Answer:
One of the sides is 6 cm and the other is 8 cm
Step-by-step explanation:
Let's call the unknown sides a and b. From the perimeter information (24 cm) we have:
a + b + hypotenuse = 24
a + b + 10 = 24
a + b = 14
b = 14 - a
So now we can right the Pythagorean theorem as follows:
[tex]a^2 + b^2 = hypotenuse^2\\a^2 + (14-a)^2=10^2\\a^2+ 14^2-28\,a+a^2=100\\2\,a^2-28\,a +96=0\\2\,(a^2-14\,a+48)=0\\2\,(a^2-6\,a-8\,a+48)=0\\2(a\,(a-6)-8\,(a-6))=0\\2\,(a-6)\,(a-8)=0[/tex]
and from this expression in factor form to be zero a must be 6 or a must be 8.
Therefore the solutions are a = 6 (and therefore b = 14 - 6 = 8)
or a = 8 (and therefore b = 14 - 8 = 6)
Perimeter of triangle = Sum of all sides.
One side of triangle = 10 cm
Measure of other two sides will be → 24-10
Other two sides sum will be = 14 cm
Let's assume one side as x and other as 14-x
Now hypotenuse is of 10 cm
According to Pythagorean theoram
Hypotenuse² = Perpendicular ² + base²
→ 10² = (x)² + (14-x)²
→ 100 = x² + (14-x)²
(a-b)² = a²+b² -2ab
→ 100 = x² + 196 + x² -28 x
→ 100 = 2x² + 196 - 28x
Taking 2 commen both sides
→ 50 = x² -14x + 98
→ 0 = x² -14x +98-50
→ x² -14 x +48 = 0
Factorising :-
→ x² - 6x - 8x + 48 = 0
→ x( x -6) -8(x -6) = 0
→ (x-6)(x-8) = 0
→ x = 6 or x = 8
So x is 6 or 8
Other two sides of triangle are 6 cm and 8 cm
Figure out the pattern, fill in
the blank
Answer:
384
Step-by-step explanation:
The pattern is: the sum of the multiplication of the 2 numbers underneath the blank.
48 * 8 = 384
Hope this helps! Please tell me if I did something wrong, thanks!
What is 3/15 in simplest form
Answer:
3/15 in the simplest form is 1/5....
when you divide by 3 it gives 1/5.
The fraction 3/15 in simplest form is 1/5.
What is 3/15 in simplest form?A fraction is in its simplest form if the numerator and denominator have no common factors other than 1.
In other words, you cannot divide the top and bottom any further and have them still be whole numbers. The simplest form is also called lowest terms.
In this case, 3 and 15 have a common factor, which is 3. Thus, 3/15 in simplest form will be:
3/15 = 1/5 (divide both numerator and denominator by 3)
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Make the following conversion. 4mm = _____ cm 0.04 0.4 40 400
Answer:
0.4 cm
Step-by-step explanation:
10 mm = 1 cm thus 4mm / 10 = 0.4 cm
What is this decimal expressed as a percent?
Answer:
13%Step-by-step explanation:
To fraction ;
[tex]0.13=\frac{0.13\times \:100}{100}\\\\=\frac{13}{100}[/tex]
To percentage
[tex]\frac{0.13}{1}\times \frac{100}{100}\\ \\= 13/100\\\\= 13\%[/tex]
Round 96.1825899389 to 4 decimal places.
Answer:
96.1826
Step-by-step explanation:
to make that decimal numbers in 4 decimal places, then you count the number at the right hand side after the point, when u get to the 4th digit, you stop, then if the 5th digit is more than 4, they you add 1 to the 4th digit and there u have 96.1826
The Round 96.1825899389 to 4 decimal places will be 96.1826
What is rounding a number to some specific place?Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.
Rounding to some place keeps it accurate on the left side of that place but rounded or sort of like trimmed from the right in terms of exact digits.
We need to Round 96.1825899389 to 4 decimal places.
To make that decimal numbers in 4 decimal places, then we count the number at the right hand side after the point, when u get to the 4th digit.
Therefore, the Round 96.1825899389 to 4 decimal places will be 96.1826
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i need help I legit don't understand please
Answer:
Its the "range" of x values, so from -2 to 2.
You can write it as [-2, 2]
Can you guys help me with 15/8m-11=7/4m+1
Answer:
m=96
Step-by-step explanation:
[tex]\frac{15}{8}m-11=\frac{7}{4}m+1\\\\\frac{15}{8}m -\frac{7*2}{4*2}m=1+11\\\\\frac{15-14}{8}m=12\\\\\frac{1}{8}m=12\\\\m=12*8\\\\m=96[/tex]
a circle has a radius of 7ft. Find the radian measure of the central angle 0 that intyercepts an arc of length 16ft
Answer:
2.29 rads
Step-by-step explanation:
The length of the arc of a circle of radius r is given by;
l = rθ ---------------------------(i)
Where;
l = length of the arc
θ = central angle o that intercepts that arc and measured in radians.
From the question:
l = 16ft
r = 7ft
Substitute these values into equation (i) as follows;
16 = 7θ
Make θ subject of the formula
θ = [tex]\frac{16}{7}[/tex]
θ = 2.29
Therefore, the radian measure of the central angle is 2.29 rads
Find the missing number to make these fractions equal.
Answer:
66/8 = 3/4Step-by-step explanation:
Let the unknown number be x
[tex]\frac{3}{4} = \frac{x}{8} \\\\Cross \: Multiply\\4\times x = 3 \: \times 8\\\\4x =24\\\\Divide \:both\:sides \:of\:the\:equation\: by\: 4\\\frac{4x}{4} = \frac{24}{4} \\\\x = 6[/tex]
Answer:
6
Step-by-step explanation:
Given
[tex]\frac{3}{4}[/tex] = [tex]\frac{?}{8}[/tex]
The 4 on the denominator is multiplied by 2 to obtain 8
The same operation must be applied to the numerator to make them equal.
Thus
3 × 2 = 6
[tex]\frac{3}{4}[/tex] = [tex]\frac{6}{8}[/tex] ← are equal fractions
A vertical shelving unit consists of five equal-sized square shelves arranged in a column to form a rectangle. The total area of all five shelves is 500 square inches. What is the length, in inches, of the shelving unit?
Answer:
50 inches
Step-by-step explanation:
Given that
5 equal sized square shelves arranged in a column.
Total area of five shelves = 500 sq inches
To find:
Length of shelving unit = ?
Solution:
First of all, let us find the area of each shelving unit.
Area of each shelving unit = Total area of five shelved divided by 5
Area of each shelving unit = 500 [tex]\div[/tex] 5 = 100 sq units.
Each shelving unit is of square shape and area of a square is given as:
Area = [tex]Side^2[/tex]
100 = [tex]Side^2[/tex]
So, side of shelve = 10 inches
Now, there are 5 squares in the shelving unit.
So, length of shelving unit = [tex]10 \times 5 = \bold{50 \ inches}[/tex]
Move the center of rotation back to the origin (0, 0) of the coordinate plane. Now alter pentagon ABCDE by moving one or more line segments on the pentagon to a different location. Rotate the pentagon using the slider. How many times does the pentagon map back onto itself in this situation? What can you conclude about the kinds of polygons that can map back onto themselves? Describe them.
The changed pentagon maps back onto itself only one time, when the value of α is 360°. A polygon must be regular to map back onto itself more than once. In a regular polygon, all of the sides are equal and all of the angles are equal.
Step-by-step explanation:
Answer:
The changed pentagon maps back onto itself only one time, when the value of α is 360°. A polygon must be regular to map back onto itself more than once. In a regular polygon, all of the sides are equal and all of the angles are equal.
Step-by-step explanation:
Sample Answer
a mouse runs across a 5.56 m kitchen floor in 3.42 seconds.What is the velocity of the mouse?
Answer:
v = 1.62 m/s
Step-by-step explanation:
Given that,
Distance covered by the mouse is 5.56 m is in 3.42 seconds.
We need to find the velocity of the mouse. It is equal to the total distance covered divided by time taken. So,
[tex]v=\dfrac{d}{t}\\\\v=\dfrac{5.56\ m}{3.42\ s}\\\\v=1.62\ m/s[/tex]
So, the velocity is 1.62 m/s.
What is 2x 2 + 2x - 12 = ?
Answer:
(x-6)(2x+2)
Step-by-step explanation:
2x^2 + 2x - 12
by using splitting method
2x^2 - 12x + 2x -12
taking separate common from both pairs
2x(x - 6) + 2(x - 6)
(x - 6)(2x + 2)
Which of the following expressions cannot be simplified?
A) 8x-5x
B) 8x-1
C -(8x+3)
D 8(x-2)
Answer:
B) 8x-1
Step-by-step explanation:
A) 8x-5x Like terms = 3x
B) 8x-1 Not like terms 8x-1
C -(8x+3) Distribute the minus sign -8x -3
D 8(x-2) Distribute the 8 8x - 16
Answer:
B. 8x - 1
Step-by-step explanation:
Notice that all of these expressions can be simplified except for option B. 8x-1.
Option A has two like terms, 8x and -5x which could be reduced to 3x
Option B has two distinct terms, 8x and -1 which can only be combined into 8x-1
Option C has a leading negative, and can be simplified with the distributive property to be -8x + -3
Option D has a leading 8 that can be distributed to the term (x-2) to form 8x - 16.
Thus, choose option B.
Cheers.
Han wants to convert his Canadian dollars to euros for his trip to France. He has 427 Canadian dollars. the current exchange rate is 1.28 Canadian dollars per euro. how many euros will he have.
Answer:
333.59375 Euro
Step-by-step explanation:
427 Canadian dollars converted to Euro
rate of exchange: for every 1.28 Canadian dollars=1 Euro
427 = ?? Euro
427/1.28=333.59375 Euro
The product of six and a number increased by six?
Answer: 6•(n+6)
Step-by-step explanation:
n is number
can be any letter
Answer:
6(n+6)
Step-by-step explanation:
the product means multiplication so you're going to need to multiply 6 by the number increased by 6. n represents the number, so n increased by 6 would be n+6. the parentheses represent the multiplication. put it together and you get the answer 6(n+6)
What is the solution to the equation 6 m = 60?
Answer:
m = 10
Step-by-step explanation:
Divide both sides of this equation by 6. We get:
m = 60/6 = 10.
Solution: m = 10
Answer:
m =10
Step-by-step explanation:
What is the best definition for combining like terms
Step-by-step explanation:
Combing like terms means that you combine the terms that are alike. So, if you have integers you would combine the integers. If you had a variable like x, you would combine everything with x. For instance, 2x+4+3+7x, to combine like terms add 4+3 and 2x+7x.
True or False
15. (True or False) Any 3 distinct points are always coplanar.
16. (True or False) Any 2 distinct circles are always coplanar.
17. (True or False) If 2 lines intersect once then the lines are coplanar.
18. (True or False) Two lines that are skew can sometimes intersect.
19. (True or False) An angle and a circle can have more than 3 intersections
20. (True or False) Two distinct circles can have more than 2 intersections.
21. (True or False) Any given line and point are always coplanar.
Answer:
15. True
16. False
17. True
18. False
19. True
20. False
21. True
Step-by-step explanation:
15. The three points can be taken as being two points on a line adjacent to a point which always forms a plain when the ends of the line are connected to the point
16. The two circles can be on different planes
17. With one line fixed, the other line can be rotated until both lines are in the flat plane
18. The definition of skew lines are lines in different planes that are not parallel and that do not intersect
19. Whereby the angle crosses the circumference of the circle twice, the number of intersections = 4
20. Two distinct circles can only intersect twice
21. A plane can always be drawn with any three points
Given f(x)=2x+1 evaluate f(4) Please help with this question.
Answer:
9
Step-by-step explanation:
f(x)=2x+1
f(4)=2 x 4+1
= 8+1
= 9
Answer:
Wherever we see an x , we just input 4 to find f ( 4 ) : f ( 4 ) = 2 ( 4 ) − 1 = 8 − 1 = 7
Hope this helps
please help! really needing help solve the problem
Answer:
7
Step-by-step explanation:
By Basic proportionality theorem:
[tex] \frac{10}{8} = \frac{3x - 6}{12} \\ \\ \frac{10 \times 12}{8} = 3x - 6 \\ \\ \frac{120}{8} = 3x - 6 \\ \\ 15 = 3x - 6 \\ 15 + 6 = 3x \\ 21 = 3x \\ \frac{21}{3} = x \\ 7 = x \\ \\ \huge \red { \boxed{x = 7}}[/tex]
4(-8x+5) - (-33x-26)
Answer:
Step-by-step explanation:
Use distributive property a(b+c) = a*b +a*c
4(-8x + 5) - (-33x - 26) = 4*-8x + 4 *5 - 33x * (-1) - 26*(-1)
= -32x + 20 + 33x + 26
{add like terms}
= -32x + 33x + 20 +26
= 1x + 46
Which of these below correctly solves for y of the equation 3x - 2 = 4y + 5?
Answer:
I think the answer is
y= 3/4x - 7/4
(Not sure though)
x-intercept: 3
y-intercept: 2
Answer:
y = -2/3x + 2
Step-by-step explanation:
Hey there!
Well since we already got the y-intercept to find slope we'll use the points,
(3,0) and (0,2).
Formula: [tex]\frac{y^2 - y^1}{x^2 - x^1}[/tex]
Plug in the given points,
[tex]\frac{2 - 0}{0 - 3}[/tex]
Slope = -2/3
Slope-intercept: y = -2/3x + 2
Hope this helps :)
Answer:
y = -2/3x + 2 or
2x + 3y = 6 (standard form).
Step-by-step explanation:
I am assuming you want the equation of the straight line that passes through these 2 points.
The 2 points are (3, 0 ) and (0, 2).
The slope of the line = (2 - 0) / (0 - 3)
= -2/3.
The equation is y = -2/3x + 2 ( as 2 is the y-intercept).
In standard form this is :
3y = -2x + 6
2x + 3y = 6.
The product of ten and a number
Answer:
10n
Step-by-step explanation:
n represents number, its like using X, since we don't have the information on it, we replace it with a letter.
Answer:
Let the number be n.
10× n =10n.
hope you got thè answer.
Input: 15 , Output: 5, Input: 9, Output: -1. What would be the rule now ?
Answer:
Subtract 10
Step-by-step explanation:
The first option, "take the ones digit", is obviously incorrect because the ones digit of 9 is not -1. The second one is incorrect because you are dividing by 2 and then adding 5. Dividing odd numbers by 2 will give you a decimal and a decimal plus an integer (the integer is 5 in this case) will still be a decimal (provided that the decimal is not an integer as well). However, both of the outputs are integers, so we know that the second one is wrong. The third one is wrong as well because 9 / 3 = 3, not -1. The last one is correct because 15 - 10 = 5 and 9 - 10 = -1.
Graph the interval represented in interval notation on the number line.
(-Infinite, -4] U [6, infinite)
Answer:
The upper reason is your answer.....
A bike wheel is 26 inches in diameter. What is the bike wheel's diameter in millimeters (1 inch = 25.4 millimeters)?
Answer:
660.4 millimeters.Step-by-step explanation:
1 inch = 25.4 millimeters
1 inch = 25.4 millimeters26 inches = ?
26 × 25.4
26 × 25.4= 660.4 millimeters
660.4 millimeters is the answer.
A square has a side length 15.8cm.If 3 such squares are linked side to side in a straight line, what is the perimeter of the whole shape?
Answer:
126.4 cm
Step-by-step explanation:
1. 15.8 * 3 = 47.4 (This is the length)
2. Find half of the rectangle
47.4 + 15.8 (width) = 63.2
3. Find the whole perimeter
63.2 * 2 = 126.4
Answer:
126.4
Step-by-step explanation:
If you put three squares that are all 15.8cm together, you get a rectangle that is 47.4cm by 15.8cm. To get 47.4, you multiply 15.8 x 3 because it's three 15.8 squares together. Then to find the perimeter of the rectangle, you add all the sides together to get the answer 126.4.
What is Equivalent to the square root of 16
Answer:
4
Step-by-step explanation: 4*4 is 16. 4^2 is 16. So the square root of 16 is 4.
Answer:
4
Step-by-step explanation:
4 times 4 = 16, therefore the square root of 16 must be 4