Solve:
y = 2x -11
-3y = -6x -15

Step-by-step explanation:

8 + 4(x-4) < 24

8+4x - 16 <24

4x-8<24

4x<32

x<8

Answer:

A:$4.50 x ? =$36. $36 divided by$4.50=?

B)8 divide it

C)replace the ? With x and then solve it algebraically and it would still equal to the number 8

Step-by-step explanation:

Answer:

156 ft²

Step-by-step explanation:

Given :

The rectangular sides are 12 feet by 3 feet, 12 feet by 5 feet, and 12 feet by 4 feet.

The 2 triangular sides have a base of 3 feet and height of 4 feet

We sum the area of each side:

Area of triangular side = 1/2 * base * height

Since there are 2 triangular sides :

Total area of triangular side = 2(1/2 * base * height)

Triangular side = 2 * 1/2 * 3 * 4 = 12 feet²

Area of rectangle sides = lengtb * width

Area 1 = 12 * 3 = 36 ft²

Area 2 = 12 * 5 = 60 ft²

Area 3 = 12 * 4 = 48 ft²

Total = 12 + 36 + 60 + 48 = 156 ft²

Answer:

m∠B is 70°

Step-by-step explanation:

Knowing angle A is 40°, angles B and C combine for the remaining 140°. To figure out what angle B and C are (although this question asks for B, they could very well be the same, and this could be an isosceles triangle!), use the equation (2x - 30) + (x + 20) = 140.

(2x - 30) + (x + 20) = 140 (Combine 2x and x to get 3x.)

3x - 30 + 20 = 140 (Add -30 and 20 to get -10.)

3x - 10 = 140 (Add 10 to both sides. This undoes the -10.)

3x = 140 + 10 (Add 140 and 10 to get 150.)

3x = 150 (Divide both sides by 3. This undoes the multiplication by 3.)

x = 150/3 (Divide 150 by 3 to get 50.)

x = 50

Now that we know what x is, substitute x for 50 in the equation.

(2(50) - 30) + (50 + 20) = 140

(100 - 30) + (50 + 20) = 140

70 + 70 = 140

140 = 140

Both sides are the same, so x is 50, and angle B's (and C's!) measurement is 70°. (So, yes, as I had said, this is an isosceles triangle.)

The intervals are nested, each subsequent interval is contained within the previous one. Mathematically, this means I₁ ⊇ I₂ ⊇ ... In ⊇ ... . Therefore, we have:

1. I₁ ⊇ I₂ implies [a₁; b₁] ⊇ [a₂; b₂], which means a₁ ≤ a₂ and b₁ ≥ b₂.
2. I₂ ⊇ I₃ implies [a₂; b₂] ⊇ [a₃; b₃], which means a₂ ≤ a₃ and b₂ ≥ b₃.

To show that a1 ≤ a2 ≤ ... ≤ an ≤ ..., we need to use the fact that the sequence of intervals is nested, meaning that each interval is contained within the next one.

First, we know that I1 contains I2, so every point in I2 is also in I1. That means that a1 ≤ a2 and b1 ≥ b2.

Now consider I2 and I3. Again, every point in I3 is also in I2, so a2 ≤ a3 and b2 ≥ b3.

We can continue this process for all the intervals in the sequence, until we reach In. So we have:

a1 ≤ a2 ≤ ... ≤ an-1 ≤ an

and

b1 ≥ b2 ≥ ... ≥ bn-1 ≥ bn

This shows that the endpoints of the intervals are ordered in the same way.

Given that I₁ ⊇ I₂ ⊇ ... In ⊇ ... is a nested sequence of intervals and In = [an; bn], we can show that a₁ ≤ a₂ ≤ ... ≤ an ≤ ... and b₁ ≥ b₂ ≥ ... ≥ bn ≥ ... as follows:

Since the intervals are nested, each subsequent interval is contained within the previous one. Mathematically, this means I₁ ⊇ I₂ ⊇ ... In ⊇ ... . Therefore, we have:

1. I₁ ⊇ I₂ implies [a₁; b₁] ⊇ [a₂; b₂], which means a₁ ≤ a₂ and b₁ ≥ b₂.
2. I₂ ⊇ I₃ implies [a₂; b₂] ⊇ [a₃; b₃], which means a₂ ≤ a₃ and b₂ ≥ b₃.

Continuing this pattern for all intervals in the sequence, we can conclude that a₁ ≤ a₂ ≤ ... ≤ an ≤ ... and b₁ ≥ b₂ ≥ ... ≥ bn ≥ ... .

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The respective sides of the two square pyramids are proportionate since they are comparable. Let's use A cm2 to represent the smaller pyramid's surface area.

The square of the ratio of the corresponding side lengths of comparable pyramids is equal to the ratio of their surface areas. As a result, we may construct the equation shown below:

(s_small / s_large) = (A / 2304)²

where the sides of the smaller and larger pyramids, respectively, are represented by the lengths s_small and s_large, respectively.

We are unable to immediately solve for A since we lack the precise side length data. The ratio of the surface areas is still measurable, though:

(s_small / s_large) = (A / 2304)²

Using the information provided, we can determine that the surface area of.

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Step-by-step explanation:

ffdfgjufdduudryhcoydktsnvkysoyeits

Answer:

The radius of the sphere, to the nearest cm:

\(r\approx 20\) cm

Step-by-step explanation:

The surface area of a sphere is given by the formula

A = 4πr²

where r is the radius of the sphere.

Given

The radius of the sphere can be determined such as

\(A\:=\:4\pi r^2\)

\(r\:=\:\frac{1}{2}\sqrt{\frac{A}{\pi }}\)

Plug in Surface Area of sphere =  5024, π = 3.14 in the formula

\(\:r\:=\:\frac{1}{2}\sqrt{\frac{5024}{3.14}}\:\:\)

\(r\approx 20\) cm

Therefore, the radius of the sphere, to the nearest cm:

\(r\approx 20\) cm

Answer:

d = 15.8 m

Step-by-step explanation:

Apply the Pythagorean Theorem to find the length of the diagonal.  The correct equation for this particular rectangle is

d = √(9² + 13²) = √250 = √25·√10 = 5√10

To the nearest tenth, this comes to d = 15.8 m

Answer: 15.8

Step-by-step explanation:

Answer:

48 students.

Step-by-step explanation:

Take the 166 students and subtract the 22 students traveling via car.

That leaves you with 144 stundets.

Divide the 144 students into the 3 buses.

144/3 =48

Each bus had 48 students.

Hope this helps! ^-^

-Isa

Answer:

determinant formula looks like  ad - bc in a 2 x2 matrix when it's in the from of

a b

c d

as the one is here

Step-by-step explanation:

5*2 - (-4*8)

=10 - (-32)

=10 + 32

= 42

The true statement about these triangles is that a triangle pre-image has side lengths of 12 and 5.

This is known to be a polygon that has three edges and also three vertices.

It is regarded as  a key shapes in geometry. A triangle that has a vertice of A, B, and C  as seen. The true statement about these triangles is that a triangle of that pre-image has side lengths.

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Answer:

not a dilation

Step-by-step explanation:

Answer:

15, 20, and 25

Step-by-step explanation:

You just multiply the original lengths by the scale factor (5).

Answer:

2.117 × 10^11

Step-by-step explanation:

Hope this is correct! :))

Answer:

\(2.117\)×\(10^{11}\)

Step-by-step explanation:

Scientific notation in mathematical terms is the same as standard form.

1) Top write a number in standard form (which in this case is 211,700,000,000), you need to move the decimal point 11 spaces to get in just in front of the first significant figure.

2) Because there is no visible decimal number in the given number, you just need to add a '.0' on the end of it which will give you 211700000000.0

3) You then need to count how many times you have to move the decimal point to get it to just in front of the first significant figure

Extra tips:

If your number is a decimal with multiple zeros you would need to yet again move the decimal point until it's just after the first significant figure.

Example: 0.0078 would be written as \(7.8\)×\(10^{-3}\)

Hope this helps, have a great day!!

Answer:

\({ \tt{ - \frac{3}{8} + \frac{1}{6} }} \\ { \bf{l.c.m \: of \: 8 \: and \: 6 = 24}} \\ { \tt{formular = \frac{(l.c.m \times denominator \div numerator)}{l.c.m} }} \ \\ \\ = \frac{(24 \times 8 \div - 3) + (24 \times6 \div 1)}{24} \\ = - \frac{5}{24} \)

This operation is equivalent to:

It is like a function inside a function. So, we can look for parts in h(x) that are common and call that the function inside.

As we can see, h(x) have terms with x + 4, so if we call:

We can see that h(x) becomes:

And if we substitute g(x) by x, we will get the expression of the ouside function f(x):

This way, we have:

So, the functions are:

Answer:

x>24

Step-by-step explanation:

−2x+7< −41

−2x+7−7< −41−7

−2x< −48

−2x /−2  <  −48 /−2

x>24

Answer:

\(\frac{31}{12}\)

Step-by-step explanation:

Convert 5 1/6 to an improper fraction

\(\frac{31}{6}\)

The word "of" means times or multiplies so

\(\frac{31}{6}\) x \(\frac{1}{2}\) = \(\frac{31}{12}\)

Therefore the answer is \(\frac{31}{12}\)

The area of triangle EFG, to the nearest square inch, is approximately 1061 square inches.

To find the area of triangle EFG, we can use the formula:

\(Area = (1/2) \times base \times height\)

In this case, the base of the triangle is FG, and the height is the perpendicular distance from vertex E to side FG.

First, let's find the length of FG. We can use the law of cosines:

FG² = EF² + EG² - 2 * EF * EG * cos(∠F)

EF = 72 inches

EG = 34 inches

∠F = 21°

Plugging these values into the equation:

FG² = 72² + 34² - 2 * 72 * 34 * cos(21°)

Solving for FG, we get:

FG ≈ 83.02 inches

Next, we need to find the height. We can use the formula:

height = \(EF \times sin( \angle F)\)

Plugging in the values:

height = 72 * sin(21°)

height ≈ 25.52 inches

Now we can calculate the area:

\(Area = (1/2) \times FG \times height\\Area = (1/2)\times 83.02 \times 25.52\)

Area ≈ 1060.78 square inches

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Answer:

9

Step-by-step explanation:

given

10x + 3y = 2

then

10x + 3y + 7

= 2 + 7

= 9

The number falls between \(-\frac{25}{4}\) and - 400 % is \(-\frac{43}{8}\) = 5.375

first we convert fraction into decimal number

\(-\frac{25}{4}\)  = - 6.25

and for remove percentage we divide by 100

- 400 % = - 4

from choose the option,

\(-\frac{43}{8}\)  = 5.375

- 720 % = - 7.2

\(-\frac{20}{3}\) = - 6.6

then, choose  \(-\frac{43}{8}\)  

therefore, number lies between \(-\frac{25}{4}\) and - 400 % is \(-\frac{43}{8}\) = 5.375

A fraction is any number of the form a/b where both “a” and “b” are whole numbers and b≠0. On the other hand, a rational number is a number which is in the form of p/q where both “p” and “q” are integers and q≠0.

Thus, a fraction is written in the form of m/n, where n is not 0 and m & n are whole (or natural numbers). For example, 12/23, 10/32, 12/10, 4/21. A rational number can also be written in the form of a/b, where b is not 0 and a & b are integers. For example, 15/7, -18/13, 3/-7, -6/-12.

All fractions can be termed as rational numbers; however, all rational numbers cannot be termed as fractions. Only those rational numbers in which ‘p’ and ‘q’ are positive integers are termed as fractions. Let a/b be any fraction. Now, a and b are natural numbers. Since all natural numbers are also integers, a and b are also integers. Thus, the fraction a/b is the quotient of 2 integers such that b ≠ 0. Hence, a/b is a rational number. One of the examples in which a number is a rational number but not a fraction is:

Consider the fraction 12/-32. It is a rational number but not a fraction because its denominator (n) is not a natural number.

A fraction is expressed in the form of the ratio of whole numbers, a/b and b≠0.

A rational number is also expressed in the form of a ratio, p/q, where numerator and denominator are integers and q≠0.

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Answer:

(-3, 5)

Step-by-step explanation:

Given the function :

y = - 3x - 4

We obtain the ordered pair which satisfies the function Given :

Taking the point, (-3, 5)

y = 5 ; x = - 3

Put x in the equation and check if it gives the value for y

y = - 3(-3) - 4

y = 9 - 4

y = 5

Since the value of y in the ordered pair is the same, then we choose (-3, 5)

It seems there is an error in the given vector field F⃗ = 3(x+z)i⃗ + 2j⃗ + 3zk⃗ as it does not have a component along the y-axis. Please double-check the vector field or provide the correct vector field to proceed with the calculation.

To compute the flux of the vector field F⃗ = 3(x+z)i⃗ + 2j⃗ + 3zk⃗ through the surface S given by y=x^2+z^2, with 0≤y≤16, x≥0, z≥0, oriented toward the xz-plane, we can use the surface integral.

The surface integral of a vector field F⃗ over a surface S is given by the formula:

∬S F⃗ · dS = ∬S F⃗ · (n⃗ dS)

where F⃗ is the vector field, dS is the differential area vector, and n⃗ is the unit normal vector to the surface.

In this case, the surface S is given by y=x^2+z^2, with 0≤y≤16, x≥0, z≥0. We can parameterize this surface as:

r(x, z) = xi⃗ + yj⃗ + zk⃗ = xi⃗ + (x^2+z^2)j⃗ + zk⃗

To find the normal vector n⃗ to the surface, we can take the cross product of the partial derivatives of r(x, z) with respect to x and z:

n⃗ = ∂r/∂x × ∂r/∂z

= (1i⃗ + 2xj⃗) × (0i⃗ + 2zj⃗)

= -2xz i⃗ + 2zj⃗ + 2xk⃗

Now, we can calculate the flux:

∬S F⃗ · (n⃗ dS) = ∬S (3(x+z)i⃗ + 2j⃗ + 3zk⃗) · (-2xz i⃗ + 2zj⃗ + 2xk⃗) dS

= ∬S (-6x^2z - 4xz + 6xz^2 + 6xz) dS

= ∬S (-6x^2z + 2xz + 6xz^2) dS

To evaluate this integral, we need to determine the limits of integration for x, y, and z.

Since the surface is defined by 0≤y≤16, x≥0, z≥0, we have:

0 ≤ y = x^2 + z^2 ≤ 16

Simplifying the inequality, we get:

0 ≤ x^2 + z^2 ≤ 16

From this, we can see that x and z both range from 0 to 4.

Now, we can evaluate the flux:

∬S (-6x^2z + 2xz + 6xz^2) dS = ∫∫ (-6x^2z + 2xz + 6xz^2) dA

where dA is the differential area.

Integrating over the limits 0 ≤ x ≤ 4 and 0 ≤ z ≤ 4, we can calculate the flux.

However, it seems there is an error in the given vector field F⃗ = 3(x+z)i⃗ + 2j⃗ + 3zk⃗ as it does not have a component along the y-axis. Please double-check the vector field or provide the correct vector field to proceed with the calculation.

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Answer:

Yes

Step-by-step explanation:

Yes because if you insert -39 for x and 42 for y then your equation is:

42 = -39 + 81

If you were to solve this equation it would be true.

Answer:

The number of students who spend 4 hrs or more for reading = 25/100 = 1/4

we know 100 is a factor of 300

so equivalent fraction of (25/100)

× 3 = 75/300 = 1/4

.°.The simplest answer = 1/4 = 75/300

Hope it helps

The speedometer of the car showing error and sent back to be fixed must showing speed less than 1.225 miles per minute.

As given in the question,

Distance covered by car = 10miles

Time taken by car to cover 10 miles = 8 minutes

Formula used:

Speed = ( total distance travelled ) / ( time taken )

           = 10 / 8

           = 1. 25 miles per minute

To pass the speed test ,

Range of the speedometer is 2% of the actual speed

= 2% of 1.25

= ( 2/100) × 1.25

= 0.025

Range of the speed to pass the test

= 0.025 ± 1.25

= (  1.225, 1.275)

Therefore, the speedometer of the car which was sent back to be fixed must showing the speed less than 1.225 miles per minute.

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