Answer:
$191,340.80
Step-by-step explanation:
Step 1
We find the amount that is paid monthly by the Lee's
We are told in the question that:
Cost of the house =$360,000
Down payment = $50,000
We are also told, the balance left after the down payment was made = Mortgage that is amortized at an
Interest rate of 5.25%
Time = 20 years
Hence, Mortgage amount = $360,000 - $50,000 = $310,000
Formula for monthly payment =
M= P[r(1+r)^n/((1+r)^n)-1)]
M = the total monthly mortgage payment.
P = the principal loan amount.
r = your monthly interest rate.
= rate/12
=5.25%/12 = 0.0525/12
= 0.004375
n = number of payments
= number of years × number of months
= 20 × 12 = 240 payments
Formula for monthly payment =
M= P[r(1+r)^n/((1+r)^n)-1)]
M = 310,000[0.004375(1 + 0.004375)^240/((1 + 0.004375)^240 ) - 1]
M = $2,088.92
Therefore, the monthly payment by the Lee's is $2,088.92
Step 2
We calculate the Total Amount paid by the Lee's in 20years because we are told in the question that they paid off their mortgage after 20 years
Total Amount paid = Monthly payments × Number of payments
= $2,088.92 × 240
= $501,340.80
Step 3
The third and final step is to calculate the Total interest paid for 20 years
Total Interest = Total amount paid - Mortgage amount
= $501,340.80 - $310,000
Total Interest: $191,340.80
Therefore,the interest will they have paid in total is $191,340.80
Jen plans to tile the kitchen floor. Each time covers 3 square meters. The kitchen is 4 5/6 meters wide and 5 meters long. How many times does Jen need to cover the kitchen floor?
Answer:
Jen needs approximately 8 tiles to cover the kitchen floor
Step-by-step explanation:
What we want to calculate here is the number of tiles needed to cover the kitchen floor.
The first thing we need to do here is to calculate the area of the kitchen floor.
Mathematically, that would be the product of the length of the kitchen floor and the length of the width.
That is; 4 5/6 * 5 = 29/6 * 5 = 145/6 m^2
Now, to calculate the number of tiles needed, we only need to divide the area of the kitchen floor by the area of the individual tiles
Mathematically, that would be;
145/6 ÷ 3 = 145/6 * 1/3 = 145/18 = 8.05556
This is approximately 8 tiles
Write an equation in slope-intercept form for the line with slope 1/4 and y-intercept -1. PLEASE HELP MEEE : (
Explanation:
We have the general slope intercept form y = mx+b. All we do is replace m with the given slope 1/4, and replace b with the y intercept -1.
So we have y = mx+b turn into y = (1/4)x+(-1) which simplifies to y = (1/4)x-1.
the shape of a piece is pallelogram whose adjacent side are 12m and 9 m and the corresponding diagonal is 15 .find the area of land
Answer: The area of land =108 m²
Step-by-step explanation:
In the given piece of land is in the shape of a parallelogram.
Diagonals divide it into 2 equal parts.
So, area of parallelogram = 2 x (Area of triangle with sides 12m and 9 m and 15 m)
Heron's formula :
Area of triangle = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex], where [tex]s=\dfrac{a+b+c}{2}[/tex]
Let a= 12 , b= 9 and c = 15
[tex]s=\dfrac{12+9+15}{2}=18[/tex]
Area of triangle = [tex]\sqrt{18(18-12)(18-9)(18-15)}[/tex]
[tex]=\sqrt{18\times6\times9\times3}=\sqrt{2916}=54\ m^2[/tex]
Then, area of parallelogram= 2 x 54 = 108 m²
Hence, the area of land =108 m²
What is the sum of the fractions? Use the number line to help find the answer. A. -2 B. -4/5 C. 4/5 D.2
Answer:
The answer is B.
Step-by-step explanation:
You solve it using the number line. Starting with the point at 3/5 then, you have to go backwards by 7 steps which is -4/5.
You can ignore the denorminator as all the denorminators are the same.
Answer:
-4/5
Step-by-step explanation:
The parentheses can be removed immediately since they do not affect the outcome in this problem.
then we have:
3/5 - 7/5 = -4/5
Three students used factoring to solve a quadratic equation? The equation was solve correctly by ______.The solutions of the equation are__________.
Answer:Keith
x=5,x=12
Step-by-step explanation:
Answer:
the answers are keith and -5,-12
Step-by-step explanation:
I just took the test and got a 5/5 the other person is incorrect.
if f(x)=4x-7 and g(x)=2x+4 evalvate f(x)+g(x) for x=-3
Answer:
-21
Step-by-step explanation:
We are told to find f(x) + g(x) for x= -3. Therefore, we must evaluate f(-3) and g(-3), then add them together.
First, evaluate f(-3).
f(x)=4x-7
To find f(-3), we need to substitute -3 in for x.
f(-3)= 4(-3)-7
Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction First, multiply 4 and -3.
f(-3)= -12-7
Next, subtract 7 from -12
f(-3)= -19
Next, find g(-3).
g(x)=2x+4
To find g(-3), substitute -3 in for x.
g(-3)= 2(-3)+4
Solve according to PEMDAS. First, multiply 2 and -3.
g(-3)= -6+4
Next, add -6 and 4
g(-3)= -2
Now, we can add f(-3) and g(-3) together.
f(-3) + g(-3)
f(-3)= -19
g(-3)= -2
-19 + -2
Add
-21
Answer:
-21
Step-by-step explanation:
Adding f and g together, we get (f + g)(x) = 4x + 2x -7 + 4, or
= 6x - 3
Now replace x with -3. We get:
(f + g)(-3) = 6(-3) - 3 = -21
A florist gathered data about the weekly number of flower deliveries he made to homes and to businesses for several weeks. He used a graphing tool to organize the data in a scatter plot, with x representing the number of home deliveries and y representing the number of deliveries to businesses. Then he used the graphing tool to find the equation of the line of best fit: y = 0.555x + 1.629. Based on the line of best fit, approximately how many deliveries are predicted to be made to homes during a week with 50 deliveries to businesses?
Answer:
The number of deliveries that are predicted to be made to homes during a week with 50 deliveries to business is 87 deliveries
Step-by-step explanation:
The data categorization are;
The number of home deliveries = x
The number of delivery to businesses = y
The line of best fit is y = 0.555·x + 1.629
The number of deliveries that would be made to homes when 50 deliveries are made to businesses is found as follows;
We substitute y = 50 in the line of best fit to get;
50 = 0.555·x + 1.629 =
50 - 1.629 = 0.555·x
0.555·x = 48.371
x = 48.371/0.555= 87.155
Therefore, since we are dealing with deliveries, we approximate to the nearest whole number delivery which is 87 deliveries.
Answer:87
Step-by-step explanation:
Please help find these angle for me plz!
Answer:
<DEF = 40°<EBF = <EDF = 56°<DCF = <DEF =40°<CAB = 84°Step-by-step explanation:
In triangle DEF, we have:
Given:
<EDF=56°
<EFD=84°
So, <DEF =180° - 56° - 84° =40° (sum of triangle angles is 180°)
____________
DE is a midsegment of triangle ACB
( since CD=DA(given)=>D is midpoint of [CD]
and BE = EA => E midpoint of [BA] )
According to midsegment Theorem,
. (DE) // (CB) "//"means parallel
. DE = CB/2 = FB =CF
___________
DEBF is a parm /parallelogram.
Proof: (DE) // (FB) [(DE) // (CB)]
AND DE = FB
Then, <EBF = <EDF = 56°
___________
DEFC is parm.
Proof: (DE) // (CF) [(DE) // (CB)]
And DE = CF
Therefore, <DCF = <DEF =40°
___________
In triangle ACB, we have:
<CAB =180 - <ACB - <ABC =180° - 40° - 56° =84° (sum of triangle angles is 180°)
[tex]HOPE \: THIS \: HELPS.. GOOD \: LUCK![/tex]
Please answer it in two minutes
Answer:
0.9
I guess.
If yes
.. Follow me..
I need this answered in ONE minute
Place the indicated product in the proper location on the grid. Write your answer in descending powers of x. (x^ 2 + 3x + 1)(x^2 + x + 2)
Answer:
[tex]x^4 + 4x^3 + 6x^2 + 7x + 2[/tex]
Step-by-step explanation:
We are asked to multiply the given polynomials.
[tex](x^ 2 + 3x + 1) \times (x^2 + x + 2)[/tex]
Multiply each term of the first polynomial to each term of the second polynomial.
[tex]x^ 2 \times (x^2 + x + 2) = x^4 + x^3 + 2x^2[/tex]
[tex]3x \times (x^2 + x + 2) = 3x^3 + 3x^2 + 6x[/tex]
[tex]1 \times (x^2 + x + 2) = x^2 + x + 2[/tex]
Add the results
[tex](x^4 + x^3 + 2x^2) + (3x^3 + 3x^2 + 6x) + ( x^2 + x + 2)[/tex]
Combine the like terms
[tex]x^4 + 4x^3 + 6x^2 + 7x + 2[/tex]
The answer is written in descending powers of x.
Find the 20th term from the last term of the AP:3,8,13,..., 253.
Answer:
158
Step-by-step explanation:
The sequence is 3, 8, 13, ..., 253.
Going backwards, it's 253, 248, 243, ..., 3.
First term is 253, common difference is -5.
The nth term is:
a = 253 − 5(n − 1)
The 20th term is:
a = 253 − 5(20 − 1)
a = 158
Identify the ventez of the graph. Tell whether it is a minimum or maximum.
Answer:
2nd option: the lowest point on the graph is (-2, -2). this is where both sides of the parabola converge. from this point, both lines go up. this means the vertex is a minimum.
The value 4 is a lower bound for the zeros of the function shown below.
f(x) = 4x^3 – 12x^2 – x + 15
A) True
B) False
Answer:
False roots are x = -1 or x = 5/2 or x = 3/2
Step-by-step explanation:
Solve for x:
4 x^3 - 12 x^2 - x + 15 = 0
The left hand side factors into a product with three terms:
(x + 1) (2 x - 5) (2 x - 3) = 0
Split into three equations:
x + 1 = 0 or 2 x - 5 = 0 or 2 x - 3 = 0
Subtract 1 from both sides:
x = -1 or 2 x - 5 = 0 or 2 x - 3 = 0
Add 5 to both sides:
x = -1 or 2 x = 5 or 2 x - 3 = 0
Divide both sides by 2:
x = -1 or x = 5/2 or 2 x - 3 = 0
Add 3 to both sides:
x = -1 or x = 5/2 or 2 x = 3
Divide both sides by 2:
Answer: x = -1 or x = 5/2 or x = 3/2
Answer:
False
Step-by-step explanation:
f(x) = 4x³ - 12x² - x + 15
Set output to 0.
Factor the function.
0 = (x + 1)(2x - 3)(2x - 5)
Set factors equal to 0.
x + 1 = 0
x = -1
2x - 3 = 0
2x = 3
x = 3/2
2x - 5 = 0
2x = 5
x = 5/2
4 is not a lower bound for the zeros of the function.
In the figure, ABC is mapped onto XYZ by a 180° rotation. Angle B corresponds to which angle in XYZ?
Answer:
x
Step-by-step explanation:
Need help ASAP please
Points A(-l, y) and B(5,7) lie on a circle with centre 0(2, -3y). Find the values of y. Hence, find the radius of the circle
Answer:
The answer is below
Step-by-step explanation:
Points A(-l, y) and B(5,7) lie on a circle with centre O(2, -3y). This means that AB is the diameter of the circle and OA = OB = radius.
For two points X([tex]x_1,y_1[/tex]) and Y([tex]x_2, y_2[/tex]), the coordinates of the midpoint (x, y) between the two points is given as:
[tex]x=\frac{x_1+x_2}{2},y=\frac{y_1+y_2}{2}[/tex].
For A(-l, y) and B(5,7) with center O(2, -3y), the value of y can be gotten by:
[tex]For\ x\ coordinate:\\2=\frac{-1+5}{2}\\ 2=2.\\For\ y\ coordinate:\\-3y=\frac{y+7}{2}\\ -6y=y+7.\\-6y-y=7\\-7y=y\\y=-1[/tex]
The value of y is -1. Therefore A is at (-1, -1) and O is at (2, -3(-1))= (2, 3)
The radius of the circle = OA. The distance between two points X([tex]x_1,y_1[/tex]) and Y([tex]x_2, y_2[/tex]) is given as:
[tex]|OX|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\\Therefore\ the\ radius \ |OA|\ is :\\|OA|=\sqrt{(2-(-1))^2+(3-(-1))^2}=\sqrt{25}=5[/tex]
The radius of the circle is 5 units
In a survey conducted by the marketing agency 11mark, 241 of 1000 adults 19 years of age or older confessed to bringing and using their cell phone every trip to the bathroom (confessions included texting and answering phone calls).
(a) What is the sample in this study? What is the population of interest?
(b) What is the variable of interest in this study? ls it qualitative or quantitative?
(c) Based on the results of this survey, obtain a point estimate for the proportion of adults 19 years of age or older who bring their cell phone every trip to the bathroom.
(d) Explain why the point estimate found in part (c) is a statistic. Explain why it is a random variable. What is the source of variability in the random variable?
(e) Construct and interpret a 95% confidence interval for the population proportion of adults 19 years of age or older who bring their cell phone every trip to the bathroom.
(f) What ensures that the results of this study are representative of all adults 19 years of age or older?
Answer: kindly check explanation
Step-by-step explanation:
A) The sample is a fraction of the total population used in the study.
The sample is 1000 19 years of age or older U.S adult.
The population : all U.S adults aged 19 or older.
B.) Confession about bringing cell phone to the bathroom and it is a qualitative variable
C.) point estimate (p) :
Total number of sample = 1000
Number who confessed to bring cellphone = 241
p = 241/ 1000
= 241/1000 = 0.241
D.) The point estimate was deduced from the sample information and not the population. Random selection because selection is unbiased.
E.) 95% confidence interval (CI)
95% CI = (1 - 0.95) = 0.05
For a two-tailed test : 0.05 / 2 = 0.025
Z - score = 1.96
Error : (√[p(1 - p) / n])*z
1.96 * √0.241(1-0.241)/1000
1.96* √0.000182919
1.96 * 0.0135247
= 0.0265085
Boundary :
(0.241 - 0.0265085), (0.241 + 0.0265085)
(0.2144915, 0.2675085)
F) The sample can be said to be representative of the total population since the sampling was performed and participants were chosen at random.
The revenue of selling a new video game is modeled by the equation can be modeled by the equation f(x)=-3x^2 + 21x + 54 where x is the price of the game and y is the revenue. Find the price of the game, x, that would result in no revenue.
Answer:
x = 9Step-by-step explanation:
Given the revenue of selling a new video game modeled by the equation f(x)=-3x² + 21x + 54 where x is the price of the game and y is the revenue, to calculate the price of game x that would result in no revenue, we will set the revenue f(x) to be zero and then solve the resultinf equation.
at f(x) = 0;
0 = -3x² + 21x + 54
0 = -x² + 7x + 18
Multiplying through by minus sign
x² - 7x - 18 = 0
Factorizing the resulting expression;
x² - 9x+2x - 18 = 0
(x² - 9x)+(2x - 18) = 0
x(x-9)+2(x-9) = 0
(x-9)(x+2) = 0
x-9 = 0 and x+2 = 0
x = 9 and -2
Neglecting the negaive value of x;
x = 9
Hence, the price of the game, x, that would result in no revenue is 9.
with a y-intercept 10, x-intercept 2, and equation of axis of symmetry x-3=0
Answer: f(x) = -3x^2 + 3x - 2
Explain: x of vertex: [tex]x[/tex] = [tex](-\frac b{2}{a} )[/tex] = [tex]-\frac{3}{-6} = \frac{1}{2}[/tex]
y of vertex: y = [tex]f (\frac{1}{2} ) = - \frac{3}{4} + \frac{3}{2} -2=-\frac{5}{4}[/tex]
y-intercept: y = -2
x-intercept: y = 0
D = b[tex]^[/tex]^2 - 4ac = 9 - 24 = - 15 <0. There are no real roots (no x-intercepts) because D<0.
Since a <0, parabola opens downward. The parabola is below the x-axis
EXPLANATION NEEDED:
In right triangle ABC, ∠ B is a right angle and sin ∠ C = x. cos ∠ A =
a. √x² - 1
b. √1 - x²
c. x
d. √x² + 1
e. x²
Answer:
C. xStep-by-step explanation:
AC denotes the length of the hypotenuse and AB and BC denote the lengths of the other two sides, so:
[tex]\cos(\angle A)=\dfrac{AB}{AC}=\sin(\angle C)=x[/tex]
PLEASE HELP!!!
These dot plots show the ages in years) for a sample of two types of fish.
Explanation:
The median is the center of the distribution. We see that the center of the shark's distribution is to the left compared to the koi's center. Therefore, the shark's median age is smaller. Choice A is one of the answers.
The spread is exactly what it sounds like: how spread out the data is. Mathematically we use the standard deviation, or sometimes the range, to find out how spread out things are. The koi distribution is more spread out. The shark's data is more clumped together. This is why choice B is the other answer.
Center: Sharks have lower median age than Koi.
Spreads: The ages of koi are more spread out.
What is dot plot?A dot plot is a standardized way of displaying the distribution of data based on a five number summary.
What is the median in a dot plot?The center line in the dot plot shows the median for the data .
What is the spread of data?Spread of data is measured in terms how far the data differs from the mean.
According to the given question
We have a dot plots for the two fishes sharks and Koi.
According to the given dot plot
Most ages of the sharks is lower than the koi.
⇒ Sharks are lower than koi.
So, the center: Sharks have lower median age than Koi.
Also, the ages of Koi are wide spreading.
⇒ The ages of koi are more spread out
Therefore, Spreads: The ages of koi are more spread out.
Hence, option A and B are correct.
Learn more about dot plot here:
https://brainly.com/question/22746300
#SPJ2
Factor the polynomial.
X2-13x+30
Answer:
[tex] \ \boxed{(x - 3)(x - 10)}[/tex]Step-by-step explanation:
[tex] {x}^{2} - 13x + 30[/tex]
Write -13x as a difference
[tex] {x}^{2} - 3x - 10x + 30[/tex]
Factor out x from the expression
[tex]x(x - 3) - 10x + 30[/tex]
Factor out -10 from the expression
[tex]x(x - 3) - 10(x - 3)[/tex]
Factor out x-3 from the expression
[tex](x - 3)(x - 10)[/tex]
Hope I helped!
Best regards!!
please solve i will give brainiest 100 point question ****** do the whole page please
Answer:
a) point (2, 1) is when the ball is on it's way down at 2 seconds
b) vertex (1, 2) is the highest the ball goes, which is 2 at 1 second.
c) y-intercept (0, 1) at time zero the ball is starting at a height of 1.
d) Points (0, 1) and (2, 1) are the points at which the ball starts and when it is in the same position from the ground as when it started, which is 1.
e) zero (x-int) is when the ball hits the ground at 2.5 seconds.
Step-by-step explanation:
Answer:
See below
step by step explanation
A. (2 , 1 ) is point on the parabola . It represents that the height of the ball after 2 second have passed.
b. The vertex is at ( 1 , 2 ) . It represent that the maximum height of the ball which is 2 units to at t = 1 second
c. The y - intercept is ( 0 , 1 ) . It represent that the initial height of ball at t = 0 second is 1 unit.
d. Point ( 0 , 1 ) and ( 2 , 1 )
This point represent the set of point having equal height at two different time. It represents how long before the ball reaches the same height from the starting point.
e. The zero or x - intercept is ( 2.5 , 0 )
It represent the time taken by ball before it reaches the ground.
Hope this helps...
Best regards!!
The slope of the line below is 4 . Which of the following is the point slope form of that line ? ( top answer gets )
Answer:
C
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Here m = 4 and (a, b) = (- 3, - 4) , thus
y - (- 4) = 4(x - (- 3)) , that is
y + 4 = 4(x + 3) → C
Factor the polynomial.
X2+3x-54
Answer:
[tex] \mathrm{(x + 9)(x - 6)}[/tex]Step-by-step explanation:
[tex] {x}^{2} + 3x - 54[/tex]
Write 3x as a difference
[tex] {x}^{2} + 9x - 6x - 54[/tex]
Factor out x from the expression
[tex]x(x + 9) - 6x - 54[/tex]
Factor out -6 from the expression
[tex]x(x + 9) - 6(x + 9)[/tex]
Factor out x+9 from the expression
[tex](x + 9)(x - 6)[/tex]
Hope I helped!
Best regards!
Answer: (x + 9)(x - 6)
Step-by-step explanation:
x² + 3x - 54 Find 2 numbers whose product is -54 and sum is +3
∧
-1 + 54
-2 + 27
-3 + 18
-6 + 9 = +3 This works!
Place those digits in the parentheses and it is now factored.
(x - 6)(x + 9)
A recent national survey found that high school students watched an average (mean) of 7.8 movies per month with a population standard deviation of 0.5. The distribution of number of movies watched per month follows the normal distribution. A random sample of 30 college students revealed that the mean number of movies watched last month was 7.3. At the 0.05 significance level, can we conclude that college
Answer:
Step-by-step explanation:
Given that :
Mean = 7.8
Standard deviation = 0.5
sample size = 30
Sample mean = 7.3 5.4772
The null and the alternative hypothesis is as follows;
[tex]\mathbf{ H_o: \mu \geq 7.8}[/tex]
[tex]\mathbf{ H_1: \mu < 7.8}[/tex]
The test statistics can be computed as :
[tex]z = \dfrac{X- \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \dfrac{7.3- 7.8}{\dfrac{0.5}{\sqrt{30}}}[/tex]
[tex]z = \dfrac{-0.5}{\dfrac{0.5}{5.4772}}[/tex]
[tex]z = - 5.4772[/tex]
The p-value at 0.05 significance level is:
p-value = 1- P( Z < -5.4772)
p value = 0.00001
Decision Rule:
The decision rule is to reject the null hypothesis if p value is less than 0.05
Conclusion:
At the 0.05 significance level, there is sufficient information to reject the null hypothesis. Therefore ,we conclude that college students watch fewer movies a month than high school students.
Please answer please question
Answer:38
Step-by-step explanation:multiple
suppose for an angle theta in a right triangle cos theta = C. Sketch and label this triangle, and then use it to write the other five trig functions of theta in terms of C.
Answer:
[tex]sin\theta = \sqrt{1-C^2}[/tex]
[tex]tan\theta = \dfrac{\sqrt{1-C^2}}{C}[/tex]
[tex]cot\theta = \dfrac{C}{\sqrt{1-C^2}}[/tex]
[tex]sec\theta = \dfrac{1}{C}}[/tex]
[tex]cosec\theta = \dfrac{1}{\sqrt{1-C^2}}[/tex]
Step-by-step explanation:
Given that:
[tex]\theta[/tex] is an angle in a right angled triangle.
and [tex]cos\theta = C[/tex]
To find:
To draw the triangle and write other five trigonometric functions in terms of C.
Solution:
We know that cosine of an angle is given by the formula:
[tex]cosx =\dfrac{Base}{Hypotenuse}[/tex]
Here, we are given that [tex]cos\theta = C[/tex] OR
[tex]cos\theta = \dfrac{C}{1}[/tex]
i.e. Base = C and Hypotenuse of triangle = 1
Please refer to the right angled triangle as per given statements.
[tex]\triangle PQR[/tex], with base PR = C units
and hypotenuse, QP = 1 unit
[tex]\angle R[/tex] is the right angle.
Let us use pythagorean theorem to find the value of perpendicular.
According to pythagorean theorem:
[tex]\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}[/tex]
[tex]1^{2} = C^{2} + QR^{2}\\\Rightarrow QR = \sqrt {1-C^2}[/tex]
[tex]sin\theta = \dfrac{Perpendicular}{Hypotenuse}\\\Rightarrow sin\theta = \dfrac{\sqrt{1-C^2}}{1}\\\Rightarrow sin\theta = \sqrt{1-C^2}[/tex]
[tex]tan\theta = \dfrac{Perpendicular}{Base}\\\Rightarrow tan\theta = \dfrac{\sqrt{1-C^2}}{C}[/tex]
[tex]cot\theta = \dfrac{Base}{Perpendicular}\\\Rightarrow cot\theta = \dfrac{C}{\sqrt{1-C^2}}[/tex]
[tex]sec\theta = \dfrac{Hypotenuse}{Base}\\\Rightarrow sec\theta = \dfrac{1}{C}}[/tex]
[tex]cosec\theta = \dfrac{Hypotenuse}{Perpendicular}\\\Rightarrow cosec\theta = \dfrac{1}{\sqrt{1-C^2}}[/tex]
Find each product.
(5-x2+2)(-3)
PLEASE HELP!!! ASAP!!!
Answer:
[tex]3x^2 - 21[/tex] (did you mean for the equation to be [tex](5 - x^2 + 2) \cdot -3[/tex]?)
Step-by-step explanation:
Multiplying -3 by each term:
[tex]-3 \cdot 5 = -15[/tex]
[tex]-x^2 \cdot -3 = 3x^2[/tex]
[tex]-3 \cdot 2 = -6[/tex]
[tex]-15-6 = -21[/tex]
So the equation comes out to [tex]3x^2 - 21[/tex] .
Hope this helped!
Pls answer this question with steps (proof).
Answer:
Step-by-step explanation:
Since triangle BCE is a right angle triangle, we would determine angle BEC by applying the tangent trigonometric ratio. Therefore,
Tan BEC = 6/3 = 2
Angle BEC = Tan^-1(2)
Angle BEC = 63.4°
The sum of the angles on a straight line is 180°. This means that
Angle AED + angle DEC + angle BEC = 180
Angle AED = 180 - (45 + 63.4) = 71.6°
Angle ADE = angle AED = 71.6°
Angle CDE + angle ADE = 180(sum of angles on a straight line)
Angle CDE = 180 - 71.6 = 108.4°
To get line EC, we would apply Pythagoras theorem. Therefore
EC² = 3² + 6² = 45
EC = √45 = 6.71 cm
The sum of the angles in a triangle is 180°
Therefore,
Angle ECD = 180 - (45 + 108.4) = 26.6°
By applying sine rule,
6.71/sin108.4 = ED/sin26.6 = DC/Sin45
6.71/sin108.4 = ED/sin26.6
Cross multiplying, it becomes
6.71sin26.6 = EDsin108.4
ED = 6.71sin26.6/sin108.4
ED = 3.00608/0.949 = 3.18cm
The area of a triangle is
Area = 1/2abSinC
Therefore, area of triangle EDC = 1/2 ×
ED × EC × SinDEC
Area = 1/2 × 6.71 × 3.18 × sin45
Area = 1/2 × 6.71 × 3.18 × 0.707
Area = 7.54 cm²