Answer:
C. 135
Step-by-step explanation:
The value of the expression when x = 5 is 135.To find the value of the expression when x = 5, substitute the value of x into the expression and perform the calculations:
Expression: [tex](2x^2 / x) + x(100 - 15x)[/tex]
Now, replace x with 5:
[tex](2 * 5^2 / 5) + 5(100 - 15 * 5)[/tex]
Calculate the values within the parentheses first:
[tex](2 * 25 / 5) + 5(100 - 75)[/tex]
Now, perform the arithmetic inside each set of parentheses:
[tex](50 / 5) + 5(25)\\50 / 5 = 10[/tex]
Now, continue:
10 + 5 * 25 = 10 + 125 = 135
So, the value of the expression when x = 5 is 135.
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In a right triangle, sin(40 - 2) = cos(32)'. What is the value of x?
O 10
O 15
O 20
O 25
Answer:
x = 25
Step-by-step explanation:
Correct question
In a right triangle Sin (40-x)=cos(3x) what is the value of x
Since Sin theta = Cos(90-theta)
Sin (40-x) = Sin(90-3x)
40 - x = 90 - 3x
-x+3x = 90 - 40
2x = 50
x = 25
Hence the value of x is 25
what number represents the same amount as 4 tens+0 ones
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]
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)
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Find the exact value of sin2Θ if tanΘ=[tex]\frac{-2\sqrt{5} }{5}[/tex] and 90 < Θ < 180.
Answer:
[tex]sin 2 \theta = \frac{4 \sqrt5}{9}[/tex]
Step-by-step explanation:
Identities used :
[tex]1. sin^2 \theta = 1 - cos^2\theta\\\\2. tan^2 \theta + 1 = sec^2 \theta\\\\3.cos \theta = \frac{1}{sec \theta} \\\\4. sin 2 \theta = 2 sin\theta cos\theta[/tex]
[tex]Given \ tan \theta = -\frac{2 \sqrt5}{5}\\[/tex]
[tex]we \ know \ tan ^2 \theta + 1 = sec^2\theta[/tex]
[tex](-\frac{2 \sqrt 5}{5})^2 + 1 = sec^2 \theta\\\\\frac{4 \times 5}{25 } + 1 = sec^2 \theta \\\\\frac{20 + 25}{ 25} = sec^2 \theta \\\\\frac{45}{25} = sec^2 \theta \\\\sec \theta = \sqrt{ \frac{45}{25}}\\\\sec \theta = \sqrt{ \frac{9 \times 5}{5 \times 5}} \\\\sec \theta = \frac{3 \sqrt {5}}{5}\\\\[/tex]
[tex]We \ know \ cos \theta = \frac{1}{ sec \theta}[/tex]
[tex]So , \cos \theta = \frac{5}{3 \sqrt5}[/tex]
[tex]Next \ sin^2 \theta = 1 - cos^2 \theta[/tex]
[tex]= 1 - (\frac{5}{3 \sqrt5})^2\\\\=1 - \frac{25}{9 \times 5}\\\\=1 - \frac{25}{45}\\\\=\frac{45 - 25}{45}\\\\=\frac{20}{45}\\\\=\frac{4}{9}[/tex]
[tex]sin \theta = \sqrt{ \frac{4}{9}} = \frac{2}{3}[/tex]
[tex]Find \ sin 2 \theta[/tex]
[tex]sin 2 \theta = 2 (sin \theta \times cos \theta)[/tex]
[tex]= 2 \times \frac{2}{3} \times \frac{5}{3\sqrt5}\\\\= \frac{4 \times \sqrt5 \times \sqrt5}{9 \times \sqrt 5}\\\\=\frac{4 \sqrt5}{9}[/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.
decompose 17x^3+7x^2-17x-7 divided by (x-1)^2(x+1)^2 into partial fraction
..........................................................................................................................................................................................................................................................................................................................................................................................................................................................
Find the distance between the points given.
(-3,-4) and (0,0)
Answer: 5 Units
Step-by-step explanation:
whats the answer to this
Answer:
its the 2nd one
hope that helps<3
Answer:
jhkkkhj
Step-by-step explanation:
jkjkjkjkj
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
Use the drop-down menus to correctly relate each pair of numbers
manee help meh son
Answer:
Sorry for the late response, I had to have lunch.
1. >
2. =
3. <
4. >
Step-by-step explanation:
Have a great summer :)
Need help with probabilities (math) plz
Answer:
What is your question for probabilities?
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.
I need helped really need this question to be answer!
Answer:
the answer for your question is b
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
Convert 23cm2 into mm2
Answer:
2300 mm^2
Step-by-step explanation:
A
B
С
D
If mZACD = 70°, then mZBCD = [? ]°
Answer:
35 is correct
Step-by-step explanation:
hope this helps.
Answer:
35°
Step-by-step explanation:
Angle ACD is 70°. The little tick marks on the angle mean both sides of the split are the same amount. This means if you divide the angle in half, you will find out what both of them are equal to.
A paper company needs to ship paper to a large printing business. The paper will be
shipped in small boxes and large boxes. Each small box of paper weighs 50 pounds
and each large box of paper weighs 80 pounds. A total of 19 boxes of paper were
shipped weighing 1280 pounds altogether. Determine the number of small boxes
shipped and the number of large boxes shipped.
Answer:
16 boxes large
Step-by-step explanation:
if the weigth is 1280 wilhich means its 1280÷80 =16
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:
[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!
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
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.
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:
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
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)
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
pleaaseee explain !!
Answer:
64
Step-by-step explanation:13+51=64
Find the IQR: (find the median, then find the median of the first group and then the next group. Now subtract big median minus the small median.) 20, 17, 16, 3, 7, 45
Answer:
13
Step-by-step explanation:
The IQR = Interquartile Range is the difference between the first and third quartile
Rearranged data set:
3, 7, 16, 17, 20, 45
Step 1
We find the first quartile = Q1
= 1/4(n + 1)th number
n = 6
= 1/4(6 + 1)th
= 1/4(7)th
= 1 3/4th number
This = 7
Step 2
We find the third quartile = Q3
= 3/4(n + 1)th number
n = 6
= 3/4(6 + 1)th
= 3/4(7)th
= 21/4th number
= 5 1/4 th number
This = 20
Step 3
IQR = Q3 - Q1
= 20 - 7
= 13
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%
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
