Answer:
No
Step-by-step explanation:
Using the converse of Pythagoras' identity.
If the longest side squared is equal to the sum of the squares of the other 2 sides then the triangle is right.
The longest side = 61, thus
61² = 3721
12² + 60² = 144 + 3600 = 3744 ≠ 3721
Thus these sides do not form a right triangle.
The diagonals of a rhombus are 14 and 48cm. Find the length of a side of the rhombus.
Step-by-step explanation:
Let ABCD be a rhombus. So, AC (AC = 14 cm) and BD (BD=48 cm) will be its diagonals. Let us assume that diagonals are intersecting at point O.
Since, diagonals of a rhombus are perpendicular bisector.
[tex] \because \: OA = \frac{1}{2} \times AC \\ \\
\therefore \: OA = \frac{1}{2} \times 14
\\ \\ \huge \red{ \boxed{\therefore \: OA = 7 \: cm}} \\ \\ \because \: OB = \frac{1}{2} \times BD \\ \\ \therefore \: OB = \frac{1}{2} \times 48 \\ \\ \huge \red{ \boxed{\therefore \: OB = 24 \: cm}} \\ \\ In \: \triangle OAB, \: \: \angle AOB=90° \\ \therefore \: by \: Pythagoras \: Theorem \\ AB= \sqrt{OA^2 +OB^2 } \\ = \sqrt{7^2 +24^2 } \\ = \sqrt{49+576 } \\ = \sqrt{625 } \\ \huge \orange{ \boxed{\ \therefore \:AB= 25 \: cm.}}[/tex]
Hence, length of a side (or all) is 25 cm.
Final answer:
To find the length of a side of a rhombus with diagonals measuring 14 cm and 48 cm, one can use Pythagoras' theorem on the right-angled triangles formed by half the diagonals. The length of the side of the rhombus is calculated to be 25 cm.
Explanation:
The question involves finding the length of a side of a rhombus given the lengths of its diagonals. According to the properties of a rhombus, the diagonals bisect each other at right angles. In this case, the diagonals are 14 cm and 48 cm long. Therefore, we have two right-angled triangles formed by the diagonals, with each triangle having legs of 7 cm (half of 14 cm) and 24 cm (half of 48 cm).
To find the length of a side of the rhombus, we can use Pythagoras' theorem, which states that in a right-angled triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse.
Applying Pythagoras' theorem:
Let the length of each side of the rhombus be s.
Use the right-angled triangle with sides 7 cm and 24 cm to solve for s (hypotenuse).
Calculate s² = 7² + 24².
So, s² = 49 + 576.
s² = 625.
Therefore, s = [tex]\sqrt{625}[/tex] = 25 cm.
Hence, the length of a side of the rhombus is 25 cm.
PROBLEM
Write the equation of the line that passes through (0, -6) and (4, 10).
Answer:
y= 4x-6
Step-by-step explanation:
The equation of a line is usually written in the form of y=mx+c, where m is its gradient and c is its y-intercept.
Let's find the gradient, m, first.
[tex]gradient = \frac{y1 - y2}{x1 - x2} [/tex]
Using the above formula,
[tex]m = \frac{10 - ( - 6)}{4 - 0} \\ m = \frac{10 + 6}{4} \\ m = \frac{16}{4} \\ m = 4[/tex]
Subst. the value of m into the equation.
y=4x+c
To find c, substitute a coordinate into the equation.
When x=0, y= -6,
-6= 4(0) +c
c= -6
Thus, the equation of the line is y= 4x -6.
the values of x and y vary directly and one pair of values are given. write an equation that relates to the values x and y. simplify completely.
x=-4 y=6
Answer:
y = -3/2 x.
Step-by-step explanation:
y = kx where k is a constant.
6 = -4k
k = 6/-4 = -3/2
So the equation is y = -3/2 x.
Which expression of is equivalent to 1/3(9 - 18x) + 1/4(8x - 12
following expression [tex]1/3(9 - 18x) + 1/4(8x - 12)[/tex] is equal to [tex]-4x[/tex] . Kindly match with your options!
Step-by-step explanation:
Here we have , following expression to evaluate . 1/3(9 - 18x) + 1/4(8x - 12 or , [tex]1/3(9 - 18x) + 1/4(8x - 12)[/tex] :
⇒ [tex]\frac{1}{3}(9 - 18x) + \frac{1}{4}(8x - 12)[/tex]
⇒ [tex]\frac{1(4)}{3(4)}(9 - 18x) + \frac{1(3)}{4(3)}(8x - 12)[/tex]
⇒ [tex]\frac{(9 - 18x)(4)}{3(4)} + \frac{(8x - 12)(3)}{4(3)}[/tex] { Making denominator of both terms same ! }
⇒ [tex]\frac{(9 - 18x)(4)+(8x - 12)(3)}{12}[/tex]
⇒ [tex]\frac{9(4) - 18(4)x+8(3)x - 12(3)}{12}[/tex]
⇒ [tex]\frac{36- 72x+24x - 36}{12}[/tex]
⇒ [tex]\frac{ -48x}{12}[/tex] { Simplifying even further }
⇒ [tex]-4x[/tex]
Therefore , following expression [tex]1/3(9 - 18x) + 1/4(8x - 12)[/tex] is equal to [tex]-4x[/tex] . Kindly match with your options!
Final answer:
The equivalent expression for 1/3(9 - 18x) + 1/4(8x - 12) is -4x.
Explanation:
The given expression is 1/3(9 - 18x) + 1/4(8x - 12).
We need to distribute the fractions across the terms inside the parentheses:
Multiply 1/3 by each term in the first set of parentheses: (1/3 * 9) - (1/3 * 18x).Multiply 1/4 by each term in the second set of parentheses: (1/4 * 8x) - (1/4 * 12).Simplify each term: 3 - 6x + 2x - 3.Combine like terms: (3 - 3) + (-6x + 2x).The final simplified expression is -4x.Therefore, the equivalent expression is -4x.
What are the two ways to solve a system of equations algebraically
Find the area of a trapezoid
Answer:
Area of trapezoid = 32√3
Step-by-step explanation:
Using Pythagoras theorem
8² = (4√3)² + x²
64 = 48 + x²
x² = 64 - 48
x² = 16
x = √16
x = 4
Area of trapezoid = ½(a + b) h
Where a = 10 - 4 = 6
b = 10
h = 4√3
Area of trapezoid = ½(6 + 10) × 4√3
= ½ × 16 × 4√3
= 8 × 4√3
= 32√3
What's the sum of 6ft feet 10 in and 8 ft 9 inches
15 ft. 7 in is the sum of 6 feet 10 inches and 8 feet 9 inches.
6 feet 10 inches + 8 feet 9 inches
= 14 feet 19 inches
= 15 feet 7 inches
A train travels at a constant speed of 24 miles per hour. Which equation and table show the correct relationship between h , the number of hours, and d , the distance traveled?
24h=d.
if you multiply 24 by the number of hours than you will get the distance.
if you traveled for 2hours than you would have traveled 48miles because if you multiply 24 by 2 you get 48.
In the equation 24 is distance traveled in 1 hour.
Answer:
24h=d
Step-by-step explanation:
0=0
2=48
4=96
7=168
its just multiples of 24 :)
Simplify 3 ^4. -------------------------------------------------------------------
Answer:81
Step-by-step explanation:
3x3x3x3
Answer:81
Step-by-step explanation:
3.3.3.3=81
Your help is deeply is appreciated.
Answer:
x = 3
Step-by-step explanation:
[tex]\\4x^2-2x=30\\\\x=3\\4(3)^2-2(3)=30\\4(9) - 6 =30\\36 - 6 = 30\\30 = 30 \\\\x=4\\4(4)^2-2(4)=30\\4(16) - 8 =30\\64 - 8 = 30\\56\neq 30[/tex]
56 is not equal to 30
after five days in her new job, karen has $800 in her bank account. if she is adding exactly $50 to her account each day, when will her balance reach $1000? explain.
Answer:
After 4 more days
Step-by-step explanation:
The remaining amount of money needed to reach the goal is $200 this is because 1000-800=200
Now we divide the 200 by the amount Karen earns a day
200/50=4
That means after 4 more days Karen will have $1000
sarah has already knit 17 centimeters of a scarf, and canknit 1 centimeter each night. How many nights will sarah have to spend knitting in order to knit a total of 34 centimeters of scarf?
Answer:
17 nights.
Step-by-step explanation:
The total length of the scarf that should be knitting = 34 cm
Sarah has already knit 17 centimeters of a scarf.
So, the remaining = 34 - 17 = 17 cm
Sarah can knit 1 centimeter each night.
So, the number of nights will Sarah have to spend knitting = 17/1 = 17 nights.
Which expression is equivalent to x + 2x + y + 2y?
Answer:
3x + 3y
Step-by-step explanation:
X + 2X = 3X
Y + 2Y = 3Y
In this expression, we can combine the like terms to simplify it.
Explanation:To simplify the expression x + 2x + y + 2y, we can combine the like terms. Like terms are terms that have the same variables raised to the same power. In this case, the terms 2x and x are like terms because they both have the variable x raised to the power of 1. Similarly, the terms 2y and y are like terms because they both have the variable y raised to the power of 1.
So, when we combine the like terms, the expression becomes 3x + 3y.
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can someone help me?
Answer:
registration fee: $50monthly fee: $80Step-by-step explanation:
Let r and m represent the registration fee and the monthly fee, respectively. We are told that the charges are ...
370 = r + 4m
530 = r + 6m
This is your system of equations.
__
Subtract the first equation from the second to start the solution.
(530) -(370) = (r +6m) -(r +4m)
160 = 2m . . . . . . simplify
80 = m . . . . . . . . divide by 2
Using this value in the first equation, we find ...
370 = r + 4(80)
50 = r . . . . . . . . . . . . subtract 320
The registration fee is $50; the monthly fee is $80.
ErvIn bowled 7 games last weekend. his scorers are : 155,165,138,172,193,142. what is the range of ErvIn scores
The range of Ervin's scores is 55.
Range is the difference between the largest number and the smallest number.
To find the range of a set of values, first sort the values numerically (smallest to largest). With this set, it would look like this: 138, 142, 155, 165, 172, 193. Lastly, subtract 138 from 193 to find the range. By doing so, you will get 55 as an answer.
I hope this helps!
The range of ErvIn's scores is 55.
The range of ErvIn's scores is calculated by finding the difference between the highest and lowest scores.
Arrange the scores in numerical order: 138, 142, 155, 165, 172, 193.
Find the highest score: 193.
Find the lowest score: 138.
Subtract the lowest score from the highest score to find the range: 193 - 138 = 55.
A zookeeper predicted that the weight of a newborn lion would be 2.8 pounds.
When the zoo’s lion gave birth, the newborn weighed 3.5 pounds.
What is the zookeeper’s percent error? Round to the nearest percent.
There is 20% error in zookeeper's calculations.
Step-by-step explanation:
Given,
Approx weight of newborn lion = Approx value =2.8 pounds
Exact weight of newborn lion = Exact value = 3.5 pounds
Percent error = [tex]\frac{|approx-exact|}{exact}*100[/tex]
Percent error = [tex]\frac{|2.8-3.5|}{3.5}*100\\[/tex]
Percent error = [tex]\frac{|-0.7|}{3.5}*100[/tex]
Percent error = [tex]\frac{70}{3.5}[/tex]
Percent error = 20%
There is 20% error in zookeeper's calculations.
Final answer:
To find the zookeeper's percent error, subtract the predicted weight from the actual weight to find the absolute error, divide by the actual weight, multiply by 100, and round to the nearest percent. The percent error in predicting the weight of the newborn lion is 20 percent.
Explanation:
To calculate the zookeeper's percent error in predicting the weight of a newborn lion, we follow these steps:
Round to the nearest percent.
The zookeeper predicted the weight would be 2.8 pounds, but the actual weight was 3.5 pounds. So the absolute error is:
|Predicted Weight - Actual Weight| = |2.8 pounds - 3.5 pounds| = 0.7 pounds
Then, divide the absolute error by the actual weight:
0.7 pounds / 3.5 pounds = 0.2
Multiply by 100 to convert to a percentage:
0.2 × 100 = 20%
Since we round to the nearest percent, the zookeeper's percent error is 20 percent.
What is the center of the data?
Number of Laps Around a Track
A dot plot going from 1 to 5. 1 has 8 dots, 2 has 6 dots, 3 has 4 dots, 4 has 2 dots, and 5 has 1 dot.
The center is
.
Answer:
2
Step-by-step explanation:
8+6+4+2+1 =21
Total 21 dots/observations
Centre at 11th dot which corresponds to 2
Number of Laps Around a Track. A dot plot going from 1 to 5, 1 has 8 dots, 2 has 6 dots, 3 has 4 dots, 4 has 2 dots, and 5 has 1 dot, the center is 2.
What is center?The location is sometimes alluded to as the data collection's "core." The two metrics that are most frequently used to identify the "center" of both the data are the mean (average) and the median. To find the weighted mean of 50 people, add up all 50 weights once more and divide by 50.
Order the data and locate the number that divides the information into two equal portions to determine the median weight of both the 50 individuals. Because it is unaffected by the specific numerical values of the outliers, the median is typically a better indicator of the center if there are extreme values or outliers. The most popular way to measure the center is with the mean.
8+6+4+2+1 =21
21 dots/observations
Centre at 11th dot which corresponds to 2
Therefore, the center is 2.
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Which relationship describes angles 1 and 2?
Can't be 2 answers.
supplementary angles
complementary angles
adjacent angles
vertical angles
Answer:
Vertical angles
Step-by-step explanation:
Two non-adjacent angles formed by the intersection of two lines are called vertical angles.
(x - 1)2 = 4
how do i do this
Answer:
x = 3
Step-by-step explanation:
(x - 1)2 = 4
how to get this solved is very simple.
first step to apply is the BODMAS RULE
B..................... bracket
O..................... of
D.....................Division
M.................... multiplication
A..................... addition
S.................... Subtraction
so (x - 1)2 = 4
we have,
2x - 2 = 4 ( by opening the bracket)
collect the like terms
2x = 4+2
divide both sides by 2
2x/2 = 6/2
x = 3
to check if your answer is correct put the value of x = 3 into the question and see if the right hand side will equal to the left handside
(x - 1)2 = 4
(3-1)2=4
2(2)=4
4=4.............................. proved
NEED HELP ASAP!! Fill in the chart with the correct end behavior. Enter your answer as either infinity or negative infinity.
Answer:
Column 1:
Positive infinity
Negative infinity
Column 2:
Negative infinity
Positive infinity
Oliver has three green balls, two red balls , five yellows balls , and four orange balls in a bucket . He randomly chooses one ball out of the bucket without looking.
What is the probability he chooses a yellow ball?
If he removes all of the orange balls first, then what is the probability that he will choose a red ball out of the bucket?
Answer:
The probability that he chooses a yellow ball is 5/14. If he removes all the orange balls, the probability that he will choose a red ball is 2/10.
Step-by-step explanation:
Simple logic.
Which function has a graph that is a straight line?
y=−x3+14
y=−87+2x
y=−52+8x
y=−9+6x
C. Is your answer
y=−52+8x
A hamilton multitouch watch was originally priced at $450 . At a closing of Alpha Omega jewelry shop, the watch is being reduced by 0.2 . What is the new selling price?
Answer:
$449.8
Step-by-step explanation: 450-0.2
The question is about calculating the new price of a Hamilton multitouch watch which was priced originally at $450, and is reduced by 20%. The new selling price of the watch is $360.
Explanation:The problem at hand is telling us that a Hamilton multitouch watch, which originally costs $450, is experiencing a price reduction of 0.2 or 20%. To calculate the new selling price, we need to multiply the original price of $450 by the reduction rate of 0.2 and then subtract that value from the original price.
The calculation would look like this: $450 * 0.2 = $90. This suggests that the watch is being discounted by $90.
Following, to calculate the new selling price, subtract the discount from the original price: $450 - $90 = $360. Thus, the new selling price of the Hamilton multitouch watch is $360.
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Please help :( I don’t u derstand it
Answer:
[tex]\frac{3}{(2x+7)}[/tex]
Step-by-step explanation:
[tex]\frac{3x +3}{2x^2 + 9x + 7}[/tex]
[tex]\frac{3(x + 1)}{(2x + 7)(x + 1)}[/tex]
[tex]\frac{3}{(2x+7)}[/tex]
Answer: [tex]\frac{3}{(2x+7)}[/tex]
GRAPH BELOW:
Sharing kicks a ball from the ground into the air with an upward velocity of 64ft per second. The function h=-16t^2+64t models the height h, in feet, of the ball at time t, in seconds. When will the ball reach the ground again.
h = -16t^2 + 64t
When the ball reaches the ground, h will equal zero.
0 = -16t^2 + 64t
16t^2 = 64t
16t = 64
t = 4 seconds
Answer:
the first answer the other person put is the correct one
Step-by-step explanation:
just Dubble checked it
ABC is an obtuse triangle. Given that CB = 20, the measure of A = 30°, and the measure of B = 45°, which of the expressions listed would be used to find how long CA is? (Note: For ABC, where a, b, and c are the lengths of the sides opposite A, B, and C, respectively, SinA/a=SinB/b=SinC/c.)
1. 45sin20/sin30
2. 20sin30/sin45
3. 20sin45/sin30
4. sin45/20sin30
Answer:
option 3
Step-by-step explanation:
Using the Sine rule in Δ ABC, that is
[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex], that is
[tex]\frac{20}{sin30}[/tex] = [tex]\frac{CA}{sin45}[/tex] ( cross- multiply )
CA × sin30° = 20 × sin45° ( divide both sides by sin30° )
CA = [tex]\frac{20sin45}{sin30}[/tex] → (3)
A family of two adults and three children went to a water park. Admission to the water park costs $18 per person. Nora used the expression 2 (18) + 3 (18) to model the total cost for the family, and Alex used the expression 5 (18). Which property of operations makes both of their expressions correct?
associative property
commutative property
distributive property
identity property
Answer
Distributive Property.
Step-by-step explanation:
First you solve for the first equation by multiplying 2 by 18 which is 36. Then 3 times 18 which is 54. Then you add them together to get 90.
Next you solve for the second equation by multiplying 5 by 18 which is 90.
Both of these equations are solved by the distributive property because your distributing the number outside of the parenthesis.
What is the range of the function
A square root can’t be a negative value, so the root would be greater than or equal to zero.
Range:
Y>=O
[O, infinity)
which is the qoutient of 1/5 divided by 3
Answer:
1/5
Step-by-step explanation:
Answer:
[tex]\frac{1}{15}[/tex]
Step-by-step explanation:
[tex]\frac{1}{5}[/tex]÷[tex]\frac{3}{1}[/tex]
[tex]\frac{1}{5}[/tex]·[tex]\frac{1}{3}[/tex]
[tex]\frac{1}{15}[/tex]
is 3x to the power of 2 a function ?
Answer:
No
Step-by-step explanation:
Because in a function for every one x there is one y.
Answer:
YES.
Step-by-step explanation:
f(x) = 3x^2.
This is a parabola which opens upwards ( roughly U shaped) so it will pass the vertical line test and is a function.