Area of first rectangle= 5×2=10units
Area of second rectangle= 3×2= 6 units
Area of third rectangle = 5×2= 10 units
Now,
Total area of figure = 10+6+10= 26units✓
Answer:
26
Step-by-step explanation:
we want to figure out the area of the composite figure notice that the composite figure contains three rectangles therefore in order to find the area of the composite figure we need find the area of the rectangles first
finding the area of the first & last rectangles:
the first and last rectangles are congruent therefore they will have the same area thus
[tex] \displaystyle A _{ \rm 1)rect} = A _{ \rm 3)rect} = l \times w[/tex]
from the figure we obtain:
[tex]l = 5[/tex][tex]w = 2[/tex]thus substitute:
[tex] \displaystyle A _{ \rm 1)rect} = A _{ \rm 3)rect} = 5\times 2[/tex]
simplify multiplication:
[tex] \displaystyle A _{ \rm 1)rect} = A _{ \rm 3)rect} = 10[/tex]
finding the area of the middle rectangle:
the middle rectangle has a length and width of 3 and 2 respectively Thus
[tex] \displaystyle A _{ \rm 2)rect} =3 \times 2[/tex]
simplify multiplication:
[tex] \displaystyle A _{ \rm 2)rect} =6[/tex]
finding the area of the composite figure:
[tex] \rm \displaystyle A _{ \rm composite} = A _{ \rm 1)rect} + A _{ \rm 2)rect} + A _{ \rm 3)rect} [/tex]
substitute what we got:
[tex] \rm \displaystyle A _{ \rm composite} = 10 + 6 + 10[/tex]
simplify addition:
[tex] \rm \displaystyle A _{ \rm composite} = \boxed{ 26}[/tex]
hence,
the answer is 26 square units
PLEASE HELP!!!
Select the correct answer.
Which function has an average rate of change of -4 over the interval [-2, 2]?
Answer:
D.
Step-by-step explanation:
Find the average rate of change of each given function over the interval [-2, 2]]:
✔️ Average rate of change of m(x) over [-2, 2]:
Average rate of change = [tex] \frac{m(b) - m(a)}{b - a} [/tex]
Where,
a = -2, m(a) = -12
b = 2, m(b) = 4
Plug in the values into the equation
Average rate of change = [tex] \frac{4 - (-12)}{2 - (-2)} [/tex]
= [tex] \frac{16}{4} [/tex]
Average rate of change = 4
✔️ Average rate of change of n(x) over [-2, 2]:
Average rate of change = [tex] \frac{n(b) - n(a)}{b - a} [/tex]
Where,
a = -2, n(a) = -6
b = 2, n(b) = 6
Plug in the values into the equation
Average rate of change = [tex] \frac{6 - (-6)}{2 - (-2)} [/tex]
= [tex] \frac{12}{4} [/tex]
Average rate of change = 3
✔️ Average rate of change of q(x) over [-2, 2]:
Average rate of change = [tex] \frac{q(b) - q(a)}{b - a} [/tex]
Where,
a = -2, q(a) = -4
b = 2, q(b) = -12
Plug in the values into the equation
Average rate of change = [tex] \frac{-12 - (-4)}{2 - (-2)} [/tex]
= [tex] \frac{-8}{4} [/tex]
Average rate of change = -2
✔️ Average rate of change of p(x) over [-2, 2]:
Average rate of change = [tex] \frac{p(b) - p(a)}{b - a} [/tex]
Where,
a = -2, p(a) = 12
b = 2, p(b) = -4
Plug in the values into the equation
Average rate of change = [tex] \frac{-4 - 12}{2 - (-2)} [/tex]
= [tex] \frac{-16}{4} [/tex]
Average rate of change = -4
The answer is D. Only p(x) has an average rate of change of -4 over [-2, 2]
Answer:
see photo
Step-by-step explanation:
Plato/Edmentum
Explain how to solve 4^(x+3)=7 using the change of base formula log_by=log y/ log b. Round to the nearest thousandth
Answer:
x = -1.59
Step-by-step explanation:
We are here given a equation and we need to solve out for x. The given equation is ,
[tex]\sf\longrightarrow 4^{( x +3)}= 7[/tex]
Take log to the base " e " on both sides , so that we can remove the variable from the exponent .
[tex]\sf\longrightarrow log_e 4^{x+3}= log_e 7[/tex]
Simplify using the property of log , [tex]\sf log a^m = m log a [/tex] , we have ,
[tex]\sf\longrightarrow (x + 3) ln 4 = ln 7 [/tex]
Distribute by opening the brackets ,
[tex]\sf\longrightarrow x ln 4 + 3 ln 4 = ln 7[/tex]
This can be written as ,
[tex]\sf\longrightarrow x ln 4 = ln 7 - 3ln4 [/tex]
Divide both sides by ln 4 ,
[tex]\sf\longrightarrow x = \dfrac{ ln7}{ln 4 } - \dfrac{ 3ln4}{ln4} [/tex]
Simplify ,
[tex]\sf\longrightarrow x = \dfrac{ ln4 }{ln7 } -3[/tex]
On simplifying , we will get ,
[tex]\sf\longrightarrow \boxed{\blue{\sf x = -1.59 }}[/tex]
Please help me with this
Answer:
1/6 for white and 1/2 for black
Step-by-step explanation:
My knowledge!
Hope it helps!
Answer:
4/15
Step-by-step explanation:
There are 6 white+4black = 10 marbles in the bag
P (white) = white marbles / total marbles = 6/10 = 3/5
We keep the marble
There are 5 white+4black = 9 marbles in the bag
P (black) = black/total = 4/9
P(white, black no replacement) = 3/5 * 4/9 = 3/9 *4/5 = 1/3*4/5 = 4/15
Mrs. Ella bought something's bought 3 lb of apples. The price is $2.49 per pound. How much did she pay for the three pounds of apples ?
Answer:
$7.47
Step-by-step explanation:
Take the number of pounds and multiply by the price per pound
3 * 2.49
7.47 for 3 pounds of apples
Answer:
7.49
Step-by-step explanation:
Given: 3 pounds, and 2.49 for each pound
Multiply:
2.49 × 3
₁ ₂
2.49
× 3
----------
7. 47
Mrs. Ella bought 3 pounds of apples for $7.49
Work out the circumference of this circle 7.5
Answer:
47.12
Step-by-step explanation:
C=2πr=2·π·7.5≈47.12389
PLEASE HELP WILL MARK BRAINLIEST!
Answer:
a. 125 degrees
b. 62 degrees
c. 58 degrees
d. 130 degrees
Step-by-step explanation:
I assume these are the inner angles of the polygons.
remember, for a polygon with n sides we can fully split it into n-2 triangles without overlap.
each of these triangles has an angle sum of 180 degrees.
to get the total inner angle sum of the polygon, we need to multiply 180 by (n-2) (= the number of triangles).
out of that total we can then calculate the size of the missing angle.
a. 6 sides, therefore 4 triangles
4×180 = 720 degrees
the missing angle is
angle = 720 - 88 - 152 - 125 - 105 - 125 = 125
b. 5 sides, 3 triangles
3×180 = 540 degrees
angle = 540 - 109 - 111 - 140 - 118 = 62
c. 4 sides, 2 triangles
2×180 = 360
angle = 360 - 60 - 142 - 100 = 58
d. 7 sides, 5 triangles
5×180 = 900
angle = 900 - 90 - 120 - 140 - 150 - 120 - 150 = 130
Solve 7x + 1 < 4(x - 2).
A. {x | x > 3}
B. {x | x > -3}
C. {x | x < -3}
D. {x | x < 3}
Given:- 7x + 1 < 4(x - 2)
Solving It:-7x + 1 < 4(x - 2)
7x + 1 < 4x - 8
7x - 4x < -8 -1
3x < -9
x < -9/3
x < -3
So Correct Solution Set Will BeC. {x | x < -3}Hope This Helps Youwhich algebraic expression represents this word description?
the product of two and the difference between eleven and a number
a. 2(11-x)
b. 11-2x
c. 2x-11
d. 2(x-11)
Step-by-step explanation:
c. 2x-11 this is the answer
hope this helps you
have a nice day:)
Please help, explain too and I will give brainliest :)
Answer:
c
Step-by-step explanation:
Answer:
C. 37 degrees
Step-by-step explanation:
27, 36, 45 is just a larger 3, 4, 5 triangle. The smallest angle is across from the smallest side. With those in mind, we have 37, 53, and 90 degrees as the angles for a 3, 4, 5 triangle. We pair the 27, (the three when we reduce) with the smallest angle, the 37.
I'm sure you can do it with an actual formula, but i can't recall. Cheers
Hellllllllp plsss!! Due in very soon maths
Answer: 23, 27,29
Those im absolutely positive about.
Im not sure abt the rest
Step-by-step explanation:
Find the volume
Help me please
Answer:
54piecm^3
Step-by-step explanation:
pie x radius ^2 x h
= v
pie x 9
= 9pie x 6
= 54pie
what would be the u to usub and what would be the steps to solving this integral?
Presumably, ln⁵(x) is the same as (ln(x))⁵ (as opposed to a quintuply-nested logarithm, log(log(log(log(log(x)))))).
Then substituting u = ln(x) and du = dx/x gives
[tex]\displaystyle\int\frac{\mathrm dx}{x\ln^5(x)} = \int\frac{\mathrm du}{u^5} = -\frac1{4u^4}+C = \boxed{-\frac1{4\ln^4(x)}+C}[/tex]
HELP ME WITH THIS PROBLEM PLEASE!!
Answer:
w ≈ 33.9 in
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
w² + w² = 48²
2w² = 2304 ( divide both sides by 2 )
w² = 1152 ( take the square root of both sides )
w = [tex]\sqrt{1152}[/tex] ≈ 33.9 in ( to the nearest tenth )
Given a circle with centre O and radius 2.4cm. P is a point such that the lenght of the tengent from Q to the circle is 4.5cm. Find the lenght of OP
Answer:
5.1 cm
Step-by-step explanation:
(Probable) Question;
Given a circle with center O and radius 2.4 cm. P is a point on the tangent that touches the circle at point Q, such that the length of the tangent from P to Q is 4.5 cm. Find the length of OP
The given parameters are;
The radius of the circle with enter at O, [tex]\overline{OQ}[/tex] = 2.4 cm
The length of the tangent from P to the circle at point Q, [tex]\overline{PQ}[/tex] = 4.5 cm
The length of OP = Required
By Pythagoras's theorem, we have;
[tex]\overline{OP}[/tex]² = [tex]\overline{OQ}[/tex]² + [tex]\overline{PQ}[/tex]²
∴ [tex]\overline{OP}[/tex]² = 2.4² + 4.5² = 26.01
[tex]\overline{OP}[/tex] = √26.01 = 5.1
The length of OP = 5.1 cm
pls help me solve this multiplication fractions. (show work)
Answer:
32:3/4
33:4/3
34:40
35:48
geometry help translations
Answer:
A' (9,4)
B' (8,-1)
C' (5,1)
Answered by GAUTHMATH
Answer:
A' = 9,4
B' = 8,-1
C' = 5,1
Step-by-step explanation:
Does this graph show a function? Explain how you know.
Answer:
A is the correct one
cause according to function rule the vertical line should cut only on a one point to be function
as here we can see that vertical line cuts here at two point
The slope of a line is 5/9 and the slope of another line is -975. The two lines
are
Answer:
the third option - they are perpendicular to each other.
Step-by-step explanation:
for a perpendicular slope we need to exchange the x and y values (remember, a slope is the ratio of y/x) and flip the sign.
and that is exactly what happened here.
If the point A at (5, 3) is rotated clockwise about the origin through 90°, what
will be the coordinates of the new point?
Answer:
(5,-3) in the 4th quadrant
Step-by-step explanation:
The arithmetic mean of 10 consecutive even integers is 3. What is the least of these 10 even integers?
PLS HELP WILL GIVE BRAINLIEST
Answer:
-6
Step-by-step explanation:
2n can be the smallest integer, and 2n + 18 will be the largest integer.
The sum of this, divided by two, will result in the average/mean.
(2n + 2n + 18)/2 = 3
Multiply each side by 2:
(2n + 2n + 18)/2 ⋅ 2 = 3 ⋅ 2
2n + 2n + 18 = 6
Combine the like terms:
4n + 18 = 6
Subtract 18 from both sides:
4n + 18 - 18 = 6 - 18
4n = -12
Divide each side by 4:
4n/4 = -12/4
n = -3
Since we decided to go by 2n:
2n = 2(-3) = -6
how can the graph of g(x) =x2+4 be obtained from the graph of f(x) =x2
Answer:
see explanation
Step-by-step explanation:
Given f(x) then f(x) + c is a vertical translation of f(x)
• If c > 0 then a shift up of c units
• If c < 0 then a shift down of c units
The graph of g(x) is the graph of f(x) shifted up by 4 units
Fill in the blank and dropdown menus to form a true statement below.
Answer:
the polygon above has 6 sides . It is a hexagon with 6 obtuse angles interior angles equal to 720° .
Answer:
the polygon above has 6 sides . It is a hexagon with 6 obtuse angles interior angles equal to 720° .
Step-by-step explanation:
Solve + 17 = 20 for x and plot its value on the number line given below.
Answer:
x=12
Step-by-step explanation:
x/4 + 17 =20
Subtract 17 from each side
x/4 +17-17 =20-17
x/4 = 3
Multiply each side by 4
x/4 *4 = 3*4
x =12
Delta math please help
Answer:
[tex]\approx 13.0[/tex]
Step-by-step explanation:
The Pythagorean theorem is a formula that relates the sides of a right triangle. This formula states the following:
[tex]a^2+b^2=c^2[/tex]
Where (a) and (b) are the legs or the sides adjacent to the triangle angle of the right triangle. Parameter (c) represents the hypotenuse or the side opposite the right angle of the right triangle. Substitute the given values into the formula and solve for the unknown:
[tex]a = 7\\b = 11[/tex]
[tex]a^2+b^2=c^2[/tex]
[tex]7^2+11^2=c^2[/tex]
Simplify,
[tex]7^2+11^2=c^2\\\\49 + 121= c^2\\\\170=c^2[/tex]
Inverse operations,
[tex]170=c^2\\\\\sqrt{170}=c\\\\\\c \approx 13.0384[/tex]
Please help please please help
Answer:
Step-by-step explanation:
Number Estimate using a single digit and power of 10
23,898,497 2 × 10⁷
0.000136 1 × 10⁻⁴
26,857 3 × 10⁴
0.0302 3 × 10⁻²
The floor is in the shape of square. Louis measures the area as 445 square feet. Find the diagonal of the floor.
Answer:
29.83 ft
Step-by-step explanation:
First, you find the square root of 445, which is 21.09.
Then you use the Pythagorean theorem, which is a^2 + b^2 = c^2
because a and b are the same value you plug it in
21.09^2+21.09^2 = c^2
You end up getting:
c^2=889/5762
You then square root both sides to get:
c = 29.83, which is option 3
PLEASE HELP ITS TIMED!!!!
Answer:
It's A
Step-by-step explanation:
DO FOIL
-10d^4+(5+12)d^2s-6s^2=-10d^4+17d^2s-6s^2
Answer:
the first answer: -10a^4 + 17a^2s-6s^2
Step-by-step explanation:
What ordered pairs are the solutions of the system of equations in the graph below?
Answer:
(- 8, 8 ) and (- 4, 1 )
Step-by-step explanation:
The solution to a system of equations given graphically is at the points of intersection of the two
They intersect at (- 8, 8 ) and (- 4, 1 ) ← solutions
Building 1 (Circle) : Rotate 270 degrees counterclockwise around the origin. Building 2 (Square): Reflect across the y axis. Building 3 (Triangle): Reflect across the y axis, then translate 3 up and 2 to the left. Building 4 (L-Shape) : The points A (3, 8), B (6, 8), C (6, 3), and D (5, 3) need to be transformed to points A'' (–3, 1), B'' (–6, 1), C'' (–6, –4), and D'' (–5, –4). Avoid the pond, which is an oval with an origin at (0, 0), a width of 4 units, and a height of 2 units.
Answer:
See explanation
Step-by-step explanation:
The question is incomplete, as some coordinates to transform are not given.
I will, however, give a general explanation.
Rotate circle 270 degrees counterclockwise
This implies that, we rotate the center of the circle and the rule of this rotation is:
[tex](x,y) \to (y,-x)[/tex]
Assume the center is: (5,3), the new center will be: (3,-5)
Reflect square across y-axis
The rule is:
[tex](x,y) \to (-x,y)[/tex]
If the square has (3,5) as one of its vertices before rotation, the new point will be (-3,5).
Reflect triangle across y-axis, then 3 units up and 2 units left
The rule of reflection is:
[tex](x,y) \to (-x,y)[/tex]
If the triangle has (3,5) as one of its vertices before rotation, the new point will be (-3,5).
The rule of translating a point up is:
[tex](x,y) \to (x,y+h)[/tex] where h is the unit of translation
In this case, h = 3; So, we have:
[tex](-3,5) \to (-3,5+3)[/tex]
[tex](-3,5) \to (-3,8)[/tex]
The rule of translating a point left is:
[tex](x,y) \to (x-b,y)[/tex] where b is the unit of translation
In this case, b = 2; So, we have:
[tex](-3,8) \to (-3+2,8)[/tex]
[tex](-3,8) \to (-1,8)[/tex]
The L shape
[tex]A = (3, 8)[/tex] [tex]A" = (-3, 1)[/tex]
[tex]B = (6, 8)[/tex] [tex]B"= (-6, 1)[/tex]
[tex]C = (6, 3)[/tex] [tex]C" = (-6, -4)[/tex]
[tex]D = (5, 3)[/tex] [tex]D" = (-5, -4)[/tex]
Required
The transformation from ABCD to A"B"C"D"
First, ABCD is reflected across the y-axis.
The rule is:
[tex](x,y) \to (-x,y)[/tex]
So, we have:
[tex]A' = (-3,8)[/tex]
[tex]B' = (-6,8)[/tex]
[tex]C' = (-6,3)[/tex]
[tex]D' = (-5,3)[/tex]
Next A'B'C'D' is translated 7 units down
The rule is:
[tex](x,y) \to (x,y-7)[/tex]
So, we have:
[tex]A"= (-3,8-7) = (-3,1)[/tex]
[tex]B"= (-6,8-7) = (-6,1)[/tex]
[tex]C"= (-6,3-7) = (-6,-4)[/tex]
[tex]D"= (-5,3-7) = (-5,-4)[/tex]
A bat and a ball cost 1.10$ in total. The bat costs 1 dollar more than the ball. How much does the ball cost?
Answer:
$0.5
Step-by-step explanation:
A + B = 1.10
A=1 +B
now A + B = 1.10
A - B = 1 (B cancels out)
2A = 2.10
A= 1.05
A + B = 1.10
substitute A value
1.05 + B = 1.10
B= 1.10-1.05
B=$ 0.5
