Answers
Answer:
answer is -0.8333
round about -0.834
Step-by-step explanation: I hope this helps.
Answer:
Related Questions
10. A car dealership offers a loan with 3.9% interest for 36 months, and you plan to purchase a car for $19,500. You can afford a down payment of $2,500.(a) What will your monthly payment be? $(b) How much will you pay in total for the car? $(c) How much will you pay in interest over the life of the loan? $
Answers
The monthly payment formula is :
[tex]M=P\times\frac{r(1+r)^n}{(1+r)^n-1}[/tex]where M is the monthly payment
P is the Financed amount
r is the rate of interest monthly, annual rate divided by 12
n is the number of payments
From the problem,
The financed amount is the difference between the car's cost and the down payment.
P = $19,500 - $2,500
P = $17000
The monthly interest rate is :
r = 3.9%/12 or 0.039/12 = 0.00325
n = 36 months
The monthly payment will be :
[tex]\begin{gathered} M=17000\times\frac{0.00325(1+0.00325)^{36}}{(1+0.00325)^{36}-1} \\ M=501.15 \end{gathered}[/tex]a. M = $501.15
b. The total payment for the car is monthly payment multiplied by the number of payment made together with the downpayment.
501.15 x 36 + 2500 = $20,541.4
c. The interest is the difference between the total payment made and the financed amount.
I = 501.15 x 36 - 17,000 = $1,041.4
French cooks usually weigh ingredients. A French recipe uses 225 grams of granulated sugar.How many cups are needed if there are 2 cups of sugar per pound: (Note that you are changingfrom units of weight, grams, to units of volume, cups. There are 453.5 grams/pound)cups
Answers
Given:
The amount of granulated sugar used fo French fries, x=225 g.
1 pound=2cups.
1 pound=453.5g.
Since 1 pound =453.5 g,
[tex]1\text{ g=}\frac{1}{453.5}\text{ pound}[/tex]Therefore, 225 grams can be expressed in pound as,
[tex]\begin{gathered} 225\text{ g=}225\text{ g}\times\frac{\frac{1}{453.5}pound}{1\text{ g}} \\ =\frac{225}{453.5}pound \\ \cong0.496\text{ pound} \end{gathered}[/tex]Since 1 pound =2 cups, we can write
[tex]\begin{gathered} 0.496pound=0.496pound\times\frac{2cup}{1\text{ pound}} \\ =0.992\text{ cups} \\ \cong1\text{ cup} \end{gathered}[/tex]Therefore, 1 cup is needed.
if the area of polygon A is 72 and Q is a scaled copy and the area of Q is 5 what scale factor got 72 to 5
Answers
A area= 72
Q area =5
So, if we multiply the A area by the square of the scale factor ( since they are areas) we obtain area Q:
72 x^2 = 5
Solving for x:
x^2 = 5/72
x = √(5/72)
x= 0.26
A psychologist has designed a questionnaire to measure individuals' aggressiveness. Suppose that the scores on the questionnaire are normally distributed with
a standard deviation of 90. Suppose also that exactly 10% of the scores exceed 700. Find the mean of the distribution of scores. Carry your intermediate
computations to at least four decimal places. Round your answer to at least one decimal place.
Answers
μ = 782.02 is the mean of the distribution of scores by standard deviation.
What is standard deviation in math?
A statistical measurement called standard deviation examines how far away from the mean a set of statistics is. Standard deviation, to put it simply, gauges the degree of dispersion between numbers in a data collection. The variance's square root is used to generate this metric.we have from standard normal table that
P(Z > 1.282) = 0.1
Therefore the given Z score of a score of 700 is given thus 1.282.
the z score is given:
x - μ / α = 1.282
700 - μ / 90 = 1.282
Therefore μ = (700 - 90)*1.282 = 782.02
So we have that μ = 782.02
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Find the value of variable a given the transformation is an isometry.
Answers
Answer:
• a =10
,• b = 4
Explanation:
An isometry is a rigid transformation that preserves length and angle measures, as well as perimeter and area.
This means that the two right triangles are congruent.
Thus, we have that:
[tex]\begin{gathered} 3a=30 \\ 10b=40\degree \end{gathered}[/tex]Next, we solve for a and b.
[tex]\begin{gathered} 3a=30 \\ \text{Divide both sides by 3} \\ \frac{3a}{3}=\frac{30}{3} \\ a=10 \end{gathered}[/tex]Likewise:
[tex]\begin{gathered} 10b=40\degree \\ \text{Divide both sides by 10} \\ \frac{10b}{10}=\frac{40\degree}{10} \\ b=4 \end{gathered}[/tex]The values of a and b are 10 and 4 respectively.
Below is the graph of a parabola with its vertex and another point on the parabola labeled.Write an equation of the parabola.(-2,4).(1, -2)
Answers
The vertex form of a parabola is given by:
[tex]x=a(y-k)^2+h[/tex]Where the vertex is:
[tex]\begin{gathered} V(h,k)=(-2,4) \\ so\colon \\ x=a(y-4)^2-2 \\ x=a(y-4)^2-2 \end{gathered}[/tex]for (1,-2):
[tex]\begin{gathered} 1=a(-2-4)^2-2 \\ 1=a(-6)^2-2 \\ 1=36a-2 \\ solve_{\text{ }}for_{\text{ }}a\colon \\ 36a=1+2 \\ 36a=3 \\ a=\frac{3}{36} \\ a=\frac{1}{12} \\ \end{gathered}[/tex]therefore:
[tex]x=\frac{1}{12}(y-4)^2-2[/tex]Cameron can run 3.6 miles for every 4 miles Juliette runs. If Juliette ran 7.6 miles, how far will Cameron run? 6.84 miles68.4 miles6 miles68 miles
Answers
lets set up a proportion here
cameroon runs 3.6 miles for every 4 miles Juliette runs
3.6 miles(C).................................................... 4 miles (J)
? miles(C)...........................................................7.6 miles (J)
cameron will run= (7.6*3.6)/4=6.84 miles
Cameron will run 6.84 miles
In the picture, the first answer circled is the original answer of the problem. My math teacher simplified this to get the second circled answer. Could you explain how he simplified it?
Answers
We have an algebraic problem where we have to solve for "w"
[tex]3x+2k=\frac{15y}{9w-18v}[/tex]Solving for "w"
[tex]\begin{gathered} 9w-18v=\frac{15y}{3x+2k} \\ w=\frac{\frac{15y}{3x+2k}}{9}+\frac{18v}{9} \\ w=\frac{15y}{27x+18k}+2v \end{gathered}[/tex]The previous result is the solution to the problem without simplifying, the error is that you have in the image, in the denominator the factor "23x" in reality this is "27x"
Now we can simplify this by taking out the third part of the whole fractional term
For him we divide everything by 3, being the third part of 15, 27, and 18 respectively 5, 9, and 6.
[tex]w=\frac{5y}{9x+6k}+2v[/tex]I need some help solving this It’s from my ACT prep guide
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We can convert a measure from radians to degrees by taking into account that π radians is equivalent to 180°.
Then, we can convert a measure in radians into degrees by multiplying by 180°/π.
We can convert 7π/11 into degrees as:
[tex]\frac{7\pi}{11}\cdot\frac{180\degree}{\pi}=\frac{7\cdot180\degree}{11}\approx114.55\degree[/tex]Answer: 114.55°
The Oldest rocks on Earth are about 4 x 10^9 years old. For which of these ages could this be an approximation?
A. 3,862,100,000 years
B. 3.849999999x10^9 years
C. 0.000000004 years
D.4,149,000,000 years
E.3.45x10^9 years
Answers
4149000000 is the approximation age of oldest rock. The precise amount is not known with certainty. Similar to proximity or approximately, the word "approximation" is derived from the Latin Proximus, which meaning "nearest."
What is approximation age?The precise amount is not known with certainty. Similar to proximity or approximately, the word "approximation" is derived from the Latin Proximus, which meaning "nearest." The closest estimate you can make without knowing something's exact size or measurement is called an approximation.
Despite the fact that approximation is most usually used in relation to numbers, it is also regularly used in relation to mathematical functions, forms, and physical laws. In science, the term "approximation" can refer to using a less complex method or model when the proper one is challenging to use.
For this, sampling techniques like Markov chain Monte Carlo and significance sampling as well as variationally methods like mean-field approximations and assumed density filtering have been used.
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Find the length to the nearest whole number of the diagonal (hypotenuse) of a square with 30 cm on a side. Round answers to the nearest tenth if necessary. Your answer
Answers
Notice that we can draw a triangle in the square , and that the length of the square's diagonal is the same as the length of the triangle's hypotenuse. The triangle is a right triangle therefore it satisfies the Phytagorean Theorem. To calculate for it's hypotenuse , we will use:
[tex]c^2=a^2+b^2[/tex]where c is the hypotenuse, and a, b are the other legs of the triangle.
[tex]\begin{gathered} c^2=30^2+30^2 \\ c^2=1800 \\ c=\sqrt[]{1800} \\ c=42.43 \end{gathered}[/tex]Since the hypotenuse of the triangle is 42.43 cm. Therefore, the square's diagonal is also 42.43 cm
Answer:
The square's diagonal is 42.43 cm
2.3 I can apply the Pythagorean Theorem and Triangle Inequality.Which of the following could be lengths for a triangle?Show your work on a separate piece of paper.(Select all that apply.)5, 6, 9D 4,8, 127, 8, 17Are any of the selected triangles above right triangles?How do you know?Suami
Answers
For the triangle with sides 5, 6 and 9, you have:
5 + 6 > 9
5 + 9 > 6
9 + 6 > 9
9² ≠ 5² + 6²
≠ 25 + 36
≠ 61
Then, it is not a right triangle
For the triangle with sides 4, 8 and 12:
4 + 8 ≥ 12
in this case the triangle inequality is not present
12² ≠ 4² + 8²
Then, it is not a right triangle
For the triangle with sides 7, 8 and 17:
7 + 8 < 17
in this case the triangle inequality is not present
17² ≠ 8² + 7²
Then, it is not a right triangle
The coordinates of three vertices of a rectangle are (3,7), (-3,5), and (0,-4). What are the coordinates of the fourth vertex?A. (6,-2)B. (-2,6)C. (6,2)D. (-2,-6)
Answers
ANSWER
A. (6, -2)
EXPLANATION
Let's graph these three vertices,
The fourth vertex must be at the same distance from (0, -4) as vertex (3, 7) is from (-3, 5),
Note that the horizontal distance between these two points is 6 units and the vertical distance is 2 units. The fourth vertex is,
[tex](0+6,-4+2)=(6,-2)[/tex]Hence, the fourth vertex is (6, -2)
What are the domain and range of y = cot x? Select onechoice for domain and one for range.
Answers
ANSWER:
A. Domain: x ≠ n
D. Range: All real numbers
STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]y=\cot\left(x\right)[/tex]The domain of a function is the interval of input values, that is, the interval of x while the range is the interval of output values, that is, the interval of y.
In the cotangent function, x cannot take the value of radians (nor its multiples), since it is not defined, while the range is continuous on all real numbers.
That means the correct options are:
A. Domain: x ≠ n
D. Range: All real numbers
How do I get my answer?
Answers
Answer:
[tex] \frac{2}{9 {d}^{14} } [/tex]
Step-by-step explanation:
[tex] \frac{ {4d}^{ - 5} }{18 {d}^{9} } = \frac{4}{18} \times \frac{ {d}^{ - 5} }{ {d}^{9} } = \frac{2}{9} {d}^{ - 14} = \frac{2}{ {9d}^{14} } [/tex]
Which graph represents the function over the interval [−3, 3]?f(x)=⌊x⌋−2
Answers
Given:
[tex]f(x)=x-2\text{ ,\lbrack-3,3\rbrack}[/tex]Which family spends the largest dollar amount on transportation?Family AFamily BFamily C
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Which family spends the largest dollar amount on transportation?
a) Family A
b) Family B
c) Family C
Step 2:
The details of the solution are as follows:
a) Family A
Total income $ 5, 400
Amount spent on Transportation =
[tex]\begin{gathered} 11\text{ \% of \$ 5,400} \\ \frac{11}{100}\text{ x \$ 5, 400} \\ =\text{ }\frac{59400}{100} \\ =\text{ 594} \\ =\text{ \$ 594} \\ So,\text{ Family A spent \$ 594 on Transportation} \end{gathered}[/tex]b) Family B
Total income $ 4,675
Amount spent on Transportation =
+
[tex]\begin{gathered} 13\text{\% of \$ }4,675 \\ \frac{13}{100}\text{ x \$ }4,675 \\ =\text{ }\frac{60775}{100} \\ =607.75 \\ =\text{ }607.\text{ 75 dollars} \\ So,\text{ Family B spent \$ 607.75 on Transportation} \end{gathered}[/tex]c) Family C:
Total income $ 6,675
Amount spent on Transportation =
+
[tex]\begin{gathered} 9\text{\% of \$ }6,675 \\ \frac{9}{100}\text{ x \$ }6,675 \\ =\text{ }\frac{60,075}{100} \\ =600.75 \\ =\text{ }600.75\text{ dollars} \\ So,\text{ Family C spent \$ 600.75 on Transportation} \end{gathered}[/tex]CONCLUSION:
From the above analysis,
we can see that Family B spent the largest dollar amount on Transportation with the sum of $ 607. 75 ( which is 13% of $ 4,675)
f(x) = log 2(x+3) and g(x) = log 2(3x + 1).(a) Solve f(x) = 4. What point is on the graph of f?(b) Solve g(x) = 4. What point is on the graph of g?(c) Solve f(x) = g(x). Do the graphs off and g intersect? If so, where?(d) Solve (f+g)(x) = 7.(e) Solve (f-g)(x) = 3.
Answers
Given
[tex]\begin{gathered} f(x)=log_2(x+3) \\ and \\ g(x)=log_2(3x+1) \end{gathered}[/tex]a)
[tex]\begin{gathered} f(x)=4 \\ \Rightarrow log_2(x+3)=4 \\ \Leftrightarrow x+3=2^4 \\ \Rightarrow x+3=16 \\ \Rightarrow x=13 \end{gathered}[/tex]The answer to part a) is x=13. The point on the graph is (13,4)
b)
[tex]\begin{gathered} g(x)=4 \\ \Rightarrow log_2(3x+1)=4 \\ \Leftrightarrow3x+1=2^4 \\ \Rightarrow3x+1=16 \\ \Rightarrow3x=15 \\ \Rightarrow x=5 \end{gathered}[/tex]The answer to part b) is x=5, and the point on the graph is (5,4).
c)
[tex]\begin{gathered} f(x)=g(x) \\ \Rightarrow log_2(x+3)=log_2(3x+1) \\ \Rightarrow\frac{ln(x+3)}{ln(2)}=\frac{ln(3x+1)}{ln(2)}] \\ \Rightarrow ln(x+3)=ln(3x+1) \\ \Rightarrow x+3=3x+1 \\ \Rightarrow2x=2 \\ \Rightarrow x=1 \\ and \\ log_2(1+3)=log_2(4)=2 \end{gathered}[/tex]The answer to part c) is x=1 and graphs intersect at (1,2).
d)
[tex]\begin{gathered} (f+g)(x)=7 \\ \Rightarrow log_2(x+3)+log_2(3x+1)=7 \\ \Rightarrow log_2((x+3)(3x+1))=7 \\ \Leftrightarrow(x+3)(3x+1)=2^7 \\ \Rightarrow3x^2+10x+3=128 \\ \Rightarrow3x^2+10x-125=0 \end{gathered}[/tex]Solving the quadratic equation using the quadratic formula,
[tex]\begin{gathered} \Rightarrow x=\frac{-10\pm\sqrt{10^2-4*3*-125}}{3*2} \\ \Rightarrow x=-\frac{25}{3},5 \end{gathered}[/tex]However, notice that if x=-25/3,
[tex]log_2(x+3)=log_2(-\frac{25}{3}+3)=log_2(-\frac{16}{3})\rightarrow\text{ not a real number}[/tex]Therefore, x=-25/3 is not a valid answer.
The answer to part d) is x=5.
e)
[tex]\begin{gathered} log_2(x+3)-log_2(3x+1)=3 \\ log_2(\frac{x+3}{3x+1})=3 \\ \Leftrightarrow\frac{x+3}{3x+1}=2^3=8 \\ \Rightarrow x+3=24x+8 \\ \Rightarrow23x=-5 \\ \Rightarrow x=-\frac{5}{23} \end{gathered}[/tex]The answer to part e) is x=-5/23
If the time to climb the mountain took an hour more than the time to hike down how long was entire hike?
Answers
4.8 mi
Explanation
[tex]\text{time}=\text{ }\frac{\text{distance}}{\text{rate}}[/tex]
Step 1
Set the equations
a) uphill
let
rate1= 1.5 miles per hour
time= unknow= t1
distance = x
b) down hille
rate=4 miles per hour
time=time2=one hour less than the time to climb = t1-1
distance = x
so
replacing
[tex]\begin{gathered} t_1=\frac{x}{1.5\frac{mi}{\text{hour}}}\rightarrow t_1=\frac{x}{1.5}\rightarrow equation(1) \\ t_2=\frac{x}{4\frac{mi}{\text{hour}}} \\ \text{replace t}_2=t_1-1 \\ t_1-1=\frac{x}{4} \\ \text{add 1 in both sides} \\ t_1-1+1=\frac{x}{4}+1 \\ t_1=\frac{x}{4}+1\rightarrow equation(2) \end{gathered}[/tex]Step 2
solve the equations
[tex]\begin{gathered} t_1=\frac{x}{1.5}\rightarrow equation(1) \\ t_1=\frac{x}{4}+1\rightarrow equation(2) \end{gathered}[/tex]set t1= t1
[tex]\begin{gathered} t_1=t_1 \\ \frac{x}{1.5}=\frac{x}{4}+1 \\ \frac{x}{1.5}=\frac{x+4}{4} \\ 4x=(x+4)1.5 \\ 4x=1.5x+6 \\ subtract\text{ 1.5 x in both sides} \\ 4x-1.5x=1.5x+6-1.5x \\ 2.5x=6 \\ \text{divide both sides by 2.5} \\ \frac{2.5x}{2.5}=\frac{6}{2.5} \\ x=2.4 \end{gathered}[/tex]it means the distance to the top of the mountain is 2.4 miles, so the entire hike is twice that amount
total distance=2.4 mi*2
total distance=4.8 miles
Step 3
now, the times
[tex]\begin{gathered} t_1=\frac{x}{1.5} \\ t_1=\frac{2.4}{1.5} \\ t_1=1.6\text{ hours} \\ t_2=t_1-1 \\ t_2=1.6-1=\text{ 0.6 hours} \end{gathered}[/tex]table
I hope this helps you
8You are asked to draw a triangle withside lengths of 10 inches, 7 inches, and2 inches. How many triangles like thiscan you draw?A. OneB. ThreeC. TwoD. Zero
Answers
ANSWER
D. Zero
EXPLANATION
The triangle inequality states that the sum of any two sides of a triangle is greater than the third side,
All these inequalities must be true to be able to form a triangle with the given sides,
[tex]\begin{gathered} 7+10>2\Rightarrow17>2\Rightarrow true \\ 2+10>7\Rightarrow12>7\Rightarrow true \\ 7+2>10\Rightarrow9>10\Rightarrow false \end{gathered}[/tex]Hence, no triangle can be formed with these side lengths.
Find the lateral surface area of thiscylinder. Round to the nearest tenth.8ft4ftLSA = [ ? ] ft2—
Answers
Solution
Step 1:
Write the lateral surface area or curved surface area of a cylinder:
[tex]Lateral\text{ surface area = 2}\pi rh[/tex]Step 2:
Write the given data
Height h = 8ft
Radius r = 4 ft
Step 3:
Substitute in the formula to find the lateral surface area.
[tex]\begin{gathered} Lateral\text{ surface area = 2}\pi rh \\ =\text{ 2 }\times\text{ 3.142 }\times\text{ 4 }\times\text{ 8} \\ =\text{ 201.1 ft}^2 \end{gathered}[/tex]Final answer
201.1
Answer A= f(x)>0 on the interval x <0 Answer B=f(x)>0 on the interval x<0 Answer C=is f(x)<0 on the interval 00 on the interval 00 on the interval 1
Answers
EXPLANATION
Given the function f(x)= -x ²+4x - 3, the statements that apply are:
A) TRUE
B) FALSE
C) TRUE
D) FALSE
E) FALSE
F) TRUE
G) TRUE
H) FALSE
Determine the value of each limit for the function below.f(x)=x/(x-2)^2(a) lim f(x). (b) lim f(x)x---2^-. x---2^+
Answers
We will have the following:
a)
[tex]\lim _{x\rightarrow2^-}\frac{x}{(x-2)^2}=\infty[/tex]b)
[tex]\lim _{x\rightarrow2^+}\frac{x}{(x-2)^2}=\infty[/tex]In ATUV, the measure of ZV=90°, TV = 28, UT = 53, and VU = 45. What ratiorepresents the cosecant of ZU?
Answers
cosecant = hypotenuse / opposite side
hypotenuse = 53
opposite side = 28
cosecant U = 53/28
Miscavage Corporation has two divisions: the Beta Division and the Alpha Division.
The Beta Division has:
sales of $320,000,
variable expenses of $158,100,
and traceable fixed expenses of $72,300.
The Alpha Division has:
sales of $630,000,
variable expenses of $343,800,
and traceable fixed expenses of $135,100.
The total amount of common fixed expenses not traceable to the individual divisions is $137,200.
What is the total company's net operating income?
Answers
The total net operating income (NOI) of both divisions is $1,03,500.
What is net operating income?Real estate professionals use the formula known as Net Operating Income, or NOI, to quickly determine the profitability of a specific investment. After deducting required operating costs, NOI calculates the revenue and profitability of investment real estate property. Let's say, for illustration purposes, that you own a duplex with a gross monthly income of $2,000 and monthly operating expenses of $400. You would start with your annual gross income ($24,000) and deduct your operating expenses ($4,800) to arrive at your net operating income.So, the total net operating income:
The formula for net operating income: NOI = Gross Income - Operating ExpensesNow, substitute the values and get the NOI as follows:
NOI = Gross Income - Operating ExpensesNOI = (Sales+Sales) - [(variable expenses + variable expenses) + (fixed expenses + fixed expenses) + 137,200] NOI = (320,000+630,000) - [(158,100 + 343,800) + (72,300 + 135,100) + 137,200]NOI = 9,50,000 - (5,01,900 + 2,07,400 + 137,200)NOI = 9,50,000 - 8,46,500NOI = 1,03,500Therefore, the total net operating income (NOI) of both divisions is $1,03,500.
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WhichIs 9.56556555... a rational or irrationalnumber? Highlight the correct answer below.181a)Whicha) Rational numberb) Irrational numberthat ap
Answers
Answer
Option B is correct.
9.56556555... is an irrational number.
Step-by-step Explanation
Rational numbers are numbers that can be expressed as a clear fraction consisting of the numerator and the denominator both being integers.
The decimal form or decimal expansion of a rational number terminates after a particular/finite number of digits (e.g., 0.25, 0.762 etc.) or begins to repeat/recur the same sequence over and over again (e.g., 0.333..., 0.267267... etc)
Anything other than these two rules, the number is regarded as an irrational number.
The number given is 9.56556555...
The dots indicate thst the numbers after the decimal point conbtinue till eternity.
Observing the numbers after the decimal point for the given number, one can see that 565 repeats once and then the number after the second 565 is 55, indicating that the 565 doesn't recur till infinity.
Since the numbers after the decimal point doesnt contain a finite number of digits and the numbers don't recur till infinity, we can conclude that 9.56556555... isn't a rational number.
Hope this Helps!!!
Two students measured a box in class. They used a digital scale and found that the mass was 400 grams. They then measured the box found the length is 2cm, the width is 2cm, and the height is 1cm. What is the density of the object
Answers
Explanation
Step 1
the density of an object is given by:
[tex]\begin{gathered} density=\frac{mass_{object}}{volume_{object}} \\ \end{gathered}[/tex]Let
mass: 400 grams
length's box=2 cm
width´s box= 2 cm
height's box= 1 cm
Step 2
find the volume of the box
[tex]\begin{gathered} \text{Volume}=\text{ length}\cdot width\cdot height \\ \text{replacing} \\ \text{Volume= 2 cm }\cdot\text{ 2 cm }\cdot\text{ 1 cm} \\ \text{Volume}=\text{ 4 cubic cm} \end{gathered}[/tex]Step 3
finally, replace the values of mass and volume in the density equation
[tex]\begin{gathered} density=\frac{mass_{object}}{volume_{object}} \\ density=\frac{400\text{ grm}}{4cm^3} \\ \text{density}=100\frac{gr}{cm^3} \end{gathered}[/tex]I hope this helps you
I need this done in 20 minutes please and thank you
Answers
An isosceles triangle in the one that has 2 equal sides, means that it also has two equal angles
this means that:
[tex]\begin{gathered} ifJK=KL \\ \text{then,}\measuredangle KJL=\measuredangle KLJ \\ \end{gathered}[/tex]using the properties of the triangle
[tex]\begin{gathered} \measuredangle KJL+\measuredangle KLJ+\measuredangle JKL=180 \\ 2\cdot\measuredangle KLJ+\measuredangle JKL=180 \\ 2\cdot34+\measuredangle JKL=180 \\ \measuredangle JKL=180-68 \\ \measuredangle JKL=112 \end{gathered}[/tex]5. 8.G.1.5 Right triangle ABC and right triangle ACD overlap as shown below. Angle DAC measures 20° and angle BCA measures 30°. B D to 20- A 30° C not drawn to scale What are the values of and y?
Answers
In any triangle, the sum of the internal angle is always up to 180º.
Then, for triangle ABC:
[tex]90º+30º+(x+20º)=180º[/tex]Use it to solve x:
[tex]\begin{gathered} 90º+30º+x+20º=180º \\ x=180º-90º-30º-20º \\ x=40º \end{gathered}[/tex]In the triangle ACD:
[tex]90º+20º+(y+30º)=180º[/tex]Use it to solve y:
[tex]\begin{gathered} 90º+20º+y+30º=180º \\ y=180º-90º-20º-30º \\ y=40º \end{gathered}[/tex]Then, the value for x is 40º and the value for y is also 40ºLawn20 meters-WalkwayGazeboRHQ15 metersA bag of grass seed costs $64.26. If agardener wants to calculate the costofgrass seed required to plant the lawn,what additional information wouldhe need to know?A the location of the walkwayBthe perimeter of the lawnс the weight of one bag of grass seedD the area that can be covered byone bag of seed
Answers
He needs option D. Because the perimeter is not the total area (it is only the distance in meters/centimeters that surround the lawn, we need to know how much area a bag of grass seeds covers, for us to know how many to buy. Also, we need the area of the walkway, since it is not covered by grass
The area of a triangle is:
[tex]Area\text{ = }\frac{b(h)}{2}[/tex]But, since there is a walkway that isn't covered in grass, we need to subtract the circle area from the triangle area
Area of circle:
[tex]Area\text{ = }\pi r^2[/tex]Then the total area of the lawn :
[tex]Area\text{ Lawn = }\frac{b(h)}{2}\text{ - \lparen}\pi r^2)[/tex]