a ladder 25 feet long is leaning against the wall of a building. initially, the foot of the ladder is 7 feet from the wall. the foot of the ladder begins to slide at a rate of 2 ft/sec, causing the top of the ladder to slide down the wall. the location of the foot of the ladder, its x coordinate, at time t seconds is given by x(t)

Number 7 is not a factor of the number 49t + 30.

A factor is a number which divides another number by itself and leaves no remainder.

In other sayings, if multiplying 2 whole numbers yields a product, the numbers being multiplied are factors of a product because of product is divisible by them.

For the given problem,

The equation is given as 49t + 30

For any value of t the number (49t will get completely divide by 7  leaving no remainder behind).

But 30 is not the factor of 7 as it will leave the remainder 2.

Thus, adding number 30 with 49t will result in a number which is not completely divisible by 7.

Thus, 7 is not a factor of number 49t + 30.

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If a car with an initial speed of 36 km/h accelerates at a uniform rate of 2.4 m/s^2 for 2.5 seconds. The final speed is 16m/s and displacement of the car during this time is 32.5m.

23.7 km/h = 10 m/s

Using this formula to find the speed  vf = vi + a(Dt) for the final speed

Where:

Initial speed = 10 m/s

Acceleration = 2.4 m/s2

Time = 2.5 s

Let plug in the formula

vf = (10 m/s) + (2.4 m/s2)(2.5 s)

vf = 16m/s  fast car

Now, let's find or determine  the displacement

Using this  formula  Dx = vi(Dt) + 1/2a(Dt)2

Let plug in the formula

Dx = (10 m/s)(2.5 s) + 1/2(2.4 m/s2)(2.5 s)²

Dx = 32.5 m

Therefore we can conclude that the speed is 16m/s and the displacement is  32.5 m.

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Answer:

20%

Step-by-step explanation:

10% of 55 is 5.5 so 20% is 11 which is how much extra he paid

The integer solutions for the given system of inequalities  6-4b>0 , 3b-1>0  is b=1 .

In the question ,

the system of inequalities is given as

6-4b>0

3b-1>0

Solving the first inequality ,

6-4b>0

simplifying further , we get

6>4b

4b<6

b<6/4

b<3/2

b<1.5     ....(i)

Solving the second inequality ,

3b-1>0

simplifying further , we get

3b>1

b>1/3

b>0.3      ...(ii)

Combining the equation(i) and equation(ii) from above , we get ,

0.3 < b < 1.5

So, the integer solutions lying between 0.3 < b < 1.5 is b=1 .

Therefore , the integer solutions for the given system of inequalities is b=1 .

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Answer:

(8,4) 8 is on the x axis and 4 is on the y axis

When working with unknowable numbers, we can simplify equations by using the distributive property. If the equation be 10x² - (9x + 4x²) + 7 + (5x - 8) then we get 6x² - 4x - 1.

The distributive property of binary operations in mathematics generalizes the distributive law, which states that in elementary algebra, equality is always true.

Let the equation be 10x² - (9x + 4x²) + 7 + (5x - 8)

Apply rule: a +(b + c) = a + b + c

7 + (5x - 8) = 7 + 5x - 8

= 10 x²- (9 x + 4 x²) + 7 + 5x - 8

simplifying the above equation, we get

= -(9x + 4x²) + 10x² + 5x + 7 - 8

Subtract the numbers: 7 - 8 = -1

= -(9x + 4x²) + 10x² + 5x - 1

Apply the distributive law: -(a + b) = -a - b = 0

-(9x + 4x²) = - 9x - 4x²

= -9x - 4x² + 10x² + 5x - 1

Add similar elements:

-4x² + 10x² = 6x² = -9x + 6x² + 5x - 1

simplifying the above equation, we get

= 6x² - 9x + 5x - 1

Add similar elements: -9x + 5x = -4x

= 6x² - 4x - 1

Therefore, by simplifying the equation, we get 6x² - 4x - 1.

The complete question is:

Simplify 10x² - (9x + 4x²) + 7 + (5x - 8)

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[tex] \frac{7}{10} x - 2 = \frac{2}{5} x + \frac{8}{3} \\ \frac{7}{10} x - \frac{4}{5} x = \frac{8}{3} + 2 \\ \frac{3}{10} x = \frac{14}{3} \\ x = \frac{14}{3} \div \frac{3}{10} \\ x = \frac{14}{3} \times \frac{10}{3} \\ x = \frac{140}{3} [/tex]

[tex]y = ( \frac{7}{10})( \frac{140}{3} ) - 2 \\ y = \frac{980}{30} - 2 \\ y = \frac{98}{3} - 2 \\ y = \frac{196}{3} - \frac{6}{3} \\ y = \frac{190}{3} \\ y = 63 \frac{1}{3} [/tex]

BE AWARE THERE WAS NO NEED FOR ME TO SOLVE THE EQUATION I JUST WANTED TO SHOW YOU HOW IT'S DONE THE ANSWER NOW TO YOUR QUESTION IS THERE IS 1 PAIR OF ANSWER BUT TWO ANSWERS FOR THE VARIABLES.

Answer:

ALL THE ANSWERS AND THE EXPLANATION ARE IN THE PIC I JUSTV ATTACHED!!

Step-by-step explanation:

a) As per the given percentage, the number of registered voters in the town who cast the votes are 155,952.

b) Reese claim is incorrect. The number he mentioned as registered voters is greater than the actual number of registered voters..

Percentage:

A percentage is a number or ratio which can be expressed as a fraction of 100.

For example, 57% can be written as 57/100.

Given,

The register voters and other in the town cast their vote on the election day.

a. In that particular town, 273,600 votes were cast in an election. And there are 57% of those who were registered voted.

Here we need to find how many registered voters are there in the town.

b. Reese claims that there are 60% of the registered voters cast 273,600 votes, there would be fewer registered voters than above.

Now we have also need to find whether his statement is correct or not with the reason.

Let x be the total number of registered voter who cast the vote.

From the given details, we know that, there are 273,600 voters are cast.

And 57% of them are registered voters.

So, it can be calculated as follows,

=> x  = 273600 of 57%

=> x = 273600 x 57%

=> x = 273600 x 57/100

=> x = 2736 x 57

=> x = 155, 952

Therefore, there are 155,952 registered voter in the town who cast the vote.

Based on these calculation we know that, Reese claims is incorrect because there the number of registered voters is 155, 952 which is not equal to the number he mentioned.

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The simplest form of the given multiplication 7 1/2x2/3 = 5.

The given multiplication is;

7 1/2x2/3

Where, 7 1/2 is in the mixed fraction, convert it in simple fraction.

7 1/2 = (7×2 + 1)/2

7 1/2 = 15/2

Now, put the value in multiplication and find.

= 15/2 × 2/3

Multiply the numerators and denominators of each digit

= 30/6

Divide each digit by 6

= 5

Thus, the simplest form of the digit 7 1/2x2/3 after multiplication is found 15.

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IfIf a 4,800-pound wrecking ball is held in static equilibrium by two cables, one horizontal and one at an angle of 40° from vertical .the magnitudes of the tension vectors T  and H is: 6,266.32 lb,  3,085.44lb.

Let T h = H represent the horizontal

Let Tv  represent the vertical components of the vector T

Let W wball represent the weight of the wrecking ball

Hence,

T h =H

Tv = W wball

Where:

T h = T sin 40°

Tv =T cos 40°

Magnitude of the tension vector T:

Tv =4800lb

T=Tv/ cos 40°

T = 4800lb/ cos 40°

T = 4800lb/0.766

T= 6,266.318

T=6,266.32 lb (Approximately)

Magnitude of the tension vector H

W=T  h

T h =(4800lb) sin 40°

T h =(4800lb) 0.6428

H = 3,085.44lb

Therefore we can conclude that tension vector T magnitudes is 6,266.32lb and that of tension vector H magnitudes is 3,085.44lb.

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Answer:

the change was -10f

Step-by-step explanation:

if you start at five and go down to five you were going down 10 digits so it would be -10

Answer:

the first choice

Step-by-step explanation:

C reflection of point D over x and y axis

The algebraic expression for the difference of 13 and m is 13 - m

Algebraic expressions are simply defined as mathematical expressions made up of variables, terms, coefficient, constants, and factors

They are also composed of arithmetic or other known mathematical operations which includes;

Examples of an algebraic expressions;

2x - y + 4

Where;

Given the statement

The difference of 13 and m

Difference here signifies subtraction

m is the variables

It is represented as: 13 - m

Hence, the expression is 13 - m

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The complete question:

Write the algebraic expression for the difference of 13 and m

Answer:

(-∞, -3) and (-1, ∞)

Step-by-step explanation:

A function is increasing when the gradient is positive.

A function is decreasing when the gradient is negative.

A function is stationary when the gradient is zero.

From inspection of the given graph, the turning points of the function are (-3, 3) and (-1, -1).  Therefore, the gradient is zero at these points.

From inspection of the graph:

Therefore, the function is increasing on the intervals (-∞, -3) and (-1, ∞).

Answer:

6.73 i think

Step-by-step explanation:

.................

x = 6

Step 1: Simplify both sides of the equation.

5045x + 3000 = 5545x

Step 2: Subtract 5545x from both sides.

5045x + 3000 − 5545x = 5545x − 5545x

−500x + 3000 = 0

Step 3: Subtract 3000 from both sides.

−500x + 3000 − 3000 = 0 − 3000

−500x=−3000

Step 4: Divide both sides by -500.

−500x/−500 = −3000/−500

Answer: x=6

The probability that none of the solar panels are defective is 0.97.

So, the faulty solar panel percentage, p = 1/200 = 0.005.

Sample size, n = 6 likelihood that there are no damaged solar panels:

So, the probability: 0.97

Therefore, the probability that none of the solar panels are defective is 0.97.

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The quantity of food that was sold on Tuesday will be 9999995 kilograms.

From the information, it was stated that the department store sold 1 million kilograms of food for vegetables and other foodstuffs.

It was stated that on Tuesday, that sold 5 less than what they sold the previous day.

Therefore, the quantity that was sold on Tuesday will be:

= Quantity sold previous day - 5

= 1,000,000 - 5

= 9999995 kilograms

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A department store sold 1 million kilos of food in total between vegetables, meat, fish, bakery but on Tuesday they sold much less, exactly 5 less food than on Monday how many kilos of food did they sell on Tuesday

Answer: x=5.5

Step-by-step explanation:

All three medians of a triangle intersect at one point, which is called the centroid or center of gravity of the triangle, and are divided by this point into two parts in the ratio 2:1

Hence,

[tex]\displaystyle\\\frac{6x+12}{x+17}=\frac{2}{1} \\[/tex]

Multiply both part of the equation by (x+17):

[tex]6x+12=2(x+17)\\6x+12=2(x)+2(17)\\6x+12=2x+34\\6x+12-2x=2x+34-2x\\4x+12=34\\4x+12-12=34-12\\4x=22\\[/tex]

Divide both parts of the equation by 4:

[tex]x=5.5[/tex]

The test hypothesis using 0.05 significance level has the following results:

Part 1:

State the null and alternative hypotheses for treatments:

Null hypothesis=treatment means do not differ

Alternative hypothesis=The means are different

State the decision rule for treatments:

Table value of F(1,2)=18.51

If the calculated F>18.51, reject the null hypothesis

Decision: Treatments

Calculated F=43.75 >18.51, here, we reject the null hypothesis

Hence, we conclude that the treatment means differ.

Part 2:

State the null and alternate hypotheses for blocks.

Null hypothesis=block means do not differ

Alternative hypothesis: At least on pair of means are different

Also, state the decision rule for blocks:

Table value of F(2,2)=19.0

If the calculated F >19.0, reject the null hypothesis

Decision: Blocks

Calculated F=8.14 < 19.0, we do not reject the null hypothesis

Hence, we conclude that the block means do not differ.

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The quotient when 0.03 is divided by 0.148 after rounding it off is 0.2.

According to the question,

We have the following information:

0.03 is divided by 0.148

And it can be simply expressed as 0.03/0.148

Now, we have the quotient as:

0.2027

Now, when rounding off the numbers we know that the digits from where we are rounding off we look at the right next to that digit and when that digit is greater than 5 then the digit should be increased by 1 and when that digit is less than 5 then the digit should be the same.

So, we will round it off by taking the underlined digit to be next to first 2:

So, the digit is 0.

Butt if we are taking the underlined digit as 2 to be the next 2 then the digit next to it is 7 which is greater than 5.

Then, we have:

0.2

Hence, the quotient when 0.03 is divided by 0.148 after rounding it off is 0.2.

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The gcf of 15 and 36 is 3 and   15 + 36 by distributive property is 51.

What is gcf?

The gcf(greatest common factor) is the greatest factor that divides both numbers. To find the greatest common factor, first list the prime factors of each number. 18 and 24 share one 2 and one 3 in common. We multiply them to get the GCF, so 2 * 3 = 6 is the GCF of 18 and 24.

What is distributive property?

According to the distributive property, multiplying the sum of two or more addends by a number produces the same result as when each addend is multiplied individually by the number and the products are added together.                         A (B + C) = AB + AC.

Given that, 15 and 36

Factor of 15 = 3 × 5

Factor of 36 = 2 × 2 × 3 × 3

gcf of 15 and 35 is 3 because 3 only one 3 is common in both the number.

Applying distributive property on 15 an 35 = 15 + 36

                                                                      = 3×5 + 3×12

                                                                      = 3(5 + 12)

                                                                      = 3(17) = 51

Therefore, the gcf of 15 and 36 is 3 and   15 + 36 by distributive property is 51.

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Ignore the angles of triangle DEF. They complicate things when they don't need to be like that.

The distance from E to F is 3 units since there are 3 spaces between the points. Or you could subtract the x coordinates of each point, so 7-4 = 3.

So far we have one pair of congruent sides

EF = BC = 3

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

Let's use the distance formula to find the distance from D to E

[tex]D = (x_1,y_1) = (3,-1) \text{ and } E = (x_2, y_2) = (7,-4)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(3-7)^2 + (-1-(-4))^2}\\\\d = \sqrt{(3-7)^2 + (-1+4)^2}\\\\d = \sqrt{(-4)^2 + (3)^2}\\\\d = \sqrt{16 + 9}\\\\d = \sqrt{25}\\\\d = 5\\\\[/tex]

Segment DE is exactly 5 units long.

We have another pair of congruent sides between the two triangles

AB = DE = 5

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

We'll use the distance formula one last time to find the length of side FD.

[tex]D = (x_1,y_1) = (3,-1) \text{ and } F = (x_2, y_2) = (4,-4)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(3-4)^2 + (-1-(-4))^2}\\\\d = \sqrt{(3-4)^2 + (-1+4)^2}\\\\d = \sqrt{(-1)^2 + (3)^2}\\\\d = \sqrt{1 + 9}\\\\d = \sqrt{10}\\\\\sqrt{10} \approx 3.162278 \approx 3.2\\\\[/tex]

Side FD is approximately 3.2 units long, which matches with AC = 3.2

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

Here are the three paired sides that are congruent to one another

Since we have three pairs of congruent sides, we can use the SSS (side side side) congruence theorem to prove the triangles are congruent.

Congruent triangles are identical copies or clones of one another. One triangle is just a reflected and translated version of the other.

This means they have the same corresponding angle measures, and the same corresponding side lengths.

with the ticket price at $11 the average attendance has been 28000. when the price dropped to $10, the average attendance rose to 34000. Then the equation is y= -6000x+94000

We need to write expression of the attendance in terms of the price of the tickets.  We can determine the percentage increase of the attendance by decreasing the tickets price. We can have two points:

(11,28000) and (10,34000)

We have calculate the slope:

m= ( 34000 - 28000)/ (10-11)

m= - 6000

Substitute point into:

y= mx  +c

28000= -6000*11+c

28000+66000=c

94000=c

The equation is:

y= -6000x+94000

where x is the ticket price and y is the attendance.

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