4th Grade
What fraction does x represent?

Answer: First option 120 sq.in

Solution:

Perimeter of the base of the prism: p=20"=20 in

Height of the prism: h=6"=6 in

Lateral area of the prism: Al=?

Al=p*h

Replacing the known values in the formula above:

Al=(20 in)*(6 in)

Al=120 sq.in

3. AB ~= CE

4. CE ~= AC

5. Definition of isosceles triangle

6. Transitive Property of Congruence

Find how far the car can travel on one gallon of gas, by dividing total miles by number of gallons:

105 miles / 7 gallons = 15 miles per gallon.

Now multiply that by the number of gallons to find total miles:

15 miles per gallon x 9 gallons = 135 total miles.

Answer:

Unit rate of driving (speed) is 50 miles per hour

Step-by-step explanation:

Michael drove 350 miles in 7hrs

Speed = Distance ÷ time

Speed= 350 miles ÷ 7 hours = 50 miles per hour.

1.  Consider the expression [tex]-5a^4(2a^2+4)=-10a^6-20a^4.[/tex]

Start with left side and use dustributive property :

[tex]-5a^4(2a^2+4)=-5a^4\cdot 2a^2-5a^4\cdot 4=-10a^6-20a^4.[/tex]

This option is true.

2. Consider the expression [tex]-4x^2(2x^2+5)=-8x^4-20x^2.[/tex]

Start with left side and use dustributive property :

[tex]-4x^2(2x^2+5)=-4x^2\cdot 2x^2-4x^2\cdot 5=-8x^4-20x^2.[/tex]

This option is true.

3. Consider the expression [tex]-6y^4(4y^2+2)=-24y^8-12y^4.[/tex]

Start with left side and use dustributive property :

[tex]-6y^4(4y^2+2)=-6y^4\cdot 4y^2-6y^4\cdot 2=-24y^6-12y^4\neq -24y^8-12y^4.[/tex]

This option is false.

4. Consider the expression [tex]-4b^3(5b^2+3)=-20b^6-12b^3.[/tex]

Start with left side and use dustributive property :

[tex]-4b^3(5b^2+3)=-4b^3\cdot 5b^2-4b^3\cdot 3=-20b^5-12b^3\neq -20b^6-12b^3.[/tex]

This option is false.

Answer: A, B - true, C, D - false.

Answer

−5a⁴(2a²+4)=−10a⁶−20a⁴ is correct.

−4x²(2x²+5)=−8x⁴−20x²  is correct.

−6y⁴(4y²+2)=−24y⁸−12y⁴ is NOT correct.

−4b³(5b²+3)=−20b⁶−12b³  is NOT correct.

Explanation

Equation 1

−5a⁴(2a²+4)=−10a⁶−20a²    ⇒ −5a⁴(2a²+4) = ( −5a⁴×2a²)+ ( −5a⁴×4)

                                                                      = -10a⁶ - 20a⁴

−5a⁴(2a²+4)=−10a⁶−20a² is correct

Equation 2

−4x²(2x²+5)=−8x⁴−20x²        ⇒   −4x²(2x²+5) = (-4x²×2x²) + (-4x²×5)

                                                                           = -8x⁴ - 20x²

−4x²(2x²+5)=−8x⁴−20x²  is correct.

Equation 3

−6y⁴(4y²+2)=−24y⁸−12y⁴     ⇒ −6y⁴(4y²+2) =  (−6y⁴×4y²) + (-6y⁴×2)

                                                                       = -24y⁶ - 12y⁴

−6y⁴(4y²+2)=−24y⁸−12y⁴ is NOT correct.

Equation 4

−4b³(5b²+3)=−20b⁶−12b³       ⇒ −4b³(5b²+3) = (−4b³×5b²) + (-4b³×3)

                                                                           = -20b⁵ - 12b³

−4b³(5b²+3)=−20b⁶−12b³  is NOT correct.                                        

Answer:

5.13 feet

Step-by-step explanation:

Engine is driving the propeller with a radius of 8 feet and its centerline 13 feet above the ground.

And the speed is 700 revolutions per minute, the height of one propeller tip as a function of time is given by:

[tex]h=13+8 \sin(700t)[/tex]

We have been asked to find the value of height, 'h', when t=4 minutes.

Plugging the value of time, 't', in the equation, we already know that we need to use degrees (not radians) we get:

[tex]h=13+8 \sin (700 \times 4)[/tex]

[tex]h=13+8 \sin (2800)[/tex]

[tex]h=13+8 \times (-0.984)[/tex]

[tex]h=13+(-7.872)[/tex]

[tex]h=13-7.872[/tex]

[tex]h=5.128\approx 5.13[/tex]

So the height of one propeller tip at t=4 minutes is 5.13 feet.

I think the answer is 2.7 hours

Using the formula Time = Distance ÷ Speed, we find that the driver would spend approximately 1.67 hours on the first 100 miles and 0.91 hours on the last 50 miles. Adding these two times gives a total travel time of approximately 2.58 hours.

The first thing you need to do is calculate the time spent in each part of the trip. To calculate time, we use the formula Time = Distance ÷ Speed. For the first 100 miles at 60 mi/h, it takes: Time = 100 miles ÷ 60 mi/h = 1.67 hours. Moving on to the next 50 miles at 55 mi/h, it takes: Time = 50 miles ÷ 55 mi/h = 0.91 hours.

Adding these two times together gives us the total time for the trip: 1.67 hours + 0.91 hours = 2.58 hours. So, the driver would take approximately 2.58 hours to reach his destination if he traveled 100 miles at 60 mi/h and the remaining 50 miles at 55 mi/h.

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Note that RT is the whole line segment, and RS and ST are parts of it

RS = 6y + 5

ST = 2y - 3

RT = 12y - 14

Set the equation

RS + ST = RT

(6y + 5) + (2y - 3) = 12y - 14

Simplify. Combine like terms

6y + 2y + 5 - 3 = 12y - 14

(6y + 2y) + (5 - 3) = 12y - 14

8y + 2 = 12y - 14

Note the equal sign. What you do to one side, you do to the other. Isolate the variable (y). Subtract 12y from both sides, and 2 from both sides.

8y (-12y) + 2 (-2) = 12y (-12y) - 14 (-2)

8y - 12y = -14 - 2

Simplify. Combine like terms

(8y - 12y) = (-14 - 2)

-4y = -16

Isolate the y. Divide -4 from both sides

-4y/-4 = -16/-4

y = (-16)/-4

y = 4

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4 is your answer for y.

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hope this helps

y = - [tex]\frac{3}{4}[/tex] x  - [tex]\frac{7}{2}[/tex]

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 6, 1 ) and (x₂, y₂ ) = (2, - 5 )

m = [tex]\frac{-5-1}{2+6}[/tex] = [tex]\frac{-6}{8}[/tex] = - [tex]\frac{3}{4}[/tex]

the partial equation is

y = - [tex]\frac{3}{4}[/tex] x + c

to find c substitute either of the 2 given points into the partial equation

using (- 6, 1 ), then

1 = [tex]\frac{9}{2}[/tex] + c ⇒ c = 1 - [tex]\frac{9}{2}[/tex] = - [tex]\frac{7}{2}[/tex]

y = - [tex]\frac{3}{4}[/tex] x - [tex]\frac{7}{2}[/tex] ← equation of line

The length of CD is -9 to 7 = 16 units long

CE is 1/4 of that length, so 16 x 1/4 = 4 units long.

Add 4 to C: -9 + 4 = -5

Point E would be located at -5.

Final answer:

The value of an expression will be negative when the sum of the two numbers subtracted from a given first number is greater than the initial number itself, resulting in a negative outcome after applying the appropriate rules for addition and subtraction.

Explanation:

The value of an expression involving the subtraction of two numbers from a given first number will be negative under specific conditions. When the combination of the two numbers to be subtracted is larger than the first number, the result will be negative. To understand this, let's consider the basic rules of addition and subtraction with positive and negative numbers:

In subtraction, we change the sign of the number being subtracted and then apply the rules of addition:

Therefore, to have a negative result, the magnitude of the sum of the two numbers being subtracted should exceed the first number and, reflecting the sign rules, should result in a negative value. For instance, if the first number is 1 and the two numbers to subtract are 3 and 5, the expression would be 1 - (3 + 5) = 1 - 8 = -7, resulting in a negative value.

The question centers on mathematics, where we calculate the number of cookies Tovah needs and explore probability and trading scenarios related to assorted cookies and resource allocation.

The subject of this question is Mathematics, particularly focusing on basic arithmetic, probability, and problem-solving. Tovah needs a total of 700 cookies and already has 300 cookies. To determine how many more cookies Tovah needs, we can subtract the number she already has from the total number needed: 700 - 300 = 400. Hence, she needs to obtain 400 more cookies.

Additionally, when discussing assorted cookies, we can delve into probability and combinatorics. For instance, if we consider a scenario with cookies containing chocolate, nuts, or both, we can calculate the probability that a certain combination is selected. This involves understanding percentages, probability trees, and independence of events.

Lastly, we can explore resource allocation and trading as seen in examples where individuals barter items like chocolate bars or Halloween candy. This introduces concepts like gains from trade and distribution of resources, which are essential to economic mathematics.

Answer: 11A + 8B

Step-by-step explanation:

Answer:

The required number of bowls are 5.  

Step-by-step explanation:

Given : A sugar bowl holds 237 grams. You have a one kilogram bag of sugar.

To find : Estimate how many bowls of sugar you can fill from the bag?

Solution :

1 bowl can hold 237 gram of sugar.

We have, 1 kg of sugar or 1000 gram of sugar.                

According to question,

237 gram of sugar can hold in 1 bowl.

So, 1 gram of sugar can hold in [tex]\frac{1}{237}[/tex] bowl.

1000 gram of sugar can hold in [tex]\frac{1000}{237}[/tex] bowl.      

1000 gram of sugar can hold in [tex]4.21[/tex] bowl.  

Which means, The required number of bowls are 5.

As 4 bowls have [tex]237\times 4=948[/tex] grams of sugar.

Sugar left is 1000-948=52 grams

That 52 grams is filled into 5th bowl.                  

ANSWER

The correct answers are option B and C

EXPLANATION

A linear function with slope [tex]m=1[/tex] and y - intercept [tex]0[/tex] has equation, [tex]f(x)=x[/tex]

Option A

[tex]f(-1)=-1[/tex]

[tex]g(-1)=(-1)^2=1[/tex]

Therefore [tex]f(-1) \ne g(-1)[/tex]

Option B

[tex]f(1)=1[/tex]

[tex]g(1)=(1)^2=1[/tex]

Therefore [tex]f(1) = g(1)[/tex]

Option C

[tex]f(0.5)=0.5[/tex]

[tex]g(0.5)=(0.5)^2=0.25[/tex]

Therefore [tex]f(x) > g(x)[/tex]

on [tex](0,1)[/tex] See graph also.

Option D

At y-intercept, [tex]x=0[/tex]

This implies that,

[tex]f(0)=0[/tex]

[tex]g(0)=(0)^2=0[/tex]

Therefore g(x) does not have a greater y-intercept.

The function f(x) with a slope of 1 and a y-intercept of 0 is compared with the quadratic function g(x)=x^2. f(1) is equal to g(1) and f(x) is greater than g(x) on the interval (0,1).

The function g(x)=x^2 is a quadratic function, and the function f(x) with a slope of 1 and a y-intercept of 0 is a linear function. Let's evaluate the given statements:

In summary, the true statements are: f(1) is equal to g(1), and f(x) is greater than g(x) on the interval (0,1).

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My answer for 0.79 x 3.7 is 2.923. It is 2.923 because when you do the problem on paper that is what you get. Also not to be rude or nothing im good at math.

[tex]Solution, 0.79\cdot \:3.7=2.923[/tex]

[tex]Steps:[/tex]

[tex]\mathrm{Multiply\:without\:the\:decimal\:points,\:then\:put\:the\:decimal\:point\:in\:the\:answer}, 79\cdot \:37=2923[/tex]

[tex]79\cdot \:37, \mathrm{Line\:up\:the\:numbers}, \begin{matrix}\space\space&7&9\\ \mathrm{x}&3&7\end{matrix}[/tex]

[tex]\mathrm{Multiply\:the\:top\:number\:by\:the\:bolded\:digit\:of\:the\:bottom\:number}, \begin{matrix}\space\space&\textbf{7}&\textbf{9}\\ \mathrm{x}&3&\textbf{7}\end{matrix}[/tex]

[tex]\mathrm{Mutliply\:the\:bold\:numbers}:\quad \:9\cdot \:7=63[/tex][tex]\mathrm{Carry\:}6\mathrm{\:to\:the\:column\:on\:the\:left\:and\:write\:}3\mathrm{\:in\:the\:result\:line}[/tex][tex]\frac{\begin{matrix}\space\space&6&\space\space\\ \space\space&7&\textbf{9}\\ \mathrm{x}&3&\textbf{7}\end{matrix}}{\begin{matrix}\space\space&\space\space&3\end{matrix}}[/tex]

[tex]\mathrm{Add\:the\:carried\:number\:to\:the\:multiplication}:\quad \:6+7\cdot \:7=55[/tex], [tex]\mathrm{Carry\:}5\mathrm{\:to\:the\:column\:on\:the\:left\:and\:write\:}5\mathrm{\:in\:the\:result\:line}, \frac{\begin{matrix}\space\space&5&\textbf{6}&\space\space\\ \space\space&\space\space&\textbf{7}&9\\ \mathrm{x}&\space\space&3&\textbf{7}\end{matrix}}{\begin{matrix}\space\space&\space\space&5&3\end{matrix}}[/tex]

[tex]\mathrm{Add\:the\:carried\:digit,\:}5\mathrm{,\:to\:the\:result}, \frac{\begin{matrix}\space\space&5&6&\space\space\\ \space\space&\space\space&7&9\\ \mathrm{x}&\space\space&3&7\end{matrix}}{\begin{matrix}\space\space&5&5&3\end{matrix}}[/tex]

[tex]\frac{\begin{matrix}\space\space&\space\space&\textbf{7}&\textbf{9}\\ \space\space&\mathrm{x}&\textbf{3}&7\end{matrix}}{\begin{matrix}\space\space&5&5&3\end{matrix}}[/tex]

[tex]\frac{\begin{matrix}\space\space&\space\space&2&\space\space\\ \space\space&\space\space&7&\textbf{9}\\ \space\space&\mathrm{x}&\textbf{3}&7\end{matrix}}{\begin{matrix}\space\space&5&5&3\\ \space\space&\space\space&7&\space\space\end{matrix}}[/tex]

[tex]\frac{\begin{matrix}\space\space&2&\textbf{2}&\space\space\\ \space\space&\space\space&\textbf{7}&9\\ \mathrm{x}&\space\space&\textbf{3}&7\end{matrix}}{\begin{matrix}\space\space&5&5&3\\ \space\space&3&7&\space\space\end{matrix}}[/tex]

[tex]\frac{\begin{matrix}\space\space&2&2&\space\space\\ \space\space&\space\space&7&9\\ \mathrm{x}&\space\space&3&7\end{matrix}}{\begin{matrix}\space\space&5&5&3\\ 2&3&7&\space\space\end{matrix}}[/tex]

[tex]\frac{\begin{matrix}\space\space&\space\space&7&9\\ \space\space&\mathrm{x}&3&7\end{matrix}}{\begin{matrix}0&5&5&3\\ 2&3&7&0\end{matrix}}[/tex]

553+2370=2923, =2.923

ITS 4!! THE ANSWE IS 4!!! BRAINLIEST?!?!

Answer:

42.7716% of the variation in the number of bags of trash collected can be explained by differences in the number of volunteers.

Step-by-step explanation:

The correlation coefficient (r) between the number of volunteers x and the number of bags of trash collected y is 0.654

For finding the percent of the variation in one variable explained by the other variable, we just need to take square of the correlation coefficient.

Here,  [tex]r=0.654[/tex]

So,  [tex]r^2 = (0.654)^2 = 0.427716[/tex]

Now, for converting it into percentage, we will multiply it by 100.

So, [tex]0.427716*100\% = 42.7716 \%[/tex]

Thus, 42.7716% of the variation in the number of bags of trash collected can be explained by differences in the number of volunteers.

Final answer:

About 42.8% of the variation in the bags of trash collected can be attributed to the number of volunteers, as indicated by the squared correlation coefficient (0.654²).

Explanation:

The correlation coefficient (r) measures the strength and direction of a linear relationship between two variables. When squared to calculate the coefficient of determination (r²), it represents the proportion of the variance in the dependent variable that is predictable from the independent variable. In the given scenario, with a correlation coefficient of 0.654, the coefficient of determination would be 0.654², which calculates to approximately 42.8%. This percentage indicates that about 42.8% of the variation in the number of bags of trash collected (y) can be explained by the variation in the number of volunteers (x).

answer is (-7,2)

y = -x -5

y= x+9

Both equations have y on the left hand side

So we equate both equations

We replace -x-5 for  y in the second equation

-x -5 = x+9

Subtract x on both sides

-2x -5 = 9

Now add 5 on both sides

-2x = 14

Divide by -2 from both sides

x = -7

Now plug in -7 for x in the first equation

y = -x -5

y = -(-7)  -5= 7-5 = 2

So answer is (-7,2)

1. You have the following system of equations:

[tex]\left \{ {{y=-x-5} \atop {y=x+9}} \right.[/tex]

2. Therefore, you have that [tex]y=y[/tex], then:

[tex]-x-5=x+9[/tex]

3. Solve for [tex]x[/tex]:

[tex]-5-9=x+x\\2x=-14\\x=-7[/tex]

3. Now, substitute this value into one the original equations:

[tex]y=x+9\\y=-7+9\\y=2[/tex]

The answer is: (-7,2)

I think that the answer is the 4th triangle hope this helped.

That would be triangle DEF and the last one (M - -)

The corresponding sides  compared with triangle ABC are not in same ratio

The answers to your question are,

12,001, 12,562, 12,999

-Mabel <3

12,001, 12,562, 12,999 .

Is your answers, hope this helps.

~hEcKiNsHoBe

Given

One month julia collected 8.4 gallons of rainwater.

she used 5.2 gallons of rainwater to water her garden

6.5 gallons of rainwater to water flowers

Find out how much was the supply of rainwater increased or decreased by the end of the month.

To proof

As given in the question

One month julia collected 8.4 gallons of rainwater

she used 5.2 gallons of rainwater to water her garden and 6.5 gallons of rainwater to water flowers

Total water she used in the month = 5.2 gallons + 6.5gallons

                                                         = 11.7 gallons

Let the supply of rainwater increased or decreased by the end of the month

be x .

Than the equation become in the form

x + 8.4 = 11.7

x = 3.3 gallons

Therefore the supply of rainwater increased or decreased by the end of the month is 3.3 gallons.

Hence proved

Total rainwater collected by Julia = 8.4 gallons

Water used for watering garden = 5.2 gallons

Water used for watering flowers = 6.5 gallons

Hence, total water used by Julia = [tex]5.2+6.5=11.7[/tex] gallons

11.7 gallons were used and only 8.4 gallons were collected , so supply of rainwater decreased by [tex]11.7-8.4=3.3[/tex] gallons

The method would be the best to ensure they select the "most talented" soccer players is They watch the players during tryouts and then put them on a list in order from the most skilled to the least skilled and then select the top six from the list.

The correct option is (A).

A. This method involves observing the players during tryouts and then ranking them from the most skilled to the least skilled. By selecting the top six players from this ranked list, the team is more likely to pick the most talented individuals based on their performance and skills demonstrated during the tryouts.

Option B (selecting the first six that show up) may not necessarily guarantee selecting the most talented players as eagerness to show up early does not always correlate with soccer skills.

Option C (selecting randomly from a hat) is not ideal because it does not take into account the players' actual skills and performance during tryouts. It relies solely on chance.

Option D (selecting the top three and bottom three) may overlook potentially talented players who fall in the middle range. Additionally, selecting the bottom three solely based on being the least skilled may not be fair or accurate.

Therefore, option A is the most suitable method for ensuring the selection of the "most talented" soccer players.

complete question given below:

A local club team is holding tryouts for six spots on the soccer team. Since there is not much time before a very important tournament they need to select the best players. Which method would be the best to ensure they select the "most talented" soccer players?

A. They watch the players during tryouts and then put them on a list in order from the most skilled to the least skilled and then select the top six from the list.

B. The first day of tryouts they select the first six that show up as they figure those are the most eager for a spot.

C. They place all of the names of the people trying out in a hat and theselect six out of the hat. Those are the ones that are chosen.

D. They watch the players during tryouts and then put them on a list in order from the most skilled to the least skilled and then select the top three and the bottom three from the list.

Utilize open tryouts, structured evaluations, scouting, fitness assessments, game simulations, background checks, objective evaluation, expert consultation, feedback, and review.

To ensure the selection of the most talented soccer players for the local club team, the following method can be adopted:

1. **Open Tryouts**: Organize open tryouts where any interested player can participate. This allows for a wide pool of talent to be assessed.

2. **Structured Evaluation**: Develop a structured evaluation system that includes various aspects of soccer skills such as dribbling, passing, shooting, defending, and game intelligence. Each player should be assessed on these criteria.

3. **Scouting**: Utilize scouts who have a keen eye for talent to observe players in local leagues, school teams, or other relevant competitions. They can provide insights into players who may not have attended the tryouts.

4. **Physical Fitness Assessment**: Soccer requires a good level of physical fitness. Conduct physical fitness assessments to gauge players' endurance, speed, agility, and strength.

5. **Game Simulations**: Organize scrimmages or small-sided games during tryouts to see how players perform in real-game situations. This can reveal their decision-making abilities, teamwork skills, and adaptability.

6. **Background Checks**: Consider players' past performances, achievements, and behavioral aspects. Look for players who demonstrate dedication, discipline, and a positive attitude.

7. **Objective Evaluation**: Ensure that the selection process is fair and transparent, with scores and assessments being recorded objectively. Avoid biases based on personal preferences or relationships.

8. **Consult Coaches and Experts**: Involve experienced coaches or soccer experts in the selection process. They can provide valuable insights and perspectives on players' potential and suitability for the team.

9. **Feedback and Review**: Provide feedback to players after the tryouts, highlighting areas of improvement and offering guidance for future development. Additionally, periodically review the selected players' performance to ensure they continue to meet the team's standards.

By combining these methods, the local club team can maximize the chances of selecting the most talented soccer players for their upcoming tournament.

By simplifying both sides of the equation, then isolating the variable.

x = 1

Answer:

x=1

Step-by-step explanation:

1. Move the terms: move the variable to the left hand side and change it sign

2. Move the constant to the right hand side and change its sign

3. Collect like terms

4. Calculate the difference

5. Divide both sides of the equation by -3, therefore x = 1

please mark brainliest! :)

The difference would be:

1,517.