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frozen
2 months ago
15

PLEASE HELP!

Mathematics
2 answers:
PIT_PIT [12.4K]2 months ago
8 0

To replicate the BAC angle, the next action is to extend the DE ray away from the BAC angle

Further explanation

Angles are formed by two rays that originate from the same point

Common terminology includes vertex, corner, and angle measure

Typically, angles are expressed in degrees

Angles can be identified using a single letter related to the vertex or through three letters, with the vertex placed between two others

Steps to duplicate the BAC angle:

  • 1. Construct the DE line
  • 2. With a compass, draw a circle centered at A. This circle will intersect lines BA and BC at points F and G
  • 3. Utilize the segment tool to form a segment from the drawn circle's radius
  • 4. Use the Compass to select the AG radius segment
  • 5. Create a circle centered at D with the same radius as AG
  • 6. Label where this circle intersects with the DE as H
  • 7. Construct the FG segment, using the compass tool on this segment
  • 8. Draw a circle centered at H, intersecting the previous circle centered at D at point I
  • 9. Draw the DI line

Thus, BAC is congruent to HDI

Learn more

circumference of the circle

chord, diameter

steps for angle duplication  

Keywords: circle, angle duplication, segment tool, compass tool, radius

PIT_PIT [12.4K]2 months ago
8 0

Answer: Identify the intersection point of circle D and line DE

Step-by-step explanation:

You might be interested in
Which values of a, b, and c correctly complete the division?<br>1/4÷5/6=1/a×b/c​
PIT_PIT [12445]

Answer:

The proper values for a, b, and c to accurately complete the division are: a = 4, b = 6, and c = 5.

Step-by-step explanation:

To solve any fraction division, we should follow these three steps:

1. Invert the divisor into its reciprocal.

2. Alter the division sign to a multiplication sign and perform the multiplication.

3. Simplify the result if it can be

Thus, we obtain:

1/4 ÷ 5/6 = 1/4 * 6/5

The valid values for a, b, and c to correctly finalize the division are: a = 4, b = 6, and c = 5.

6 0
1 month ago
Two functions are shown in the table below. Function 1 2 3 4 5 6 f(x) = −x2 + 4x + 12 g(x) = −x + 6 Complete the table on your o
Svet_ta [12734]

For \fbox{\begin \\\math{x}=6\\\end{minispace}} the function f(x)=-x^{2} +4x+12 and g(x)=-x+6 both yield the same result.

Detailed breakdown:  

The functions involved are

f(x)=-x^{2}+4x+12

g(x)=-x+6

Step 1:  

Insert x=1 in f(x)=-x^{2} +4x+12 to find the value of f(1).

f(1)=-1^{2} +4(1)+12\\f(1)=-1+4+12\\f(1)=15

Insert x=1 in g(x)=-x+6 to find the value of g(1).

g(1)=-1+6\\g(1)=5

Step 2:

Insert x=2 in f(x)=-x^{2} +4x+12 to obtain the value of f(2).

f(2)=-2^{2} +4(2)+12\\f(2)=-4+8+12\\f(2)=16

Substitute x=2 into g(x)=-x+6 to find the value of g(2).

g(2)=-2+6\\g(2)=4

Step 3:

Replace x=3 in f(x)=-x^{2} +4x+12 to find the value of f(3).

f(3)=-3^{2} +4(3)+12\\f(3)=-9+12+12\\f(3)=15

Also, replace x=3 in g(x)=-x+6 to find the value of g(3).

g(3)=-3+6\\g(3)=3

Step 4:

Insert x=4 in f(x)=-x^{2} +4x+12 to find the value of f(4).

f(4)=-4^{2} +4(4)+12\\f(4)=-16+16+12\\f(4)=12

Also, replace x=4 in g(x)=-x+6 to obtain the value of g(4).

g(4)=-4+6\\g(4)=2

Step 5:

Insert x=5 in f(x)=-x^{2} +4x+12 to obtain the value of f(5).

f(5)=-5^{2} +4(5)+12\\f(5)=-25+20+12\\f(5)=7

Replace x=5 in g(x)=-x+6 to find the value of g(5).

g(5)=-5+6\\g(5)=1

Step 6:

Insert x=6 into f(x)=-x^{2} +4x+12 to find the value of f(6).

f(6)=-6^{2} +4(6)+12\\f(6)=-36+24+12\\f(6)=0

Also, substitute x=6 in g(x)=-x+6 to obtain the value of g(6).

g(6)=-6+6\\g(6)=0

Step 7:

According to the provided condition f(x)=g(x).

(a). Insert f(x)=-x^{2} +4x+12 and g(x)=-x+6 into the previously mentioned equation.

-x^{2} +4x+12=-x+6

(b). Multiply through by -1 on both sides.

x^{2} -4x-12=x-6

(c). Move the term x-6 to the left side of the equation.

x^{2} -4x-12-x+6=0\\x^{2} -5x-6=0

(d). Divide the middle term so that its sum equals 5 and the product equals 6.

x^{2} -(6-1)x-6=0\\x^{2} -6x+x-6=0\\x(x-6)+1(x-6)=0\\(x+1)(x-6)=0\\x=-1,6

From the analysis above, it is noted that for x=6 both functions f(x) and g(x) yield the same outcome.

Using a direct approach:

f(x)=g(x)\\\Leftrightarrow-x^{2} +4x+12=-x+6\\\Leftrightarrow-x^{2} +4x+12+x-6=0\\\Leftrightarrow-x^{2} +5x+6=0\\\Leftrightarrow-x^{2} +6x-x+6=0\\\Leftrightarrow x^{2} -6x+x-6=0\\\Leftrightarrow x(x-6)+1(x-6)=0\\\Leftrightarrow(x+1)(x-6)=0\\\Leftrightarrow x=6,-1

The table representing function f(x)=-x^{2} +4x+12 and g(x)=-x+6 is included below.

For more information:

1. What is the y-intercept of the quadratic function f(x) = (x – 6)(x – 2)? (0,–6) (0,12) (–8,0) (2,0)

2. Which is the graph of f(x) = (x – 1)(x + 4)?

6 0
1 month ago
Given that Ray E B bisects ∠CEA, which statements must be true? Select three options. m∠CEA = 90° m∠CEF = m∠CEA + m∠BEF m∠CEB =
tester [12383]

Answer:

Attached is the question in consideration.

m\angle CEA =90 \ (deg)

m\angle BEF=135\ (deg)

\angle CEF forms a straight line.

\angle AEF depicts a right triangle.

The options 1,4,5,6 represent the correct answers.

Step-by-step explanation:

⇒ Given that \ ray\ AE  is ⊥FEC it constitutes a right triangle, leading to m\angle CEA =90\ (deg).

⇒ The measure for \angle BEF =135\ (deg) equals \angle BEF =\angle AEB +\angle AEF = (45+90)=135\ (deg) as \angle AEB bisects \angle AEC, implying that \angle AEB is half of \angle AEC, thus  \angle AEB = 45\ (deg).

⇒\angle CEF represents a straight line, as the angle measures across it yield 180\ (deg).

⇒ The angle measure for \angle AEF = 90\ (deg) is derived from the linear pair concept.

Since \angle CEA + \angle AEF = 180\ (deg), inserting the values of  m\angle CEA =90\ (deg) leads to \angle AEF = 90\ (deg).

The other two options are incorrect as:

  • m\angle CEF=m\angle CEA + m\angle BEF = (90+135)=225

       it surpasses 180\ (deg) while \angle CEF is a               

      straight line.

  • Also, m\angle CEB=2(m\angle CEA) is inaccurate.

     As \angle CEA = 90\ (deg) and \angle CEB=45\ (deg)

Thus, we have a total 4 valid answers.

The confirmed options are 1,4,5,6.

5 0
2 months ago
Read 2 more answers
A major department store chain is interested in estimating the mean amount its credit card customers spent on their first visit
Inessa [12570]

Answer: D) \$50\pm\$11.08

Step-by-step explanation:

Based on the provided information, we have

Sample size: n= 15

sample mean: \overline{x}=\$50.50

Sample standard deviation: s= $20

Since the population standard deviation is not known, we utilize a t-test.

For a significance level of 95% confidence: \alpha=1-0.95=0.05

Critical t-value : t_{n-1, \alpha/2}=t_{014,0.025}=2.145  [Using the Student's t-value table]

The required 95% confidence interval yields:-

\overline{x}\pm t_{n-1, \alpha/2}\dfrac{s}{\sqrt{n}}\\\\ =\$50.50\pm(2.145)\dfrac{\$20}{\sqrt{15}}\\\\\approx \$50\pm\$11.08

Thus, the sought-after 95% confidence interval for the mean amount spent by credit card customers during their initial visit to the new store in the mall, assuming normal distribution of the spending amounts, is:

\$50\pm\$11.08

5 0
2 months ago
Identify an expression that is equivalent to 0.3(12y)
PIT_PIT [12445]
The result is 3.6y. By multiplying 0.3 by 12, we arrive at 3.6, and we include the variable y.
3 0
2 months ago
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