Use the formula for the area of a circle: A=πr^2
The radius will be half the width of the cloth so 52÷2=26
26^2=676
Multiply by π given as 3.14
676×3.14=2122.64 square inches.
The symbol (carat) ^ is used to indicate an exponent when the keyboard doesn't have superscript.
Answer:
B
Step-by-step explanation:
2,122.64 in2
A closed cylinder has a radius of 3cm and height 7 cm. find its total surface area.
The total surface area of the cylinder is 188.4 cm².
Given that, the radius of the cylinder=3 cm and the height of the cylinder=7 cm.
We need to find the total surface area of the cylinder.
What is the formula to find the total surface area of the cylinder?The formula for the total surface area of a given cylinder whose radius is r and height is h is 2πr (h + r).
Now, 2×3.14×3(7+3)=188.4 cm².
Therefore, the total surface area of the cylinder is 188.4 cm².
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ASAP A ramp into a building forms an 8° angle with the ground. If the entry point of the ramp is 7 feet from the building, how many feet from the ground is the end of the ramp? Round the solution to the nearest hundredth.
Answer: .98 feet
Step-by-step explanation: Took the test
Answer:
.98
Step-by-step explanation:
i took the quiz
which of the following is equal to the rational expression when x ≠ -4 or 16
Answer:
A
Step-by-step explanation:
(x^(2)-16)/((x-16)(x+4))=
[(x+4)(x-4)]/(x-16)(x+4)=
x-4/x-16
Answer:
A. [tex] \dfrac{x - 4}{x - 16} [/tex]
Step-by-step explanation:
[tex] \dfrac{x^2 - 16}{(x - 16)(x + 4)} = [/tex]
[tex] = \dfrac{(x - 4)(x + 4)}{(x - 16)(x + 4)} [/tex]
[tex] = \dfrac{x - 4}{x - 16} [/tex]
Which type of triangles can be formed by taking the cross-section of a cube?
Answer:
2 Right Angled Triangles
Step-by-step explanation:
URGENT!!LAST QUESTION!!!! PLS JUST TAKE A LOOK! EASY BUT I AM DUMB!!!!!! WILL GIVE BRANLIEST!!1 A photograph measures five inches wide and six inches long. The picture is enlarged to fit on a wall. If the new larger picture is 150 inches wide, how long is it? A) 210 inches B) 250 inches C) 180 inches D) 200 inches
Answer:
c) 180in
Step-by-step explanation:
So first you divide 150 by 5 to know by how much it was increased
150/5=30
Then multiply the length by that same 30 since it was scaled up by 30
30*6=180
Answer:
C) 180 because you do ratio of 5:6 = 150:X. X=180 because 150/5=30 so you take 30x6 = 180
Tanya buys 12 water bottles. Of these bottles, 5 hold 300 milliliters each and 7 hold 1.5 liters each. Part A How much water, in milliliters, does Tanya buy? Enter your answer in the box. Part B How much water, in liters, does Tanya buy? Enter your answer in the box.
Answer:
A- 12,000ml
B- 12l
Step-by-step explanation:
To find milliliters:
1.5l = 1500ml
300(5) + 1500(7) = (1500 + 10500 =) 12,000ml
To find liters:
300 ml = 0.3l
0.3(5) + 1.5(7) = (1.5 + 10.5 =) 12L
Hope this helps!
Among fatal plane crashes that occurred during the past 70 years, 581 were due to pilot error, 56 were due to other human error, 579 were due to weather, 555 were due to mechanical problems, and 526 were due to sabotage. Construct the relative frequency distribution. What is the most serious threat to aviation safety, and can anything be done about it? Complete the relative frequency distribution below. Cause Relative Frequency Pilot error nothing% Other human error nothing% Weather nothing% Mechanical problems nothing% Sabotage nothing%
Answer:
[tex]\begin{array}{ccc}cause&accidents&frequency\\pilot\ error&581&0.253\\human\ error&56&0.024\\weather&579&0.252\\mechanical&555&0.242\\sabotage&526&0.229\end{array}[/tex]
Pilot error, better training of pilots may reduce accidents.
Step-by-step explanation:
The total number of crashes is:
[tex]n = 581+56+579+555+526\\n=2297\ crashes[/tex]
The relative frequency is given by the number of accidents caused by each factor divided by the total number of accidents. The relative frequency distribution is:
[tex]\begin{array}{ccc}cause&accidents&frequency\\pilot\ error&581&0.253\\human\ error&56&0.024\\weather&579&0.252\\mechanical&555&0.242\\sabotage&526&0.229\end{array}[/tex]
The most serious threat to aviation safety is pilot error, a better training of current and future pilots could be a solution to reduce accidents.
Al mediodía me he comido la mitad de una tortilla de patatas. A la hora de la merienda, Ana ha tomado un tercio de la tortilla original, y para cenar, Luis se ha tomado tres cuartas partes de lo que quedaba. ¿Qué fracción de la tortilla queda al final del día?
Answer:
[tex]\frac{1}{24}[/tex]
Step-by-step explanation:
La mitad es 1/2 y un tercio es 1/3. Como una persona se comió 1/2 y Ana 1/3, puedes determinar lo que se comieron sumando:
[tex]\frac{1}{2}[/tex]+[tex]\frac{1}{3}[/tex]=[tex]\frac{3+2}{6}[/tex]=[tex]\frac{5}{6}[/tex]
Como se comieron 5/6, puedes restar esto de 6/6 para determinar cuanto quedó de la tortilla:
[tex]\frac{6}{6}-\frac{5}{6}= \frac{6-5}{6} =\frac{1}{6}[/tex]
De acuerdo a esto, quedó 1/6 de la tortilla. Luis tomó tres cuartas partes de lo que quedaba, lo que significa que quedó 1/4 de 1/6. Para encontrar la fracción de la tortilla que quedó puedes dividir 1/6 entre cuatro para saber a cuanto corresponde una cuarta parte de 1/6:
[tex]\frac{1}{6}[/tex]÷4= [tex]\frac{1/6}{4}= \frac{1}{6*4}=\frac{1}{24}[/tex]
De acuerdo a esto, la fracción de la tortilla que quedó al final del día es [tex]\frac{1}{24}[/tex].
The equation of a circle is x2 + y2 + 6y = 7. What are the coordinates of the center and the length of the radius of the circle?
Step-by-step explanation:
x2+y2+6y+(9-9)=7
x2+y2+6y+9=16
x2+(y+3)2=16
center:(0,-3)
r:4