In the image shown, line n is a transversal cutting lines l and m.

∠3 = 2x + 30
∠5 = 3x + 1

What is the measure of ∠5?

Answer:

x = 2

Step-by-step explanation:

The 2 coordinate points have the same x- coordinate of 2

This indicates that the line passing through them is vertical with equation

x = c

Where c is the value of the x- coordinates the line passes through, thus

x = 2 ← equation of line

Answer:

1,450 & 1,500

Step-by-step explanation:

it occured 7 times each

sorry for my hand writing

Answer:

In 20 weeks they will have the same amount of money.

Step-by-step explanation:

Answer:

y=mx+b form; m is the slope

Step-by-step explanation:

So the slope would be the m

Answer: -a/b

Step-by-step explanation:

ax+by=c right?

then slope = -a/b

Answer: -16

Step-by-step explanation:

slope=rise/run

slope=2-(-4)/-3-(-2)=6/-1=-6

y=mx+b

2=(-6)-3+b

b=-16

Answer:

3_561938 you are your

Step-by-step explanation:

3AM said

Answer: Bobby’s interquartile range is 113, while Amelia’s is 179. A lower interquartile range means Bobby’s scores are closer to the median.

Step-by-step explanation:

Answer:

his rang is 113 and amelis is 179

Step-by-step explanation:

Answer:

[tex]\large\boxed{\bold{SLOPE}=\dfrac{1}{3}}[/tex]

Step-by-step explanation:

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

[tex]y=mx+b[/tex]

m - slope

b - y-intercept (0, b)

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

From the graph we have two points (0, 4) → b = 4, and (3, 5).

Calculate the slope:

[tex]m=\dfrac{5-4}{3-0}=\dfrac{1}{3}[/tex]

If you want the equation of a line, then put the value of m and b to the equation of a line:

[tex]y=\dfrac{1}{3}x+4[/tex]

Answer:

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

Step-by-step explanation:

First, find the rate of change [slope]:

[tex]\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \\ \frac{3 - 4}{9 - 12} = \frac{1}{3}[/tex]

Then plug these coordinates into the Slope-Intercept Formula instead of the Point-Slope Formula since you get it done much swiftly that way. It does not matter which ordered pair you choose:

−4 = ⅓[−12] + b

−4

[tex]\displaystyle ±0 = b \\ \\ y = \frac{1}{3}x[/tex]

_______________________________________________

−3 = ⅓[−9] + b

−3

[tex]\displaystyle ±0 = b \\ \\ y = \frac{1}{3}x[/tex]

**You see? I told you it did not matter which ordered pair you choose because you will ALWAYS get the exact same result.

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Answer:

The answer is...

Step-by-step explanation:

y = 1/3x

--or--

y = x/3

Both forms of writing are equivalent, so either choice would be correct. I hope this helps!

Answer:

32760 ways

Step-by-step explanation:

Suppose we all want to play different games, so 4 different games. At the first game there are 15 choices, at the 2nd game there are 14, the 3rd one there are 13 selections, and at the last there are only 12 options to select from. Then the total number of ways you can choose the 4 games is

15*14*13*12 = 32760 ways

There are 1,365 ways to choose four games out of the 15 available games.

Step 1

To find the number of ways you can choose four games out of the 15 available games, we use the combination formula:

[tex]\[ C(n, k) = \frac{n!}{k!(n-k)!} \][/tex]

Where  n is the total number of games (15) and  k is the number of games to choose (4).

Step 2

Plugging in the values:

[tex]\[ C(15, 4) = \frac{15!}{4!(15-4)!} \][/tex]

[tex]\[ = \frac{15!}{4! \times 11!} \][/tex]

[tex]\[ = \frac{15 \times 14 \times 13 \times 12}{4 \times 3 \times 2 \times 1} \][/tex]

[tex]\[ = \frac{32,760}{24} \][/tex]

[tex]\[ = 1,365 \][/tex]

You can choose the four games out of the 15 available games in 1,365 ways, calculated using the combination formula.

Answer:

a. After 2 weeks the first plant will be taller.

b. After 10 weeks the second plant will be taller.

c. After 4 weeks both the plant will be of the same height.

d. This is the condition for the height of the first plant is greater than that of the second plant.

Step-by-step explanation:

The first plant was 5 cm tall and the second plant was 4 cm.

Again, the first plant has grown 0.5 cm a week and the second plant has grown 0.75 cm a week.

So, the height of the first plant after W weeks will be (5 + 0.5W) cm. and the height of the second plant after W weeks will be (4 + 0.75W) cm.

a. After 2 weeks the first plant will be (5 + 2× 0.5) = 6 cm.

And after 2 weeks the second plant will be (4 + 2 × 0.75) = 5.5 cm

So, after 2 weeks the first plant will be taller.

b. After 10 weeks the first plant will be (5 + 10× 0.5) = 10 cm.

And after 10 weeks the second plant will be (4 + 10 × 0.75) = 11.5 cm

So, after 10 weeks the second plant will be taller.

c. If 5 + 0.5w = 4 + 0.75w, give w = 4 weeks, then this means that after 4 weeks both the plant will be of the same height.

d. If, 5 + 0.5w > 4 + 0.75w, then it means that this condition is for the height of the first plant will be more than the second plant. (Answer)

a. After 2 weeks: First plant: 6 cm (taller), Second plant: 5.5 cm b. After 10 weeks: First plant: 10 cm. Second plant: 11.5 cm (taller) c. Solution to 5+0.5w=4+0.75w is w=4, where both plants are equal in height (5 cm). d. Inequality 5+0.5w>4+0.75w indicates the first plant is taller before w=4 weeks.

a. To determine which plant is taller at the end of 2 weeks, let's calculate their heights:

- First plant after 2 weeks: [tex]\( 5 + 0.5 \cdot 2 = 5 + 1 = 6 \)[/tex] cm

- Second plant after 2 weeks: [tex]\( 4 + 0.75 \cdot 2 = 4 + 1.5 = 5.5 \)[/tex] cm

Since 6 cm (first plant) > 5.5 cm (second plant), the first plant is taller at the end of 2 weeks.

b. Now, let's calculate their heights after 10 weeks:

- First plant after 10 weeks: [tex]\( 5 + 0.5 \cdot 10 = 5 + 5 = 10 \) cm[/tex]

- Second plant after 10 weeks: [tex]\( 4 + 0.75 \cdot 10 = 4 + 7.5 = 11.5 \) cm[/tex]

Since 11.5 cm (second plant) > 10 cm (first plant), the second plant is taller at the end of 10 weeks.

c. The equation given is [tex]\( 5 + 0.5w = 4 + 0.75w \)[/tex]. This equation represents the point in time (number of weeks, w) when both plants will have the same height. Solving for w:

[tex]\[ 5 + 0.5w = 4 + 0.75w \][/tex]

Subtract 0.5w from both sides:

[tex]\[ 5 = 4 + 0.25w \][/tex]

Subtract 4 from both sides:

[tex]\[ 1 = 0.25w \][/tex]

Divide both sides by 0.25:

[tex]\[ w = \frac{1}{0.25} = 4 \][/tex]

Therefore, w = 4  represents the number of weeks after which both plants will have the same height, which is 5 cm.

d. The inequality [tex]\( 5 + 0.5w > 4 + 0.75w \)[/tex] represents the point in time (number of weeks, w) when the first plant's height (5 cm + 0.5w) exceeds the second plant's height (4 cm + 0.75w). Solving for w:

[tex]\[ 5 + 0.5w > 4 + 0.75w \][/tex]

Subtract 4 from both sides:

[tex]\[ 1 + 0.5w > 0.75w \][/tex]

Subtract 0.5w from both sides:

[tex]\[ 1 > 0.25w \][/tex]

Divide both sides by 0.25:

[tex]\[ w < \frac{1}{0.25} = 4 \][/tex]

Therefore, the solution to [tex]\( 5 + 0.5w > 4 + 0.75w \)[/tex] represents the number of weeks w when the first plant is taller than the second plant. This happens for ( w < 4 ) weeks.

Answer:

y=x+3

Step-by-step explanation:

y-y1=m(x-x1)

m=(y2-y1)/(x2-x1)

m=(4-3)/(1-0)

m=1/1=1

y-3=1(x-0)

y-3=x

y=x+3

Answer:

x = 8

Step-by-step explanation:

x/x+4=2/3

3x = 2x + 8

x = 8

Answer:

The ladder is approx 14.21 feet long.

Step-by-step explanation:

The base of the ladder is 7 feet from the fence, which is 2 feet from the building, so it will be 9 feet from the building.

The top of the ladder will reach the window which is 11 feet from the ground.

In this way, we get a right triangle with the ladder as the hypotenuse, that we have to find.

Let the hypotenuse be x.

Using the Pythagorean Theorem, we get;

Hence, the ladder is approx 14.21 feet long.

Answer:

-3

Step-by-step explanation:

start at the y axis where x= 0, go over one and down till your reach the next intersection of the graph, this is over one down three, or -3 for every x over

Answer:

The mean income for African American households in 2008 was $ 45,613 (Rounded to the nearest dollar)

Step-by-step explanation:

1. Given the information from the table, let's calculate the mean income for African Americans households of a certain country in 2008.

For a successful work, first of all we need to take the data from two columns : Midpoint Salary and Frequency (in  thousands):

Mean income = (10,000 * 4,491) + (30,000 * 3.844) + (50,000 * 2,500) + (70,000 * 1,498) + (90,000 * 875) + (125,000 * 994) + (175,000 * 323) + (225,000 * 72)/ Sum of all the frequency (in thousands)

Mean income = (10,000 * 4,491) + (30,000 * 3.844) + (50,000 * 2,500) + (70,000 * 1,498) + (90,000 * 875) + (125,000 * 994) + (175,000 * 323) + (225,000 * 72)/ Sum of all the frequency (in thousands)

Mean income = 665'815,000/ 14,597

Mean income = $ 45,613 (Rounded to the nearest dollar)

To calculate the mean income of African American households in 2008, add up all the income amounts and divide by the number of households. Without specific data, an exact mean cannot be given.

In order to estimate the mean income for African American households in 2008, we need to use the given data set. However, without knowing the information in the data set, a concrete answer cannot be provided.

Generally, you would add up all the income amounts for all households included in the study, and then divide by the number of households. This would provide the average, or mean, income.

Here is an example using hypothetical data:

https://brainly.com/question/15079191

#SPJ3

Answer:

4

Step-by-step explanation:

if x = 32 and y = 2, then you just have to substitute the numbers in:

[tex]\frac{32}{4 * 2}[/tex]

so,

[tex]\frac{32}{8}[/tex]

then you simplify

[tex]\frac{4}{1}[/tex]

so the answer is 4

Answer:

2

Step-by-step explanation:

Replace the variables with the real numbers

32/4 2

Multiply

4 x 3 = 12

Divide

32 / 12 = 2⅔

2⅔ ≈ 2

Answer: 2

Edit: Instead, go with D.) 4

Answer:

○ C. [tex]\displaystyle y = \frac{1}{2}x + 10[/tex]

Step-by-step explanation:

9 = ½[−2] + b

−1

[tex]\displaystyle 10 = b \\ \\ y = \frac{1}{2}x + 10[/tex]

** Perpendicular Lines have OPPOSITE MULTIPLICATIVE INVERSE RATE OF CHANGES [SLOPES], so −2 becomes ½.

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Judy needs to buy 4 packages of cookies for her party, with each package containing 6 cookies to serve her 24 friends.

Judy wants to buy some cookies for her birthday party, ensuring each of her 24 friends receives one cookie. Cookies are sold in packages of 6. To calculate the number of packages she needs, divide the total number of friends by the number of cookies in a package.

Calculation: 24 friends ÷ 6 cookies per package = 4 packages

Judy needs to buy 4 packages of cookies to have enough for each friend to have one cookie.

Answer:

a) 1 time

b) 1.75%

Step-by-step explanation:

a) The given expression is 1,000(1.0175)^2

Here,

1,000 is the principal (Present Value); (1.0175 = 1 + 0.0175) is the compounding interest rate; and 2 is the number of period (Years).

Since two means 2nd year, therefore, the interest is compounded every year. Hence, it is annual compounding interest.

If the interest rate is compounded annually, the interest will be paid one time each year or period.

b) From part a, if we break the expression,

1,000 is the principal (Present Value); (1.0175 = 1 + 0.0175) is the compounding interest rate; and 2 is the number of period (Years).

Since the interest rate is to be compounded annually, the percentage will not affect.

(1.0175 = 1 + 0.0175) in this expression, one is added to the interest to make the future compounding value.

Therefore, 0.0175 is the interest rate. If we take it to the percentage -

0.0175 x 100 = 1.75%.

Answer:

a) 1 time

b) 1.75%

Step-by-step explanation:

yes

The remainder when a cubic polynomial is divided by (x-2)(x-3) can be found using the given remainders with (x-2) and (x-3) separately, resulting in a = 3 and b = -2. Hence, the remainder is 3x - 2. Then, using the condition that f(1)=1 and f(x) is cubic with a leading coefficient of 1, we can determine the entire function and Q(x).

Given that a polynomial f(x) has remainders when divided by (x-2) and (x-3), we can establish that:

From these conditions, we derive two equations:

Solving these simultaneously gives us a = 3 and b = -2. Thus, the remainder when f(x) is divided by (x-2)(x-3) is 3x - 2.

Considering f(x) is cubic and the coefficient of x^3 is 1, f(x) = x^3 + px^2 + qx + r, and since f(1)=1, we can find out Q(x) by plugging the values a, b, and f(1) into the polynomial f(x) and comparing it with the standard cubic form. This will lead us to determine the function Q(x).

Answer:

Δ ABC ≅ Δ FDE ≅ Δ GIH

Step-by-step explanation:

Between Δ ABC and Δ FDE, given that  

(i) AB = DF  

(ii) BC = HI and DE = HI, hence, BC = DE

(iii) ∠ B = ∠ D

Hence, by Side-Angle -Side i.e. SAS criteria Δ ABC ≅ Δ FDE

Again, between Δ ABC and Δ GIH, given that  

(i) AB = GI

(ii) BC = HI and  

(iii) ∠ B = ∠ I.

Hence, by Side-Angle-Side i.e. SAS criteria Δ ABC ≅ Δ GIH.

Therefore, Δ ABC ≅ Δ FDE ≅ Δ GIH (Answer)

Answer:

a. 16 gallons

b. 32

Step-by-step explanation:

Let the full capacity of the tank is x gallons.

a. It is given that 12 gallons of water fill a tank to [tex]\frac{3}{4}[/tex] capacity.

Hence, we can write [tex]\frac{3x}{4} = 12[/tex]

⇒ [tex]x = \frac{4 \times 12}{3} = 16[/tex] gallons.

b. If the tank is filled to capacity, then there will be 16 gallons of water, with which [tex]\frac{16}{\frac{1}{2} } = 32[/tex] numbers of half-gallon bottles of be filled with water. (Answer)

Answer:

∠B = 130°

Step-by-step explanation:

The opposite angles of a parallelogram are congruent, thus

∠D = ∠B, that is

10x - 20 = 9x - 5 ( subtract 9x from both sides )

x - 20 = - 5 ( add 20 to both sides )

x = 15

Hence

∠B = 9x - 5 = (9 × 15) - 5 = 135 - 5 = 130°

Answer:

15

Step-by-step explanation:

9x-5=10x-20

X-20=-5

X=15

Answer:

The yield to maturity of the bonds is 11%

Explanation:

Price at which the bonds is currently trading = 283.30$

Face Value = $1000

Coupon rate = 2%

Hence the coupon bond rate = $1000 ×2%

= [tex]1000\times \frac{2}{100}[/tex]

=$20

Years to maturity: 20 years

Formula used:  

=[tex]\frac{(C+ (\frac{(F-P)}{n}))}{(\frac{(F+P)}{2})}[/tex]

Where C is the bond coupon rate

F is the face value

P is the price

N is the number of years

=[tex]\frac{(20 +(\frac{(1000-283.30)}{20})}{(\frac{(1000+283.30)}{2})}[/tex]

=11%

The yield to maturity of the bonds is 11%

Answer:

a)  The amount of edging needed = 7.54 meters

b)  Cost to edge the garden = $32.80

Step-by-step explanation:

a)

the amount of edging needed is basically the circumference (perimeter) of the circle. It has the formula:

[tex]C=2\pi r[/tex]

Where

C is the circumference

r is the radius

Given, diameter = 2.4, radius is HALF of it, so

r = 2.4/2 = 1.2

Now, finding circumference:

[tex]C=2\pi r\\C=2\pi (1.2)\\C=7.54[/tex]

The amount of edging needed = 7.54 meters

b)

$4.35 is needed to edge 1 meter, since we need 7.54 meters, we find the total cost by multiplying 4.35 with 7.54, so we have:

4.35*7.54 = $32.80

Cost to edge the garden = $32.80

The center of the ellipse is (10 , -4) and its vertices are (17 , -4) , (3 , -4)

Step-by-step explanation:

The standard form of the equation of an ellipse with center (h , k)  

and major axis parallel to x-axis is [tex]\frac{(x-h)^{2}}{a^{2}}+\frac{(y-k)^{2}}{b^{2}}=1[/tex]  

∵ The equation of the ellipse is [tex]\frac{(x-10)^{2}}{49}+\frac{(y+4)^{2}}{4}=1[/tex]

- Compare it by the standard form of the equation of an ellipse

∴ h = 10 and k = -4

∴ a² = 49 and b² = 4

∵ The center of the ellipse is (h , k)

∴ The center of the ellipse is (10 , -4)

∵ Its vertices are (h + a , k) and (h - a , k)

∵ a² = 49

- Take square root for both sides

∴ a = 7

∵ h = 10 and k = -4

- Substitute the values of h , a , k in the vertices above

∴ Its vertices are (10 + 7 , -4) and (10 - 7 , -4)

∴ Its vertices are (17 , -4) and (3 , -4)

The center of the ellipse is (10 , -4) and its vertices are (17 , -4) ,

(3 , -4)

Learn more:

You can learn more about the conics in brainly.com/question/4054269

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Answer:

207,50

Step-by-step explanation:

1% = 2,5

2,5x25 = 62,5 250 - 62,5 = 187,5

2,5x8 = 20

187,5+20= 207,50

Answer:

The answer is,

[tex](-1) \times \frac {1}{2} \times (-1) \times (1)[/tex]

Step-by-step explanation:

The given product is,

[tex]\frac {-4}{5} \times \frac{3}{5} \times \frac{-6}{7} \times \frac {5}{6}[/tex]

= [tex]\frac {12}{35}[/tex]

[tex]\simeq 0.3429[/tex] ---------------------(1)

Now, the first product to compare is,

[tex](-1) \times \frac {1}{4} \times (-1) \times (-1)[/tex]

= - 0.25 ----------------------------(2)

The second product to compare is,

[tex](-1) \times \frac {1}{2} \times (-1) \times (1)[/tex]

= 0.5 ------------------------(3)

The 3rd product to compare is,

[tex]\frac {-4}{2} \times \frac {3}{2} \times \frac{-2}{5} \times \frac {5}{2}[/tex]

= 3 ----------------------------(4)

The 4th product to compare is,

[tex]\frac {-3}{4} \times \frac {-3}{4} \times \frac {-1}{5} \times \frac {1}{2}[/tex]

= [tex]\frac {-9}{160}[/tex]

= 0.05625 -----------------(5)

Comparing all the values , we get (3) is closest to (1).

Hence, we get, the answer is,

[tex](-1) \times \frac {1}{2} \times (-1) \times (1)[/tex]

Answer:

-6(p+13)

Step-by-step explanation:

-5(3p+3)+9(-7+p)

-15p-15-63+9p

-15p+9p-15-63

-6p-15-63

-6p-78

simplify

-6(p+13)

Answer:

-6p-78

Step-by-step explanation:

Khan

BTW: Its 100% correct