The direct route from Marta's apartment to work is a road that is a straight line. The road is closed for repairs. Marta had to drive 8 miles west and then 6 miles south to get to work. She returned home by the same route. How many miles would she have saved round-trip if she had taken the direct route?
She would have to take 5.29 miles to save round-trip if she had taken the direct route.
What is the Pythagoras theorem?The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.
The direct route from Marta's apartment to work is a road that is a straight line. The road is closed for repairs.
Marta had to drive 8 miles west and then 6 miles south to get to work. She returned home by the same route.
Let's consider x to be the direct route.
By Pythagoras theorem, we can find the direct route
[tex]x^{2} = 8^{2} +6^{2} \\\\x^{2} = 64 - 36\\\\x^{2} = 28\\\\x= \sqrt{28} \\\\x= 5.29[/tex]
Thus, She would have to take 5.29 miles to save round-trip if she had taken the direct route.
Learn more about Pythagoras theorem;
https://brainly.com/question/343682
#SPJ1
A 2-cup bottle of glass cleaner costs $9.12. What is the price per fluid ounce
Answer:
$0.57
Step-by-step explanation:
In one cup there are eight fluid ounces
To find the cost per fluid ounce all you have to do is divide the price by how many ounces]
To find ounces= 2x8=16
To find price per ounce 9.12/16= .57
mr jones told his students they each need half of a piece of paper calvin cut his piece of paper horizontally and mathew cut his piece of paper diagonally which student has the larger area on his half piece of paper
Answer:
Both
Step-by-step explanation:
After cutting the paper, both Calvin and Matthew have the same area. Calvin cut his into two rectangles that are each half the area of the original piece of paper. Matthew cut his paper into two equivalent right triangles that are also half the area of the original piece of paper.
lisa rides her bike 15.25 miles to and from her job each week. How many miles does she bike in all to and from work in 19.5 weeks?
Answer:
297.375 miles
Step-by-step explanation:
Since lisa rides 15.25 miles in 1 week and we are looking for how many miles she rides in 19.5 weeks, we must multiple 15.25 miles by 19.5 because she rides 15.25 miles, 19.5 times.
15.25*19.5=297.375
In the given figure x = 145°. What theorem can be used to prove the lines p and q are parallel?
A) Same side interior angles converse theorem
B) Corresponding angles converse theorem
C) Alternate exterior angles converse theorem
D) Alternate interior angles converse theorem
34.321 greater than 34.3211
Answer:
It's not
Step-by-step explanation:
To know this, you have to put a zero to the right.
So it'd be 34.3210, and as you can see, 34.3211 is greater
please help me it's urgent
Answer: go to the website
Step-by-step explanation:
Please see attached photo for problem from my homework set.
Answer: (x - 1)(x - 23)
Step-by-step explanation:
First, we can factor the x² part:
(x)(x)
Next, we will look at the -24x and +23
-> We need two numbers that multiply to 23 and add to -24
-> 23 is a prime number, so we will use 1 and 23
For -24, 1 and 23 must be added together. Since a negative times a negative is a positive, and a negative plus a negative is a positive, we will turn them into -1 and -23.
This gives us a final answer of:
(x - 1)(x - 23)
Answer: (x - 1)(x - 23)
Step-by-step explanation:
attached the picture below of the working...
hope that helps...
Which is the correct option, I’m very confused by this question?
sin2x=
Answer:
The answer is definitely Option A
...............................................the problem below is so hard...................................
Answer:
16 cm
Step-by-step explanation:
Circumference of a circle
We are told that the string is wound symmetrically around a circular rod.
Now, the circumference of the rod is 4 cm and length is 12 cm.
Now, circumference is also the length of a circle. Thus, one wound of the string will be equal to the circumference of the rod.
Thus, one wound = 4 cm
Since the string makes 4 turns about the rod, then;
Length of string = 4 × 4 = 16 cm
hopes this helps ya out
Write 8 statements and reasons for the proof
Answer:
Step-by-step explanation:
Expand: f(z) = z / (z-1) (2-z) as Laurent series for |z| < 1
Most problems like this can be done with two tools only: partial fractions, and the result 1/(1−w)=1+w+w2+⋯ for |w|<1. So first split your function f into 1/(z−2)−1/(z−1). I will show you how to cope with one of these factors, 1/(z−2). Writing this as −1211−z/2 is tempting but no good: the "1/(1−w)" expansion will converge only for |z/2|<1, not on the regions you are supposed to care about. So you take out a factor of z−1 instead:
1/(z−2)=z−111−2/z
The final term can be expanded with the 1/(1−w) series, valid for |2/z|<1 that is |z|>2. So that does give you a Laurent series valid in the right region (once you multiply bu z−1. These methods can be used to solve all of your problems.
Partial fractions:
[tex]f(z) = \dfrac z{(z-1)(2-z)} = -\dfrac1{1-z} + \dfrac2{2-z}[/tex]
For |z| < 1, we have
[tex]\displaystyle \frac1{1-z} = \sum_{n=0}^\infty z^n[/tex]
and
[tex]\displaystyle \frac2{2-z} = \frac1{1-\frac z2} = \sum_{n=0}^\infty \left(\frac z2\right)^n[/tex]
(The latter series is valid for |z/2| < 1 or |z| < 2, but |z| < 1 is a subset of this region.)
Then
[tex]\boxed{f(z) = \displaystyle \sum_{n=0}^\infty \left(\frac1{2^n} - 1\right) z^n}[/tex]
What is the value of x
Answer:
your answer is 20.
Step-by-step explanation:
x^2+4^2=(2+x)^2
urgent help please! ^^ <3
Answer:
Lower quartile = 6
Median = 8
Upper quartile = 9
Step-by-step explanation:
If you take away a number from each end of the number set one by one, you will end up with 7 and 9 in the middle. To find the median between two numbers, add them together then divide them by 2.
7 + 9 = 16
16 ÷ 2 = 8
_________________
To find the lower and upper quartiles, split the number set into two where the median is, then, find the median of those two sections.
Lower quartile: 4, 5, 6, 6, 7
Median = 6
-
Upper quartile: 9, 9, 9, 9, 9
Median = 9
So, the median of the whole set is 8, the lower quartile is 6, and the upper quartile is 9.
hope this helps!
Brainliest for who can help!!
I think it's like this.
Hope this helps
Find the volume of the sphere. Round your answer to the nearest tenth.
Answer:
Step-by-step explanation:
Remark
All you need do is find the radius and put it into the formula V = (4/3) pi r^3.
Givens
d = 12 yards
r = d/2
Solution
r = 12 yds/2 = 6 yds
V = 4/3 pi r^3
V = 4/3 * 3.14 * 6*6*6
V = 904.32
Answer 904.4 yd^3
The equation of the trend line is y = −0.36x + 12.6.
Use the equation of the trend line to predict the wind chill for a wind speed of 33 mi/h. Round your answer to the nearest degree.
Answer:
−1\°
Step by step explation:
Let
x -----> the wind speed in mi/h
y ----> the wind chill in °F
we have
y=-0.36x+12.6y=−0.36x+12.6
so
For x=38 mi/h
substitute in the linear equation and solve for y
y=-0.36(38)+12.6=-1.08\°y=−0.36(38)+12.6=−1.08\°
Round to the nearest degree
-1.08=-1\°−1.08=−1\°
Can y’all help me pls
Answer:Sure, what do you need help with
Step by step explanation:
Sure, what do you need help with
Ayden is 1.85 meters tall. At 2 p.m., he measures the length of a tree's shadow to be 39.55 meters. He stands 35.4 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
The height of the tree is 4.15m
We are given that
Height of Joshua, h=1.85 m
Length of tree's shadow, L=39.55 m
Distance between the tree and Joshua=35.4 m
We have to find the height of the tree.
BC=35.4 m
BD=39.55m
What is the height?CD=BD-BC
CD=-35.4 m=4.15 m
EC=1.45 m
All right triangles are similar. When two triangles are similar then the ratio of their corresponding sides is equal.
[tex]\triangle ABD=\triangle ECD[/tex]
[tex]\frac{AB}{EC}=\frac{BD}{CD}[/tex]
Substitute the values
[tex]\frac{AB}{1.45}=\frac{39.55\times 1.45}{4.15} \\\\AB=20.39[/tex]
Hence, the height of the tree=20.39 m
To learn more about the height visit:
https://brainly.com/question/73194
#SPJ1
Analyze the diagram below and complete the instructions that follow.
8
Find the value of y.
A. y = 2
B. Y=4sqrt3/3
C. y = 4
D. Y=4sqrt3
Answer:
y = 4
Step-by-step explanation:
Thewtriangle on the right side has a 90° angle and a 30°, so the third angle is 60°. That makes the triangle a 30-60-90 right angle. The short leg is half the length of the hyptenuse.
y = 8/2 = 4
Answer: C. y = 4
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answer:
227
Step-by-step explanation:
Since they give you the hypotenuse length of 290in and they ask you to find the length os the adjacent angle, use the cosine to find side b.
So you do tan38=b/290 then calculate.
The true answer is 226.5728 but they ask you to round.
Celia bought a bag of 12 goldfish for $3.
What is the cost of 1goldfish?
Answer:
0.25
Step-by-step explanation:
Answer:
0.25
Step-by-step explanation:
3÷12=0.25
12 goldfish for $3
Larissa spent $280 per month on
clothes and a total of $2,920 for food
and entertainment during the last
5 months. How much should Larissa
expect to pay for clothes, food, and
entertainment in 1 year?
Answer:
Larissa would spend a total of: $7,680 in 1 year
Step-by-step explanation:
Factor the expression using the greatest common factor 16x + 12y
Answer:
4(4x + 3y)
Step-by-step explanation:
Given expression: 16x + 12y
Factors of 16: 1, 2, 4, 8, 16
Factors of 12: 1, 2, 3, 4, 6, 12
Therefore, the greatest common factor of 16 and 12 is 4.
As the expression has two variables, the variables cannot be factored.
Therefore, factored expression: 4(4x + 3y)
16x+12y
Factor each
16x=4×4x12y=4×3yTake 4 common as GCF
16x+12y4(4x+3y)Estimate how many times larger 5*10^8 is than 24*10^6.
A) 10 times
B) 20 times
C) 50 times
D) 100 times
Answer:
10 times
Step-by-step explanation:
Solve for y: 5( 3y+4) = 6( 2y-2/3)
Answer: y= -8
Step-by-step explanation:
5( 3y+4) = 6( 2y-2/3)15y+20=12y-415y-12y=-4-203y=-24y=-24/3y= -8Find the surface area of the cylinder. Round your answer to the nearest tenth.
Pls help i need an A my mom is going to get mad at me pls help i will give 62 points
Answer:
Both of those tables show a proportional relationship between x and y.
Step-by-step explanation:
In the second table the values all equal 0.75 when divided.
In the first table the values all equal 1.25 when divided.
Patricia was having fun playing a card game. To win the game, she
needed the next two cards dealt to be yellow cards. There are 12
cards left in the deck, and three are[yellow.
What is the probability that the two cards dealt to Patricia will both
be yellow?
Answer:
25
%
Step-by-step explanation:
te puedes subcribirte a mi canal se llama navegando con incognito
The probability that the two cards dealt to Patricia will both be yellow
is 1/4.
What is the probability?In mathematics, probability refers to the likelihood of an occurrence occurring. Simply put, how frequently the incidence occurs over a certain period of time.
Given, there are 12 cards left in the deck, and three are yellow.
To find the probability:
The probability= number of yellow cards in the deck / total number of cards in the deck.
= 3/12
= 1/4
Therefore, the probability is 1/4.
To learn more about the probability;
brainly.com/question/11234923
#SPJ2
The directions on a box of Luigi’s Pizza Mix are as follows: Spread the dough to the edges of a circular pan or a 10-inch by 14-inches rectangular pan. You will need to use the following formulas to answer the questions below. For a circle: A = πr2 where π = 3.14C = 2πr For a rectangle: A = lw P = 2l + 2w a. If you used the same amount of dough, how large a circular pan would you need to make a pizza of the same area and thickness as one made in the rectangular pan? *
The circular pan must have a radius of 6.68 inches.
How large a circular pan would you need?
The area of the circular pan just be the same as the area of the rectangular pan.
The rectangular pan is 10in by 14 in, so its area is:
A = 10in*14in = 140in^2
Then the circular pan must have an area:
A' = 3.14*r^2 = 140in^2
We can solve this for r:
r = √(140in^2/3.14) = 6.68 in
The circular pan must have a radius of 6.68 inches.
If you want to learn more about areas:
https://brainly.com/question/24487155
#SPJ1