In the triangle ABC shown below, DE is parallel to BC. Find the length of DB.
20
10
D
E
х
B
15
с

Answer:

x = -4, 4

Step-by-step explanation:

Hi there!

[tex]x^2-16=0[/tex]

Rewrite 16:

[tex]x^2-4^2=0[/tex]

The difference of squares rule states that [tex]a^2-b^2=(a+b)(a-b)[/tex]. With this, apply the difference of squares to the equation:

[tex](x+4)(x-4)=0[/tex]

The zero-product property states that if the product of two numbers is 0, then one of the numbers must be equal to zero. Set each term equal to 0 and find the solutions:

[tex]x+4=0\\x=-4[/tex]

[tex]x-4=0\\x=4[/tex]

Therefore, the solutions are -4 and 4.

I hope this helps!

Answer:

0.05 metre

5×10^5 kilometer

1.9685

Answer:

A'(6, 2), B'(6, 5), C'(3, 6) and D'(2, 1)

Step-by-step explanation:

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

If a point A(x, y) is reflected over the y axis, the new point is at A'(-x, y).

From the document attached, the vertices of the quadrilateral is at A(-6, 2), B(-6, 5), C(-3, 6) and D(-2, 1). Hence if quadrilateral ABCD is reflected over the y axis, the new point is at A'(6, 2), B'(6, 5), C'(3, 6) and D'(2, 1).

Answer:

[tex] \frac{1}{288} [/tex]

Step-by-step explanation:

the 1 will always stay the same because all of them are 1's

4×6=24

24×12=288

Answer:

garage bozo

Step-by-step explanation:

Answer:

(-6,18)

Step-by-step explanation:

3x + 2y = 18

2y= -3x + 18

y=-3/2 x + 18

give x=0

y=-3/2 *0+18

y=18#

y=18

3x+2(18)=18

3x+36=18

3x=18-36

3x=-18

x=-18/3

x=-6

Answer:

The half-life for the zombie population is of 8 years.

Step-by-step explanation:

Exponential equation:

An exponential equation has the following format:

[tex]N(t) = N(0)(1-r)^t[/tex]

In which N(0) is the initial value and the part [tex](1-r)^t[/tex] is related to the decay.

In this question:

[tex]N(t) = 300(0.5)^{\frac{t}{8}}[/tex]

Thus N(0) = 300, that is, initial population of 300.

What is the half-life for the zombie population?

This is t for which N(t) = 0.5*300 = 150. So

[tex]N(t) = 300(0.5)^{\frac{t}{8}}[/tex]

[tex]150 = 300(0.5)^{\frac{t}{8}}[/tex]

[tex](0.5)^{\frac{t}{8}} = \frac{150}{300}[/tex]

[tex](0.5)^{\frac{t}{8}} = 0.5[/tex]

[tex](0.5)^{\frac{t}{8}} = (0.5)^1[/tex]

Equal exponents, so:

[tex]\frac{t}{8} = 1[/tex]

[tex]t = 8[/tex]

The half-life for the zombie population is of 8 years.

Answer:

it should be the same answer....?

Step-by-step explanation:

Answer:

The 84% confidence interval for the population proportion that claim to always buckle up is (0.74, 0.80).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

They randomly survey 387 drivers and find that 298 claim to always buckle up.

This means that [tex]n = 387, \pi = \frac{298}{387} = 0.77[/tex]

84% confidence level

So [tex]\alpha = 0.16[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.16}{2} = 0.92[/tex], so [tex]Z = 1.405[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.77 - 1.405\sqrt{\frac{0.77*0.23}{387}} = 0.74[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.77 + 1.405\sqrt{\frac{0.77*0.23}{387}} = 0.8[/tex]

The 84% confidence interval for the population proportion that claim to always buckle up is (0.74, 0.80).

Answer:

450 foe

Step-by-step explanation:

Answer:

153.86.

Step-by-step explanation:

Formula for area of a circle: A= Pi R (R is radius) squared. First fill in the numbers: 3.14x7^2 Then Solve for the squared: 7^2=49, then finally multiply 49x3.14 which gets you to 153.86.

Answer: This can not be answered unless you choose a bigger photo.

Step-by-step explanation:

Sorry

Answer:

5.625

Step-by-step explanation:

You just have to multiply 1.5 by 3.75 which is 5.625.

So there are 5.625 grams of fat in 3.75 servings.

5.625 grams of fat are in 3.75 servings.

You just have to multiply 1.5 by 3.75 which is 5.625.

So there are 5.625 grams of fat in 3.75 servings.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Learn more about the unitary method here https://brainly.com/question/24587372

#SPJ2

Answer:

is that 3x or mutiply sign

Answer:

3x^2-4x+1

Step-by-step explanation:

Answer:

$315

Step-by-step explanation:

He earns $63 everyday, and then you just have to multiply that by 5 since he works 5 days in a week.

Answer:

Step-by-step explanation:

Answer:

18o rotational symetry  

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

9514 1404 393

Answer:

  (x -6)^2 +(y -6)^2 = 10

Step-by-step explanation:

To use the standard form equation for a circle, we need to know the center and the square of the radius. The center can be read from the graph as (6, 6). The square of the radius can be found using the distance formula.

  d^2 = (x2-x1)^2 +(y2-y1)^2

The radius is the distance between the two points shown, so we have ...

  d^2 = (7-6)^2 +(9-6)^2 = 1^2 +3^2 = 10

__

The equation of a circle centered at (h, k) with radius r is ...

  (x -h)^2 +(y -k)^2 = r^2

For (h, k) = (6, 6) and r^2 = 10, the equation is ...

  (x -6)^2 +(y -6)^2 = 10

Answer:

[tex]f(x) = 2x + 5[/tex]

[tex]g(x) = (x - 6)^2[/tex]

Step-by-step explanation:

Given

(a) to (d)

Required

Which will give:

[tex]f(g(x)) = 2(x - 6)^2 + 5[/tex]

Equate the expression in bracket to g(x)

[tex]g(x) = (x - 6)^2[/tex]

Replace g(x) with x in: [tex]f(g(x)) = 2(x - 6)^2 + 5[/tex]

[tex]f(x) = 2x + 5[/tex]

Using the exponential notation, the correct expression which represents 5 × 5 × 5 × 5 is 5⁴

Given tha expression :

Number of 5's = 4

The number of 5's can be used as the power of the base, since the base is common.

Base = 5

Hence,

5 × 5 × 5 × 5 = 5⁴

Learn more : https://brainly.com/question/25629067

Answer: b= - -log10(7)+3/2

Step-by-step explanation: log 10 (7) -2b-9=-6 : b= - -log10(7)+3/2 (Decimal : b = -1.07745...)

so these are the steps how I got it I did log 10 (7)-2b-9=-6 subtract log 10 (7) -9 from both sides log 10 (7)-2b-9-(log10(7)-9)=-6-(log 10 (7) -9)

Simplify -2b= -log10(7)+3

Divide both sides by -2  -2b/2= - log 10(7)/-2+ 3/-2 if you simplify it should give you b= - -log10(7)+3/2 that should be your answer but i'm not sure those I think that's how you do it let me know if you got it right bye!

Answer:

Arc EC = 58°

Step-by-step explanation:

First, find the value of x.

m<D = ½(arc EC) => Inscribed Angles Theorem

Substitute

2x - 5 = ½(5x - 27)

Multiply both sides by 2

2(2x - 5) = 5x - 27

4x - 10 = 5x - 27

Collect like terms

4x - 5x = 10 - 27

-x = -17

Divide both sides by -1

x = 17

Find arc EC:

Arc EC = 5x - 27

Plug in the value of x

Arc EC = 5(17) - 27 = 85 - 27

Arc EC = 58°

Answer:6

Step-by-step explanation:

The original number that was multiply by 5 instead of 3 is 6.

The equation that can be used to represent the informatioin in the question is:

5x - 3x = 12

Where x is the original number

In order to determine the value of x, take the following steps

Combine similar terms: 2x = 12

Divide both sides by 2

x = 6

To learn more about multiplication, please check: https://brainly.com/question/3385014

Answer:

[tex]4x + 5y = 10 - - - (a) \\ - x - 8 = 3y \\ - x - 3y = 8 \\ x + 3y = - 8 - - - (b) \\ 4 \times (b) - (a) : \\ = > 0x + 7y = - 42 \\ y = - 6 \\ x - 21 = - 8 \\ x = 13 \\ { \boxed{x = 13}} \\ { \boxed{y = - 6}}[/tex]

Answer:(10,-6)

Step-by-step explanation:

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