Members of alachua district choir were given the choice between romanticism or gothic style singing which style they preferred sing for the state competition

Answer:

[tex]100^x=10^{2x+5}\\100 = 10^2[/tex]

simplifies to

[tex]10^{2x}=10^{2x+5}\\2x = 2x+5\\0=5[/tex]

no solution

Answer:

[tex]Area = 30[/tex]

Step-by-step explanation:

Given

Rectangle coordinates

[tex]A = (0,4)[/tex]

[tex]B = (4,2)[/tex]

[tex]C = (1,-4)[/tex]

[tex]D =(-3,-2)[/tex]

Required

The area of the rectangle

The area is calculated as:

[tex]Area = Length* Width[/tex]

The length of the rectangle will be represented as:

[tex]Length = AB = CD[/tex]

And the width is:

[tex]Width = BC = AD[/tex]

Calculate distance AB using:

[tex]AB = \sqrt{(x_1 - x_2)^2 +(y_1 - y_2)^2 }[/tex]

Where:

[tex]A = (0,4)[/tex] --- [tex](x_1,y_1)[/tex]

[tex]B = (4,2)[/tex] [tex]--- (x_2,y_2)[/tex]

[tex]AB = \sqrt{(0 - 4)^2 +(4 - 2)^2 }[/tex]

[tex]AB = \sqrt{(- 4)^2 +(2)^2 }[/tex]

[tex]AB = \sqrt{16 +4 }[/tex]

[tex]AB = \sqrt{20}[/tex]

Calculate distance BC using:

[tex]BC = \sqrt{(x_1 - x_2)^2 +(y_1 - y_2)^2 }[/tex]

[tex]C = (1,-4)[/tex] [tex]---(x_1,y_1)[/tex]

[tex]B = (4,2)[/tex] [tex]--- (x_2,y_2)[/tex]

[tex]BC = \sqrt{(1 - 4)^2 +(-4 - 2)^2 }[/tex]

[tex]BC = \sqrt{(- 3)^2 +(-6)^2 }[/tex]

[tex]BC = \sqrt{9 +36}[/tex]

[tex]BC = \sqrt{45}[/tex]

So, the area is:

[tex]Area = Length * Width[/tex]

[tex]Area = AB * BC[/tex]

[tex]Area = \sqrt{20} * \sqrt{45}[/tex]

[tex]Area = \sqrt{20 * 45}[/tex]

[tex]Area = \sqrt{900[/tex]

[tex]Area = 30[/tex]

Answer:

I'm not sure of the answer

Answer:

I think A ................

Answer:

1114 ft

Step-by-step explanation:

tan 22°=450/d

==>d=450/tan 22°=1113.7890... ≈1114 (ft)

Answer:

what do u need help with there isn't anything attached

Step-by-step explanation:

Answer:

please put correct question

answer is in attachment!

Answer:

3.24m

Step-by-step explanation:

SOH

sin(26)=O/7.4

O=7.4 sin(26)

O=3.24 (3sf)

Answer: $26901

Step-by-step explanation:

From the information given, we are informed that Walter's home was originally valued at $29,275 but that after some improvement, it is now valued at $56,176.

Therefore, the increase in the worth of Walter's home will now be the difference in the values given above. This will be:

= $56,176 - $29275

= $26901

Answer:

123 cm^2

Step-by-step explanation:

for the rectangles its

#1     5(4)=20 cm^2

#2    5(7)= 35 cm^2

#3     5(8) = 40 cm^2

for the triangles its

4(7)(.5)(2)= 28 cm^2

4(7)= 28 cm^2

I get the .5 from the triangle area formula

and since the triangles are equal I multiplied it by 2 again so the .5 cancels out.

in the end you add them all up which is 20+35+40+28 = 123 cm^2

An equivalent rational expressions with denominator (x+3), (x−4) and (x+4) is (3x²+6x-16)/(x³+3x²-16x-48).

The given denominator are (x+3), (x−4) and (x+4).

A mathematical expression that may be rewritten to a rational fraction, an algebraic fraction such that both the numerator and the denominator are polynomials.

Here, an equivalent rational expressions is

[tex]\frac{1}{x+3}+\frac{1}{x-4} +\frac{1}{x+4}[/tex]

The LCM of denominators is (x+3)(x-4)(x+4)

= (x+3)(x²-16)

= x(x²-16)+3(x²-16)

= x³-16x+3x²-48

= x³+3x²-16x-48

Now, [tex]\frac{(x-4((x+4)+(x+3)(x+4)+(x+3)(x-4)}{x^3+3x^2-16x-48}[/tex]

= (x²-16+x²+7x+12+x²-x-12)/(x³+3x²-16x-48)

= (3x²+6x-16)/(x³+3x²-16x-48)

Hence, an equivalent rational expressions with denominator (x+3), (x−4) and (x+4) is (3x²+6x-16)/(x³+3x²-16x-48).

Learn more about the rational expressions here:

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Answer:

I believe they're the same because the last part of the equation is the same

Step-by-step explanation:

because 3/x-4+4 they both are the same

Answer:

30%

Step-by-step explanation:

Answer: Its 18%

Step-by-step explanation: To get the answer subtract 96 from 78

Answer:

[tex]h_t=9ft[/tex]

Step-by-step explanation:

From the question we are told that:

Height of child [tex]h_c=3ft[/tex]

Height of child's shadow  [tex]h_c_s=2ft[/tex]

Height of tree's shadow [tex]h_t_s=6ft[/tex]

Since position of Sun remains constant  

Generally the equation for Height of tree h_t mathematically given by

 [tex]h_t=f_{ts}\frac{h_c}{h_c_s}[/tex]

 [tex]h_t=6*\frac{3}{2}[/tex]

 [tex]h_t=9ft[/tex]

Answer: [tex]171.4\%[/tex]

Step-by-step explanation:

Given

Time is extended from 28 days to 76 days

The percentage increase is given by

[tex]\Rightarrow \dfrac{\text{New-original value}}{\text{original value}}\times 100[/tex]

Putting values

[tex]\Rightarrow \dfrac{76-28}{28}\times 100=\dfrac{48}{28}\times 100\\\\\Rightarrow 171.4\%[/tex]

Thus, the percentage increase in time is [tex]171.4\%[/tex]

Answer:

False

Step-by-step explanation:

Given that

There are 126000 people living in a town

Out of which 52920 people in the town own a car

So based on this, the group announces that fewer than 40% of residents own a car

We need to find out the statement is correct or not

So here we determine the percentage

= 52,920 ÷ 126,000

= 42%

Since it is more than 40%

So the given statement is false

Answer:B

Step-by-step explanation:

The value of P(x) the difference between the annual income and the amount spent in a year is,

⇒ P(x) = 2x² - 20x - 5

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Given that;

The function f (x) = 4x² – 20x describes the café's total annual income. And, The function C(x) = 2x² + 5 describes the total amount the café spends in a year.

Hence, The value of P(x) the difference between the annual income and the amount spent in a year is,

⇒ P(x) = 4x² - 20x - 2x² - 5

⇒ P (x) = 2x² - 20x - 5

Thus, The value of P(x) the difference between the annual income and the amount spent in a year is,

⇒ P(x) = 2x² - 20x - 5

Learn more about the subtraction visit:

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Answer:

16,384π/3

Step-by-step explanation:

V = (4/3)πr³

V = (4/3)π(16³)

V = 16,384π/3

Answer:

Step-by-step explanation:

Equation

V = (4/3) pi r^3

Givens

r = 16

Solution

V = (4/3) pi 16^3

V = (1.3333) * 3.14 * 4096

V = 171148.5

None of those answers agree with mine. Are those the real choices?

Answer:

Step-by-step explanation:

32

Answer:

20ft.

Step-by-step explanation:

The perimeter is 40ft. You are starting at the perimeter of the pool swimming inward, you will have to swim half of that distance to reach the center.

Answer:

I do not understand ummmm

Given:

The three points are W(0,-2), I(2,0) and L(5,k).

To find:

The value of k for which the given points are collinear.

Solution:

We know that, three points are collinear if the area of the triangle formed by these three points is 0.

[tex]\dfrac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|=0[/tex]

[tex]x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)=0[/tex]

The three points are W(0,-2), I(2,0) and L(5,k). So,

[tex]0(0-k)+2(k-(-2))+5(-2-0)=0[/tex]

[tex]0+2(k+2)+5(-2)=0[/tex]

[tex]2k+4-10=0[/tex]

[tex]2k-6=0[/tex]

Adding 6 on both sides, we get

[tex]2k=6[/tex]

[tex]k=\dfrac{6}{2}[/tex]

[tex]k=3[/tex]

Therefore, the correct option is E.

Answer:

use ma th wa y (its all together)

Step-by-step explanation:

Answer:

10. The number of cupcakes Sheldon would have to buy to recieve the same number of cupcakes in a package would be 30 cupcakes in a package.

Step-by-step explanation: Find the least common denominator (LCD) of six and ten which is, 30.

11.  The greatest number of necklaces Samuel would have to make is four.

Step-by-step explanation: Divide 148 necklaces by 36 strings and the answer will be four necklaces.

12. The greatest length, in feet, of each piece of ribbon Karen, would have to cut is six feet.

Step-by-step explanation: Find the greatest common denominator (GCD) of 18 and 12 which is, six.

13. Find the least common denominator of five and three which is, 15 minutes.

Step-by-step explanation:

Jacob will finish his laps in these following minutes, supposing he starts at zero.

3 minutes, 6 minutes, 9 minutes, 12 minutes, 15 minutes...

That is, all instants of time which are multiples of three.

Betty

5 minutes, 10 minutes, 15 minutes, 20 minutes, 25 minutes, ...

That is, all instants of time which are multiples of five.

Answer:

the amount paid by Sarah is $20.64

Step-by-step explanation:

Given that

The total cost of the dinner is $61.92

And her friends pay 2 by 3

We need to find out the amount paid by Sarah

Since her friends pay 2 by 3 of the total cost

That means the remaining should be paid by Sarah i.e. 1 by 3

So, we need to multiply 1 by 3 with the total cost of the dinner i.e.

= 1 ÷3 × $61.92

= $20.64

Hence, the amount paid by Sarah is $20.64

Answer:

k = 6.5

Step-by-step explanation:

The question relates to the association of the association of the equation of a graph point(s) on the graph

The given equation of the graph, is y = 2·x + c

The value of 'c' is a constant

We note that the value of 'c' can be found when x = 0, as follows;

y = 2·x + c = 2 × 0 + c = c

∴ When x = 0, y = c

From the graph, when x = 0 we have the y-intercept, the point the graph crosses the y-axis, which is the point y = -3

Therefore;

When x = 0, y = -3 = c

∴ c = -3

The equation of the graph becomes, y = 2·x + (-3) = 2·x - 3

y = 2·x - 3

The other given point on the graph is the point (k, 10)

The value k is the x-value when y = 10

Substituting y = 10 in the equation for the graph gives the x-value at the point y = 10 as follows;

10 = 2·x - 3

2·x = 13

x = 13/2 = 6.5

x = 6.5 (when y = 10)

Therefore the point (k, 10) = (6.5, 10)

By comparing the two equal coordinates, we have;

k = 6.5.

Answer:

Right rectangle.

Step-by-step explanation:

The rectangle will be a right rectangle only if the opposite sides are parallel to each other.

This means that RQ should be parallel to ST

And RS should be parallel to QT

Each side can be represented by a line with a restricted domain, and we know that two lines are parallel only if they have the same slope.

Remember that the slope relates to how a change in the x-value makes a change in the y-value.

Then if two segments have, for a fixed change in the x-value, the same change in the y-value, we can conclude that those segments are parallel.

So here to see if the lines are parallel, we just need to compare the changes between the endpoints of each segment.

Let's start with segments QR and TS

First let's look at the segment QR, and let's try to find the difference in the coordinates between R and Q.

In the graph, we can see that R is 3 units above and one unit to the right of Q.

Now let's do the same for the other segment:

In the graph, we also can see that S is 3 units above and one unit to the right of T.

So these two lines will have the same slope:

Only with this, we can conclude that sides QR and TS are parallel.

Now with the other two segments: RS and QT.

Similar to the above case, for the segment RS we can see that S is 4 units at the right and 1 unit below R.

For the segment QT, we can see that T is 4 units at the right and one unit below Q.

So segments RS and QT have the same slope, thus, the segments are parallel.

Then we can conclude that this is a right rectangle.

Answer: 2 pounds

Step-by-step explanation: if each day the dog gets 1/3 pounds, then after two days the dog would get 2/3 pounds. 3 days would be 1 pound, so after 6 days that would be 2 pounds.