the figure shown is composed of two cubes.
Which equation shows the surface area
of the figure?
S.A. = 6(5-5) + 6(3-3) 2(3-3)
What is the surface area of
the figure shown?
S.A.
cm²
8
3 cm
5 cm

The two options that represent circles with a diameter of 12 units and a center on the y-axis are:

(x - 0)² + (y - 0)² = 6², which simplifies to x² + y² = 36

(x - 0)² + (y - 12)² = 6², which simplifies to x² + (y - 12)² = 36

What is circle?

A circle is a geometric shape that consists of all points in a plane that are equidistant from a fixed point called the center.

A circle with a diameter of 12 units and a center on the y-axis will have the equation of the form x² + (y - k)² = r², where k is the y-coordinate of the center and r is the radius of the circle.

The y-coordinate of the center is on the y-axis, so it is 0.

The radius of the circle is half of the diameter, which is 6 units.

Substituting these values in the general equation, we get x² + y² = 36.

Therefore, the equations that represent circles with a diameter of 12 units and a center on the y-axis are:

(x - 0)² + (y - 0)² = 6², which simplifies to x² + y² = 36

(x - 0)² + (y - 12)² = 6², which simplifies to x² + (y - 12)² = 36

So, the options that represent these equations are:

x² + (y – 3)2 = 36

(x – 4)² + y² = 36

x2 + (y + 8)2 = 36

Therefore, the two options that represent circles with a diameter of 12 units and a center on the y-axis are:

(x - 0)² + (y - 0)² = 6², which simplifies to x² + y² = 36

(x - 0)² + (y - 12)² = 6², which simplifies to x² + (y - 12)² = 36.

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The value that should be the area of the circle, B whole be = About 900 in². That is option C.

The formula that can be used to calculate the area of a circle = πr²

But area of circle B can be estimated using the dimensions provided for circle A.

That is;

circle A Diameter = 20 in

Circle A area = 300 in²

Circle B diameter = 60 in

Circle B diameter = X

If , 20 in = 300

60 in = X

Make X the subject of formula;

X = 60×300/20

= 18000/20

= 900 in²

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Answer:

A'B'C'D' will be smaller than ABCD.

Step-by-step explanation:

A is at (5, 10) so A' will be at (0.8*5, 0.8*10) = (4, 8).

By applying the same rule B' will be the point (8,8).

C' will be (8, 4) and D' (4, 4).

So the lengths of the new square will be 4 units so its smaller than ABCD.

(The sides of ABCD are 5 units long)

Answer:

in the first worksheet in number (3) we are asked to factorize certain equations (mainly quadratics)

so in number one we have the quadratic equation as 4x²-12x+9. so this is an expression not equation and so therefore it is represented as the formula ax²+bx²+c

[tex]therefore \: a = 4 \\ \: \: \: \: b = - 12 \\ \: \: \: c = 9 \\ [/tex]

therefore 4 multiplied by 9 equals 36.

then we find a number that is a factor of 36 but can add to get -12. that number is -6 therefore substitute in the eqn

[tex]4 x^{2} - 6x - 6x + 9[/tex]

then factorize to get an answer of

[tex](2x - 3)(2x - 3)[/tex]

The equivalent expressions are:

5(2 + x + y) + 10

10 + 5x + 5y - 3x + 3x

10 + 2x + 3y + 2x + 2y + 5

2(5 + x) + 5y

We have,

10 + 2x + 5y + 3x can be simplified by combining like terms:

= 10 + 2x + 3x + 5y

= 10 + 5x + 5y

Any expression that simplifies to 10 + 5x + 5y is equivalent to 10+2x+5y+3x.

For example:

5(2 + x + y) + 10

10 + 5x + 5y - 3x + 3x

10 + 2x + 3y + 2x + 2y + 5

2(5 + x) + 5y

All of these expressions have different forms, but they simplify to the same value as 10 + 2x + 5y + 3x when the terms are combined.

Thus,

The equivalent expressions are:

5(2 + x + y) + 10

10 + 5x + 5y - 3x + 3x

10 + 2x + 3y + 2x + 2y + 5

2(5 + x) + 5y

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Answer: D exactly 1 line

Step-by-step explanation:

Answer:

Shira uses 20% of her paycheck for bills.

Step-by-step explanation:

100% - 35% - 30% - 15% = 20%

Answer:

6 , 5, 12,39

Step-by-step explanation:

The coefficients of the expressions K - 1/3d are 1 and -1/3

From the question, we have the following parameters that can be used in our computation:

K - 1/3d

The coefficients of expressions is the number beside the variable in the expression

Using the above as a guide, we have the following:

Coefficient of k = 1

Coefficient of d = -1/3

Hence, the coefficients are 1 and -1/3

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The vector translation of kite A to kite B and kite B to kite C indicates;

a. The coordinates of the vertices of the kite B are; (4, 10), (3, 4), (3, 3), and (5, 2)

Please find attached the drawing of the kite B created with MS Excel

b. The location of the coordinates of the vertices of the kite C are; (-2, 1), (-3, 1), (-3, 0), (-1, -1)

Please find attached the diagram of the location of the kite C created with MS Excel

c. The vector is [tex]\binom{-2}{4}[/tex]

d. The vector is; [tex]\binom{2}{-4}[/tex]

A translation transformation is a transformation in which involves the displacement of the figure to a new location.

a. The vector translation [tex]\binom{4 }{7}[/tex] indicates that the kite is translated 4 units to the right and 7 units upwards

The coordinates of the vertices of the kite A are; (0, -3), (-1, -3), (-1, -4), and (1, -5)

The coordinates of the vertices of the kite B are therefore;

b. The coordinates of the vertices of the kite C obtained from the translation of the kite B by the vector [tex]\binom{-6 }{-3}[/tex] are;

(-2, 1), (-3, 1), (-3, 0), (-1, -1)

c. The vector translation that maps kite A onto kite C is therefore;

Translation to the right of kite A with respect to kite C = -2 - 0 = -2

Translation upwards from kite A to kite C = 1 - (-3) = 4

The translation that maps kite A onto kite C is; [tex]\binom{-2 }{4}[/tex]

d) The vector translation that maps kite C onto kite A can be found as follows;

Translation to the right of kite C with respect to kite A = 0 - (-2) = 2

Translation upwards from kite C to kite A = -3 - 1 = -4

The vector translation that maps kite C onto kite A is; [tex]\binom{2}{-4}[/tex]

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Answer:

480

Step-by-step explanation:

320 divided by 2 (50%) is 160, so add that to the original 320 to get 480.

Answer:

After writing the values of x and y in terms of z , and substituting them in the third equation we get:

x=-1/5

y=11/5

z=-2

By answering the presented question, we may conclude that In decimal form, the answer is 0.15, which is close to option A, 0.148. As a result, the answer is A. 0.148.

According to Euclidean geometry, a square is an equilateral quadrilateral having four equal sides and four equal angles. It is often referred to as a rectangle with two nearby sides of equal length. A square is an equilateral quadrilateral because it has four equal sides and four equal angles. Square angles are 90-degree or straight angles. Also, the diagonals of the square are evenly spaced and divide at a 90-degree angle. an adjacent rectangle with two equal sides. a quadrilateral with four equal-length sides and four right angles. A parallelogram with two adjacent, equal sides forming a right angle. A rhombus with straight sides.

To determine the answer, multiply the areas of the shaded squares by the overall area of the figure.

Assuming that both squares are the same size, we may combine the fractions using a common denominator:

2/12 + 2/15 = 5/60 + 4/60 = 9/60 = 3/20

As a result, the entire shaded area is 3/20 of the total area of the diagram.

We can't discover the exact area of the graphic because it's not presented. As a result, we can only represent the answer in fractions or decimals.

In decimal form, the answer is 0.15, which is close to option A, 0.148. As a result, the answer is A. 0.148.

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Answer:

Step-by-step explanation:

Without more information about the translation, it is not possible to determine the coordinates of A' and B'.

The translation could have shifted line AB in any direction and by any distance, so there are many possible sets of coordinates for A' and B'.

The graph of the inequalities is attached

Graphing a nonlinear inequality involves following a similar process as graphing a linear inequality, but with some additional considerations:

Simplify the inequality as much as possible to get it into a standard form.

Identify the shape of the inequality. Is it a parabola, a circle, a hyperbola, or some other shape?

Determine the direction of the inequality. Is it "greater than" or "less than" the given value?

Plot the curve that represents the boundary of the inequality, using the shape and standard form of the inequality.

Determine whether the inequality is "strict" (i.e., greater than or less than) or "non-strict" (i.e., greater than or equal to, or less than or equal to). the situation in the problem is strict

Shade the area of the graph that satisfies the inequality, based on the direction of the inequality and whether it is strict or non-strict.

The graph is attached

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Step-by-step explanation:

You have to compare each side.

If they have the same ending, they are like terms.

1. E

2. A

3. D

4. B

5. C

The integral [tex]\int\limits^a_{-a} \int\limits^{\sqrt{a^2 - y^2}}_{-\sqrt{a^2 - y^2}} \int\limits^{\sqrt{a^2 -x^2 - y^2}}_{-\sqrt{a^2 - x^2 - y^2}} (x^2z + y^2z + z^3) dz dx dy[/tex] when evaluated is 0

Given that

[tex]\int\limits^a_{-a} \int\limits^{\sqrt{a^2 - y^2}}_{-\sqrt{a^2 - y^2}} \int\limits^{\sqrt{a^2 -x^2 - y^2}}_{-\sqrt{a^2 - x^2 - y^2}} (x^2z + y^2z + z^3) dz dx dy[/tex]

To change to spherical coordinates, we need to express x, y, and z in terms of spherical coordinates: r, θ, and Φ .

In particular, we have

[tex]x &= r \sin\phi \cos\theta, \\y &= r \sin\phi \sin\theta, \\z &= r \cos\phi[/tex]

The Jacobian for the transformation is r² sin(Φ), and the limits of integration become

[tex]-a &\leq x \leq a \quad \Rightarrow \quad 0 \leq r \leq a, \\-\sqrt{a^2 - y^2} &\leq y \leq \sqrt{a^2 - y^2} \quad \Rightarrow \quad 0 \leq \phi \leq \frac{\pi}{2}, \\-\sqrt{a^2 - x^2 - y^2} &\leq z \leq \sqrt{a^2 - x^2 - y^2} \quad \Rightarrow \quad 0 \leq \theta \leq 2\pi.[/tex]

Substituting into the integral, we have

[tex]&\int_{0}^{a} \int_{0}^{\frac{\pi}{2}} \int_{0}^{2\pi} (r^2\sin^2\phi\cos\theta\cdot r\cos\phi + r^2\sin^2\phi\sin\theta\cdot r\cos\phi + r^3\cos^3\phi) r^2 \sin\phi,d\theta d\phi dr \[/tex]

[tex]&\quad = \int_{0}^{a} \int_{0}^{\frac{\pi}{2}} \int_{0}^{2\pi} (r^3\sin^2\phi\cos\theta\cos\phi + r^3\sin^2\phi\sin\theta\cos\phi + r^3\cos^3\phi) \sin\phi, d\theta d\phi dr[/tex]

[tex]&\quad = \int_{0}^{a} \int_{0}^{\frac{\pi}{2}} \int_{0}^{2\pi} r^3\sin\phi\cos\phi (\sin^2\phi\cos\theta + \sin^2\phi\sin\theta + \cos^2\phi) , d\theta d\phi dr \[/tex]

[tex]&\quad = \int_{0}^{a} \int_{0}^{\frac{\pi}{2}} \int_{0}^{2\pi} r^3\sin\phi\cos\phi (\sin^2\phi + \cos^2\phi) , d\theta d\phi dr \[/tex]

[tex]&\quad = \int_{0}^{a} \int_{0}^{\frac{\pi}{2}} \int_{0}^{2\pi} r^3\sin\phi\cos\phi, d\theta d\phi dr \[/tex]

[tex]&\quad = \int_{0}^{a} \int_{0}^{\frac{\pi}{2}} 0, d\theta d\phi dr \&\quad = 0[/tex]

Therefore, the value of the integral is 0.

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Answer:

The mode is 77.43

Step-by-step explanation:

The mode is asking which number do you see the most.

Helping in the name of Jesus.

The interest rate needed for an investment of $5700 to double in 7 years if interest is compounded continuously is approximately 9.9%.

We have,

The formula for continuous compounding is:

A = Pe^(rt)

where A is the final amount, P is the initial principal, e is the mathematical constant approximately equal to 2.71828, r is the interest rate, and t is the time in years.

We want to find the interest rate needed for an investment of $5700 to double in 7 years, so:

2P = Pe^(rt)

Divide both sides by P:

2 = e^(rt)

Take the natural logarithm of both sides:

ln 2 = rt ln e

Since ln e = 1, we have:

ln 2 = rt

Solve for r:

r = ln 2 / t

r = ln 2 / 7

r ≈ 0.099

Thus,

The interest rate needed for an investment of $5700 to double in 7 years if interest is compounded continuously is approximately 9.9%.

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Answer:

v1=15mph, v2=35mph

Step-by-step explanation:

We have the values:

s=400mi (distance travelled)

t=8h (time)

v1=x, v2=x+20 (first and second speed)

We need to work out v1 and v2.

The formula for time is equal to distance over speed. t=s/v

Because the two ships are colliding, the formula will be t=s/v1+v2

Plug in given values:

8h=400mi/x+x+20

8h=400mi/2x+20

Cross multiply:

400=8(2x+20)

400=16x+160

-16x=-240 (Divide by -16)

x=15, which means that v1=15mph

To work out v2, all we must do is add 20 to 15mph and we get v2=35mph.

Hope this helps!

The rate of rise of the temperature is determined as 2 ⁰C/hr.

The rate at which the temperature rises this morning is the measure of increase in the temperature per unit hour.

Mathematically, the formula for the rate of rise of the temperature is calculated as follows;

Rate = ΔT/Δt

where;

The rise in temperature is given as 2⁰C

The change in time is given as 1 hour

The rate of rise of the temperature = 2⁰ C / 1 hr = 2 ⁰C/hr

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After answering the presented questiοn, we can cοnclude that The οnly οptiοn fοr the equatiοn tο be true is if N is an οdd multiple οf 5, i.e., N must be οdd.

Integers include zerο, pοsitive integers, and negative numbers represented by a minus sign. A negative number is the additive reciprοcal οf the pοsitive number tο which it is equal. In mathematical nοtatiοn, a bοld Z οr a bοld "mathbb Z" is cοmmοnly used tο signify a grοup οf integers. An integer is a pοsitive, negative, οr zerο integer that is nοt a fractiοn (prοnοunced IN-tuh-jer). Integers include the numbers -5, 1, 5, 8, 97, and 3,043. Nοn-integer instances include 1.43, 1 3/4, 3.14, and οther numbers. Integers are a set οf integers and their inverses. The set οf integers dοes nοt include decimals οr fractiοns.

If (3N + 5) is a multiple οf 10, it may be written as 10x fοr sοme integer x.

Thus far, we have:

3N + 5 = 10x

3N = 10x - 5

3N = 5(2x - 1)(2x - 1)

We can see that the left side οf the equatiοn is a multiple οf three, while the right side is a multiple οf five.

The οnly οptiοn fοr the equatiοn tο be true is if N is an οdd multiple οf 5, i.e., N must be οdd.

As a result, B is the right answer. N is οdd.

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Answer:

Step-by-step explanation:

Step 1:- 10x - 15y - 6x + 4y

Step 2:- 4x - 11y

Answer:

x=(11/4)y or

y=(4/11)x

Step-by-step explanation:

Answer:

According to the Central Limit Theorem, the sampling distribution of sample means would have a mean of 5.4 years.

Step-by-step explanation:

For a normally distributed random variable X, with mean and standard deviation, the sampling distribution of sample means with size n can be approximated to a normal distribution with mean and standard deviation.

As long as n is at least 30, the Central Limit Theorem can also be applied to skewed variables.

We have the following problem:

Answer:

Step-by-step explanation:

The mean of the sampling distribution of sample means can be calculated using the formula:

μM = μ

where μ is the population mean and M is the sample mean.

Thus, μM = μ = 5.4 years.

Therefore, the mean of the sampling distribution of sample means would also be 5.4 years.

The evaluation of the sinusoidal function for the blood pressure of the individual indicates that the period, maximum and minimum blood pressure and the times are;

(a) 1/60 minutes

(b) Maximum (systolic) blood pressure = 110 mmHg

Minimum (diastolic) blood pressure = 50 mmHg

(c) The times are; n/60 + 1/240

A sinusoidal function is a periodic function based on the sine or cosine of an angle.

The specified function can be presented as follows;

p(t) = 80 + 30·sin(120·pi·t)

(a) The function is a sinusoidal function of the form; y = A·sin(B·(x - C)) + D

Where;

A = The amplitude

B = 2·π/Period

C = The phase shift

D = The vertical shift

Comparing, we get;

C = 0, D = 80, x = t

Therefore;

y = A·sin(B·(t)) + 80

B = 120·π

The period = 2·π/(120·π) = 1/60

(b) The maximum and minimum values are obtained when sin(120·pi·t) = ±1 as follows;

Maximum value = pmax = 80 + 1 × 30 = 110

Minimum value = pmin = 80 - 1 × 30 = 50

The systolic or maximum blood pressure = 110 mmHg

The diastolic or minimum blood pressure = 50 mmHg

(c) When the blood pressure is maximum, we get;

p(t) = 80 + 30·sin(120·pi·t) = 110

80 + 30·sin(120·pi·t) = 110

sin(120·pi·t) = (110 - 80)/30 = 1

120·pi·t = arcsine(1) = pi/2 + 2·n·pi

120·t = 1/2 + 2·n

t = (1/2 + 2·n)/120 = 1/240 + n/60, where n is an integer value

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The pattern formed will always be true due to the constant shape realized or gotten from all the patterns formed and that constant shape in it all is a triangle.

A triangle is a closed two-dimensional figure with three straight sides and three angles. Triangles can be classified according to the length of the sides and the size of the angles.

The triangle is an important geometric shape in mathematics and is used in fields such as architecture, engineering and physics.

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Answer:

log5[x^2z^9w√(x^4-81)]

Using the properties of logarithms, we can rewrite the given expression as a sum and/or difference of logarithms as follows:

log5[x^2z^9w√(x^4-81)] = 2log5(x) + 9log5(z) + log5(w) + 0.5log5(x^4-81)

Note that the square root (√) can be expressed as a exponent of 0.5, and we can use the properties of logarithms to split the logarithm of a product into a sum of logarithms of individual factors.

Step-by-step explanation:

Answer:

A & D

Step-by-step explanation:

the numerator is greater than the denominator

Answer:

Step-by-step explanation: