63 = 3x + 15 solve for x simplify your answer as much as possible

The answer is

x = 7, -7, √2, -√2

Add the two equations to get

x2 + y2 = 74

Eliminate y from the first by solving for y and using that result:

(x2 − 14) = x√74 - x2

square both sides, then condense:

x4 − 51x2 + 98 = 0

These ready factors:

(x−7)(x+7)(x−√2)(x+√2)=0

I'll let you handle it from there, but keep in mind that if we square all sides, we might find roots that need to be pulled out afterward.

Therefore,

x = 7, -7, √2, -√2

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Answer:

(2x + 5)/(x + 4) = 1

and

6x - 19 = 3x - 10

Step-by-step explanation

Linear euqations are the equation for the straight line. When graphed both equations will be straight lines.

Hope this helps you!

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:

4.5

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.

Scaled copy of the polygon with scale factor 3 is given below.

A polygon is a closed polygonal chain made up of a finite number of straight line segments and is a type of planar figure in geometry. A polygon is a region that is bounded by a bounding circuit, a bounding plane, or both.

A polygonal circuit's segments are referred to as its edges or sides. A polygon is a geometric object with two dimensions and a finite number of sides. A polygon's sides are made up of segments of straight lines that are joined end to end.

Polygons include shapes like triangles, quadrilaterals, pentagons, and hexagons. The shape's number of sides is indicated by the name. A quadrilateral has four sides, whereas a triangle has three.

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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:

see explanation

Step-by-step explanation:

each term inside the parenthesis is raised to the exponent outsie, that is

(2xy)³

= 2³ × x³ × y³ ← 2³ = 2 × 2 × 2 = 4 × 2 = 8

= 8x³y³

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.

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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Answer:

Slope = 1/2 or 0.5

Step-by-step explanation:

Picking two integer points on the line, (any)

(-3, 2) and (-1, 3)

We can find the slope

(3-2)/(-1-(-3)

=1/2

:]

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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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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Answer: have you tried m a t h w a y

Step-by-step explanation:

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

Hope this helps! Please like!!

:)

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:

the answer is A...

Step-by-step explanation:

Calculate Area (A):

The area formula for a square is denoted below:

A = s2

Taking the square root of both sides, we get:

s = √A

s = √3

s = 1.7320508075689

The number of milligrams of medication medication left after 6 hours is; 50 milligrams.

The number of milligrams of medication medication left after 7 hours is; 35.36 milligrams.

The number of milligrams of medication medication left after 8 hours is; 25 milligrams.

It follows from the task content that the amount of medications left in the patient's body be determined in each case.

Recall the formula for the amount of substance remaining for half life situations is as follows;

A = N (1/2)^(t/half-life)

Since half life = 2 hours and N = 400 milligrams;

Hence;

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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].

Answer:

Hope the picture will help you

Answer:

2.718

Step-by-step explanation:

let x = .027^2/3

x=.027^.67

applying natural log on both sides

lnx = ln.027^.67

lnx = .67ln.027

lnx = 2.42004

applying antilog on both sides

x = e^2.42004

x = 2.718

thus, .027^2/3 = 2.718

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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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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Kelly gets 38.59 miles per gallon of gasoline

Miles drove by Kelly = 238 miles

Gasoline used by the car = 6 1/6 gallons

Gasoline used in the car in improper fraction = 37/6 gallons

Average fuel economy: Average fuel economy of a car gives the distance covered by the car in one gallon of gasoline. This is an important factor to consider while buying or using a car as it is a major source of expenditure for the car.

To calculate miles per gallon we use the following formula:

Miles per gallon = Miles driven/ Gasoline used in the car

= 238/(37/6)

= 238*6/37

= 38.59

Miles per gallon = 38.59

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The speed for maximum car mileage will be 48 mph. The maximum gas mileage will be 29.5 mpg.

We are provided with an equation for mileage of car as

m(x) =  -0.028x² + 2.688x  -35.012

here , variable 'x' is the speed of the car.

Now

for the maximum speed of the car we have to first take the derivative of m(x) and then for the boundary value condition by  putting the derivative equal to zero.

comparing to the equation  ax² + bx + c , if the value of

'a' is positive, then we have minimum value at 1st derivative = 0

'a' is negative we have maximum value .

in this case a = -0.028 ( -ve) so we will have a maxima at 1st derivative.

so, dm/dx = -0.056x + 2.688

putting the 1st derivative = 0 , we have

x = 48

therefore , car gets maximum gas mileage at speed of 48 mph.

Also , putting this value in equation (1) we will get max. mileage.

so max. mileage = -0.028 (48)² + 2.688 x 48 - 35.012

                           = -64.512 + 129.024 - 35.012

                           = 29.5

so the maximum gas mileage will be 29.5 mpg .

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To paint the circular table top Beth need to buy 2 cans of paint .

In the question ,

it is given that ,

the radius of the circular table top is = 3 feet

So , the area of the circular table top is = π*r² = π*(3)²

= 9π

= 28.26

also given that

area covered by 1 small can of paint = 15 sq. feet

So , the number of cans needed to paint the table top is = (area of table top)/(area covered by 1 small can of paint)

On substituting the values , we get

number of cans needed to paint the table top is = 28.26/15

= 1.884

≈ 2

Therefore , To paint the circular table top Beth need to buy 2 cans of paint  .

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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:

Angle LMN = 180 - 142

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

x = 180 - 90 - 38

= 52° (sum of angles in triangle=180)

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