Congruent triangles have equal corresponding sides and angles.
The measure of the side lengths are: [tex]\mathbf{DF = 16m}[/tex], [tex]\mathbf{JH = 14m}[/tex] and [tex]\mathbf{GJ = 19m}[/tex]The measure of the angles are: [tex]\mathbf{\angle G = 34^o}[/tex], [tex]\mathbf{\angle J = 41^o}[/tex] and [tex]\mathbf{\angle F = 105^o}[/tex]The given parameters are:
[tex]\mathbf{\triangle D EF \cong \triangle GJH}[/tex]
[tex]\mathbf{EF = 14m}[/tex]
[tex]\mathbf{D E = 19m}[/tex]
[tex]\mathbf{GH = 16m}[/tex]
[tex]\mathbf{\angle D = 34^o}[/tex]
[tex]\mathbf{\angle H = 105^o}[/tex]
[tex]\mathbf{\triangle D EF \cong \triangle GJH}[/tex] means that triangles DEF and GHJ are congruent triangles.
So, we have:
[tex]\mathbf{DF = GH}[/tex]
This gives
[tex]\mathbf{DF = 16m}[/tex]
Also, we have:
[tex]\mathbf{JH = EF}[/tex]
This gives
[tex]\mathbf{JH = 14m}[/tex]
Also, we have:
[tex]\mathbf{GJ = DE}[/tex]
This gives
[tex]\mathbf{GJ = 19m}[/tex]
The following angles are also congruent
[tex]\mathbf{\angle F = \angle H}[/tex]
This gives
[tex]\mathbf{\angle F = 105^o}[/tex]
Also, we have:
[tex]\mathbf{\angle G = \angle D}[/tex]
This gives
[tex]\mathbf{\angle G = 34^o}[/tex]
The measure of angle J is then calculated using
[tex]\mathbf{\angle J + \angle H + \angle G = 180^o}[/tex]
This gives
[tex]\mathbf{\angle J + 105 + 34= 180^o}[/tex]
[tex]\mathbf{\angle J + 139= 180^o}[/tex]
Subtract 139 from both sides
[tex]\mathbf{\angle J = 41^o}[/tex]
Read more about congruent triangles at:
https://brainly.com/question/4364353
I need help this goes towards my grade so please be correct
Answer:
0 us the answer for this question
please help... ABCD is a quadrilateral
What is (-2) power 35?
Answer: − 34359738368
A jacket usually sells for $68.00. If the jacket is 40% off, and sales tax is 6%, what is the total price of the jacket, including tax?
Answer:
$ 43.25
Step-by-step explanation:
68 - 40% = 40.8
40.8 + 6% = $ 43.25
which expression is equivalent to 2(5 - 3x)
First answer gets Brainliest!
Answer: 10 - 6x
2 x 5 = 10
2 x 3 = 6
therefore: 10 - 6x
I hope this helps!
Answer:
the answer is 10-6x
Step-by-step explanation:
by multiplying 2 by 5 and -3x
u will get ur 10-6x
There are 32 students in your class. After voting for the class representative, Alan received 3 times as many votes than David. How many votes did Alan receive?
Answer:
alan received 24 votes
Step-by-step explanation:
bark
The mean of 7 numbers is 15. When an 8 thnumber is added, the mean decreases to 12. What is the 8 thnumber?.
Answer:
-9?????????????????????????
Step-by-step explanation:
Ron is 25 years old and is retiring at the age of 65. When he retires, he will need a monthly income of $4,123 for 20 years. If Ron contributes 10% of his monthly income to a 401(k) paying 5.5% compounded monthly, will he reach his goal for retirement given that his monthly income is 3,142.23? If he does not make his goal then state by what amount he will need to supplement his income. Round all answers to the nearest cent.a.Ron will meet his monthly goal of exactly $4,123 for retirement.b.Ron will meet his monthly goal of $4,123 for retirement with an excess of $125.34.c.Ron will not make his monthly goal of $4,123 and will need $359.74 to supplement his monthly income when he retires.d.Ron will not make his monthly goal of $4,123 and will need $450.61 to supplement his monthly income when he retires.
Ron will not make his monthly goal of $4,123 and will need $359.74 to supplement his monthly income when he retires.
What is Compound interest?Compound interest simply means that the interest associated with a bank account, loan, or investment increases exponentially over time.
Given monthly income of Ron is $3,142.23
Ron is 25 years old and is retiring at the age of 65. so he has 40 years to contribute.
Total amount he contribute in 40 years paying 5.5% compounded monthly is given by
interest rate(r) = 0.055/12
time period = 40 years = 480 months
Principal amount = $314.223
Future value = [tex]P(\frac{(1+r)^{n}-1 }{r} )[/tex]
Substitute, we get,
= 3142.23 [tex].10(\frac{(1+\frac{0.055)^{12.40}-1) }{12} }{\frac{0.055}{12} }[/tex]
Thus, future value is $547074.681009.
After retirement his monthly income when he has $547074.681009 amount.
P = (A.i/2)/(1-(1+i/12)⁻ⁿ)
Putting values, we get,
P = (547074.68×0.55/12)/1-(1+0.055/12)⁻²⁴⁰
P = $3763.25
He will receive a monthly income of $3763.25.
But given he will need a monthly income of $4,123 for 20 years, which is not met by Ron.
So, the amount he needs to supplement his monthly income when he retires by (4123-3763.25)= $359.74
Hence, Ron will not make his monthly goal of $4,123 and will need $359.74 to supplement his monthly income when he retires.
For more references on Compound interest, click;
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If a triangle is equilateral, then all the sides in the triangle are congruent.If all the sides in a triangle are congruent, then all the angles are congruent.
Answer:
Where's the question?
Step-by-step explanation:
Write an equation in slope intercept form of the line
Answer: y=-1/4x+4
Step-by-step explanation:
slope goes down 1, and right 4 so it's -1/4. Y-intercept is positive 4 so it will be +4
Anyone help for brainlist:)
Determine the graph of the function -->f(x)=2^x−1
Answer:
it is D
Step-by-step explanation:
Exponential functions have a horizontal asymptote. The equation of the horizontal asymptote is y = − 1 . Horizontal Asymptote: y = − 1
linear equations
1. 4= x + 2
2. 6= x-3
3. 7= a + 4
4. 6= x - 7
5. 1= c - 2
6. 5= s + 2
7. x + 3=10
8. c + 4= 4
9. 3= b + 2
10. 6 + c= 10
11. 7= x + 3
12. x + 1= 9
13. x + 3= 15
14. y -6 = 4
15. x - 7 = 4
16. 6= x - 4
17. x - 4 = 2
18. x - 9 = 2
spilled $40 into the ratio of 3:7
Answer:
$12/$28
Step-by-step explanation:
Let x and y represent the two amounts of money adding up to $40.
Assume that x is the smaller amount. Then:
x 3
----- = ----- Remembering that x + y = $40, we get x = $40 - y
y 7
amd sp we have
$40 - y 3
-------------- = ------ which, after cross-multiplication, is $280 - $7y = 3y
y 7
Simplifying this, we get $280 = 10 y, so that y must be $28. If y = $28, x must be $40 - $28, or $12.
$12
Then $40, split in the ratio 3/7, is the ratio ----------------
$28
Check: Note that $12 + $28 = $40, as required, and that $12/$28 = 3/7.
Josh, Ben and Rick have 70 marbles altogether. The ratio of the number marbles Josh has to the number of marbles Rick has is 1: 2. However, Ben has 15 marbles fewer than Rick. How many marbles does Ben have?
Answer:
Ben has 19 marbles
Step-by-step explanation:
First taking that josh and ricks ratio is 1:2, this would set up in an equation as [tex]2j = r[/tex] and with ben having 15 less than rick, his formula would be [tex]r = b + 15[/tex] as well as the total of all the boys marbles together being this [tex]j+r+b=70[/tex]
Now we put all of these equations into a set to answer them.
[tex]2j = r\\ r = b + 15\\j+r+b=70[/tex]
First we solve for j
[tex]2j = r\\ j=\frac{1}{2} r[/tex]
Then substitute j
[tex]j+r+b=70\\ \frac{1}{2}r+r+b=70\\ 2b+3r=140[/tex]
Then simplify and multiply by 2 to even out
[tex]r = b + 15\\ -b+r=15\\2b+3r=140[/tex]
Now eliminate the b variable and combine equations
[tex]2b+3r=140\\-2b+2r=30[/tex]
[tex]5r=170[/tex]
Now divide and solve for r
[tex]5r=170\\r=34[/tex]
Now we know Rick has 34 marbles of the 70 marbles, so we can substitute his number back into the original equation
[tex]-b+34=15\\b=19[/tex]
Now we know Ben has 19 marbles of the remaining 36, and can substitute his number as well
[tex]j=\frac{1}{2}(34)\\j=17[/tex]
And now we know how much everyone has, to check we rewrite all the equations with their respective numbers
[tex]11+34+19=70\\2(17)=34\\34=19+15[/tex]
[tex]70=70\\34=34\\34=34[/tex]
Which means the ordered pairing of (b, j, r) is (19, 17, 34)
9/12 as an equivelant fraction
Answer:
3/4
Step-by-step explanation:
9/12
Divide the top and bottom by 3
9/3 = 3
12/3 = 4
The fraction becomes 3/4
what is 39/17 as a decimal rounded to the nearest tenths?
help needed please im stuck
Answer:
a) b^3
b) x^3
Step-by-step explanation:
It can be helpful to think of the exponent as specifying the number of times the base is a factor in the product. Of course, common factors in the numerator and denominator cancel.
a)[tex]\dfrac{b^7}{b^4}=\dfrac{b\cdot b\cdot b\cdot b\cdot b\cdot b\cdot b}{b\cdot b\cdot b\cdot b}=b\cdot b\cdot b=b^{7-4}=\boxed{b^3}[/tex]
__
b)[tex]\dfrac{x\cdot x^5}{x^2\cdot x}=\dfrac{x\cdot x\cdot x\cdot x\cdot x\cdot x}{x\cdot x\cdot x}=x\cdot x\cdot x=x^{6-3}=\boxed{x^3}[/tex]
The minute hand of a clock turns 6 degrees per minute. In ten minutes the minute hand turns what fraction of a full 360 turn?
Answer:
25%
Step-by-step explanation:
15 times 6 is 90
90 is 25 % of 360
a) 60 square meters in square centimeters.
Answer:
600,000 cm²
Step-by-step explanation:
We know the conversion from meters to centimeters to be
1 m = 100 cm.
We need the conversion factor from square meters to square centimeters.
Start with
1 m = 100 cm
Square both sides.
(1 m)² = (100 cm)²
1 m² = 10,000 cm²
Now that we have the correct conversion factor from m² to cm², we can do the conversion of 60 m² into cm².
60 m² × (10,000 cm²)/(1 m²) = 600,000 cm²
Find the reference angle for -369°
a.
9°
c.
99°
b.
81°
d.
171°
Please select the best answer from the choices provided
A
B
C
D
Answer:
A. 9
Step-by-step explanation:
will give brain for right answer
Answer:
luna
Step-by-step explanation:
compare the y values when x=0. looking at the table, gracey was 1 lb at week 0, and looking at the graph, Luna was 2 lbs at week 0 (y-intercept) so luna was heavier at birth
What does x equal in the equation 10= 0.0048(x - 50)^2 + 6?
Answer:
x=\frac{0.48+\sqrt{0.0768}}{0.0096},\:x=\frac{0.48-\sqrt{0.0768}}{0.0096}
Step-by-step explanation:
(x-50)^2 is x^2+2500-100x*.0048 is .0048x. 2500*0.0048 is 12, and -100*0.0048=-.48.
So, we have .0048x^2+12-.48x+6, which is
.0048x^2+18-.48x=10. USing the quadratic formula, we get
x=\frac{0.48+\sqrt{0.0768}}{0.0096},\:x=\frac{0.48-\sqrt{0.0768}}{0.0096}
(Enter into symbolab.com to see theanswer)
Let ABC be an isosceles triangle with AB = AC and ∠BAC=30°. Side AB and the median AD contain points Q and P respectively (points P and Q are not at point A) in such a way that PC=PQ. Find m∠PQC.
Answer:
15°
brainlest
Step-by-step explanation:
Since P is on the median of ΔABC, it is equidistant from points B and C as well as from C and Q. Thus, points B, C, and Q all lie on a circle centered at P. (See the attached diagram.)
The base angles (B and C) of triangle ABC are (180° -30°)/2 = 75°. This means arc QC of the circle centered at P has measure 150°. The diameter of circle P that includes point Q is defined to intersect circle P at R.
Central angle RPC is the difference between arcs QR and QC, so is 180° -150° = 30°. Inscribed angle RQC has half that measure, so is 15°. Angle PQC has the same measure as angle RQC, so is 15°.
Angle PQC is 15°.
Name
Lily Daku November 17, 2021 pec
Common Core Standards Practi
Selected Response
co
1. Find the slope of the line that
passes through the points (-1,9)
and (3, 17).
The stock price of the company was $38. The stock price fell to $12.60. Which is the closest to the percent decrease in this stock price?
Answer:
66.8421% decrease
Step-by-step explanation:
1. How well do you work with fractions and decimals? (2 point)
I can explain how fractions and decimals are related. I can convert fractions to decimals and decimals to
fractions without needing help
I can usually convert fractions to decimals and decimals to fractions, but sometimes I make mistakes
I can sometimes convert fractions to decimals and decimals to fractions, but I need more practice with
this
I do not understand how fractions and decimals are related, or how to convert them.
Step-by-step explanation:
when you get a decimal like 0.02 and you want to express it in fraction,this is a simple trick.
first,put your pen at the point and move it forward till you end at the last number.
While you move the pen over each value, you will count the number of jumps and record the number of jumps in zeros i. e
2÷100 and it means that,the last 1or 3or 3whole numbers will become the numerator
make x the subject of the formula
y=a √x
Answer:
Y^2/a = x
Step-by-step explanation:
Y = a sqr X
Square both sides
Y^2 = a * x
Divide a
Y^2/a = x
Answer:
[tex] x = \dfrac{y^2}{a^2} [/tex]
Step-by-step explanation:
[tex] y = a\sqrt{x} [/tex]
Square both sides.
[tex] (y)^2 = (a\sqrt{x})^2 [/tex]
[tex] y^2 = a^2(\sqrt{x})^2 [/tex]
[tex] y^2 = a^2x [/tex]
Divide both sides by a².
[tex] \dfrac{y^2}{a^2} = x [/tex]
Switch sides.
[tex] x = \dfrac{y^2}{a^2} [/tex]
Please help me asap
DO NOT USE LINKS
Can someone please help me
Answer:
[tex]y = + - \sqrt[4]{ \frac{3}{2} x} [/tex]
What is the midpoint between points (4, 7) and (1, 1)?
Enter your answer down below
Answer:
(2.5, 4)
Step-by-step explanation:
(4, 7) (1, 1)
midpoint formula is ( (x1 + x2) / 2 , (y1 + y2) / 2 )
=>( (4 + 1)/2 , (7 + 1)/2 )
=> (5/2, 4)
=> (2.5, 4)