Answer:
Step-by-step explanation:
The triangle inequality theorem states that the sum of any two sides of a triangle os greater than the third side.
■■■■■■■■■■■■■■■■■■■■■■■■■■
First triangle:
Let a,b and c be the sides of the triangle:
● a = 10
● b = 20
● c = 30
Now let's apply the theorem.
● a+b = 10+20=30
That's equal to the third side (c=30)
●b+c = 50
That's greater than a.
● a+c = 40
That's greater than b.
These aren't the sides of a triangel since the first inequality isn't verified.
■■■■■■■■■■■■■■■■■■■■■■■■■
Second triangle:
● a = 122
● b = 257
● c = 137
Let's apply the theorem.
● a+b = 379
That's greater than c
● a+c = 259
That's greater than b
● b+c = 394
That's greater than a
So 122,257 and 137 can be sides of a triangle.
■■■■■■■■■■■■■■■■■■■■■■■■■■
The third triangle:
● a = 8.6
● b = 12.2
● c = 2.7
Let's apply the theorem:
● a+b = 20.8
That's greater than c
● b+c = 14.9
That's greater than a
● a+c = 11.3
That isn't greater than b
So theses sides aren't the sides of triangle.
■■■■■■■■■■■■■■■■■■■■■■■■■■
● a = 1/2
● b = 1/5
● c = 1/6
Let's apply the theorem.
● a+b = 7/10
That's greater than c
● a+c = 2/3
That's greater than b
● b+c = 11/30
That isn't greater than a
So these can't be the sides of a triangle.
Last question.... please help
Answer:
B {-10 , -6 , 10}
Step-by-step explanation:
D= {-1 , 0 , 4}
When x = -1 ;
y = 4x - 6
y = 4*(-1) -6
= -4 - 6
y = -10
When x = 0,
y = 4 *0 -6
y = -6
When x = 4,
y = 4*4 - 6
= 16 - 6
y = 10
Range = { -10, -6 , 10}
Find the range of f(x) = –x + 4 for the domain {–3, –2, –1, 1}.
Answer:
{3, 5, 6, 7}
Step-by-step explanation:
Plug in each number form the domain and solve for f(x). The set of f(x) values is the range.
f(x) = -x + 4
f(-3) = -(-3) + 4 = 7
f(-2) = -(-2) + 4 = 6
f(-1) = -(-1) + 4 = 5
f(1) = -1 + 4 = 3
Range: {3, 5, 6, 7}
find the area of the shaded region
One shaded triangle has a base of 4.5 ft and a height of 9 ft, so its area is 0.5 * 4.5 * 9 = 20.25.
There are two such triangles, so the area of the shaded region is 40.5.
jim buys a calculator that is marked 30% off. If he paid $35, what was the original price?
Answer:
x = 50
Step-by-step explanation:
Let x be the original price.
He got 30% off
The discount is .30x
Subtract this from the original price to get the price he paid
x - .30x = price he paid
.70x = price he paid
.70x = 35
Divide each side by .7
.70x/.7 = 35/.7
x=50
Pls answer I really need help
Brainlist and thank you will be the reward thank you so much!!!
Answer:
0.667 ✅Step-by-step explanation:
This is best solved using a proportion.
The formula is soy/vinegar = soy/vinegar where one of these is a variable.
Here we have:
[tex]\frac{150}{100} = \frac{1}{x}[/tex]
Now, we solve this by cross multiplying.
150x = 100
Dividing both sides by x, we get x = 2/3 or about 0.667.
Checking:
[tex]\frac{150}{100} = \frac{1}{0.667}[/tex]
1.5 = 1.5 ✅
I'm always happy to help :)The dosage for a certain drug calls for 20mg per kg per day and is divided into two doses(1every 12 hours) if a person weighs 197 pounds how much of the drug should be given each dose
Answer:
893.42
Step-by-step explanation:
1kg=2.205pounds
so 20mg is for 2.205pounds
therefore for 197pounds will be 1784.84mg
but the dose is once every 12hrs meaning twice a day so divide 1784.84/2 to get the pounds
An inchworm (exactly one inch long, of course) is crawling up a yardstick (guess how long that is?). After the rst day, the inchworm's head (let's just assume that's at the front) is at the 3" mark. After the second day, the inchworm's head is at the 6" mark. After the third day, the inchworm's head is at the 9" mark. Let d equal the number of days the worm has been crawling. (So after the rst day, d = 1.) Let h be the number of inches the head has gone. Let t be the position of the worm's tail.
What property is 21+(36+19)
Answer:
76
Step-by-step explanation:
21+(36+19)
21+(55)
21+55
=76
Answer:
The identity property
Step-by-step explanation:
I took it on Egd.
Which expressions are equivalent to -3(2w+6)-4−3(2w+6)−4minus, 3, left parenthesis, 2, w, plus, 6, right parenthesis, minus, 4 ? Choose all answers that apply: Choose all answers that apply: (Choice A) A 6w-146w−146, w, minus, 14 (Choice B) B 2(-3w+(-11))2(−3w+(−11))2, left parenthesis, minus, 3, w, plus, left parenthesis, minus, 11, right parenthesis, right parenthesis (Choice C) C None of the above
Answer:
B. 2{-3w+(-11)}Step-by-step explanation:
Given the expression, -3(2w+6)-4, we are to look for an equivalent expression for the equation.This is as shown:
Step 1: Open the parenthesis
= -3(2w+6)-4
= -3(2w)-3(6)-4
= -6w-18-4
Step 2: Simplify the resulting expression in step 1
= -6w-18-4
= -6w - 22
Step 3: factor out the common values from each term. Since the common value is 2, on factoring we will have;
2{-3w+(-11)}
Hence the equivalent expression is 2{-3w+(-11)}
Answer:
a and b
Step-by-step explanation:
no.
12. Solve the systems of linear equations using the substitution method.
x=y - 2
4y = x + 23
Answer:
x=5 and y=7
Step-by-step explanation:
x + 2 = y (equation 1)
x + 23 = 4y (equation 2)
(equation 2) - (equation 1)
This gives,21 = 3y
y = 21/3
y = 7.
Put y = 7 into equation 1 to find x
x + 2 = 7
x = 7 - 2
x = 5.
Top Hat Soda has 300,000 milliliters of cola to bottle. Each bottle holds 500 milliliters. How many bottles will the cola fill?
Answer:
600 bottlesStep-by-step explanation:
Given that Top Hat Soda has 300,000 millilitres of cola to bottle and,
a bottle is 500 millilitres in capacity.
To find the amount of bottles that will fill the Top Hat Soda,
we have to divide Top Hat Soda by the 500 millilitres bottle
we have:
Number of bottles needed to fill Top Hat Soda= 300,000/500 = 600 bottles.
Hence 600 bottles will fill the Top Hat Soda
how many are 8 raised to 2 ???
Answer:
The correct answer would be 64 because 8 times 8 would be 64 therefore the answer is 64
Step-by-step explanation:
whats the squareroot of 18
Answer:
it should be 4.24264068712 looked it up
Answer:
18 doesn't have a square root but you can simplify it
[tex] \sqrt{18 } [/tex]
then you take 9 which is a square number and divide it to get 3 which you'll place on the outside
[tex] 3\sqrt{2} [/tex]
The equation of line WX is 2x + y = −5. What is the equation of a line perpendicular to line WX in slope-intercept form that contains point (−1, −2)?
Answer: [tex]y=\dfrac12x-\dfrac{3}{4}[/tex]
Step-by-step explanation:
Given, The equation of line WX is 2x + y = −5.
It can be written as [tex]y=-2x-5[/tex] comparing it with slope-intercept form y=mx+c, where m is slope and c is y-intercept, we have
slope of WX = -2
Product of slopes of two perpendicular lines is -1.
So, (slope of WX) × (slope of perpendicular to WX)=-1
[tex]-2\times\text{slope of WX}=-1\\\\\Rightarrow\ \text{slope of WX}=\dfrac{1}{2}[/tex]
Equation of a line passes through (a,b) and has slope m:
[tex]y-b=m(x-a)[/tex]
Equation of a line perpendicular to WX contains point (−1, −2) and has slope [tex]=\dfrac12[/tex]
[tex]y-(-2)=\dfrac{1}{2}(x-(-1))\\\\\Rightarrow\ y+2=\dfrac12(x+1)\\\\\Rightarrow\ y+2=\dfrac12x+\dfrac12\\\\\Rightarrow\ y=\dfrac12x+\dfrac12-2\\\\\Rightarrow\ y=\dfrac12x-\dfrac{3}{4}[/tex]
Equation of a line perpendicular to line WX in slope-intercept form that contains point (−1, −2) [tex]:y=\dfrac12x-\dfrac{3}{4}[/tex]
ast week, the Vargas family drove 30 miles in their car and 15 miles in their truck. The letter m stands for the total number of miles they drove. Which equation can you use to find m?
Answer:
m = 30 + 15
Step-by-step explanation:
The distance traveled by the Vargas family in their car is 30 miles while the distance traveled when using their truck is 15 miles. To get the total distance traveled, we need to add the distance traveled by the truck and the distance traveled by the car. Since m stands for the total number of miles they drove, the equation needed to find the total distance traveled (m) is given as:
m = 30 + 15
m = 45 miles
Which recrusive formula can be used to generate the sequence shown, where f(1)=5 and n>=1 5,-1,-7,-13,-19
Answer:
a_n = 11 - 6n
Step-by-step explanation:
you can observe every next element is smaller then the previous one by 6
a_n = 5 - 6*(n-1)
a_n = 5 - 6n + 6
a_n = 11 - 6n
Choose which of the following demonstrate a dilation centered at the origin: (x,y)→(1.5x,1.5y) choose a graph.
The dilation rule (x,y) --> (1.5x, 1.5y) says to multiply each coordinate by the scale factor 1.5
Point A in blue is located at (5,5). After dilation, it will move to A ' (7.5, 7.5)
Point B is located at (0,2) and it moves to B ' (0,3)
Point C is located at (1,-1) and it moves to C ' (1.5, -1.5)
This all matches with what is shown below, so the answer is choice B
You pack sandwiches for a hike with your friends. Each sandwich takes 2 slices of bread, and each hiker eats one sandwich.
How many slices of bread are used for n hikers?
Given that:-
→ 1 sandwich = 2 slices of bread.
→ 1 hiker = 1 sandwich.
→ Then we have to find number of bread slices for n hikers .
→ Number of bread slices for 1 hiker = 2
→ Number of bread slices for 2 hikers = 2 × 2
→ For 3 hikers = 3 × 2
So in similar way
→ Number of bread slices for n hikers = 2×n → 2n
So 2n is the answer.
Matrix multiplication is not commutative. Why?
Answer:
For matrix multiplication to work, the columns of the second matrix have to have the same number of entries as do the rows of the first matrix. ... In particular, matrix multiplication is not "commutative"; you cannot switch the order of the factors and expect to end up with the same result.
The specifications for the diameter of a molded part are 10 mm ± 0.5 mm. The actual average and standard deviation from 250 parts sampled is 10.1 mm and 0.1 mm, respectively. The process can be characterized as:
Answer: Capable
Step-by-step explanation: The capability of a process could be exaplained as a measure of the ability of a process to produce part within specified limits by making use of statistical measurement. In determining if a certain process is capable or not, the value of process capability (Cp) is measured, in most cases, a process is deemed capable by having a Cp value of 1.33 or higher.
Cp formula :
(Upper specification limit(USL) - Lower specification limit(LSL) ) / 6* standard deviations
Diameter = 10 mm ± 0.5 mm
Standard deviation = 0.1mm
USL = 10 + 0.5 = 10.5
LSL = 10 - 0.5 =. 9.5
Cp = (10.5 - 9.5) / 6*0.1
Cp = 1/0.6
Cp = 1.6666
Cp = 1.67
Hence, the process is capable
How many solutions does the system have?
Answer:
B. no solutionsStep-by-step explanation:
Left sides of both equations are the same sum (8x+2y), so the right sides also has to be the same. They are not so there is no solutions.
{If they are the same then system has infinitely many solutions.}
Can someone explain probability with permutations and combinations and explain where they are applied?
Answer:
If the order doesn't matter then we have a combination, if the order do matter then we have a permutation. One could say that a permutation is an ordered combination. The number of permutations of n objects taken r at a time is determined by the following formula: P(n,r)=n!
Step-by-step explanation:
To calculate the probability of a combination, you will need to consider the number of favorable outcomes over the number of total outcomes. Combinations are used to calculate events where order does not matter. In this lesson, we will explore the connection between these two essential topics.
Answer:
combination : If the order of numbers or operations does not matter
Permutation : when the order of numbers matter ( common example most teachers use : a code of 4 numbers has to be in a certain order and the numbers are from 0 to 9 , how many permutation can you make if you use the number one time)
P=n!/(n-r)!
n! ( are number from 0-9 we have 10 numbers)
r is the number of digits in the code = 4
n!=10*9*8*7*6*5*4*2*1
(n-r)!=(10-4)!=6!=6*5*4*3*2*1
P=5040 ways ( if the order matter)
If the order does not matter
Combination C(n,r)=n!/(n-r)!r!
C(10,4)=(10*9*8*7*6*5*4*2*1)/[(6*5*4*3*2*1)(4*3*2*1)]
1. Solve each equation.
a. 5x – 2=8
b. 4x – 3= 2x + 9
C. 6x + 3 = 2x + 8
And show work
Answer:
a. 5×=8+2
5×=10
b. 4×-2×=9+3
2×=13
c. 6×-2×=8-3
4×=5
The number of fish in the lake can be modeled by exponential regression equation y equals 14.08 * 2.08 X where X represents the year which is the best prediction for the number of fish in your 6 round your answer to the nearest whole number
Answer:
1140
Step-by-step explanation:
The best prediction for the number of fish in year 6 is 1517.
What is regression?Regression is a statistical method used to analyze the relationship between two or more variables.
It helps to identify and quantify the relationship between the dependent variable (also called the response variable) and one or more independent variables (also called the explanatory variables or predictors).
We have,
To find the best prediction for the number of fish in year 6, we need to substitute x = 6 into the exponential regression equation:
So,
y = 14.08 x [tex]2.08^x[/tex]
y = 14.08 x [tex]2.08^6[/tex]
y = 14.08 x 107.6176
y = 1516.672768
Rounding to the nearest whole number, the best prediction for the number of fish in year 6 is 1517.
Thus,
The best prediction for the number of fish in year 6 is 1517.
Learn more about regressions here:
https://brainly.com/question/28178214
#SPJ7
Given: cos(3x – Pi) = Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction, where 0 ≤ x < 180° Which values represent the solutions to the equation? {10°, 110°, 130°} {20°, 100°, 140°} {30°, 330°, 390°} {60°, 300°, 420°}
Answer:
Step-by-step explanation:
Given the expression cos(3x-π) = -√3/2, we are to find the values of x that represent the solutions to the equation.
cos(3x-π) = -√3/2
take inverse cos of both sides
cos⁻¹[cos(3x-π)] = cos⁻¹[-√3/2]
3x-π = cos⁻¹[-√3/2]
3x-π = -30°
since 180° = π rad
Hence;
3x- 180° = -30°
3x = -30°+ 180°
3x = 150°
x = 150°/3
x = 50°
Since cos is negative in the first second and 3rd quadrant;
3x-180° = -30°
In the second quadrant;
3x-180° = 180-30
3x - 180 = 150
3x = 150+180
3x = 330
x = 110°
In the third quadrant;
3x-180° = 270+30
3x - 180 = 300
3x = 300+180
3x = 480
x = 480/3
x = 160
I need help with these 3 questions plzzz.
Answer:
6. No. See explanation below.
7. 18 months
8. 16
Step-by-step explanation:
6. To rewrite a sum of two numbers using the distributive property, the two numbers must have a common factor greater than 1.
Let's find the GCF of 85 and 99:
85 = 5 * 17
99 = 3^2 + 11
5, 3, 11, and 17 are prime numbers. 85 and 99 have no prime factors in common. The GCF of 85 and 99 is 1, so the distributive property cannot be used on the sum 85 + 99.
Answer: No because the GCF of 85 and 99 is 1.
7.
We can solve this problem with the lest common multiple. We need to find a number of a month that is a multiple of both 6 and 9.
6 = 2 * 3
9 = 3^2
LCM = 2 * 3^2 = 2 * 9 = 18
Answer: 18 months
We can also answer this problem with a chart. We write the month number and whether they are home or on a trip. Then we look for the first month in which both are on a trip.
Month Charlie Dasha
1 home home
2 home home
3 home home
4 home home
5 home home
6 trip home
7 home home
8 home home
9 home trip
10 home home
11 home home
12 trip home
13 home home
14 home home
15 home home
16 home home
17 home home
18 trip trip
Answer: 18 months
8.
First, we find the prime factorizations of 96 an 80.
96 = 2^5 * 3
80 = 2^4 *5
GCF = 2^4 = 16
Answer: 16
Solve 8
4. Given the following pattern of shapes, choose the mathematical expression showing th
changes for each iteration if b is the number of boxes in the previous iteration
a) b + 1
b) b + 2
c) 6-1
d) 6-2
Answer:
b)b+2
Step-by-step explanation:
3+2=5
5+2=7
so for the next iteration 2is added.
Is the data point, P, an outlier, an influential point, both,Is the data point, P, an outlier, an influential point, both, or neither? The regression equation for a set of paired data is ^y = 6 + 4x. The correlation coefficient for the data is 0.92. A new data point(13,74) is added to the set.
outlier
neither
influential point
Both
Answer: Both
Step-by-step explanation:
Outliers are the data points that are away from the overall pattern.Influential point is an outlier that affect the slope of the regression line.Given: The regression equation for a set of paired data is [tex]\hat{y}=6+4x[/tex]. The correlation coefficient for the data is 0.92.
A new data point(13,74) is added to the set.
Put x= 13 , we get
[tex]\hat{y}=6+4(13)=6+52=58[/tex].
Predicted value of y= 58 which is different from 74.
So, the new data point(13,74) is an influential point as it can affect the slope.
Thus, (13,74) is both outlier and influential point.
Hence, the correct option is "Both".
have two one-quart jars; the first is filled with water, and the second is empty. I pour half of the water in the first jar into the second, then a third of the water in the second jar into the first, then a fourth of the water in the first jar into the second, then a fifth of the water in the second jar into the first, and so on. How much water in quarts is in the first jar after the $10^{\textrm{th}}$ pour? Express your answer as a common fraction.
Answer:
water in quarts is in the first jar after 10th pour = 12/11
Step-by-step explanation:
Let X represent first jar and Y represents second jar.
have two one-quart jars; the first is filled with water, and the second is emptyLets give the initial value of 2 to the first jar which is filled with water. Lets say there are two liters of water in first jar.
Lets give the initial value of 0 to the second as it is empty.
So before any pour, the values are:
X: 2
Y: 0
pour half of the water in the first jar into the secondAfter first pour the value of jar X becomes:
Previously it was 2.
Now half of water is taken i.e. half of 2
2 - 1 = 1
So X = 1
The value of jar Y becomes:
The half from jar X is added to second jar Y which was 0:
After first pour the value of jar Y becomes:
0 + 1 = 1
Y = 1
a third of the water in the second jar into the firstAfter second pour the value of jar X becomes:
Previously it was 1.
Now third of the water in second jar Y is added to jar X
1 + 1/3
= (3 + 1)/3
= 4/3
X = 4/3
After second pour the value of jar Y becomes:
Previously it was 1.
Now third of the water in Y jar is taken and added to jar X so,
1 - 1/3
= (3 - 1)/3
= 2/3
Y = 2/3
a fourth of the water in the first jar into the secondAfter third pour the value of jar X becomes:
Previously it was 4/3.
Now fourth of the water in the first jar X is taken and is added to jar Y
= 3/4 * (4/3)
= 1
X = 1
After third pour the value of jar Y becomes:
Previously it was 2/3
Now fourth of the water in the second jar X is added to jar Y
= 2/3 + 1/4*(4/3)
= 2/3 + 4/12
= 1
Y = 1
a fifth of the water in the second jar into the firstAfter fourth pour the value of jar X becomes:
Previously it was 1
Now fifth of the water in second jar Y is added to jar X
= 1 + 1/5*(1)
= 1 + 1/5
= (5+1) / 5
= 6/5
X = 6/5
After fourth pour the value of jar Y becomes:
Previously it was 1.
Now fifth of the water in Y jar is taken and added to jar X so,
= 1 - 1/5
= (5 - 1) / 5
= 4/5
Y = 4/5
a sixth of the water in the first jar into the secondAfter fifth pour the value of jar X becomes:
Previously it was 6/5
Now sixth of the water in the first jar X is taken and is added to jar Y
5/6 * (6/5)
= 1
X = 1
After fifth pour the value of jar Y becomes:
Previously it was 4/5
Now sixth of the water in the first jar X is taken and is added to jar Y
= 4/5 + 1/6 (6/5)
= 4/5 + 1/5
= (4+1) /5
= 5/5
= 1
Y = 1
a seventh of the water in the second jar into the firstAfter sixth pour the value of jar X becomes:
Previously it was 1
Now seventh of the water in second jar Y is added to jar X
= 1 + 1/7*(1)
= 1 + 1/7
= (7+1) / 7
= 8/7
X = 8/7
After sixth pour the value of jar Y becomes:
Previously it was 1.
Now seventh of the water in Y jar is taken and added to jar X so,
= 1 - 1/7
= (7-1) / 7
= 6/7
Y = 6/7
a eighth of the water in the first jar into the secondAfter seventh pour the value of jar X becomes:
Previously it was 8/7
Now eighth of the water in the first jar X is taken and is added to jar Y
7/8* (8/7)
= 1
X = 1
After seventh pour the value of jar Y becomes:
Previously it was 6/7
Now eighth of the water in the first jar X is taken and is added to jar Y
= 6/7 + 1/8 (8/7)
= 6/7 + 1/7
= 7/7
= 1
Y = 1
a ninth of the water in the second jar into the firstAfter eighth pour the value of jar X becomes:
Previously it was 1
Now ninth of the water in second jar Y is added to jar X
= 1 + 1/9*(1)
= 1 + 1/9
= (9+1) / 9
= 10/9
X = 10/9
After eighth pour the value of jar Y becomes:
Previously it was 1.
Now ninth of the water in Y jar is taken and added to jar X so,
= 1 - 1/9
= (9-1) / 9
= 8/9
Y = 8/9
a tenth of the water in the first jar into the secondAfter ninth pour the value of jar X becomes:
Previously it was 10/9
Now tenth of the water in the first jar X is taken and is added to jar Y
9/10* (10/9)
= 1
X = 1
After ninth pour the value of jar Y becomes:
Previously it was 8/9
Now tenth of the water in the first jar X is taken and is added to jar Y
= 8/9 + 1/10 (10/9)
= 8/9 + 1/9
= 9/9
= 1
Y = 1
a eleventh of the water in the second jar into the firstAfter tenth pour the value of jar X becomes:
Previously it was 1
Now eleventh of the water in second jar Y is added to jar X
= 1 + 1/11*(1)
= 1 + 1/11
= (11 + 1) / 11
= 12/11
X = 12/11
After tenth pour the value of jar Y becomes:
Previously it was 1.
Now eleventh of the water in Y jar is taken and added to jar X so,
= 1 - 1/11
= (11-1) / 11
= 10/11
Y = 10/11
Answer:
6/11
Step-by-step explanation:
1/2 + (1/2)(2/11) = 6/11
sus
