To make some draperies, an interior decorator needs 12 1/4 yards of material for the den and 8 1/2 yards for the living room. If the material comes only in 21-yard bolts, how much will be left over after completing both sets of draperies?

Answer:

Area = 14.5

Step-by-step explanation:

Let's label the given coordinates A, B, C;

Thus;

A = (2, 3)

B = (-1, 0)

C = (2, -4)

From the coordinate geometry formula, the formula for area of a triangle with 3 vertices is;

Area = [Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By)]/2

Area = [2(0 - (-4)) + (-1)(-4 - 3) + 2(3 - (-4))]/2

Area = 29/2

Area = 14.5

Answer:

1=85

2=10

3=108

Step-by-step explanation:

Number 1: Calculate each angle...and you know a straight line is 180°. N the interior sum of a quadrilateral is always 360°.

Number2: Use corresponding, alternate and interior angles method. It will help

Number 3: It's just about solving the interior sum of the pentagon

Answer:

2. 10 degrees

3. 108 degrees

Step-by-step explanation:

sorry I reposted it because the previous answer was deleted and plz mark me as a brainliest.

Answer:

its 540 bro

Step-by-step explanation:

Answer:

the answer is B, comment if you need explanation

Step-by-step explanation:

Answer:

x+115=180 x=65

90+65+y=180 y=25

Step-by-step explanation:

Answer:

strangely worded question....

[tex]361^{1/2} = \sqrt{361}[/tex]

Step-by-step explanation:

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

Explanation:

Notice how (19)^2 = 19*19 = 361

This shows that 19 is a square root of 361. We can say [tex]\sqrt{361} = \sqrt{19^2} = 19[/tex]

Similarly, (-19)^2 = (-19)*(-19) = 361. The two negatives cancel each other out. So that's why there are two solutions to [tex]x^2 = 361[/tex] which are x = 19 and x = -19.

So far that accounts for answer choices B and D.

-------------------------------------------

The other two answers are [tex]-361^{1/2}[/tex] and [tex]361^{1/2}[/tex] (choices C and F) because anything to the 1/2 power represents a square root.

[tex]x^{1/2} = \sqrt{x}[/tex]

anything to the 1/3 power is a cube root

[tex]x^{1/3} = \sqrt[3]{x}[/tex]

anything to the 1/4 power is a fourth root

[tex]x^{1/4} = \sqrt[4]{x}[/tex]

and so on.

-------------------------------------------

Side note: For choice C, the exponent is done first before we apply the negative. So technically we could say [tex]-1*(361)^{1/2}[/tex] for choice C to mean the same exact thing. If your teacher said [tex](-361)^{1/2}[/tex] then this would not be an answer because this results in a non-real number.

Answer:

D is the correct answer.

Please thank me

Step-by-step explanation:

Answer:

4000*0.03*9=1080

4000+1080=5080

umm but like thats not one of the answers sorry

Hope This Helps!!!

Step-by-step explanation:

4000*3% = 120

120*9= 1080

1080+4000=5080

Answer:

-4/15

Step-by-step explanation:

Mathematically, we know that;

alpha= -b/a and beta = c/a

a refers to the coefficient of the x^2 which is 2

b is the coefficient of x which is 3

c is the last number which is 5

alpha = -b/a = -3/2

beta = c/a = 5/2

1/alpha = -2/3

1/beta = 2/5

so we have the sum as;

-2/3 + 2/5

= -5(2) + 3(2)/15 = (-10 + 6)/15 = -4/15

Answer:

[tex]y_1 = -2[/tex] and [tex]y_2 = 4[/tex]

Step-by-step explanation:

[tex] \sqrt{10y + 24} - 3 = y + 1[/tex]

Move the constant to the right-hand side and change their sign.

[tex] \sqrt{10y + 24} = y + 1 + 3 [/tex]

combine like terms

[tex] \sqrt{10y + 24} - 3 = y + 4[/tex]

Square both side to remove square brackets.

10y + 24 - 3 = y²+ 8y + 16

Move the expression to the left-hand side and change its sign.

10y + 24 - y² - 8y - 16 = 0

Combine like terms

10y - 8y + 24 - 16 - y² = 0

2y + 8 - y² = 0

Use commutative property to reorder the terms.

-y² + 2y + 8 = 0

Change the sign of expression.

y² -2y -8 = 0

split -2y

y² + 2y - 4y - 8 = 0

Factor out y from the first pair and -4 from the second equation.

y ( y + 2 ) - 4 ( y + 2 ) = 0

Factor out y+2 from the expression.

( y + 2 ) ( y - 4)

When the products and factors equals 0, at least one factor is 0.

y + 2 = 0

y - 4 = 0

Solve for y

y = -2

y = 4

When we plug the both solution as y we found that both is true solution of this equation.

This equation has two solutions which are -2 and 4.

Answer:

Solution given:

[tex] \sqrt{10y + 24} - 3 = y + 1[/tex]

keep the constant term in one side

[tex] \sqrt{10y + 24} =y+1+3[/tex]

solve possible one

[tex]\sqrt{10y+24}=y+4[/tex]

now

squaring both side

[tex](\sqrt{10y+24})²=(y+4)²[/tex]

10y+24=y²+8y+16

taking all term on one side

10y+24-y²-8y-16=0

solve like terms

8+2y-y²=0

doing middle term factorisation

8+4y-2y-y²=0

4(2+y)-y(2+y)=0

(2+y)(4-y)=0

either

y=-2

or

y=4

y=-2,4

Answer:      I believe the answer would be 1.3

           HOWEVER, if you do have to round to the nearest tenth then the answer would be 1

Step-by-step explanation:    

2x+7 = 12x - 6

(subtract 2x from both sides)

7 = 10x - 6

(add 6 to both sides)

13 = 10x

(divide 13/10)

1.3 = x

Answer:

d. p - 15 = 49

Step-by-step explanation:

p = original price

The price was reduced by 15 dollars.

The new price is p - 15.

The new price is 49.

p - 15 = 49

Answer: d. p - 15 = 49

answer is C. 252 ft^2

split the figure into two pieces and first figure out the rectangle (shown in turquoise).

If you multiply the width and length (18*6) you should get 108.

Then figure out the trapezoid (in magenta). the formula is (a+b)/2*h where a and b are the bases and h is the height. the bases are given, 6 and 18. to find the height, subtract the entire figure's height by 6, which is 18-6 and gives us 12. so the formula converted to this problem is (6+18)/2*12. simplify parenthesis and get 24/2*12. 24/2=12, so multiply 12*12. The area of the trapezoid is 144. Add the areas of both figures together and get 252.

Answer: C. (0, -3)

Step-by-step explanation:

You don't even need to find the function, just mentally graph every point in the options on the graph.

The line is not dotted, showing that the inequality is probably either ≥ or ≤, so points on the line do count as solution.

Answer:

[tex]x = 0.143[/tex]

[tex]P(High\ |\ Cancer) = 0.215[/tex]

Not independent

Step-by-step explanation:

Given

See attachment for proper table

Solving (a): The missing probability

First, we add up the given probabilities

[tex]Sum = 0.242+0.047+0.079+0.391+0.098[/tex]

[tex]Sum = 0.857[/tex]

The total probability must add up to 1.

If the missing probability is x, then:

[tex]x + 0.857 = 1[/tex]

Collect like terms

[tex]x = -0.857 + 1[/tex]

[tex]x = 0.143[/tex]

Solving (b): P(High | Cancer)

This is calculated as:

[tex]P(High\ |\ Cancer) = \frac{n(High\ n\ Cancer)}{n(Cancer)}[/tex]

So, we have:

[tex]P(High\ |\ Cancer) = \frac{0.079}{0.242+0.047+0.079}[/tex]

[tex]P(High\ |\ Cancer) = \frac{0.079}{0.368}[/tex]

[tex]P(High\ |\ Cancer) = 0.215[/tex]

Solving (c): P(Leukemia) independent of P(High Wiring)

From the attached table

[tex]P(Leukemia\ n\ High\ Wiring) = 0.242[/tex]

[tex]P(Leukemia) = 0.242 + 0.391 =0.633[/tex]

[tex]P(High\ Wiring) = 0.242+0.047+0.079=0.368[/tex]

If both events are independent, then:

[tex]P(Leukemia\ n\ High\ Wiring) = P(Leukemia) * P(High\ Wiring)[/tex]

[tex]0.242 = 0.633 * 0.368[/tex]

[tex]0.242 \ne 0.232[/tex]

Since the above is an inequality, then the events are not independent

f ( - 2 ) = 5 × 3^( - 2 )

f ( - 2 ) = 5 × 1/9

f ( - 2 ) = 5/9

[tex] \frac{3}{8} \div \frac{4}{9} \\ = \frac{3}{8} \times \frac{9}{4} \\ = \frac{27}{32} [/tex]

Hope it helps!!!

Thanks!!!

Answer:

Following are the solution to the given points:

Step-by-step explanation:

For question 1:

[tex]\to 3^{-4}= \frac{1}{3^4}=\frac{1}{81}=0.0123456789[/tex]

For question 2:

[tex]\to (-2)^{3}\cdot(-2)^{4}\cdot(-2)^{-1}=-8\cdot-16\cdot -\frac{1}{2}= 128\cdot -\frac{1}{2}=-64[/tex]

For question 3:

[tex]\to 7^{-4} \div 7^{-2}= \frac{1}{7^{4}} \div \frac{1}{7^{2}}=\frac{1}{7^{4}} \times \frac{7^{2}}{1}=\frac{1}{7^{2}} =\frac{1}{49} =0.0204081633[/tex]

For question 4:

[tex]\to [(-3)^{2}]^3= (-3)^{2\cdot 3}= (-3)^{6}=729[/tex]

For question 5:

[tex]\to [5 \cdot (-3)]^{2}= 25 \cdot 9=225[/tex]

For question 6:

[tex]\to [(10 \div 5)]^{3}= [(\frac{10}{5})]^{3}=[2]^{3}=8[/tex]

For question 7:

[tex]\to 10^6 \cdot 10^{-4} \cdot 10^2= 10^6 \cdot \frac{1}{10^{4}} \cdot 10^2= 10^2 \cdot 10^2=10^4=10,000[/tex]

For question 8:

[tex]\to (-4)^{-5}=\frac{1}{(-4)^{5}}=- \frac{1}{1,024}=-0.0009765625[/tex]

For question 9:

[tex]\to \frac{2^3}{2^4}= \frac{8}{16}=\frac{1}{2}=0.5[/tex]

For question 10:

[tex]\to (-6)^3 \cdot (-6)^5 \cdot (-6)^{-5}= (-6)^3 \cdot (-6)^5 \cdot \frac{1}{(-6)^{5}}= (-6)^3 =-216[/tex]

Answer:

angle 1

Step-by-step explanation:

Using the trigonometric mnemonic SOH CAH TOA, we know that cos or cosine is the ratio between the adjacent side and hypotenuse side.

This means that if cos A = 0.48, A is the measure of the angle which it's relative adjacent side divided by the hypotenuse of the triangle will be around 0.48.

Let's try angle 2, cos (angle 2) = adjacent / hypotenuse = 7.8 / 8.9 = 0.876404494382 ≈ 0.87 ≠ 0.48. Since the proportions are not equal, this angle cannot be the one marked as A.

Since angle 3 is a right angle, the adjacent could be either side so it cannot be correct. Thus angle 1 is correct.

Answer:

O D

Step-by-step explanation:

f+g(x)

3x+10+2x-4

3x +2x+6

Answer:

3/5

Step-by-step explanation:

prependicular / hypotenuse

sin C=ED/CD

=3/5

Given:

Consider the given equation is:

[tex](2\cdot 2^2)^x=64[/tex]

To find:

The value of x.

Solution:

We have,

[tex](2\cdot 2^2)^x=64[/tex]

It can be written as:

[tex](2\cdot 4)^x=8\times 8[/tex]

[tex]8^x=8^2[/tex]

On comparing the exponents of both sides, we get

[tex]x=2[/tex]

Therefore, the value of x is 2.

Answer:

[tex]s =\frac{25 + 26 + 17}{2} = 34[/tex]

[tex] = \sqrt{34 \times 9 \times 8 \times 17} [/tex]

[tex]17 \times 3 \times 2 \times 2 = 204cm ^{2} [/tex]

area ∆ BEC

[tex] = \frac{1}{2} \times 17 \times h = 204[/tex]

[tex]h = \: \frac{204 \times 2}{17} = 24[/tex]

[tex]area \: trap \: \: abcd \\ = \frac{1}{2}(60 + 77) \times 24 \\ = 137 \times 12 = 1644cm ^{2} [/tex]

Step-by-step explanation:

#keep learning!!

9514 1404 393

Answer:

  C

Step-by-step explanation:

The ellipse y-intercepts are ±3, the x-intercepts are ±9, eliminating choices A and B. The parabola is shaded inside, eliminating choice D.

The correct choice is the third one.

Hello,

[tex]Let's\ say \\\\z=\sqrt{3+4*i} =a+b*i\\\\z^2=3+4*i=(a+b*i)^2=a^2-b^2+2i*a*b\\\\\\if \ a\neq 0\\\left\{\begin{array}{ccc}a^2+b^2&=&3\\2ab=4\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}b=\dfrac{2}{a}\\a^2-(\dfrac{2}{a})^2=2\\\end{array}\right.\\\\\\a^4-4=3*a^2\\a^4-3a^2-4=0\\\\\Delta=(-3)^2-4*1*(-4)=25=5^2\\\\a^2=4\ or \ a^2=-1 (impossible)\\\\So:\\(a=2\ and\ b=1)\ or\ (a=-2\ and\ b=-1)\\[/tex]

Roots are thus 2+i and -2-i

There is an other using a geometrical formula (formule de Moivre)

answer

4

2

Step-by-step explanation:

4x+3y=19

4x=19-3y

4x=16

x=16/4

x=4

2x+5y=20

5y=20/2x

5y= 10

y=10/5

y=2

Answer:  =360h+335

Step-by-step explanation:

Answer:

306h + 281

Step-by-step explanation:

-7 + 18(17h + 19)

-7 + 306h + 288

306h + 281

Answer:

9.32m is the height of. the tree from the ground.

Answer:

C

Step-by-step explanation:

its asking for y, on the graph, the line is placed on point 4

Answer:

Y = - 7/4 X + 31/4

Step-by-step explanation:

M = 14/-8 = - 7/4

6 = - 7/4 + B

24 = -7 + 4B

31 = 4B

B = 31/4