Multiply. Write your answer as a fraction in simplest form. ​

The dimensions of the rectangle will be equal to 10 by 4.

A rectangle may be defined as the closed figure having four sides with the interior angles equal to 90°. it has two dimensions the length and the width. The area of a rectangle may be defined as the product of its length and width. According to the question the area of the rectangle is given as 40 square units. Let us assume the length as 'l' units and width as 'b' units. It is given that length is 6 units greater than the width that is l = (b + 6).

Now, the area of the rectangle = l×b

40 = (b + 6)×b

40 = b² + 6b

=> b² + 6b - 40 = 0

=> b = [-6 ± √(36 + 160)]/2

=> b = (-6 ± 14)/2

=>b = 4 units, since width cannot be negative.

Now, length = b + 6 = 10 units.

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The correct option; Angle BAD is congruent to angle BCA, is requited to show ΔDBA ≅ ΔCBA by side-angle-side congruence theorem.

If all 3 corresponding sides are equal as well as all 3 corresponding angles seem to be equal in measure, two triangles are said to be congruent.

side-angle-side congruence theorem: By SAS rule, two triangles are said to be congruent if any two sides and the angle would include between the sides with one triangle are equivalent to a corresponding two sides and also the angle would include here between sides of the second triangle.

For the given triangles;

ΔDBA and ΔCBA

Side AC = Side AD

Side AB = Side AB  (common)

Thus, to make both triangles congruent the angles falling in between these two triangles must be equal.

Thus,  Angle BAD is congruent to angle BCA,

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Answer:

4 hours

Step-by-step explanation:

he was gone for 5 hours, he spent an hour driving.

5 - = 4 hours at work.

Answer:

4 hours

Step-by-step explanation:

says he was gone 4 hours, he was at work

Answer:

Angle LMN = 180 - 142

= 38° (sum of angles on a straight line=180)

x = 180 - 90 - 38

= 52° (sum of angles in triangle=180)

Tomato sauce will the new can hold is 743[tex]cm^{3[/tex]

let take  us  take,

V = Sh

[tex]S_{1} =S_{2}[/tex]        

[tex]h_{1[/tex] = 12 cm

[tex]h_{2}[/tex]  = 60 cm

[tex]\frac{V_{1} }{V_{2} } = \frac{h_{1} }{h_{2} }[/tex]

[tex]\frac{1487}{v_2} } = \frac{12}{60}[/tex]

= 743[tex]cm^{3[/tex]

Height means the vertical distance, either between the top and bottom of something or between the bottom and the thing above it. height refers to being tall or short as measured vertically.

Height is a way of measuring someone or something from the bottom to the top or from the head to the feet. In other words, height indicates how tall someone or something is. We can compare how tall we will be when we grow up. We often compare the average height of men and women in different countries.

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The probability that the shorts of the basketball team will be of a different color than the jersey is 2/3.

Probability can be found using the following formula;

probability = number of favorable outcomes or events ÷ total number of outcomes or events

In order to calculate the probability that the shorts will be of a different color than the jersey, we first determine the total number of combinations that are possible;

1- Black-Black

2- Black-White

3- Black-Gold

4- Gold-Black

5- Gold-White

6- Gold-Gold

Hence there are a total of 6 possible combinations of shorts and jerseys out of which 2 are the same and 4 are different.

Therefore the probability that the shorts will be of a different color can be calculated as follows;

probability = number of favorable outcomes or events ÷ total number of outcomes or events

probability = 4 ÷ 6

probability = 2/3

Hence, 2/3 is the probability that the shorts will be of a different color than the jersey.

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By using the fact that ∠4 and ∠5 add up to 180° and ∠5 = ∠7, we conclude that the measures of the angles are:

∠5 = ∠7 = 56°.

For angles formed by the interception between lines meet the following property.

If the angles are one next to the other, the measures add up to 180°.

If not, then the two angles have the same measure.

This means that:

∠5 = ∠7

∠8 = ∠6

And so on.

If the two horizontal lines are parallel, then:

∠5 = ∠1

And we know that:

∠4 + ∠1 = 180°

124° + ∠1 = 180°

∠1 = 180° - 124° = 56°

Then we get that:

∠5 = ∠7 = 56°.

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Answer:

5x2 + 24x + 20

Step-by-step explanation:

Using fraction, He consumes 1/4 pound of lunch meat each day.

A fraction, expresses a piece of a whole, a fraction, such as one-half, eight-fifths, or three-quarters, specifies the number of components of a respective size.

Given,

He consumes 2 pounds of beef in 8 days.

We need to determine how much meat he consumes each day.

To ascertain:

He consumes 2/4 of a pound of beef in a day.

= 1/4

He thus consumes 1/4 pound or less of lunch meat every day.

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Answer: x=3

Step-by-step explanation: Multiply both sides of the equation by 3 to get 4x+2x=x+15. Combine like terms. (underlined) 6x=x+15. Move variable to left side and change its sign. 6x-x=15. Combine like terms again. 5x=15. Divide both sides of the equation by 5 to get x=3.

Answer:

y=2X - 6

Step-by-step explanation:

find the slope using the 2 points

m = 8-2/7-3 = 2

substitute 4,2 in the equation y=mx+b and solve for b.

2 = 2x4+b

b=-6

y = 2x - 6

Answer:

Slope intercept formula: y = 2x -6

Point Slope formula y = 2x-6

Step-by-step explanation:

1) Find the slope

2) Choose a point and plug it into the equation y = mx+b

3) Solve for b

4) Plug-in new slope (m) and new y-intercept (b) into equation y = mx+b

Solving:

4 = x1

2 = y1

7 = x2

8 = y2

to find slope with slope formula:

m = y2-y1/x2-x1 = 8-2/7-4 = 6/3 = 2

now plug in,

y = 2x+b

to find b, take any one of the pair

(i will choose (4,2) )

2 = 2(4) + b

now solve for b,

2 = 8+b

b = -6

Slope intercept formula: y = 2x -6

for point slope: y-y1 = m(x-x1)

as we know our slope is 2 and points are (0,-6) where 0 is x1 and -6 is y1

now we plug in,

y-(-6) = 2(x-0)

y+6 = 2x

Point Slope formula y = 2x-6

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Answer:

$187.5

Step-by-step explanation:

.

Answer:

187.50

Step-by-step explanation:

7.5(25)=187.50

hope this helped

have a good day^^

Answer: x=560 miles per hour

Step-by-step explanation:

[tex]\displaystyle\\2.25=\\\\2\frac{1}{4}= \\\\\frac{2*4+1}{4}=\\\\\frac{8+1}{4}=\\\\\frac{9}{4}\ hours[/tex]

The second plane left at 10:00 a.m. so, him fly was 1.25 hours:

[tex]\displaystyle\\1.25=\\\\1\frac{1}{4}=\\\\\frac{1*4+1}{4}=\\\\\frac{4+1}{4} =\\\\\frac{5}{4} \ hours[/tex]

Let x represent the first plane's average rate

Hence, (x-108) represent the second plane's average rate

So,

[tex]\displaystyle\\\frac{9}{4}x+\frac{5}{4} (x-108)=1825\ \ \ \ (1)\\[/tex]

Multiply both parts of the equation by 4:

[tex]9x+5(x-108)=7300\\\\9x+5x-540=7300\\\\14x-540+540=7300+540\\\\14x=7840[/tex]

Divide both parts of the equation by 14:

[tex]x=560\ miles/hour[/tex]

Answer:

Second Choice: 8.73b + 171.48 > 381

Step-by-step explanation:

This is a tricky question because the first two choices both represent an inequality that satisfy the conditions

First, let's eliminate obvious wrong choices.

If b represents the number of bags of dog food and one bag costs $8.73, there should be term 8.73b somewhere in the inequality since 8.73b represents the total $ cost of b bags of dog food.

This means we can eliminate the last two choices

Let's deal with the knowns and compute the dollar amounts of each of the products being donated

30 cans of cat food at $0.57 per can = 0.57 x 30 = $17.10

34 cans of dog food at $0.84 per can = 0.84 x 34 = $28.56

18 bags of cat food at $$6.99 per bag = 6.99 x 18 = $125.82

The sum of these is $171.48

She is also donating b bags of dog food at $8.73 per bag = 8.73 x b = $8.73b

So the total cost of the donation =
8,73b + 171.48 which has to exceed 381

So the inequality is
8.73b + 171.48 > 381

Which is the choice you have selected and I believe it is correct

Now, the tricky part comes because if you subtract 171.84 from both sides of the inequality we get

8.73b > 318 - 171.48

Both inequalities are equivalent but we would not write an inequality of the type where the RHS is a mathematical expression. We would instead simplify the right hand side and write it as

8.73b > 209.52    (381-171.48 = 209.52)

I believe the way the question is worded is the LHS should be the $sum of all the donations and the RHS the minimum value.

So the best choice is choice 2: 8.73b + 171.48 > 381

i hope that helps.

Answer:

1.  R

2.  IR

3.  R

4.  IR

5.  IR

6.  R

7.  R

8.  IR

9.  R

10. R

Step-by-step explanation:

Note on #5: purchasing something on sale that you were already going to buy would be responsible, but not simply BECAUSE the item is on sale and you were not already needing to purchase it.

The expression of (x-9)(x+6) as a trinomial is x²  -3x - 54

A trinomial is an algebraic expression that has three non-zero terms.

In a simpler terms, the definition of a trinomial is a math equation that has three terms which are connected by plus or minus notations.

Therefore, let's express  (x-9)(x+6) as a trinomial.

Hence,

(x-9) (x+6) = x²  + 6x - 9x - 54

Finally,

x²  + 6x - 9x - 54 = x²  -3x - 54

Therefore, the trinomial form of (x-9)(x+6)  is  x²  -3x - 54

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The height of the cone to the nearest tenth of a centimeter is 17.40 cm.

From the given information provided in the question, we can solve this problem by following a few steps.

The surface area of a right pyramid is 258 cm² according to the question.

The surface area of the cone is equal to the surface area of the right pyramid. Therefore the surface area of the cone is also 258 cm².

The surface area of a cone is denoted as ( πrh + πr² ).

Where h is denoted as the height and, r is denoted as the radius of the cone which is 4 cm.

Hence the surface area of the cone is,

SA = (π× 4× h+ π× 4² ) cm²

Now, we can generate an equation, as both represent the value of the surface area of the cone.

(π× 4× h+ π× 4² ) = 258

Or, (12.56h + 39.44) = 258             [ The value of π is 3.14 ]

Or, 12.56h = 258 - 39.44                [ subtracting 39.44 from both sides ]

Or, 12.56h = 218.56

Or, h = 218.56/12.56                       [ dividing both sides by 12.56]

Or, h = 17.40

Now, we can conclude that the height of the cone is 17.40 cm.

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Answer: 4x + 11 = 4(8)  

Step-by-step explanation:

The function is given to be:

The object hits the ground when the function is equal to zero:

Solving the equation by factorization, we have:

Since the time cannot be negative, then the time will be 3 seconds.

Therefore, it will take 3 seconds for the object to hit the ground.

The evaluation of  f(-1) given the quadratic equation f(x)=(x-2)^2 + 3 gives 12

Given the quadratic equation f(x)=(x-2)^2 + 3. To evaluate to f(-1), we will substitute x = -1 into the equation:

Since f(x)=(x-2)^2 + 3

Therefore  f(-1) = (-1 - 2)^2 + 3

                       = (-3)^2 + 3

                       = 9 + 3 = 12

Therefore, the value of c is 12. This shows the concept of functions and equations.

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–π/2 is the exact value of arcsine (-1).

The six main inverse trigonometric functions include arcsin. It is the sine function's inverse trigonometric function. The mathematical symbol for arcsin, commonly known as inverse sine, is arcsin x or sin-1x (read as sine inverse x). Sin-1x is not the same as (sin x)-1; that is, sin-1x is not the reciprocal function of sin x. This is an important distinction to make. We may use the six inverse trigonometric functions arccos, arcsin, arctan, arcsec, arccsc, and arccot to calculate angles. Arcsin x calculates the angle that corresponds to the right-angled triangle's perpendicular to hypotenuse ratio. We shall examine the idea of arcsin in this article and determine its formula. We'll also talk about the domain and range.

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So, if we apply the power's rule, we notice that if the base is the same, the exponents can be substracted. Like this

So the answer is 1 / x to the 9th power

Answer:

b = ca

c = ba

Step-by-step explanation:

Answer:

u = -7

Step-by-step explanation:

26 = -12u - 9 + 7u

combine u terms on right side:

26 = -5u - 9

add 9 to both sides:

26 + 9 = -5u - 9 + 9

35 = -5u

divide both sides by -5:

35/-5 = -5u/-5

u = -7

Based on mathematical operations, the number of people that 10 gallons of punch can serve is 192 persons.

The number of people can be determined using mathematical operations of multiplication based on converting the gallons to ounces and division.

The number of gallons of punch to serve at the first meeting = 10 gallons

The quantity of punch per serving = 8 ounces

1 gallon = 153.722 ounces

10 gallons = 1537.22 ounces

The persons that can be served 8 ounces from the 10 gallons = 192 (1,537.22/8).

Thus, mathematically, from the 10 gallons of punch, the PTA can serve 192 persons.

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We were informed that the net income will be $725,000, since that value represents 30% of the total annual sales we can apply a rule of three to solve the problem. We do that by making 30% represent $725,000 in the same proportion that 100% represents the total anual sales, x. We have:

We can cross multiply to find the value of "x".

The total annual sale on this year will be approximately $2,416,666.667.

HG is the answer.

hope this helps

The first one is GH Segment.

Both shapes are similar. The figure on the right is a scaled version of the figure on the left. The VU edge in the left figure corresponds to the GH edge in the right figure.

The second one is %[tex]150[/tex].

As can be seen, the VU edge is [tex]2[/tex] units long while the GH edge is [tex]3[/tex] units long. By proportioning these edges and multiplying by [tex]100[/tex], we find the scaling factor. It is [tex]\frac{3}{2}[/tex].

The cheaper plan here would be plan A. The equation that is written in terms of the plans on movies is  0 < x < 5

For the plan A, we would have the function to be given as

A = 1x + 18

This is due to thge fact that this plan is said to cost  $18 per month plus $1 per movie watched.

For plan B the function would have to be:

B = 3x + 8

The equation that we would have here would be

1x + 18 <  3x + 8

= x - 3x < 8 - 18

= -2x < -10

x < 5

Hence we would have the equation as 0 < x < 5

Cheaper plan

1x6 + 18  = 24

3x 6+ 8 = 18 + 8 = 26

Plan A id cheaper

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