X^2+8x-35=0 which number would be added to complete the square

The measure of ∠E will be equal to 38°.

Given,

m∠BFE = 118° and m∠C = 86°

And BF bisects ∠ABD

From the Property of Linear Pair,

∠AFB + ∠BFE = 180°

=> ∠AFB + 118° = 180°

=> ∠AFB = 62°

Now, we can see that ∠AFB and ∠FBD are equal because they are alternate angles.

And ∠FBD and ∠ABF are equal because BF bisects ∠ABD.

So, In ∆ABF,

∠AFB + ∠ABF + ∠BAF = 180° (because of the angle sum property of a triangle)

=>62° + 62° + ∠BAF = 180°

=>∠BAF = 180° - 124°

=> ∠BAF = 56°

Similarly, in ∆ABE,

∠A +∠C  +∠E = 180°

=> 56° + 86° + ∠E = 180°

=> ∠E = 38°

Therefore, m∠E = 38°.

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Answer:29

Step-by-step explanation:

9+4 spots times five days

Answer:

  y = -3x +6

Step-by-step explanation:

You want to solve the equation 6x +2y = 12 for y.

We can isolate the y-term by subtracting 6x from both sides.

  6x -6x +2y = -6x +12

  2y = -6x +12 . . . . . . . . . . simplify

Then we can get y by itself by dividing both sides by 2:

  2y/2 = -6x/2 +12/2

  y = -3x +6 . . . . . . . . . . . simplify

The expression for y is  y = -3x +6.

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Answer:

Explanation:

Given the ordered pair (-2, 4 1/2), where x = -2 and y = 4 1/2 = 9/2 = 4.5. Plotting this point, we'll have;

Note that quadrants are numbered in an anti-clockwise manner with the top right portion of the graph as Quadrant I. Looking at the plotted point, we can see that it lies in Quadrant II.

Step 1

Write the equation of a line in slope point form

Where;

Step 2

Find the equation to represent the cost of the topsoil.

The equation that represents the cost of the topsoil is

y=30x

Step 3

Find how the cost of the topsoil compares to the cost of the mulch.

The number of students that enrolled = 3,500 students.

This is defined as the intake of individuals into an organism or students into an institution through adherence to specific orders given by the administrative department of the organisation.

The number of students that apply= 20,000 students

The percentage of students that are accepted= 70% of 20,000

That is, 70/100× 20,000

= 1400000/100

= 14,000 students.

The quantity of students that actually enroll = 25% of 14,000

That is, 25/100× 14000

= 350000/100

= 3,500 students.

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Answer:

S': (2, 1)

T': (5, 3)

U': (1, -4)

S'': (1, 3)

T'': (4, 5)

U'': (0, -2)

Step-by-step explanation:

Hi!

For Reflection Across the X-Axis use this :

(x, y) -> (x, - y)

So :

S': (2, 1)

T': (5, 3)

U': (1, -4)

and then the question also asks for a translation so we follow what it gave us:

S'': (1, 3)

T'': (4, 5)

U'': (0, -2)

Please ask me any questions that you still may have!

and Have a great day! :)

Answer:

S' (2, 1)         S'' (1, 3)

T' (5, 3)        T'' (4, 5)

U' (1, -4)       U'' (0, -2)

Step-by-step explanation:

The preimage is S (2,-1), T (5, -3) U(1,4).

Preimage: the original figure prior to a transformation.

The directions say to reflect the preimage over the x-axis.

To do this, follow this transformation rule: (x, y) → (x, -y)

This means keep the x-coordinate as it is, but then change the sign of the y-coordinate.

S (2, -1) → S' (2, 1)

T (5, -3) → T' (5, 3)

U (1, 4) → U' (1, -4)

Next, take the coordinates from the last transformation then translate it using the rule: (x, y) → (x-1, y+2)

This means subtract 1 from the x-coordinate, then add 2 to the y-coordinate.

S' (2, 1) → S'' (1, 3)

T' (5, 3) → T'' (4, 5)

U' (1, -4) → U'' (0, -2)

Notice that each time you do a transformation, you add an apostrophe next to the letter. In math, this symbol is called a 'prime symbol.'

I hope this helped! Let me know if you have any questions.

A place where two or more curves, lines, or edges converge is known as a vertex in geometry (plural: vertices or vertexes), and it is frequently identified by letters like,,,. As a result of this definition, vertices are the intersection of two lines that create an angle as well as the corners of polygons and polyhedra.

The solutions are:

P' = (-4,-7)

Q ' = (-8,-7) (-8,-7)

R ' = (-3,3) (-3,3)

All you have to do is flip the provided points P, Q, and R's x and y coordinates.

The common principle is (x,y) —-> (y,x)

Thus, when we reflect across the line y = x, something like P = (-7,-4) becomes P'= (-4,-7). The similar approach is taken with the other points.

How do you locate a triangle's vertices?

Finding the triangle's vertices on the line y = x as an image

The steps below are used to locate a triangle's vertices using its midpoints:

Identify the midpoints' x and y values;

Calculate the midpoint using the following equations: A = (x 1+ x 3 - x 2, y 1 + y 3-y 2); B = (x 1+x 2-x 3, y 1+y 2-y3); C = (x 2+x 3-x 1, y 2 + y 3 -y 1);.

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The rational numbers are √75, 2. √7, √0. 36, √0. 0144, √3/77, -√36/49

A rational number can simply be described as a number that is expressed as the ratio of two even or odd integers.

The denominator of the fraction or ratio must be greater than zero.

Rational numbers are represented mathematically as a quotient, say x/y of two integers such that y ≠ 0, that is, the denominator is not equal r equivalent to zero.

It is formed from dividing on integer(whether odd or even) by another integer.

The numbers; √75, 2. √7, √0. 36, √0. 0144, √3/77, -√36/49 are all rational numbers

Hence, the numbers are √75, 2. √7, √0. 36, √0. 0144, √3/77, -√36/49

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It seems there is some missing info on this question. However, if you are simplifying, then the simplified version of the given expression would be...

[tex]10a^1^9[/tex]

Hope this helps!

The three consecutive even integers such that one less than four times the third is equal to five more than the sum of the first two is -4,-2,0.

An integer is a whole number irrespective of the sign that the integer is all whole numbers that are going from 0 to infinite or 0 to minus infinite.

Integer ; ....-2 , -1 , 0 , 1 , 2 , .....

Integers are non-decimal numbers and all integers are rational numbers.

Let's assume that first, even integer is x

Then the second and third will be x + 2,x + 4 respectively.

As per the given,

1 less than 4 times the third → 4(x+4) - 1

It is equal to the 5 more than the sum of x and x + 2

So, x + x + 2 + 5

Therefore,  4(x+4) - 1 = x + x + 2 + 5

4x + 16 - 1 = 2x + 7

4x + 15 = 2x + 7

2x = 7 - 15

x = -4

So integers are -4,-2,0

Hence "The three consecutive even integers such that one less than four times the third is equal to five more than the sum of the first two is -4,-2,0".

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ANSWER

EXPLANATION

We want to find the probability that the average of all participants in the study was fewer than 10,200 breaths each night.

To do this, first, we have to find the z-score corresponding to the sample mean:

where x = sample mean

μ = population mean

σ = standard deviation

n = sample size

Therefore, the z-score is:

Now, using the standard normal table, we can find P(z < 1.01).

Therefore, the probabilityis:

That is the answer.

Hello!

First, let's write the coordinates of each vertex of this parallelogram:

• A (-4, 2)

• B (2, 2)

• C (5, -2)

• D (-1, -2)

As line AB is parallel to the x-axis, we can find its measurement without formulas. We just need to count the number of squares from one point to the other.

So,

We will follow the same reasoning to calculate CD (because it's also parallel to the x-axis).

Now we have to use the formula of the distance between two points to calculate the sides BC and DA. The formula is:

As we know the formula, let's replace it with the coordinates:

We can solve it using the same formula as I used to solve BC, but now I'll show you how to solve it using Pythagoras Theorem (I think it will be easier). Look:

Solving by Pythagoras, we'll obtain:

Remembering: the perimeter is the sum of all the sides of a figure. So, we will have:

Data:

• Monthly budget: $15

• Price of a package of ramen: $1.48

• Price of a music download: $1.15

Procedure:

Answer: 10.1

Using equations we now know that the distance of the first part of the Yuna's swim is 0.7 miles.

So, let 'x' be the distance of the 1st part and 'y' be the time in hours of the 1st part.

Plot the equations on the graph as follows:

(Refer to the graph attached below)

Be obtain:

Therefore, using equations we now know that the distance of the first part of the Yuna's swim is 0.7 miles.

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The complete question is given below:
In training for a triathlon, Yuna swam 1.9 miles in the open ocean, which took her 2 hours. For the first part of her swim, she averaged 1.4 miles per hour. For the second part of her swim, she swam against the current and started to tire, so her average speed decreased to 0.8 mph. What was the distance of the first part of Yuna's swim? Round to the nearest tenth as needed. The distance in the first part of her swim was miles.

Answer:

.7

Step-by-step explanation:

Answer:

r=√6a/5m-1

Step-by-step explanation:

m=√6a+r/5r

cross multiply

5mr=√6a+r

5mr-r=√6a

factorise

r(5m-1)=√6a

divide both sides by the coefficient of r

r=√6a/5m-1

hope it helps

please mark brainliest

Answer:

hope it helps u

MATHEMATICS IS OUR OWN LANGUAGE,LETS TALK TOGETHER

We will have the following:

First, we can see that the probability of picking an even number at first is:

And then, the probability of picking another even card without replacing the previous one will be:

Now, the probability of this happening one after the other will be:

So, the probability will be of 20%.

Both Adam and Rena re both correct regarding the expression.

An expression simply means an illustration that can be used to represent a scenario or situation.

From the information, Adam writes the expression d−0.75d to find the sale price of the game if the original price is d dollars.

Rena correctly writes another expression, 0.25d, that will also find the sale price of the game if the original price is d dollars.

In this case, they are both correct. This can be illustrated as:

= 1 - 0.75d

= 0.25d

Note that the information was answered based on the information given.

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Answer:  The slope is [tex]\frac{1}{2}[/tex].

Step-by-step explanation:

[tex]Slope = \frac{y_{2}-y_{1} }{x_{2}-x_{1} } =\frac{-1-2}{1-7} =\frac{-3}{-6} =\frac{3}{6}=\frac{1}{2}[/tex]

The coordinates of G is (d+c, b)

This is because the opposite sides of any parallelogram are equal in length, and so the length of side HG is equal to the length of side EF.

a) The length of side HG is equal to the horizontal distance (x2 - x1): xG - 0

The length of side EF is equal to the horizontal distance (x2 - x1): d - (-c) = d +c

Thus:

xG - 0 = d + c

xG = d + c

Therefore the x-coordinate of G is d + c

b) To find the y-coordinate of G, we also apply the idea that sides GF and HE are equal.

The length of side GF is equal to the vertical distance (y2 - y1): yG - 0

The length of side HE is equal to the vertical distance (y2 - y1): b - 0

Thus:

yG - 0 = b -0

yG = b

Therefore the y-coordinate of G is b

Finally, the coordinates of G is (xG, yG) = (d+c, b)

Option a is correct using algebric formulas.

(x + y)³ = x³ + y³ +3xy( x + y )

(x + y + z)² = x² + y² + z² + 2( xy + yz + zx )

So breaking it into

(( x + y )³)² = (x³ + y³ +3xy( x + y ))²

(x³ + y³ +3xy( x + y ))² = x^6 + y^6 + 9x²y²(x² + y² + 2xy) + 2( x³y³ + 3xy^4( x + y ) + 3x^4y( x + y) )

x^6 + y^6 + 9x²y²(x² + y² + 2xy) + 2( x³y³ + 3xy^4( x + y ) + 3x^4y( x + y) )

So after rearranging the terms

we get  (x + y)^6 as

x6 + 6x5y + 15x4y2 + 20x³y3 + 15x²y4 + 6xy5+y6

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Answer: [tex]6\sqrt{6}+4 \times 6\sqrt{6}-4[/tex] yards

Step-by-step explanation:

Let the length of the walkway be x yards. Then,

[tex](18-2x)(26-2x)=200\\\\4x^2 -88x+468=200\\\\4x^2-88x+268=0\\\\x^2 -22x+77=0\\\\x=\frac{22 \pm \sqrt{22^2 -4(77)}}{2}\\\\=11 \pm 3\sqrt{6}[/tex]

However, [tex]x=11+3\sqrt{6} > 18[/tex], which is illogical, so we take [tex]x=11-3\sqrt{6}[/tex].

So,

[tex]18-2x=18-2(11-3\sqrt{6})=6\sqrt{6}-4\\\\26-2x=26-2(11-3\sqrt{6})=4+6\sqrt{6}[/tex]

The equation of the Pythagorean Theorem  in the triangle  is 25^2 = 24^2 + 7^2

From the question, the side lengths of the triangle are given as

25, 24 and 7

The Pythagorean Theorem states that:

Hypotenuse^2 = Sum of the squares of the other sides

Where

The other sides are the smaller sides

This in other words mean that:

Other sides = 24 and 7

Hypotenuse = 25

Substitute the known values in the above equation

25^2 = 24^2 + 7^2

Hence, the Pythagorean Theorem equation is 25^2 = 24^2 + 7^2

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800 miles is going to be the distance that separates the two aircraft. The distance between the two airplanes will be 1,300 kilometers at the very least.

It is important to keep in mind that the two aircraft's combined speed will be equal to the sum of their separate speeds when calculating their overall speed. In addition, the pilots of the two aircraft have one hour to find each other.

According to the information that was provided, the distance that separates the aircraft after they have flown for forty-five minutes is two hundred miles. As a result, the following will constitute the remaining distance:

= 1 hour - 45 minutes = 15 minutes.

When this occurs, the distance between the planes will be as follows:

= 200/15 × 60

= 200 × 4

= 800 miles

As a result, there will be a gap of 1300 kilometers between the two aircraft.

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The solution set of real numbers that are 3 units from -2 is :

|x +2| = 3

Here

Function : |x +2| = 3

since ,

|x +2| = 3 => x + 2 = 3 ∨ x + 2 = -3

x = 3 - 2 ∨ x = -3 - 2

x = 1 ∨ x = -5

| - 2 - 1 | = | -3| = 3

| -2 -(-5) | = | -2 + 5 | = 3.

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Answer:

Surface area= 6(5·5)+6(3·3)-2(3·3)

Step-by-step explanation:

first figure out the surface area of both cubes

for the larger cube- 5 multiplied by 5 for the area of one side then multiplied by 6 for all faces

for the smaller cube- 3 multiplied by 3 for the area of one side then multiplied by 6 for all the faces.

the cubes are touching on one face, this is the whole area of one side of the 3 by 3 cube, meaning two of these faces must be subtracted to find the surface area of the whole shape

hope that helps

Step-by-step explanation:

open the bracket

y - 1 = 3x - 12

add 1 to both sides

y = 3x - 11

I think that should be it

Answer:

AB

Step-by-step explanation:

the angles DCB and ACB are supplementary angles (together 180°).

simply because the sum of all angles around a single point on one side of a line is suggests 180° (it represents a half-circle).

so, the inner angle ACB is

ACB = 180 - 50 = 130°

because the sum of all angles in a triangle is also always 180°, there are only 50° left for the other 2 angles.

so, the inner angle at C is clearly the largest angle in the triangle ABC.

the larger an angle, the longer the opposing side.

the largest angle has the longest opposing side in the triangle.

the opposing side of the inner angle C is AB. and that is therefore the longest side in the triangle ABC.

28-6x = 2x -84

Add 6x to both sides:

28 = 8x -84

Add 84 to both sides

112 = 8x

Divide both sides by 8

X = 112/8

X = 14

The equations of the line according to the given points will be:

We know that,

The equation of a line passing through two points is:

( y -y 1) / ( x - x1 ) = ( y2 - y1 ) / ( x2 - x1 )  

(y - 2) / (x - 5) = (-4 - 2) / (3 - 5)

=> (y - 2) / (x - 5) = -6 / -2

=> y - 2 = 3 (x - 5)

=> 3x - 15 - y + 2 = 0

=> 3x - y - 13 = 0

Some more equations of the same line can be calculated just by multiplying the coefficients of x and y so that they remain proportional to the previous equation.

For Example,

Here we can see that the coefficients of x and y and also the constant term are proportional to every equation compared with each other.

These lines are also called coincident lines.

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