answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
notka56 [123]
2 years ago
12

If EBC = 31a - 2 and EBH = 4a + 45 find HBC

Mathematics
1 answer:
Zigmanuir [339]2 years ago
8 0

Answer:

The measure of angle HBC is m∠HBC=61°

Step-by-step explanation:

In this problem we have that

The line BH bisects angle EBC,

see the attached figure to better understand the problem

then

m∠EBC=m∠EBH+m∠HBC

m∠EBH=m∠HBC

so

m∠EBC=2(m∠EBH)

substitute the given values and solve for a

31a-2=2(4a+45)\\31a-2=8a+90\\31a-8a=92\\23a=92\\a=4

<em>Find the measure of angle EBH</em>

m∠EBH=(4(4)+45)=61°

Remember that

m∠EBH=m∠HBC

therefore

The measure of angle HBC is m∠HBC=61°

You might be interested in
Akira Chang's uncle dies without a will, leaving an estate of $945,000. His heirs consist of a wife and two adult children. His
OLEGan [10]
Let w represent the amount the wife receives.
.. w +2*(2/3*w) = 945,000
.. 7/3w = 945,000
.. w = (3/7)*945,000 = 405,000

The wife will receive $405,000.
5 0
1 year ago
A thin sheet of ice is in the form of a circle. If the ice is melting in such a way that the area of the sheet is decreasing at
elena-14-01-66 [18.8K]

Answer:

dx/dt  =  0,04 m/sec

Step-by-step explanation:

Area of the circle is:

A(c) =π*x²      where   x is a radius of the circle

Applying differentiation in relation to time we get:

dA(c)/dt   =  π*2*x* dx/dt    

In this equation we know:

dA(c)/dt  = 0,5 m²/sec

And are looking for dx/dt then

0,5  = 2*π*x*dx/dt    when the area of the sheet is 12 m²  (1)

When  A(c) = 12 m²      x = ??

A(c)  =  12  =  π*x²      ⇒    12  =  3.14* x²    ⇒  12/3.14  =  x²

x²  = 3,82     ⇒   x  = √3,82    ⇒  x = 1,954 m

Finally plugging ths value in equation (1)

0,5  = 6,28*1,954*dx/dt

dx/dt  =  0,5 /12.28

dx/dt  =  0,04 m/sec

7 0
1 year ago
Read 2 more answers
Which of the following groups has terms that can be used interchangeably with the others?1. Percentage, Probability, and Proport
Dafna1 [17]

Answer: 1) Percentage, Probability, Proportion

Step-by-step explanation:

In statistics,

▪Proportion means a fraction of the total.

▪Percentage means a number or a ratio, expressed as a fraction of 100. Here, the total is 100.

▪Probability which may look slightly different from the other two means a number between 0 and 1, showing the exact likelihood of an event happening. Which in context can mean, a number showing a fraction of an event happening out of the whole (0 to 1).

▪Critical value means a point in hypothesis testing on the test distribution that is compared to the test statistic to determine whether to reject the null hypothesis.

In the four definitions, the odd one out is Critical Value.

So the option without critical value in it is option 1) Percentage, Probability, Proportion since we can use the three interchangeable.

6 0
2 years ago
Read 2 more answers
Quincy feeds his dog 2.75 cups food each day each cup of dog food costs $1.25. He multiplies the numbers together to determine h
Flura [38]

2times1 because 2.75 take the 75 off and 1.25 take the 25 off so you multiply 2 and 1 so 2times1 equals 2

6 0
2 years ago
What type of triangle has side lengths 12, 13, and 2√3?
Travka [436]

Answer:

The triangle is an obtuse scalene triangle

Step-by-step explanation:

we know that

if c^{2}=a^{2}+b^{2} --------> is a right triangle

if c^{2}>a^{2}+b^{2} --------> is an obtuse triangle

if c^{2} --------> is an acute triangle

where

c is the greater side

we have

c=13\ units

a=12\ units

b=2\sqrt{3}\ units

so

c^{2}=13^{2}=169

a^{2}+b^{2}=12^{2}+(2\sqrt{3})^{2}=156

so

c^{2}>a^{2}+b^{2} -------> is an obtuse triangle

Remember that

The given triangle has three different length side

so

Is a scalene triangle

therefore

The triangle is an obtuse scalene triangle

4 0
1 year ago
Other questions:
  • Gillian purchased 25 books at the library book sale. Each hardcover book cost $1.50, and each paperback book cost $0.50. Gillian
    9·2 answers
  • for every 5 coins carmen gets, she gives 2 to her brother Frankie. If carmen has 9 coins, how many does frankie have?
    15·1 answer
  • What is the midpoint of a line segment with the endpoints (-6, -3) and (9, -7)?
    6·1 answer
  • If x=6 is the only x-intercept of the graph of a quadratic equation, which statement best describes the discriminant of the equa
    6·1 answer
  • A shop sells three types of boots sales are usually in the ratio of 6:2:3 last month 24 football boots were sold how many boots
    14·1 answer
  • Triangle XYZ with vertices X(0, 0), Y(0, –2), and Z(–2, –2) is rotated to create the image triangle X'(0, 0), Y'(2, 0), and Z'(2
    15·2 answers
  • If a study determines the difference in average salary for subpopulations of people with blue eyes and people with brown eyes is
    13·1 answer
  • Factor to write an equivalent expression: 26a - 10
    13·2 answers
  • On a coordinate plane, a piecewise function has 3 lines. The graph shows cleaning time in hours on the x-axis and total cost in
    12·1 answer
  • 12 pots cost $27 . what is the cost of 8 pots?​
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!