Leora had some money in her wallet. She spent $18.62 buying groceries and had $43.55 left. How much money did she have in her wallet before she bought the groceries?
$24.93
$35.93
$45.41
$62.17

K is the midpt. of AB.

Its in the middle of AB so its the midpt.

Answer:

The prove of the given identity is shown below:

Step-by-step explanation:

It seems that the question involves the proving of a trigonometric identity.

Therefore, we are going to work independently on each side of the equal sign.

We start by considering [tex]cos(\alpha)=cos(\frac{\alpha}{2} +\frac{\alpha}{2})[/tex] since the angle alpha is the same as the addition of two halves of it. Then we apply the identity for the cosine of an addition of angles: [tex]cos (\frac{\alpha}{2} +\frac{\alpha}{2})=cos(\frac{\alpha}{2})*cos(\frac{\alpha}{2})-sin(\frac{\alpha}{2})*sin(\frac{\alpha}{2})= cos^2(\frac{\alpha}{2})-sin^2(\frac{\alpha}{2})[/tex]

and now we use the Pythagorean identity to replace the cosine square expression:

[tex]cos^2(\frac{\alpha}{2})=1-sin^2(\frac{\alpha}{2})[/tex]

in the difference of square trig functions we had arrived to:

[tex]cos^2(\frac{\alpha}{2})-sin^2(\frac{\alpha}{2})=1-sin^2(\frac{\alpha}{2})--sin^2(\frac{\alpha}{2})=1-2\,sin^2(\frac{\alpha}{2})[/tex]

We have arrived at the exact same expression the original identity shown on the righthand side of the equal sign, so we have proved the identity.

Answer:

23) 7b+14

yea I guess the rest remain the same

Answer:

The number of ways is 6435

Step-by-step explanation:

Given

[tex]Male = 6[/tex]

[tex]Female = 5[/tex]

[tex]Students = 4[/tex]

Required

Number of ways a group of 8 can be formed

Here, I'll assume each category of people are distinct:

Hence;

[tex]Total = Male + Female + Students[/tex]

[tex]Total = 6 + 5 + 4[/tex]

[tex]Total = 15[/tex]

Number of ways is then calculated as follows:

[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]

Where

[tex]n = 15\ and\ r = 8[/tex]

So, we have:

[tex]^{15}C_8 = \frac{15!}{(15 - 8)!8!}[/tex]

[tex]^{15}C_8 = \frac{15!}{7! * 8!}[/tex]

[tex]^{15}C_8 = \frac{15 * 14 * 13 * 12 * 11 * 10 * 9 * 8!}{7!8!}[/tex]

[tex]^{15}C_8 = \frac{15 * 14 * 13 * 12 * 11 * 10 * 9}{7!}[/tex]

[tex]^{15}C_8 = \frac{15 * 14 * 13 * 12 * 11 * 10 * 9}{7 * 6 *5 * 4 * 3 * 2 * 1}[/tex]

[tex]^{15}C_8 = \frac{32432400}{5040}[/tex]

[tex]^{15}C_8 = 6435[/tex]

Hence, the number of ways is 6435

Answer:

the region of the circle in polar coordinate can be expressed as:

[tex]\mathbf{- \dfrac{\pi}{2} \leq \theta \leq \dfrac{\pi}{2} , 0 \leq r \leq 11 cos \theta}[/tex]

Step-by-step explanation:

Given that:

[tex]x^2 +y^2 = 11x[/tex]

This implies that :

[tex](x-5.5)^2 + y^2 = 5.5^2[/tex]

center (5.5, 0) and radius = 5.5

The relation between the cartesian coordinates (x,y) and the polar coordinates (r, θ) is as follows:

x = rcosθ

y = rsinθ

Thus, [tex]x^2 + y^2 = r^2[/tex]

[tex]x^2 + y^2 = 11x[/tex]

[tex](rcos \theta)^2 + (r sin \theta)^2 = 11(rcos \theta)[/tex]

[tex]r^2 = 11r cos \theta[/tex]

Thus, the angle θ runs between [tex]- \dfrac{\pi}{2}[/tex] to [tex]\dfrac{\pi}{2}[/tex]

Therefore, the region of the circle in polar coordinate can be expressed as:

[tex]\mathbf{- \dfrac{\pi}{2} \leq \theta \leq \dfrac{\pi}{2} , 0 \leq r \leq 11 cos \theta}[/tex]

The required region is,

[tex]x=\frac{11}{2}+\frac{11}{2}cos\theta , 0\leq \theta\leq2\pi \\y=\frac{11}{2}sin\theta ,0\leq r \leq \frac{11}{2}[/tex]

Given circle is,

[tex]x^2 +y^2 = 11x[/tex]

Computation:

Solving the given circle,

[tex]x^2-11x+y^2=0\\x^2-2(\frac{11x}{2})+y^2=0[/tex]

Adding [tex]\frac{11}{2}[/tex] both sides we get,

[tex]x^2-2(\frac{11x}{2})+\frac{121}{4}+y^2=\frac{121}{4}\\(x-\frac{11}{2})^2+y^2=(\frac{11}{2})^2[/tex]

It represents a circle having the radius [tex]\frac{11}{2}[/tex] and centred at [tex](\frac{11}{2},0)[/tex]

So, in polar coordinate,

[tex]x=\frac{11}{2}+\frac{11}{2}cos\theta , 0\leq \theta\leq2\pi \\y=\frac{11}{2}sin\theta ,0\leq r \leq \frac{11}{2}[/tex]

Learn More:https://brainly.com/question/12482360

Answer:

14+=+2L+%2B+2%28L-3%29 Simplify and solve for L

14+=+2L+%2B+2L+-+6 Combine like-terms.

14+=+4L-6 Add 6 to both sides.

20+=+4L Divide both sides by 4.

5+=+L The length is 5 meters.

W+=+L-3

W+=+5-3

W+=+2meters.

The width is 2 meters.

P+=+2L%2B2W

P+=+2%285%29%2B2%282%29

P+=+10%2B4

P+=+14meters.

Step-by-step explanation:

Answer: $2421.90

Step-by-step explanation:

Since a yard is 3 feet, we can say the foyer is 3 yards by 6 yards (9 feet is 3 yards and 18 feet is 6). The area of a square is x*y, so the area of each floor is 3*6 = 18 square yards. Since there are 5 homes, there are 5 * 18 = 90 total square yards to laminate. That means that the total cost is 90 * 26.91 = $2421.90.

The total cost for the foyer for the 5 homes is $ 2421.9.            

Given that,

A builder is building 5 new homes. Each home has a foyer measuring 9 feet by 18 feet. Laminate flooring for each foyer costs $26.91 per square yard. What is the cost of the laminate floors for the foyers in all 5 homes is to be determined.

In mathematics, it deals with numbers of operations according to the statements.

Here,
1 yard = 3 feet
Now
The measure of foyer = 9 feet x 18 feet = 9 /3 yard x 18 / 3 yard.
Area of the foyer = 3 x 6
                            = 18-yard square
Area of the  foyer of 5 homes = 5 * 18
                                                  = 90-yard square,

The total cost of a foyer for 5 homes = 90 * 26.91
                                                    = $2,421.9

Thus, the total cost for the foyer for the 5 homes is $ 2421.9.

Learn more about arithmetic here:

brainly.com/question/14753192

#SPJ2

Answer:

5.33

Step-by-step explanation:

It is a repetitive decimal.

Answer:

2/3 7/9 4/5 13/15

Step-by-step explanation:

Answer:

96 books

Step-by-step explanation:

because when you have 48 books on 6 shelves it is 8 books per shelf so it is 96 because 12 times 8 equals 96

Answer:

2 m/s

Step-by-step explanation:

Notice that the slope of the time period from 0s to 20s is linear.  This means we can simply look at the distance traveled over the amount of time.  So the distance and time both start at 0.  At 20s, the distance is 40m.

So we can say the following to find the slope:

(40m - 0m) / (20s - 0s) == 40m / 20s == 2 m/s

Hence, the average speed between 0s and 20s is 2m/s.

Cheers

Answer:hi

Step-by-step explanation:

Answer: if x = O in the denominator of the first term or if x = -2 in the second term, the results are undefined.

Step-by-step explanation: If the denominator of a fraction is 0 there is no number that solves it because it is impossible to divide by zero.

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{1}}}}}[/tex]

Step-by-step explanation:

The value of the term having the index 0 equals to 1.

So, [tex] \sf{ {x}^{0} }[/tex] = 1

Hope I helped!

Best regards! :D

Answer:

its (2,8)

Step-by-step explanation:

the point is the  multiple of the abscissa 1 and ordinate 4 if we multiply 2 with 1 and 4 we get (2,8) and the ratio is also same

or it can be all the multiples of 1 and 4

thank u

Answer:

Meter

Step-by-step explanation:

The standard unit of length based on the metric system is a meter (m). According to the length that needs to be measured, we can convert a meter into various units like millimeters (mm), centimeter (cm), and kilometer (km).

Answer:

3.278 * 10 ^ 2

Step-by-step explanation:

To change a number to scientific notation you:

Move the decimal point to the left to make the number have 1 number before the decimal point.

From there you multiply by 10 to the power 2 the number of decimal points you moved.

So the answer is 3.278 * 10^2

HOPE IT HELPED

Answer:

3.6 miles

Step-by-step explanation:

since his house is 8 inches away and 2 inches =0.9miles

we just need to multiply. Divide 8 by 2 .

4× 9 = 36 so just add the decimal

0.9× 4= 3.6 miles

Answer:

[tex] x = \frac{1}{2} y + 3[/tex]

Step-by-step explanation:

[tex]y = 2x - 6 \\ y + 6 = 2x \\ \frac{y + 6}{2} = x \\ \frac{y}{2} + 3 = x \\ \huge \red{ \boxed {x = \frac{1}{2} y + 3}}[/tex]

Answer: 15 degrees

Step-by-step explanation:

Answer:

x < x and -3x < -3x

Step-by-step explanation:

x cannot be less than itself so there would be no solution.

Answer: It is 3 and negative -3

Step-by-step explanation:3 units away from zero forwards and back are both 3 but one is negative

Answer: 3 and negative -3

hope this helps

Answer: 4.86

Step-by-step explanation: 2.75+.75 = 3.5  1 for the cookies 4.5*0.08 = 0.36

4.5+.36 = 4.86.

Answer:

Add

−

6 n and 5n.− 32m − n

Step-by-step explanation:

Answer:

[tex]f \leqslant 3[/tex]

Step-by-step explanation:

[tex]5f + 7 \leqslant 22 \\ 5f \leqslant 15 \\ f \leqslant 3[/tex]

Answer: $9.86

Step-by-step explanation:

$11.60 ⋅ 8.5 = $98.60

$98.60 / 10 = $9.86