X, Y and Z form the vertices of a triangle with area 59.7cm2. If XZ = 21.5cm and XY = 13.5cm, work out the acute angle ∠YXZ. Round to 1 DP.
Answers
Answer: The acute angle ∠YXZ = 24.3°.
Step-by-step explanation:
If in triangle ABC, C is the angle included between sides a and b then
Area of triangle = [tex]\dfrac12a\cdot b\cdot sin C[/tex]
here, XZ = 21.5cm and XY = 13.5cm are sides that includes acute angle ∠YXZ..
Area of a triangle = 59.7cm²
then, as per given, we have
[tex]59.7=\dfrac12(21.5)(13.5)\ \sin X\\\\\Rightarrow\ 59.7=145.125\ \sin X\\\\\Rightarrow\ \sin X = \dfrac{59.7}{145.125}\\\\\Rightarrow\ \sin X =0.41137\\\\\Rightarrow\ X = \sin ^{-1}(0.41137)\approx24.3^{\circ}[/tex]
Hence, the acute angle ∠YXZ = 24.3°.
Related Questions
A and B together complete a work in 20days. They worked together for 5days and B leaves. How long will A takes to finish the remaining work if A alone can finish the work 36days.
Answers
Answer:
27 days
Step-by-step explanation:
A alone, rate per day = 1/36
A and B together, rate per day = 1 / 20
Total Workdone for 5 days :
1/ 20 * 5 = 5 / 20 = 1/4
Fraction of work left :
1 - 1/4 = 3/4
3 / 4 * 36 /1
= (3 * 36) / 4
= 108 / 4
= 27 days
Melanie earns $7.40 per hour working at a grocery store. She works 14.25 hours this week. How much does she earn this week?
Answers
Answer:
$105.45
Step-by-step explanation:
$7.40 x 14.25 = $105.45
She earns $105.45 after working for 14.25 hours.
Albert mixes 10 grams of 15% sugar and 25 grams of 10% sugar syrup. How many grams of sugar does the mixture contain?
Answers
Answer:
4 grams
Step-by-step explanation:
Find how many grams of sugar are in each mixture:
10(0.15)
= 1.5
25(0.1)
= 2.5
Add these together:
1.5 + 2.5 = 4
So, the mixture contains 4 grams of sugar
Someone please explain how to get the answers
Answers
Answer:
[tex] m\angle A =40\degree [/tex]
[tex] m\angle D =40\degree [/tex]
Step-by-step explanation:
By inscribed angle theorem:
[tex] m\angle A = \frac{1}{2} \times 80\degree [/tex]
[tex] m\angle A =40\degree [/tex]
[tex] m\angle D= \frac{1}{2} \times 80\degree [/tex]
[tex] m\angle D =40\degree [/tex]
Last year, Michael opened an investment account with $5400. At the end of the year, the amount in the account had decreased by 23.5%. How much is this
decrease in dollars? How much money was in his account at the end of last year
Answers
Proving trapezoid theorems Geometry
Answers
Answer:
ΔABD ≅ ΔACD by SAS, therefore;
[tex]\overline {BD} \cong \overline {CA}[/tex] by CPCTC
Step-by-step explanation:
The two column proof is presented as follows;
Statement [tex]{}[/tex] Reason
ABCD is a trapezoid [tex]{}[/tex] Given
[tex]\overline {BA} \cong \overline {CD}[/tex] [tex]{}[/tex] Given
[tex]\overline {BC} \parallel \overline {AD}[/tex] [tex]{}[/tex] Definition of a trapezoid
ABCD is an isosceles trapezoid [tex]{}[/tex] Left and right leg are equal
∠BAD ≅ ∠CDA [tex]{}[/tex] Base angle of an isosceles trapezoid are congruent
[tex]\overline {AD} \cong \overline {AD}[/tex] [tex]{}[/tex] Reflexive property
ΔABD ≅ ΔACD [tex]{}[/tex] By SAS rule of congruency
[tex]\overline {BD} \cong \overline {CA}[/tex] [tex]{}[/tex] CPCTC
CPCTC; Congruent Parts of Congruent Triangles are Congruent
SAS; Side Angle Side rule of congruency
Answer:
Step-by-step explanation:
just did it
Find the area of the circle. Use 3.14 or 22/7 for pi. Round your answer to the nearest hundredth, if necessary.
Answers
Step-by-step explanation:
Given
diameter (d) = 9 ft
radius (r) = 9/2 = 4.5 ft
Area of the circle
= πr²
= 3.14 * ( 4.5) ²
= 3.14 * 20.25
= 63.585
= 63.59 ft
Hope it will help :)
can someone please help me, i have to turn this in soon.
Answers
4x - (-6) what’s the answer
Answers
Answer:
4x + 6
Step-by-step explanation:
If i remember correctly, two minuses make a positive, so -(-6) would turn into +6. I dont think that you can add a number with a variable to a regualar number so the answer is as simplified as it can get. If that one is wrong, try 10x. Hope this helps!
Another math problem
Answers
Answer:
sorry no se la respuesta
What is an equation of the line that passes through the points (4,-4) and (-4,-4)
Answers
Answer:
Step-by-step explanation:
Use the formula x-x1/x1-x2 = y-y1/y1-y2
can someone please help? i’ll mark brainliest!!
Answers
Answer:
z+5 z+2 Z i think
Step-by-step explanation:
the lenght is longer to shorter
Answer:
angle # > angle * > angle $
Step-by-step explanation:
Since z + 5 > z+ 1 > z
So, angle # > angle * > angle $ (Angle opposite to greater side is greater and opposite to smallest side is smallest)
help...........................
Answers
Answer:
Could you please repeat the question?
Answer:
Answer:
Step-by-step explanation:
What help!
Thanks for free points!
Have a nice day!
what's [2+(2x3)]x5.
Answers
Paul will pay for his new car in 36 monthly payments. If his car loan is for $20,538 then how much will Paul pay each month?
Answers
Answer:
570.50
Step-by-step explanation:
I think it's the correct answer maybe it is maybe it's not
Paul has acquired a car loan of amount $20,538 and is paying off the loan amount in 36 months.
This means that Paul will be paying $570.50 every month till the completion of 36 months.
The given parameters for the calculation of the monthly installment:
Loan amount= $20,538 Total months to repay the loan= 36 monthsCalculation of the monthly amount of Paul's loan:
[tex]\begin{aligned}\text{Monthly installment of loan}= \frac{\text{Total Amount of Loan Acquires}}{ \text{Total Time taken to Repay off the Loan}} \end{aligned}.[/tex]
[tex]\begin{aligned}\text{Monthly Installment of Loan}= \frac{\$20,538}{36}\end{aligned}[/tex]
[tex]\begin{aligned}\text{Monthly Installment of Loan}=\$570.50\end{aligned}[/tex]
Therefore, the monthly installment of paul will be $57.50.
To know more about the calculation of installment, refer to the link below:
https://brainly.com/question/84351
What is the interest rate in A = 12,000(1 + 0.07/4)^(4)(4)
Answers
a=(3•107^16)/(40•400^14)
Which theorem proves these triangles are similiar for brainliest
Answers
[tex]{\huge{\pink{\mathcal{AA\:postulate࿐❤}}}} [/tex]
You roll a 6-sided die. What is P(factor of 10)? Write your answer as a percentage rounded to the nearest tenth.
Answers
Answer:
5 is the factor of 10. 5% of 10
solve for x in : 5^{2x-1} =12^{x}
Answers
Answer:
x=2.192785
Step-by-step explanation:
52x−1=12x
log(52x−1)=log(12x)
(2x−1)*(log(5))=x*(log(12))
2x−1=(
log(12)
log(5)
)*(x)
2x−1=1.543959*x
2x−1=1.543959x
2x−1−1.543959x=1.543959x−1.543959x 1.543959x
0.456041x−1=0
0.456041x−1+1=0+1
0.456041x=1
0.456041x
0.456041
=
1
0.456041
0.456041)
x=2.192785
Answer:
x = 2.19
Step-by-step explanation:
Given that,
An equation, [tex]5^{2x-1} =12^{x}[/tex]
To find,
The value of x.
Solution,
We have,
[tex]5^{2x-1} =12^{x}[/tex]
Taking log both sides,
[tex]\text{log}(5^{2x-1})=\text{log}(12^x)[/tex]
We know that,
[tex]\text{log}\ a^n=n\ \text{log}a[/tex]
So,
[tex](2x-1)\text{log}5=x\ \text{log}12[/tex]
So,
[tex](2x-1)0.6989=1.0791x\\\\1.3978x-0.6989=1.0791x\\\\1.3978x-1.0791x=0.6989\\\\0.3187x=0.6989\\\\x=\dfrac{0.6989}{0.3187}\\\\x=2.19[/tex]
So, the value of x is equal to [tex]2.19[/tex].
Reference,
https://brainly.com/question/14968632
A basket holds n apples. You pick (2n − 3) apples, and your friend picks (n + 4) apples.
How many baskets would you need if you collected 10 apples with your friend?
Answers
Answer:The equation would be 3n+1 apples.
Step-by-step explanation:
Which expression is equivalent to 3 (x – 9) + 6?
A. 3x - 3
B. 3x - 21
C. 15 - 3x
D. 33 - 3x
Answers
in sandy religious, a doodlebug digs a cone shaped pit to trap other insects. A typical pit has a radius of 1 inch and depth of 2 inches approximately how much sand would a doodle bug move to create the pit?
( PLEASE HELP ASAP)
Answers
Answer:
its c
Step-by-step explanation:
i took the test and got 100
A meteorologist found that the rainfall in Campbell during the first half of the month was 3/10 of an inch. At the end of the month, he found that the total rainfall for the month was 1/2 of an inch. How much did it rain in the second half of the month?
Answers
Answer: 1/5
Step-by-step explanation:
Let the amount of rainfall in the second half of the month be represented by x.
From the information given in the question, the equation formed will be:
3/10 + x = 1/2
x = 1/2 - 3/10
x = 5/10 - 3/10
x = 2/10
x = 1/5
Therefore, the answer is 1/5
GUYS PLEASE ANSWER THIS QUESTION BELOW. I AM 1 BRAINLIEST AWAY FROM EXPERT AND NEED SOMEONE ELSE TO ANSWER THIS QUESTION SO I CAN GET BRAINLIEST! YOU DON'T NEED TO ANSWER IT RIGHT JUST TYPE SOMETHING RANDOM!! Thank you!!
https://brainly.com/question/21569168?exp=25-1
Answers
Answer:
Done :)
Step-by-step explanation:
Best of luck!
through (2,3); slope = -2
Answers
Answer:
y=-2x+7
Step-by-step explanation:
See image
What is (f + g)(x)?
f(x) = -4x
g(x) = -x^2 + 6x
Answers
Please help with ALEKS >-< ..................................
Answers
Answer:
4.5
Step-by-step explanation:
From the file, we see that;
Horizontal distance from bottom of ladder to side of house = 2
Length of ladder leaning against side of the house = 4 m.
Now we want to find the distance from the top of the ladder to the ground which we can call d.
Thus we can find it from pythagoras theorem.
d = √(2² + 4²)
d = √(4 + 16)
d = √20
d = 4.47
To the nearest tenth gives;
d = 4.5
Lita has 4 bananas and Liza has 8 bananas. They give some bananas to their
friends. What is the biggest number of bananas each of their friends get if each of
them receive the same number of bananas?
1. What is asked for in the problem?
2. How will you solve the problem?
3.What is the answer to the problem?
Eggs are sold in trays of 4 and 6. What is the smallest number of eggs that can
be sold using the trays?
4.How will you solve the problem?
5.What is the answer to the problem?
pa help po please kailangan na po kase e
Answers
Answer:
hi kpop fan
Step-by-step explanation:
she is blackpink jisoo in your profile pick right
Answer:
they will receive 4 banana
2 to the power of 6 times 9x if x=12
Answers
Answer:
[tex]6 {}^{2} = 36 [/tex]
[tex]x = 12[/tex]
[tex]9 \times 12 = 108[/tex]
[tex]108 \times 36 = 3888[/tex]
(−3⋅10^3 )⋅(4⋅10^6)=???
Answers
Answer:
-1.19164 x 10^8
Step-by-step explanation: