Step-by-step explanation:
let the cost of the bench = x
the cost of the garden table = x + 82
x + (x + 82) = 668
2x + 82 = 668
2x = 586
x = 293
The bench costs $293 and the garden table costs 293 + 82 = $375
can you mark me as brainliest, it will help me a lot. thank you in advance
The height of a triangle is 4cm more than twice the length of the base.The area of the triangle is 35 square cm.Find the height of the triangle.
Answer:
14cm
Step-by-step explanation:
Algebra is the way!
But seriously, let's model this algebraically.
We know the that the area of a triangle is represented by:
[tex]A = \frac{1}{2} base*height[/tex]
we'll use b and h to represent base and height
[tex]A = \frac{1}{2} b*h[/tex]
Okay, so you are given the area of the triangle already. It is [tex]35 cm^2[/tex]. SO you have:
[tex]35 = \frac{1}{2} bh[/tex]
Now here's the tricky bit of the question. You have 2 unknown variables, oh no! How will you solve? The key to this is simple, in a case where you have 2 or more unknown variables, ALWAYS think to yourself, "can I represent this variable in terms of another"?
In this case you can. They tell you what the height of the triangle is, in terms of the length of the base. They tell you, height is 4 cm more than 2 times the base.
So replace h in this equation with 2b + 4.
[tex]35 = \frac{1}{2} (b)(2b+4)\\\\35 = \frac{1}{2}(2b^2 + 4b)\\ 70 = 2b^2 + 4b\\0 = 2b^2 + 4b - 70\\0 = (2)(b^2 + 2b - 35)\\0 = (b +7)(b - 5)\\\\b = 5\\b\ \neq -7[/tex]
Okay, so you know the base of the triangle is 5 cm. The question asks for height, so what you're going to do is refer back to what h is.
We found that [tex]h = 2b + 4[/tex]
sub in 5 into that:
[tex]h = 2(5) + 4 = 14[/tex]
Therefore the height of the triangle is 14cm.
Answer:
Step-by-step explanation:
Givens
Area = 1/2 B* H
B = B
H = 2*B + 4
Area = 35
Solution
35 = 1/2 * B * (2B + 4) Multiply both sides by 2
35*2 = 2*(1/2) * B * (2B + 4) Combine
70 = B(2B + 4) Remove the Brackets.
70 = 2B^2 + 4B Subtract 70 from both sides.
2B^2 + 4B - 70 = 0 Divide everything by 2
B^2 + 2B - 35 = 0 Factor
(B + 7)(B - 5)
B+7 = 0 will give a minus number. Geometry does not allow minus numbers.
B - 5 = 0
B = 5
But what you want is the height.
h = 2b + 4
h = 2*5 + 4
Answer: h = 14
Re write the quadratic function in standard form y=(x+5)(x-2)
Answer:
y = x^2 + 3x - 10
Step-by-step explanation:
x*x + 5*x + -2*x + 5*-2
= x^2 + 3x + -10
PLEASE RATE!! I hope this helps!!
Please help!! I will give brainliest :)
Answer: I think its 75 percent
Step-by-step explanation:
Answer:
75%
Step-by-step explanation:
The shaded is part of the poster 9/12
To convert 9/12 into a percent
100 ÷ 12 = 8.3333333333333
[tex]\frac{9*8.3333333333}{12*8.3333333333} = \frac{75}{100}[/tex]
The side of a goal in soccer is the shape of a right trapezoid. The dimensions are shown below. What is the area of the net needed for both sides of the goal? Чft 8 ft 10 ft
Answer:
[tex]61^{2}[/tex]
Step-by-step explanation:
So area equals {(B+b) x h} / 2 the two bases are 4 and 10 which is 14 the height is 8 so 14 times 8 is 112. 112 divided by 2 is 61. I hope this helps.
Solve (images attached) can u check if correct
Answer:
Yes it's correct
Step-by-step explanation:
90 + 40 = 130
180 - 130 = 50
Did i do this right?
Answer:
yes
Step-by-step explanation:
please solve for x please use statement reason
AE || BC
===》 DCB angle = DAE angle
AC /
__________________________________
Thus :
DCB angle = x
And also we know that the submission of interior angles of any triangle must equals to 180 degrees so :
In BCD triangle :
B + C + D = 180
x + x + D = 180
D = 180 - 2x
__________________________________
In the other hand we know that :
BDC angle + BDA angle = 180
because they make a straight line together so ;
180 - 2x + 50 = 180
- 2x = 180 - 230
- 2x = - 50
x = 25
And we're done...
Have a great time ♡
8 out of 9 people in a class of 360 people are right handed, what is the percentage or right handed people and left. Then how many people out of the class of 360 is left and right handed.
Answer:
88.889% are right handed, 11.111% are left handed, ~320 people are right handed in a class of 360, ~40 people are right handed.
Step-by-step explanation:
The fraction 8/9 is equal to .88889, or 88.889%
Likewise, the fraction 1/9 (remainder) is equal to .11111, or 11.111%
By multiplying 360 by these fractions to get the number of people who fit these criteria in the sample, you get:
360*8/9 = 320 people right handed.
360*1/9 = 40 people left handed.
Cheers!
The researcher had to throw out some surveys because the
participants didn't complete them in full. What happened
to the power? Why?
Urgente!!! Doy 20 puntos
Answer:
74-7, 0, +9Step-by-step explanation:
Hope this helps
Use rounding to estimate the product of 5, 555 and 4, 444. Round both numbers to the nearest thousand to find your answer.
The solution is
Step-by-step explanation:
5,555 can be rounded up to 6,000 because the 5 next to the five thousand will make it go up. while the 4,444 will round to 4,000 . I don't have a clear answer but I hope this helps.
5 A bag of tiles contains 6 green, 4 yellow, and 5 blue tiles. If one tile is pulled at random what is the probability of NOT choosing a green tile.
Make sure to give your probability as a fraction in simplest form.
Answer:
3/5
Step-by-step explanation:
6+4+5 = 15
5+4 = 9
9/15 = 3/5
Answer:
3/5
Step-by-step explanation:
Since it given that a bag of tiles contains:
6 green
4 yellow
5 blue
To Find:
If one tile is pulled at random what is the probability of NOT choosing a green tile.
Solve:
knowing that there are a total of 15 tiles {6+5+4=15}
And there is 6 green tiles
Thus, 15 - 6 = 9
Hence, the probability of Not Choosing a green tiles before simplest form is 9/15
GCD - 3
Divide both the numerator and denominator by the GCD
9 ÷ 3/15 ÷ 3
Reduced fraction = 3/5
Therefore, the probability of Not choosing a green tiles is 3/5
~Lenvy~
How many more quarters does
Tommy need before he has $3.00
in quarters?
What is the probbability of flipping a coin 15 times and getting heads 6 times?
Answer:
if I'm wrong let me know 25
Are the ratios 5:4 and 20:16 equivalent?
Answer:
yes
Step-by-step explanation:
If you take 20 and divide by 4 you get 5. if you take 16 and also divide by 4, you will get 4.
40 feet in one hour = what speed in inches per second
Answer:
1728000
Step-by-step explanation:
40 feet is 480, then convert hour tom minute (times 60) then times 60 again to convert minute to second (times 60)
Hope this helps!
Solve for d
Can you pls help me?
Dylan purchased a new car in 1993 for $26,300. The value of the car has been depreciating exponentially at a constant rate. If the value of the car was $2,700 in the year 2001, then what would be the predicted value of the car in the year 2006, to the nearest dollar?
The predicted value of the car in the year 2006 to the nearest dollar would be $651.
What is the predicted value of the car?The first step is to determine the rate of depreciation
g = (FV/PV)^(1/n) - 1
Where:
FV = value of the car in 2001
PV = value of the car in 1993
n = number ofyears = 8
(2700/26,300)^(1/8) - 1 = -24.76%
Now determine the value of the car in 2006
2700x ( 1 - 0.2476)^5 = $651
To learn more about depreciation, please check: https://brainly.com/question/25552427
An amount of R351 is made up with 114 coins (R2 coins and R5 coins only). How many R2 coins are there? How many R5 coin are there?
Answer:
41
Step-by-step explanation:
For this, you have to make two equations;
One that calculates the amount of coins
and one that calculates the amount of R
I'm going to set
R2 = x
R5 = y
To make this a bit easier to look at
So to do the number of coins, you want to do this:
x + y = 114
This is saying that the total amount of R2 coins plus the total amount of R5 coins will add up to 114
Then, you want to calculate the worth of them.
2(x) + 5(y) = 351
This is saying that for ever R2 coin there is, it will increase the total by 2, and every R5, it will increase the total by 5. When you add these together, it will come out to 351.
Then you have to solve the system of equations:
x + y = 114
2x + 5y = 351
-2 * (x + y = 114)
2x + 5y = 351
-2x + -2y = -228
2x + 5y = 351
3y = 123
y = 41
Since y is the amount of R5 coins, we know we have 41 R5 coins.
So the answer is
41
Abby is shooting a rocket off the top of a 128 foot tall building at a velocity of 96 feet per second. The equation to represent this is h(t) = -16t? +960 + 128 where h(t) represents the height of the rocket and t is the time after takeoff.
What is the maximum height of the rocket?
How many seconds does ot take to get to the maximum height?
Find the time it takes (in seconds) for the rocket to crash to the ground.
Answer:
a) 272 feet
b) 3 seconds
c) 7.123 seconds
Step-by-step explanation:
A graphing calculator provides an easy way to answer questions about the parameters of a quadratic function. Here the graph shows ...
a) the maximum height is 272 feet
b) it takes 3 seconds to get there
c) the rocket crashes after about 7.123 seconds
__
You can solve this algebraically by rewriting the equation in vertex form.
h(t) = -16t² +96t +128 . . . . . . given
h(t) = -16(t² -6t) +128 . . . . . . . factor out leading coefficient
h(t) = -16(t² -6t +9) +128 -(-16)(9) . . . . complete the square
h(t) = -16(t -3)² +272 . . . . . . write in vertex form
The vertex of the height function is (3, 272) meaning the rocket reaches a maximum height of 272 feet after 3 seconds.
__
The zero of the function can be found to be ...
0 = -16(t -3)² +272
0 = (t -3)² -17 . . . . . . divide by -16
t -3 = ±√17 . . . . . . add 17, take the square root
t = 3 +√17 ≈ 7.123106 . . . . . positive time value for h(t) = 0
It takes about 7.12 seconds for the rocket to crash.
You invested $8,307 into stocks of a company that were priced at $12.75/sh. You decide to sell the stock. What is the sale amount if the stock is selling at $11.95/sh?
This is a spinner for a game board. color the spinner to show 20% chance of black and 80% chance of red.
Answer:
Step-by-step explanation:
Divide the circle into 10 parts and color 2 parts black and 8 parts red.
In 1994, the moose population in a park was measured to be 4180. By 1999, the population was measured again to be 3480. If the population continues to change linearly: Find a formula for the moose population, P, in terms of t, the years since 1990. P(t)=? What does your model predict the moose population to be in 2002?
"If the population continues to change linearly", meaning the pattern or equation is the equation of a straight line.
[tex](\stackrel{x_1}{1994}~,~\stackrel{y_1}{4180})\qquad (\stackrel{x_2}{1999}~,~\stackrel{y_2}{3480}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3480}-\stackrel{y1}{4180}}}{\underset{run} {\underset{x_2}{1999}-\underset{x_1}{1994}}}\implies \cfrac{-700}{5}\implies -140[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4180}=\stackrel{m}{-140}(x-\stackrel{x_1}{1994}) \\\\\\ y-4180 = -140x + 279160 \\\\\\ y = -140x+283340~\hfill \boxed{P(t)=-140t+283340}[/tex]
what if t = 2002?
[tex]P(2002)=-140(2002)+283340\implies P(2002)= 3060[/tex]
Mark rolls 2 fair dice and adds the results from each.
Work out the probability of getting a total that is a factor of 18.
Answer:
1/3
Step-by-step explanation:
Factors of 18 are 1,2,3,6,9
PU
The data set below represents the different costs of a refrigerator at a local home improvement store.
$777, $498, $619. $379. $895, $1,256, $1,052
b. What is the median of the second half of the data? (third quartile) 379
T
Using the median concept, it is found that the third quartile is of is of $1,052.
What is the median of a data-set?The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.
In this problem, the ordered data-set is:
$379, $498, $619, $777, $895, $1,052, $1,256.
Hence, the median of $777 divides the data-set into two halfs:
The first half is: $379, $498, $619.The second half is: $895, $1,052, $1,256.Hence, the third quartile, which is the median of the second half, is of $1,052.
More can be learned about the median concept at https://brainly.com/question/25215461
For f(x) = 2x+1 and g(x) = y2 - 7, find (f+ g)(x).
Answer:
D
Step-by-step explanation:
When you look for (f+g)(x), we are in essence say that we're looking for f(x)+g(x)
=(2x+1)+(x^2-7). (substitute for f(x) and g(x))
=2x+1+x^2-7. (remove the brackets by substituting positive 1 into g(x))
=2x+x^2-6 (add like terms- in this case 1-7=6)
=x^2+2x-6 (rearrange the equation)
Help me please, thank you
Answer:
Option D is your correct answer
I think it will help.
A passport consists of 2 letters followed by 2 digits. How many different passports can be formed?
67,600 different passwords can be formed.
26 x 26 x 10 x 10 = 67,600 (26 letters in the alphabet and 10 from 0-9)
6. Higher Order Thinking The manager of a restaurant wants to add two new side dishes to the menu. She surveys customers about side dish preferences and records the results in the table shown at the right. a. Find the experimental probability that a customer prefers either baked potato or asparagus. b. Find the experimental probability that a customer prefers either steamed broccoli or sweet potato.
Using it's concept, considering the number of desired and total outcomes, it is found that the probabilities are given by:
a. 0.6 = 60%.
b. 0.4 = 40%.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In an experimental probability, these numbers of outcomes are taken from previous trials.
Researching the problem on the internet, it is found that there is a total of 127 + 44 + 95 + 104 = 370 customers.
Item a:
127 + 95 = 222 customers prefer either baked potato or asparagus, hence the probability is given by:
p = 222/370 = 0.6 = 60%.
Item b:
44 + 104 = 148 customers prefer either steamed broccoli or sweet potato, hence the probability is given by:
p = 148/370 = 0.4 = 40%.
More can be learned about probabilities at https://brainly.com/question/14398287
how many integers from 100 to 999, inclusive, don't include the numbers 2,4,6,8? PLS HELP I WILL MARK BRAINLIEST
Answer:
243
Step-by-step explanation:
999-100= 899 integers
200s 400s 600s 800s excluded so 400 numbers excluded
899 - 400 = 499
20s 40s 60s 80s which are 40 integers x 4 = 160
499 - 160 = 339
2s 4s 6s 8s which are 4 integers x 6 x 4 ( 4 from each 100 ) = 96
339 - 96 = 243 integers