In store A a scarf cost $12, and in store B the same scarf is on sale for $8. How many scarfs can be bought in store B with the amount of money, excluding sales tax, needed to buy 10 scarfs in store A

Area of the given polygon is required.

The area of the polygon is A. [tex]147\ \text{square units}[/tex]

The polygon is a rectangle with one corner of the rectangle removed.

The removed area is a square.

The area of the complete rectangle is

[tex]13\times 12=156\ \text{square units}[/tex]

Area of the removed square

[tex]3\times 3=9\ \text{square units}[/tex]

The area of the polygon is

[tex]156-9=147\ \text{square units}[/tex]

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The perfect square [tex](x-a)^2[/tex] can be expanded as follows:

[tex](x-a)^2=x^2-2ax+a^2[/tex]

So, we have to think of the term [tex]-8x[/tex] as [tex]-2ax[/tex], which implies [tex]a=4[/tex].

Thus, we have to add [tex]a^2[/tex], i.e. 16, to complete the perfect square:

[tex](x-4)^2 = x^2-8x+16[/tex]

Answer:

63 donuts

Step-by-step explanation:

210 donuts -> 10 hours

  x  donuts -> 3 hours

This is already setup for a proportion:

[tex]\frac{210}{x}=\frac{10}{3}[/tex]

Cross multiply:

[tex]3(210)=10x[/tex]

Simplify:

[tex]630=10x[/tex]

Divide both sides by 10:

[tex]\frac{630}{10}=x[/tex]

Simplify:

[tex]63=x[/tex]

63 donuts can be made in hours.

The division is one of the four fundamental arithmetic operations. The number of donuts that can be made in 3 hours time period is 63 donuts.

The division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.

Given that 210 donuts can be made in 10 hours. Therefore, the number of donuts that can be made per hour are:

Number of donuts per hour = 210 donuts / 10 hour

                                              = 21 donuts / hour

Now, the number of donuts that can be made in 3 hours are,

Number of donuts = 21 donuts / hour × 3 donuts

                               = 63 donuts

Hence, the number of donuts that can be made in 3 hours time period is 63 donuts.

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Answer:

20) 30°; 21) 21,1; 22) 6,2

Step-by-step explanation:

For the first image, you have to do csc⁻¹ 2 [OR sin⁻¹ ½] because you are solving for an angle measure. When evaluated, you get 30°.

For the second image, you have to do 13sec 52° = x [OR 13\cos 52° = x]. When evaluated, you get an approximate measure of 21,1.

For the third image, you have to do 6csc 75° = x [OR 6\sin 75° = x]. When evaluated, you get an approximate measure of 6,2.

Extended information on Trigonometric Ratios

O\H = sin θ

A\H = cos θ

O\A = tan θ

H\A = sec θ

H\O = csc θ

A\O = cot θ

I am joyous to assist you anytime.

Answer:

1080

Step-by-step explanation:

looking at the ratio of 1 : 3 : 6, we can say that the pupils are divided into 1 + 3 + 6 = 10 "parts".

Indian are 1 part, Malay are 3 parts, and Chinese are 6 parts.

So 3x (3 parts of malay) is 360 more than 1x (1 part of Indian). Thus:

3x - 360 = x

2x = 360

x = 180

We know chinese is 6 parts, or 6x, so Chinese would be 6 (180) = 1080

Hence, there are 1080 chinese pupils

The square root of 9 is 3, but the negative square root of 9, which is -3, is less than 2 squared (4). Therefore, the answer to the question is -3.

The square root of 9 is 3. We denote the square root symbolically as √9 = 3. However, if we're looking for which square root of 9 is less than 2 squared (which is 4), we consider that every positive number has two square roots: one positive and one negative. The negative square root of 9 is -3, which is indeed less than 4. Therefore, the square root of 9 that is less than 2 squared is -3.

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Answer:

M<A is less than or equal to 90°

Step-by-step explanation:

If it is less than or equal to, then the first statement has to be false, that it is greater. This means the statement is negated because they can't work together.

Answer:

False

Step-by-step explanation:

What the attached image says that if two solids with equal heights and base areas are cut by any parallel plane to their bases then sections of equal area (volume) would be produced in them

[tex]\tan a-1=0\\\tan a =1\\\\a=\dfrac{\pi}{4}+k\pi, k\in\mathbb{Z}[/tex]

let's firstly convert the mixed fractions to improper fractions and then add.

[tex]\bf \stackrel{mixed}{2\frac{7}{10}}\implies \cfrac{2\cdot 10+7}{10}\implies \stackrel{improper}{\cfrac{27}{10}}~\hfill \stackrel{mixed}{8\frac{1}{2}}\implies \cfrac{8\cdot 2+1}{2}\stackrel{improper}{\cfrac{17}{2}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{27}{10}+\cfrac{17}{2}\implies \stackrel{\textit{using an LCD of 10}}{\cfrac{(1)27+(5)17}{10}}\implies \cfrac{27+85}{10}\implies \cfrac{112}{10}\implies \cfrac{56}{5}\implies 11\frac{1}{5}[/tex]

Answer:

Overlapping events

Step-by-step explanation:

Note that in the question, it specifically specifies that there is only a number cube (or 1 number cube). Note that the two events asked for us to solve is does not conflict at all.

Event A is asking for the probability of you rolling a prime number (1 , 3 , 5), while Event B is asking for the probability of you rolling a number larger than 4 (5 , 6). These two can occur at the same time, and both events can be confirmed by rolling the number 5.

~

Answer:

overlapping events

Step-by-step explanation:

Event A: Rolling a prime

The following are the prime numbers from 1 to 6 (inclusive):

2,3,5

Event B: Rolling a number larger than 4

The following are larger than 4 from 1 to 6 (inclusive):

5,6

Do you see any overlap?

The overlap is 5.

These are overlapping events.

Add all of the number of pizzas together

93+67+78+44+123

160+245

405

Divide by 5 because there are 5 numbers

405/5=81

81 pizzas

Answer: 81 pizzas -C.

Answer:

option D

Step-by-step explanation:

As per the contract:

"All rentals are due back by midnight of the due date as printed on the transaction receipt. "

In given case clerk did not give any transaction receipt.

so option D is correct

The clerk completed the transaction without giving Susan a receipt or otherwise informing her of the due date !

Answer:

d

Step-by-step explanation:

i just did the test

Answer:

8

Step-by-step explanation:

We are given the following expression and we are to find the simplest form of this expression:

[tex] - 3 2 ^ { \frac { 3 } { 5 } } [/tex]

First of all, we will factor the coefficient:

[tex] 3 2 = 2 ^ 5 [/tex]

Rewriting it as:

[tex] - ( 2 ^ 5 ) ^ { \frac { 3 } { 5 } }[/tex]

Applying the exponent rule [tex](a^b)^c = a^{bc}[/tex] to get:

[tex]-2^{5.\frac{3}{5}}=-2^3[/tex]

[tex]-2^3=-8[/tex]

Answer:

Is an acute triangle

Step-by-step explanation:

we have

[tex]G(7, 3),H(9, 0),I(5, -1)[/tex]

so

The polygon is a triangle

we know that

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

Remember that

If applying the Pythagoras Theorem

[tex]c^{2}=a^{2}+b^{2}[/tex] -----> is a right triangle

[tex]c^{2}>a^{2}+b^{2}[/tex] -----> is an obtuse triangle

[tex]c^{2}<a^{2}+b^{2}[/tex] -----> is an acute triangle

where

c is the greater side

step 1

Find the distance GH

[tex]G(7, 3),H(9, 0),I(5, -1)[/tex]

substitute

[tex]d=\sqrt{(0-3)^{2}+(9-7)^{2}}[/tex]

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

[tex]GH=\sqrt{13}\ units[/tex]

step 2

Find the distance HI

[tex]G(7, 3),H(9, 0),I(5, -1)[/tex]

substitute

[tex]d=\sqrt{(-1-0)^{2}+(5-9)^{2}}[/tex]

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

[tex]HI=\sqrt{17}\ units[/tex]

step 3

Find the distance GI

[tex]G(7, 3),H(9, 0),I(5, -1)[/tex]

substitute

[tex]d=\sqrt{(-1-3)^{2}+(5-7)^{2}}[/tex]

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

[tex]GI=\sqrt{20}\ units[/tex]

step 4

Let

[tex]c=GI=\sqrt{20}\ units[/tex]

[tex]a=HI=\sqrt{17}\ units[/tex]

[tex]b=GH=\sqrt{13}\ units[/tex]

Find [tex]c^{2}[/tex] ------> [tex]c^{2}=(\sqrt{20})^{2}=20[/tex]

Find [tex]a^{2}+b^{2}[/tex] ----> [tex](\sqrt{17})^{2}+(\sqrt{13})^{2}=30[/tex]

Compare

[tex]20 < 30[/tex]

therefore

Is an acute triangle

Answer:

The answer is Region C

Step-by-step explanation:

Region C has total population of Zebra as 16,400 divided by the area occupied in square km which is 625. This gives population density of approximately 26 zebras/km square

[tex] \frac{16400}{625} = 26.24[/tex]

If you follow the same procedure for other regions, you will discover that region C has the highest number of Zebras/square km which is 26.

I hope this helped?

The region that would have the greatest competition for resources is Region C.

Population density is the amount of organisms that live in a square feet of an area.

Population density = population / area

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Check the picture below.

now we simply plug all those three sides in Heron's Area Formula.

[tex]\bf \qquad \textit{Heron's area formula} \\\\ A=\sqrt{s(s-a)(s-b)(s-c)}\qquad \begin{cases} s=\frac{a+b+c}{2}\\[-0.5em] \hrulefill\\ a=5.8\\ b=9.75\\ c=7.39\\ s=11.47 \end{cases} \\\\\\ A=\sqrt{11.47(11.47-5.81)(11.47-9.75)(11.47-7.39)} \\\\\\ A=\sqrt{11.47(5.66)(1.72)(4.08)}\implies A\approx \sqrt{455.5839955} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill A\approx 21.3444~\hfill[/tex]

Answer:

area of triangle ABC is 21.39 square units.

C is the correct option.

Step-by-step explanation:

We know the formula for the area of the triangle ABC in terms of sine. The formulas are

[tex]A=\frac{1}{2}ab\sin C\\\\A=\frac{1}{2}ac\sin B\\\\A=\frac{1}{2}bc\sin A[/tex]

In the given triangle, we hae

b = 9.75

c = 7.39

A = 36.43°

Therefore, area of triangle ABC is given by

[tex]A=\frac{1}{2}bc\sin A\\\\\frac{1}{2}\cdot9.75\cdot7.39\sin36.43\\\\A=21.39[/tex]

Hence, area of triangle ABC is 21.39 square units.

C is the correct option.

Answer:

approximately 3 ....to be exact 3.1 weeks

Step-by-step explanation:

he earns 225 a week we know that right? and he has to take out 180 to pay for things... so right there you have 225-180=45 so that's 45 dollars a week he has. the MP4 player is 195 and he already has 55 dollars saved so 195-55= 140 so he still needs 140 dollars to buy it the question now is how many weeks will it take for him to save up to 140 dollars? you simply take 140÷45 (bc that's what he gets each week) and it should = 3.1

Answer: 3.1

Step-by-step explanation:

1. 225 a week in pay

2. 180 take out of pay

3. 225-180=45 a week from paycheck

4. Mp3 cost 195.00

5. 55.00 money saved

6. 195-55=140

7. 140÷45 after rounding 3.1

There is the answer

Answer:

[tex]WY=42.8\ units[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

In the right triangle WYS

Applying the Pythagoras Theorem

[tex]WY^{2}=WS^{2}+YS^{2}[/tex]

we have that

[tex]WS=XZ=42\ units[/tex]

[tex]YS=YZ-WX=19-11=8\ units[/tex]

substitute

[tex]WY^{2}=42^{2}+8^{2}[/tex]

[tex]WY^{2}=1,828[/tex]

[tex]WY=42.8\ units[/tex]

Answer: Yes it is.

Step-by-step explanation: So we are already told that segment AC is congruent to segment DC. They both have a right angle, as indicated by the angle symbol, and they share side-length BC.

According to the Hypotenuse-Leg Theorem, two right triangles that have a congruent hypotenuse and a corresponding, congruent leg are congruent triangles. AC and DC are hypotenuses and they are congruent. And BC, the shared side, is a corresponding congruent leg. And since they are both right triangles, we then know that the HL Theorem applies.

Answer:

did this problem came with a chart becuase i dont know what youre talkin about

Step-by-step explanation:

Answer:

1 triangle will satisfy the condition.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Use FOIL: (a + b)(c + d) = ac + ad + bc + bd

and i² = -1

(2 + 2i)(5 + 3i) = (2)(5) + (2)(3i) + (2i)(5) + (2i)(3i)

= 10 + 6i + 10i + 6i² = 10 + 6i + 10i + 6(-1)

= 10 + 6i + 10i - 6             combine like terms

= (10 - 6) + (6i + 10i)

= 4 + 16i

Answer:

[tex]\displaystyle 4+16i[/tex]

Step-by-step explanation:

Distributive property: ⇒ A(B+C)=AB+AC

A=2, B=2, C=5, and D=3

[tex]\displaystyle (2*5-2*3)+(2*3+2*5)i[/tex]

Simplify and refine to find the answer.

[tex]\displaystyle2*3+2*5=2*3=6, 2*5=10, 10+6=16[/tex]

[tex]\displaystyle2*5-2*3=2*5=10-2*3=2*3=6, 10-6=4[/tex]

[tex]\displaystyle 4+16i[/tex] , which is our correct answer.

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

y = mx + b

m - slope

b - y-intercept

Parallel lines have the same slope.

===========================================

We have y= -6x - 9 → m = -6

Put the value of a slope and the coordinates of the point (-2, 3) to the equation of a line:

3 = -6(-2) + b

3 = 12 + b        subtract 12 from both sides

-9 = b → b = -9

Finally:

y = -6x - 9

Answer:

See below in bold.

Step-by-step explanation:

Convert the equation into slope-intercept form:

7x - 6y = -5

6y = 7x + 5

y = (7/6) x + 5/6

- so the slope is 7/6.

The slope of a line parallel to this has the same slope 7/6.

The slope of a line perpendicular to this has a slope of - 1 / 7/6

= -6/7.

Answer:

Step-by-step explanation:

calculate the slope of given line :

7X-6Y=-5

6y = 7x+5

y=7/6 x +5/6

the slope is : 7/6

the slope of a line parallel to this lineis 7/6 ( same slope )

the slope of a line perpendicular to this line is : a    when : a× 7/6= - 1

so : a = -6/7

Answer: no

Step-by-step explanation:

Final answer:

To find the new interest rate compounded quarterly, divide the annual interest rate by the number of compounding periods per year.

Explanation:

To rewrite the equation to find the new interest rate, we need to consider the compounding frequency. Currently, the interest is compounded annually. To find the new interest rate compounded quarterly, we need to divide the annual interest rate by the number of compounding periods per year.

So, for an interest rate of 10%, the quarterly interest rate would be 10% divided by 4, which is 2.5%.

Therefore, the approximate new interest rate, compounded quarterly, would be 2.5%.

The new interest rate when compounded quarterly that would keep the future value (A) and the present value (P) the same is approximately 9.38%.

To find the new interest rate when the interest is compounded quarterly instead of annually, we need to use the compound interest formula and equate the two expressions for A.

Given:

[tex]A = 250(1.1)^_t[/tex] (interest compounded annually)

[tex]A = P(1 + r/m)^_(mt)[/tex] (compound interest formula)

Where:

A = Future value

P = Present value (250)

r = Annual interest rate

m = Number of times interest is compounded per year

t = Time in years

Step 1: Equate the two expressions for A.

[tex]250(1.1)^t = 250(1 + r/m)^_{(mt)}[/tex]

Step 2: Substitute m = 4 (interest compounded quarterly).

[tex](1.1)^t = (1 + r/4)^_{(4t)}[/tex]

Step 3: Solve for r.

[tex](1 + r/4)^4 = 1.1[/tex]

[tex]1 + r/4 = (1.1)^_{(1/4)}[/tex]

[tex]r/4 = (1.1)^_(1/4)} -1[/tex]

[tex]r= 4((1.1)^_(1/4)} -1)[/tex]

r ≈ 0.0938 or 9.38%

Answer:

answer is D

Step-by-step explanation:

3x-4=4x+10

3x=4x+14

-1x=14

x= -14

Answer:

-14

Step-by-step explanation:

It's multiple choice so we could plug in values of x and see which makes f(x)=g(x) true.

What I mean is would could plug in values of x to see which gives us

3x-4=4x+10 is true.

Or we could just solve it.

3x-4=4x+10

Subtract 3x on both sides:

-4=1x+10

-4=x+10

Subtract 10 on both sides:

-14=x

So x=-14 would make f(x)=g(x) hold.

Let's check it and see!

f(-14)=3(-14)-4=-42-4=-46.

g(-14)=4(-14)+10=-56+10=-46.

They have the same value of -46 so x=-14 is certainly going to make f(x)=g(x) be true.

Answer:

5 sqrt2.

Step-by-step explanation:

sqrt8 = sqrt4 * sqrt2 = 2 sqrt2

sqrt18 = sqrt9 * sqrt2 = 3 sqrt2

So simplifying:

5sqrt 8 - sqrt18 - 2 sqrt2

= 5*2sqrt2 - 3 sqrt 2 - 2 sqrt2

= 10 sqrt2 - 5 sqrt2

= 5 sqrt2 (answer).

For this case we must simplify the following expression:

[tex]5 \sqrt {8} - \sqrt {18} -2 \sqrt {2}[/tex]

Rewriting we have:

[tex]8 = 2 * 2 * 2 = 2 ^ 2 * 2\\18 = 9 * 2 = 3 ^ 2 * 2\\5 \sqrt {2 ^ 2 * 2} - \sqrt {3 ^ 2 * 2} -2 \sqrt {2} =[/tex]

We have that by definition of properties of roots and powers it is fulfilled:

[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

So:

[tex]5 * 2 \sqrt {2} -3 \sqrt {2} -2 \sqrt {2} =\\10 \sqrt {2} -3 \sqrt {2} -2 \sqrt {2} =\\10 \sqrt {2} -5 \sqrt {2} =\\5 \sqrt {2}[/tex]

Answer:

[tex]5 \sqrt {2}[/tex]