Answer:
Answer x = 8
Step-by-step explanation:
(5x + 4) + (8x - 18)= 90 The two angles must be complementary for this to work. Remove the brackets
5x + 4 + 8x - 18 = 90 Collect like terms
13x - 14 = 90 Add 14 to both sides
13x = 104 Divide by 13
x = 8 Answer
Check
Sin(8*8 - 18) = sin(64 - 18) = sin(46) = 0.7193
Cos(5*8 + 4) = cos(44) = 0.7193
This problem is very interesting. Thanks for posting.
help asap 23 points please help
The local bank charges 2%.
When the balance is $600, the local bank would charge: 600 x 0.02 = $12
This means if the balance is higher the $600, the local bank would charge more than $12.
The answer would be the second choice: The fee at the local bank will be more than the fee at the local credit union only when the account balance is more than $600.
Find b and then solve the equation: d (b−5)x2−(b−2)x+b=0, if one of its roots is 1/2
ANSWER
[tex]b = \frac{1}{3} [/tex]
[tex]x = \frac{1}{2} \: or \: x = - \frac{1}{7} [/tex]
EXPLANATION
The given expression is
[tex](b - 5) {x}^{2} - (b - 2)x + b = 0[/tex]
If
[tex]x = \frac{1}{2} [/tex]
is a root, then it must satisfy the given equation.
[tex](b - 5) {( \frac{1}{2} )}^{2} - (b - 2)( \frac{1}{2} )+ b = 0[/tex]
[tex](b - 5) {( \frac{1}{4} )} - (b - 2)( \frac{1}{2} )+ b = 0[/tex]
Multiply through by 4,
[tex](b - 5)- 2(b - 2)+4 b = 0[/tex]
Expand:
[tex]b - 5- 2b + 4+4 b = 0[/tex]
Group similar terms;
[tex]b - 2b + 4b = 5 - 4[/tex]
[tex]3b = 1[/tex]
[tex]b = \frac{1}{3} [/tex]
Our equation then becomes:
[tex]( \frac{1}{3} - 5) {x}^{2} - ( \frac{1}{3} - 2)x + \frac{1}{3} = 0[/tex]
[tex]( - \frac{14}{3} ) {x}^{2} - ( - \frac{5}{3} )x + \frac{1}{3} = 0[/tex]
[tex] - 14{x}^{2} + 5x + 1= 0[/tex]
Factor:
[tex](2x - 1)(7x + 1) = 0[/tex]
[tex]x = \frac{1}{2} \: or \: x = - \frac{1}{7} [/tex]
A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing a face card or a 4?
Answer:
44%
Why? Because there is only 4 of each and you have so many more chances to pull a different card.
Expand the following log:
[tex]log_{b} (\frac{x^{3} }{y^{2} })[/tex]
SHOW ALL WORK.
Answer:
[tex]\log_b(\frac{x^3}{y^2} )=3\log_b(x)-2\log_b(y)[/tex]
Step-by-step explanation:
The given logarithmic expression is
[tex]\log_b(\frac{x^3}{y^2} )[/tex]
Recall and use the quotient rule of logarithms;
[tex]\log_b(MN)=\log_b(M)-\log_b(N)[/tex];
We apply this property to obtain;
[tex]\log_b(\frac{x^3}{y^2} )=\log_b(x^3)-\log_b(y^2)[/tex]
Recall again that;
[tex]\log_b(M^n)=n\log_b(M)[/tex]
We apply this property also to obtain;
[tex]\log_b(\frac{x^3}{y^2} )=3\log_b(x)-2\log_b(y)[/tex]
What is m∠C ? Anyone willing to help me (:
Answer:
50°Step-by-step explanation:
Use the cosine law:
[tex]AB^2=CB^2+CA^2-(CB)(CA)\cos(\angle C)[/tex]
We have:
[tex]AB=6,\ CB=6.5,\ CA=7.5[/tex]
Substitute:
[tex]6^2=6.5^2+7.5^2-2(6.5)(7.5)\cos(\angle C)[/tex]
[tex]36=42.25+56.25-97.5\cos(\angle C)[/tex]
[tex]36=98.5-97.5\cos(\angle C)[/tex] subtract 98.5 from both sides
[tex]-62.5=-97.5\cos(\angle C)[/tex] divide both sides by (-97.5)
[tex]\cos(\angle C)\approx0.641\to m\angle C\approx50^o[/tex]
For what values of k does the function y = cos(kt) satisfy the differential equation 9y'' = −100y? (enter your answers as a comma-separated list.)
Answer:
-10/3, 10/3
Step-by-step explanation:
(In this answer I will use y' to denote the derivative of y with respect to t. You shouldn't normally do this because y' normally means the derivative of y with respect to x but I'll be a bit messy for this case)
First calculate the derivatives:
[tex]y=\cos(kt) \Rightarrow y'=-k\sin(kt) \Rightarrow y'' = -k^2\cos(kt)[/tex].
Then plug the derivtes y'' and y into the equation:
[tex]-9k^2\cos(kt) = -100\cos(kt)[/tex]
Solve the equation for k:
[tex]100\cos(kt) - 9k^2\cos(kt) = 0 \\\\\Rightarrow \cos(kt)(100-9k^2) = 0[/tex]
So then we have that [tex]y=\cos(kt)[/tex] satisfies the differential equation when [tex]\cos(kt) = 0[/tex] or when [tex]100-9k^2=0[/tex] (or both). The solutions to these equations are:
[tex]\left \{ {{\cos(kt)=0 \Rightarrow k=\frac{n\pi}{2t}} \atop {100-9k^2 = 0 \Rightarrow k= \pm \sqrt{\frac{100}{9}}=\pm \frac{10}{3}}} \right.[/tex]
I understand that looks a bit complicated and I doubt you would have to give your answers in terms of t so if it asks for a separated list of answers I would go for:
k = -10/3, 10/3.
The values are [tex]k = \pm \frac{10}{3}[/tex].
-----------------------------
To find the values of k, we have to replace the derivatives into the equation.The function is:
[tex]y = \cos{kt}[/tex]
The derivatives are:
[tex]y^{\prime}(t) = -k\sin{kt}[/tex]
[tex]y^{\prime\prime}(t) = -k^2\cos{kt}[/tex]
The equation is:
[tex]9y^{\prime\prime} = -100y[/tex]
Replacing:
[tex]-9k^2\cos{kt} = -100\cos{kt}[/tex]
[tex]9k^2 = 100[/tex]
[tex]k^2 = \frac{100}{9}[/tex]
[tex]k = \pm \sqrt{\frac{100}{9}}[/tex]
[tex]k = \pm \frac{10}{3}[/tex]
Those are the values.
A similar problem is given at https://brainly.com/question/24348029
Identify the area of the trapezoid. Help with this please!
Answer:
[tex]\large\boxed{A=112x\ m^2}[/tex]
Step-by-step explanation:
The formula of an area of a trapezoid:
[tex]A=\dfrac{b_1+b_2}{2}\cdot h[/tex]
b₁, b₂ - bases
h - height
We have
b₁ = 17x m , b₂ = 11x m, h = 8 m.
Substitute:
[tex]A=\dfrac{17x+11x}{2}\cdot8=\dfrac{28x}{2}\cdot 8=14x\cdot 8=112x[/tex]
If five different players have to be placed in five different positions on team, how many different ways might his be done
What is the domain of the function
y=In(x+2)
Answer:The domain: x > -2\to x\in(-2;\ \infty)
Step-by-step explanation:
y = ln(x + 2)
D:
x + 2 > 0 |subtract 2 from both sides
x > -2
Answer: The domain: x > -2\to x\in(-2;\ \infty)
Answer:
[tex]\large\boxed{x>-2\to x\in(-2,\ \infty)}[/tex]
Step-by-step explanation:
[tex]\text{The domain of}\ \log_ax:\\\\a>0\ \wedge\ a\neq1\ \vedge\ x>0\\=========================\\\\y=\ln(x+2)\\\\\text{The domain:}\\\\x+2>0\qquad\text{subtract 2 from both sides}\\\\x+2-2>0-2\\\\x>-2\to x\in(-2,\ \infty)[/tex]
The area of a rectangular room is 120 square feet. The width is 10 feet. What is the length?
The length of the rectangular room is 12 ft
To find the length of the rectangular room by using the formula for the area of a rectangle:
Area = Length * Width
Given that Area of a rectangular room = 120 [tex]ft^{2}[/tex]
Width = 10 ft
Length = ?
To calculate the length of the rectangular room,
Length = Area/Width
Length = 120/10
Length = 12 ft
Therefore, the length of the rectangular room is 12 ft
Average speed of automobile = 35 mph.
Time of travel = 2.5 hrs.
Distance traveled = _____.
14
32.5
37.5
87.5
Answer:
87.5
Step-by-step explanation:
35*2.5= 87.5
since you are finding distance you have to multiply speed and time
hope this helps :)
The sum of two numbers is 9 and there difference is 1.What are those two numbers
Final answer:
To find the two numbers where their sum is 9 and their difference is 1, set up two equations x + y = 9 and x - y = 1. Solve these equations simultaneously to get the numbers 5 and 4.
Explanation:
The question asks to find two numbers where their sum is 9 and their difference is 1. The solution involves setting up two equations based on the information given:
Let the first number be x and the second number be y.
The sum of the two numbers is 9, so we have the equation x + y = 9.
The difference between the two numbers is 1, leading to the equation x - y = 1.
We can solve these two equations simultaneously to find the values of x and y. Adding the two equations together leads to 2x = 10, which simplifies to x = 5. Substituting x back into one of the original equations, for example, x + y = 9, we get 5 + y = 9, which simplifies to y = 4.
Therefore, the two numbers are 5 and 4.
In a carnival game, a person wagers $2 on the roll of two dice. if the total of the two dice is 2, 3, 4, 5, or 6 then the person gets $4 (the $2 wager and $2 winnings). if the total of the two dice is 8, 9, 10, 11, or 12 then the person gets nothing (loses $2). if the total of the two dice is 7, the person gets $1.75 back (loses $0.25). what is the expected value of playing the game once?
Answer: a loss of 4 cents
Step-by-step explanation:
The probability of rolling a sum of 2, 3, 4, 5, or 6 is [tex]\dfrac{15}{36}[/tex] which earns $2.00
The probability of rolling a sum of 28, 9, 10, 11, or 12 is [tex]\dfrac{15}{36}[/tex] which loses $2.00
The probability of rolling a sum of 7 is [tex]\dfrac{6}{36}[/tex] which loses $0.25
[tex]\bigg(\dfrac{15}{36}\times \$2.00\bigg)+\bigg(\dfrac{15}{36}\times -\$2.00\bigg)+\bigg(\dfrac{6}{36}\times -\$0.25\bigg)=\boxed{-\$0.04}[/tex]
The expected value of playing the game once is -$0.62, indicating an expected average loss of 62 cents per game.
Explanation:The expected value of playing the game once is -$0.62, rounded to the nearest cent. This means that if you play the game repeatedly over a long string of games, you would expect to lose 62 cents per game, on average. The expected value indicates an expected average loss, so it is not recommended to play this game to win money.
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(6Q) Find the log .
Answer:
c. 4.9713
That's the answer
A rational function is a function whose equation contains a rational expression.A.Trueb.False
The answer is true because false would mean that it’s another crazy definition. But yes it is true
A rational function is a fractional expression in the form f(x) = p(x)/q(x), where q(x) cannot be zero.
Example: f(x) = 3x/(4x - 2).
True is the answer.
Solve the equation. Round to the nearest hundredth. Show work.
[tex]2.8[/tex] · [tex]13^{4x} +4.8 = 19.3[/tex]
Answer:
Final answer is approx x=0.16.
Step-by-step explanation:
Given equation is [tex]2.8\times 13^{4x} +4.8 = 19.3[/tex]
Now we need to solve equation [tex]2.8\times 13^{4x} +4.8 = 19.3[/tex] and round to the nearest hundredth.
[tex]2.8\times 13^{4x} +4.8 = 19.3[/tex]
[tex]2.8\times 13^{4x} = 19.3-4.8 [/tex]
[tex]2.8\times 13^{4x} = 14.5 [/tex]
[tex]13^{4x} = \frac{14.5}{2.8} [/tex]
[tex]13^{4x} = 5.17857142857 [/tex]
[tex]\log(13^{4x}) = \log(5.17857142857) [/tex]
[tex]4x \log(13) = \log(5.17857142857) [/tex]
[tex]4x = \frac{\log(5.17857142857)}{\log\left(13\right)} [/tex]
[tex]4x = 0.641154659628 [/tex]
[tex]x = \frac{0.641154659628}{4} [/tex]
[tex]x = 0.160288664907 [/tex]
Round to the nearest hundredth.
Hence final answer is approx x=0.16.
In the xy- plane, the graph of which of the following equations is a line with a slope of 5?
A. 5x – y =7
B. y – -5x+7
C. y – 7 – 1/2(x–3)
D. y = 7x + 5
E. 5x + 5y =10
Answer: Option A.
Step-by-step explanation:
By definition, the equation of the line in slope-intercept form is:
[tex]y=mx+b[/tex]
Where m is the slope of the line and b is the y-intercept.
Let's solve for y from the equation A, as following:
[tex]5x-y=7\\-y=-5x+7\\(-1)(-y)=(-5x+7)(-1)\\y=5x-7[/tex]
As you can see in the equation:
[tex]m=5\\b=7[/tex]
Therefore, the option A is the answer.
In Mathematics, the slope of a line is represented by 'm' in the equation y=mx+b. By comparing the provided options with this format, we find option A has the equation of a line with a slope of 5.
Explanation:In the subject of
Mathematics
, particularly
Algebra
, the equation of a line in the form y=mx+b represents a straight line on the xy-plane, where 'm' is the slope and 'b' is the y-intercept. With this in mind, we analyze the given options.
5x – y =7: This equation rearranged to y = 5x - 7 has a slope of 5. y – -5x+7: This equation is not well formatted, it is rejected.y – 7 – 1/2(x–3): This equation rearranged to y = 1/2x + 5.5 has a slope of 1/2, not 5. y = 7x + 5 : This equation has a slope of 7, not 5. 5x + 5y =10: This equation rearranged to y = -x + 2 has a slope of -1, not 5.Therefore, option A has a line with a slope of 5.
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Given RQ = 20 inches and PR = 25 inches what is the m∠Q ?
Answer:
73.2°
Step-by-step explanation:
Use Law of Sines to solve:
(Sin 50)/20 = (Sin B)/25
Solve for Sin B
[25(Sin 50)]/20 = Sin B
Use Sin^-1 x to solve (sine inverse)
Sin^-1 ( [25(Sin 50)]/20 ) = B
B = 73.24685774
Answer:
73 degreesStep-by-step explanation:
Use the sine law:
[tex]\dfrac{RQ}{\sin(\angle P)}=\dfrac{PR}{\sin(\angle Q)}[/tex]
We have
[tex]RQ=20\ in\\\\m\angle P=50^o\to\sin50^o\approx0.766\\\\PR=25\ in[/tex]
Substitute:
[tex]\dfrac{20}{0.766}=\dfrac{25}{\sin(\angle Q)}[/tex] cross multiply
[tex]20\sin(\angle Q)=(25)(0.766)[/tex]
[tex]20\sin(\angle Q)=19.15[/tex] divide both sides by 20
[tex]\sin(\angle Q)=0.9575\to m\angle Q\approx73^o[/tex]
The wind was blowing quite strongly when Jenny was baby-sitting. She was outside with the children, and they were throwing their large plastic ball up into the air. The wind blew the ball so that it landed approximately 3 feet east and 4 feet north of where it was thrown into the air.
Answer:
Option d
Step-by-step explanation:
If the ball landed 3 feet east of where it was thrown, then it moved 3 units horizontally along the x-axis.
If you moved 4 units to the north then we can say that 4 units were moved on the y axis
Therefore, the original matrix [tex]\left[\begin{array}{cc}x\\y\end{array}\right][/tex] is transformed in the matrix [tex]\left[\begin{array}{cc}x+3\\y+4\end{array}\right][/tex]
Therefore, the answer is [tex]\left[\begin{array}{cc}x+3\\y+4\end{array}\right][/tex]
Answer:
d
Step-by-step explanation:
fr ong
If $n \cdot 1 \cdot \frac{1}{2} \cdot \frac{1}{3} \cdot \frac{1}{4} \cdot \frac{1}{5} = \frac{1}{2} \cdot \frac{1}{4} \cdot \frac{1}{6} \cdot \frac{1}{8} \cdot \frac{1}{10}$, what is the value of $n$? Express your answer as a common fraction.
[tex]n\cdot1\cdot\dfrac12\cdot\dfrac13\cdot\dfrac14\cdot\dfrac15=\dfrac n{5!}[/tex]
[tex]\dfrac12\cdot\dfrac14\cdot\dfrac16\cdot\dfrac18\cdot\dfrac1{10}=\dfrac{3\cdot5\cdot7\cdot9}{10!}[/tex]
So we have
[tex]\dfrac n{5!}=\dfrac{3\cdot5\cdot7\cdot9}{10!}[/tex]
[tex]n=\dfrac{3\cdot5\cdot7\cdot9}{6\cdot7\cdot8\cdot9\cdot10}[/tex]
[tex]n=\dfrac{3\cdot5}{6\cdot8\cdot10}[/tex]
[tex]n=\dfrac1{2\cdot8\cdot2}[/tex]
[tex]n=\dfrac1{32}[/tex]
Answer:
3
Step-by-step explanation:
trust me , it worked
Please help me out :)
Answer:
(-a, 0).
Step-by-step explanation:
The long diagonal corresponds to the y-axis. S is the same distance from the y-axis as Q.
Which of the following is the third term of the expansion (a + b) n ?
C(n, 2)a^(n-2) - b^2
C(n, 3)a^(n-3) - b
C(n, 2)a^2 - b^(n - 2)
Answer:
The third term of the expansion [tex](a+b)^n[/tex] is [tex]C(n,2)\cdot a^{n-2}\cdot b^{2}[/tex].
Step-by-step explanation:
According to the binomial expansion,
[tex](a+b)^n=C(n,0)a^{n}+C(n,1)a^{n-1}b+...+C(n,n)b^n[/tex]
So, the rth term of this expansion is
[tex]C(n,r-1)a^{n-r+1}b^{(r-1)}[/tex]
We have to find the third term of the expansion [tex](a+b)^n[/tex] is
[tex]C(n,3-1)a^{n-3+1}b^{(3-1)}[/tex]
[tex]C(n,2)\cdot a^{n-2}\cdot b^{2}[/tex]
Therefore the third term of the expansion [tex](a+b)^n[/tex] is [tex]C(n,2)\cdot a^{n-2}\cdot b^{2}[/tex].
Claim amounts for wind damage to insured homes are independent random variables with common density f(x) = ( 3 x4 , x > 1 0 , otherwise where x is amount of claim in thousands. (a) find the probability that a claim is below average? [19/27] (b) suppose 3 claims will be made. what is the expected value of the largest of the three claims? [2.025] (c) suppose 3 claims will be made. what is the expected value of smallest of the three claims?[1.125]
Final answer:
The random variable X represents claim amounts for wind damage to insured homes. The probability that a claim is below average is 19/27. The expected value of the largest claim is 2.025 and the expected value of the smallest claim is 1.125.
Explanation:
a. The random variable X represents the claim amounts for wind damage to insured homes.
b. To find the probability that a claim is below average, we first need to calculate the average claim amount. We can do this by finding the expected value of X, which is given by E(X) = ∫[10,∞]x * f(x) dx, where f(x) is the density function of X. Evaluating this integral, we get E(X) = 19/27. Therefore, the probability that a claim is below average is P(X < E(X)) = P(X < 19/27) = 19/27.
c. The expected value of the largest of the three claims can be calculated by finding the maximum of three independent random variables with density f(x). Since the density is continuous, the probability that the maximum claim amount is less than or equal to x is given by P(X₁ ≤ x, X₂ ≤ x, X₃ ≤ x) = [F(x)]³, where F(x) is the cumulative distribution function of X. To find the expected value, we need to find the maximum amount x such that [F(x)]³ = 1/2. Solving this equation, we get x ≈ 2.025.
d. Similarly, the expected value of the smallest of the three claims can be calculated by finding the minimum of three independent random variables with density f(x). The probability that the minimum claim amount is greater than or equal to x is given by P(X₁ ≥ x, X₂ ≥ x, X₃ ≥ x) = [1 - F(x)]³. To find the expected value, we need to find the minimum amount x such that [1 - F(x)]³ = 1/2. Solving this equation, we get x ≈ 1.125.
Please help!
f(x)= 3x/ x^2-16
a) x= -16
b) x= -4
c) x= 0
d) x= 4
e) x= 16
Answer:
x = 1 and x = 2
x = 4 and x = -4
Step-by-step explanation:
Vertical asymptotes appear where the function does not have a value. This is most commonly when the denominator of a rational function is 0. Find the asymptotes by factoring the denominator and setting it equal to 0. Then solve for x.
First equation
x² - 3x + 2 factors into (x-1)(x-2)
When x-1 = 0, x = 1. When x-2=0, x = 2. The V.A. are at x = 1 and x = 2.
Second equation
x² - 16 factors into (x+4)(x-4)
When x+4= 0, x = -4. When x-4 = 0, then x = 4. The V.A. are at x = -4 and x = 4.
Final answer:
The function f(x) = 3x/(x² - 16) is defined for x = -16, x = 0, and x = 16, but undefined for x = -4 and x = 4, where it has vertical asymptotes.
Explanation:
The question requires evaluating the function f(x) = 3x/ x²-16 for different values of x. When we evaluate this function, we must pay attention to the values at which the function is undefined, which is when the denominator x^2 - 16 equals zero. This occurs when x = -4 or x = 4, as these values make the denominator (x + 4)(x - 4) equal to zero.
For x = -16, the function is defined and f(-16) can be calculated.For x = -4, the function is undefined as the denominator will be zero.For x = 0, the function is defined and f(0) = 0.For x = 4, the function is undefined as well.For x = 16, the function is defined and f(16) can be calculated.Options (b) and (d) correspond to the values at which the function has vertical asymptotes, as the denominator becomes zero and the function value approaches infinity.
What is the inverse of the following statement? If two triangles are congruent, then their corresponding angles are congruent. If two triangles are congruent, then their corresponding angles are congruent. If the corresponding angles of two triangles are congruent, then the triangles are congruent. If two triangles are not congruent, then their corresponding angles are not congruent. If the corresponding angles of two triangles are not congruent, then the triangles are not congruent.
Answer:
The two triangles may be congruent, but additional information is needed about the third angle in each triangle
Answer:
If the corresponding angles of two triangles are not congruent, then the triangles are not congruent.
Step-by-step explanation:
What is the inverse of the following statement? If two triangles are congruent, then their corresponding angles are congruent.
Inverse of a statement means its opposite or negating both the hypothesis and conclusion of a conditional statement.
So, the inverse of the given statement will be :
If the corresponding angles of two triangles are not congruent, then the triangles are not congruent.
A girl makes 12 foul shots for every 8 that she misses.How many shots did she make if she shot 125 foul shots
Answer: There are 208 shots she make if she shot 125 foul shots.
Step-by-step explanation:
Since we have given that
Number of foul shots = 12
Number of shots she misses = 8
Total number of shots = 12+8=20
So, if the number of foul shots = 125
We need to find the number of shots she make.
According to question, we get that
[tex]\dfrac{12}{20}=\dfrac{125}{x}\\\\12x=125\times 20\\\\12x=2500\\\\x=\dfrac{2500}{12}\\\\x=208.33\\\\x\approx 208[/tex]
Hence, there are 208 shots she make if she shot 125 foul shots.
Factor the expression below.
[tex]x^{2} - 10x + 25[/tex]
A. (x - 5)(x - 5)
B. (x + 5)(x + 5)
C. (x - 5)(x + 5)
D. 5(x2 - x + 5)
Answer:
A. (x - 5)(x - 5)
Step-by-step explanation:
We will do this the old fashioned way...just plain old factoring.
This polynomial is of the form
[tex]y=ax^2+bx+c[/tex]
The product of a and c have to add up to equal the "middle" term, -10.
a = 1, b = -10, c = 25
a * c = 1 * 25 = 25
Now we need the factors of 25 to find the combination of factors that will result in a -10. The factors of 25 are: 1, 25 and 5, 5
5 and 5 add up to be 10, but since we need a -10, we will use -5 and -5. The product of -5 * -5 = 25, so we are not messing anything up by using the negative 5.
Putting them in order in standard form we have
[tex]x^2-5x-5x+25[/tex]
Factor by grouping:
[tex](x^2-5x)-(5x+25)[/tex]
There is an x common to both terms in the first set of parenthesis, so we will factor that out; there is a 5 common to both terms in the second set of parenthesis, so we will factor that out:
x(x - 5) - 5(x - 5)
NOW what's common in both terms is the (x - 5) so we factor THAT out, and what's left gets grouped together:
(x - 5)(x - 5)
A flower is 9 3/4 inches tall.In one week,it grew 1 1/8 inches.How tall is the flower at the end of the week?
Answer:
the length of flower at the end of week is 10 7/8 inches.
Step-by-step explanation:
Original height = 9 3/4 inches
=> 39/4 inches
Growth in one week = 1 1/8 inches
=> 9/8 inches
The height by the end of week = Original height + growth
=> 39/4 + 9/8
=> (39*2)/4*2 + 9/8
=> 78/8 + 9/8
=> 87/8 inches
=> 10 7/8 inches
Therefore, the length of flower at the end of week is 10 7/8 inches.
Final answer:
To find the height of the flower at the end of the week, add the initial height of 9 3/4 inches to the growth of 1 1/8 inches, resulting in a new height of 10 7/8 inches.
Explanation:
The question asks how tall the flower will be at the end of the week after growing an additional 1 1/8 inches from its original height of 9 3/4 inches. To find the answer, you simply add these two measurements.
First, convert the mixed numbers to improper fractions to make them easier to add:
9 3/4 inches is the same as (9 × 4 + 3)/4 = 39/4 inches.1 1/8 inches is the same as (1 × 8 + 1)/8 = 9/8 inches.Now, add the two improper fractions together:
(39/4) + (9/8) = (39/4) × (2/2) + (9/8) = (78/8) + (9/8) = 87/8
Convert 87/8 back to a mixed number:
87 divided by 8 is 10 with a remainder of 7, so the mixed number is 10 7/8 inches.
So, the flower will be 10 7/8 inches tall at the end of the week.
What is COS A?
3/4
4/3
3/5
4/5
Answer: third option
Step-by-step explanation:
As you can see in the figure attached, the triangle is a right triangle.
Then, you can calculate cosA as it is shown below:
- You need to remember the following:
[tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex]
- Now, you must substitute values. Based on the figure:
[tex]adjacent=3\\ hyppotenuse=5[/tex]
[tex]\alpha=A[/tex]
Therefore, you obtain that cosA is:
[tex]cosA=\frac{3}{5}[/tex]
Answer:
Cos A = 3/5
Step-by-step explanation:
We are given a right angled triangle, ΔBCD, with all three side lengths known and we are to find the value of Cos A.
We Cos is the ratio of the base of the triangle to its hypotenuse, with respect to the angle (here angle A).
Considering the angle A, our perpendicular is CD, base is BC and hypotenuse BD.
Therefore, Cos A = BC/BD = 3/5
Ben is building a workshop in his backyard with dimensions as shown in the figure. Ben is planning to air-condition the workshop using a window-unit air conditioner. He needs to determine the BTU's (British Thermal Units) required to cool the building. For a new construction with good insulation, there should be 2 BTU per cubic foot. What is the minimum capacity for the window air conditioner that Ben need to purchase.
Answer:
2160 BTU
Step-by-step explanation:
Ben looks at his plan and realizes that his building can be viewed as a triangular prism sitting on a cube.
Calculating the volume of a cube is easy… Length x Width x Height (LWH)… so 12 x 10 x 8 = 120 x 8 = 960 cubic feet for the cube part.
For the prism, it’s almost the same… but divided by 2 : (LWH)/2, so… (12 x 10 x 2) / 2 = (120 x 2) / 2 = 240 / 2 = 120 cubic feet for the prism part.
Total for the building : 960 + 120 = 1080 cubic feet
Since 2 BTU per cubic foot, the power of the unit needs to be at least 1080 x 2 = 2160 BTU.