The lengths of the diagonals of rectangle ABCD intersect at E. If AE =x+4 and CE= 3x-12. What is the length of BD?
SOMEONE HELP ME ASAP PLEASE
Answers
Answer:
DB = 24
Step-by-step explanation:
First, note that the diagonals of a rectangle are equal and bisect each other. In other words, DB = CA and CE = EA and DE = BE.
Also, AE + CE = CA
So, using this, we can write this equation:
AE = CE
x + 4 = 3x -12
Subtract 4 from both sides.
x = 3x -16
Subtract 3x from both sides.
-2x = -16
Divide both sides by -2
x = 8
Then, substitute this into AE + CE = CA
x + 4 + 3x - 12 =
8 + 4 + 24 - 12 = 24
Then, because CA = DB,
DB = 24
I hope this helps! Feel free to ask any questions! :)
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................
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Try using pythagorus or trigonometry
Answer:
(i)DAG=17°
(ii)∠FEC=73°
(iii)∠AGC=73°
Step-by-step explanation:
In rhombus,
AB=BC=CD=AD
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DAG=17°
(ii)∠FEC=73°
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Kevin and Christy both saved money for their class trip. Kevin saved the same amount each week. The total amount that Kevin saved at the end of every two weeks is shown in the table below.
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Step-by-step explanation:
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Step-by-step explanation:
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bit. ly / 3ecQGGN
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Factor the expression using the GCF.
24+64x
Answers
Answer:
8 (3 + 8x)
Step-by-step explanation:
Factor down the two values. The two multiples for 24 can be 8 and 3. The two multiple for 64 can 8 and 8. Overall, both the values are multiples of 8.
You put 8 out of the bracket since it's the GCF. 24 goes 3 times and 64 goes 8 times.
= 8 (3 + 8x)
determining slope and y-intercept
Use the following table to answer questions #15 and #16.
Answers
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Slope. -2.5
Y-intercept. 15
-9 + 5 = on a number line
Answers
Answer/Step-by-step explanation:
First you would plot -9 on the number line
Then you would go to the right 5 times which would take you to -4 and that would be you answer.
(Sorry I could not find a number line to plot but I hope you get the idea)
Hope this helps :)
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Answer:
2
Step-by-step explanation:
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I got the answer but i need like a step by step explanation because i dont get it :/
Answers
Answer:
(0, -2) and (3, 1)
Step-by-step explanation:
y = x - 2, y = (x - 1)² - 3
To solve this problem, we need to find when the x and ys in both equations are equal.
So,
y = x - 2 = y = (x - 1)² - 3
x - 2 = (x - 1)² - 3
Simplify right side.
x - 2 = x² - 2x - 2
Subtract both sides by (x² - 2x - 2)
x - 2 - (x² - 2x - 2) = 0
Simplify.
-x² + 3x = 0
Factor x.
x (-x + 3) = 0
Because the only way to get a product of 0 is to multiply a number by 0, either x = 0 or (-x + 3) = 0 (x would be 3 in this equation)
So, x = 0 or x = 3
Now, to find y, plug x = 0 x = 3 into one of the equations.
When x = 3, y = x - 2 = 3 - 2 = 1
When x = 0, y = x - 2 = 0 - 2 = -2
Just in case, let's check these values.
Put x = 0 and y = -2 into y = (x - 1)² - 3
-2 = (0 - 1)² - 3 = (-1)² - 3 = 1 - 3 = -2
So, x = 0 and y = -2 is correct.
Put x = 3 and y = 1 into y = (x - 1)² - 3
1 = (3 - 1)² - 3 = 2² - 3 = 4 - 3 = 1
So, x = 3, y = 1 is correct.
Thus, the answers are
(0, -2) and (3, 1)
I hope this helps! Feel free to ask any questions!
PLEASE HELP URGENT WILL MARK BRAINLIEST
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Answer:
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2 x
— = -----
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x = ???
Answers
9514 1404 393
Answer:
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Step-by-step explanation:
Maybe you want to find x such that ...
2/7 = x/(x +10)
2(x +10) = 7x . . . . . . multiply by 7(x+10)
20 = 5x . . . . . . . . . . subtract 2x, simplify
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_____
Additional comment
You can almost solve this "by inspection" if you recognize the difference of the denominator and numerator is 5 on the left and 10 on the right. If you multiply the fraction on the left by 2/2, you get 4/14, the values in x/(x+10) in the fraction on the right.
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And
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Answer:
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Step-by-step explanation:
cos ( α ) = √ 6/ 6 and sin ( β ) = √ 2/4 . Find tan ( α − β )
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Answer:
[tex] \purple{ \bold{ \tan( \alpha - \beta ) = 1.00701798}}[/tex]
Step-by-step explanation:
[tex] \cos( \alpha ) = \frac{ \sqrt{6} }{6} = \frac{1}{ \sqrt{6} } \\ \\ \therefore \: \sin( \alpha ) = \sqrt{1 - { \cos}^{2} ( \alpha ) } \\ \\ = \sqrt{1 - \bigg( {\frac{1}{ \sqrt{6} } \bigg )}^{2} } \\ \\ = \sqrt{1 - {\frac{1}{ {6} }}} \\ \\ = \sqrt{ {\frac{6 - 1}{ {6} }}} \\ \\ \red{\sin( \alpha ) = \sqrt{ { \frac{5}{ {6} }}} } \\ \\ \tan( \alpha ) = \frac{\sin( \alpha ) }{\cos( \alpha ) } = \sqrt{5} \\ \\ \sin( \beta ) = \frac{ \sqrt{2} }{4} \\ \\ \implies \: \cos( \beta ) = \sqrt{ \frac{7}{8} } \\ \\ \tan( \beta ) = \frac{\sin( \beta ) }{\cos( \beta ) } = \frac{1}{ \sqrt{7} } \\ \\ \tan( \alpha - \beta ) = \frac{ \tan \alpha - \tan \beta }{1 + \tan \alpha . \tan \beta} \\ \\ = \frac{ \sqrt{5} - \frac{1}{ \sqrt{7} } }{1 + \sqrt{5} . \frac{1}{ \sqrt{7} } } \\ \\ = \frac{ \sqrt{35} - 1 }{ \sqrt{7} + \sqrt{5} } \\ \\ \purple{ \bold{ \tan( \alpha - \beta ) = 1.00701798}}[/tex]
A storage room measures 9 1⁄2 feet by 6 feet by 9 1⁄2 feet. What is the volume of the storage room?
Answers
Answer:
C
Step-by-step explanation:
Volume formula: width*length*height
Ok, so let's plug in the numbers.
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Answer is C
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Step-by-step explanation:
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Answers
9514 1404 393
Answer:
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look at the explanation <33
Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
The way to find the area of a triangle is to multiply height and width then divide by two and 125 is the area. Then that means 125=250/2.
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please solve!! 4 (x-6) + 10 = 6
Answers
[tex]\huge\text{Hey there!}[/tex]
[tex]\textsf{4(x - 6) + 10 = 6}[/tex]
[tex]\textsf{Distribute}[/tex]
[tex]\textsf{4(x) + 4(-6) + 10 = 6}[/tex]
[tex]\textsf{4x - 24 + 10 = 6}[/tex]
[tex]\textsf{COMBINE the LIKE TERMS}[/tex]
[tex]\textsf{(4x) + (-24 + 10) = 6}[/tex]
[tex]\textsf{-24 + 10 = -14}[/tex]
[tex]\textsf{4x - 14 = 6}[/tex]
[tex]\textsf{ADD 14 from BOTH SIDES}[/tex]
[tex]\textsf{4x - 14 + 14 = 6 + 14}[/tex]
[tex]\textsf{CANCEL out: -14 + 14 because that gives you 0}[/tex]
[tex]\textsf{KEEP: 6 + 14 because that helps us solve for x}[/tex]
[tex]\underline{\textsf{6 + 14 = 20}}[/tex]
[tex]\textsf{New equation: 4x = 20}[/tex]
[tex]\textsf{DIVIDE 4 from BOTH SIDES}[/tex]
[tex]\mathsf{\dfrac{4x}{4}=\dfrac{20}{4}}[/tex]
[tex]\textsf{CANCEL out}[/tex]: [tex]\mathsf{\dfrac{4}{4}}[/tex] [tex]\textsf{because that gives you 1}[/tex]
[tex]\textsf{KEEP}[/tex]: [tex]\mathsf{\dfrac{20}{4}}[/tex] [tex]\textsf{because that solves and gives you x}[/tex]
[tex]\mathsf{TEMPORARY\ EQUATION: x = \dfrac{20}{4}}[/tex]
[tex]\mathsf{\dfrac{20}{5}=5}\\\\\\\mathsf{20\div4 = 5}\\\\\\\textsf{\bf x = 5}\large\checkmark[/tex]
[tex]\boxed{\boxed{\large\textsf{Answer: \underline{\bf x = 5}}}}\huge\checkmark[/tex]
[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Can someone please check my answer???
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Answer:
is 1 means -1?whats -----means?
Step-by-step explanation:
Combine like terms and write 4y+5y^2-6-5y+27-1y^2 in standard form
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Answer:
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