Julia has 2 children who are 4 years apart in age. Julia is four times older than her youngest child. The sum of the ages of Julia and her 2 kids is 76 years

Answer:

Step-by-step explanation:

Since angle ABD is 133 degrees and the sum of the angles in a triangle is 180 degrees, it means that

m∠ DAB + 133 + 22 = 180

m∠ DAB = 180 - 155 = 25 degrees

Also, ∆ ADC is an isosceles triangle because two of its sides are equal. It also means that the base angles are equal. Thus,

m∠ A = m∠ B

Therefore,

m∠ A + m∠ B + angle D = 180

m∠ A + m∠ B = 180 - 22 × 2

m∠ A + m∠ B = 180 - 44 = 136

m∠ A = m∠ B = 136/2 = 68 degrees

m∠ CAB + m∠ DAB = m∠ A

Therefore,

m∠ CAB = 68 - 25 = 43 degrees

Since ∆ ABC is isosceles, then

m∠ CAB = m∠ ACB

m∠ ACB = 43 degrees

m∠ ABC = 180 - (43 × 2) = 180 - 86

m∠ ABC = 94 degrees

m∠ BCD = 68 - m∠ ACB

m∠ BCD = 68 - 43 = 25 degrees

Final answer:

By substituting x with 14 in each option, it is determined that option D, which is f(x) = x + 9, is the correct function where f(14) equals 23.

Explanation:

The student is asking to find the function for which f(14)=23. To answer this, we substitute x with 14 in each of the given options and see which one results in f(x) being equal to 23.

Substitute x=14 in f(x)=12x−20: f(14)=12(14)−20=168−20=148, which is not 23.

Substitute x=14 in f(x)=14x+23: f(14)=14(14)+23=196+23=219, which is not 23.

Substitute x=14 in f(x)=3x−7: f(14)=3(14)−7=42−7=35, which is not 23.

Substitute x=14 in f(x)=x+9: f(14)=14+9=23, which is the correct answer.

The correct function is D. f(x)=x+9.

Answer:

[tex]A = 5 {x}^{2} + 6x + 1[/tex]

Step-by-step explanation:

[tex]A = \frac{(a + b)h}{2} = \frac{(6x - 5 + 4x + 7)(x + 1)}{2} = \frac{(10x + 2)(x + 1)}{2} = \frac{2(5x + 1)(x + 1)}{2} = 5 {x}^{2} + 6x + 1[/tex]

Yo sup??

This question can be solved by applying the properties of similar triangles

the triangle with sides 5x and 20 is similar to the triangle with sides 45 and 36

therefore we can say

5x/45=20/36

x=5 units

Hope this helps

Answer: 15

Step-by-step explanation:Do 27-12 and you get 15

Answer:

15 students don't have a home computer

Step-by-step explanation:

Take the total amount of students, which is 27 and take the amount that do have home computers, which is 12, and subtract.

So, 27 - 12 = 15

The answer is 1/4. Set up a proportion to solve for x. Another way is to use unit analysis.

The answer is 1/4.

The scale factor is 1:4.

First, set up a proportion.
1 gallon/4 quarts=3 gallons/x quarts
Next, cross multiply to solve for x.
1/4-3/x
1x=3x4

Another way to solve the same problem is to use unit analysis.
First, write the unit conversion as a fraction.

One more framing of fractions and their relationship to multiplication and division: dividing by 8 is the same as multiplying by. Multiplying by is the same as dividing by 2. Multiplication and division are thus essentially the same, only having to flip the number or fraction upside-down into its reciprocal.

Use the quadratic equation to find x
x= -.0024, .00139
.001-.0024 is negative, which can't happen in real life so we know x actually equals .00139

(13x6)+89 with the power of 2 is 7999

Answer:

a) Mean = 1

b) Variance = 0.9      

Step-by-step explanation:

We are given the following in the question:

P(Success of exploration) = 0.1

Then the number of adults follows a binomial distribution, where

[tex]P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}[/tex]

All the explorations are independent.

where n is the total number of observations, x is the number of success, p is the probability of success.

Here n = 10, p = 0.1

a) Mean number of successful explorations

[tex]\mu = np = 10(0.1) = 1[/tex]

b) Variance number of successful explorations

[tex]\sigma^2 = np(1-p) = (10)(0.1)(1-0.1) = 0.9[/tex]

Answer: the length of Maria's piece of string is 45 inches.

the length of Katy's piece of string is 39 inches

Step-by-step explanation:

Let x represent the length of Maria's piece of string.

Let y represent the length of Katy's piece of string.

When they put the two pieces of string together end to end, the total length is 84inches. This means that

x + y = 84 - - - - - - - - - - - -1

Maria's string is 6 inches longer than Katy's. This means that

x = y + 6

Substituting x = y + 6 into equation 1, it becomes

y + 6 + y = 84

2y + 6 = 84

2y = 84 - 6 = 78

y = 78/2 = 39

x = y + 6 = 39 + 6

x = 45

Answer: It is not possible that two triangles that are similar and not congruent in spherical geometry.

Step-by-step explanation:

For instance, taking a circle on the sphere whose diameter is equal to the diameter of the sphere and inside is an equilateral triangle, because the sphere is perfect, if we draw a circle (longitudinal or latitudinal lines) to form a circle encompassing an equally shaped triangle at different points of the sphere will definately yield equal size.

in other words, triangles formed in a sphere must be congruent and also similar meaning having the same shape and must definately have the same size.

Therefore, it is not possible for two triangles in a sphere that are similar but not congruent.

Two triangles in sphere that are similar must be congruent.

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{-5x -10= -20}\\\\\large\text{ADD 10 to BOTH SIDES}\\\mathsf{-5x - 10 + 10 = -20 + 10}\\\\\large\text{SIMPLIFY IT!}\\\mathsf{-5x = -20 + 10}\\\mathsf{-5x = -10}\\\\\large\text{DIVIDE -5 to BOTH SIDES}\\\mathsf{\dfrac{-5x}{-5}= \dfrac{-10}{-5}}\\\\\large\text{SIMPLIFY IT!}\\\mathsf{x = \dfrac{-10}{-5}}\\\\\mathsf{x = 2}\\\\\\\huge\textbf{Therefore, your answer is: \boxed{\mathsf{Option \ A. \ 2}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

Step-by-step explanation:

In this question we are given with an equation that is -5x - 10 = -20 . And we are asked to find it's solution ( value of x ).

Solution : -

[tex] \longmapsto \qquad \: - 5x - 10 = - 20[/tex]

Step 1 : Adding 10 to both sides :

[tex] \longmapsto \qquad \: - 5x - \cancel{10 }+ \cancel{10} = - \bold{20 }+ \bold{10}[/tex]

On further calculations , We get :

[tex] \longmapsto \qquad \: - 5x = - 10[/tex]

Step 2 : Dividing with -5 on both sides :

[tex] \longmapsto \qquad \: \dfrac{ \cancel{- 5}x}{ \cancel{- 5}} = \cancel{ \dfrac{ - 10}{ - 5} }[/tex]

On further calculations , we get :

[tex] \longmapsto \qquad \: \ \: \pink{\underline{ \boxed{\frak{x = 2}}}}[/tex]

Verifying : -

Now we're verifying our answer by substituting value of x in given equation. So ,

Therefore , our answer is correct .

This does NOT represent a function.

There should only be one pair per input and output, but this graph has multiple.

Answer: the rate of the wind is 6.2 mph

Step-by-step explanation:

Let x represent the rate of the wind.

Joe traveled against the wind in a small plane for 3hours. If the speed of the plane in still air is 180 mph, then the total speed with which the plane flew is

(180 - x) mph

Distance = speed × time

Therefore, distance travelled against the wind is

3(180 - x)

= 540 - 3x - - - - - - - - - - - - - -1

The return trip with the wind took 2.8 hours.

the total speed with which the plane flew is

(180 + x) mph

Therefore, distance travelled with the wind is

2.8(180 + x)

= 504 + 2.8x - - - - - - - - - - - - - -2

Since the distance is the same, then

540 - 3x = 504 + 2.8x

540 - 504 = 2.8x + 3x

5.8x = 36

x = 36/5.8 = 6.2

Answer: d. 25

Step-by-step explanation:

Let x be the total number of students in the class.

As per given :

Number of students want ice cream party = 20% of x= 0.20x

[we divide percent by 100 to convert it into decimal.]

Actual number of students want ice cream party =5

⇒  0.20x=5

Divide both sides by 0.20 , we get

⇒ x=  [tex]\dfrac{5}{0.20}=\dfrac{500}{20}=25[/tex]

Hence, the total number of students in the class.= 25

Thus , the correct answer is d. 25

To find the difference in the total number of glue sticks that Mr. Davis and Ms. Wilson purchased, subtract the number of glue sticks each person bought from one another.

To find the difference in the total number of glue sticks that Mr. Davis and Ms. Wilson purchased, we can subtract the number of glue sticks each person bought from one another.

Mr. Davis bought 5 packages of glue sticks, and each package has a certain number of glue sticks in it.

Ms. Wilson bought 8 packages of glue sticks, and each package also has a certain number of glue sticks in it.

To find the difference, subtract the total number of glue sticks from Mr. Davis from the total number of glue sticks from Ms. Wilson.

For example, if each package of glue sticks contains 4 glue sticks, Mr. Davis purchased 5 x 4 = 20 glue sticks. Ms. Wilson purchased 8 x 4 = 32 glue sticks. The difference is 32 - 20 = 12 glue sticks.

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Answer:

Reflection about either the x- axis or y- axis.

Step-by-step explanation:

It is likely that the triangle shows a mirror image when it has been rotated at point C so that it matches ΔADC.

The triangles are congruent if the sides and angles are equal. The only way to effect the change is through a rotation.

In fact, two objects are said to be congruent if they can be transformed into another shape by translation, rotation, and reflection.

The resulting image is a distinct figure that can fit and match the other completely.

In this case, the triangle is rotated through 180⁰ so the resulting image is a reflection or mirror image.

Answer:

If two pairs of angles and the included side are congruent, the triangles are congruent.

Step-by-step explanation:

itsLearning

Answer:

The shark are fed [tex]\frac16 \ ton[/tex] of fish during the night.

Step-by-step explanation:

Given:

Weight of fish fed in the morning = [tex]\frac{2}{15}\ ton[/tex]

Also Given:

During the afternoon feeding the weight of fish fed will be 1/15 of a ton more than the fish fed during the morning.

Weight of fish fed in the afternoon = [tex]\frac{2}{15}+\frac{1}{15}=\frac{2+1}{15}=\frac{3}{15}\ ton[/tex]

Total fish fed in whole day = [tex]\frac12 \ ton[/tex]

We need to find the Weight of fish fed in the night.

Solution:

Now we can say that;

Weight of fish fed in the night can be calculated by by subtracting Weight of fish fed in the morning and Weight of fish fed in the afternoon from Total fish fed in whole day .

framing in equation form we get;

Weight of fish fed in the night = [tex]\frac{1}{2}-\frac{2}{15}-\frac{3}{15}= \frac{1}{2}-(\frac{2}{15}+\frac{3}{15})=\frac{1}{2}-\frac{2+3}{15}= \frac{1}{2}-\frac{5}{15} = \frac{1}{2}-\frac{1}{3}[/tex]

Now we will use LCM for making the denominator common we get;

Weight of fish fed in the night = [tex]\frac{1\times3}{2\times3}-\frac{1\times2}{3\times2} = \frac{3}{6}-\frac{2}{6}[/tex]

Now denominator are common so we will solve the numerators.

Weight of fish fed in the night = [tex]\frac{3-2}{6}=\frac16 \ ton[/tex]

Hence The shark are fed [tex]\frac16 \ ton[/tex] of fish during the night.

Answer:

  64

Step-by-step explanation:

10 ft is 4 times 2 1/2 ft, so the larger container has dimensions of 4 crates in every direction. That is, it will hold 4^3 crates, or 64 crates.

Answer:

So, 22 batches of cookies can the baker make.

Step-by-step explanation:

A baker has 15 cups of flour.

He sets aside 4 cups.

So, the remaining cups = 15 - 4 = 11

A cookie recipe that calls for 1/2 cup of flour.

So, x batches of cookies can the baker make with 11 cups

Use the ratio and proportional

1 : 1/2 = x : 11   ⇒ multiply both sides by 2

2 : 1 = 2x : 22

solve for x

2x = 2 * 22

x = 22

So, 22 batches of cookies can the baker make.

She can make 22 batches of cookies.

Given that there are 15 cups of flour. The baker sets aside 4 cups.

So remaining (15 - 4) = 11 cups.

Let she can make x batches.

Given each batch takes 1/2 cup.

That means she will need [tex]x\cdot\frac{1}{2}=\frac{x}{2}[/tex] cups.

According to the question:

[tex]\frac{x}{2}=11\\x=22[/tex]

So she can make 22 batches of cookies.

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Answer:

The higher you go in the good chain the lower the population.

Explanation:

In the food web, there are only a few sharks since in the food chain they are higher. Just 10% energy is retained in the tissues once the energy is moved from one trophic level to another, and the leftover power is emitted as metabolic energy.

If an animal is high up the energy ladder, the individual has less resources; thus, a few of the highest predators are present in an ecosystem.

Answer:

because there are more sharks than seals in the area

Step-by-step explanation:

Answer: Total amount invested in both accounts is $1875

Step-by-step explanation:

Let x represent the amount invested at 11%.

Let y represent the amount invested at 5%.

She invests four times as much in an account paying 11% as she does in an account paying 5%. This means that

x = 4y

The formula for determining simple interest is expressed as

I = PRT/100

Where

P represents the principal

R represents the rate of investment

T represents the time in years.

Considering the amount invested at 11%,

I = (x × 11 × 1)/100 = 0.11x

Considering the amount invested at 5%,

I = (y × 5 × 1)/100 = 0.05y

If she earns $183.75 in interest in one year from both accounts combined, it means that

0.11x + 0.05y = 183.75 - - - - - - - - - -1

Substituting x = 4y into equation 1, it becomes

0.11 × 4y + 0.05y = 183.75

0.44y + 0.05y = 183.75

0.49y = 183.75

y = 183.75/0.49

y = 375

x = 4y = 375 × 4

x = 1500

Total amount invested in both accounts is

1500 + 375 = $1875

Amy invested a total of $1875 in both simple interest accounts. She placed $375 into the account with a 5% interest rate and $1500 into the account with an 11% interest rate to achieve the total interest income of $183.75 in one year.

Amy invests money in two simple interest accounts. One account pays 11% interest, while the other pays 5%. If she puts four times as much into the 11% account as the 5% account, we can set up the following equations to find out how much she invested altogether:

We can use the formula for simple interest which is Interest = Principal × Rate × Time, where the principal is the initial amount of money invested, the rate is the interest rate, and the time is the period of time over which the money is invested.

So, the total interest earned from both accounts is:

Interest from 5% account + Interest from 11% account = $183.75

(x × 0.05 × 1) + (4x × 0.11 × 1) = $183.75

0.05x + 0.44x = $183.75

0.49x = $183.75

Now, solve for x:

0.49x = $183.75

x = $183.75 / 0.49

x = $375

Since x represents the amount invested at 5%, Amy invested $375 in the 5% account. To find the total investment:

Total investment = x + 4x

Total investment = $375 + 4(×$375)

Total investment = $375 + $1500

Total investment = $1875

Answer:

  (n -4)(n +1)^2 = n^3 -2n^2 -7n -4

Step-by-step explanation:

The least common denominator is the smallest denominator that lets you write the sum as a single fraction.

  [tex]\dfrac{n^5}{n^2+2n+1}+\dfrac{-4}{n^2-3n-4}=\dfrac{n^5}{(n+1)^2}+\dfrac{-4}{(n+1)(n-4)}\\\\=\dfrac{n^5}{(n+1)^2}\cdot\dfrac{n-4}{n-4}+\dfrac{-4}{(n+1)(n-4)}\cdot\dfrac{n+1}{n+1}=\dfrac{n^5(n-4)-4(n+1)}{(n+1)^2(n-4)}\\\\=\dfrac{n^6-4n^5-4n-4}{n^3-2n^2-7n-4}[/tex]

The least common denominator is ...

  (n-4)(n+1)^2 = n^3 -2n^2 -7n -4

After 10 s, the bucket has rotated [tex]180^{\circ}[/tex]

Step-by-step explanation:

The motion of the bucket on the water wheel is a periodic motion, which means that it repeats itself periodically. The period of the motion is the time it takes for the bucket to returns to its original position: it can be found from the graph by looking at after how much time the graph has again the same shape.

We see that if we  start from x = 0 seconds, then the graph has the same shape again (=it has completed one full cycle) at x = 20 seconds, so the period is

T = 20 s

This also means that in a time of 20 seconds, the bucket has covered a full revolution, so an angle of

[tex]\theta=360^{\circ}[/tex]

Therefore, in order to find how many degrees x the bucket has rotated in

t = 10 s

We  can use the rule of three:

[tex]\frac{\theta}{T}=\frac{x}{t}[/tex]

And solving for x, we find

[tex]x=\frac{\theta t}{T}=\frac{(360)(10)}{20}=180^{\circ}[/tex]

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Answer:

(a) and (b) are correct but (c) is not correct

Step-by-step explanation: (c) P(nA)*P(nB) + P(nA/nB)

0.20*0.30 + 0.10 = 0.060 + 0.10 = 0.160

Based on the simple interest formula, the annual interest rate paid when borrowing $960 and repaying $1170 a month later is approximately 262.5%.

This problem can be solved by using the formula for calculating simple interest, which is Interest = Principal (P) * Rate (R) * Time (T). In this case, the difference between what you paid and what you borrowed, $1170 - $960 = $210, is the interest you paid. Therefore, we can use the given information to set up the equation 210 = 960 * R * (1/12), because the time period T is 1 month, or 1/12 of a year. By solving this equation, we find that the annual interest rate is approximately 262.5%.

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Answer:

[tex]50w+100 \ge 18000[/tex]

Step-by-step explanation:

Each seven-letter word is worth 50 points. [tex]w[/tex] words are then worth [tex]w\times50=50w[/tex].

Since Sal gets 100 points for playing the game, his points total after [tex]w[/tex] words is [tex]50w +100[/tex]. If he wants to break the record, he must get, at least, 18000 points. "At least" in inequality means [tex]\ge[/tex] (just as "at most" means [tex]\le[/tex]). Then the required inequality is

[tex]50w+100 \ge 18000[/tex].

Note that the question says "18000 or more", which is why we used the [tex]\ge[/tex] symbol. If the phrase had been "more than 18000", we would have used [tex]>[/tex].

Answer:

Scully will catch up with Mulder by 7:30 PM.

Step-by-step explanation:

Consider the provided information.

Mulder leaves the office at 9​:30a.m. averaging 57mph.

Scully leaves at 10​:00​a.m., following the same path and averaging 60 mph.

Distance covered by Mulder between 9:30 AM and 10:00 AM:

[tex]\frac{57}{2}= 28.5[/tex] miles

Let t is the time taken by Scully to catch up with​ Mulder.

After leaving office Scully needs to cover extra distance of 28.5 miles because Mulder leaves the office earlier.

Therefore total distance cover by them is:

[tex]28.5+57t=60t[/tex]

[tex]28.5=60t-57t[/tex]

[tex]28.5=3t\\t=9.5[/tex]

Hence, it would take 9 hours 30 minutes to catch up Mulder.

10 am + 9 hours 30 minutes = 7:30 pm

Therefore, Scully will catch up with Mulder by 7:30 PM.

Final answer:

Scully will catch up with Mulder at 7:30 p.m. by closing the initial 28.5 miles gap at a rate of 3 mph faster than Mulder.

Explanation:

To determine when Scully will catch up with Mulder, we need to calculate the relative speeds at which the two are traveling and how long it will take for Scully to close the gap that Mulder has created by leaving earlier. Since Mulder left at 9:30 a.m. and Scully left at 10:00 a.m., Mulder has a half-hour head start. In that half-hour, traveling at 57 mph, Mulder will have covered 28.5 miles (because 0.5 hours × 57 mph = 28.5 miles).

Scully is traveling at 60 mph, which is 3 mph faster than Mulder. So, Scully closes the gap by 3 miles every hour. To catch up 28.5 miles at a rate of 3 miles per hour, Scully will need 9.5 hours (because 28.5 miles ÷ 3 mph = 9.5 hours).

We need to add this time to Scully's departure time to find out when she will catch up. Therefore, adding 9.5 hours to 10:00 a.m. yields 7:30 p.m. So, Scully will catch up with Mulder at 7:30 p.m.

The temperature at 10 pm was -1 degree.

To find the temperature at 10 pm, we need to start with the temperature at 8am. Since the temperature was 3 degrees below zero at 8 am, we can add the rise of 14 degrees by 1 am to get the temperature at 1 am. Then, we need to subtract the 12 degree drop by 10 pm to find the temperature at that time.

Starting with 8 am: -3 degrees

Add 14 degrees: -3 + 14 = 11 degrees at 1 am

Subtract 12 degrees: 11 - 12 = -1 degree at 10 pm

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