Mathematics High School

The vertex angle of an isosceles triangle is 20° less than the sum of the base angles. Which system of equations can be used to find the measure of the vertex and base angles?

A)
v + 2b = 180; 2b - 20 = v


B)
v + 2b = 180; 2b + 20 = v


C)
v - 2b = 180; v + 2b = -20


D)
v - 2b = 180; -2b - 20 = v

Answers

Answer 1

The answer to the above question can be explained as under -

We know that, the sum of angles of triangle is 180°.

So, vertex angle plus base angles are equal are equal to 180°.

Let the vertex angle be represented by "v" and base angles be represented by "b".

Thus,  v + b + b = 180°

So,  v + 2b = 180°

Next, the question says, the vertex angle is 20° less than the sum of base angles.

Thus, 2b - 20° = v

Thus, we can conclude that the correct option is A) v + 2b = 180°, 2b - 20° = v

Answer 2

The correct system of equations for an isosceles triangle where the vertex angle is 20 degrees less than the sum of the base angles is v + 2b = 180 for the sum of the angles, and 2b - 20 = v for the relationship between the base angles and the vertex angle. Option A is correct.

The correct system of equations to find the measure of the vertex and base angles of an isosceles triangle, where the vertex angle is 20° less than the sum of the base angles, is given by option A. The two equations can be described as follows:

The sum of the angles in a triangle is 180°, leading to the equation: v + 2b = 180.The vertex angle v is 20° less than the sum of the base angles, giving us the equation: 2b - 20 = v.

To solve for the angles, you would substitute the expression for v from the second equation into the first and then solve for b, which represents the measure of each base angle. Once you have b, you can find v by substituting b back into the second equation.

Related Questions

the diagonals of a rhombus are 12 centimeters and 16 centimeters. what is the length of one side of the rhombus?

Answers

in a rhombus, the diagonals meet at right-angles, and they bisect each other, namely they cut each other in half, check the picture below.

thus we can use the pythagorean theorem to get one side, keeping in mind that, slanted as it may be, all sides in a rhombus are equal in length.

Solve the quadratic equation. 8x2 + 16x + 8 = 0 A) 1 B) -1 C) 1 and 8 D) 1 and -1

Answers

[tex]8x^2+16x+8=0\\\\8(x^2+2x+1)=0\ \ \ |:8\\\\x^2+2x+1=0\\\\x^2+x+x+1=0\\\\x(x+1)+1(x+1)=0\\\\(x+1)(x+1)=0\\\\(x+1)^2=0\iff x+1=0\\\\\boxed{x=-1}[/tex]
Answer: B. -1

PLEASE HELP 50 point will give brainlyest
Evaluate 81000−−−−√3 .


1/125

6/500

8/500

2/10

Answers

when I did it I got 140296.11541307
THE ANSWER IS B: 6/500 :) JUST LIKE IT AND VOTE ON IT PLZ THANK U AND HAVE A OOF DAY XD have a good day lel

The Venn diagram represents the results of a survey that asked participants whether they would want a bird or a fish as a pet.



Enter your answers in the boxes to complete the two-way table based on the given data.

Answers

Answer with Step-by-step explanation:

As we can see the venn diagram:

number of bird+fish=6

number of bird+not fish=8

number of fish+not bird=19

and number of not fish and not bird=22

Hence, we get the following table

                        Fish           Not Fish            Total

Bird                6                    8                       14

Not Bird         19                  22                       41

Total               25                 30                       55

                Fish    Not Fish   Total

Bird            6            18           14

Not Bird    19           22          41

Total          25           30         55

I need help on this show steps pleaseeee!!!

Answers

Step #1 - convert 1 ⅓ into a mixed number,

[tex] \frac{1}{2}r - \frac{1}{3} - \frac{4}{3} = - \frac{7}{3} [/tex]

Step #2 - calculate the sum or difference of - ⅓ by -4/3,

[tex] \frac{1}{2}r - \frac{5}{3} = - \frac{7}{3} [/tex]

Step #3 - Multiply both sides by 6,

[tex] \frac{1}{2} (6)r - \frac{5}{3} (6) = - \frac{7}{3} (6)[/tex]

[tex]3r - 10 = - 14[/tex]

Step #4 - Move constant ( - 10 ) to the right and change its sign,

[tex]3r = - 14 + 10[/tex]

Step #5 - Calculate the sum

[tex]3r = - 4[/tex]

Step #6 - Divide both sides by 3 so we can isolate the variable r,

[tex]r = - \frac{4}{3} [/tex]

~~

I hope that helps you out!!

Any more questions, please feel free to ask me and I will gladly help you out!!

~Zoey

suppose you drop a tennis ball from a height of 15 feet. After the ball hits the floor, it rebounds to 85% of its previous height. how high will the ball rebound after its third bounce? round to the nearest tenth

Answers

The answer would be 10.84

Help me solve this please!

Answers

The problem statement suggests you use a calculator. A graphing calculator can give the answers you seek.

a) The calculator shows 5 solutions:
  {5π/23, 5π/17, 25π/23, 25π/17, 45π/23}
These have approximate decimal values of
  {0.6830, 0.9240, 3.4148, 4.6200, 6.1466}

b) The calculator shows 2 solutions with approximate decimal values of
  {1.2925, 4.4341}

c) The calculator shows 2 solutions with approximate decimal values of
  {1.3694, 4.9137}

_____
This (desmos) calculator displays intercepts to 3 decimal places. Since you want 4 decimal places, some additional refinement of the answer was necessary. That was accomplished using Newton's method iteration. The details are not shown. A suitable graphing calculator (for example, a TI-84) will supply the intercept coordinates to full calculator accuracy.

A catapult is malfunctioning and not throwing objects in the intended manner. The builders have modeled the path of the objects thrown by using the following parametric equations. rewrite the parametric equations by eliminating the parameter.
x(t)=2t-1
y(t)= square root of t; t> or equal to 0

Answers

Answer:

The equation is [tex]y ^ 2 = \frac{x + 1}{2}[/tex]

Step-by-step explanation:

The parameter that we have is t. We want to eliminate this parameter in both equations, therefore in the first equation we solve for t and in the second equation we solve for the variable t.

We have:

[tex]x = 2t-1\\\\x + 1 = 2t\\\\t = \frac{x + 1}{2}[/tex]

Now we solve the other equation for t.

[tex]y= \sqrt{t}[/tex]

[tex]y ^ 2 = t[/tex]     because   [tex]t> 0[/tex]

As [tex]t = y ^ 2[/tex] and also [tex]t = \frac{x + 1}{2}[/tex]

Then:

[tex]y ^ 2 = \frac{x + 1}{2}[/tex]

The correct answer is:

D. [tex]x=2y^{2} -1, y\geq 0[/tex]

12x2 = 18x
i need someone to explain this

Answers

we have that
12x² = 18x------> 12x²-18x=0-----> divided by 12----> x²-(3/2)*x=0
this is the equation of a vertical parabola 
x²-(3/2)*x=0-----> x*(x-1.5)=0
the x-intercepts of the parabola are
x=0
x=1.5

using a graph tool
see the attached figure

Need help on this question

Answers

Total Area: T.A.=2*Ab+Al

Area of the base: Ab=p*K

Semi-perimeter of the base: p
p=P/2
Perimeter of the base: P=20
p=P/2=20/2→p=10
Ab=p*k=10*K→Ab=10K

Lateral Area of the prism: Al
Al=P*h
Height of the prism: h=6
Al=P*h=20*6→
Al=120

T.A.=2*Ab+Al
T.A.=2*(10K)+120
T.A.=20K+120
T.A.=120+20K

Answer: (120+20K)



please help- Your supposed to find x, y, and z and round to the nearest tenth

Answers

Didn't you mean "you are" or "you're?"

You didn't indicate which problem you wanted your helper to focus on.  So I will arbitrarily choose #2.

This large triangle is made up of two smaller triangles:  the smaller triangle has sides of 2 and x and hypotenuse of y.  The larger triangle has sides x and 5 and hypotenuse z.  Look carefully:  The largest triangle has hypotenuse (2+5) and sides y and z.  Now you have three equations in three unknowns and thus have enough info to find the values of x, y and z.

Think about this.  What should you do first?  Type back your ideas.  Then I'll help you solve this problem.

on Sunday Mary pay $6 each on two tickets to a movie theater movies for $9.58 each Mary paid with 3 $20 bills how much changed

Answers

$50.42







hjdjdjdjdbdhshssjdjdjdjdj

Kenny is making creamy rice pudding his recipe requires 4 cups of milk he has a quart of milk in his fridge dose he have enough milk explain

Answers

yes, because 4 cups = 1 quart 

What is the point-slope equation of the line with a slope 4/3 that goes through the point (-4,6)?

Answers

[tex]\bf (\stackrel{x_1}{-4}~,~\stackrel{y_1}{6})~\hspace{10em}slope = m\implies \cfrac{4}{3}\\\\\\\begin{array}{|c|ll}\cline{1-1}\textit{point-slope form}\\\cline{1-1}\\y-y_1=m(x-x_1)\\\\\cline{1-1}\end{array}\implies y-6=\cfrac{4}{3}[x-(-4)]\implies y-6=\cfrac{4}{3}(x+4)[/tex]

Answer:

The point-slope form of the equation is y - 6 = 4/3(x + 4), which is answer B.

Step-by-step explanation:

In order to find the point-slope form of any equation, start with the base form of the equation.

y - y1 = m(x - x1)

Now input the slope given as m, and the point in for x1 and y1.

y - y1 = m(x - x1)

y - 6 = 4/3(x - -4)

y - 6 = 4/3(x + 4)

how do I solve (x-5)(x-1)=0

Answers

With this equation, you'd distribute one set of parenthesis into the other. Doing so you'd get "X^2 - 1x - 5x + 5 = 0". Simplified, you'd have "X^2 - 6x + 5 = 0"

Next, you'd find the factors of 5, that when multiplied equal 5, and when added, equal -6. Being that 5 is a prime number (a number that is only divisible by 1 and itself) those numbers are 1 and 5. Both numbers have to be negative, in order to get -6.

-1*-5 = 5
-1 + -5 = -6

Finally you split up the X^2 to a single x with each of the factors and make it equal to zero (X - 1 = 0) and (X - 5 = 0). Then you solve each.

(X - 1 = 0) Add 1 to each side. X = 1
(X - 5 = 0) Add 5 to each side. X = 5

I hope this helps!

What is the value of x? Round the answer to the nearest tenth. The diagram is not drawn to scale.

Answers

x = 50 

Reason: Chord AB and Chord CD are equal.

We have been given that the chords AB and CD are equal.

Now, we know that two equal chords subtends equal angle at the center of the circle.

The chord CD subtends and angle CPD at the center and the chord AB subtends an angle APB at the center.

Hence, from above mentioned theorem, we can say that

[tex]\angle CPD = \angle APB[/tex]

Now, we have been given that

[tex]\angle CPD =50 ^{\circ} [/tex]

[tex]\angle APB =x ^{\circ} [/tex]

Hence, we have

[tex]x=50^{\circ}[/tex]

How do you use properties of exponents and logarithms to rewrite functions in equivalent forms and solve equations?

Answers

Some of the logarithmic properties most used to solve equations are the following.
 1) log (a) ^ b = b * log (a)
 2) log (a * b) = log (a) + log (b)
 3) log (a / b) = log (a) - log (b)
 These logarithmic properties can be used to solve equations.
 For example:
 2 ^ x = 56
 If we apply to this equation the logarithm function on both sides that we have left
 log (2) ^ x = log (56)
 This function is equivalent to the first.
 If we now apply the property 1) of the previous logarithms, we can reveal x of the equation.
 x * log (2) = log (56)
 x = log (56) / log (2)
 x = 5,807
 Thus, thanks to the properties of the logarithms, this exponential function could be solved

Final answer:

To use properties of exponents and logarithms effectively, one must apply specific rules such as the logarithm of a product being the sum of the logarithms and the logarithm of a number raised to an exponent being the product of the exponent and the logarithm. Log transformations help linearize and solve equations involving exponents.

Explanation:

To rewrite functions in equivalent forms and solve equations using the properties of exponents and logarithms, one must understand several key rules and relationships. For example, the common logarithm (log) indicates the power to which 10 must be raised to equal a given number.

Two essential properties we use are:

The logarithm of a product of two numbers is the sum of the logarithms of the two numbers (log xy = log x + log y).The logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number (log x^n = n log x).

Exponential and logarithmic functions are inverses. This relationship allows us to simplify complex expressions and solve exponential equations by taking the logarithm of both sides. For instance, the natural logarithm (ln or loge) and the base e exponential are inverse functions, so ln (e^x) = x and e^(ln x) = x.

A log transformation can linearize functions that involve an exponent by taking the log of both sides of the equation. This technique is valuable in solving equations where the variable is an exponent.

Which triangles are similar?

a
b
c
d

Answers

i think A. and D.

hope that's right!!!
Hey there!

The two triangles that are similar are triangles A and D.

I hope this helped! :-)

"the placement test for a college has scores that are normally distributed with a mean of 600 and a standard deviation of 60.if the college accepts only the top 1​% of​ examinees, what is the cutoff score on the test for​ admission?"

Answers

The cutoff will be evaluated as follows:
let the cutoff be x

but
P(x>0.01)=1-P(x<0.01)=1-0.01=0.99
the z value corresponding to 0.99% is z=2.33
thus
2.33=(x-600)/60
solving for x we get:
139.8=x-600
x=739.8

someone help me please

Answers

For this case we have the following functions:
 f (x) = 3x + 1
 g (x) = x ^ 2 - 6
 Subtracting both functions we have:
 (f-g) (x) = f (x) - g (x)
 (f-g) (x) = (3x + 1) - (x ^ 2 - 6)
 (f-g) (x) = 3x + 1 - x ^ 2 + 6
 (f-g) (x) = - x ^ 2 + 3x + 7
 Answer:
 (f-g) (x) = - x ^ 2 + 3x + 7
 option B

When he was 40 Keefer began investing $150 per month in various securities for his retirement savings. His investments averaged a 4.5% annual rate of return until he retired at age 70. What was the value of Keefer's retirement savings when he retired? Assume monthly compounding of interest.

Answers

At retirement, Keefer will have saved for 30 (that is, 70-40) years.
Monthly saving, P = $150, Annual rate of return, R = 4.5% = 0.045.

Therefore, future value (FV) at the time of retirement will be;

FV = P*[1+(R/12)^12*30]/(R/12)
Substituting all the parameters;
FV = 150*[1+(1+0.045/12)^360]/(0.045/12) = $113.907.92

Plato explains that we know geometry by _________.

Answers

Plato explains that we know geometry by our gain knowledge through recollection. Our soul is what recollects this place hence we came where there exist unchanging truths. Delivered the theory of Forms, according to which the world people know by means of the senses is just an imitation of the eternal, pure, eternal, and fixed world of the Forms.

Help Geometry!!
AC is tangent to circle O at A. If , m<BY= 24 , what is m<YAC?

a) 48

b) 156

c) 78

d) 132

Answers

we know that
The inscribed angle measures half of the arc it comprises.
so
∡BAY=BY/2------> 24/2------> 12°

angles YAC and BAY are complementary angles
∡YAC+∡BAY=90°
∡YAC=90-∡BAY-------> ∡YAC=90-12-----> 78°

the answer is
78°

HELP!!!!!!NEED TO PASS!!!!WILL GIVE THE BRAIN!!!!!!!!!!!

Answers

Shifting left means adding a number to x.

So, x³ shifted 5 units to left will be (x + 5)³

Shifting 4 units upwards means adding 4 to the function value,

So, previous function shifted 4 units up will be (x + 5)³ + 4

Thus, g(x) = (x + 5)³ + 4

So, option b gives the correct answer



So, option b gives the correct answer

What is the linear function that best fits the data set?

Answers

Answer: Fourth option y=-3x+15
Please, see the attached file.
Thanks.

My brother owes me $10. I already have $10. My dads friend gave me and him $20 to split in half. He gave me the $20 and took my $10. Does he still owe me. Explain plz

Answers

Yes...     You have $10
               your brother is supposed to give you $10
               he gives you the money the friend told him to and you would have $20 PLUS the ten that he owes you. That would make you have $30. He took youre ten and gave you 20 but you were supposed to have 20 in the first place. He needs to give you the ten back he owes you. 

Find the value of the combination 9 c 4

Answers

9C4= 126.

Hope this helps

Alan is giving a basic math test in his class. One of the questions in the test is about finding two factors of the number 221. Which are the two factors of the given number? The two factors of the number 221 are ___ and ____.

Answers

1,13,17 are three of them 

The two factors of the number 221 are 13 and 17. 
A factor refers to a whole number, which fits evenly into another whole number. Thus, factors are the numbers, which we multiply together to get another number. The two numbers that can be multiply together to get 221 are 13 and 17.

A car is traveling at a speed of 50 miles per hour. Each wheel of the car makes 770 revolutions per minute. To the nearest tenth of an inch, what is the diameter of each car wheel? (Note: 1 mile = 5,280 feet)

Answers

Answer: 21.8 inches

Given:

A car is traveling at a speed of 50 miles per hour. Each wheel of the car makes 770 revolutions per minute.

To get the diameter of each car wheel

Get first the length of revolution (circumference of the wheel) in inches.

Speed=50 miles/hr

=50miles/60 minutes

= 0.833333 miles/minute

=.833/5280=4400ft= 52,800 inches/minute

Since there are 770 revolutions per minute, per revolution  (circumference of the wheel) =

=52,800/770

=68.57 inches

Formula of diameter given the circumference is:

D=C/π 

D=68.57/3.14

D= 21.8 inches 

Answer:

21.8

Step-by-step explanation:

just took test

Simplify the square root of 864.
I cant remember this, please tell me how you got the answer.

Answers


[tex] \sqrt{864} [/tex]
[tex] \sqrt{4 \times 216} [/tex]
[tex] \sqrt{4 \times 4 \times 54} [/tex]
[tex] \sqrt{4 \times 4 \times 2 \times 27} [/tex]
[tex] \sqrt{4 \times 4 \times 2 \times 9 \times 3} [/tex]
now take out the pairs.
[tex]4 \sqrt{2 \times 9 \times 3} [/tex]
take out any of the square roots like 9
[tex]4 \times 3 \sqrt{2 \times 3} [/tex]
Now put it all back together.
[tex]12 \sqrt{6} [/tex]
I believe that is the answer.
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