A triangle is a 2-dimensional shape that has 3sides and 3 interior angles. The height of the isosceles triangle is approximately 49.5cm
Pythagoras theoremThe theorem states that the square of the hypotenuse is equal to the sum of the square of other two sides.
From the given question, the hypotenuse is 50cm and the base of the triangle is 14cm
Determine the height using the expression
h² = 50² - (14/2)²
h² = 2500 - 7²
h² = 2500 - 49
h = √2451
h = 49.5cm
Hence the height of the triangle is approximately 49.5cm
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martin can read 4 pages in 7 minutes. at this rate,how long will it take him to read 9 pages
Answer:
5.14 minutes
Step-by-step explanation:
4 pages / 7 minutes = 0.57 minutes per page
0.57 minutes/pg * 9 pages = 5.14 minutes
(5x − 32)°
(3x - 4)º
Help meee
Answer:
x = 27
Step-by-step explanation:
(5x - 32) + (3x - 4) = 180
8x - 36 = 180
x = 216
x = 27
m<NQR = 5x - 32 = 5*27 - 32 = 103
m<QRP = 3x - 4 = 3*27 - 4 = 77
A board is 72 cm in length and must be cut so that one piece is 12 cm longer than the other piece . find the leg of each piece
One of the boards is 30 inches long and the other board is 12 inches longer so it has to be 42 inches long. The sum of the lengths of the two boards is 72 cm and one of the boards is 12 inches longer than the other.
Here,
A board is 72 cm in length and must be cut so that one piece is 12 cm longer than the other piece .
We have to find the leg of each piece.
What is Length, Width and height?
The length, width and height of an object are the different dimensions in linear units. length is the longest side of a shape, width is the shorter side, and height is the vertical dimension of the shape.
Now,
If you're going to cut the 72 inch board into two pieces, you can call one of the pieces x units long.
And, since the other piece is 12 inches longer than your first piece, its length is x + 12.
And, when you place these two pieces back together, their lengths should add up to be 72 inches.
You can write this last statement about adding the two pieces together to get a 72 inch piece
In equation form as:
x + (x+12) = 72
2x + 12 = 72
To solve this begin by subtracting 12 from both sides;
2x = 60
Now just divide both sides by 2 to find that:
x = 30
So, one of the boards is 30 inches long and the other board is 12 inches longer so it has to be 42 inches long. The sum of the lengths of the two boards is 72 cm and one of the boards is 12 inches longer than the other.
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Find each product.
29. (r-1)(7r+2)
31. x²(3x-2)(5x+1)
37. (m-n+k)(m+2n-3k)
43. (2m+3)(2m-3)
45. (4x²-5y)(4x²+5y)
Answer:
29. 7r^2-5r-2
31. 15x^4-7x^3-2x^2
37. -3k^2-2km+5kn+m^2+mn-2n^2
43. 4m^2-9
5. 16x^4 - 25y^2
Step-by-step explanation:
To solve these you expand the polynomial and use the FOIL method.
Find the value of y is x = -3
y = 4x² + 2x - 9
Find the derivative of the function using the definition of derivative. f(x) = kx d
Derivatives are essential for solving calculus and differential equation problems then the derivative of this function is [tex]$f^{\prime}(x)=k$[/tex]
What is meant by derivatives?The rate of change of a function with respect to a variable in Mathematics. Derivatives are essential for solving calculus and differential equation problems.
Given a traditional unbent position, f(x) = kx + d, where k is the pitch and (0, d) is the y-intercept.
a) Consider our position at two distinct points first:
f(x) = kx + d
f(x + h) = k(x + h) + d = kx + kh + d
Evaluate the derivative, then
[tex]$\lim h \rightarrow x \frac{f(x+h)-f(x)}{h}[/tex]
substitute the values in the above equation, we get
[tex]$&=\lim h \rightarrow x \frac{(k x+k h+d)-(k x+d)}{h} \\[/tex]
simplifying the above equation, we get
[tex]$&=\lim h \rightarrow x \frac{k h}{h} \\[/tex]
[tex]&=\lim h \rightarrow x k \\[/tex]
= k
Therefore, the derivative of this function is [tex]$f^{\prime}(x)=k$[/tex]
b. Since the actual function is linear, its part is all real numbers by definition.
c. Since the product is a constant function, its part is all real digits by meaning.
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I GIVE BRAINLIEST FOR ALL QUESTIONS
The lengths of the sides of a triangle are 3, 4, 5. Can the triangle be a right triangle?
yes
no
Answer: No.
Step-by-step explanation: The sides are all different. Therefore, it cannot be a right angle.
(i think)
Answer:
Yes.
Step-by-step explanation:
By converse of Pythagoras' Theorem,
[tex]5 {}^{2} = 4 {}^{2} + 3 {}^{2} [/tex]
25 = 16 + 9
Therefore, the triangle is a right-angled triangle.
Hope this helped! ^^
Find the equation of the linear function represented by the table below in slope-
intercept form.
Answer: y =
X
y
0
-8
1
2
3 4
28
1 10 19
Submit Answer
Answer:
xxx 20
Step-by-step explanation:
please answer the question in the photo
Answer:no
Step-by-step explanation:
sides ab and de are equivalent and sides fd and ca are equivalent but when it comes to sides bc and ef they are not with the scale factor as 2
A quadratic function is shown on the graph.
an upward opening parabola beginning with closed circle at negative 2 comma 4, which decreases to a vertex at 0 comma 0 and then increases to an open circle at 3 comma 9
What is the range of the function?
{x | −2 ≤ x < 3}
{x | −2 < x ≤ 3}
{y | 0 ≤ y < 9}
{y | 0 < y ≤ 9}
Answer:
{y | 0 ≤ y < 9}
Step-by-step explanation:
The range is all the y-values; all the y's on the graph, or if you had an equation, all the y's that could be produced by that equation.
Right away, you know if the question is RANGE, the sets showing x are NOT the answer.
On the graph shown the lowest point is at (0,0) and it IS actually on the graph, so we use a >= symbol that has the "or equal to" bar under the > symbol.
The biggest y-value on the graph is the 9, but it's an open point, so exactly9 is technically NOT on the graph. So we use a < symbol without the bar underneath.
He bought a pair of boots that cost 10 and spent the rest on hats that cost 8 each
Answer:
Oh! WoW
Very nice questions .
Step-by-step explanation:
Please provide full question
Express 15 km as a percentage of 120 km
The expression of 15km as a percentage of 120km as required in the task content is; 12.5%
What percentage representation is 15km of 120km as required in the task content?Since it follows from convention that a percentage is a representation of an entity as a fraction of a hundred partitions.
On this note, the percentage representation is such that;
15km of 120km is;
(15/120) × 100%
0.125 × 100%
= 12.5%.
Ultimately, 15km is 12.5% of 120km.
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The total cost of tuition at johnson community college is $180 per credit hour. each student also has to pay $100 in fees. write an equation that represents the tuition cost, c, for x credit hours taken.
The equation is 180x+ 100
What is equation?An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra. Algebra is used when you do not know the exact number in a calculation.
Given:
cost of tuition = $180
each student pay = $100
let the number times of credit be x hours.
Son the equation is 180x+ 100
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Sheila put $350 in a savings account for 1 year. The annual interest rate was 3% per year.
a) How much simple interest did the money earn her in 1 year?
b) How much money was in the account after 1 year?
Please answer fast and show how u got the answer step by step thank u
The simple interest was $10.5 and the amount after 1 year would be $360.5 in her account.
What is the simple interest?Simple interest is defined as interest paid on the original principal and calculated with the following formula:
S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r% and is to be written as r/100
We have been given data as
Principal amount (P) = $350
Time (T) = 1 year
The rate of interest (R) = 3%
Simple interest= P × R × T
Simple interest = 350 × 3/100 × 1
Simple interest = $10.5
So the amount after 1 year would be P + S.I. = 350 + 10.5 = $360.5
Therefore, the simple interest would be $10.5 and the amount after 1 year would be $360.5.
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Can an inverse and
contrapositive both have false truth values?
Answer:
thyjdbbdhehwjwnwjehe
A 7 cm string that is fastened at both sides is plucked. what is the wavelength of the n = 4 standing wave?
The wavelength of the n = 4 standing wave is 3.5cm.
Standing Waves:
A standing wave is a stationary wave, which means that the wave oscillates in time but the peak amplitude does not move in space. This can happen in a stationary medium from an interference due to two waves traveling in opposite directions. For a harmonic wave, the string's displacement in the y-direction from the x-position and time t can be calculated by using the expression
y(x ,t)=2Asin(2πxλ)cos(ωt)
where A is the maximum displacement in the y-direction, λ
is the wavelength, and ω is the angular frequency. Given a taut string of length L, and assuming the the driving force is at x=0, the boundary conditions are
y(0,t)=0y(L, t)=2Asin(2πLλ)cos(ωt)=0
Given the latter boundary condition, a standing wave occurs when sin(2πLλ)=0=sin(nπ). The condition for the standing wave is then of the form n=2Lλ.
The condition where the standing wave occurs is given by the expression n=4Lλ, where n is a positive integer value, L is the string length, and λ is the wavelength. We calculate the wavelength of an n=4 standing wave as follows:
λ=4Ln=4(7 cm) / 2
= 14 /2
= 3.5cm.
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The shaded region displayed in the graph does not include the dashed line. Which of the following best represents all the shaded points?
An artist plans to sell $300 of prints online each week. This month, she is within $22 of her goal.
Part A: Define a variable and write an absolute value equation to represent the scenario.
Part B: Solve the equation, showing all steps.
Part C: What are the minimum and maximum amounts that the artist received for her products?
Answer:
A) |x - 1200| = 22
B) x = 1222, x = 1178
C) Minimum = $1,178
Maximum = $1,222
Step-by-step explanation:
Part ADefine the variable:
Let x = revenue from prints sold this month.Given information:
The artist plans to sell $300 of prints each week.This month, she is within $22 of her goal.If the artist plans to sell $300 of prints each week, then she plans to sell approx $1200 of prints each month, since there are approximately 4 weeks in each month.
If she is within $22 of her goal, this month then:
⇒ |x - 1200| = 22
Part BTo solve an equation containing an absolute value, set the contents of the absolute value equal to both the positive and negative value of the number on the other side of the equation, then solve both equations:
Equation 1
⇒ x - 1200 = 22
⇒ x - 1200 + 1200 = 22 + 1200
⇒ x = 1222
Equation 2
⇒ x - 1200 = -22
⇒ x - 1200 + 1200 = -22 + 1200
⇒ x = 1178
Part CTherefore:
Minimum amount the artist received = $1,178Maximum amount the artist received = $1,222What strategy would be the best to solve this problem?
Ann-Marie bought apples. She kept one-third for herself and gave the rest to 4 friends. Each friend got 2 apples. How many apples did Ann-Marie buy?
What strategy would be the best to solve this problem?
A. guess, check and revise
B. work backwards
C. use a formula
D. look for patterns
Answer:
look for patterns also, Ann purchased 12 apples
Step-by-step explanation:
x apples
1/3 of x, (x - x/3) = (3x - x) /3 = 2x/3
Number of people who shared (2x/3) = 4 with each getting 2Total number shared = 4 * 2 = 8Fraction shared = total shared2x/3 = 8Multiply both sides by 3(2x/3) * 3 = 8 * 32x = 24x = 12
The formula for the area of a circle is shown, where d
is the diameter. A=πd2(exponent is the2) over 4
What is the equation for the diameter d
of a circle in terms of the area A? a: d=4πA. b: d=A4π−−√ c: d=2Aπ−−√. d: d=4π−−√A2
Answer:
Step-by-step explanation:
A washer and a dryer cost $995 combined. The washer cost $45 more than the dryer. What is the cost of the dryer?
When a washer and a dryer cost $995 combined. If the washer cost $45 more than the dryer, then the cost of the dryer is $475
The combined cost of a washer and a dryer = $995
Consider the cost of a dryer as x
The washer cost $45 more than the dryer.
The cost of the washer = x+45
Then the equation will be
x+x+45 = 995
2x+45 = 995
2x = 950
x = 950/2
x = 475
The cost of the dryer is $475
Hence, when a washer and a dryer cost $995 combined. If the washer cost $45 more than the dryer, then the cost of the dryer is $475
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what is equivalent 3x−4y=6?
Answer:
y=(3/4)x - (3/2)
Step-by-step explanation:
3x−4y=6
isolate the y variable
-4y=-3x+6
divide by -4
y=(3/4)x - (3/2)
it is equivalent because it is the same equation just in a different form
Police stop every fifth car at a sobriety checkpoint.
Answer:
20%
Step-by-step explanation:
Every fifth car would be 1/5 or 20%
By paying $1500 cash and the balance is equal monthly payments, how many months would it take to pay for a car costing $12,495?
The monthly installments need to be paid is $10995.
To determine the number of months needed to pay off the remaining balance. We need to know the monthly installment.
What is installments?When you get an installment loan, you get the money you borrowed or the item you bought right away.
You pay it off in installments, which are regularly scheduled payments that may include interest. For a set number of months, or years, you generally owe the same amount on every installment. When the loan is fully repaid, the account is permanently closed.Now, as per the question;
Amount paid in cash = $1500
Remaining balance which is to be paid as monthly installments
= $12495 - $1500
=$12495 − $1500
=$10995
Thus, the monthly installments are $10995.
Now, to determine the number of months needed to pay off the remaining balance. The monthly installment is need to be known.
As a result, information on monthly installments is lacking.
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The complete question is-
What necessary piece of information is missing that prevents solving the problem? By paying $1500 cash and the balance in equal monthly payments, how many months would it take to pay for a car costing$12,495?
The ratio of boys to girls in the entire 7th grade is 7 to 8. Given this ratio, which two class compositions are possible?
A. 40 boys; 35 girls
B. 48 boys; 42 girls
C. 56 boys; 64 girls
D. 67 boys; 68 girls
E. 84 boys; 96 girls
Answer: c and e are correct answer.
Step-by-step explanation:
PLEASE HELP ASAPPP !!! WILL GIVE BRAINLIEST AND 5 STAR RATING
Which fractions are equivalent to 0.4? Select all that apply.
Answer:
Step-by-step explanation:
2/5 or 4/10 or 8/20 or 16/40
Simplify the expression. 3 + 2 • 4 Question 1 options: 9 11 20 24
Answer:
11
Step-by-step explanation:
3 + 2 × 4 ( multiplication before addition )
= 3 + 8
= 11
(7.26x10^6)-(1.3x10^4) in scientific notation
Answer: 7.247 x 10^6
Step-by-step explanation:
(7.26x10^6)-(1.3x10^4)
⇒ 7.247 x 10^6
Scientific notation of given expression = 7.247× 10⁶
What is scientific notation?Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.
For example,
650,000,000 can be written in scientific notation as 6.5 ✕ 10⁸.
Given expression
(7.26x10⁶)-(1.3x10⁴)
It can be written as
= (7.26×1000000) - (1.3 × 10000)
= 7260000 - 13000
= 7247000
= 7.247× 10⁶
Hence, 7.247× 10⁶ is the scientific notation of given expression.
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Lola has 4 1 2 cups of rice. she uses 3 4 of the rice to make sushi rolls for dinner. she uses the rest of the rice to make rice pudding for dessert. how much rice does lola use for the rice pudding?
Lola used 15/4 or [tex]3 \frac{3}{4} [/tex] cups of rice for pudding.
Amount of rice Lola has = [tex]4 \frac{1}{2} [/tex] cups
Converting from mixed fraction to improper fraction
Amount of rice Lola has = (2×4 + 1)/2
Amount of rice Lola has = 9/2 cups
Now, to find the amount of rice used for rice pudding, we will simply subtract the rice left with her after being used for sushi rolls.
Amount of rice used for pudding = Amount of rice Lola has - Amount of rice used to make sushi rolls
Amount of rice used for pudding = 9/2 - 3/4
Performing subtraction to find the amount of rice used for pudding
Taking LCM we get 4
Amount of rice used for pudding = (9×2 - 3)/4
Amount of rice used for pudding = (18 - 3)/4
Amount of rice used for pudding = 15/4
In mixed fraction, the amount of rice used for pudding = [tex]3 \frac{3}{4} [/tex]
Hence, Lola used 15/4 or [tex]3 \frac{3}{4} [/tex] cups of rice for pudding.
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