Answers
Answer:
The measure of the vertex angle is 94 degrees ⇒ A
Step-by-step explanation:
In any triangle, the sum of the measures of its interior angle is 180°In the isosceles triangle, the two base angles are equal in measures∵ In an isosceles triangle, the measure of the base angle = (2x + 5)
∵ The base angles of the isosceles triangles are equal in measures
∴ The measures of the base angles are (2x + 5), (2x + 5)
∵ The measure of the vertex angle = (5x - 1)
∵ The sum of the measure of the three angles = 180°
∴ (2x + 5) + (2x + 5) + (5x - 1) = 180
→ Add the like terms in the left side
∵ (2x + 2x + 5x) + (5 + 5 + -1) = 180
∴ 9x + 9 = 180
→ Subtract 9 from both sides
∴ 9x + 9 - 9 = 180 - 9
∴ 9x = 171
→ Divide both sides by 9 to find x
∴ x = 19
→ Substitute the value of x in the measure of the vertex angle to find it
∵ The measure of the vertex angle = 5x - 1
∴ The measure of the vertex angle = 5(19) - 1
∴ The measure of the vertex angle = 95 - 1
∴ The measure of the vertex angle = 94°
∴ The measure of the vertex angle is 94 degrees
Related Questions
A bacteria triples its original population in 25 hours (A=3A0). How big will its population be in 100 hours?
Answers
Answer:
81 times the original size.
Step-by-step explanation:
AA0ktA=3A0=?=?=25hours=A0ekt
Substitute the values in the formula.
3A0=A0ek⋅25
Solve for k. Divide each side by A0.
3A0A0=e25k
Take the natural log of each side.
ln3=lne25k
Use the power property.
ln3=25klne
Simplify.
ln3=25k
Divide each side by 25.
ln325=k
Approximate the answer.
k≈0.044
We use this rate of growth to predict the number of bacteria there will be in 100 hours.
AA0ktA=3A0=?=ln325=100hours=A0ekt
Substitute in the values.
A=A0eln325⋅100
Evaluate.
A=81A0
At this rate of growth, we can expect the population to be 81 times as large as the original population.
Answer:
81
Step-by-step explanation:
A person who weighs 100 pounds on Earth weighs 16.5 pounds on the moon. If a boy weighs 60 pounds on Earth, how much does he weigh on the moon?
Answers
Answer:
The answer is 10 Pounds.
Step-by-step explanation:
You get 10 pounds because you divide your weight by 6 and 60 divided by 6 is 10.
Answer:
3.636363636
Step-by-step explanation:
Because that is 16.5 percent of 60, you can find this by dividing 60 by your percentage your trying to find of it, 16.5 in this case.
{4,5,6} is a subset of {4,5,6} True False
Answers
They are the same numbers so they have to be the subset of each other
Hellp pls this is not a quiz
Answers
Answer:
The answer is D.
Step-by-step explanation:
Remember, think of what they would be like on a number line. The negative number closest to zero is greater than the negative numbers farther from zero. Any number that is to the left of a certain number is less than, if that makes any sense.
PLZ HELP MEEEE!!!
Hannah is trying to figure out how tooth size is determined in two different wolves. In wolf 1, the copies of the gene are different from each other. In wolf 2, the copies of the gene are the same as each other. How does this affect how many types of proteins there are in each tooth cell?
a
Wolf 1 has one type of protein for the tooth size feature. Wolf 2 has one type of protein for the tooth size feature.
b
Wolf 1 has two types of protein for the tooth size feature. Wolf 2 has one type of protein for the tooth size feature.
c
Wolf 1 has two types of protein for the tooth size feature. Wolf 2 has two types of protein for the tooth size feature.
d
It is impossible to say anything about proteins from the given information.
Answers
Answer:
It is impossible to say anything about proteins from the given information.
Step-by-step explanation:
Given three data points: (x0, f(x0)), (x1, f(x1)), and (x2, f(x2)), prove the expression for the coefficient b2 in the quadratic interpolation is:________
Answers
Answer:
attached below is the prove
Step-by-step explanation:
In order to prove the expression for coefficient b[tex]_{2}[/tex] we have to find b[tex]_{0}[/tex] and b[tex]_{1}[/tex]
F(x) = [tex]b_{0} + b_{1} ( x - x_{0} ) + b_{2} ( x - x_{0} ) (x - x_{1} )[/tex]
i) Determine b[tex]_{0}[/tex]
at x = x[tex]_{0}[/tex]
b[tex]_{0}[/tex] = f(x[tex]_{0}[/tex] )
ii) Determine b[tex]_{1}[/tex]
at x = [tex]x_{1}[/tex]
f ([tex]x_{1}[/tex]) = f ([tex]x_{0}[/tex] ) + b[tex]_{1}[/tex] [tex](x_{1} - x_{0} )[/tex] + 0
[tex]b_{1} = \frac{f(x_{1} )-f(x_{0} )}{(x_{1}-x_{0} ) }[/tex]
prove of the expression for the coefficient B2 in the quadratic interpolation
attached below is the detailed prove
Chris got 28 out of 35 correct in his test. What fraction of the marks did he get wrong? Give your answer in its simplest form.
Answers
Answer:
3/35
Step-by-step explanation:
Chris got 28 out of 35 correct in his test
So
he get wrong=3
fraction= 3/35
So 3/35 is the answer
I need help on this question, I can't seem to understand piecewise functions!! ITS SO HARD.
Answers
Answer:
[tex]f(x)\left \{ {{3x+1 if x\leq 0} \atop {-3x+1 if x>0}} \right.[/tex]
Step-by-step explanation:
So if we first graph the given equation, we'll see the graph I've attached below.
Remember that piecewise functions are functions that change based on the circumstances. I know that sounds super confusing, but it's actually really simple!
In this case, for example, we see the line increasing from -∞ to [tex]0[/tex], and then suddenly going downwards and decreasing. That's a good spot for us to notice because that indicates a change. We notice that the function looks different when [tex]x<0[/tex] or [tex]x>0[/tex]. If you break the function into those two parts, you see that they are just linear equations, but they're only visible when x is either greater than or less than 0.
Now that we notice this pattern, we can find the equation of the lines for both lines.
The points (-3,-8) and (-1,-2) are points on the first line, the one that increases (on the left). We can use those points to find the slope of the first line. Remember the slope equation:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
Plug in your points:
[tex]m=\frac{-2-(-8)}{-1-(-3)}[/tex]
[tex]m=\frac{6}{2}[/tex]
[tex]m=3[/tex]
So, the slope of the first line is 3. The y-intercept, looking at the graph, is 1. The equation of the first line is [tex]y=3x+1[/tex]. We'll need this later.
Let's do the same thing for the second line. Just looking at the graph, we can see that this is the same exact line, just with a negative slope. So, the equation for the second line is [tex]y=-3x+1[/tex].
So now we can set up a piecewise function.
[tex]f(x)\left \{ {{3x+1} \atop {-3x+1}} \right.[/tex]
The two functions in the bracket are the two different functions used in this graph. Now we need to figure out where each function is effective. Well, they share a y-intercept. Remember that a true function cannot have two points with the same x value. So the first function is effective to the left of x=0, while the second is effective to the right of x=0. In other words, when [tex]x\leq 0[/tex], [tex]f(x)=3x+1[/tex]. But, when [tex]x>0[/tex], [tex]f(x)=-3x+1[/tex]. Now our piecewise function looks like this:
[tex]f(x)\left \{ {{3x+1 if x\leq 0} \atop {-3x+1 if x>0}} \right.[/tex]
And that is our piecewise function for the original function.
I know this is confusing, so please let me know if you have any questions! I hope this helps!
From a standard deck of 52 cards, you’re dealt 5 cards. How many hands have at least one spade and at least one queen?
Answers
Answer: c
Step-by-step explanation:
I took the quiz
Identify the terms in the expression. Separate your terms with a comma.
−12a−4b+9−3a
Answers
x + 1 - x = 1
Solve the equation
Thanks
Answers
20 POINTS
All side lengths in quadrilateral PQRS measure 6 units. A transformation maps
PQRS to P'Q'R'S'. All sides of P'Q'R'S' measure 3 units. Is the mapping isometric?
Explain.
Answers
An isometric transformation is a transformation that preserves the distance and angles between a pre-image and its image. Examples are: translation, reflection, rotation.
Answer:
No, the side lengths are not preserved.
This is a non isometric transformation.
Please help
What is the absolute value of the number indicated on the number line?
A. 3
B. -4
C. 4
D. -3
Answers
Answer:
C
Step-by-step explanation:
A number's absolute value is its distance from zero. -4 is 4 units from zero so its absolute value is 4
Hope this helps!
Answer:
4
Step-by-step explanation:
absolute value is is the non negative value of that number (example 3=3, -4=4
Which of the following phrases could represent the expression k - 4?
four less a number
a number less than four
a number decreased by four
a number subtracted from four
Answers
Answer:
a number decreased by four
Step-by-step explanation:
Find the measure of each angle 9-17. PLZZZ HELP will give brainliest!!!! Pleaseee help!!!!!
Answers
Answer:
Step-by-step explanation:
l║m and line t is the transversal line intersecting these parallel lines.
9). If m∠7 = 100°,
m∠3 = m∠7 = 100° [Since, ∠3 and ∠7 are alternate interior angles]
10). m∠7 = 95°
m∠6 + m∠7 = 180° [Consecutive interior angles]
m∠6 = 180° - m∠7
m∠6 = 180° - 95°
m∠6 = 85°
11. m∠1 = 120°
m∠1 = m∠5 = 120° [Alternate exterior angles]
12. m∠4 = 20°
Since, m∠4 = m∠6 = 20° [Vertically opposite angles]
And m∠6 + m∠7 = 180° [Consecutive interior angles]
20° + m∠7 = 180°
m∠7 = 160°
13. m∠3 = 140°
m∠3 + m∠6 = 180° [Linear pair of angles]
m∠6 = 180° - m∠3
= 180° - 140°
= 40°
m∠6 = m∠8 = 40° [Corresponding angles]
14. m∠4 = 30°
m∠4 + m∠1 = 180° [Consecutive exterior angles]
m∠1 = 180° - 30°
m∠1 = 150°
15. m∠4 = 40°
m∠4 = m∠2 = 40° [Corresponding angles]
16. m∠7 = 125°
m∠6 + m∠7 = 180° [Consecutive interior angles]
m∠6 = 180° - 125°
= 55°
m∠6 = m∠4 = 55° [Vertically opposite angles]
17. m∠1 + m∠3 = 230°
Since, m∠1 = m∠3 [Corresponding angles]
m∠3 + m∠3 = 230°
m∠3 = [tex]\frac{230}{2}[/tex]
= 115°
m∠3 + m∠6 = 180° [Linear pair of angles]
m∠6 = 180° - 115°
m∠6 = 65°
Elias’s teacher has given him a rectangle that is 15 feet by 20 feet. She has asked him to create a new rectangle using a scale factor of 8/3. Elias says that will be a reduction because the scale factor is a fraction. Is he correct? Explain.
Answers
Answer:
17.68 feat long
Step-by-step explanation:
Answer:
17.68 feet
Step-by-step explanation:
If Toni is trying to calculate her net worth, which of the following items would go on the liabilities list? *
A. Original sale price of her car
B.Her Mortgage
C.Savings account balance
D. Value of her 401(k) plan
Answers
Answer:
B.Her Mortgage
Step-by-step explanation:
The net worth is the value that left after deducting the liabilities from the assets
Here as per the given options, the original sale price of the car, saving account balance and the value of her 401(k) plan is an asset
While the liabilities is the mortgage that took by her as she has to repay the amount taken by the financial insititution. It is her responsibility to pay back all the dues to the bank
Therefore the option B is correct
The perimeter of a rectangular picture frame is 62 inches. The length of the 1
frame is one more than twice its width. What are the length and the width
of the frame?
Answers
Answer- each width = 10, each length = 21
Explanation: from the question we know that L=2w + 1 and we also know that a rectangle has the perimeter of 62 when we plug it in the equation we will get 62= 2(2w+1+w) we will multiply the 2 now and we will get 62=4w+2+2w we will combine like terms and we will minus two from both sides ending up with 60=6w we will divide six from both sides and we will get w=10 then we will use l=2w+1 to find the length and it will be 21
Yooo
Does anyone know the answers to these 2?
1. Solve each of the quadratic equations.
3x = 0.5x2
A. x = -6 or x = 0
B. x = -4 or x = 3
C. x = -2 or x = 1.5
D. x = 0 or x = 6
2. See image below
Answers
Answer: the first one is d the second one is c
Step-by-step explanation: e2020
Determine if triangle XYZ with coordinates x (1, 1), y (5,6) and z (6,2) is a right triangle
Answers
Answer:
No(im not totally sure though because its slanted.)
Step-by-step explanation:
desmos.
Tip of 20% on a $5 meal
Answers
Answer:
$1
Step-by-step explanation:
20% of $5 = 0.20*5 = $1.00
2. There is a 50% chance that Elaine will be late to school, a 40% chance that she will be late to
school and eat breakfast, and a 60% chance that she will be late for school or eat breakfast. What
is the probability that Elaine will eat breakfast?
(1 Point)
30%
Ο Ο
40%
50%
Ο Ο
60%
Answers
Answer:
50%
Step-by-step explanation:
Given that:
P(late) = P(L) = 50% = 0.5
P(Eat) = P(E) =?
P(LnE) = 40% = 0.4
P(LuE) = 60% = 0.6
P(LuE) = P(L) + P(E) - P(LnE)
0.6 = 0.5 + x - 0.4
0.6 = 0.1 + x
0.6 - 0.1 = x
0.5 = x
P(E) = 0.5
0.5 * 100% = 50%
There are 24 more students in the seventh grade class than the number g in the eighth grade class. The seventh grade class has 160 students. Write and solve an equation to find the number of students in the eighth grade class.
Answers
Answer:
y= 8th grade class,
y + 24 =160
subtract 24 from both sides
y=136
there are 136 students in the eight grade class
Step-by-step explanation:
Answer:
136 students
Step-by-step explanation:
7th grade= 160 students
8th grade= g students
g= 160-24
g= 136 students
- I hope this helps have a great day!
Can some one please help with this question
Answers
Answer:
5x + 9
Step-by-step explanation:
f(x) = 3x+4
g(x) = 2x + 5
(f+g)(x)
(3x+4) + (2x + 5)
= 5x + 9
// however I'm unsure
Suppose that you plan on taking a summer job selling magazine subscriptions. The magazine company will pay you $1.25 for selling the first subscription. For each additional subscription sold, the magazine company will pay you 25 cents more than what was paid for the previous subscription. How much will you earn by selling 200 magazine subscriptions?
Answers
Answer:
the organize is a explanation to the earth
Step-by-step explanation:
yan lang alam ko
Write a word problem that could be solved with the equation
0.15x + 200 650
Answers
Answer:
13.3
Step-by-step explanation:
the amount of water in a barrel decreased is 9 5/8 pints in 7 weeks
Answers
Answer:
1 3/8 in one week
Step-by-step explanation:
The perimeter of a rectangle is 80 cm. The width is 10 cm more than twice the length. What
is the length and width of this rectangle? P=2W+2L
Answers
Answer:
L=10cm , W=30cm
Step-by-step explanation:
First use the given that W=10+2*L
Use P=2W+2L=80, substitute W in the perimeter formula
2(10+2L)+2L=80 and solve for L,
20+4L+2L=80 isolate variable L and combine like terms,
6L=80-20,
L=10, so W=10+2*10=10+20=30
Work out (7 x 10^5) divided by (2 x 10^2)
Answers
Answer: 3500
Step-by-step explanation:
7x10^5
————-
2x10^2
= 700,000/200
= 3,500
Children may ask what is 6+100, 6+100 equals to 106
Answers
Answer:
ye thats true..
Step-by-step explanation:
