The diagram below shows the dimensions of a triangular park built in a new housing development. Two side lengths and one angle measure are given.
What is the measure of angle X? Round the answer to the nearest tenth.
Answers
[tex]x = 50.5 \degree[/tex]
EXPLANATION
We use the sine rule for solving triangles.
This is given by the formula,
[tex] \frac{ \sin(A) }{a} = \frac{ \sin(B) }{b} = \frac{ \sin(C) }{c} [/tex]
From the triangle,
[tex] \frac{ \sin(x) }{60} = \frac{ \sin(40) }{50} [/tex]
We multiply both sides of the equation by 60 to get,
[tex] sin(x) = \frac{ 60\sin(40 \degree) }{50} [/tex]
[tex] sin(x) = 0.7713[/tex]
We solve for x to obtain,
[tex] x = arcsin(0.7713)[/tex]
[tex] x = 50.475[/tex]
To the nearest tenth, we round to one decimal place to get,
[tex] x = 50.5 \degree[/tex]
Related Questions
Find the equation, (f(x) = a(x-h)2+ k), for a parabola containing point (-1,0) and having (-3, 4) as a vertex. What is the standard form of the equation?
Answers
Which of the binomials below is a factor of this trinomial? 5x2 + 20x + 15
Answers
5 x^2 + 20 x + 15
Factor 5 out of 5 x^2 + 20 x + 15:
5 (x^2 + 4 x + 3)
The factors of 3 that sum to 4 are 3 and 1. So, x^2 + 4 x + 3 = (x + 3) (x + 1):
Answer: 5 (x + 3) (x + 1)
factor X + 1 is the answer
What is the scale factor when △RST is dilated to △R'S'T'? What is the value of x?
A. Scale factor 0.75, x = 8
B. Scale factor 0.75, x = 4.5
C. Scale factor 1.3, x = 8
D. Scale factor 1.3, x = 4.5
Answers
x = 6* 6 / 4.5
x = 36/4.5
x = 8
SF = 4.5 / 6 = 0.75
answer
A. Scale factor 0.75, x = 8
Can someone graph these 2 equations for me??
y=5(1/2)^x +4
y=4(1/6)^(x+2)
Answers
Given the geometric sequence where a1 = 2 and r = √2 find a9
32
32√2
256
256√2
Answers
a9= 2*V2^8=2*2^4=2^5
⇒ a9 = 32
Answer: First option is correct.
Step-by-step explanation:
Since we have given that
There is a geometric sequence:
where a₁ = 2
r = √2
We need to find a₉:
As we know the formula for "nth term ":
[tex]a_n=ar^{n-1}\\\\a_9=ar^{9-1}\\\\a_9=ar^8\\\\a_9=2\times (\sqrt{2})^8\\\\a_9=32[/tex]
Hence, First option is correct.
helppppppppppppppppppppppppppppppppppp
Answers
Inverse property of multiplication
Explanation:
The inverse property of multiplication means that each terms undoes the function of the other. The main purpose of the inverse property in multiplication is to obtain 1.
In the given:
17/3 * 3/17
We will find that the 17 in the numerator is cancelled with the 17 in the denominator and the 3 in the numerator is cancelled with the 3 in the denominator.
Therefore, the final answer is 1.
Hope this helps :)
Please helpppp now 99 points
The table below represents a linear function f(x) and the equation represents a function g(x):
x f(x)
−1 −15
0 −10
1 −5
g(x)
g(x) = 2x + 8
Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x). (6 points)
Part B: Which function has a greater y-intercept? Justify your answer. (4 points)
Answers
In order to find the slope of [tex]f(x)[/tex] we can use the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
So, using first two pairs from the given table we have:
[tex]m=\frac{-10-(-15)}{0-(-1)}=\frac{-10+15}{1}=\frac{5}{1}=5[/tex]
Every linear function has the following general look:
[tex]y=mx+b[/tex], where [tex]m[/tex] is the slope of the function.
Applying that general look to our function [tex]g(x)[/tex] we see that it's slope equals 2.
So, we can say that value of [tex]f(x)[/tex] is growing two and half more times faster then value of [tex]g(x)[/tex] as their slopes' ratio is 5:2.
Part B:
The y-intercept of function is it's value in case x is equal 0.
Using the given table we find that the y-intercept of [tex]f(x)=-10[/tex]
As for [tex]g(x)[/tex], let's substitute x value with 0 and solve the equation:
[tex]g(x)=2\cdot0+8=8[/tex]
So, the function [tex]g(x)[/tex] has greater y-intercept then function [tex]f(x)[/tex].
PLEASE FULL ANSWERS! need all the help I can get
Answers
You need a value at x = 2 that makes 4x = 8
2 equations, 2 unknowns. This think has to have an answer.
cx^2 + d = 2 when x = 1
c(1)^2 + d = 2
c + d = 2
cx^2 + d = 8 when x = 2
4c + d = 8
c + d = 2 Subtract
3c = 6
c = 2
Now go back and solve for d
c + d = 2
d = 0
==========
That should make it continuous at every point.
You should take note that h(x) has a problem at x = 2. The graph is well behaved at less than x =2 and it is well behaved at x > 2. It is just x = 2 that's the double ugly part of the problem. Check your givens above to make sure you understand what I'm saying. If you don't give me a shout.
PLEASE HELP!! FIRST CORRECT ANSWER GETS BRAINLIEST!!
Answers
∠RQW and ∠TQU are vertical angles
∠RQS and ∠UQV are vertical angles
and so on
B should be your answer
hope this helps
What is the measure in radians for the central angle of a circle whose radius is 8 cm and intercepted arc length is 5.6 cm? Enter your answer as a decimal in the box.
Answers
central angle theta (in radians) = arc length / radius
So theta = 5.6/8 = 0.7 radians
The central angle measure for a circle with an 8 cm radius and a 5.6 cm intercepted arc length is 0.7 radians.
The question asks to find the measure in radians for the central angle of a circle with a radius of 8 cm and an intercepted arc length of 5.6 cm. To calculate the central angle in radians, we use the formula θ = [tex]\frac{l}{r}[/tex], where θ is the central angle in radians, l is the arc length, and r is the radius of the circle. Substituting the given values, we get θ = [tex]\frac{5.6}{8}[/tex]
Through calculation, θ = 0.7 radians. So, the measure of the central angle that intercepts an arc length of 5.6 cm in a circle with a radius of 8 cm is 0.7 radians.
Jerry's beginning balance in his checkbook was $457.56. He made deposits of $20, $80, and $165 and wrote checks for $216.58. His bank charge was $3.50. What was his ending balance for the month? a. $552.10 b. $505.98 c. $722.56 d. $502.48
Answers
First, when Jimmy make deposits, he should add the amount of the deposits from the amount he has in the bank.
Second, when Jimmy write checks, he should deduct the amount of the checks from the amount he has in the bank.
And third, he should also deduct any bank charges from the amount he has in the bank.
From the question we know that Jimmy made deposits of $20, $80, and $165, so he should add those amounts to the money he has in the bank:
[tex]Balance=457.56+20+80+165[/tex]
[tex]Balance=722.56[/tex]
We also know that he wrote checks for $216.58, so he should subtract the amount from the balance:
[tex]Balance=722.56-216.58[/tex]
[tex]Balance=505.98[/tex]
Last but not least, the bank charged Jimmy $3.50, so we should subtract that amount from the balance too:
[tex]Balance=505.98-3.50[/tex]
[tex]Balance=502.48[/tex]
Notice that you can also add/subtract all the deposits, checks, and bank charges all at once:
[tex]Balance=457.56+20+80+165-216.58-3.50[/tex]
[tex]Balance=502.48[/tex]
Either way we can conclude that his ending balance for the month was $502.48; therefore, d is the correct answer.
The radius of the base of a cylinder is 10 centimeters, and its height is 20 centimeters. A cone is used to fill the cylinder with water. The radius of the cone's base is 5 centimeters, and its height is 10 centimeters. The number of times one needs to use the completely filled cone to completely fill the cylinder with water is ?
Answers
Solution:
Let volume of cylinder be K times more than volume of Cone.
⇒K × Volume of Cone = Volume of Cylinder
[tex]K \times \frac{\pi\times r^2 \times h }{3}=\pi \times R^2 \times H\\\\K \times 5^2 \times 10= 3 \times 10^2 \times 20\\\\250 K=3 \times 100 \times 20\\\\K=\frac{6000}{250}\\\\K=24[/tex]
⇒Number of times one needs to use the completely fill cone to completely fill the cylinder with water is=24
how do I get from step 3 to step four? please explain.
sin x = opposite over hypotenuse
sin 45° = 50 over x
0.707106781 ≈ 50 over x
(0.707106781)x ≈ 50
x ≈ 70.71
Answers
Hope this helped :*
Jordan needs 6 3/10 gallons of milk to make 4 1/2 gallons of ice cream. How many gallons of milk will jordan need to make one gallon of ice cream
Answers
you may need to round it if necessary
hope this helps :)
Answer:
[tex]1\frac{2}{5}[/tex] gallon of milk is needed to make one gallon of ice cream
Step-by-step explanation:
Using unitary method,
Unitary method is a method use to find the value of a unit quantity.
[tex]6\frac{3} {10}[/tex] gallon of milk needed to make [tex]4\frac{1}{2}[/tex] gallon of milk
[tex]\frac{63}{10}[/tex] gallon of milk needed to make [tex]\frac{9}{2}[/tex] gallon of ice cream
One gallon of ice cream needed = [tex]\frac{63}{10} \times \frac{2}{9}[/tex] gallon of milk
= [tex]\frac{7}{5}[/tex] gallon of milk
= [tex]1\frac{2}{5}[/tex] gallon of milk
Thus, [tex]1\frac{2}{5}[/tex] gallon of milk is needed to make one gallon of ice cream.
PLEASE!!!!!!!!!!!!!HURRY!!!!!!!!!!!!!!!!!!!!!!!20 points!!!!!!!!!!!!!!!!!!!!!!1
A group of children are asked whether they prefer vanilla or chocolate ice cream. The data are collected in the table.
Answers
You want to buy an item that costs $100. Which of these is the most cost-effective choice for buying the item?
answers :
a.using a paid membership card to buy it at a 10 percent discount
b.buying it online at a 10 percent discount with a $5 shipping charge
c.buying it at a 10 percent discount without sales tax
Answers
Elizabeth rode her bike 6 1/2 miles from her house to the library and then another 2 2/5 miles to her friend Milo's house. If Carson's house is 2 1/2 miles beyond Milo's house, how far would she travel from her house to Carson's house?
Answers
Answer:
Step-by-step explanation:
11.4
According to these three facts, which statements are true? - Circle D has center (2, 3) and radius 7. - Circle F is a translation of circle D, 2 units right. - Circle F is a dilation of circle D with a scale factor of 2.
A) Circle F and circle D are similar.
B) The center of circle F is (0, 3).
C) The radius of circle F is 28.
D) Circle F and circle D are congruent.
(Again, you can choose more than one option.)
Answers
In this parallelogram m angle bad =75 so m angle bcd
Answers
we know that
m angle bad =75°
remember that on parallelogram
(∠A + ∠B) = 180°
[Since, sum of the interior angles on the same side of the transversal is 180°]
therefore
∠B=180°-∠A=180°-75°=105°
∠B=105°
Similarly
∠B + ∠C = 180°
∠C + ∠D = 180°
and ∠D + ∠A = 180°
Thus, the sum of any two adjacent angles of a parallelogram is 180°.
m angle bcd=∠C=180-∠B=180°-105°=75°
the answer is m angle bcd=75°
Brenda invests $4,848 in a savings account with a fixed annual interest rate of 5% compounded 2 times per year. What will the account balance be after 6 years?
Answers
She invests some amount in a saving account of fixed interest compounded half-yearly. It says to find its Future Value after six years.
The principal amount is P = $4,848.
Annual interest rate is 5% i.e. r = 0.05
Compounding period is two times per year i.e. n = 2.
Time of investment is t = 6 years.
We know the formula of Future Value is given by :-
[tex] FV=P*(1+\frac{r}{n})^{nt} [/tex]
We can plug the given values in the formula to calculate the answer.
[tex] FV = 4848*(1+\frac{0.05}{2})^{(2*6)} \\\\
FV = 4848*(1+0.025)^{(12)} \\\\
FV = 4848*(1.025)^{(12)} \\\\
FV = 4848*(1.344888) \\\\
FV = 6520.02102 [/tex]
Hence, future value of investment after six years is 6,520.02 dollars.
The question involves calculation of compound interest. The formula to use is A = P (1 + r/n)^(nt), where P is the principal amount, r is the annual interest rate, t is the time in years, n is the number of times interest is compounded per year and A is the amount of money accumulated after n years.
Explanation:This question involves the concept of compound interest. Compound interest is calculated each period on the original deposit, or principal, along with any interest previously earned. Unlike simple interest which only takes into account the principal amount, compound interest accounts for the interest that accumulates on the initial amount as well as the interest that has previously been added.
In Brenda's case, as she's benefiting from compounded interest, the formula to use here is A = P (1 + r/n)^(nt), where P is the principal amount, r is the annual interest rate, t is the time in years, n is the number of times interest is compounded per year and A is the amount of money accumulated after n years.
So, plug in the given values: P=$4848, r=0.05 (as 5% = 5/100), t=6, and n=2 (since it's compounded semi-annually). This will allow us to find the final account balance after 6 years.
Learn more about Compound Interest here:https://brainly.com/question/14295570
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The population of a local species of dragon fly can be found using an infinite geometric series where a1=36 and the common ratio is 1/2 write the sum in sigma notation and calculate the sum that will be the upper limit of this population
Answers
[tex]a_0=72\\ a_1=72* \dfrac{1}{2}=36 \\ ...\\ a_i=72* \dfrac{1}{2^i} \\\\ \lim_{n \to \infty} \sum_{i=0}^{\infty}\ a_i = \lim_{n \to \infty}72* \sum_{i=0}^{\infty}\ \dfrac{1}{2^i} \\\\ =72* \lim_{n \to \infty} \dfrac{1-\frac{1}{2^{n+1}}}{1-\frac{1}{2}} \\\\ =72*2=144 [/tex]
How many ways can 6 students desks be arranged in a row permutation or combination?
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= 6*5*4*3*2*1 = 720
The area of a rectangle is 56 cm. The length is 2 cm more than x and the width is 5 cm less than twice x. solve for x. Round to the nearest whole number.
Answers
Answer: The answer is actually 6.
Step-by-step explanation:
The value of x is 6, rounded to the nearest whole number.
To solve for x given the conditions:
1. Define the variables based on the problem:
- Length of the rectangle [tex](\( L \)) = \( x + 2 \)[/tex]
- Width of the rectangle [tex](\( W \)) = \( 2x - 5 \)[/tex]
2. Write the equation for the area of the rectangle:
- Area [tex](\( A \)) = \( L \times W \)[/tex]
- Given that the area is 56 cm², we have:
[tex]\[ (x + 2)(2x - 5) = 56 \][/tex]
3. Expand the equation:
[tex]\[ (x + 2)(2x - 5) = 2x^2 - 5x + 4x - 10 = 2x^2 - x - 10 \][/tex]
4. Set up the equation:
[tex]\[ 2x^2 - x - 10 = 56 \][/tex]
5. Move all terms to one side of the equation to set it to zero:
[tex]\[ 2x^2 - x - 10 - 56 = 0 \] \[ 2x^2 - x - 66 = 0 \][/tex]
6. Solve the quadratic equation using the quadratic formula:
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]\\ where \( a = 2 \), \( b = -1 \), and \( c = -66 \).[/tex]
7. Calculate the discriminant:
[tex]\[ \Delta = b^2 - 4ac = (-1)^2 - 4(2)(-66) = 1 + 528 = 529 \][/tex]
8. Calculate the roots:
[tex]\[ x = \frac{-(-1) \pm \sqrt{529}}{2(2)} = \frac{1 \pm 23}{4} \][/tex]
So, the solutions are:
[tex]\[ x = \frac{1 + 23}{4} = \frac{24}{4} = 6 \][/tex]
and
[tex]\[ x = \frac{1 - 23}{4} = \frac{-22}{4} = -5.5 \][/tex]
Since x must be a positive value in the context of this problem, we have: x = 6
9. Verify the solution:
Length L = x + 2 = 6 + 2 = 8 cm
Width W = 2x - 5 = 2(6) - 5 = 12 - 5 = 7 cm
Area = [tex]\( 8 \times 7 = 56 \)[/tex] cm², which matches the given area.
Therefore, ( x = 6).
What is the Value of X? Sin(x+22 degree) = Cos( 2x-7 degree) I might have a idea of what it is but I’m not sure
Answers
Hey !!
Check the attachment.
Hope it helps you :)
The value of x in the equation Sin(x+22 degrees) = Cos(2x-7 degrees) can be found by using the identity sin(90° - x) = cos(x), leading to x = 22.67° (or in radians by converting degrees to radians).
To find the value of x in the equation Sin(x+22 degrees) = Cos(2x-7 degrees), we can utilize the trigonometric identity sin(90° - x) = cos(x). By setting the angle inside the cosine to equal 90° - (x + 22°), we can equate this to (2x - 7°) as both represent the same cosine value.
So we have the equation 90° - (x + 22°) = 2x - 7°. Solving for x, we combine like terms: 68° = 3x, which then gives us x = 68°/3. Therefore, x = 22.67°, which is the angle in degrees.
If we needed to find x in radians, we would have to convert degrees to radians by using the conversion factor: π radians = 180°. This would yield x as x = (22.67°/180°) * π.
Need help ASAP
Which statements are true? Select each correct answer.
40m^6−4=4(10m^6−1)
6m^2+18m=6m^2(1+3m)
32m^4+12m^3=4m^3(8m+3)
15m^3−6m=3m(5m^2−6m)
Answers
The networking organization you joined is throwing a party. You are in charge of buying the chips, which cost two dollars and fifty cents per bag and salsa, which costs four dollars per jar. The chips & salsa budget you are given totals $60. The inequality 2.5x + 4y 60 represents the possible combinations of chips (x) and salsa (y) you can buy. graph of the inequality 2.5 x plus 4 y is less than or equal to 60 Which of the following does not represent a solution to the inequality?
Answers
Explanation:
These are the propositions missed:
10 bags of chips and 2 jars of salsa
20 bags of chips and 2 jars of salsa
14 bags of chips and 5 jars of salsa
18 bags of chips and 6 jars of salsa
Solution:
The inequality that you have to graph is:
2.5x + 4y ≤ 60
To graph that you:
1) draw the line 2.5x + 4y = 60
That is the same that:
4y = -2.5x - 60
y = - (2.5/4)x - 60/4
y = -0.625x - 15
That is a line with y-intercept 15 and x-intercpet 15/0.625 = 24.
So, use those two points (0,15) and (24,0) to draw the line.
The sign ≤ implies that the region of solution is below the line (of course in the first quadrant, because x ≥ 0 and y ≥ 0).
The pair (18,6) is not inside the region (it is aboe the line).
You can prove it:
2.5(18) + 4 (6) = 45 + 24 = 69 which is greater than 60, and so it does not fit into the inequality. This is, the money to spend on 18 bags of chips and 6 jars of salsa exceeds the budget of $60. That is why that option is not a solution.
In a rectangle, a diagonal forms a 36° angle with a side. Find the measure of the angle between the diagonals, which lies opposite to a shorter side.
Answers
Answer:
The answer is 72 degrees
Step-by-step explanation:
The picture that Helpmetnx showed does work. But they made a mistake and assumed that the diagonal is a angle bisector, and it's not.
1. rectangle ABCD, BD & AC are the diagonals. ∠ABD =36 degrees
2. ∠ABD= ∠BDC = 36 - alternate interior angles
3. ∠DBC = 90 - 36 = 54. ∠DBC =∠ADB = ∠BCA = 54
4. Now we know that the triangle formed between the two diagonals is a isosceles triangle because of base angle theorem.
5. 180 - 54*2 = 72 degrees
I hope this helps!
Simplify the expression. 3–9 • 36 • 36
Answers
To simplify expressions, one needs to apply rules correctly, such as combining like terms and using exponentiation rules. The process includes correctly applying the rule that simplifies multiplications of the same base by adding their exponents. Cubing exponentials involves multiplying the original exponent by 3.
Explanation:To simplify mathematical expressions, it's crucial to follow the correct rules and operations. In this case, the example provided shows the exponentiation and multiplication rules. Specifically, when dealing with expressions like 3².3⁵, this is equivalent to multiplying 3 x 3 and then taking that result and multiplying it by 3 five more times. According to the rule xPx9 = x(p+q), where x is the base and p and q are the exponents, it simplifies to adding the exponents when the base number is the same and multiplied together.
The process of simplifying expressions involves several steps:
Identifying like terms and combining them.Applying the rules of exponents correctly.Dividing or multiplying to simplify equations as demonstrated with loop equations, dividing by a constant to simplify the equation.Additionally, when cubing exponentials, one should cube the digit normally and multiply the existing exponent by 3, a rule demonstrated in squaring operations as well.
The municipality of Waterloo needs $915,000 from property tax to meet its budget. The total value of
assessed property in Waterloo is $14,000,000. What is the tax rate per dollar? (Round your answer to the
nearest thousandth.)
A. $.07
B. $.065
C. $.0655
D. $.071
Answers
If h(x) = 6 - x, what is the value of ( h o h)(10)?
Answers
Although if x=10 then 6-10=-4.