replace x with a for this exercise
we use this formula to factor
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]where a=5, b=-3 and c=-14
[tex]x=\frac{-(-3)\pm\sqrt[]{(-3)^2-4(5)(-14)}}{2(5)}[/tex][tex]\begin{gathered} x=\frac{3\pm\sqrt[]{9+280}}{10} \\ \\ x=\frac{3\pm\sqrt[]{289}}{10} \\ \\ x=\frac{3\pm17}{10} \end{gathered}[/tex]we have two roots
[tex]\begin{gathered} x=\frac{3+17}{10} \\ x=2 \end{gathered}[/tex]and
[tex]\begin{gathered} x=\frac{3-17}{10} \\ \\ x=-\frac{7}{5} \end{gathered}[/tex]so the simplified equation is
[tex](x-2)(x+\frac{7}{5})[/tex]now replace x for a
[tex](a-2)(a+\frac{7}{5})[/tex]Consider the following when d = 14 ft. Give both exact values and approximations to the nearest hundredth.(a) Find the circumference of the figure.ftftx(b) Find the area of the figure.ft?x7A²teh
(a)Recall that the circumference of a circle is given by the following formula:
[tex]C=\pi d.[/tex]Where d is the diameter of the circle.
Substituting d=14 ft in the above formula, we get:
[tex]C=\pi(14ft)\approx43.98ft\text{.}[/tex](b) Recall that the area of a circle is given by the following formula:
[tex]A=\frac{\pi d^2}{4}.[/tex]Substituting d=14 ft in the above formula, we get:
[tex]A=\frac{\pi(14ft)^2}{4}=49\pi ft^2\approx153.94ft^2.[/tex]Answer:
(a)
Exact solution:
[tex]14\pi ft.^{}[/tex]Approximation:
[tex]43.98\text{ ft.}[/tex](b) Exact solution:
[tex]49\pi ft^2\text{.}[/tex]Approximation:
[tex]153.94ft^2.[/tex]How much would you need to deposit in an account now in order to have $20,000 in the account in 4 years? Assume the account earns 5% interest.I want answer and explanation.
The rule of the simple interest is
[tex]\begin{gathered} I=PRT \\ A=P+I \end{gathered}[/tex]I is the amount of interest
P is the initial amount
R is the interest rate in decimal
T is the time
We need to find the initial amount if the new amount is $20,000, the interest rate is 5% for 4 years, then
A = 20000
R = 5/100 = 0.05
T = 4
Substitute them in the rules above
[tex]\begin{gathered} I=P(0.05)(4) \\ I=0.2P \\ 20000=P+0.2P \\ 20000=1.2P \\ \frac{20000}{1.2}=\frac{1.2P}{1.2} \\ 16666.67=P \end{gathered}[/tex]You need to deposit $16,666.67
The rule of the compounded interest
[tex]A=P(1+r)^t[/tex]A is the new amount
P is the initial amount
r is the interest rate in decimal
t is the time
A = 20000
r = 0.05
t = 4
Substitute them in the rule above
[tex]\begin{gathered} 20000=P(1+0.05)^4 \\ 20000=P(1.05)^4 \\ \frac{20000}{(1.05)^4}=\frac{P(1.05)^4}{(1.05)^4} \\ 16454.05=P \end{gathered}[/tex]You need to deposit $16,454.05
There is a total of $4,840 in an account after 2 years of earning compound interest at a rate of 10%. What was the original amount invested?
In order to find the original amount invested, we can use the following formula:
[tex]P=P_0(1+i)^t[/tex]Where P is the final amount, P0 is the original amount, i is the interest rate and t is the amount of time invested.
So, using P = 4840, i = 10% = 0.1 and t = 2, we have:
[tex]\begin{gathered} 4840=P_0(1+0.1)^2_{} \\ 4840=P_0\cdot1.1^2 \\ 4840=P_0\cdot1.21 \\ P_0=\frac{4840}{1.21} \\ P_0=4000 \end{gathered}[/tex]So the original amount invested is $4,000.
How to graph this and how to solve the equation
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
The graphs of the two equations:
[tex]\begin{gathered} y=\text{ }\frac{-1}{5}x\text{ - 6} \\ y=\text{ }\frac{3x}{5}-\text{ 2} \end{gathered}[/tex]is as follows:
CONCLUSION:
From the graphs above, we can see that the solution to the graphs is:
[tex](x,\text{ y \rparen = \lparen - 5, - 5\rparen}[/tex]consider the graph of the function f(x)= 10^x what is the range of function g if g(x)= -f(x) -5 ?
SOLUTION
So, from the graph, we are looking for the range of
[tex]\begin{gathered} g(x)=-f(x)-5 \\ where\text{ } \\ f(x)=10^x \\ \end{gathered}[/tex]The graph of g(x) is shown below
[tex]g(x)=-10^x-5[/tex]The range is determined from the y-axis or the y-values. We can see that the y-values is from negative infinity and ends in -5. So the range is between
negative infinity to -5.
So we have
[tex]\begin{gathered} f(x)<-5\text{ or } \\ (-\infty,-5) \end{gathered}[/tex]So, comparing this to the options given, we can see that
The answer is option B
IF P(A)=0.2 P(B)=0.1 and P(AnB)=0.07 what is P(AuB) ?A.0.13 B. 0.23 C. 0.3 D.0.4
ANSWER
P(AuB) = 0.23
STEP-BY-STEP EXPLANATION:
Given information
P(A) = 0.2
P(B) = 0.1
P(AnB) = 0.07
What is P(AUB)
[tex]P(\text{AuB) = P(A) + P(B) }-\text{ P(AnB)}[/tex]The next step is to substitute the above data into the formula
[tex]\begin{gathered} P(\text{AuB) = 0.2 + 0.1 - 0.07} \\ P(\text{AuB) = 0.3 - 0.07} \\ P(\text{AuB) = 0.23} \end{gathered}[/tex]For the situation select expression or equation that is not equivalent to the rest.A $79 hoodie is on sale for 25% off.
Given:
$79 hoodie is on sale for 25% off
We can solve or express this in many ways;
If it is 25% off, then the price is;
(100% - 25%) x 79
= (75%) x 79
= (0.75) (79)
OR
The price is;
79 - 25%(79)
= 79 - (0.25)(79)
OR
0.75 x 79 is the same as;
(1 - 0.25)(79)
Therefore, the expression or equation that is NOT equivalent to the rest is
25/100 (79)
If Triangle ABC is dilated by a scale factor of 3 and the length of side AB is 15 inches, what is the length of side A'B'? Complete the statement: The length of side A'B' would be inches. Your answer
If Triangle ABC is dilated by a scale factor of 3 and the length of side AB is 15 inches, what is the length of side A'B'? Complete the statement: The length of side A'B' would be inches.
To find out the length side of A'B' multiply the length side AB by the scale factor
so
A'B'=3*(15)=45 inches
A new statue in a local park has a length (L), width (W), and height (H) (all in feet) that can be expressed by a system of equations. L+W=28L+H=26W+H=22What is the width of the statue?
To determine the width of the statue:
[tex]\begin{gathered} L+W=28\ldots\ldots..(1) \\ L+H=26\ldots\ldots\ldots(11) \\ W+H=22\ldots\ldots..(111) \end{gathered}[/tex]A local park has a length (L), width (W), and height (H) (all in feet)
Solve equation 1 and 2 simultaneously,
[tex]\begin{gathered} L+W=28 \\ L+H=26 \\ \text{Subtract equation (1) - (11)} \\ W-H=2\ldots\ldots\ldots(IV) \end{gathered}[/tex]Solve equation 3 & 4 simultaneously, make W the subject of formular
[tex]\begin{gathered} W+H=22 \\ W-H=2 \\ \text{Add the two equation} \\ 2W=24 \\ \text{divide both side by 2} \\ \frac{2W}{2}=\frac{24}{2} \\ W=12 \end{gathered}[/tex]Therefore the value of width of the statue = 12 feet
What is the sequence that has a recursive formula A(n)= A(n-1)+4 where A(1)=3
1) Considering that, let's find each term:
[tex]\begin{gathered} a_1=3 \\ a_n=a_{n-1}+4 \\ a_2=a_1+4\Rightarrow a_2=3+4=7 \\ a_3=a_2+4\Rightarrow a_3=7+4\text{ =11} \\ a_4=11+4\text{ }\Rightarrow a_4=15 \end{gathered}[/tex]2) So the sequence is
[tex](3,7,11,15,\ldots)[/tex]As each term, from the 2nd one is 4 units more that's why we can make it using a recursive formula
Solve triangle ABC. (If an answer does not exist, enter DNE. Round your answers to one decimal place.) a = 3.0, b = 4.0, C = 58°
Answer
A = 46.3°
B = 75.7°
c = 3.5
Explanation
We will be using both Cosine and Sine rule to solve this.
For Cosine rule,
If a triangle ABC has angles A, B and C at the points of the named vertices of the tringles with the sides facing each of these angles tagged a, b and c respectively, the Cosine rule is given as
c² = a² + b² - 2ab Cos C
a = 3.0
b = 4.0
C = 58°
c² = 3² + 4² - 2(3)(4)(Cos 58°)
c² = 9 + 16 - (24)(0.5299)
c² = 25 - 12.72 = 12.28
c = √12.28 = 3.50
To find the other angles, we will now use Sine Rule
If a triangle ABC has angles A, B and C at the points of the named vertices of the tringles with the sides facing each of these angles tagged a, b and c respectively, the sine rule is given as
[tex]\frac{\text{ Sin A}}{a}=\frac{\text{ Sin B}}{b}=\frac{\text{ Sin C}}{c}[/tex]So, we can use the latter parts to solve this
[tex]\frac{\text{ Sin B}}{b}=\frac{\text{ Sin C}}{c}[/tex]B = ?
b = 4.0
C = 58°
c = 3.5
[tex]\begin{gathered} \frac{\text{ Sin B}}{4}=\frac{\text{ Sin 58}\degree}{3.5} \\ \text{ Sin B = }\frac{4\times\text{ Sin 58}\degree}{3.5}=0.9692 \\ B=Sin^{-1}(0.9692)=75.7\degree \end{gathered}[/tex]We can then solve for Angle A
The sum of angles in a triangle is 180°
A + B + C = 180°
A + 75.7° + 58° = 180°
A = 180° - 133.7° = 46.3°
Hope this Helps!!!
Find the point-slope equation for the line through (0,-2) and (4,1)
ANSWER:
STEP-BY-STEP EXPLANATION:
We can calculate the value of the slope using the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]we replace each value and we will be left with the following:
[tex]undefined[/tex]Consider the quadratic f(x)=x^2-x-30Determine the following ( enter all numerical answers as integers,fraction or decimals$The smallest (leftmost) x-intercepts is x=The largest (rightmost)x-intercepts is x=The y-intercept is y=The vertex is The line of symmetry has the equation
ANSWER
Smallest x-intercept: x = -5
Largest x-intercept: x = 6
y-intercept: y = -30
The vertex is (1/2, -121/4)
Line of symmetry x = 1/2
EXPLANATION
Given:
[tex]f(x)\text{ = x}^2\text{ - x - 30}[/tex]Desired Results:
1. Smallest x-intercept: x =
2. Largest x-intercept: x =
3. y-intercept: y =
4. The vertex is
5. Equation of Line of symmetry
1. Determine the x-intercepts by equating f(x) to zero (0).
[tex]\begin{gathered} 0\text{ = x}^2-x-30 \\ x^2-6x+5x-30\text{ = 0} \\ x(x-6)+5(x-6)=0 \\ (x-6)(x+5)=0 \\ x-6=0,\text{ x+5=0} \\ x\text{ = 6, x = -5} \end{gathered}[/tex]The smallest and largest x-intercepts are -5 and 6 respectively.
2. Determine the y-intercept by equating x to 0
[tex]\begin{gathered} y\text{ = \lparen0\rparen}^2-0-30 \\ y\text{ = -30} \end{gathered}[/tex]y-intercept is -30
3a. Determine the x-coordinate of the vertex using the formula
[tex]x\text{ = -}\frac{b}{2a}[/tex]where:
a = 1
b = -1
Substitute the values
[tex]\begin{gathered} x\text{ = -}\frac{(-1)}{2(1)} \\ x\text{ = }\frac{1}{2} \end{gathered}[/tex]3b. Determine the y-coordinate of the vertex by substituting x into the equation
[tex]\begin{gathered} y\text{ = \lparen}\frac{1}{2})^2-\frac{1}{2}-30 \\ y\text{ = }\frac{1}{4}-\frac{1}{2}-30 \\ Find\text{ LCM} \\ y\text{ = }\frac{1-2-120}{4} \\ y\text{ = -}\frac{121}{4} \end{gathered}[/tex]4. Determine the line of symmetry
In standard form the line of symmetry of a quadratic function can be identified using the formula
[tex]\begin{gathered} x\text{ = -}\frac{b}{2a} \\ x\text{ = }\frac{1}{2} \end{gathered}[/tex]L is the midpoint of JM. K is the midpoint of JL. JL = 15. What is thelength of KM?
We can draw the situation as:
So, if L is the midpoint of JM, JL is equal to LM and JM is equal to 2 times JL
JL = LM
JL + LM = JM
JL + JL = JM
2JL = JM
We can calculate JM using JL as:
2JL = JM
2*15 = JM
30 = JM
Then, if K is the midpoint of JL, JK is equal to KL and JL is 2 times JK
JL = 2JK
Replacing JL by 15, we get:
15 = 2JK
15/2 = JK
7.5 = JK
Finally, KM can be calculated as:
KM = JM - JK
KM = 30 - 7.5
KM = 22.5
Answer: 22.5
Solve each of the following equations. Show its set on a number line. |4x-4(x+1)|=4
Solving this equation, we have:
[tex]\begin{gathered} |4x-4\mleft(x+1\mright)|=4 \\ |4x-4x-4|=4 \\ |-4|=4 \\ 4=4 \end{gathered}[/tex]Since the final sentence is always true, the solution set is all real numbers.
Showing it in the number line in blue, we have:
How do I solve this problem? 1 - 9/5x = 8/6
The given equation is
[tex]1-\frac{9}{5x}=\frac{8}{6}[/tex]Adding -1 on both sides, we get
[tex]1-\frac{9}{5x}-1=\frac{8}{6}-1[/tex][tex]-\frac{9}{5x}=\frac{8}{6}-1[/tex][tex]\text{Use 1=}\frac{6}{6}\text{ as follows.}[/tex][tex]-\frac{9}{5x}=\frac{8}{6}-\frac{6}{6}[/tex][tex]-\frac{9}{5x}=\frac{8-6}{6}[/tex][tex]-\frac{9}{5x}=\frac{2}{6}[/tex][tex]-\frac{9}{5x}=\frac{1}{3}[/tex]Using the cross-product method, we get
[tex]-9\times3=5x[/tex][tex]-27=5x[/tex]Dividing by 5 into both sides, we get
[tex]-\frac{27}{5}=\frac{5x}{5}[/tex][tex]x=-\frac{27}{5}=-5.4[/tex]Hence the required answer is x=-5.4.
What is the value of 9 − (−4)?
Answer:13
Step-by-step explanation:
Step-by-step explanation:
remember, when 2 signs and/operations come together, for addition/subtraction and multiplication/division it always applies :
+ + = +
- + = -
+ - = -
- - = +
and therefore,
9 - (-4) = 9 + 4 = 13
a minus meeting a minus always results in a plus.
Type the correct answer in each box, у 5 4 3 2. 1 -5 -3 -2 -1 2 3 6 5 -1 -2 3 -4 5 The equation of the line in the graph is y= ghts reserved
Given data:
The first point on the graph is (-1,0).
The second point on the graph is (0, -1).
The expression fo the equation of the line is,
[tex]\begin{gathered} y-0=\frac{-1-0}{0-(-1)}(x-(-1)) \\ y=-(x+1) \\ y=-x-1 \\ \end{gathered}[/tex]Thus, the equation of the line is y=-x-1
A radio tower is located 250 feet from a building. From a window in the building, a person determines that the angle of elevation to the top of the tower is 31∘ and that the angle of depression to the bottom of the tower is 29∘
How tall is the tower? ____________ feet.
Given a radio tower of 250 feet and angles of 31 and 29 degrees, the height of the tower is given as 308.58 ft
What is angle of depression?This is the term that is used to refer to the angle that lies between the horizontal line and the object that would be observed from the horizontal line.
In the question we have the following data
b = 250 feet
angles = 31 degrees, 29 degrees
for the top α = 31 degrees, β = 59
For the bottom α = 29 degrees, β = 61 degrees
We have the formula as
a /sin α = b / sin β = c
tan ∅ = opp / adj
for ΔOCA
h1 = 250 x tan 39 degrees
= 250 x 0.8098
= 202.45
h2 = OCB
= 250 x tan 23
= 250 x 0.4245
= 106.125
The height h = h1 + h2
= 202.45 + 106.125
= 308.58
The height of the tower is 308.58 ft
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Consider the line y= 3/5x-3Find the equation of the line that is parallel to this line and passes through the point (3, 4).Find the equation of the line that is perpendicular to this line and passes through the point (3, 4).
a) y = 3/5x + 11/5
b) y = -5/3x + 9
Explanation:[tex]\begin{gathered} a)\text{ }y\text{ = }\frac{3}{5}x\text{ - 3} \\ \text{compare with equation of line:} \\ y\text{ = mx + b} \\ m\text{ =slope, b = y-intercept} \\ m\text{ =slope = 3/5} \\ b\text{ = -3} \end{gathered}[/tex]For a line to be parallel to another line. the slope of the 1st line will be equalt to the slope of the 2nd line:
slope of 1st line = 3/5
So, the slope of the 2nd line = 3/5
Given point: (3, 4) = (x, y)
To get the y-intercept of the second line, we would insert the slope and the point into the equation of line
[tex]\begin{gathered} y\text{ = mx + b} \\ 4\text{ = }\frac{3}{5}(3)\text{ + b} \\ 4\text{ = 9/5 + b} \\ 4\text{ - }\frac{\text{9}}{5}\text{ = b} \\ \frac{20-9}{5}\text{ = b} \\ b\text{ = 11/5} \end{gathered}[/tex]The equation of line parallel to y = 3/5x - 3:
[tex]\begin{gathered} y\text{ = mx + b} \\ y\text{ = }\frac{3}{5}x\text{ + }\frac{11}{5} \end{gathered}[/tex][tex]b)\text{ line perpendicular to y = 3/5x - 3}[/tex]For a line to be perpendicular to another line, the slope of one will be the negative reciprocal of the second line
Slope of the 1st line = 3/5
reciprocal of 3/5 = 5/3
negative reciprocal = -5/3
slope of the 2nd line (perpendicular) = -5/3
We need to get the y-intercept of the perpendicular line:
[tex]\begin{gathered} \text{given point: (3,4) = (x, y)} \\ y\text{ = mx + b} \\ m\text{ of the perpendicular = -5/3} \\ 4\text{ = }\frac{-5}{3}(3)\text{ + b} \\ 4\text{ = -5 + b} \\ 4\text{ + 5 = b} \\ b\text{ = 9} \end{gathered}[/tex]The equation of line perpendicular to y = 3/5x - 3:
[tex]\begin{gathered} y\text{ = mx + b} \\ y\text{ = }\frac{-5}{3}x\text{ + 9} \end{gathered}[/tex]Answer this, please
Zachariah and Khai collect stamps. Zachariah has 7 American stamps out of 12 stamps. Khai has 15 American stamps out of 24 stamps. Which statement is correct?
Zachariah has a higher ratio of American stamps than Khai because 7 over 12 is greater than 15 over 24.
Khai has a higher ratio of American stamps than Zachariah because 7 over 12 is less than 15 over 24.
Zachariah has a higher ratio of American stamps than Khai because 7 over 12 is less than 15 over 24.
Zachariah and Khai have the same ratio of American stamps.
The last statement would be true, because you would convert 7/12 into a fraction and 15/24 into a fraction. From their fraction eyes to State you would turn them into decimals and then percentiles.
Answer:
D: They are both the same
Step-by-step explanation:
I took the test
In basketball, " one on one" free throw shooting ( commonly called foul shooting) is done as follows: if the player makes the first shot(1point), she is given a second shot. If she misses the first shot, she is not given a second shot. Christine, a basketball player, has a 70% free throw record. (she makes 70% of her free throws). Find the probability that, given one-on-one free throw shooting opportunity, Christene will score one point.
If she will be able to shoot the first shot and miss the second shot, then she will obtain 1 point.
Thus, the probability that Christine will get the first shot is as follows:
[tex]P(1pt)=(0.7)(0.3)=0.21[/tex]where the first factor is the probability that she will shoot the first shot and the second factor is the probability that she missed the second shot. Thus, the probability of obtaining 1 point is 21% or 0.21.
what is a unit rate for meter per second if a car travels 274 m in 17 seconds
The rate is 274m/17s = 16.1176m/s
23.What is the missing piece of information required to provethese triangles congruent?a) QYQYb) NYPYC) ZN 2 Pd) QY is the perpendicular bisector
In this case, the information that is explicitly seen in the graph is that we have 2 pairs of equal sides.
The missing information, that can also be seen in the picture, is that we have a shared side that is QY.
If we applied the reflexive property, we know that:
[tex]QY\cong QY[/tex]and then we know that we have 3 pairs of equal sides, what proves that the triangles are congruent.
Answer: QY = QY (Option A).
Given that figure ABCD is a dilation of figure KLMN, find the missing values:(note that values are slightly different because of a round-off error)
• Given the dimensions of ABCD:
m∠A = 71.68 degrees
m∠C = 47.68 degrees
m∠D = 141.87 degrees
CD = 4
AD = 6
BC = 8
• Dimensions of KLMN:
m∠K = 71.52 degrees
m∠L = 98.87 degrees
m∠M = 47.53 degrees
KL = 10
KN = 15
MN = 10
Let's find the missing values.
Given that figure ABCD is a dilation of KLMN, both figures are similar.
• Similar figures have proportional corresponding sides.
,• Similar figures have equal corresponding angles.
Therefore, we have the corresponding sides:
AB ⇔ KL
BC ⇔ LM
CD ⇔ MN
AD ⇔ KN
The corresponding angles are:
m∠A = m∠K
m∠B = m∠L
m∠C = m∠M
m∠D = m∠N
Thus, to find the missing values, we have:
• X = m∠B = m∠L = 98.87 degrees
X = 98.87 degrees.
• Y = m∠N = m∠D = 141.87 degrees.
Y = 141.87 degrees
• To find the value of ,a,, apply the proportionality equation:
[tex]\frac{AB}{AD}=\frac{KL}{KN}[/tex]Plug in values and solve for a:
[tex]\begin{gathered} \frac{a}{6}=\frac{10}{15} \\ \\ \text{Cross multiply:} \\ 15a=10\times6 \\ \\ 15a=60 \\ \\ a=\frac{60}{15} \\ \\ a=4 \end{gathered}[/tex]• To find the value of ,b,, apply the proportionality equation:
[tex]\begin{gathered} \frac{DC}{BC}=\frac{NM}{LM} \\ \\ \frac{4}{8}=\frac{10}{b} \\ \\ \text{Cross multiply:} \\ 4b=10\times8 \\ \\ 4b=80 \\ \\ b=\frac{80}{4} \\ \\ b=20 \end{gathered}[/tex]ANSWER:
• X = 98.87°
,• Y = 141.87°
,• a = 4
,• b = 20
A model of a 51 foot long airplane is 25 in long how is is a tire that is 1/6 tinch
The length of the tire on the airplane given the length of the tire on the model is 17 / 50 foot.
What is the length of the tire?The first step is to determine the scale of the model. In order to determine the scale, divide the length of the airplane by the length of the plane in the model.
Scale of the model = length of the airplane / length of the model
51 / 25 = 1 inch represents 2 1/25 foot
The next step is to multiply the scale determined in the previous step by the length of the tire.
Length of the tire on the airplane = scale x length of the tire in the model
1 / 6 x 2 1/25
1/6 x 51 / 25 = 17 / 50 foot
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Find the surface area of the triangular prism. 13 in. 5 in. 4 in. 12 in.
The first face is a triangle with height 5in and base 12in
Traingular face area = 1/2 x bh
=1/2 x 12 x 5
= 30 in^2
The area of the other triangular base = 30 in^2
Area of left side face = Length x breadth
= 5 x 4 = 20in^2
Area of the slant face = Length x breadth
= 13 x 4 = 52in^2
Area of the bottom face = Length x breadth
= 12 x 4 = 48in^2
Total surface area = 30 in^2 + 30 in^2 + 20in^2 + 52in^2 + 48in^2
=180in^2
Given that the two triangles are similar find the unknowns length of the side labeled in
The unknown length of the side labeled n is 10.5 units
Explanation:Given:
Two similar triangles with one unknown
To find:
the unknown length of the side labelled n
For two triangles to be similar, the ratio of their corresponding sides will equal
[tex]\begin{gathered} side\text{ with 36 corresponds to side with 27} \\ side\text{ with 14 corresponds to side with n} \\ The\text{ ratio:} \\ \frac{14}{n}\text{ = }\frac{36}{27} \end{gathered}[/tex][tex]\begin{gathered} crossmultiply: \\ 14(27)\text{ = 36\lparen n\rparen} \\ 36n\text{ = 378} \\ \\ divide\text{ both sides by n:} \\ \frac{36n}{36}\text{ = }\frac{378}{36} \\ n\text{ = 10.5} \end{gathered}[/tex]The unknown length of the side labeled n is 10.5 units
I need to know how to 53 evaluate the inverse trigonometric function give answers in both radians and degrees
GIVEN:
We are given the following trigonometric expression;
[tex]Tan^{-1}(-1)[/tex]Required;
We are required to evaluate and answer both in radians and in degrees.
Step-by-step solution;
We shall begin by using the trig property;
[tex]tan^{-1}(-x)=-tan^{-1}(x)[/tex]Therefore, we now have;
[tex]tan^{-1}(-1)=-tan^{-1}(1)[/tex]We now use the table of common values and we'll have;
[tex]tan^{-1}(1)=\frac{\pi}{4}[/tex]Therefore;
[tex]-tan^{-1}(1)=-\frac{\pi}{4}[/tex]We can now convert this to degrees;
[tex]\begin{gathered} Convert\text{ }radians\text{ }to\text{ }degrees: \\ \frac{r}{\pi}=\frac{d}{180} \end{gathered}[/tex]Substitute for r (radian measure):
[tex]\begin{gathered} \frac{-\frac{\pi}{4}}{\pi}=\frac{d}{180} \\ \\ -\frac{\pi}{4}\div\frac{\pi}{1}=\frac{d}{180} \\ \\ -\frac{\pi}{4}\times\frac{1}{\pi}=\frac{d}{180} \\ \\ -\frac{1}{4}=\frac{d}{180} \end{gathered}[/tex]Now we can cross multiply;
[tex]\begin{gathered} -\frac{180}{4}=d \\ \\ -45=d \end{gathered}[/tex]Therefore,
ANSWER:
[tex]\begin{gathered} radians=-\frac{\pi}{4} \\ \\ degrees=-45\degree \end{gathered}[/tex]Which number is not a solution to3(x+4)−2≥7?-2-12 1
The inequality is:
[tex]3(x+4)-2\ge7[/tex]now we solve the inequality for x
[tex]\begin{gathered} 3(x+4)\ge7+2 \\ 3(x+4)\ge9 \\ x+4\ge\frac{9}{3} \\ x+4\ge3 \\ x\ge3-4 \\ x\ge-1 \end{gathered}[/tex]This means that all the number, from -1 to infinit are solution of the inequality, and the only option that is not a solution is a) -2
