In △ABC, m∠A=45°. The altitude divides side AB into two parts of 20 and 21 units. Find BC.
Answers
Answer:
29 units
Step-by-step explanation:
BC is a side of ACB, which is a 45 45 90 triangle. BC = AB/sqrt2
If In △ABC, m∠A=45°. The altitude divides side AB into two parts of 20 and 21 units. Then BC is 29 units
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Given,
In △ABC, m∠A=45°. The altitude divides side AB into two parts of 20 and 21 units.
We need to find BC
In triangle ACD,
tan 45° = CD/AD
CD = tan 45° x AD
= 1 x 20= 20 units
In triangle CDB,
tanФ = CD/BD
Ф = tan⁻¹(CD/BD)
= tan⁻¹(20/21)
= 43.6°
so, sin 43.6° = CD/BC
BC = CD/sin 43.6°
= 20/0.689
= 29 units
Hence the length of BC will be 29 units.
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Related Questions
11) Describe the number and type of roots for 2x2 + 19x - 33 = 0.[A] 2 real solutions [B] 2 complex solutions [C] 1 real solution[D] 1 complex solution
Answers
Explanation:
The first thing we will do is to solve for x in the equation:
Using factorization method:
The factors are +22 and -3. This because the addition of this number will give you the coefficient of x (19) while the multiplication will give -66
Susanna has played the piano for s years. Patrick has played the piano for 4 more than twice the number of years that susanna has been playing the piano. which expression correctly shows the number of years that Patrick has been playing the piano.2s + 44s + 22 (s + 4)(s - 4) ÷ 3none of the above
Answers
Given data:
The expression for Patrick paly Piano is,
[tex]P=2s+4[/tex]Thus, the first option is correct.
a polynomial function has four turning points and two zeros. it’s degree could be ___? select all that apply 4567
Answers
SOLUTION
A polynomial function with real coefficients has four turning points and two zeros could be a degree 6 or any higher even degree because a polynomial with degree n has at most (n - 1) turning points.
So, it cannot be a degree 4.
It cannot be a degree 5 because it has two real zeros, and then three complex roots. A polynomial function with real coefficients cannot have an odd number of complex roots.
Answer:
6
Step-by-step explanation:
edge 23
How can I know how many students scored 5 in their test?
Answers
Based on the given table, consider that the value in the column frequency specifies the number of times that a certain score (first column) is repeated in a given data.
In this case, the value of the frequency for a specific score determines the number of students with such a score in their tests.
As you can notice, for the value of the frequency equal to 3, the corresponding value of the score is 5. It means that 3 student get 5 scores in their tests.
The day's high temperature in Detroit, Michigan was recorded as 50°F. Use the formula C=59(F−32) to write 50°F as degrees Celsius.
Answers
Given:
The day's high temperature in Detroit, Michigan was recorded as 50°F.
[tex]C=\frac{5}{9}(F-32)[/tex]Required:
To convert the 50°F as degrees Celsius.
Explanation:
Consider
[tex]C=\frac{5}{9}(F-32)[/tex]For F=50,
[tex]\begin{gathered} C=\frac{5}{9}(50-32) \\ \\ =\frac{5}{9}(18) \\ \\ =5\times2 \\ \\ =10\degree C \end{gathered}[/tex]Final Answer:
[tex]C=10\degree C[/tex]Approximately how old would you be in the years if you lived 1,000,000 hours? round your answer to the nearest whole number.
Answers
First let's see how many hours are in a year:
[tex]\begin{gathered} 1\text{ year }\rightarrow\text{ 365 days} \\ 1\text{ day }\rightarrow\text{ 24 hours} \\ \Rightarrow1\text{ year }\rightarrow365\cdot24=8760\text{ hours} \end{gathered}[/tex]We found that 1 year has 8769 hours, then if we lived 1,000,000 hours, we have to divide it by 8760 to know the number of years lived:
[tex]\frac{1000000}{8760}=114.15[/tex]therefore, you would have lived 114.15 years
(X-3) times (4x+2) yawing distributive property
Answers
For two binomials, the distributive property is:
[tex](a+b)\cdot(c+d)=a\cdot c+a\cdot d+b\cdot c+b\cdot d[/tex]So, let's solve this problem.
Step 01: Multiply the first term of the binomial (x - 3) by both terms of the binominal (4x + 2).
[tex](x-3)\cdot(4x+2)=x\cdot4x+x\cdot2+\cdots_{}[/tex]Step 02: Multiply the second term of the binomial (x - 3) by both terms of the binominal (4x + 2).
[tex](x-3)\cdot(4x+2)=x\cdot4x+x\cdot2+(-3)\cdot4x+(-3)\cdot2[/tex]Step 03: Multiply the terms.
[tex]=4x^2+2x-12x-6[/tex]Step 04: Add like terms.
[tex]=4x^2-10x-6[/tex]Answer:
[tex]4x^2-10x-6[/tex]Find a polynomial function P(x)with the given zeros.4, 3, 8
Answers
Given the word problem, we can deduce the following information:
The zeroes are: 4, 3, 8
To determine the polynomial function P(x) with the given zeroes, we follow the process as shown below:
[tex]\begin{gathered} (x-4)(x-3)(x-8)=0 \\ \\ \end{gathered}[/tex]We first expand (x-4)(x-3):
[tex](x-4)(x-3)=x^2-7x+12[/tex]Next, we expand (x^2-7x+12)(x-8):
[tex]\begin{gathered} (x^2-7x+12)(x-8)=x^2(x)+x^2(-8)-7x(x)-7x(-8)+12(x)+12(-8) \\ Simplify \\ =x^3-15x^2+68x-96 \end{gathered}[/tex]Hence,
[tex]x^3-15x^2+68x-96=0[/tex]Therefore, the polynomial function is:
[tex]P(x)=x^3-15x^2+68x-96[/tex]Solve the equation for y in terms of x. After that, replace y & solve with function notation f(x). Once you solve that, find f(4).y+3x^2=4f(x)=____f(4)=____
Answers
Given:
[tex]y+3x^2=4[/tex]We have that y f(x), so solve for f(x):
[tex]\begin{gathered} y+3x^2-3x^2=4-3x^2 \\ y=4-3x^2 \\ f(x)=4-3x^2 \end{gathered}[/tex]And for f(4):
[tex]f(4)=4-3(4)^2=4-3(16)=4-48=-44[/tex]Answer:
[tex]\begin{gathered} f(x)=4-3x^{2} \\ f(4)=-44 \end{gathered}[/tex]Erin is buying produce at a store. She buys c cucumbers at $0.89 each and a apples at $0.99 each. What does the expression 0.89c + 0.99a represent? The expression represents the
Answers
One cucumber costs $0.89, so with Erin buys "c" cucumbers, the price he will pay for the cucumbers is the unitary price (0.89) times the number of cucumbers ("c"), so the price is 0.89c.
One apple costs $0.99, so with Erin buys "a" apples, the price he will pay for the apples is the unitary price (0.99) times the number of apples ("a"), so the price is 0.99a.
Then, to find the final price Erin will pay, we just need to sum both prices: all the cucumbers and all the apples:
Final price = 0.89c + 0.99a
So the expression represents the final price (or cost) Erin will pay for all products.
A scientist needs 270 milliliters of a 20% acid solution for an experiment. The lab has available a 25% and a 10% solution. How many milliliters of the 25% solution and how many milliliters of the 10% solution should the scientist mix to make the 20% solution?
Answers
Given:
A scientist has 5% and a 10% acid solution in his lab.
He needs 270 milliliters of a 20% acid solution.
To find the amount of 25% solution and how many milliliters of the 10% solution should the scientist mix to make the 20% solution:
Here,
The dearer percentage is 25%.
The cheaper percentage is 10%.
The mean percentage is 20%.
Using the mixture and allegation method,
The ratio of the litters of cheaper (10% solution) to dearer value (25% solution) is,
[tex]\begin{gathered} (\text{Dearer value-mean): (Mean-Ch}eaper\text{ value)} \\ (25-20)\colon(20-10) \\ 5\colon10 \\ 1\colon2 \end{gathered}[/tex]So, the number of liters to be taken from 10% solution is,
[tex]\frac{1}{3}\times270=90\text{ liters}[/tex]So, the number of liters to be taken from 25% solution is,
[tex]\frac{2}{3}\times270=180\text{ liters}[/tex]Hence, the answer is
Solve the quadratic equation using any algebraic method.
X²-11x+30=0
Answers
Answer:
5, 6
Step-by-step explanation:
using Vieta's formulas:
x₁ + x₂ = 11
x₁*x₂ = 30
x₁ = 5
x₂ = 6
Which of the following are a qualitative catecorical variables
Answers
A qualitative variable, also called a categorical variable, is a variable that isn’t numerical. It describes data that fits into categories.
From the given options below, the arrival status of a train ( early, on time, late, canceled) and a person's blood type are the only qualitative variables.
Hence, Option 3 and Option 5 are the correct answers.
NEED HELP ASAP
What is the value of X? Justify each step
Answers
The value of x = 3 ,where ,
AC = 32 , AB = 2x , BC = 6x + 8 .
Solution:Here given,
AB = 2x
BC = 6x + 8
AC = 32
AC = (AB + BC) (Rule of addition).
So ,
2x + 6x + 8 = 32 (by applying substitution rule) .
In the equation AB + BC = AC, substitute for AB, BC, and AC.
Simplifying,
8x + 8 = 32
2x + 6x + 8 = 32 (when simplified by incorporating similar terms).
8x = 24
8x = 32 - 8
8x = 24
On dividing both sides by 8
8x / 8 = 24/8
x = 3
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find the value or measure. Assume all lines that appear to be tangent are tangent. mPM=
Answers
Segments that crosses around a circle
MN ^2 = OP • ON
mm
then 59° = (
In physics, the Ideal Gas Law describes the relationship among the pressure, volume, and temperature of a gas sample. This law is represented by the formula PV = nRT, where P is the pressure, V is the volume, T is the temperature, n is the amount of gas, and R is a physical constant. Select all the equations that are equivalent to the formula PV = nRT.
Answers
The equations that are equivalent to the formula PV = nRT are V = nRT/P, n = PV/RT and R = PVnT. Option B, C and D
How to determine the equationsFrom the information given, we have that;
The Ideal Gas law is represented as;
PV = nRT
Given that;
P is the pressure V is the volumeT is the temperaturen is the amount of gasR is a physical constantSubject of formula is described as the variable expressed in terms of other variables in an equation.
It is made to stand on its own on one end of the equality sign.
Let's make 'V' the subject of formula
Divide both sides by the coefficient of V which is the variable 'P', we have;
V = nRT/P
Making 'R' the subject of formula, we have
R = PV/ nT
Making 'n' the subject of formula, we have;
n = PV/RT
Hence, the equations are options B, C and D
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The complete question:
In physics, the Ideal Gas Law describes the relationship among the pressure, volume, and temperature of a gas sample. This law is represented by the formula PV = nRT, where P is the pressure, V is the volume, T is the temperature, n is the amount of gas, and R is a physical constant. Which of the equations below are equivalent to the formula PV = nRT? Select all that apply. A. P = VnRT B. V = nRT/P C. n = PV/RT D. R = PVnT E. T = nR/PV
Answer:Pv=NRT
Step-by-step explanation:
Find the distance between the two points. Write your answer as a decimal rounded to the hundredths place if needed.
Answers
We need to find the distance between the two points given. Use the distance formula:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Replace using P1(3,-9) and P2(-2,4):
[tex]d=\sqrt[]{((-2)_{}-3_{})^2+(4_{}-(-9)_{})^2}[/tex][tex]d=\sqrt[]{(-5)^2+(13)^2}[/tex][tex]d=13.9283[/tex]Rounded to the hundredths:
[tex]d=13.93[/tex]For which equation would x = 12 not be a solution?96 ÷ x = 89 x - 7 = 101x + 4 = 105 + 4 x = 53
Answers
Notice that:
1)
[tex]\frac{96}{12}=8.[/tex]Therefore x=12 is a solution to
[tex]96\div x=8.[/tex]2)
[tex]9*12-7=108-7=101.[/tex]Therefore x=12 is a solution to:
[tex]9x-7=101.[/tex]3)
[tex]12+4=16\ne10.[/tex]Therefore x=12 is not a solution to:
[tex]x+4=10.[/tex]4)
[tex]5+4*12=5+48=53.[/tex]Therefore x=12 is a solution to:
[tex]5+4x=53.[/tex]Answer: Third option:
[tex]x+4=10.[/tex]Algebra Find the value(s) of the variables in each kite.
Answers
56º,34º
1) A kite is a quadrilateral that according to the following theorem:
2) And examining that picture, we can tell that the angle labeled as 8x is congruent to its opposite counterpart.
3) In addition to this, but not less important that bigger diagonal bisects that the other pair of opposite angles. So we can sketch the following
So we can pick one triangle and write out the following according to the Triangle sum theorem:
[tex]\begin{gathered} 8x+(5x-1)+90=180 \\ 8x+5x-1+90=180 \\ 13x+89=180 \\ 13x=180-89 \\ \frac{13x}{13}=\frac{91}{13} \\ x=7 \end{gathered}[/tex]4) Finally, let's plug into each one the quantity of x and get the measure of those angles:
Use the data below to complete the following calculationm=76,37,27
Answers
Answer:
Σmf = 23347
Σm²f = 1621631
(Σmf)² = 545082409
Explanation:
The symbol Σ means that we need to sum all the products of m and f.
So, Σmf is equal to:
Σmf =76(94) + 37(92) + 27(63) + 98(62) + 62(81)
Σmf = 7144 + 3404 + 1701 + 6076 + 5022
Σmf = 23347
Then, to find Σm²f, we need to find the square of m, so:
Σm²f = (76)²(94) + (37)²(92) + (27)²(63) + (98)²(62) + (62)²(81)
Σm²f = 5776(94) + 1360(92) + 729(63) + 9604(62) + 3844(81)
Σm²f = 542944 + 125948 + 45927 + 595448 + 311364
Σm²f = 1621631
Finally, (Σmf)² is equal to:
(Σmf)² = (23347)²
(Σmf)² = 545082409
Therefore, the answers are:
Σmf = 23347
Σm²f = 1621631
(Σmf)² = 545082409
Apply the product rule to rewrite the product below using a single base and exponent then simplify: 3^2 *3^3 our base is Answerour exponent is Answerthis simplifies to Answer
Answers
Explanation:
[tex]3^2\text{ }\times3^3[/tex][tex]\begin{gathered} \text{The expression has same base.} \\ \text{Base = 3} \\ We\text{ take one base and bring the exponents together} \\ \text{The sign betw}en\text{ them changes from multiplication to addition} \end{gathered}[/tex][tex]\begin{gathered} 3^2\text{ }\times3^3\text{ = }3^{2\text{ + 3}} \\ \text{Exponent = 2 + 3} \\ \text{Exponent = 5} \end{gathered}[/tex][tex]\begin{gathered} \text{Simplifying:} \\ 3^{2+3}=3^5 \\ 3^5\text{ = 243} \end{gathered}[/tex]The employees in a firm earn $8.50 an
hour for the first 40 hours per week, and
1.5 times the hourly rate for any hours
worked over 40. How much does an
employee who works 52 hours in one
week eam?
Answers
Using mathematical operations, we know that the salary of a person working for 52 hours a week will be $493.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands. The rules that specify the order in which we should solve an expression involving multiple operations are known as the order of operations. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, and Addition Subtraction (from left to right).So, the amount earned by a person who works 52 hours a week:
Salary if a person works for 40 hours: $8.50 per hourSalary if a person works for more than 40 hours: 1.5 times $8.50 per hour that is, 8.50 × 1.5 = $12.75 per hour.So, if a worker works for 52 hours, his salary will be:
52 - 40 = 12 Hours40 × 8.50 = $34012 × 12.75 = $153Sum: $493Therefore, using mathematical operations, we know that the salary of a person working for 52 hours a week will be $493.
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solve for rv=r+at, for r
Answers
Since we need to solve for r we have to leave that variable alone in one side of the equation. We notice that at is adding in the right side, then it goes to the left side substracting, that is:
[tex]v-at=r[/tex]Therefore:
[tex]r=v-at[/tex]in the last part we only switch the sides of the equation.
Express your answer as a polynomial in standard form.f(x) = x^2 + 6x +7g(x) = x + 2Find: g(f(x)
Answers
1) Firstly, let's find the composite function g(f(x)) plugging into the x variable in g(x) the function f(x):
[tex]\begin{gathered} g(f(x))=(x^2+6x+7)+2 \\ g(f(x))=x^{2}+6x+9 \end{gathered}[/tex]2) To write that as the standard form, let's replace g(f(x)) with "y" and write the polynomial orderly to the greatest coefficient to the least one.
[tex]y=x^2+6x+9[/tex]help meeeeeeeeee pleaseeeeeeeeeee!!!
thank youu
Answers
The required domain and the range of the given function is (0, ∞) and (-8, -2) respectively.
Given that,
A graph of the function is shown we have to determine the domain and range of the function with the help of the graph.
The domain is defined as the values of the independent variable for which there is a certain value of the dependent variable exists in the range of the function.
Here,
As of the graph,
The graph describes as only the positive real number because the graph only consists of the positive x-axis, so the domain of the function is all positive real numbers. While the ordinate of the graph is describe for -8 to -2 on the negative y-axis thus the rang of the given function lies between -8 to -2.
Thus, the required domain and the range of the given function is (0, ∞) and (-8, -2) respectively.
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Xandro's Lighting Company purchased a dozen light bulbs for 900 pesos each. This purchased was subject to a trade discount of 25%. What was the total net price?
Answers
Total price of one dozen light bulbs will be equal to
[tex]12\times900=10800[/tex]Total trade discount is equal to (list price x trade discount rate)
[tex]\text{Discount }=10800\times0.25=2700[/tex]So, the net price will be (List price - discount)
[tex]\text{Net price = 10800-2700=}8100[/tex]Therefore, the total net price is 8100 pesos.
1. What would you do with each problem in order to get it in its simplest properform? Use words to explain the specific details to why you used thatprocess/rule.Number 2 a and b
Answers
Given
[tex]-6y^0\text{ and \lparen-6y\rparen}^0[/tex]The solutions can be seen below.
Explanation
[tex]\begin{gathered} a)\text{ }-6y^0=-6\times y^0=-6\times1=-6 \\ b)\text{ }(-6y)^0=1 \end{gathered}[/tex]In "a," only the y-value is raised to the power of 1 hence, the reason why y^0 became 1 which then multiplies -6 to get -6. However, in "b", the entire expression is raised to the power of zero, which will then give 1 as the answer.
A paving company has 24 employees, 15 with gross earnings of $365 per week and 9 with gross earnings of $385 per week. What is the total social security and medicade for the first quarter of the year
Answers
The total social security and medicade for the first quarter of the year is $17,781.66.
How to calculate the tax?The computation will be:
Gross earning per week = 15 * 365 + 9 * 385
= $8,940 per week
Here, the number of weeks is 13 in each quarter:
Gross earning =$8,940 * 13
= $116,220
Social security tax = $116,220 * 6.2%
= $7,205.64
Medicare tax = $116,220 * 1.45%
= $1,685.19
Total = $7,205.64 + $1,685.19
= $8,890.83
Now, to involve the employer's share it is required to multiply the total tax by 2
Therefore,
Total tax remitted to IRS = $8,890.83 * 2
= $17,781.66
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3
y + yz + z + y use y = -2, and z = 6
Answers
Step by step
3y + yz + z + y
Use y= -2 and z = 6
Substitute values for y and z
3(-2) + (-2*6) + 6 + (-2)
Multiply first per PEMDAS rule
-6 + (-12) + 6 + (-2)
Add and subtract
= -14
Sofia ordered sushi for a company meeting. They change plans and increase how many people will be at the meeting, so they need at least 100 pieces of sushi in total. Sofia had already ordered and paid for 24 pieces of sushi, so she needs to order additional sushi. The sushi comes in rolls, and each roll contains 12 pieces and costs $8. Let R represent the number of additional rolls that Sofia orders.Which inequality described this scenario?What is the least amount of additional money sofia can spend to get the sushi they need?
Answers
Answer:
the least amount Sofia can spend is $608
