Answers
Answer:
75
Step-by-step explanation:
In this problem, AC and BD should be set equal to each other.
3x + 15 = 4x - 5
You would then solve for x, which is x = 20.
Plug 20 back in the equation for AC, 3(20) + 15, to get 75.
The length of AC is 75.
What is a rectangle?A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
We have,
AC = 3x + 15
BD = 4x - 5
AC and BD are diagonals of the rectangle.
The diagonals of a rectangle are equal.
Now,
AC = BD
3x + 15 = 4x - 5
15 + 5 = 4x - 3x
20 = x
Now,
AC = 3x + 15
= 3 x 20 + 15
= 60 + 15
= 75
Thus,
AC = 75
Learn more about rectangles here:
https://brainly.com/question/15019502
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Related Questions
(first question btw)
please help i will mark brainliest if correct!
Answers
Answer:
(3,9)
Step-by-step explanation:
Because the translation moves 1 in the x direction and 4 in the y direction, you just add those to the starting x and y coordinates.
(2+1, 5+4)
(3, 9)
Tristan made 98 bracelets in 7 hours and Denita made 56 bracelets in 4 hours. These rates are equivalent because they have the same _____ .
A) unit rate
B) ratio
C) rate
Answers
Answer:
A) unit rate
Hope this helps
Dave wants to put a row of tiles in his kitchen. The row has to be 3 meter long. Each tiles is a square, with 25 cm sides. How many tiles does he need?
Answers
Answer:the answer is b or c
Step-by-step explanation:
Jaidee invests $2,628 in a retirement account with a fixed annual interest rate of 2.33% compounded 12 times per year. How long will it take for the account balance to reach $3,726.18?
Answers
Answer:
The time it will take for the account balance to reach $3,726.18 is 15 months.
Step-by-step explanation:
The information provided is:
Jaidee invests $2,628 in a retirement account With a fixed annual interest rate of 2.33% Compounded 12 times per year, i.e. compounded monthly.Final account balance: $3,726.18The formula of compound interest (compounded monthly) is:
[tex]A=P(1+\frac{r}{12})^{12t}[/tex]
Compute the value of t as follows:
[tex]3726.18=2628\times (1+\frac{0.0233}{12})^{12t}\\\\\frac{3726.18}{2628}= (1.00194167)^{12t}\\\\1.41787671= (1.00194167)^{12t}\\\\\log(1.41787671)= 12t\times \log(1.00194167)\\\\12t=\frac{\log(1.41787671)}{\log(1.00194167)}\\\\t=14.99995\\\\t\approx 15[/tex]
Thus, the time it will take for the account balance to reach $3,726.18 is 15 months.
Write the equation for a parabola with the focus at
(-1, 4) and the equation of the directrix x = 5.
(x + 1)2 = 3(y-4)
(y-4)2 = 12(x + 1)
(y-2)2 = -3(x – 4)
(y-4)2 = –12(x - 2)
Answers
Since the graph is facing the left, the starting equation would be (y - k)2 = -4p(x - h).
(h, k) is the vertex of the graph. If you plot the focus and the directrix, you can see that the distance is 6. Divide 6 by 2, thus the vertex should be 3 squares away from the focus and 3 squares away from the directrix. The vertex is (2, 4). And since the distance from the focus to the vertex and the distance from the directrix to the vertex is 3, P = 3.
Insert the numbers in and you should get the last choice.
Plz help me with this question
Answers
Answer:
123
Hope this helped!
If two thirds of a number is 56, what is three- quarters of that number?
Answers
Answer:
63
Step-by-step explanation: Let n represent the number. If two third of n = 56, n must be 56 times the reciprocal of 2/3 (3/2) 56 time 3/2 = 84. three quarter of 84 is 84 times 3/4 = 63
NEED ANSWER ASAP THE TEST IS TIMED!!!!!!!
Find the slope of the line that contains the two points (6, -2) and (-3, 1).
Answers
Answer:
5/-1
Step-by-step explanation:
y1-y2/x1-x2
Edward wanted to buy a skateboard. The original price of the skateboard was $90. The store was having a sale where everything in the store was markdown 35%, or 35% off. What was the price of the skateboard after the markdown or discount?
Answers
Answer:
$58.5Step-by-step explanation:
Step one:
Given data
original price of Skate board= $90
Also there was a 35% discount on the original price.
the idea now is to find what 35% of $90 is.
=(35/100)*90
=0.35*90
=31.5
hence 35% of $90 is $31.5, the discounted price is $31.5
Step two:
The markdown price is the original price- the discounted price
90-31.5= $58.5
Therefore the price of the skateboard is $58.5
5x - 2y = 26 y + 4 = x
Answers
What is the answer to 3z−6/7−2z = 1.2/3.2 ? Please help
Answers
Answer:
= 1.23214285
Step-by-step explanation:
Explanation:
Step 1:collect like terms
Step 2:convert the decimals into fraction
Step 3:reduce the fraction with 5
Step 4:reduce the fraction with 2
Step 5:move the constant to the right hand side and change its sign
Step 6:add the fractions
what is the following sum ?
Answers
Explanation:
I added a picture so please check it
Is this relation a function? Justify your answer.
10
9
8
7
B
5
4
.
3
2
1 2 3 4 5 6 7 8 9 10 11
A. Yes, because every x- and y-value is positive.
OB. No, because two points with the same x-value have different ya
values,
OC. Yes, because the number of x-values is the same as the number o
y values
D. No, because two points with the same y-value have different x-
values
Answers
Answer:
B
Step-by-step explanation:
Eveey input must have exactly one output, x is always the input and y is the output and there are two y outputs on one x input so it is not a function.
Hope this helps! If you have any questions on how I got my answer feel free to ask. Stay safe!
The radius of a circle is 5 kilometers. What is the length of a 90° degree arc?
Answers
Answer:
s =5*π/2 km
Step-by-step explanation:
arc length s = rθ
where θ =central angle in radians
r = 5km
θ = 90 degrees = 90 degrees/360degrees * 2π = [tex]\frac{1}{4}[/tex](2π) = π/2
s =5*π/2 km
Put the equation 2x+3y=1470 in function notation
Answers
Answer:
y = -[tex]\frac{2}{3}[/tex]x + 9
Step-by-step explanation:
Whitney's bill at a diner came up to $26.00. What would her total be if she included a 20% tip?
Tax using the percent equation.
Answers
So Whitney would include a $5.20 tip which would make the total $31.20.
Please mark as Brainliest if it helped!
a store sells jump ropes. each jump rope costs the same amount. during a sale, the store reduces the price of each jump rope by $1.25. jada spends $15.08 on 2 jump ropes at the sale price.
Answers
Answer:
she spent $7.45 on each rope at the sale price. The original price would have been $8.70
Step-by-step explanation:
Positive negative or no correlation?
Answers
Answer:
positive correlation
Answer:
animal
Step-by-step explanation:
find the slope of the line through (4,1) and (6,3)
Answers
Katie Haddad earns $394 per week. She is married and
claims 3 children as dependents. The state tax rate in Haddad's
state is 2% of taxable income. What amount is withheld from
her weekly pay for state income tax?
Answers
Answer:
$78.8
Step-by-step explanation:
When 3(2x + 5) is added to 2(2x − 4) the resulting expression is?
Answers
Answer:
10x + 7
Step-by-step explanation:
3(2x + 5) added to 2(2x - 4) is the same as 3(2x +5) + 2(2x - 4)
Remember PEMDAS
P – Parentheses (distribution)
E – Exponents
M – Multiplication
/D – Division (whichever comes first from left to right)
A – Addition
/S – Subtraction (whichever comes first from left to right)
First, we will distribute the left side.
3(2x + 5)
3 * 2x = 6x
3 * 5 = 15
Add them together to get:
6x + 15
6x + 15 + 2(2x - 4)
We must now distribute the right side.
2 * 2x = 4x
2 * -4 = -8
Add them together to get:
4x -8
We now have:
6x + 15 + 4x - 8
Let's combine like terms.
6x and 4x are like terms.
Combine: 6x + 4x = 10x
15 and -8 are like terms.
15 - 8 = 7
Now we have 10x + 7
Since 10 and 7 don't have any GCF, we have our answer.
10x + 7
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Math Enthusiast
Evaluate |x^2 +9x| at x = -4
Answers
|16 - 36|
|-20|
20
Use the Binomial Theorem/Pascal's Triangle to expand (2a + 2b)^5
Answers
Answer:
32a^5+160a^4b+320a^3b^2+320a^2b^3+160ab^4+32b^5
============================================================
Explanation:
Let's use Pascal's Triangle
In the row that starts with 1,5,... we have the values 1,5,10,10,5,1
These will be the coefficients of the terms.
Let x = 2a and y = 2b
We want to expand out (x+y)^5
Using pascals triangle, we get the following expansion
(x+y)^5 = 1x^5y^0+5x^4y^1+10x^3y^2+10x^2y^3+5x^1y^4+1x^0y^5
The numbers in bold are the coefficients 1,5,10,10,5,1 found earlier.
Note how the exponents for x start at 5 and count down to 0; while the y exponents start at 0 and count up to 5. For any term, the x and y exponents always add to 5 for the expansion of (x+y)^5. In general, the exponents of any term will add to n for (x+y)^n.
At this point, we plug in x = 2a and y = 2b
Since this will clutter things a bit, I'll do it term by term
1x^5y^0 = 1(2a)^5(2b)^0 = 1(32a^5)(1) = 32a^55x^4y^1 = 5(2a)^4(2b)^1 = 5(16a^4)(2b) = 160a^4b10x^3y^2 = 10(2a)^3(2b)^2 = 10(8a^3)(4b^2) = 320a^3b^210x^2y^3 = 10(2a)^2(2b)^3 = 10(4a^2)(8b^3) = 320a^2b^35x^1y^4 = 5(2a)^1(2b)^4 = 5(2a)(16b^4) = 160ab^41x^0y^5 = 1(2a)^0(2b)^5 = 1(1)(32b^5) = 32b^5So in the end, the expression (2a+2b)^5 expands out to
32a^5+160a^4b+320a^3b^2+320a^2b^3+160ab^4+32b^5
The binomial theorem uses the same basic idea, but instead of using Pascal's Triangle to get the coefficients, you'll use the nCr combination formula.
Answer: [tex](2a+2b)^5 =32a^5+160a^4b+320a^3b^2+320a^2b^3+160ab^4+32b^5[/tex].
Using Pascal's triangle we get:
[tex](x+y)^5 = 1x^5y^0+5x^4y^1+10x^3y^2+10x^2y^3+5x^1y^4+1x^0y^5[/tex]
Here, x = 2a and y = 2b
So the terms become:
[tex]1x^5y^0 = 1(2a)^5(2b)^0 = 1(32a^5)(1) = 32a^5\\5x^4y^1 = 5(2a)^4(2b)^1 = 5(16a^4)(2b) = 160a^4b\\10x^3y^2 = 10(2a)^3(2b)^2 = 10(8a^3)(4b^2) = 320a^3b^2\\10x^2y^3 = 10(2a)^2(2b)^3 = 10(4a^2)(8b^3) = 320a^2b^3\\5x^1y^4 = 5(2a)^1(2b)^4 = 5(2a)(16b^4) = 160ab^4\\1x^0y^5 = 1(2a)^0(2b)^5 = 1(1)(32b^5) = 32b^5\\[/tex]
Hence: [tex](2a+2b)^5 =32a^5+160a^4b+320a^3b^2+320a^2b^3+160ab^4+32b^5[/tex]
Learn more: https://brainly.com/question/13769924
what is the solution for x in the equation?
Answers
Answer:
x = 5/2 is the answer to the question
4. On the day Alex was born, his father invested $5000 in an account with a 1.2% annual growth rate.
Answer the questions below.
(a) Write a function, A(t), that represents the value
of this investment t years after Alex's birth.
(b) Use your equation to determine how much the
investment will be worth when Alexander turns
21
Answers
Answer:
Answer:
A) A(t) = 5000(1 + 0.012)t
B) A(t) = 106260
Step-by-step explanation:
A) 5000 is the initial amount, 1 + 0.012 is the interest rate, and t represents the years.
B) When we plug 21 into the equation, we get 106260.
I hope this helps!
Using graph paper, determine the line described by the given point and slope. Click to show the correct graph below. (0,6) and -1
Answers
Answer:
Can't tell
Step-by-step explanation:
Hear me out. There is no graph hear, so I can't answer. Just letting you know
Decide whether this statement is always true, never true, or sometimes true, and explain why: In a quadratic equation of the form 0 = ax2 + bx + c, there will be two real solutions if a and c are of opposite signs
Answers
Answer:
Always true
Step-by-step explanation:
Here, we want to evaluate if the given statement is true
The discriminant D can be calculated using the formula;
b^2 - 4ac
if D is greater than 0, then we will have only real roots
In a case where a and c are of opposite signs;
then -4ac will always give a positive value which can be added to b^2
This positive value will ensure that D is greater than zero and hence we can have only real roots
So this assertion is always true if a and c are of opposite signs
can't figure this out
Answers
Answer:
2.55%
Step-by-step explanation:
You have 11 years to make $500, To do this, take the 11 and multiply it by the percentage, after that, do $2000 divided by 11 x (percentage) answer. Then you will have the difference, which should roughly equal $556, which is slightly over $500 but you can't have it under so this is the best answer.
please help! no rush though :)
1.6 x 10^5kg and 8 x 10^3kg
(i need it with too but if you can’t it’s all good!)
Answers
Answer:
160000 kg and 8000
Step-by-step explanation:
move decimal to the right five times
move decimals to right 3 times
Please help due tn I need this done
Answers
1) (2x+3)(x-2)
2x^2 -4x + 3x -6
2x^2 -x -6
2) x^2 +10x +24
(x+12)(x-2)
3) 6x^2 -13x +6
(2x )(3x ) not sure on this one
4) x^2 +8x +15
(x+3)(x+5)
x= -3 x=-5
5) x^2 -4x -45
(x+5) (x-9)
x=-5 x=9
hope this helps, if you need any help understanding what happens just ask
