The length of the hypotenuse of a 45°-45°-90° triangle is 22. Find the length of one leg.

Answer:

The length of the painting, including the frame.

Step-by-step explanation:

We are given that a painting includes a frame of a fixed width around the painting and the total area of the painting is represented by the expression:

[tex](4+2x)(9+2x)[/tex]

We are to determine what does [tex](9+2x)[/tex] represent.

(9+2x) represents the length of the painting, including the frame because [tex](4+2x)(9+2x)[/tex] is the area of the painting including the frame. The longer side [tex](9+2x)[/tex] represents the length.

To find the length of the side of a square using area, find the square root of the area.

Side = √206 = 14.35 feet.

Answer:

309 Cm.

Step-by-step explanation:

Since the dimensions of the Large Jewelry Box is tripled, and all the sides are only added together, the answer of the question is simply the Surface Area of the Small Jewelry Box x 3.

103 x 3 OR 103 + 103 + 103 = 309.

_______________________________________

100 + 100 + 100 = 300

3 + 3 + 3 = 9

300 + 9 = 309.

Answer:

x = 17

Step-by-step explanation:

Since the triangles are similar then corresponding angles are congruent.

∠ I = ∠P ← substitute values and solve for x

3x + 4 = 72 - x ( add x to both sides )

4x + 4 = 72 ( subtract 4 from both sides )

4x = 68 ( divide both sides by 4 )

x = 17

Answer:

4. Option 3: 65.1 cm^2

5. Option 3: 3.4 inches^2

Step-by-step explanation:

Question 4 :

We can see that there is a rectangle and a half circle in the picture.

So we will find the area of both separately

For the area of rectangle

Area=length*width

=8*5

=40 cm^2

We know that the line which is representing the diameter has length 8 cm

To find the radius

r=d/2

=8/2

=4 cm

As we cannot find the area of half circle, we will find the area of full circle and will divide it in half.

So,

area= πr^2

=3.14*(4)

=3.14*16

=50.24 cm^2

Area of half circle=(Area of full circle)/2

=50.24/2

=25.12 cm^2

So the area of shape will be

Area of rectangle+area of half circle

=40 cm^2+25.12 cm^2

=65.12 cm^2

Rounding off to nearest 10 will give 65.1 cm^2

So, option 3 is the correct answer ..

Question 5 :

To find the area of shaded region we have to find the area of circle and area of square in which it is inscribed

So,

area of circle= πr^2

=3.14*(2)^2

=3.14*4

=12.56 inches^2

And to find the area of square we need one of its side, we can clearly see that the diameter of circle will be equal to the side of square

So,

Side of square=s=r*2

=2*2

=4 inches

Area of square=s^2

=4^2

=16 inches^2

To find the area of shaded region we have to subtract the area of circle from the area of square

So,

Area of Shaded Region=Area of Square-Area of Circle

=16-12.56

=3.44 inches^2

Rounding off to the nearest 10 will give 3.4 inches^2 ..

So, option 3 is the correct answer ..

Answer:

D ans

Step-by-step explanation:

equation of circle=(x-h)^2+(y-k)^2=r^2

Answer:

(x+3)2 + (y + 5)2 = 16

Step-by-step explanation:

The area of the complete circle is PI x 11^2 = 379.94 cm^2

The shaded part is 30 degrees out of 360 degrees

The shaded area = 379.94 x 30/360 = 31.66 = 31.7 cm^2.

The answer is B.

Answer:

∠6 = 80°

Step-by-step explanation:

∠5 and ∠6 form a straight angle and are supplementary, hence

∠5 + ∠6 = 180 ← ∠5 = 100° ( given ), hence

100 + ∠6 = 180 ( subtract 100 from both sides )

∠6 = 80°

Answer:

Center (7, -5) and radius=6

Step-by-step explanation:

The question is on center and radius of a circle

The general circle equation is given as (x-h)² + (y-k)²= r² where the center is (h,k) and radius is r

Given   (x-7)^2 + (y+5)^2 = 36?

            (x-7)²  + (y+5)²= 6²

h=7 and y=-5 and r=6

ANSWER

Center:(7,-5)

Radius:r=6

EXPLANATION

The given circle has equation;

[tex] {(x - 7)}^{2} + {(y + 5)}^{2} = 36[/tex]

We can rewrite this as:

[tex]{(x - 7)}^{2} + {(y - - 5)}^{2} = {6}^{2} [/tex]

Comparing this to the standard equation of the circle:

[tex]{(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} [/tex]

we have h=7,k=-5, and r=6.

Therefore the center (h,k)=(7,-5) and the radius is r=6.

Answer:

[tex]\large\boxed{x=\dfrac{-3+\sqrt{40+10\sqrt{10}}}{2}}[/tex]

Step-by-step explanation:

[tex]2\log x=3-2\log(x+3)\\\\Domain:\ x>0\ \wedge\ x+3>0\to x>-3\\\\D:x>0\\============================\\2\log x=3-2\log(x+3)\qquad\text{add}\ 2\log(x+3)\ \text{to both sides}\\\\2\log x+2\log(x+3)=3\qquad\text{divide both sides by 2}\\\\\log x+\log(x+3)=\dfrac{3}{2}\qquad\text{use}\ \log_ab+\log_ac=\log_a(bc)\\\\\log\bigg(x(x+3)\bigg)=\dfrac{3}{2}\qquad\text{use the de}\text{finition of a logarithm}\\\\x(x+3)=10^\frac{3}{2}\qquad\text{use the distributive property}[/tex]

[tex]x^2+3x=10^{1\frac{1}{2}}\\\\x^2+3x=10^{1+\frac{1}{2}}\qquad\text{use}\ a^n\cdot a^m=a^{n+m}\\\\x^2+3x=10\cdot10^\frac{1}{2}\qquad\text{use}\ \sqrt[n]{a}=a^\frac{1}{n}\\\\x^2+3x=10\sqrt{10}\qquad\text{subtract}\ 10\sqrt{10}\ \text{from both sides}\\\\x^2+3x-10\sqrt{10}=0\\\\\text{Use the quadratic formula}\\\\ax^2+bx+c=0\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\a=1,\ b=3,\ c=-10\sqrt{10}\\\\b^2-4ac=3^2-4(1)(-10\sqrt{10})=9+40\sqrt{10}\\\\x=\dfrac{-3\pm\sqrt{40+10\sqrt{10}}}{2(1)}=\dfrac{-3\pm\sqrt{40+10\sqrt{10}}}{2}\\\\x=\dfrac{-3-\sqrt{10+10\sqrt{10}}}{2}\notin D[/tex]

Step-by-step explanation:

You already know that proper fractions have numerators smaller than the denominators, such as 1/2, 2/10 or 3/4, making them equal less than 1. The improper fraction has a numerator larger than the denominator. And mixed numbers have a whole number sitting next to a proper fraction -- for example, 4 3/6 or 1 1/2. As you work on converting improper fractions, you’ll find yourself using your knowledge of division.

Write down the improper fraction -- for example, 27/6. The fraction bar means you need to divide 27 by 6.

Divide 27 by 6. The answer is 4, with a remainder of 3. Use the answer as the whole number part of the mixed number, and place the remainder over the original denominator: 4 3/6.

Reduce the fraction, if necessary. For example, 3/6 equals 1/2 (the lowest common denominator of 3 and 6 is 3, so divide both the numerator and the denominator by 3 to reduce the fraction to 1/2).

If it is a mixed number fraction:  1 1/2

1. multiple the whole number and the denominator 2 x 1 = 2

2. Add that to the numerator 2+1= 3

*Denominator stays the same

3. example answer is...  3/2

******* only mixed numbers can be converted into improper fractions

Answer:

The ratio is 15:13 (15 boys to 13 girls).

There are 28 students in all

13/28 of the students are girls.

Step-by-step explanation:

For the ratio, you simply need to put the information on the correct side of the colon [:]. The total amount of students is calculated by adding the numbers together. Finally, the fraction of girls in the class is found by adding the number of girls above the number of total students.

Answer:

Given:

Number of girls in class = 13

Number of boys in class = 15

Ratio of boys to girls,

[tex]\frac{Number\:of\:boys}{Number\:of\:girls}=\frac{15}{13}[/tex]

Ratio = 15 : 13

⇒ Total number of student = 13 + 15 = 28

Fraction of students are girls = [tex]\frac{13}{28}[/tex]

Answer: C: 27 just took the test..

Step-by-step explanation:

Answer:

Step-by-step explanation

I don't know if you are asking for a formula but Compound interest is calculated by multiplying the initial principal amount by one plus the annual interest rate raised to the number of compound periods minus one. The total initial amount of the loan is then subtracted from the resulting value.

She is as mean as my cat.

This is a simile that makes sense because the ferocity of “she” is compared to the ferocity of my cat, which is unmatched.

Answer:

Step-by-step explanation:

3x+2(x-9)=8x+x-14

3x+2-9x=8x+x-14

add3xand-9x

-6x+2=8X+x-14

8X +X=9X

-6X+2=9X-14

+6X to both sides

2=3x-14

subtract 2 on both sides

3x/-12

the answer is -8

Answer:

The actual answer is 1!

Step-by-step explanation

Answer:

a: C = $4.70d, (d ≤ 5, C = $4.70d - $1   ?:   d ≥ 5, C = $4.70d)

b.(1) dvd returned after 4 days = ($4.70 × 4) - $1 ⇒ $18.8 -$1   ⇒ $17.8

  (2) dvd returned after 7 days = $4.70 × 7  ⇒ $32.9

Answer:

$0.09

Step-by-step explanation:

1 pound = 16 ounces

So 2 pounds = 32 ounces

Write a proportion:

$2.88 / 32 oz = x / 1 oz

Solve:

x = $0.09

The price per ounce is $0.09.

Final answer:

To find the price per ounce of a 2-pound broccoli bag costing $2.88, divide the total price by the number of ounces (32), resulting in a price per ounce of $0.09.

Explanation:

To calculate the price per ounce of a 2-pound bag of broccoli that costs $2.88, you first need to know the total number of ounces in the bag. Since there are 16 ounces in 1 pound, a 2-pound bag contains 32 ounces (16 ounces/pound x 2 pounds). To find the price per ounce, you divide the total price of the bag by the total number of ounces.

Price per ounce calculation:

Total price of the bag = $2.88

Total ounces in the bag = 32 ounces

Price per ounce = Total price of the bag / Total ounces in the bag

Price per ounce = $2.88 / 32 ounces

Therefore, the price per ounce is $0.09.

Final answer:

To find the probability that Ricardo will have a quiz on Tuesday, Thursday, or Friday, we add the individual probabilities for each of those days, resulting in a total probability of 60%.

Explanation:

Probability is a measure of the likelihood of an event occurring. To find the probability that Ricardo will have a quiz on Tuesday, Thursday, or Friday, we add the individual probabilities for each of those days.

Probability of having a quiz on Tuesday = 0.2

Probability of having a quiz on Thursday = 0.1

Probability of having a quiz on Friday = 0.3

Total probability = Probability on Tuesday + Probability on Thursday + Probability on Friday = 0.2 + 0.1 + 0.3 = 0.6. Expressing this as a percentage, we get 60%.

The length of the rectangle is 6 units.

Answer:

Step-by-step explanation:

[tex]\bold{Q4}\\\text{We have}\\\text{two right triangles with legs a = 4m and b = 7m}\\\text{three rectangles}\ 7m\ \times 38m,\ 8.06m\ \times\ 38m\ \text{and}\ 4m\ \times\ 38m\\\\\text{The formula of an area of a right triangle:}\\\\A=\dfrac{ab}{2}\\\\\text{substitute:}\\\\A_1=\dfrac{(4)(7)}{2}=\dfrac{28}{2}=14\ m^2\\\\\text{The formula of an area of a rectangle}\ l\ \times w:\\\\A=lw\\\\\text{substitute:}\\\\A_2=(7)(38)=266\ m^2\\A_3=(8.06)(38)=306.28\ m^2\\A_4=(4)(38)=152\ m^2\\\\\text{The Surface Area:}[/tex]

[tex]S.A.=2A_1+A_2+A_3+A_4\\\\S.A.=2(14)+266+306.28+152=752.28\ m^2[/tex]

[tex]\bold{Q11}\\(look\ at\ the\ picture)\\\\\text{The formula of a volume of a pyramid:}\\\\V=\dfrac{1}{3}BH\\\\B-\text{area of a base}\\H-\text{height}\\\\\text{In the base we have the square. The formula of an area of a square with side a:}\\\\A=a^2\\\\\text{We have}\ a=12ft.\ \text{Substitute:}\\\\B=12^2=144\ ft^2\\\\\text{For}\ H\ \text{we need use the Pythagorean theorem:}\\\\H^2+6^2=10^2\\\\H^2+36=100\qquad\text{subtract 36 from both sides}\\\\H^2=64\to H=\sqrt{64}\\\\H=8\ m[/tex]

[tex]\text{Substitute:}\\\\V=\dfrac{1}{3}(144)(8)=(48)(8)=384\ ft^3[/tex]

To find out how much Jennifer has saved, you start by tripling the amount Matthew has saved, which is $81. Then you subtract $26 from the result to get $217. Therefore, Jennifer has saved $217.

From the problems statement, we can model Jennifer's savings using the mathematical model, where Jennifer's savings is equal to triple Matthew's savings minus $26. Given that Matthew’s savings amount to $81, we can multiply Matthew's savings by three, which equals $243. Then, to find Jennifer's savings, we subtract $26 from $243 resulting in $217. Therefore, Jennifer has $217 saved.

https://brainly.com/question/33031196

#SPJ2

Answer:

The equation of the circle is (x + 3)² + (y + 5)² = 36

Step-by-step explanation:

* Lets revise the standard form of the equation of the circle

- The center-radius form of the circle equation is in the format  

  (x – h)² + (y – k)² = r², where the center is the point (h, k) and  

  the radius is r.  

- This form of the equation is helpful, because you can easily find  

  the center and the radius.

* Now lets solve the problem

∵ The center of the circle is (-3 , -5)

∵ The center of the circle in the equation is (h , k)

∴ h = -3

∴ k = -5

∴ The equation of the circle is (x - -3)² + (y - -5)² = r²

∴ The equation is (x + 3)² + (y + 5)² = r²

* Now lets find the value of r²

∵ The length of the radius of the circle is 6 units

∴ r = 6

∴ r² = (6)² = 36

∴ The equation of the circle is (x + 3)² + (y + 5)² = 36

Answer:

x = 30517578124/29296875

Step-by-step explanation:

Solve for x:

3125 = 3 x + 1/9765625

Put each term in 3 x + 1/9765625 over the common denominator 9765625: 3 x + 1/9765625 = (29296875 x)/9765625 + 1/9765625:

3125 = (29296875 x)/9765625 + 1/9765625

(29296875 x)/9765625 + 1/9765625 = (29296875 x + 1)/9765625:

3125 = (29296875 x + 1)/9765625

3125 = (29296875 x + 1)/9765625 is equivalent to (29296875 x + 1)/9765625 = 3125:

(29296875 x + 1)/9765625 = 3125

Multiply both sides of (29296875 x + 1)/9765625 = 3125 by 9765625:

(9765625 (29296875 x + 1))/9765625 = 9765625×3125

(9765625 (29296875 x + 1))/9765625 = 9765625/9765625×(29296875 x + 1) = 29296875 x + 1:

29296875 x + 1 = 9765625×3125

9765625×3125 = 30517578125:

29296875 x + 1 = 30517578125

Subtract 1 from both sides:

29296875 x + (1 - 1) = 30517578125 - 1

1 - 1 = 0:

29296875 x = 30517578125 - 1

30517578125 - 1 = 30517578124:

29296875 x = 30517578124

Divide both sides of 29296875 x = 30517578124 by 29296875:

(29296875 x)/29296875 = 30517578124/29296875

29296875/29296875 = 1:

Answer:  x = 30517578124/29296875

For this case:

We rewrite the equation as:

[tex]5 ^ {- 10 + 3x} = 3.125[/tex]

We find ln on both sides of the equation to remove the exponent variable:

[tex]ln (5 ^ {- 10 + 3x}) = ln (3,125)[/tex]

Applying properties of logarithm we have:

[tex](-10 + 3x) ln (5) = ln (3.125)[/tex]

We apply distributive property:

[tex]-10ln (5) + 3xln (5) = ln (3,125)[/tex]

We clear the value of "x":

[tex]3xln (5) = ln (3,125) + 10ln (5)\\x = \frac {ln (3.125)} {3ln (5)} + \frac {10ln (5)} {3ln (5)}\\x = \frac {ln (3.125)} {3ln (5)} + \frac {10} {3}[/tex]

ANswer:

[tex]x = \frac {ln (3.125)} {3ln (5)} + \frac {10} {3}[/tex]

Answer:

Step-by-step explanation:

ΔYVH and ΔYBA are similar. Therefore the corresponding sides are in proportion:

[tex]\dfrac{YH}{YA}=\dfrac{YV}{YB}[/tex]

We have

[tex]YH=x,\ YA=17,\ YV=16+22=38,\ YB=16[/tex]

Substitute:

[tex]\dfrac{x}{17}=\dfrac{38}{16}[/tex]            cross multiply

[tex]16x=(17)(38)[/tex]              divdie both sides by 16

[tex]x=\dfrac{(17)(38)}{16}\\\\x=40.375[/tex]

Answer:

-68 could  be a potential outlier, but other than that, the data seems pretty steady.

The association between the altitude and the temperature is the higher up in the atmosphere you are, the colder it gets.

Answer:

$4,100

Step-by-step explanation:

Final answer:

The dealership's profit from selling the two vehicles, after considering a 15% markup on the four-door sedan and a 25% markup on the trade-in vehicle, was $4,100.

Explanation:

To calculate the dealership's profit on the two vehicles, we need to consider the markup on each transaction.

Profit from the Four-Door Sedan

The dealership purchased the sedan for $19,000 and sold it at a 15% markup. The markup is calculated as 15% of the purchase price:

Markup on sedan = 0.15 times $19,000 = $2,850

The selling price of the sedan would thus be:

Sell price of sedan = Purchase price + Markup = $19,000 + $2,850 = $21,850

Profit from the Trade-In Vehicle

After trading in the first car and effectively reducing its cost by $5,000, the dealership then sells the trade-in at a 25% markup. First, we calculate the trade-in's sale price:

Trade-in value = $5,000

Markup on trade-in = 0.25 times $5,000 = $1,250

Sell price of trade-in = Trade-in value + Markup = $5,000 + $1,250 = $6,250

Total Profit

The total profit is the sum of profits from both vehicles:

Total profit = Markup on sedan + Markup on trade-in = $2,850 + $1,250 = $4,100

Therefore, the dealership's profit on these two vehicles was $4,100.

Answer:

Step-by-step explanation:

√(-245)=√(49×5×i^2)=7√5 i=0+7√5 i

Answer:

[tex]\sqrt{-245}[/tex]  in the form a + bi is [tex]0+7\sqrt{5}i[/tex]

Step-by-step explanation:

We know that

       [tex]i=\sqrt{-1}[/tex]

We need to find  [tex]\sqrt{-245}[/tex]

     [tex]\sqrt{-245}=\sqrt{-1}\times \sqrt{245}=i\sqrt{245}=i\sqrt{49\times 5}=i\times 7\sqrt{5}[/tex]

[tex]\sqrt{-245}[/tex]  in the form a + bi is [tex]0+7\sqrt{5}i[/tex]

"Dr. Paul Opler states, "I have some information on butterfly weights but not exact weights for the largest and smallest butterflies. However, I can make pretty good guesses. I have weights ranging from 0.3 gram for a large swallowtail to 0.04 gram for a small butterfly called the elf."

from the intern3t

Answer:

It would most likely 0.02 - 0.03 because if u think about it there wings don't weight more than about 0.1  and if the wings can hold up the body of the butterfly then i would assume that it would weight between 0.02 - 0.03.

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\dfrac{2}{3}(n-6)=5n-43\qquad\text{multiply both sides by 3}\\\\2(n-6)=15n-129\qquad\text{use the distributive property}\\\\2n-12=15n-129\qquad\text{add 12 to both sides}\\\\2n=15n-117\qquad\text{subtract}\ 15n\ \text{from both sides}\\\\-13n=-117\qquad\text{divide both sides by (-13)}\\\\n=9[/tex]

The equation 2/3(n-6) = 5n - 43 is solved by distributing, combining like terms, and isolating the variable n to find that n = 9.

To solve the equation 2/3(n-6) = 5n - 43, first distribute the 2/3 across the parentheses: 2/3n - 2/3  6 = 5n - 43. This simplifies to 2/3n - 4 = 5n - 43. Next, add 4 to both sides to get 2/3n = 5n - 39. Multiply everything by 3 to clear the fraction: 2n = 15n - 117. Now, we will subtract 15n from both sides to get -13n = -117. Finally, divide by -13 to find n: n = 9. This is the value of n that solves the original equation.