Final answer:
To simplify the expression sqrt(18) + sqrt(50), find the square roots of 18 and 50 individually and then add them together.
Explanation:
To simplify the expression sqrt(18) + sqrt(50), we need to find the square roots of 18 and 50 individually and then add them together. The square root of 18 is approximately 4.2426 and the square root of 50 is approximately 7.0711. Adding these two values gives us approximately 11.3137. Therefore, the simplified expression is sqrt(18) + sqrt(50) = 11.3137.
When does the graph of a quadratic function open up?open down?
The graph of a quadratic function opens up when a (<,>,=) 0 and opens down when a (<,>,=) 0
Answer:
1. >
2. <
Step-by-step explanation:
When a > 0, the graph opens upwards, or positively, because the way the line curves is determined by a.
When a < 0, the graph opens downwards, or negatively, for the same reason.
Final answer:
The graph of a quadratic function opens upwards when the coefficient of the squared term is positive (a > 0), and opens downwards when this coefficient is negative (a < 0).
Explanation:
The graph of a quadratic function opens up or down based on the sign of the coefficient of the squared term (usually represented as 'a' in the quadratic equation ax2 + bx + c). When this coefficient a is positive (a > 0), the parabola opens upwards. Conversely, if the coefficient a is negative (a < 0), the parabola opens downwards. The orientation of the parabola reflects whether the quadratic function has a minimum value (opening upwards) or a maximum value (opening downwards).
The full question is shown below
Answer:
n = 3
Step-by-step explanation:
Ratio from Triangle A to Triangle B is 2:1.
n+2 = 5
n = 3
Which triangle defined by the given points on the coordinate plane is similar to the triangle illustrated?
Answer:
The correct option in the attached image is:
D. (-1, 1), (-1, 5), (-7, 1)
Step-by-step explanation:
Please refer to the attached image.
The length of the horizontal segment of the graphed triangle is 3. The length of the vertical segment of the triangle graphed is 2. We will use the Pythagorean theorem to find the length of the missing side thus:
x² = 2²+3²
x² = 4+9
x² = 13
x = √13 or 3.6
This makes our side lengths 2, 3, and 3.6
For option A, our vertices are (-1, 1), (-1, 4), (-6, 1). This means the length of the horizontal segment 5 and the length of the vertical segment 3. This missing side length is calculated thus:
x² = 5²+3²
x² = 25+9
x² = 34
x = √34 or 5.83
This is not proportional to the triangle drawn, so it is not similar.
For option B, our vertices are (-1, 1), (-1, 5), and (-6, 1). This makes the horizontal segment 5 units long and the vertical segment 4 units long. This makes the missing side length
x² = 4²+5²
x² = 16+25
x² = 41
x = √41 or 6.4
These are not proportional to the triangle drawn, so the triangles are not similar.
For option C, our vertices are (-1, 1), (-1, 4) and (-7, 1). This makes the length of the horizontal segment 6 and the length of the vertical segment 3. This makes the missing side length
x² = 3²+6²
x² = 9+36
x² = 45
x = √45 or 3√5 or 6.7
These sides are not proportional to the sides of the triangle drawn, so the triangles are not similar.
For option D, our vertices are (-1, 1), (-1, 5) and (-7, 1). This makes the length of the horizontal segment 6 and the length of the vertical segment 4. This makes the missing side length
x² = 6²+4²
x² = 36+16
x² = 52
x = √52 or 2√13 or 7.21
These sides are all twice as long as the sides of the triangle drawn, this indicates that the triangles are similar. Therefore our answer is D.
3. Assume lines that look tangent are tangent. Find the length of the line
segment indicated by the ?
Answer:
20
Step-by-step explanation:
The point of contact of the tangent and the diameter of the circle is a right angle.
Thus the triangle with legs 12 and 2 × 8 = 16 is right
Using Pythagoras' identity.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
?² = 12² + 16² = 144 + 256 = 400 ( take the square root of both sides )
? = [tex]\sqrt{400}[/tex] = 20
Final answer:
The question deals with mathematics, specifically the slope of tangent lines, use of the Pythagorean theorem, and solving scale ratios and proportions. Students need to find specific lengths using provided endpoints, hypotenuse calculations, and scale conversions.
Explanation:
The student appears to be asking about finding the length of a line segment in a geometric context, possibly related to tangents to curves and the Pythagorean theorem. The student is likely working with a diagram or curve not provided here, so it is important to make use of available data points or diagrams in the course material. Furthermore, when working with scales and ratios for determining lengths, the process involves setting up a proportion, solving for the unknown value by cross-multiplying and dividing.
For the slope of the tangent line to a curve:
Identify the endpoints of the tangent line that corresponds to given positions and times.
Find the slope of the tangent line, denoted as 'v', by using the change in position over the change in time.
For the Pythagorean theorem:
Calculate the length of the hypotenuse as the square root of the sum of the squares of the other two sides.
Use significant figures appropriately to represent the precision of your result.
For solving ratios and proportions:
Set up the proportion based on given scale lengths and distances.
Solve for the unknown by cross-multiplying and dividing.
How do I solve this equation
Answer: 14
Step-by-step explanation:
the question is just asking you to replace the x and y with the corresponding numbers.
x = 4
y = -3
Since x is 4 squared it would be 16.
-4 times -3 equals positive 12.
That would make the equation
(16 + 12) divided by 2
16 + 12 = 28 divide that by 2 and you’ll get 14.
Answer: 14
Step-by-step explanation:
First plug 4 in for x.
4^2 is equal to 16 because 4 x 4 is 16.
Next, plug in -3 for y.
-4 x -3
4 times 3 is 12 and they are both negative, therefore it turns out as a positive 12.
Then add the numbers on the top of your equation.
16+12=28.
Finally divide the sum by 2.
28 divided by 2= 14
Your answer is 14.
Hope this helps!
1. What is the probability of rolling a number less
than 3 or a six on a standard 6-sided die?
a. 1/6
b. 1/3
c. 1/2
d. 1
e. 3
I'm giving 20 points if you answer correctly
Answer:
1/2
Step-by-step explanation:
There are 2 numbers less than 3. (1 and 2) and one 6 on a dice. Therefore there is a 3 out of 6 chance of rolling one of these 3 numbers (1, 2, and 6). This can be represented as 3/6 which would simplify to 1/2 or 50%.
It can also be found this way...
Probability = Number of desired outcomes ÷ number of possible outcomes. Therefore 3 ÷ 6 = 0.5 which is equal to 50% or 1/2.
I hope you choose my answer so you do well on your assignment! I've gotten an A in math every year :)
Answer:
1/2
Step-by-step explanation:
need help will give brainist
Answer:
1: -2.33 or -7/3
2: - 2.16 or -13/6
3: 3.49 x 10^4
4: 4.28*10-7
5: 0.81 or 9/11
6. 3
7: 8
8: 9 or up
9: 5 or up
10: 0-36
I hope any of this helps.... :D
Absolute 10.7 of percent 11
Answer: = 11.88
This is a 3 step / 4 show workings.
10.7 + Percentage increase = 11%
10.7 + (11% × 10.7) = 10.7 + 11% × 10.7
(1 + 11%) × 10.7 = (100% + 11%) × 10.7
111% × 10.7 = 111 ÷ 100 × 10.7
111 × 10.7 ÷ 100 = 1,187.7 ÷ 100
11.877 ≈ 11.88
Which word BEST describes the number 12 in the expressions 12x − 3(y + 3) + 9x?
A) coefficient
B) constant
C) exponent
D) term
A grocer is making 26 pounds of a batch of
mixed nuts containing cashews and peanuts. The
peanuts cost $2.95 per pound, and the cashews
cost $9.95 per pound. How many pounds of each
item are in the mix if the total value of the mixed
nuts is $132.70?
Answer:
rdgvvsssddas
Step-by-step explanation:
42423412
The label on Lulu’s new roll of tape shows that the roll has 7 meters of tape.
Lulu uses 3,000 millimeters of tape. How many meters does Lulu have left?
(1,000 mm = 1 m)
__ m
Answer:
4 meters
Step-by-step explanation:
7-3=4 m
Answer: Lulu has 4 meters of tape left.
Hope this helps!!
PLEASE HELP QUICK I WILL MARK BRAINLIEST!
Which value for Y in the table would be least likely to indicate an association between the variables?
A plane flies 610 mi with the wind in the same time that it takes to fly 440 mi against the wind. If this plane flies at the rate of 219 mi in still air, what is the speed of the wind? Round to the nearest whole number, if necessary.
Hope it helps I alrady solved it
There are 4 jacks in a standard deck of 52 playing cards. If Patricia selects a card at random, what is the probability that it will be a jack?'
Look at the attached picture⤴
Hope it will help you.
Answer:
1/13
Step-by-step explanation:
Evaluate f(3) for the piecewise function:
f(x) = StartLayout enlarged left-brace 1st Row StartFraction 3 x Over 2 EndFraction + 8, x less-than negative 6 2nd row negative 3 x minus 2, negative 4, less-than-or-equal-to x less-than-or-equal-to 3 Third row 4 x + 4, x greater-than 3 EndLayout
Which value represents f(3)?
Answer:
8
Step-by-step explanation:
Step-by-step explanation: -3x - 2
-3 x 3 = -9
-9 -2 = -11
-11 is the answer.
An equation is shown below 12 -9 + c=12 .What value of c makes the equation true?
A 0
B 3
C 9
D 12
Answer:9
Step-by-step explanation:
12-9=3 12-3=9 3+9=12
So C=9
Hey there!
[tex]\large\boxed{c=9}[/tex]
12 - 9 + c = 12
Combine like terms.
3 + c = 12
Subtract 3 from each side of the equation.
3 - 3 + c = 12 - 3
c = 9
Check:
12 - 9 + c = 12
12 - 9 + 9 = 12
3 + 9 = 12
12 = 12
Hope this helps!
Please help, I have no idea
Answer:
I THINK all but C apply for the second one. Just suggesting, but I hope it helps.
Which of the following geographical features can be found in Central Asia? Select all that apply.
Brahmaputra River
Caspian Sea
Fedchenko Glacier
Himalaya Mountains
Tian Shan Mountains
Timor Sea
the answers are:
Caspian Sea
Fedchenko Glacier
and Tian Shan Mountains
Step-by-step explanation:
i got it right in my quiz
1. The resting heart rates for a sample of individuals are normally distributed with a mean of 70 and a standard deviation of 10 Find the percentage rates of heart rates less than 60.
2. The resting heart rates for a sample of individuals are normally distributed with a mean of 70 and a standard deviation of 10 Find the percentage rates of heart rates less than 80.
3. The resting heart rates for a sample of individuals are normally distributed with a mean of 70 and a standard deviation of 10 Find the percentage rates of heart rates greater than 50.
PLSSS
Answer:
Step-by-step explanation:
Looking at the information given, the population mean and population standard deviation are known. We would apply the formula
z = (x - µ)/σ
Where
x = sample mean
µ = population mean
σ = population standard deviation
From the information given,
µ = 70
σ = 10
1) x = 60
The probability that the heart rate if an individual is less than 60 is expressed as
P(x < 60)
z = (60 - 70)/10 = - 1
Looking at the normal distribution table, the probability corresponding to the z score is 0.16
The percentage rates of heart rates less than 60 is 0.16 × 100 = 16%
2) x = 80
The probability that the heart rate if an individual is less than 80 is expressed as
P(x < 80)
z = (80 - 70)/10 = 1
Looking at the normal distribution table, the probability corresponding to the z score is 0.84
The percentage rates of heart rates less than 80 is 0.84 × 100 = 84%
3) x = 50
The probability that the heart rate if an individual is greater than 50 is expressed as
P(x > 50) = 1 - P(x ≤ 50)
z = (50 - 70)/10 = - 2
Looking at the normal distribution table, the probability corresponding to the z score is 0.23
P(x > 50) = 1 - 0.23 = 0.77
The percentage rates of heart rates greater than 50 is 0.77 × 100 = 77%
What is the limit of the infinite series ?
∑n=1∞(3n^5/6n^6+1)
The limit of the given infinite series is undefined.
Explanation:The given series is:
∑n=1∞(3n5/6n6+1)
To find the limit, we can simplify the series by dividing the numerator and denominator by the highest power of n:
∑n=1∞(3/n-1/6n-1+n-6)
As n approaches infinity, the terms containing n-1 and n-6 approach 0, so we are left with:
∑n=1∞(3/n)
This is a harmonic series with the form 1+1/2+1/3+1/4+... which is known to diverge. Therefore, the limit of the given infinite series is undefined.
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May i please know the awswers im giving alot of points and this subject confuses me greatly
Answer:
1.circle
2.triangle
3.trapezoid
4.parallelogram
Step-by-step explanation:
Odette has two investments that she purchased at the same time. Investment 1 cost $10,000 and earns 4% interest each year. Investment 2 cost $8000 and earns 6% interest each year.
Write exponential growth functions
that could be used to find v1(t) and v2(t), _________________________________
the values of the investments after t years.
Find the value of each investment after 5 years.
Explain why the difference between their values, ____________________________ which was initially $2000, is now less
Answer: The functions are v1(t)=10000*(1.04)^5 and v2(t)=8000(1.06)^5
v1(5)=12166$
v2(5)=10705 $
Step-by-step explanation:
Given:
Investment cost for 1st=10,000$ ,at 4%rate.
Investment cost for 2nd=8000$ ,at 6% rate.
To Find:
Exponential growth functions ,
that could be used to find v1(t) and v2(t),
the value of each investment after 5 years
And difference between their values.
Solution:
Consider for 1st investment function be v1(t) and for 2nd be v2(t)
and t be time period
Exponential growth is given by, as time function,
v(t)=initial cost*(1+rate)^time period.
for 1st investment its cost is 10000$ at 4 % rate.
[tex]v1(t)=10000(1+0.04)^t[/tex]
[tex]v1(t)=10000(1.04)^t[/tex]
for 2nd investment its cost is 8000$ at 6% rate.
[tex]v2(t)=8000(1+0.06)^t[/tex]
[tex]v2(t)=8000(1.06)^t[/tex]
For t=5 calculating for both investment,
[tex]v1(5)=10000(1.04)^5[/tex]
[tex]=10000*1.2166[/tex]
v1(5)=12166 $
For 2nd investment,
[tex]v2(5)=8000(1.06)^5[/tex]
[tex]=8000*1.3382[/tex]
v2(t)=10705.8 $
Now after 5 years the difference is =v1(t)-v2(t)
Which is about 1460 $ only.
This because of the both functions depends upon time,initial investment and rate of interest .
Here time period being same.But the rate of interest are different and initial values are different.
Galila a sprinkler that sprays water in a circle. The circle has a 20-foot radius. Which of the following equations can be used to determine the circumference of the circle created by sprinkler water?
QUICK!!!
Find measure of arc CE
A. 40°
B.50°
C.75°
D.80°
Answer:
Option B is the right choice.
Step-by-step explanation:
Given:
An are CE and an inscribed angle CBE.
Measure of inscribed angle CBE = 25 °
We have to find the measure of the arc CE.
Concept:
An inscribed angle is an angle with its vertex on the circle.The measure of an inscribed angle is half the measure the intercepted arc. Measure of inscribed angle = 1/2 × measure of intercepted arc .To find the measure of arc CE.
⇒ [tex]\angle CBE = \frac{1}{2} \times m\ (arc\ CE)[/tex]
⇒ [tex]2\times \angle CBE = m\ (arc\ CE)[/tex]
⇒ [tex]2\times 25 = m\ (arc\ CE)[/tex]
⇒ [tex]50 = m\ (arc\ CE)[/tex]
Measure of intercepted arc CE = 50 degrees.
The measure of arc CE = 50° so, option B is the right choice.
A young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly. He started at 90 kilograms and gained weight at a constant rate of 8 lbs. a week.
a. Write a function to represent this situation. Use x and y as your variables.
b. What would his weight be after 8 weeks?
a) The function that represent this situation is y = 90 + 8x.
b) His weight be after 8 weeks is 154 lbs.
Step-by-step explanation:
It is given that,
He started at 90 kilograms.And gained weight at a constant rate of 8 lbs a week.a) Write a function to represent this situation. Use x and y as your variables.
Let 'x' be the number of weeks he gained weight.Let 'y' be the total weight.Hence the equation can be framed as,
Total weight = starting weight + weight gained in x weeks.
We know that, each week he gains 8 lbs. Therefore, for 8 weeks he gained 8x lbs of weight.
⇒ y = 90 + 8x.
∴ The function that represent this situation is y = 90 + 8x.
b) What would his weight be after 8 weeks?
To find his week after 8 weeks, substitute x=8 in the function y = 90 + 8x.
⇒ 90 + 8(8)
⇒ 90 + 64
⇒ 154 lbs.
∴ His weight be after 8 weeks is 154 lbs.
Solve for x. 3/x-1 - 1/x^-1=5/x-1
Please show all work
3/(x-1) - 1/(x^2-1) = 5/(x-1)
Subtract 3/(x-1) from both sides
-1/(x^2-1) = 2/(x-1)
Factor x^2 - 1
-1/[(x-1)(x+1] = 2/(x-1)
Multiply by (x-1)(x+1) on both sides
-1 = 2 (x+1)
-1 = 2x + 2
Subtract 2 from both sides
-3 = 2x
Divide by 2 on both sides
-3/2 = x
Answer:
x = -3/2
Step-by-step explanation:
[tex]\frac{3(x+1)}{(x-1)(x+1)} - \frac{1}{(x-1)(x+1)} = \frac{5(x+1)}{(x-1)(x+1)} \\[/tex] Find the common denominator
3(x+1) - 1 = 5(x+1) Distribute
3x + 3 -1 = 5x +5 Combine Like terms
3x + 2 = 5x + 5 Solve for x
2 = 2x +5
-3 = 2x
x = -3/2
Adam Stewart
Monthly Income Statement
May 2016
Adam has recently obtained a loan with a monthly
minimum payment of $30 dollars.
How will Adam's net income change with the added
expense?
Income (after Taxes)
Total Income
$3100
What will be Adam's total expenses now?
Wages
$3,100
Expenses
What will be Adam's new net income?
$70
Food
Rent
Transportation
$150 Clothing
$850 Medical insurance
$110 Car insurance
$90
$40
Total expenses:
$1,310
Net income (income - expenses):
$1,790
Answer:
How will Adam’s income change with the added expense?: it will decrease
Total expenses: $1,340
New net income:$1,760
Step-by-step explanation:
Answer:
it will decrease
Total expenses: $1,340
New net income:$1,760
Giving out 30 points whoever answers!! A dot plot titled Number of classes going from 3 to 7. 3 has 5 dots, 4 has 6 dots, 5 has 5 dots, 6 has 4 dots, 7 has 3 dots. The dot plot shows the number of classes taken by the students at South High School.
The shape of the data is
A.) Skewed left.
B.) Skewed right.
C.) Symmetrical.
D.) From 3 to 7.
Answer:
b
Step-by-step explanation:
Answer:
B - Skewed right.
Step-by-step explanation:
Trust me!!!!
The nth term of a sequence is n +7
a) Work out the first three terms of the sequence,
b) Work out the tenth term of the sequence,
Generating Bequence
Step-by-step explanation:
Tn = n + 7
The first three terms of the sequence is
T1 = 1 + 7 = 8
T2 = 2 +7 = 9
T3 = 3 + 7 = 10
--------------------
The first three terms of the sequence is 8 , 9 and 10
Now
The tenth term of the sequence is
T10 = 10 + 7 = 17
Hope it will help you. :)
a) The first three terms of the sequence is given by 8 , 9 , 10 respectively
b) The tenth term of the sequence is a₁₀ = 17
What is Arithmetic Progression?An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"
The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁
Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]
Given data ,
Let the arithmetic progression be represented as A
Now , the equation will be
A = n + 7 be equation (1)
a)
when n = 1
Substitute the value of n = 1 in the equation , we get
The value of a₁ = 1 + 7 = 8
when n = 2
Substitute the value of n = 2 in the equation , we get
The value of a₂ = 2 + 7 = 9
when n = 3
Substitute the value of n = 3 in the equation , we get
The value of a₃ = 3 + 7 = 10
b)
The tenth term of the arithmetic sequence is when n = 10
Substitute the value of n = 10 in the equation , we get
The value of a₁₀ = 10 + 7 = 17
Hence , the tenth term of the AP is a₁₀ = 17
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Find the area of the isosceles triangle.
13 cm/
10 cm
Answer:
(assuming the height is 13 and the width is 10 or vice versa) 65
Step-by-step explanation:
a = 1/2 base × height
1/2 13 × 10 or 10×13
130 ÷ 2
65
Area of isosceles triangle = [tex]\( \frac{13\sqrt{231}}{4} \)[/tex] square centimeters, approximately 43.03 square centimeters.
To find the area of an isosceles triangle, you can use the formula:
[tex]\[ Area = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]
Since it's an isosceles triangle, the height divides the triangle into two right-angled triangles of equal size.
Given:
Base = 13 cm
Height = ?
To find the height, we can use the Pythagorean theorem.
Let's denote the height as [tex]\( h \),[/tex] and half of the base (since the triangle is isosceles, and the height splits the base into two equal parts) as [tex]\( \frac{13}{2} \).[/tex]
Then, using the Pythagorean theorem:
[tex]\[ (\text{height})^2 + \left(\frac{13}{2}\right)^2 = 10^2 \]\[ (\text{height})^2 + \left(\frac{13}{2}\right)^2 = 100 \]\[ (\text{height})^2 + \frac{13^2}{2^2} = 100 \]\[ (\text{height})^2 + \frac{169}{4} = 100 \]\[ (\text{height})^2 = 100 - \frac{169}{4} \]\[ (\text{height})^2 = \frac{400}{4} - \frac{169}{4} \]\[ (\text{height})^2 = \frac{231}{4} \][/tex]
Now, let's solve for the height:
[tex]\[ \text{height} = \sqrt{\frac{231}{4}} \]\[ \text{height} = \frac{\sqrt{231}}{\sqrt{4}} \]\[ \text{height} = \frac{\sqrt{231}}{2} \][/tex]
Now that we have the height, we can calculate the area using the formula:
[tex]\[ Area = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]
Substituting the values:
[tex]\[ Area = \frac{1}{2} \times 13 \times \frac{\sqrt{231}}{2} \]\[ Area = \frac{13 \sqrt{231}}{4} \][/tex]
So, the area of the isosceles triangle is [tex]\( \frac{13 \sqrt{231}}{4} \)[/tex] square centimeters.
The complete question is here.
Find the area of the isosceles triangle with a base of 13 cm and a height of 10 cm.