Given statement 'To find the length of the hypotenuse of a right triangle, take the square root of the difference of the squares of the legs.' is False.
In given question,
We have been given a statement 'To find the length of the hypotenuse of a right triangle, take the square root of the difference of the squares of the legs.'
We know that a hypotenuse is the largest side of a right triangle.
According to Pythagoras theorem,
in a right triangle c² = a² + b²
where c is the hypotenuse of a right triangle
a, b are perpendicular sides of the right triangle
This means, to find the length of the hypotenuse of a right triangle, take the square root of the sum of the squares of the legs.
Therefore, given statement 'To find the length of the hypotenuse of a right triangle, take the square root of the difference of the squares of the legs.' is False.
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The relation between degrees Fahrenheit F and degrees Celsius C is described by the function F = (9/5)C+32 . In the following ordered pairs, the first element is degrees Celsius and the second element is its equivalent in degrees Fahrenheit. Find the unknown measure in each ordered pair.
d. (q, 19)
5:9 is degrees Celsius and the second element is its equivalent in degrees Fahrenheit.
What does a temperature in Fahrenheit mean?
Water freezes at 32 degrees Fahrenheit and boils at 212 degrees Fahrenheit on the Fahrenheit scale, which is used to measure temperature.It is denoted by the °F sign. The temperature had risen to 100 degrees Fahrenheit by mid-morning.F = (9/5)C+32
F = C x 9/5 + 32
C = (F - 32) x 5/9
The above equations could easily be derived by the following relationships:
Freezing Point = 0C or 32F and Boiling Point = 100C or 212F
Range from freezing point to boiling point = 100C or 180F,
i.e. C : F = 100:180 = 5:9
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om drove at a constant speed of 50 miles per hour for 2.5 hours.
Albert drove at a constant speed of 65 miles per hour for 2 hours.
Who drove farther? How many more total miles did he drive?
Use the equation d=r×t to solve.
Albert drove 5 miles farther than Tom if their speed were 50mi/h and 65 mi/hr.
What is the distance?Distance is the size or extent of the displacement between two places. Remember that the travel distance between two points is not the same as their distance from one another. The distance traveled is the total distance traveled to get from one place to another. Distance traveled is not a vector.
Tom's distance is calculated as
Put D= D₁, r = 50 miles per hour, and t = 2.5 hours in the distance formula
D₁ = (50 mi/h)·(2.5 h)
D₁ = 125 mi
Albert's distance is calculated as
Put D= D₂, r = 65 miles per hour, and t = 2 hours in the distance formula
D₂ = (65 mi/h)·(2 h)
D₂ = 130 mi
Comparing both the distances
Albert drove 130 -125 = 5 miles farther than Tom.
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Write an equation of each line in standard form with integer coefficients.
a line through (3,1) with slope 0
The equation of the line in standard form passing through the point (3 , 1) with slope equal to 0 is y = 1.
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).
Using the point slope form, plug in the values of the slope and the point to set up the equation.
(y - y1) = m(x - x1)
where m = 0 and (x1 , y1) = (3 , 1)
(y - 1) = 0(x - 3)
y - 1 = 0
y = 1
Since the variable(s) is already isolated at one side and the constant on the other side, the equation is y = 1 already in standard form.
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Find the area under the normal curve between the values z=-2.61 and z=0.4
Round your answer to 4 decimal places.
Answer:
0.6508
Step-by-step explanation:
The standard normal distribution has a mean μ= 1 and standard deviation σ = 0
The area under the normal curve for any z value say Z i.e. P(z ≤ Z) can be read off from the Standard Normal Tables or just use a statistical calculator
Using a calculator is best
I see the lower z score as - 2.61 and the upper z score as 0.4
P(-2.61 ≤ z ≤ 0.4) = P(0.4) - P(-2.61)
P(z ≤ 0.4) = 0.65542
P(z ≤ -2.6) = 0.0045271
P(z ≤ 0.4) - P(z ≤ -2.6) = 0.65542 - 0.0045271 = 0.6507588 = 0.6508 rounded to 4 decimal places
(Note: some calculators are able to directly compute the area between two z values)
please help!!
In the figure below angle ADB = (7x + 2) degrees and angle CDB = (3x - 2). Find the measure of the angle ADB.
The measure of the angle ADB is 65 degrees
How to find the measure of the angle ADB?The angles are given as
Angle ADB = (7x + 2) degrees
Angle CDB = (3x - 2) degrees
The angles are complementary angles
This means that they add up to 90 degrees
So, we have:
ADB + CDB = 90
This gives
7x + 2 + 3x - 2 = 90
Evaluate
10x = 90
Divide by 10
x = 9
Substitute x = 9 in Angle ADB = (7x + 2) degrees
Angle ADB = (7 x 9 + 2) degrees
Evaluate
Angle ADB = 65 degrees
Hence, the measure of the angle ADB is 65 degrees
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2(7x-7)=14x-20
with work plss and ty :)
Answer: 0= negative 6
Step-by-step explanation:
Find x and AB if B is between A and C, AB=3x, BC=14, and AC=41.
The value of x is 9 and the measure of AB is 27.
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.
We need to Find x and AB if B is between A and C,
Given that AB=3x, BC=14, and AC=41.
AB + BC = AC
3x+14=41
3x=27
X=9
Now substitute to find the AB;
AB=3(9)
AB =27
Therefore the value of x is 9 and the measure of AB is 27.
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how many groups of 3/8 are in 1
Answer:
Step-by-step explanation:
2 2/3
x^2 + 5x - 14 factorise
Answer: (x-2)(x+7)
Step-by-step explanation:
Answer: (x+7)(x-2)
Step-by-step explanation:
[tex]x^2+5x-14=\\x^2+7x-2x-14=\\x(x+7)-2(x+7)=\\(x+7)(x-2)[/tex]
What’s the answer help pls
Explain your method for determining the efficient route of a network.
Determining the best path involves the evaluation of multiple paths to the same destination network and selecting the optimum or shortest path.
How is the best route to a network determined?
Finding the optimum route to take when sending packets is a router's main duty. The router looks through its routing table for a network address that corresponds to the packet's destination IP address in order to find the optimum route.7 types of routing protocols -
Routing information protocol (RIP)Interior gateway protocol (IGRP)Enhanced interior gateway routing protocol (EIGRP) Open shortest path first (OSPF) Exterior Gateway Protocol (EGP) Border gateway protocol (BGP) Immediate system-to-immediate system (IS-IS)Learn more about network
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The graph shows the velocity f(t) of a runner during a certain time interval:
Graph of line segment going through ordered pairs 0, 2 and 6, 8. Graph of another line segment going through ordered pairs 6, 8 and 8, 0. Label on the x axis is time in seconds, and label on the y axis is velocity in meters per second.
Which of the following describes the intercepts on the graph?
The initial velocity of the runner was 8 m/s, and the runner stopped after 2 seconds.
The initial velocity of the runner was 2 m/s, and the runner stopped after 8 seconds.
The initial acceleration of the runner was 8 m/s2, and the runner stopped after 2 seconds.
The initial acceleration of the runner was 2 m/s2, and the runner stopped after 8 seconds.
The initial velocity of the runner was 2 m/s, and the runner stopped after 8 seconds. Therefore, option (b) is correct.
The velocity of an object helps to calculate the speed of the object in a particular direction. A velocity-time graphs shows the speed and direction of an object that travels over a specific period of time. They are also known as speed-time graphs too.
The vertical axis represents the velocity of an object and horizontal axis represents the time taken to cover particular distance with the speed.
Here, the ordered pairs given in the question are (0,2), (6,8) going through one line segment and for other line segment it is (6,8) and (8,0) respectively. We have to conclude various statement that matches best for the ordered pairs given to us. Let's proceed to solve this.
For (0,2), this ordered pair conclude that: At t = 0 sec, the initial velocity of the runner was 2m/s respectively.
Similarly, for (6,8) this represents that at t = 6 sec the velocity of the runner reaches at maximum. i.e., 6m/s and acceleration is 1 m/s² also from this ordered pair for another line segment a state of deceleration begins which ultimately reduces the acceleration of an object.
For (8,0), this ordered pair represents that at t = 8 sec the velocity of the object which is the final velocity it become 0 m/s i.e., the runner stopped.
From all the ordered pair we have concluded that option (b) is correct which says that the initial velocity of the runner was 2 m/s, and the runner stopped after 8 seconds.
Hence, option (b) is correct.
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Elvira is comparing prices between two different suppliers of fresh lettuce. Val’s Veggies charges $250 for delivery plus $1.50 per bag of lettuce. Sally’s Salads charges $100 for delivery plus $4.00 per bag of lettuce. How many bags of lettuce must be purchased for Val’s Veggies to be the cheaper option?
a. Write and solve an inequality that models this situation.
b. Describe in words the quantities that would work in this situation.
c. Write your answer in both interval and set notation.
The inequality to model this situation is given by x>60 .
Inequality is defined as the relationship between a variable and a constant or two variables which can be written in the form of an equation using the notations < , > , ≤ or ≥ .
Let us consider the number of bags of lettuce bought be x.
Therefore amount needed to buy x bags from Val's veggies is :
250 + 1.5 x
And the amount needed to buy x bags from Sally's Salads is :
100 + 4 x
Now it is given that Val's Veggies need to be cheaper than Sally 's.
a) Therefore we will write an inequality and solve it for x:
∴ 250 + 1.5 x < 100 + 4 x
moving the variables and constants together
or, 1.5 x - 4 x < 100 - 250
or, - 2.5x < -150
or, x > 60
b) Therefore from the inequality we can conclude more than 60 bags of lettuce needs to be purchased for Val's cost to be cheaper.
c) Set notation: {x ∈ Z | x>60}
interval notation : x∈(60.∞)
Therefore from the inequality , the number of bags to be purchased must be more than 60.
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Determine whether each sequence is geometric. If so, find the common ratio. 1,2,4,8, . . . . .
The given sequence is geometric, with the common ratio = 2.
What is a geometric progression?A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.Given: 1, 2, 4, 8, ...
=> 2⁰, 2¹, 2², 2³, ...
We can see that the quotient of each two consecutive terms is 2, in the given sequence, following the necessary condition for a sequence to be geometric.
Thus, The given sequence is geometric, with the common ratio = 2.
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Add. Estimate to check your work. 5,238 + 2,794
The sum of 5,238 and 2,794 is 8,032.
What is addition?In math, addition is the process of adding two or more numbers together. Addends are the numbers that are added, while the sum refers to the result of the operation.
Given: 5,238 + 2,794
To add the estimate, we place the given 4-digit number 2794 below the given 4-digit number 5238, and then group the numbers into columns according to their places, such as once, tens, hundreds, and thousands.
The numbers are now added column-by-column. First, we add the number in the one's column (8+4=12), then in the tens column after carrying 1 (9+3+1=13), in the hundreds column carrying 1(2+7+1=10) and in the thousands column carrying 1 again (5+2+1=8).
So the final result of the addition is 8,032.
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In the figure is a right triangle ABC with AC=10cm and AB=6cm, What is the height AB (Theorem of Pythagoras)
Answer:
8cm
Step-by-step explanation:
Given-;
BC(base)=6cm
AC(hypotenuse)=10cm
To Find-:
AB(Perpendicular)=?
Solution-:
As we know that
Pythagoras Theorem=>H²=P²+B²
By using it
=>10²=P²+6²
=>100=P²+36
=>100-36=P²
=>64=P²
Therefore, the height of AB is 8cm.
100 POINTS! ANSWER PLEASE! Order the following rational and irrational numbers from least to greatest. -2 3/5, square root of 20, 3.9, 10/3, 3 7/8
The given rational and irrational numbers can be ordered from least to greatest as follows; -2 3/5 < 10/3 < 3 7/8 < 3.9 < √20.
What is the arrangement of the numbers in ascending order?It follows from the task content that the numbers given are rational and irrational numbers.
To order the numbers, they should be converted to decimal numbers as follows;
-2 3/5 = -2.6
√20 = 4.47
3.9 = 3.9
10/3 = 3.33
3 7/8 = 3.875
Hence, the order from least to greatest is; -2 3/5 < 10/3 < 3 7/8 < 3.9 < √20.
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Ella has 50 stickers of 10 pennies in each stack describe how to find how many pennies Ella has and all
the number of pennies that Ella has in all is 500 pennies.
Number of stickers = 50
Cost of each sticker = 10 pennies
Now, we need to find the total pennies Ella has.
We will use multiplication to find the same.
So, by using the operation of multiplication, we get that:
Number of pennies = 10 × 50 pennies.
Number of pennies = 500 pennies.
Therefore, we get that, the number of pennies that Ella has in all is 500 pennies.
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235+39429-2293= bằng bao nhiêu
Answer:
41957
Step-by-step explanation:
39429
2293
235
_______
41957
set as brainliest
given: 7(x + 2) + 4x = 6(2x - 4)
prove: x = 2/3
The solution to the equation 7(x + 2) + 4x = 6(2x - 4) gives the result x = 38
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the equation:
7(x + 2) + 4x = 6(2x - 4)
Opening the bracket gives:
7x + 14 + 4x = 12x - 24
Collecting like terms:
x = 38
The solution to the equation 7(x + 2) + 4x = 6(2x - 4) gives the result x = 38
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Evaluate: 100−20.2×4.5.
The value of given expression 100−20.2×4.5 is 9.1 .
Expression in maths is outlined because the assortment of numbers variables and functions by exploitation signs like addition, subtraction, multiplication, and division.BODMAS is Associate in Nursing descriptor for the sequence of operations to be performed whereas simplifying the mathematical expressions. Hence , BODMAS full form is Bracket, Order, Division, Multiplication, Addition, and Subtraction.We have given an expression 100−20.2×4.5 .
Using BODMAS we will first solve the multiplication term than the subtraction term .
We will do multiplication operation which is given by
20.2 × 4.5 = 90.9
Now , we will subtract 90.9 from 100 , we get
100 - 90.9 = 9.1
Hence , the value is 9.1
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2^2x+1 _5(2x)+2=0
[tex]2 {x}^{2} + 1 - 5(2x) + 2 = 0[/tex]
Answer:
2x²-10x+3=0
Step-by-step explanation:
2x²+1 - 5(2x)+2=0
2x²+1 - 10x+2=0
Combine like terms.
2x²+1 - 10x+2=0
2x²-10x+3=0
Hope this helps!
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Have a great day!
Find the value of x in each case.
Answer: 11
Step-by-step explanation:
[tex]\angle GFE=33^{\circ}[/tex] (linear pair)
[tex]\angle FEB=180^{\circ}-4x[/tex] (linear pair)
[tex]33+180-4x+x=180[/tex] (sum of angles in a triangle)
[tex]33+180-4x+x=180\\\\33-3x=0\\\\x=11[/tex]
in the following series one number is wrong find out the wrong number
a
A 132
B 42
C 48
D 59
E 84
Answer:
D - 59
Step-by-step explanation:
All the options are even except from D which is odd
Hope this helps :)
what is the least common dominator and the sum 5/8 - 5/12
Answer:
5/12
Step-by-step explanation:
Answer:
24 is the least common factor of 5/8 - 5/12.
Explain to a new student how to simplify the expression below. Show the updated expression after each step you take.
(-8)+(-3)+(-4)(7) ÷14+9(-2)
Answer:
-31
Step-by-step explanation:
You use pemdas which is
parathesis
exponents
multiply or divide, use in order
then add or subtract, use in order
(-8)+(-3)+(-4)(7)÷14+9(-2)
multiply first
-4*7=-28
(-8)+(-3)+(-28)÷14+9(-2)
Divide next
-28÷14=-2
(-8)+(-3)+(-2)+9(-2)
multiply again
9*(-2)=-18
(-8)+(-3)+(-2)+(-18)
now add
-8+(-3)=-11
(-11)+(-2)+(-18)
add again
-11+(-2)=-13
(-13)+(-18)
add for the last time
-13+(-18)=-31
Simplify 5√√2+√√2+3√√2.
OA. 8,2
OB. 7.2
O C. 6√2
OD. 9,2
Answer:
D
Step-by-step explanation:
5[tex]\sqrt{2}[/tex] + [tex]\sqrt{2}[/tex] + 3[tex]\sqrt{2}[/tex] ← factor out [tex]\sqrt{2}[/tex] from each term
= [tex]\sqrt{2}[/tex] (5 + 1 + 3)
= 9[tex]\sqrt{2}[/tex]
8 x 100 = 8 x 10^2 i don't know i need help please help!!!!!
Step-by-step explanation:
10^2=100x8 =800
800=8x100
10^2 =100.The reason is, you are basically doing 10x10=100x8=800.
how many times smaller is (4 x 10^4) than (1.25 x 10^2)
The number of times that (4 x 10⁴) is higher than (1.25 x 10²) is 3.2 × 10².
How to illustrate the information?It should be noted that the information is to find the number of times that (4 x 10⁴) is higher than (1.25 x 10²).
This will be calculated by dividing the values we have.
= (4 × 10⁴) / (1.25 × 10²)
= 3.2 × 10²
In conclusion, the number of times that (4 x 10⁴) is higher than (1.25 x 10²) is 3.2 × 10².
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Ximena has procrastinated all her homework until the very last minute. She has 2 hours to spare until midnight, which is when all her homework is due. Her biology homework will take 30 more minutes than her English homework, and her math homework will take three times as long as her biology homework. How long will each subject take?
Answer:
Step-by-step explanation:
Let,
For English = x min.
For Biology= (x+30) min.
For Math= 3(x+30) min.
2 hours= 2*60 = 120 min.
Now, x+(x+30)+3(x+30)=120
Or, x= 0 min.
For English = 0 min.
For Biology= 30 min.
For Math= 90 min
