Answer:
The area of the small square is 1 cm^2
Step-by-step explanation:
The large square consist in four identical rectangles and one small square.
Then the area of the small square will be equal to the difference between the area of the large square and the areas of the rectangles.
Because we have 4 equal rectangles, if R is the area of one rectangle, and S is the area of the large square, the area of the small square will be:
area = S - 4*R
We know that the area of the large square is 49 cm^2
Then:
S = 49cm^2
Remember that the area of a square of side length K is:
A = K^2
Then the side length of the large square is:
K^2 = 49 cm^2
K = √(49 cm^2) = 7cm
And we know that the diagonal of one rectangle is 5cm.
Remember that for a rectangle of length L and width W, the diagonal is:
D = √(L^2 + W^2)
Then:
D = √(L^2 + W^2) = 5cm
And for how we construct this figure, we must have that the length of the rectangle plus the width of the rectangle is equal to the side length of the large square, then:
L + W = 7cm
L = (7cm - W)
Replacing this in the diagonal equation, we get:
√((7cm - W)^2 + W^2) = 5cm
(7cm - W)^2 + W^2 = (5cm)^2 = 25cm^2
49cm^2 - 14cm*W + W^2 + W^2 = 25cm^2
2*W^2 - 14cm*W + 49cm^2 = 25cm^2
2*W^2 - 14cm*W + 49cm^2 - 25cm^2 = 0
2*W^2 - 14cm*W + 24cm^2 = 0
We can solve this for W using the Bhaskara's formula, the solutions are:
[tex]W = \frac{-(-14cm) \pm \sqrt{(-14cm)^2 - 4*2*(24cm^2)} }{2*2} = \frac{14cm \pm 2cm}{4}[/tex]
Then we have two solutions, and we only need one (because the length will have the other value)
We can take:
W = (14 cm + 2cm)/4 = 4cm
Then using the equation:
L + W = 7cm
L + 4cm = 7cm
L = 7cm - 4cm = 3cm
L = 3cm
Now remember that the area of one rectangle of length L and width W is:
R = L*W
Then the area of one of these rectangles is:
R = 4cm*3cm = 12cm^2
Now we can compute the area of the small square:
area = S - 4*R = 49cm^2 - 4*12cm^2 = 1cm^2
The area of the small square is 1 cm^2
Which correctly describes how the graph of the inequality 5x + 2y = 13 is shaded?
Answer:
The answer is above the solid line.
Step-by-step explanation:
Find the volume of the given figure.
Answer:
5/18
Step-by-step explanation:
Volume= length•width•height
5/6•1/2= 5/12
5/12•2/3= 10/36= 5/18
A cube root function has a turning point located at (-2,3). Write an equation that could represent this function
Answer:
f(x) = A*∛(x + 2) + 3
Step-by-step explanation:
Suppose a generic cube as:
f(x) = A*∛(x - b) + C
We will have a turning point at the x value:
x = b
Then if we have a turning point at (-2, 3)
This means that the turning point is at x = -2 and y = 3
Then b = -2
And our cube root function will be something like:
f(x) = A*∛(x - (-2)) + C
f(x) = A*∛(x + 2) + C
And we know that f(-2) = 3
then:
f(-2) = A*∛(-2 + 2) + C = 3
f(-2) = A*∛(0) + C = 3
= C = 3
Then the general equation will be something like:
f(x) = A*∛(x + 2) + 3
An advertising banner has four sections, as modeled below. Two sections are congruent trapezoids, and two sections are congruent right triangles. Which measurement is the best estimate of the area of the banner in square meters.
Answer:
The best estimate is [tex]6m^2[/tex]
Step-by-step explanation:
Given
See attachment for banner
Required
Estimate of the area
The banner has two congruent trapezoids and two congruent.
This means that, the two trapezoids have the same base lengths; the two triangles also have the same base lengths
So, we have:
[tex]B_1 = 1 + 1 = 2[/tex] -- base lengths of both trapezoids
[tex]B_2 = 1\frac{3}{4} + 1\frac{3}{4} = 1.75 + 1.75 = 3.5[/tex] -- base lengths of both triangles
The banner itself is a triangle and the dimension is:
[tex]Height = 2m[/tex]
[tex]Base = B_1 + B_2[/tex]
[tex]Base = 2m + 3.5m = 5.5m[/tex]
So, the area is:
[tex]Area = 0.5 * Base * Height[/tex]
[tex]Area = 0.5 * 5.5m * 2m[/tex]
[tex]Area = 5.5m^2[/tex]
The question asks for an estimate. So, we approximate.
[tex]Area \approx 6m^2[/tex]
Complete question is;
An advertising banner has four sections, as modeled in the attached image. Two sections are congruent trapezoids, and two sections are congruent right triangles. Which measurement is the best estimate of the area of the banner in square meters?
Answer:
6 m²
Step-by-step explanation:
Since we are told that there are two congruent trapezoid, it means that they will have same base of 1m.
This Means the total base of the entire triangle will be;
Base = 1 + 1¾ + 1 + 1¾ = 5.5 m
Height of main triangle = 2 m
Thus,
Area = ½ × 5.5 × 2 = 5.5 m²
We are looking for the best estimate, so let's approximate to the nearest whole number to get 6 m²
The distance around the world at the equator is about 42,000
A.meters
B.kilometers
C.centimeters
D. millimeters
A laptop has a listed price of $801.98 before tax. If the sales tax rate is 8.5%, find the total cost of the laptop with sales tax included.
Round your answer to the nearest cent, as necessary.
Answer 870.15
Step-by-step explanation:
The possibility of a power outage seems to grow every year because of demand and aging infrastructure. What can/should companies do to mitigate this risk?
The selling price of an item is $520. It is marked down by 10%, but this sale price is still marked up from the cost of 360$. Find the markup from cost to sale price.
Answer:
30%
Step-by-step explanation:
Answer: good luck
Step-by-step explanation:
Which triangles are similar?
Answer:
B. triangles A and C
Step-by-step explanation:
they're all right triangles but triangles A and C hAve all the same angles so they're the MOST similar
hope this helps <3
38% of 60 is?
NEED HELP
Answer:
Step-by-step explanation:
38% of 60 = [tex]\frac{38}{100}*60 = 0.38*60 = 22.8[/tex]
Answer:
Step-by-step explanation:
38% * 60
[tex]\frac{38}{100} * 60\\\\\frac{38}{5} * 3\\\\114/5 = 22.8[/tex]
PLEASE HELPPPPPPPPPPP
Answer:
45
Step-by-step explanation:
So a triangle adds up to 180 and so does a line.
180-93=87
And because of vertical angle proof, 48 is the other angle of the triangle.
87+48=135
180-135=45
Answer:
x = 45
Step-by-step explanation:
To get to the interior of the triangle from 48 use vertically opposite angles. That means that the two remote interior angles = 93
Put in simpler language
48 = interior angle
93 = x + 48
93 - 48 = x
x = 45
Is 5/4 less than -5 I need help please
The triangle shown above are similar. Write ratios of corresponding side lengths in a statement of proportionality. The images are not drawn to scale.
A. AB/YZ=BC/ZX=CA/XY
B. AB/ZX=BC/XY=CA/YZ
C. AB/XY=BC/YZ=CA/ZX
D. AB/ZX=BC/YZ=CA=XZ
Answer:
B
Step-by-step explanation:
i took the test
A square-based rectangular aquarium is filled with water. The side length of the
base is 40 cm. The height of the aquarium is 50 cm. The height of the water is
equal to half the height of the aquarium. A solid cube with side length 20 cm is
then thrown into the aquarium and sinks to the bottom.
Does the water level now reach the top of the tank? If not, how far below the top
of the tank does the water reach?
Answer:
From bottom = 30 cm
Below top = 20 cm
Step-by-step explanation:
Length & breadth of the aquarium = 40cm(as it is square)
Volume of aquarium = l x b x h
volume of aquarium = 40 x 40 x 50 = 80000 cm³
Volume of water = ½ half of aquarium
Volume of water = ½ x 80000 = 40000 cm³
Volume of the solid cube = a³ = (20cm)³ = 8000cm³
Surely, 40000>>>8000, level doesnt reach the top of the tank.
Volume acquired = 40000+8000=48000 cm³
Now, let it has reached reached a height h from the ground(bottom).
Volume = 48000 => lx b x h = 48000
=> 40 x 40 x h = 48000
=> h = 30 cm
The height at which water has reached is 30 cm(from bottom).
Thus, below the top it has reached = total height - 30 cm = 50 - 30 = 20 cm
For the angle 7π/4, draw and upload a representation of the angle on the unit circle in the coordinate plane. Place the angle in the correct quadrant. Label the reference angle and sides of the reference triangle, and identify the coordinates of the terminal point. Then, specify the exact values of the secant, cosecant and cotangent of the angle
Answer:
2eXz2
Step-by-step explanation:
write the formula of the parabola that has x-intercepts (1.3,0) and (-1.3,0), and y-intercept (0,169)
Answer:
y= 169 − [tex]100^{2}[/tex]
Step-by-step explanation:
A parabola is a symmetrical plane curve that forms when a cone intersects with a plane parallel to its side.
Standard form of a quadratic function represent a parabola.
The equation of parabola is [tex]y=-x^{2} +1.69[/tex]
Parabola:We have to find the formula for the parabola that has x- intercepts [tex](1.3,0)[/tex] and [tex](-1.3,0)[/tex], and y- intercept [tex](0,1.69)[/tex]
So that, the intercept form of the quadratic equation is;
[tex]y=a(x-p)(x-q)[/tex]
where [tex](-1.3,0)=(p,0)[/tex] and [tex](1.3,0)[/tex] is[tex](q,0)[/tex].
Since, with the vertex being at the y axis and the intercepts at the x axis means that the parabola opens down.
So that,
[tex]1.69=a(0+1.3)(0-1.3)\\ \\1.69=-1.69 a\\ \\a=-1[/tex]
Substituting value of a in above equation.
[tex]y=-1(x+1.3)(x-1.3)\\\\y=-1(x^{2}-1.69 )\\\\y=-x^{2} +1.69[/tex]
Hence, the equation of parabola is [tex]y=-x^{2} +1.69[/tex]
Learn more about the equation of parabola here:
https://brainly.com/question/4148030
Math help help help answer all 4 pls
Answer:
a) 2,350,000,000
b) 25,000,000
c) B
Step-by-step explanation:
a) 2350 X 1,000,000 = 2,350,000,000
b) 25 X 10^6 = 25,000,000
c) sqrt(90000) =300
What 1+1 help i'll give 15 points
Answer:
11
Step-by-step explanation:
am so smart
Can someone help me on this plzzz
Answer:
2z - 3w = 8
Step-by-step explanation:
Where you see z you place 10 there and where you see w you place 4 there because that's the value according to the question.
So we have 2(10) - 3(4) = 20 - 12 = 8
What is the area of the triangle?
13
12
Units 2
Help me
Answer:
30
Step-by-step explanation:
i believe that the 13 is there to throw you off. anyway to solve just do 5•12=60
60÷2=30 so 30 is area of triangle
area of triangle =1/2×base×height
area of triangle=1/2×12×5
area of triangle=30 unit²
Find the area of the triangle.
Answer:
29.394 square feet.
Step-by-step explanation:
There is no explanation for this answer.
Answer:
30 ft
Step-by-step explanation:
10 x 6 = 60
60 ÷ 2 = 30
formula : base x height ÷ 2
Take the function f(x)= square root of x+5 (then outside of square root) +1
And:
1. Reflect it along the x axis
2. translate it 4 units left
3. Translate it 3 units dow
What would be this functions NEW equation?
[tex]f(x) = - \sqrt{x + 5 + 4} + 1 - 3[/tex]
[tex]f(x) = - \sqrt{x + 9} - 2[/tex]
plss help i’ll give brainliest thank you!
Please help, my assignment is due today in an hour.
Answer:
1a, 2b, 3d, 4a, 5c, 6b, 7a, 8b, 9c, 10d, 11d, 12a, 13c, 14b, 15a, 16b
Step-by-step explanation:
The digits of this year, 2000 A.D., add up to 2. In how many other years since 1 A.D. has this happened?
Answer:
0002 0011 1010
0020 0101
0200 1001
2000 1100
9 times
Step-by-step explanation:
9 times is the right answer
What is the image of (-4,-4) after a dilation by a scale factor of 22 centered at the origin?
Help pls ? What kind of exponent does this graph have !
Answer:
I think the answer is odd. I am not sure because I don't know this topic really well.
Step-by-step explanation:
For what value of b will f(x)= x^2 + bx + 900 have -30 as its only zero? PLEASE HELP!!
Answer:
60
Step-by-step explanation:
If -30 is its only zero, than the factors are (x+30)(x+30) = [tex]x^2 + 60x + 900[/tex]
Than b = 60
The value of b of the function f (x) would be,
⇒ b = 60
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The function is,
⇒ f (x) = x² + bx + 900
And, -30 as its only zero.
Now, The value of zero of function is satisfy the function as;
⇒ f (- 30) = 0
⇒ (- 30)² + (- 30)b + 900 = 0
⇒ 900 - 30b + 900 = 0
⇒ 1,800 = 30b
⇒ b = 60
Thus, The value of b of the function f (x) would be,
⇒ b = 60
Learn more about the function visit:
https://brainly.com/question/11624077
#SPJ2
x - (2x + 1) = 8 - (3x + 2)
Answer:
x=7/2
Step-by-step explanation:
Answer:
x=7/2
Step-by-step explanation:
x-(2x+1)=8-(3x+2)
x-2x-1=8-3x-2
-x-1=6-3x
+x on both sides
-1=6-2x
-6 on both sides
-7=-2x
7=2x
÷2 on both sides
7/2=x
Hope this helps =]
the total surface area of a cone of slant height 1cm and base radius rcm is 224πcm,if r:1=2:5 find
a. correct to one decimal place,the value of r
b. correct to the nearest whole number, the value of the cone. (take π 22/7
Answer:
a. r = 8 cm
b. The volume of the cone is approximately 1,229 cm³
Step-by-step explanation:
The given parameters are;
The slant height of the cone = l cm
The base radius of the cone = r cm
The total surface area of the cone = 224·π cm
r : l = 2 : 5
Therefore, we have;
[tex]\dfrac{r}{l} = \dfrac{2}{5}[/tex]
[tex]r= \dfrac{2}{5} \times l[/tex]
The total surface area of a cone, T.S.A. = π·r·l + π·r²
The total surface area of the cone, T.S.A. cone = π × (2/5)·l² + π·((2/5)·l)²
T.S.A. cone = π × (2/5)·l² + π·((2/5)·l)² = π·((2/5)·l² + (4/25)·l²)
T.S.A. cone = π·l²·((2/5) + (4/25)) = (14/25)·π·l²
∴ T.S.A. cone = 224·π cm² = (14/25)·π·l²
l² = 224 cm² × 25/14 = 400 cm²
l = √(400 cm²) = 20 cm
[tex]r= \dfrac{2}{5} \times l = \dfrac{2}{5} \times 20 \, cm = 8 \, cm[/tex]
r = 8 cm
b. The volume of a cone, V = 1/3·π·r²·h
Where;
h = The height of the cone
By Pythagoras's theorem, h = √(l² - r²)
∴ h = √(20² - 8²) = √(336) = 4·√(21)
The height of the cone, h = 4·√(21)
The volume of the cone, V = 1/3 × (22/7) × 8² × 4·√(21) ≈ 1,229.00315781
∴ The volume of the cone, V to the nearest whole number ≈ 1,229 cm³.