Determine the equation of the parabola shown in the diagram in factored form.

The ratio of corresponding sides of the triangle are not in the same proportion, hence they are not similar.

Two triangles are said to be similar if they have the same shape and angles. Also, the ratio of their corresponding sides are to be in the same proportion.

From the image shown, if the triangles are similar, hence:

AB / DE = AC / DF = BC / EF

Hence:

5.6 / 4 = 4.9 / 3.5 ≠ 2.4 / 1.5

1.4 = 1.4 ≠ 1.6

The ratio of corresponding sides of the triangle are not in the same proportion, hence they are not similar.

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Answer:

-x^3-5x^2+10x-4

Step-by-step explanation:

(−x + 1) (x ^ 2 + 6x − 4) = (-x)(x ^ 2 + 6x − 4) + 1(x ^ 2 + 6x − 4)

= -x^3-6x^2+4x+x^2+6x-4 = -x^3-5x^2+10x-4

Answer:

x= 1.5, y= 3.5

or x= -5, y= 10

Step-by-step explanation:

Let's solve by substitution.

Label the two equations:

y= 2x² +6x -10 -----(1)

y= -x +5 -----(2)

Substitute (2) into (1):

2x² +6x -10= -x +5

2x² +6x +x -10 -5= 0

Simplify:

2x² +7x -15= 0

Factorise:

(2x -3)(x +5)= 0

2x -3= 0 or x +5= 0

2x= 3 or x= -5

x= 1.5

Now that we have found the value of x, we can find the value of y through substitution.

Substitute into (2):

y= -1.5 +5 or y= -(-5) +5

y= 3.5 or y= 10

Supplementary:

Do check out the following should you wish to learn more about solving quadratic equations!

Answer:

[tex]\displaystyle{y-1=5(x+6)}[/tex]

Step-by-step explanation:

A point-slope form is written in the equation of  [tex]\displaystyle{y-y_1=m(x-x_1)}[/tex]. Where [tex]\displaystyle{(x_1,y_1)}[/tex] is a coordinate point and [tex]\displaystyle{m}[/tex] is slope.

The definition of parallel is to both lines have same slope. The given line equation has slope of 5. Therefore, we can write the equation in point-slope form as:

[tex]\displaystyle{y-y_1=5(x-x_1)}[/tex]

Next, we are also given the point p(-6,1). Substitute [tex]\displaystyle{x_1}[/tex] = -6 and [tex]\displaystyle{y_1}[/tex] = 1 in:

[tex]\displaystyle{y-1=5[x-(-6)]}\\\\\displaystyle{y-1=5(x+6)}[/tex]

Hence, the line equation that’s parallel to y = 5x - 4 and passes through a point (-6,1) is y - 1 = 5(x + 6)

Answer:

y - 1 = 5 ( x + 6 )

Step-by-step explanation:

       Here,

          m ⇒ slope

    y = 5x - 4 ← equation of the old line

         Now it is clear to us that,

         m ⇒ slope of the line ⇒ 5

         c  ⇒ y-intercept ⇒ -4

                 That is, m = 5

                   y - y₁ = m ( x - x₁ ).

        m = slope

           ( -6 , 1 ) ⇔ ( x₁ , y₁ )

        Let us solve this now

         y - y₁ = m ( x - x₁ )

         y - 1 = 5 ( x - ( -6) )

         y - 1 = 5 ( x + 6 )

                y - 1 = 5 ( x + 6 )

Answer:

x=1

Step-by-step explanation:

Original Equation:

[tex]-5(5x+3)-5x+1= -44[/tex]

Distribute the -5

[tex]-25x-15-5x+1= -44[/tex]

Add like terms

[tex]-30x-14=-44[/tex]

Add 14 to both sides

[tex]-30x=-30[/tex]

Divide both sides by -30

[tex]x=1[/tex]

Answer:

x = 1

Step-by-step explanation:

-5(5x+3) - 5x + 1 = -44

(-5*5x -5*3) - 5x + 1 = -44

(-25x - 15) - 5x + 1 = -44

-25x - 5x - 15 + 1 = -44

-30x - 14 = -44

-30x = -44 + 14

-30x = -30

x = -30/-30

x = 1

Check:

-5(/5*1) + 3) - 5*1 + 1 = -44

-5(5+3) - 5 + 1 = -44

-5*8 - 5 + 1 = -44

-40 - 5 + 1 = -44

-45 + 1 = -44

The unit rate for every 1 student out of school, there are 10 students going to school is 10 students going to school per 1 student out of school

An equation is an expression that shows the relationship between two or more numbers and variables.

A unit rate is a ratio between two different units with a denominator of one.

If For every 1 student out of school, there are 10 students going to school, hence:

Unit rate = 10/1 = 10 students going to school per 1 student out of school

The unit rate for every 1 student out of school, there are 10 students going to school is 10 students going to school per 1 student out of school

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The coordinate of the vertex is; (h, k) = (3, -5)

The final equation of the parabola is; y = 5(x - 3)² - 5

The vertex is the coordinate of the crest or trough of the curve. Now, in the given graph, we only have a Trough which is the lowest point of the graph.

The coordinate of the vertex is; (h, k) = (3, -5)

2) Since the general equation is;

y = a(x - h)² + k

We will have;

y = a(x - 3)² - 5

At x = 2, y = 0. Thus;

0 = a(2 - 3)² - 5

a - 5 = 0

a = 5

3) The final equation of the parabola is;

y = 5(x - 3)² - 5

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Answer: 5.3

Step-by-step explanation:

[tex]12.6-(5.1+2.2)\\\\=12.6-7.3\\\\=5.3[/tex]

Answer:

Step-by-step explanation:

***I hope this helps and the explanation is helpful!***

Step-by-step explanation:

5 x 0.7 = 3.5

Answer:

k

Step-by-step explanation:

Answer:

$2

Step-by-step explanation:

If the total is $12, and he spent $6 on a notebook, he has $6 left for his 3 pencils. If each pencil costs the same, he paid $2 for each pencil.

By critically observing the basketball hoop (see attachment), we can logically deduce that the basket's height from Lisa's horizontal sight is the same as the length of the shortest leg of the right-angle triangle:

Shortest leg = 8.5 - 5

Shortest leg = 3.5 feet.

In Geometry, the sum of all the angles in a triangle is equal to 180°:

x + y + z = 180

x + y + 90 = 180

x + y = 180 - 90

x + y = 90° (complementary angle).

Therefore, the angle of depression is complementary to the angle of elevation.

Also, you should use the inverse tangent function because the lengths of the opposite and adjacent sides of the right-angle triangle are known.

Angle of depression = tan⁻¹(Opposite/Adjacent)

Angle of depression = tan⁻¹(3.5/10)

Angle of depression = 19.29° ≈ 19°.

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Answer:

3.5

congruent

inverse tangent

19

Step-by-step explanation:

Answer:

5. 68 degrees :)

6. 55 degrees :)

Step-by-step explanation:

5.

A flat line is 180 degrees so we subtract to find x :)

Lets do that now :)

180 - 112 = 68

x = 68 degrees

6.

X will be the same as 55 degrees.

All lines are tipped the same what so that is why it is 55 degrees :)

Have an amazing day!!

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Answer:

The answer is option c

Answer:

The answer is B.

Answer:

5 (rounded)

Step-by-step explanation:

by using the Pythagorean theorem you can calculate b

[tex]a^{2} + b^{2} = c^{2}[/tex]

here we have a and c

first lets times it by themselves

16 + b^2 = 36

now lets isolate b^2

b^2 = 36-16

= 20

now we have to get rid of the exponent ^2

b = 4.47....

rounding it would be 5!

Hope that helps :>

The function that is graphed is f(x) = |x - 3| + 1

The parent absolute function is:

f(x) = |x|

From the graph, we have the following transformations:

This is represented as:

(x, y) = (x - 3, y + 1)

So, we have:

f(x) = |x - 3| + 1

Hence, the function that is graphed is f(x) = |x - 3| + 1

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Answer: [tex]\frac{\sqrt{65}}{4}[/tex]

Step-by-step explanation:

By the Pythagorean theorem, the unknown side has length

[tex]\sqrt{9^{2}-4^{2}}=\sqrt{65}[/tex]

Therefore,

[tex]\tan \theta=\boxed{\frac{\sqrt{65}}{4}}[/tex]

The grid that is shaded red and blue in ratio 1 : 2 is grid (c)

The complete question is in the image

The ratio is given as:

Red : Blue = 1 : 2

There are 12 squares in each grid.

This means that:

Red : Blue = 12 * 1/(1 + 2) : 12 * 2/(1 + 2)

Evaluate

Red : Blue = 4 : 8

The grid that has 4 red and 8 blue is (c)

Hence, the grid that is shaded red and blue in ratio 1 : 2 is grid (c)

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The closest value will be 6.9 since the value is close to 49

The square root of a number can both be negative or positive. According to the question, we are to determine the square root of 47

The square root of 47 must be between the square root of 36 and square root of 64

√36 = 6

√64 = 8

This shows that the answer must be between 6 and 8. Hence the closest value will be 6.9 since the value is close to 49

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Answer: 6.9

Step-by-step explanation: just did the test

Answer: Give me the full answer and i will be able to answer it

Step-by-step explanation:

The length of GH is 15.

GH = IG

GH = 5x - 10

IG = 3x

5x - 10 = 3x

5x - 3x = 10

2x = 10

x = 10/2 = 5

GH = 5x - 10

= 5 * 5 - 10 = 25 - 10

GH = 15

<ABD = < DBC

<ABD = 10y°

<DBC = (8y + 4)°

10y° = (8y + 4)°

10y = 8y + 4

10y - 8y = 4

2y = 4

y = 4/2 = 2

The value of y is 2

<DBE = <DBC + <CBE

<DBC = 10y°

<CBE = <DBC = 10y°

y = 2

<DBC = <CBE = 10y° = 10*2° = 20°

<DBE = 20° + 20° = 40°

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The weight of 45 bushels of soya beans is 1.2247 Tons

An equation is an expression that shows the relationship between two or more numbers and variables.

The conversion factor of soyabeans is 36.744 (bu/t). Hence:

45 bushels = 45 bushels / 36.744 (bu/t) = 1.2247 Tons

The weight of 45 bushels of soya beans is 1.2247 Tons

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Answer:

13° , 29° , 138°

Step-by-step explanation:

let x be the smallest angle , then

2x + 3 is the middle angle and

2x + 3 + 109 is the largest angle

summing the 3 angles and equating to 180

x + 2x + 3 + 2x + 3 + 109 = 180 , that is

5x + 115 = 180 ( subtract 115 from 180 )

5x = 65 ( divide both sides by 5

x = 13

2x + 3 = 2(13) + 3 = 26 + 3 = 29

2x + 3 + 109 = 29 + 109 = 138

the 3 angles are 13° , 29° , 138°

Answer: 112

Step-by-step explanation:

area of the parallelogram is base times height

The measure of [tex]\theta[/tex] is 68 degrees

The complete question is in the attached image

The value of [tex]\theta[/tex] is calculate using the following cosine function

[tex]\cos(\theta) = \frac 38[/tex]

Evaluate the quotient'

[tex]\cos(\theta) = 0.375[/tex]

Take the arc cos of both sides

[tex]\theta = \cos^{-1}(0.375)[/tex]

Evaluate the arc cos

[tex]\theta = 67.97[/tex]

Approximate to the nearest degree

[tex]\theta = 68[/tex]

Hence, the measure of [tex]\theta[/tex] is 68 degrees

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