Answer:
The lengths 14, 24, and 26 cannot be the sides of a right triangle. The lengths 30, 72, 78 can be the sides of a right triangle.
Step-by-step explanation:
To prove that the lengths 14, 24, and 26 cannot be the sides of a right triangle:
a=14, b=24, c=26
Pythagoreon theorem: a^2+b^2=c^2
substitute values in: 14^2+24^2=26^2
simplify: 196+576=676
simplify again: 772=676, which is not true
This proves that the lengths 14, 24, and 26 cannot be the sides of a right triangle.
To prove that the lengths 30, 72, and 78 can be the sides of a right triangle:
a=30, b=72, c=78
Pythagoreon theorem: a^2+b^2=c^2
substitute values in: 30^2+72^2=78^2
simplify: 900+5184=6084
simplify again: 6084=6084, which is true
This proves that the lengths 30, 72, and 78 can be the sides of a right triangle.
Answer:
true, true, false,false, false,true,true,false
See explanations below
Step-by-step explanation:
If three sides can make a RIGHT triangle, then the sum of squares of the two shorter sides EQUALS the square of the third side, using the Pythatorean theorem.
Determine whether the given lengths can be sides of a right triangle. Which of the following are true statements?
The lengths 14, 24 and 26 cannot be sides of a right triangle.
TRUE, A^2+B^2-C^2=4sqrt(6)
The lengths 30, 72, and 78 can be sides of a right triangle.
TRUE, A^2+B^2-C^2= 0
The lengths 14, 24 and 26 can be sides of a right triangle.
FALSE, A^2+B^2-C^2=4sqrt(6)
The lengths 30, 72, and 78 cannot be sides of a right triangle.
FALSE, A^2+B^2-C^2= 0
The lengths 14, 24 and 26 can be sides of a right triangle.
FALSE, A^2+B^2-C^2=4sqrt(6)
The lengths 30, 72, and 78 can be sides of a right triangle.
TRUE, A^2+B^2-C^2= 0
The lengths 14, 24 and 26 cannot be sides of a right triangle.
TRUE, A^2+B^2-C^2=4sqrt(6)
The lengths 30, 72, and 78 cannot be sides of a right triangle.
FALSE, A^2+B^2-C^2= 0
What is the value of log0.5^16
Answer:
-4.81647993062
Step-by-step explanation:
Look at the image below ↓
Based on the mathematical analysis, the value of log 0.5^16 is -4.816.
What are Logarithms?A logarithm is a mathematical term that is used to describe the exponent or power to which a base must be raised to yield a given number.
In this case, to calculate the value of log0.5^16 use logarithm properties.
rewrite the expression as log(0.5)^(16).
=> log(a^b) = b * log(a)
=> 16 * log(0.5).
Given that the Logarithm is the inverse of exponentiation => log(0.5) is equal to -0.301.
Substitute this value back into the expression:
16 * (-0.301) = -4.816.
Hence, in this case, it is concluded that the correct answer to the value of log 0.5^16 is -4.816.
Learn more about Logarithms here: https://brainly.com/question/30226560
#SPJ6
5. Lisa sold costume jewelry at a bazaar. The
first hour she sold 2 bracelets and 3 rings
for a total of $26. Later a customer bought
2 rings and paid $12. All bracelets were
priced the same. All rings were priced the
same. How much did a bracelet cost?
Answer:
$4
Step-by-step explanation:
2 Bracelets + 3 rings = $26
2 rings = $12
3 rings = x
To get the cost of 1 ring you divide 12 by 2 and the answer you get is 6.
The total cost of the 3 rings is $18( $6*3)
Then you subtract the cost of both 2 bracelets and 3 rings($26) from the cost of 3 rings($18). The answer is $8. ( THIS IS THE COST OF 2 BRACELETS)
1 BRACELET= $4( $8/2)
does the table represent a function why or why not?
Answer:
Yes, because each x-value corresponds to one y value.
Step-by-step explanation:
If you look at the table, you notice that there is one output (y) for every input (x). This means that it is a function. It would NOT be a function if you had two outputs for an input. For example, there are two x values that are 6. For one coordinate pair, the table says (6,9) and (6,8). Since there are two values for the same input- it wouldn't be a function. In this case, there is an input of 4 and 5 with the same output. That is okay! Even though they have the same y value, those inputs still only have ONE output.
The number of vertices a triangle has
3
6
4
5
Jack had 4 hours of school. He spent 45 minutes in the library and 12 hour on a science lecture and had a lunch break of 25 minutes. How much time is left for the school to get over? (Write the answer as a fraction.)
Answer:
[tex]\dfrac{10}{4} \ hour[/tex]
Step-by-step explanation:
Given that :
Jack had 4 hours of school.
He spent 45 minutes in the library
1/2 hour on a science lecture and;
had a lunch break of 25 minutes
The objective is to determine how much time is left for the school to get over and we are to write the answer as a fraction.
In order to do that, we will have to convert the minutes into hours,
we all know that; 60 minutes = 1 hour.
Then,
45 minutes = (45/60)hour = 3/4 hour
25/60 minutes = 1/4 hour
Therefore, the amount of time left for the school to get over is:
= [tex]4 - (\dfrac{3}{4}+\dfrac{1}{2}+ \dfrac{1}{4})[/tex]
= [tex]\dfrac{16-(3+2+1)}{4}[/tex]
= [tex]\dfrac{16-6}{4}[/tex]
= [tex]\dfrac{10}{4} \ hour[/tex]
A builder wrote the measurements needed for a door.
height of door
2032 mm
width or door
Why did the builder write these measurements using millimetres instead of cm or m?
Answer:
Check the answer below.
Step-by-step explanation:
This is a very trivial but professional question. Note that all of millimetre, centimetre and metres are acceptable metric units but the millimetre is more preferable by builders and architects because:
1. It is easier to work with integer values on building and architectural plans, an advantage given by measuring and recording in millimetre.
2. working in millimetre allows for precision. The builder will record values that are very close to the true value
3. The measurement will be easily readable by anybody that sees it.
1 to the tenth power
Answer:
1
Step-by-step explanation:
1 to the tenth power is also 1 multiplied by 1 10 times.
1 · 1 · 1 · 1 · 1 · 1 · 1 · 1 · 1 · 1 = 1
1 to any power will always have the answer of 1.
A tank contains 8000 liters of a solution that is 40% acid. How much water should be added to make a solution that is 30% acid?
Answer:
2,666.67 L of water
Step-by-step explanation:
Solve for W:
1) 3200 = 2400 + 0.3w
2) 800 = 0.3w
Divide both sides by 0.3 to get the variable alone
3) (800)/0.3 = (0.3w)/0.3
4) w = 2,666.67 L
HALP !Find the next term of the series: -3 + -1 + 1 + ...
Answer:
3
Step-by-step explanation:
We are adding 2 each time
-3 +2 = -1
-1 +2 = 1
To get the next term add 2
1 +2 = 3
Answer: 3
Step-by-step explanation:
Need help ASAP thank you
Answer:
A. Volume = 462 cm³; Surface Area = 458 cm²
B. Volume
C. Surface area
Step-by-step explanation:
A. Given a rectangular box:
[tex] Width (w) = 3 cm [/tex]
[tex] Height (h) = 14 cm [/tex]
[tex] length (l) = 11 cm [/tex]
=>Volume of the juice box
[tex] Volume (V) = whl [/tex]
[tex] Volume (V) = 3*14*11 [/tex]
[tex] = 3*14*11 = 462 [/tex]
Volume of juice box = 462 cm³
=>Surface area (S.A) of juice box:
[tex] S.A = 2(wl + hl + hw) [/tex]
[tex] S.A = 2(3*11 + 14*11 + 14*3) [/tex]
[tex] S.A = 2(33 + 154 + 42) [/tex]
[tex] S.A = 2(229) [/tex]
[tex] S.A = 458 cm^2 [/tex]
Surface area of juice box = 458 cm²
B. Volume would be used to find the amount of juice the box can hold
C. Surface area would be used to know how much wax to buy to use in coating the box.
A cycling race is 17 miles long. The cyclists will begin at point S and ride a number of laps around a neighborhood block. After the last lap, the cyclists will sprint 2.0 miles to the finish line. A rectangle with a width of 0.75 miles and height of 0.5 miles. The 2 mile finish comes out of one corner. Using the equation w (1.5 + 1) + 2 = 17, the race's organizer determined the cyclists will need to ride 9 laps before the sprint to the finish. Which explains the error? The equation should be 0.75 w + 0.5 w + 2 = 17, and the cyclists will need to ride 12 laps before the sprint to the finish. The equation should be 2 (0.75 w + 0.5) + 2 = 17, and the cyclists will need to ride 21 laps before the sprint to the finish. The solution should be 6, and the cyclists will need to ride 6 laps before the sprint to the finish. The solution should be 8, and the cyclists will need to ride 8 laps before the sprint to the finish.
Answer:
it is c because i took test review
Step-by-step explanation:
Answer:
C The solution should be 6, and the cyclists will need to ride 6 laps before the sprint to the finish.
PLEASE HELP The equation of the line below is: y = -4x + 4. y = -2x + 4. y = 2x + 4. None of these choices are correct.
Answer:
y = 2x+4
Step-by-step explanation:
The y intercept ( where it crosses the y axis ) is 4
The slope is positive because the line goes up from the bottom left to top right
We pick two point ( -2,0) and ( 0,4)
The slope is found by
m= (y2-y1)/(x2-x1)
= ( 4-0)/(0- -2)
= 4/ (0+2)
= 4/2
= 2
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
y = 2x+4
Answer:
The equation to this line is y=-4x+4
Step-by-step explanation:
If you look at the graph you can see that the y intercept is 4.
To find the slope take two points on the graph and plug it into be y2-y1/x2-x1
I chose (0,-2) and (-1,2) So 2+2=4 and -1-0= -1 so 4/-1= -4
(OFFERING ALL THE POINTS I HAVE) Word Problem. Please help!! Part 1 of problem: The main tank has a radius of 70 feet. What is the volume of the quarter-sphere sized tank? Round your answer to the nearest whole number and use 3.14 for Pi. (Use sphere volume formula) Part 2: The theme park company is building a scale model of the killer whale stadium main show tank for an investor's presentation. Each dimension will be made 6 times smaller to accommodate the mock-up in the presentation room. How many times smaller than the actual volume is the volume of the mock-up? Part 3: Using the information from part 2, answer the following question by filling in the blank: The volume of the actual tank is __% of the mock-up of the tank.
Answer:
Part 1: 359,007 ft³
Part 2: 216 times smaller
Part 3: 21600%
Step-by-step explanation:
Part 1:
The parameters for the tank are;
The radius of the tank = 70 feet
The volume of a sphere = 4/3·π·r³
Therefore, the volume of a quarter sphere = 1/4×The volume of a sphere
The volume of a quarter sphere = 1/4×4/3·π·r³ = π·r³/3
Plugging in the value for the radius gives
Volume = π×70³/3 = 114,333.33×3.14 = 359,006.7≈ 359,007 ft³.
Part 2:
The dimension of the scale model = 1/6 × Actual dimension
Therefore, we have the radius of the sphere of the scale model = 1/6 × 70
Which gives;
The radius of the sphere of the scale model = 35/3 = 11.67 feet
The volume of the scale model = π·r³/3 = (3.14×11.67³)/3 = 1662.07 ≈ 1662 ft³
The number of times smaller the scale model is than the actual volume = (Actual volume)/(Scale model) = (359,007 ft³)/(1662 ft³) = 216 times
The number of times smaller the scale model is than the actual volume = 216 times = (1/Scale of model)³ = (1/(1/6))³ = 6³.
Part 3:
The percentage of the mock-up, x, to the volume of the actual tank is given as follows
x/100 × 1662 = 359,007
∴ x = 216 × 100 = 21600%
The percentage of the mock-up, to the volume of the actual tank is 21600%.
Answer:
Part 1: 359,007 ft³
Part 2: 216 times smaller
Part 3: 21600%
Step-by-step explanation:
Part 1:
The parameters for the tank are;
The radius of the tank = 70 feet
The volume of a sphere = 4/3·π·r³
Therefore, the volume of a quarter sphere = 1/4×The volume of a sphere
The volume of a quarter sphere = 1/4×4/3·π·r³ = π·r³/3
Plugging in the value for the radius gives
Volume = π×70³/3 = 114,333.33×3.14 = 359,006.7≈ 359,007 ft³.
Part 2:
The dimension of the scale model = 1/6 × Actual dimension
Therefore, we have the radius of the sphere of the scale model = 1/6 × 70
Which gives;
The radius of the sphere of the scale model = 35/3 = 11.67 feet
The volume of the scale model = π·r³/3 = (3.14×11.67³)/3 = 1662.07 ≈ 1662 ft³
The number of times smaller the scale model is than the actual volume = (Actual volume)/(Scale model) = (359,007 ft³)/(1662 ft³) = 216 times
The number of times smaller the scale model is than the actual volume = 216 times = (1/Scale of model)³ = (1/(1/6))³ = 6³.
Part 3:
The percentage of the mock-up, x, to the volume of the actual tank is given as follows
x/100 × 1662 = 359,007
∴ x = 216 × 100 = 21600%
The percentage of the mock-up, to the volume of the actual tank is 21600%.
The volume of a cone is 1540cm³. If its radius is 7cm, calculate the height of the cone. (Take pi = 22/7)
Answer:
30 cmGiven,
Volume of a cone = 1540 cm[tex] {}^{3} [/tex]
Radius ( r ) = 7 cm
π ( pi ) = [tex] \frac{22}{7} [/tex]
Height of cone ( h ) = ?
Now, let's find the height of cone:
Volume of cone = [tex]\pi \: {r}^{2} \frac{h}{3} [/tex]
plug the values
[tex]1540 = \frac{22}{7} \times {(7)}^{2} \times \frac{h}{3} [/tex]
Evaluate
[tex]1540 = \frac{22}{7} \times 49 \times \frac{h}{3} [/tex]
Calculate
[tex]1540 = \frac{154 \: h}{3} [/tex]
Apply cross product property
[tex]154 \: h = 1540 \times 3[/tex]
Calculate the product
[tex]154 \: h = 4620[/tex]
Divide both sides of the equation by 154
[tex] \frac{154 \: h}{154} = \frac{4620}{154} [/tex]
Calculate
[tex]h \: = 30 \: cm[/tex]
Hope this helps...
Best regards!!
Suppose $x-3$ and $y+3$ are multiples of $7$. What is the smallest positive integer, $n,$ for which $x^2+xy+y^2+n$ is a multiple of $7$? Enter your answer. I need Immediate help or you wont get the points.
In the language of modular arithmetic, we're given
[tex]x-3\equiv0\pmod7\implies x\equiv3\pmod7[/tex]
[tex]y+3\equiv0\pmod7\implies y\equiv-3\equiv4\pmod7[/tex]
Then x = 7a + 3 and y = 7b + 4 for integers a and b.
Substitute these into the quadratic expression and simplify:
[tex]x^2+xy+y^2+n\equiv0\pmod7[/tex]
[tex](7a+3)^2+(7a+3)(7b+4)+(7b+4)^2+n\equiv0\pmod7[/tex]
[tex]49a^2+42a+9+49ab+28a+21b+12+49b^2+56b+16+n \equiv 0\pmod7[/tex]
[tex]37+n\equiv 0\pmod7[/tex]
[tex]n\equiv-2\equiv5\pmod7[/tex]
which means the smallest positive integer n we are looking for is 5.
Which example illustrates the commutative property of addition for polynomials?
Answer:
The fourth.Step-by-step explanation:
The alternation of addition means you can swap places of components of sum.
(2x²+5x) and (4x²-4x) are polynominal components of the sum: (2x²+5x)+(4x²-4x)
Answer:
D
Step-by-step explanation:
got it right on edge
PLEASE ANSWER SOON! I WILL MARK BRAINLIEST! THANK YOU!
The ratio of the measures of the acute angles of a right triangle is 8:1. In degrees, what is the measure of the largest angle of the triangle?
Answer:
80°
Step-by-step explanation:
The sum of the measures of the acute angles in a right triangle is 90°. The sum of ratio measures in the ratio 8 : 1 is (8+1) = 9. Thus, each of those measures stands for 90°/9 = 10°. Then the angle ratio is ...
80° : 10° = 8 : 1
The measure of the largest acute angle in the triangle is ...
10° × 8 = 80°
10.Given the following, including the fact
that ∠ABC and ∠CBD are supplementary,
what is the value of m ∠ABC and m ∠ABC?
m ∠DBC=x−10
m ∠ABC=x+30.
Answer:
m ∠DBC=80−10=70
m ∠ABC=80+30=110
Step-by-step explanation:
m ∠DBC+m ∠ABC=180
( x−10)+(x+30.)=180
2x+20=180
2x=180-20
2x=160
x=80
>>m ∠DBC=80−10=70
>>m ∠ABC=80+30=110
Answer:
[tex]\boxed{<DBC = 70 degrees}\\\boxed{<ABC = 110 degrees}[/tex]
Step-by-step explanation:
∠ABC and ∠DBC are supplementary which means that the sum of these two angles is equal to 180.
∠ABC + ∠DBC = 180
Given that: ∠ABC = x+30 and ∠DBC = x - 10
So,
=> x+30+x-10 = 180
=> 2x+20 = 180
=> 2x = 180-20
=> 2x = 160
Dividing both sides by 2
=> x = 80
Now, Finding measures of the angles.
=> ∠DBC = x-10 = 80-10 = 70 degrees
=> ∠ABC = x+30 =80+30 = 110 degrees
Find the value of x in the data given below if the mean is 2. The values are 2, 4, 1, 1, x, 3, 2
Answer:
[tex]\boxed{x=1}[/tex]
Step-by-step explanation:
[tex]mean=\frac{sum \: of \: terms}{number \: of \: terms}[/tex]
[tex]2=\frac{2+4+1+1+x+3+2}{7}[/tex]
[tex]2=\frac{13+x}{7}[/tex]
[tex]14=13+x[/tex]
[tex]x=1[/tex]
Help please! Thanks!!
Answer: None of them
I think your teacher made a typo. See explanation below for details
=================================================
Explanation:
With math problems like this one, it is often very tricky to find integer solutions. Luckily, we're given a list of choices. Let's plug them in one at a time and see what happens.
If y = 5, then
y^2 - 7x^2 = 11
5^2 - 7x^2 = 11
25 - 7x^2 = 11
-7x^2 = 11-25
-7x^2 = -14
x^2 = -14/(-7)
x^2 = 2
But x^2 = 2 does not have any integer solutions. The two solutions are irrational. So we can rule out choice F.
Repeat for y = 4 and you should find that x^2 = 5/7, which also does not have any integer solutions. Choice G can be ruled out.
Choices H through K are even worse. Not only are there no integer solutions, but there aren't any real number solutions either (there are complex or imaginary solutions though). Plugging in y = 3 leads to x^2 = -2/7 which has imaginary solutions due to applying the square root to a negative radicand. Similar situations happen with J and K as well.
In summary, none of these answer choices are valid. We need to have two integers x and y that satisfy the equation. I think your teacher made a typo somewhere.
What is the slope of a line perpendicular to one with a slope of {-2}{3}.
Answer:
3/2
Step-by-step explanation:
Perpendicular lines have slopes that multiply to -1
m * -2/3 =-1
Multiply by -3/2 to isolate m
m * -2/3 * -3/2 = -1 * -3/2
m = 3/2
The perpendicular line has a slope of 3/2
Helppppp pleaseeeeee
Answer:
(2, 2), (5, 3), (9, 4), and (13, 5).
Step-by-step explanation:
The inverse of a function makes it so that the x-values become y-values, and y-values become x-values.
The current coordinates are (2, 2), (3, 5), (4, 9), and (5, 13).
If the function were inversed, the coordinates would be (2, 2), (5, 3), (9, 4), and (13, 5).
Hope this helps!
The following is the student's grades for a certain class
(left : grades, right : frequency)
determine :
a.) how many students have grades that are above than 73,5
b) how many students have grades that are below 75
Answer:
a) 20 students
b) 20 students
Step-by-step explanation:
a) From the given frequency table, we have to check the number of students that scored above 73.5 and add them up.
Therefore, the number of students that have grades above 73.5 are:
14 + 4 + 2 = 20 students
b) 75 falls in between 74 - 76 and we do not have the individual frequencies of the grades (74, 75, 76).
However, we can use the data we have from the table to make an assumption.
The number of students that have grades below 75 will be:
13 + 5 + 2 = 20 students
there are 48 members in a dancing club. the ratio of boys to girls in the club is 3:5 how many boys should join the club for the ratio of boys to girls to be 1:1
Answer:
12
Step-by-step explanation:
If you add the ratio you will get 8 and 1 in the ratio number represents
6 people so 5-3=2
Therefore, the no. of girls minus boys= 6×2=12
so you need 12 more boys to make it to be a ratio of 1:1
Find the solution of the system of equations shown on the graph.
Please and thank you :)
Answer:
Hey there!
The solution is where the lines intersect, and here we see that would be (-4,3)
Hope this helps :)
Need help, there are also two more questions to answer after those but I couldn’t put them in the picture, they are semicircle and radius. Thanks
Answer:
arc KL=minor arc
arc LJK=major arc
Step-by-step explanation:
so minor arc is a arc which is larger than a semicircle .
a major arc is a circle having measure less than radians.
HELPPP PLZZZZZZZZZZZZZ
1
English
TIME REMAINING
58:10
The radius of the large sphere is double the radius of
the small sphere.
How many times is the volume of the large sphere than
the small sphere?
O 2
4
6
08
Answer
2
Step-by-step explanation
The radius of the large sphere is double the radius of the small sphere
what's the value? A.-20 B.-4 C.4 D.20
Answer:
-4Option B is the correct option.
Step-by-step explanation:
[tex] {(4 - 2)}^{3} - 3 \times 4[/tex]
Subtract the numbers
[tex] = {(2)}^{3 } - 3 \times 4[/tex]
Multiply the numbers
[tex] = {(2)}^{3} - 12[/tex]
Evaluate the power
[tex] = 8 - 12[/tex]
Calculate the difference
[tex] = - 4[/tex]
Hope this helps..
Best regards!!
Answer:
[tex]\boxed{-4}[/tex]
Step-by-step explanation:
[tex](4-2)^3-3 \times 4[/tex]
Brackets or parenthesis are to be evaluated first. Subtract the numbers in the brackets.
[tex](2)^3-3 \times 4[/tex]
Evaluate the power or exponent.
[tex]8-3 \times 4[/tex]
Multiply the numbers.
[tex]8-12[/tex]
Finally, subtract the numbers.
[tex]=-4[/tex]
Are the terms CSC, SEC, and COT equivalent to the terms Sin^-1, Cos^-1, and Tan^-1? Are the three pairs of terms the same thing just written differently, or are they entirely different?
Answer:
Step-by-step explanation:
It depends on how it is written. By definition
[tex]\csc(x) = (\sin(x))^{-1} = \frac{1}{\sin(x)}[/tex]
[tex]\sec(x) = (\cos(x))^{-1} = \frac{1}{\cos(x)}[/tex]
[tex]\cot(x) = (\tan(x))^{-1} = \frac{1}{\tan(x)}[/tex]
however the functions
[tex]\sin^{-1}(x), \cos^{-1}(x), \tan^{-1}(x)[/tex] are the inverse functions of sine, cosine and tangent respectively. So, they are not equivalent functions