Answer:
c = 5
Step-by-step explanation:
This is the classic problem that the ancients (particularly the Egyptians) used extensively. When the Nile over flowed in spring, the land had to be reclaimed and surveyed in the early summer for planting. The 3-4-5 triangle was used to determine right angles for surveying purposes.
Formula
c^2 = a^2 + b^2
Givens
a = 3
b = 4
c = ?
Solution
c^2 = 3*3 + 4*4
c^2 = 9 + 16
c^2 = 25
Take the square root of both sides
To take the square root on your calculator, find the √ on the key pad. Some calculators give it a key and some have the symbol on the body of the calculator. If has its own key do it like this.
√
25
=
The answer should come up as five. If the √ is on the body of the calculator, then
2nd F
√
25
=
The same 5 will come up.
Answer
c = 5
The hypotenuse c of a right triangle with legs a = 3 and b = 4 can be found using the Pythagorean theorem, yielding c = 5
To solve for c, the hypotenuse of a right triangle when given the legs a and b, we utilize the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). This is expressed as a² + b² = c².
To solve for c when a = 3 and b = 4, we substitute these values into the theorem to get 3² + 4² = c², which simplifies to 9 + 16 = c². When we combine the values we get 25 = c². Finally, we take the square root of both sides to solve for c, resulting in c = 5.
If x = 14, which equation is true?
A 3(20- x) = 44
B 3(12-x) = 6
c 2(x - 3) = 22
D 2x-3 = 22
please I need help on this
Answer:
C
Step-by-step explanation:
Simply plug in x for all the questions to see if the x is the solution
A.) 3(20-14) = 44
3(16)=48
so A is incorrect
B.) 3(12-14) = 6
3(-2) = -6
so B is incorrect
C.) 2(14-3) =22
2(11) =22
C is correct
D.) 2(14)-3=22
28-3 = 25
so D is incorrect
Answer:
the answer would be 2(x - 3) = 22 (C)
Step-by-step explanation:
step 1:
2(x - 3) = 22
step 2: divide both sides by the equation 2
x - 3 = 11
step 3: move constant (3) to the right and change its sign
x = 11 + 3
step 4: add the numbers (11 and 3)
x = 14
Solve the inequality (n-7)>2n-3. Write the solution in set notation.
Answer:
- 4 > n and Notion form : [ -4 , -∞).
Step-by-step explanation:
Given : (n-7)>2n-3.
To find : Solve the inequality.
Solution : We have given
(n - 7) > 2 n - 3.
On adding both sides by 3
n - 7+ 3 > 2n .
n - 4 > 2n .
On subtracting b both sides by n
-4 > 2n -n.
- 4 > n.
So, we can say value of n is less than - 4 like -5,-6, -7 ........-∞
Notion form : [ -4 , -∞).
Therefore, - 4 > n and Notion form : [ -4 , -∞).
n = {n | n ∈ R, n < -4}
The given inequality is:
n - 7 > 2n - 3
Collect like terms
n - 2n > -3 + 7
-n > 4
Multiply both sides by -1 and change the sign to <
-1(-n) < -1(4)
n < -4
In set notation:
n = {n | n ∈ R, n < -4}
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If 4 students share 30 ft.² wall equally how many square feet of the wall will be painted by each student
Answer:
7.5 ft²/student
Step-by-step explanation:
This is a "unit rate" problem.
30 ft²
------------------ = 7.5 ft²/student
4 students
Each student will paint 7.5 ft² of the wall.
If a + 1 = b, then b > a. true or false?
Answer:
TRUE, because you are adding a unit more to a, then by logic laws, the quantity grow.
Best regards
Answer:
b > a - True
Step-by-step explanation:
We are given the following expression and we are to determine whether [tex] b > a [/tex] is true or not:
[tex] a + 1 = b [/tex]
Considering the given equation, if we take both the variables on one side so we will get:
[tex] 1 = b - a [/tex]
Sign of the variable [tex]a[/tex] will change to negative while [tex]b[/tex] remains positive.
It means that [tex][/tex] is greater than [tex]a[/tex] (b > a) so it is true.
If 8x + 8y = 4 and 4x + 2y = 12, what is the value of x?
A) -5
B) -
11
2
C) 5
D)
11
2
the value of x = the answer is D 11/2
Determine the Median of 40 49 62 56 68 39 50 61 54 44
The median is 52 you can put this in a stat line in a graphing calculatior
Given the even number of data set, the median which is the average of the middle two numbers in the arranged data set is 52.
What is Median?Median is simply the middle value in a set of variables arranged in a descending or ascending order.
Given the data set; 40 49 62 56 68 39 50 61 54 44.
First, we arrange is ascending order.
39 40 44 49 50 54 56 61 62 68
Since it is an even number set ( 10 )
We find the average of the middle two numbers
Median = ( 50 + 54 ) / 2
Median = 104 / 2
Median = 52
Therefore, the given the even number of data set, the median which is the average of the middle two numbers is 52.
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Consider the expression below. Place the steps required to determine the sum of the two expressions in the correct order. 3x+6/x^2-x-6 + 2x/x^2+x-12
Answer:
Help with this please
Step-by-step explanation:
i have the attachment down there
If f(x)= 2x + 5, which of these is the inverse of f(x)
Answer:
D. [tex]f^{-1}(x)=\frac{x-5}{2}[/tex]
Step-by-step explanation:
The given function is
[tex]f(x)=2x+5[/tex]
Let [tex]y=2x+5[/tex]
Interchange x and y.
[tex]x=2y+5[/tex]
Solve for y.
[tex]x-5=2y[/tex]
Divide both sides by 2
[tex]\frac{x-5}{2} =y[/tex]
Hence [tex]f^{-1}(x)=\frac{x-5}{2}[/tex]
Answer: OPTION D
Step-by-step explanation:
To find the inverse of the function given in the problem, you must apply the proccedure shown below:
1- Rewrite the function:
[tex]y=2x+5[/tex]
2- You must solve for x from the functionn, as following:
Subtract 5 from both sides of the function.Divide both sides of the function by 2. Then:[tex]y-5=2x\\\\x=\frac{y-5}{2}[/tex]
Rewrite the function as following (Substitute [tex]x=f^{-1}(x)[/tex] and [tex]y=x[/tex]:[tex]f^{-1}(x)=\frac{x-5}{2}[/tex]
what value of m is not a solution for the following inequality 3m ≤ 36
a.m=4
b.m=9
c.m=12
d.m=15
Answer:
D. m = 15Step-by-step explanation:
[tex]3m\leq36\qquad\text{divide both sides by 3}\\\\\dfrac{3m}{3}\leq\dfrac{36}{3}\\\\m\leq12\\\\a.\ m=4\leq12\to\boxed{SOLUTION}\\\\b.\ m=9\leq12\to\boxed{SOLUTION}\\\\c.\ m=12\leq12\to\boxed{SOLUTION}\\\\d.\ m=15>12\to\boxed{NOT\ A\ SOLUTION}[/tex]
HELP ASAP! GIVING BRAINLIEST!!
∆ABC has A(-3, 6), B(2, 1), and C(9, 5) as its vertices. The length of side AB is
A) (50)^1/2
B) (65)^1/2
C) (105)^1/2
D) (145)^1/2
units. The length of side BC is
A) (50)^1/2
B) (65)^1/2
C) (105)^1/2
D) (145)^1/2
units. The length of side AC is
A) (50)^1/2
B) (65)^1/2
C) (105)^1/2
D) (145)^1/2
units.
∠ABC ≈ °
A) 55.21
B) 85.16
C) 105.26
D) 114.11
Answer:
1. Option A
2. Option B
3. Option D
4. Option C
Step-by-step explanation:
The given vertices of triangle ABC are A(-3, 6), B(2,1), C(9, 5).
We have to fine the distance AB, BC and AC.
To calculate the distance between two vertices we will use the formula
[tex]d=\sqrt{(x-x')^{2}+(y-y')^{2}}[/tex]
For the length of side AB
AB=[tex]\sqrt{(2+3)^{2}+(1-6)^{2}}=\sqrt{5^{2}+5^{2}}=\sqrt{50}[/tex]
Option A. is the correct option
For the length of side BC
[tex]BC=\sqrt{(9-2)^{2}+(5-1)^{2}}=\sqrt{7^{2}+4^{2}}=\sqrt{65}[/tex]
Option B is the answer.
For the length of side AC
[tex]AC=\sqrt{(9+3)^{2}+(5-6)^{2}}=\sqrt{12^{2}+(-1)^{2}}=\sqrt{145}[/tex]
Option D is the answer.
For ∠ABC we will use the formula [tex]tan\theta =\frac{m_{1}-m_{2}}{1+m_{1}m_{2}}[/tex]
Since angle ABC is formed by two sides AB and BC
So we will find the slopes of these two lines and find the angle
Now slope of AB, [tex]m_{1}=\frac{y-y'}{x-x'}=\frac{1-6}{2+3}=\frac{-5}{5}=-1[/tex]
Slope of BC, [tex]m_{2}=\frac{5-1}{9-2}=\frac{4}{7}[/tex]
[tex]tan\theta =\frac{m_{1}-m_{2}}{1+m_{1}m_{2}}[/tex]
[tex]tan\theta =\frac{(-1)-(\frac{4}{7})}{1+(-1)(\frac{4}{7})}=\frac{\frac{-11}{7}}{1-\frac{4}{7}}=\frac{\frac{-11}{7}}{\frac{3}{7}}=\frac{-11}{7}\times \frac{7}{3}=-\frac{11}{3}=-3.67[/tex]
[tex]\theta =tan^{-1}(-3.67)=74.75[/tex]
Since angle between them [tex]tan\theta[/tex] is negative that means angle theta will be obtuse angle.
So the angle between AB and BC = (180 - 74.75) = 105.26°
Therefore Option C. 105.26° is the answer.
What is that answer to this question?
Answer:
c
Step-by-step explanation:
thats the answer
What is ⅖x=4
And how do you solve it
Answer:x=10
Step-by-step explanation:
5/2 × 2/5 = 4/1 × 5/2
Multiply and simplify and x=10
The solution to the equation 2/5x = 4 is x = 10. You can find the solution by multiplying both sides of the equation by 5/2, which cancelled out the 2/5 on the left side, and then performing the operation on the right side.
Explanation:To solve the equation 2/5x = 4, you'll first want to isolate the variable 'x' on one side of the equation. You can do this by dividing both sides of the equation by the coefficient of 'x', which is 2/5. However, instead of dividing by a fraction, it's easier to multiply by the reciprocal of the fraction.
So, we multiply both sides of the equation by 5/2. The 5/2 multiplied by 2/5 on the left side of the equation equals 1, leaving us with just 'x' on the left side of the equation.
So, you would have x = 4 * 5/2.
Now, we just perform the operation on the right side to find the value of 'x', and we get x = 20/2 = 10.
So, the solution to the equation 2/5x = 4 is x = 10.
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Solve g−17≥17. Graph the solution
Answer:
g≥34
Step-by-step explanation:
To solve the inequality g-17≥17, add 17 to both sides to get g≥34, and graphically represent it with a closed circle at 34 and shade the area to the right.
Explanation:To solve the inequality g−17≥17, add 17 to both sides of the inequality. This yields g ≥ 34. The graph of this solution will include a number line with a closed circle at 34 and a shaded area to the right of 34, indicating all the values of g that are greater than or equal to 34. When graphically representing inequalities, it is important to use a closed circle to indicate that the number is included in the solution.
Select the correct answer
Answer:
16
2
Step-by-step explanation:
Given in the question an equation
[tex]\frac{x^2 - 10x + 14}{ x-8}[/tex]
The constant term that the numerator must have = 16
To get this number add 2 in the numerator
after which the equation will become
[tex]\frac{x^2 - 10x + 14+2}{ x-8}[/tex]
[tex]\frac{x^2 - 10x + 16}{ x-8}\\[/tex]
Now by using factorisation of quadratic equation we have
[tex]\frac{(x-8)(x-2)}{x-8}[/tex]
(x-2)
but if we add and subtract 2 in the numerator then
[tex]\frac{x^2 - 10x + 16 -2}{ x-8}[/tex]
[tex]\frac{(x-8)(x-2)-2}{x-8}[/tex]
[tex](x-2)-\frac{2}{x-8}[/tex]
help on math homework plz im not good at geomatry
C= 2(3.14)r or 3.14D
so, if the diameter (d) is given just multiply it by 3.14. If the radius (r) is given multiply it by 2 then multiply that answer by 3.14 (or just multiply the radius by 6.28)
Pay attention to the units, then find the answer at the bottom.
**WILL MARK BRAINLIEST AND THANK YOU**
Evaluate
4x^2-12x+5 at x=6
A. 67
B. 77
C. 105
D. 221
Answer:
Step-by-step explanation:
D) 221
Adrian has 5 times as many stickers as Derrick. If Adrian has 325 stickers, how many stickers does Derrick have?
Answer: 1625
Step-by-step explanation: If Adrian has 5 times as many times is a keyword to know its multiplication. 325x5=1625
Derrick has 65 stickers.
Explanation:To find out how many stickers Derrick has, we need to divide the number of stickers Adrian has by 5. Since Adrian has 325 stickers, we divide 325 by 5.
325 ÷ 5 = 65.
Therefore, Derrick has 65 stickers.
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Which of the following illustrates the truth value of the given conditional statement? If 5 = 3 + 2, then 3 + 2 = 5.
Answer:
T T → T
Step-by-step explanation:
The following table represents the truth table.
(p) (q) (p->q)
T T T
T F F
F T F
F F F
Now we have the hypothesis that 5 = 3 + 2.
5 = 3 + 2 is True
Then we have the conclusion that 3 + 2 = 5.
3 + 2 = 5 is True
Therefore, we can conclude that (p->q) is True
This can also be represented as:
T T → T
Which could be the surface area of a cubic box that contains a baseball that has a diameter of 3 inches: 9 square inches, 18 square inches, 27 square inches, or 54 square inches?
Answer:
54 in²Step-by-step explanation:
Look at the picture.
The edge of the cube is equal to the diagonal of the sphere.
Therefore, the length of the cube's edge is 3 inches.
The formula of a surface area of a cube:
[tex]S.A.=6a^2[/tex]
Substitute a = 3 in:
[tex]S.A.=6(3^2)=6(9)=54\ in^2[/tex]
The square pyramid pictured below has a surface area of
Answer:
Step-by-step explanation:
Triangles
Area of a triangle = 1/2 b * slanted height
b = 6 m
h = 9 m
Area of 1 triangle = 1/2 * 6 * 9
Area of 1 triangle = 27
Area of all 4 triangles = 4*27 = 108 m^2
==================
Base area
The base is a square. All 4 sides are equal.
The formula for a square is s^2
Area = (6 m)^2
Area = 36 m^2
Total area
Total Area = 108 m^2 + 36 m ^2
Total Area = 144 m^2
your answer is 144m2
hope this helps;)
mark brainly
La Quintas population is about 954,000 and is decreasing at an annual rate of 0.1% Predict the population in 50 years
Answer:
907,450
Step-by-step explanation:
This is a problem of exponential decay. The population is decreasing at 0.1% per year.
The formula to figure this out is [tex]A=P(1+r)^t[/tex]
Where
A will be the future population (after 50 years)
P is the initial population (which is 954,000)
r is the rate of decrease (which is -0.1% or -0.001)
t is the time in years (which is 50)
Plugging these information into the formula and figuring out A will give us the answer. Shown below:
[tex]A=P(1+r)^t\\A=954,000(1-0.001)^{50}\\A=954,000(0.999)^{50}\\A=907,450.17[/tex]
Since fractional/decimal population is not feasible, we round it off.
The population in 50 years would be around 907,450
Solve 5x 2 - 7x + 2 = 0 by completing the square. What are the solutions?
Answer:
[tex]x=\frac{2}{5}[/tex] or [tex]x=1[/tex]
Step-by-step explanation:
The given quadratic equation is
[tex]5x^2-7x+2=0[/tex]
Group the constant terms on the right hand side.
[tex]5x^2-7x=0-2[/tex]
[tex]5x^2-7x=-2[/tex]
Divide through by 5.
[tex]x^2-\frac{7}{5}x=-\frac{2}{5}[/tex]
Add the square of half the coefficient of x., which is [tex](\frac{1}{2}\times- \frac{7}{5})^2=\frac{49}{100}[/tex] to both sides of the equation.
[tex]x^2-\frac{7}{5}x+\frac{49}{100}=-\frac{2}{5}+\frac{49}{100}[/tex]
The left hand side is now a perfect square.
[tex](x-\frac{7}{10})^2=\frac{9}{100}[/tex]
Take the square root of both sides;
[tex](x-\frac{7}{10})=\pm \sqrt{\frac{9}{100}}[/tex]
[tex]x-\frac{7}{10}=\pm \frac{3}{10}[/tex]
[tex]x=\frac{7}{10}\pm \frac{3}{10}[/tex]
[tex]x=\frac{7-3}{10}[/tex] or [tex]x=\frac{7+3}{10}[/tex]
[tex]x=\frac{4}{10}[/tex] or [tex]x=\frac{10}{10}[/tex]
[tex]x=1[/tex] or [tex]x=\frac{2}{5}[/tex]
Answer:
[tex]x_1=1\\\\x_2=\frac{2}{5}[/tex]
Step-by-step explanation:
- You must divide the equation by 5:
[tex]x^{2}-\frac{7}{5}x+\frac{2}{5}=0[/tex]
- Add and subtract [tex](\frac{\frac{7}{5}}{2})^2[/tex]:
[tex]x^{2}-\frac{7}{5}x+(\frac{7}{10})^2+\frac{2}{5}-(\frac{7}{10})^2=0[/tex]
Therefore, you obtain:
[tex](x-\frac{7}{10})^2-0.09=0[/tex]
-add 0.09} to both sides:
[tex](x-\frac{7}{10})^2=0.09[/tex]
- Apply square root to both sides and solve for x:
[tex]\sqrt{(x-\frac{7}{10})^2}=\sqrt{\0.09}\\x-\frac{7}{10}=\sqrt{0.09}\\\\x_1=\frac{7}{10}+\sqrt{0.09}=1\\\\x_2=-\frac{7}{10}-\sqrt{0.09}=\frac{2}{5}[/tex]
The cost of renting a private room at a restaurant is $400. There is also a charge of $25 for each person who attends. The total cost for Christian’s party at the restaurant was $775. Write an algebraic equation to represent the situation, than solve how many people people attended Christian’s party.
room=400
Ppl=25p
Total cost=775
775=25p+400 ⟨—— equation
775-400=25p
375/25=p
15=p
15 people attended his party
A rectangle with sides of lengths 5/6 inch and 1/3 inch area
Answer:
The area of the rectangle is [tex](5/18)\ in^{2}[/tex]
Step-by-step explanation:
we know that
The area of rectangle is equal to
[tex]A=LW[/tex]
where
L is the length of rectangle
W is the width of rectangle
substitute the values
[tex]A=(5/6)(1/3)=(5/18)\ in^{2}[/tex]
D O,K = (0, 2) → (0, 6) The scale factor is _____.
0
1/3
3
please help soon!!!
Answer: the answer will be 3
Step-by-step explanation:
The scale factor is 3 because the point (0, 2) becomes (0, 6) option third is correct.
What is a scale factor?The ratio among comparable dimensions of an object and a model with that object is known as an exponent in algebra. The replica will be larger if the scale factor is a whole number. The duplicate will be lowered if the step size is a fraction.
We have:
D O,K = (0, 2) → (0, 6)
The point (0, 2) becomes (0, 6)
The scale factor = 6/2 = 3
Thus, the scale factor is 3 because the point (0, 2) becomes (0, 6) option third is correct.
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What 2 numbers multiply to 30 and add to -11
Answer:
It isnt possible
Step-by-step explanation:
-5 and -6 cause when you multiply them both u get positive 30 and when you add them you get negative 11
You and three friends are comparing the amount of money you have in your bank accounts. You have a balance of -$50, and your friends have balances of $20,
-$10, and $5. Which balance is the least?
Answer:
The least balance is your own because -50$ is the farthest from 0 on the number line
Step-by-step explanation:
What is the 50th term of the arithmetic sequence 32,27,22,17,12
Answer:
- 213
Step-by-step explanation:
The n th term of an arithmetic sequence is
[tex]a_{n}[/tex] = a + (n - 1)d
where a is the first term and d the common difference
d = 27 - 32 = - 5 and a = 32, hence
[tex]a_{50}[/tex] = 32 + (49 × - 5) = 32 - 245 = - 213
The 50th term of the arithmetic sequence is -213.and this can be determined by using the [tex]\rm T^{th}[/tex] term of the arithmetic sequence formula.
Given :
Arithmetic sequence --- 32,27,22,17,12
The difference of the arithmetic operation is given by the formula:
[tex]a_2-a_1 = 27 - 32 = - 5[/tex]
The [tex]\rm T^{th}[/tex] term of the arithmetic sequence is given by the formula:
[tex]\rm T_n = a + (n-1)d[/tex]
where a is the first term, n is the total number of terms, d is the difference, and [tex]\rm T^{th}[/tex] is the term of the arithmetic sequence.
[tex]\rm T_{50} = 32 - (50-1)5[/tex]
[tex]\rm T_{50} = 32 - (49)\times 5[/tex]
[tex]\rm T_{50} = -213[/tex]
The 50th term of the arithmetic sequence is -213.
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Rolando has $120,000 in a CD at Big Bucks Bank, which just failed. If the FDIC insurance limit per depositor, per bank, is $250,000, how much will Rolando get back?
Answer:
120,000
Step-by-step explanation:
Rolando would get back 120,000. Because the insurance limit is 250k, Rolando only put in 120k, so he should get everything back.
in a probability experiment Eric flip a coin 36 times. The coin landed on head 24 times. What is the ratio of heads to tails in this experiment?
A.3/2
B.1/2
C.2/3
D.2/1
Answer:
2/3 is the correct answer so C. Hope this helps you. :)
Step-by-step explanation:
In this experiment, the ratio of heads to tails comes out to be 2/1.
Probability What is Probability?Probability is a way to gauge how likely something is to happen. Even while no event can be foreseen with absolute certainty, probability can be used to convey how likely it is that it will happen.
Formula of Probability:Probability is the ratio of the number of favourable outcomes to the total number of outcomes of an event.
The number of favourable outcomes for an experiment with 'x' and the total outcomes is represented by the symbol 's'. The following formula can be used to determine how likely an event is to occur.
Probability = Favourable Outcomes/Total Outcomes = x/s
Calculate the ratio:The total number of the outcomes are 36.
The total outcome for head is 24 times.
So, the total outcome for tail will be 36 - 24 = 12
The ratio of head to tail is = favourable outcome for heads/ favourable outcomes for tails.
Thus,
heads/ tails = 24/12
heads/tails = 2/1
Therefore, the ratio of heads to tails in the experiment is 2/1.
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