Answers
Answer:
The measure of 'x' is 6 units.
Step-by-step explanation:
Given:
An isosceles triangle.
The two equal arms length = [tex]\sqrt{13}[/tex]
Measure of the altitude = [tex]2[/tex]
Note:The altitude to the base of an isosceles triangle bisects the base.
The altitude also forms 90 degree at the base.
So, the base length can also be seen as 'x' which we can also be written as [tex]x=\frac{x}{2} +\frac{x}{2}[/tex]
And [tex]\frac{x}{2}[/tex] is a part of the right angled triangle.
Where hypotenuse = [tex]\sqrt{13}[/tex]
Perpendicular length =[tex]2[/tex]
Base length = [tex]\frac{x}{2}[/tex]
Now,
From Pythagoras formula we know that:
[tex](hypotenuse)^2 =(perpendicular)^2+ (base)^2[/tex]
Plugging the values:
⇒ [tex](hypotenuse)^2 - (perpendicular)^2 = (base)^2[/tex]
⇒ [tex]\sqrt{ (hypotenuse)^2 - (perpendicular)^2} = (base)[/tex]
⇒ [tex]\sqrt{(\sqrt{13})^2-(2)^2} =\frac{x}{2}[/tex]
⇒ [tex]\sqrt{13-4}=\frac{x}{2}[/tex]
⇒ [tex]\sqrt{9} =\frac{x}{2}[/tex]
⇒ [tex]3=\frac{x}{2}[/tex]
⇒ [tex]3\times 2=x[/tex]
⇒ [tex]6 = x[/tex]
So the value of base 'x' = 6 units.
Option D is the rigth choice.
Related Questions
Solve the following system of equations graphically.
x = -5
y = -6
What is the solution set?
Ø
{(-5, -6)}
{(-6, -5)}
Answers
Answer: The right answer is [{-5,-6]}
Explanation: I got it right on my test
Answer:
[{-5,-6]}
Step-by-step explanation:
Is a 24 square centimeter rectangle larger than a 24 square inch rectangle?
Answers
Answer:
No, a 24 square centimeter rectangle is smaller than a 24 square inch rectangle
Step-by-step explanation:
we know that
[tex]1\ in=2.54\ cm[/tex]
so
Convert in^2 to cm^2
[tex]24\ in^2=24(2.54)^2=154.8\ cm^2[/tex]
so
[tex]24\ cm^2 < 154.8\ cm^2[/tex]
therefore
[tex]24\ cm^2 < 24\ in^2[/tex]
A 24 square inch rectangle is larger than a 24 square centimeter rectangle due to unit conversion.
No, a 24 square inch rectangle is larger than a 24 square centimeter rectangle.
To compare rectangles of different units, we need to convert the units to the same measurement. Since 1 inch is equal to 2.54 centimeters, a square inch is larger than a square centimeter.
Therefore, a 24 square inch rectangle has a greater area than a 24 square centimeter rectangle.
In a class, 8/9 of the students have blue eyes.
If 32 students have blue eyes, how many students are in the class in total?
Answers
4x9=36
36 students total
Oh the other side of the balance is 4 oz and another 4 oz and on the other side is 8 oz. <— To help you find out the answer. Please I’d like some help?
Answers
11
Explanation:
4+7 = 11
And we are trying to make it 0.
So we need to add 11 more on the other side to make it even.
I NEED THE ANSWER ASAP PLEASE
Answers
78.1 degrees
What identity can be used to rewrite the expression 27x^3-64?
Answers
Option A:
Difference of cubes
Solution:
Given expression is [tex]27 x^{3}-64[/tex].
27 can be written as [tex]3^3[/tex].
64 can be written as [tex]4^3[/tex].
[tex]27 x^{3}-64=3^3x^3-4^3[/tex]
[tex]27 x^{3}-64=(3x)^3-4^3[/tex]
To find the identity to rewrite the given expression:
Option A: Difference of cubes
[tex]27 x^{3}-64[/tex] can be rewritten as [tex](3x)^3-4^3[/tex].
That means the difference of two cubes.
So, it is true.
Option B: Difference of squares
[tex]27 x^{3}-64[/tex] cannot be written as square terms.
So, it is false.
Option C: Sum of cubes
[tex]27 x^{3}-64[/tex] cannot be written as sum of cubes.
So, it is false.
Option D: Pythagorean Triples
[tex]27 x^{3}-64[/tex] cannot be written as Pythagorean Triples.
So, it is false.
Hence difference of cubes if the correct answer.
The measure of CDA is 113.42°. what is the value of x?
Answers
X3-8y3+27+18xy factorise
Answers
Answer:
this expression is not factorable
Step-by-step explanation:
Answer this question please. I need help!!☺️
Answers
Step-by-step explanation:
From the looks of it, it seems that you're factoring out the greatest common factor. I gotcha covered.
The square boxes are the biggest common factors in those equations. Hopefully, this helps!
Write as an equation/inequality. x is less than or equal to 38.
Answers
Answer:
x[tex]\leq[/tex]38
Step-by-step explanation:
bring back the x and the 38 with a space between to decide on the symbol put back i the less than sign between both terms then put a line underneath to form the symbol less than or equal to.
Abigail's car uses 3 2/3 gallons of gas every hour on a long distance trip. How many gallons does the car use in 8 1/2 hours?
Answers
Answer:
31.166 repeating
Step-by-step explanation:
Where would you put 2 1/8th on a number line?
Answers
Answer:
See diagram and explanation
Step-by-step explanation:
A number on the right is greater than a number on the left on the number line.
Mark numbers 2 and 3 on number line (number 3 is to the right from number 2, because 3 > 2).
Divide the unit segment between numbers 2 and 3 into 8 equal parts (this segment is the unit segment because the distance between 3 and 2 is 1).
Each such part represents [tex]\frac{1}{8}[/tex] of the segment.
Mark the number [tex]2\dfrac{1}{8}[/tex] next to the right from 2 (you have to take 2 and 1/8).
Find the y-intercept of the line: 9x – 8y + 5 = 0
Answers
Answer:
-8y = -9x - 5
y = (9/8)x + 5/8
Step-by-step explanation:
y-int 5/8
The y-intercept of the given line equation 9x – 8y + 5 = 0, is 5/8, which is obtained by rearranging the equation into the slope-intercept form.
Explanation:The subject pertains to finding the y-intercept of a line from a given equation, which is a topic in Algebra.
The equation given is 9x – 8y + 5 = 0. First, we need to rearrange the equation into the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
Arranging the equation, we get: -8y = -9x -5, which simplifies further to y = 9/8x + 5/8. So, the y-intercept of the line is 5/8.
Learn more about y-intercept here:https://brainly.com/question/34923499
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--x² + 5x – 8=0
What is the x
Answers
Answer:
x =(-5-√57)/2=-6.275
Step-by-step explanation:
9. Martika says factors and multiples are
related. Use the equation 6 X 7 = 42
to describe the relationship between
factors and multiples.
BBOUD SOTTO
Answers
Answer:
So the factors and multiples of 42 are 1, 2, 3, 6, 7, 14, 21, 42
Step-by-step explanation:
Factors are what you can multiply to get a number and a multiples are what you get after multiplication. We can determine the factors of 42. The multiples of 42 are:
[tex]1 x 42= 42[/tex]
[tex]2 x 21= 42[/tex]
[tex]3x 14 = 42[/tex]
[tex]6 x 7 = 42[/tex]
So the factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The multiples of 42 are 1,2,3,4,5,6 etc
So common multiples and factors are 1, 2, 3, 6, 7, 14, 21, 42
In the equation 6 X 7 = 42, 6 and 7 are factors and 42 is the multiple. Factors are numbers that can be exactly multiplied to get another number, while a multiple is a number that can be divided evenly by another number. Hence, the relationship between factors and multiples is inherently interconnected.
Explanation:In the equation 6 X 7 = 42, 6 and 7 are the factors, and 42 is the multiple. Factors are numbers you can exactly multiply together to get a another number, in this case 6 and 7 are factors of 42 because when multiplied together, they equal 42. On the other hand, a multiple is a number that can be divided by another number without leaving a remainder, so 42 can be evenly divided by 6 or 7, making it a multiple of those numbers. The relationship between factors and multiples can be seen as two sides of the same coin - factors are what you multiply together to get a multiple.
Learn more about Factors and Multiples here:https://brainly.com/question/14410356
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What would be 49.38 rounded to tenthes
Answers
Answer:
49.4
Step-by-step explanation:
Round up, since the 8 [tex]\geq[/tex] 5
which has gradient -1/2 and cuts the y-axis at 4
Answers
Answer:
y = - [tex]\frac{1}{2}[/tex] x + 4
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = - [tex]\frac{1}{2}[/tex] and c = 4, thus
y = - [tex]\frac{1}{2}[/tex] x + 4 ← equation of line
A school plans the weekly reading activities. They have 18 storys books, which is 4 books more than 2 times that of science books. What is the number of science books?
Answers
Answer:
[tex]Number\ of\ science\ books=7[/tex]
Step-by-step explanation:
[tex]Let\ number\ of\ science\ books=x\\\\Story\ books=18\\\\2\times science\ books+4=Story\ books\\\\2x+4=18\\\\Subtract\ 4\ from\ both\ the\ sides\\\\2x+4-4=18-4\\\\2x=14\\\\Divide\ both\ sides\ by\ 2\\\\\frac{2x}{2}=\frac{14}{2}\\\\x=7\\\\Number\ of\ science\ books=7[/tex]
A circle has a diameter of 7.6feet. Which measurement is the closest to the circumference of the circle in feet.
Answers
Answer:
23.9
Step-by-step explanation:
A circle has a diameter of 7.6 feet. Which measurement is closest to the circumference of the circle in feet?
TRUST ME
28v^3+16v^2-21v-12 factor by group please
Answers
Step-by-step explanation:
The given equation:
[tex]28v^3+16v^2-21v-12[/tex]
To find, the factors of [tex]28v^3+16v^2-21v-12[/tex] = ?
∴ [tex]28v^3+16v^2-21v-12[/tex]
[tex]=(4\times 7)v^3+(4\times 4)v^2-(3\times 7)v-(3\times 4)[/tex]
= [tex]4v^2(7v+4)-3(7v+4)[/tex]
= [tex](7v+4)(4v^2-3)[/tex]
= [tex](7v+4)[(2v)^2-\sqrt{3}^2][/tex]
Using the algebraic identity,
[tex]a^{2}-b^{2}=(a+b)(a-b)[/tex]
= [tex](7v+4)(2v+\sqrt{3})(2v+\sqrt{3})[/tex]
∴ The factor of [tex]28v^3+16v^2-21v-12[/tex] = [tex](7v+4)(2v+\sqrt{3})(2v+\sqrt{3})[/tex] or [tex](7v+4)(4v^2-3)[/tex]
If side A is twice as long as B and C is 25 using the Pythagorean Theorem,What are the lengths of side A and B? Round to the nearest tenth if necessary
Answers
Answer:
The lengths of side A is 22.4 and B is 11.9.
Step-by-step explanation:
Given:
If side A is twice as long as B and C is 25 using the Pythagorean Theorem.
Now, to find the lengths of side A and B.
Let the side B be [tex]x.[/tex]
So, the side A be [tex]2x.[/tex]
Side C = 25.
Now, to solve by using Pythagorean Theorem:
A² + B² = C²
[tex](2x)^2+(x)^2=(25)^2[/tex]
[tex]4x^2+x^2=625[/tex]
[tex]5x^2=625[/tex]
Dividing both sides by 5 we get:
[tex]x^2=125[/tex]
Using square root on both sides we get:
[tex]x=11.18.[/tex]
B rounding to the nearest tenth = 11.9.
Now, to get A by substituting the value of [tex]x[/tex]:
[tex]2x\\=2\times 11.18\\=22.36.[/tex]
A rounding to the nearest tenth = 22.4.
Therefore, the lengths of side A is 22.4 and B is 11.9.
Which expression is equivalent to -2(3a + 6b) + (4a - 2b)?
A) -2(a + 7b)
B) -2(a - 7b)
C) 2(a + 7b)
D) 2(a - 7b)
Answers
Answer:
Option A) -2(a+7b) is correct
Therefore -2(3a+6b)+(4a-2b)=-2(a+7b)
The equivalent expression to the given expression is -2(a+7b)
Step-by-step explanation:
Given expression is -2(3a+6b)+(4a-2b)
To find the equivalent expression to the given expression :
-2(3a+6b)+(4a-2b)
=-2(3a)-2(6b)+4a-2b ( apply the distributive property a(x+y)=ax+ay )
=-6a-12b+4a-2b
=-2a-14b ( adding the like terms )
=-2(a+7b) ( taking common term -2 outside )
Therefore -2(3a+6b)+(4a-2b)=-2(a+7b)
The equivalent expression to the given expression is -2(a+7b)
Therefore option A) -2(a+7b) is correct
so the right option is A.
HOPE THIS WILL HELP U.
IF MY ANS WAS HELPFUL, U CAN FOLLOW ME.
A turboprop plane flying with the wind flew 400 mi in 4 h. Flying against the wind, the plane required 5 h to travel the same distance. Find the rate of the plane in calm air and the rate of the wind.
Answers
Answer:
Rate of the plane in calm air is 90 miles/hr and rate of the wind of wind is 10 miles/hr
Step-by-step explanation:
Average speed of plane in with wind = 400 /4 = 100 miles/hr
Average speed of plane against wind = 400/5 = 80 miles/hr
Consider the speed of plane in wind be x miles/hr and speed of plane against wind be y miles/hr
As such speed of plane in wind would be x + y miles/hr and speed of plane against wind would be x - y miles/hr . i.e
x+y = 100
x-y = 80
by solving these two equation, we get
2x=180
x= 90 miles/hr
y=100-90
y= 10 miles/hr
hence, Rate of the plane in calm air is 90 miles/hr and rate of the wind of wind is 10 miles/hr
if a car is 200 inches long, and the truck is 75% longer, how long is the truck
Answers
Factor the expression. 36y2 – 84y – 147
(2y + 7)(6y – 7)
3(2y + 7)(6y + 7)
3(2y – 7)(6y + 7)
(2y – 7)(18y + 21)
Answers
Answer:
1) 3 (6y+7) (2y−7)
2) 12y2+28y−49
3) 36y2+168y+147
4) 36y2−84y−147
5) 3(6y+7)(2y−7)
Tickets to the garden show cost $6.75 for adults and $3.75 for children. By rounding to the nearest whole dollar, find an estimate of the cost for a family with 2 adults and 3 children to visit the garden show. A. $21 B. $23 C. $24 D. $26
Answers
Answer:
$26
Step-by-step explanation:
$6.75 - $7
$3.75 - $4
2 adults = 7x2= $14
3 children = 4x3= $12
$14 + $12 = $26
The answer is D. $26.
Suppose you are choosing between two checking accounts. One account charges you $1.50 ATM
fee every time you withdraw money from a non-sponsored ATM, and the other charges you no
ATM fees and a $15 monthly fee.
How many ATM transactions are equivalent to $15 in monthly fees?
Answers
Answer:
10
Step-by-step explanation:
$15.00 / $1.50 = 10
Select the correct answer.
The temperature on Saturday was 2°C. On Sunday, it became 4°C colder. What was the temperature on Sunday?
7O
Answers
Answer:
6C
Step-by-step explanation:
Final answer:
By subtracting the 4°C decrease from the initial temperature of 2°C, it is determined that the temperature on Sunday was -2°C.
Explanation:
The question involves a basic mathematics operation related to temperature changes. The temperature on Saturday was 2°C, and on Sunday, it became 4°C colder. To find the temperature on Sunday, you simply need to subtract 4°C from Saturday's temperature:
Saturday's temperature: 2°C
Temperature decrease: 4°C
Sunday's temperature: 2°C - 4°C = -2°C
Thus, the temperature on Sunday was -2°C.
the equivalent fraction of 2/4
Answers
Answer:
1/2
Step-by-step explanation:
u could simplify it to 1/2 pls give brainliest answer
Answer: 1/2 and if you mean multiplying 4/8 because 2 ÷ 2 = 1 and 4 ÷ 2 = 2, and if you mean multiplying 2 • 2 = 4 and 4 • 2 = 8 so those are two answers.
A math teacher graded 45 problems in 3/5 of an hour. At that rate, how many problems can she grade in one hour
Answers
Answer:
75
Step-by-step explanation:
45*1/3=15
15*5=75
Answer: 75 problems
Step-by-step explanation:
3/5 of an hour is the same as 3/5 x one hour.
one hour is the same as 60 minutes , this means that 3/5 of an hour is the same as :
3/5 x 60 = 36 minutes
This means that , the teacher graded 45 problems in 36 minutes. then in 1 minutes ;
The teacher will grade 45/36 problems
so in 60 minutes ;
the teacher will grade 45/36 x 60 = 75 problems