Answer:
[tex]\sqrt{(4-a)(4+a)} =b[/tex]
Step-by-step explanation:
16 = a^2 + b^2
16 - a^2 =b^2
4^2 - a^2 = b^2
[tex]\sqrt{4^2 - a^2} =b[/tex]
[tex]\sqrt{(4-a)(4+a)} =b[/tex]
A square is inscribed in an equilateral triangle that is inscribed in a circle.
A square is inscribed in an equilateral triangle that is inscribed in a circle. The square and circle are shaded.
Which represents the area of the shaded region?
area of the circle – area of the square – area of the triangle
area of the triangle – area of the square + area of the circle
area of the triangle + area of the square + area of the circle
area of the circle – area of the triangle + area of the square
The area of the shaded region is (area of the circle) - (area of the square) - (area of the triangle)
Option A is the correct answer
What is a triangle?A triangle is a 2-D figure with three sides and three angles.
The sum of the angles is 180 degrees.
We can have an obtuse triangle, an acute triangle, or a right triangle.
We have,
The shaded region consists of the area inside the circle but outside the square, as well as the area inside the equilateral triangle but outside the square.
Now,
The area of the circle is πr²
Since the square is inscribed in the circle, the diameter of the circle is equal to the diagonal of the square.
Let's say the side length of the square is s.
By the Pythagorean theorem,
s² + s² = (diameter)²
2s² = (2r)²
s² = r²
The area of the square is s² = r².
The area of an equilateral triangle with side length s is √(3)/4 x s².
Since the side length of the square is equal to the height of the equilateral triangle, the side length of the equilateral triangle is also equal to s.
The area of the shaded region.
= (area of the circle) - (area of the square) - (area of the triangle)
Thus,
The area of the shaded region is (area of the circle) - (area of the square) - (area of the triangle)
Learn more about triangles here:
https://brainly.com/question/25950519
#SPJ7
Can someone help me
Step-by-step explanation:
the answer is in the above image
Answer:
[tex]-12^{2}[/tex] + 9a - 5
Step-by-step explanation:
combine like terms :
-7[tex]a^{2}[/tex] - 5[tex]a^{2}[/tex] = -12[tex]a^{2}[/tex]
+3a - (-6a) = 9a
-9 - (-4) = -5
I need helped really need this question to be answer!
Answer:
the answer for your question is b
John invested $30000 in the bank for 4 years. At the end of the period, he had
$42520. Calculate
a. the interest earned
b. the rate per annum at which simple interest was earned to 1 decimal place.
Answer:
Rate = 10.4%
Step-by-step explanation:
Given :
P = $30000
A = $42520
Interest earned = 42520 - 30000 = $12520
Time = 4years
Find R
[tex]Interest = \frac{PRT}{100}[/tex]
[tex]12520 = \frac{30000 \times R \times 4}{100}\\\\12520 = 300 \times 4 \times R\\\\12520 = 1200 \times R\\\\R = \frac{12520}{1200}\\\\R = 10.43 \%[/tex]
Round to 1 decimal place, Rate = 10.4%
What are 3 equivalent ratios of 2 to 9 (fraction)? (one of them divided and one multiplied)
Answer:
Step-by-step explanation:
[tex]\frac{2}{9}=\frac{2*3}{9*3}=\frac{6}{27}\\\\\frac{2}{9}=\frac{2*4}{9*4}=\frac{8}{36}\\\\\frac{2/2}{9/2}=\frac{1}{4.5}[/tex]
I need help
Solve the expression when X =5;3(X+2)=
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {21}}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex]3 \: ( \: x + 2 \: )[/tex]
Plugging in the value [tex]x = 5[/tex] in the above expression, we have
[tex] = 3\:( \: 5 + 2 \: )[/tex]
[tex] = 3 \: ( \: 7 \: )[/tex]
[tex] = 3 \times 7[/tex]
[tex] = 21[/tex]
Note:-[tex]\sf\pink{PEMDAS\: rule.}[/tex]
P = Parentheses
E = Exponents
M = Multiplication
D = Division
A = Addition
S = Subtraction
[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35☂}}}}}[/tex]
12 less than a number is equal to the product of 7 and that number. Convert into an
equation and find the number?
Answer:
EQUATION: X - 12 = 7X. SOLUTION: X = - 2.
Step-by-step explanation:
First, we do not know the number. When the number is unknown, it is a variable. I chose the variable, "X."
12 less than signals that we subtract 12. So that would be X - 12.
A product of 7 AND that number means we multiply 7 by X. That can be notated as 7X.
12 less than X is EQUAL to the product of 7 and X. So X - 12 = 7X.
To find the solution, we want to know the value of X. Move X to one side of the equation.
X - 12 = 7X
-X -X
_________
-12 = 6X
Divide both sides by 6 to get X by itself.
X = - 2.
Please help this is due today!!
A group of 35 team members needs to be divided into smaller workgroups. If each group is to contain two, three, or four people, what is the smallest number of groups possible?
Answer:
9
Step-by-step explanation:
Since we want the fewest number of groups possible, we need to maximize the number of people in each group. Since there can be a maximum of four people in each group, we can have a maximum of [tex]\left\lfloor \frac{35}{4}\right \rfloor=8[/tex] groups of four. The final three students can form the last group, hence the smallest number of groups possible is [tex]8+1=\boxed{9}[/tex]
help me please question in the picture
Answer:
Step-by-step explanation:
that should be a triangular prism.
Find x if 5, 9, 11, 12, 13, 14, 17 and x have a mean of 12.
Answer: 15
Step-by-step explanation: 5+9+11+12+13+14+17=81
Make an equation based on this and solve for the variable (x)
81+x/8=12
12*8=96
81+x=96
96-81=15
x=15
?????????????????????
Answer:
[tex]\sqrt{x+6}[/tex]
Step-by-step explanation:
So, there are a few things we need to go over to graph a function,
When a number is outside of a root, it changes the y value. For example:
y=[tex]\sqrt{x}+6[/tex]
With the +6, y will always be 6 higher than normal.
If it was -6, then y will always be 6 lower than normal.
What if the number is inside the root? Well, it works a little differently.
Instead of changing the y value, it changes the x value. For example:
y=[tex]\sqrt{x+6}[/tex]
So if you put a number in for x, lets say -6, wht would you get?
You would get -6+6=0
The square root of 0 is 0, so when x=-6, y=0
Normally, x would have to equal 0 for the y value to be 0.
So basically, when we see the number isnide of the root, we can think the our x coordinate being subtracted by that number.
This makes since, because if we subtract the +6 from x:
x-(+6)= x-6, and -6 is our x coordinate.
If it was -6 at the start, this would also work:
x-(-6)= x+6. So our x coordinate would start at 6.
Now, lets look at our graph.
As we can see, the x values start at -6, and the y values starts at 0.
This eliminates A and D, since the +6 would change the y value, not the x.
Remember that x-6 would make x a postive 6.
x+6 however, would make x a negative 6.
So we need x+6 in a square root.
This eliminates B, since it has a x-6, making the x coordinate postive 6, not negative 6.
So c is our answer.
Hope this helps!
A ruler cost x pence. A pen costs 10 pence more than the ruler. Write an expression, in terms of x, for the cost of a pen .
A. 10x pence
B. 10- x pence
C 10 pence
D.x + 10 pence
Answer:
D. x + 10 pence
Step-by-step explanation:
Since the pen costs 10 pence more than the ruler, we need to add 10 to x.
Which is a better estimate for the length of a raisin?
A. 1 meter b. 1 centimeter
Answer:
1 centimeter
Step-by-step explanation:
nope
What is the midpoint of the line segment with endpoints (-1,7) and (3, -3)?
A. (1, 2)
B. (1,4)
C. (2, 4)
D. (2, 2)
pleaaseee explain !!
Answer:
64
Step-by-step explanation:13+51=64
A rectangular garden has a length that is modeled by the expression2X -7 and a width of 3X^2+4x. What is the area of the garden?
Answer:
A = 6x³ - 13x² - 28xStep-by-step explanation:
Area of rectangle:
A = lwGiven:
l = 2x - 7w = 3x² + 4xThe area is:
A = (2x - 7)(3x² + 4x) =
2x(3x² + 4x) - 7(3x² + 4x) =
6x³ + 8x² - 21x² - 28x =
6x³ - 13x² - 28x
Answer:
Area of rectangle = 6 x ³ - 13 x ² + 28
step by step explanation
Given That :-
Length of rectangle = 2 x - 7Width of rectangle = 3 x ²+ 4 xTo Find :-
Area of rectangleFormula Used :-Area of rectangle = Length × Width
Solution : -Using Formula
Area of rectangle = Length × Width
substitute the values.
Area of rectangle = ( 2 x - 7 ) × ( 3 x ² + 4 )
= 2 x ( 3 x ² + 4 ) - 7 ( 3 x ² + 4 )
= 6 x ³ + 8 x - 21 x ² + 28
= 6 x ³ - 13 x ² + 28
Two brothers are sharing a certain sum of money in the ratio 2/3 : 3/5, if the largest share was Gh¢500.00. How much was shared between them?
Given:
Two brothers are sharing a certain sum of money in the ratio [tex]\dfrac{2}{3}:\dfrac{3}{5}[/tex].
The largest share was Gh¢500.00.
To find:
The total amount shared between them.
Solution:
It is given that, two brothers are sharing a certain sum of money in the ratio [tex]\dfrac{2}{3}:\dfrac{3}{5}[/tex].
First we need to make the denominators common.
[tex]Ratio=\dfrac{2\times 5}{3\times 5}:\dfrac{3\times 3}{5\times 3}[/tex]
[tex]Ratio=\dfrac{10}{15}:\dfrac{9}{15}[/tex]
[tex]Ratio=10:9[/tex]
So, the two brothers are sharing a certain sum of money in the ratio 10:9.
Let the shares of two brothers are 10x and 9x respectively. So, the larger share is 10x.
It is given that the largest share was Gh¢500.00.
[tex]10x=500[/tex]
[tex]x=\dfrac{500}{10}[/tex]
[tex]x=50[/tex]
Now, the total amount shared between them is:
[tex]Total=10x+9x[/tex]
[tex]Total=19x[/tex]
[tex]Total=19(50)[/tex]
[tex]Total=950[/tex]
Therefore, the total amount shared between them is Gh¢950.00.
how to solve -4x+8y=-16
4x+3y=5
Answer:
X=2, y=-1
Step-by-step explanation:
-4x +8y=-16 equation 1
4x +3y=5 equation 2
11y=-11 add two equations to eliminate x
y=-1
solve for x by inputting y value into either equation
4x+3y=5
4x+3(-1)=5
4x-3=5
4x=8
x=2
Need help with probabilities (math) plz
Answer:
What is your question for probabilities?
The picture is above I’ll mark as brainliest.
Answer:
Width = 3 m
Step-by-step explanation:
Formula for perimeter:
P = l + w + l + w
Plug in what we know:
14 = 4 + w + 4 + w
Isolate variable w (width):
14 = 8 + 2w
6 = 2w
3 = w
Check your work:
14 = 4 + 3 + 4 + 3
14 = 7 + 7
14 = 14
Correct!
(Don't forget to add units in your answer!)
Jada makes sparkling juice by mixing 2 cups of
sparkling water with every 6 cups of apple juice.
A. How much apple juice does Jada need if she uses 6
cups of sparkling water?
B. How much sparkling water does jada need if she uses 15 cups of apple juice.
Answer:
A=36
B= 2.5
Step-by-step explanation:
If you need 1 cup of sparkling water per 6 cups of apple juice and you use 6 cups of sparking water you do 6x6=36
15 divided by 6 = 2.5
Answer:
A - 18. B - 5
Step-by-step explanation:
So, the best thing for us to do first is find the ration between apple juice and sparkling water.
Then we can answer the questions once we know the ratio.
We know that for every 6 apple juice, we need 2 sparkling water.
This is a 6 : 2 ratio.
However, we can simplfy this further by dividing the 6 and 2 by using a number that goes into both values, such as 2:
6/2 : 2/2
=
3 : 1
So this is our ratio.
Now, the first questino asks how many apple juice is needed for 6 cups of sparkling water?
We know 3 apple juce is needed for 1 sparkling water, so to find whats needed for 6, lets multiply the 3 by 6:
3*6
=
18
So we need 18 apple juice for 6 sparkling water.
Next we need to find how much sparkling water is needed for 15 cups of apple juice.
We know that for every 3 apple juice we need 1 sparkling water.
We gace 15 apple juice.
To find how much sparkling water we need, lets divide the amount of apple juice by the ratio of apple juice. This will get us how many times more sparkling water we need:
15/3
=
5
Now that we know how many times more sparkling water we need, lets multiply the sparkling water by this:
5*1
=
5
So we need 5 sparkling water for every 15 cups of apple jiuce.
Hope this helps!
2. The average daily rainfall in London during April was 3.5 mm. How much rain fell during the month?
Answer:
105mm
Step-by-step explanation:
To find the rainfall during the month of April simply multiply the number of days in April times the average daily rainfall
Number of days in April: 30
Average daily rainfall: 3.5mm
Rainfall during the month = 30 * 3.5 = 105mm
Find the sum.
b/ b^2+4b+4 + 9/b^2+7b+10
Answer:
11b^3+14b^2+b+9
---------------------------
b2
Step-by-step explanation:
what number represents the same amount as 4 tens+0 ones
Mr. vazquez determines that the area of a bathroom in his house is 25 square feet less than 1/5 of the area of the living room if the bathroom measures 35 square feet what is the area of the living room ?
Answer:200
Step-by-step explanation:
Multiply 35 by 5 to get 175. You do this because you are doing the opposite to find a larger amount. Then add 25 to get 200
can you solve this problem please
Answer:
k = 11
Step-by-step explanation:
Given the points are collinear then the slopes between consecutive points are equal.
Using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (5, 1) and (x₂, y₂ ) = (1, - 1)
m = [tex]\frac{-1-1}{1-5}[/tex] = [tex]\frac{-2}{-4}[/tex] = [tex]\frac{1}{2}[/tex]
Repeat with another 2 points and equate to [tex]\frac{1}{2}[/tex]
with (x₁, y₁ ) = (1, - 1) and (x₂, y₂ ) = (k, 4)
m = [tex]\frac{4+1}{k-1}[/tex] , then
[tex]\frac{5}{k-1}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
k - 1 = 10 ( add 1 to both sides )
k = 11
The length of a rectangle is the same as its width. If its perimeter is 32 meters, what is its area? 15points- HELP ME PLLLLLLLEEEEAAASSSEE
32 m ^2
64 m ^2
81 m ^2
16 m ^2
Answer:
64
Step-by-step explanation:
a rectangle with length and width equal is a square.
32/4 sides
equals 8 for each side.
l x w = A
8 x 8 = 64
Answer: 64 m ^2
Step-by-step explanation:
Ok well if it's length is the same as the width then we can divide the perimeter by 4 to see the length of each side
[tex]\frac{32}{4} =8[/tex]
Each side is 8m long so it's an 8x8 rectangle. Now we can find the area.
8x8=64
The area is 64 meters squared
What is the value of this expression when a = 7 and b = -4? 1201 - 6 3 OA. -6 OB. - 31 Oc. 37 D. 6
Answer:
OA . -6
Step-by-step explanation:
correct me if I'm wrong
ANSWER PLZZZZZZ!!!!!!!!!!!!!!!
Answer:
length=(3x-2)
Step-by-step explanation:
area of rectangle=length*breadth
3x^2 + 7x - 6=length * (x+3)
3x^2 +(9-2)x -6=length *(x+3)
3x^2+9x-2x-6=length*(x+3)
3x(x+3)-2(x+3)=length*(x+3)
(x+3)(3x-2)=length*(x+3)
(x+3)(3x-2)/(x+3)=length
(3x-2)=length
Answer:
(3x - 2)
Step-by-step explanation:
Given that the area A = length × width
A = 3x² + 7x - 6 ← factor to obtain length
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 3 × - 6 = - 18 and sum = + 7
The factors are + 9 and - 2
Use these factors to split the x- term
3x² + 9x - 2x - 6 ( factor the first/second and third/fourth terms )
= 3x(x + 3) - 2(x + 3) ← factor out (x + 3) from each term
= (x + 3)(3x - 2)
We know (x + 3) is the width , then (3x - 2) is the length
