[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
Let the height of rectangle be = x,
height = x base = 3x - 8Area of rectangle = base × height
[tex](3x - 8) \times (x) = 16[/tex][tex]3 {x}^{2} - 8x = 16[/tex][tex]3 {x}^{2} - 8x - 16 = 0[/tex][tex]3 {x}^{2} - 12x + 4x - 16 = 0[/tex][tex]3x(x - 4) + 4(x - 4) = 0[/tex][tex](3x + 4)(x - 4) = 0[/tex]so, there are two cases now,
Case - 1 :
[tex]3x + 4= 0[/tex][tex]3x = - 4[/tex][tex]x = \dfrac{ - 4}{3} [/tex]here, value of x (length) is negative, measure of length can't be negative, so length is not equal to -4/3
Case - 2 :
[tex]x - 4 = 0[/tex][tex]x = 4[/tex]here, value of x = 4, and satisfys the condition so
length = x = 4 in base = 3x - 8 = (3 × 4) - 8 = 12 - 8 = 4 inThe rectangle's height is 4 inches and the rectangle's base is also 4 inches.
Let's assume the height of the rectangle is 'h' inches.
According to the given information, the base of the rectangle is 8 inches shorter than three times its height. This can be expressed as:
Base = 3h - 8
The area of a rectangle is given by the formula:
Area = Length * Width
In this case, the area is given as 16 square inches. We can set up the following equation:
16 = h * (3h - 8)
Expanding the equation:
[tex]16 = 3h^2 - 8h[/tex]
Setting the equation equal to zero:
[tex]3h^2 - 8h - 16 = 0[/tex]
To solve this quadratic equation, we can use factoring, completing the square, or the quadratic formula. Let's solve it using the quadratic formula:
[tex]h = (-b \± \sqrt{b^2 - 4ac}) / (2a)[/tex]
For this equation, a = 3, b = -8, and c = -16. Plugging in the values:
[tex]h = (-(-8) \± \sqrt{(-8)^2 - 4 * 3 * (-16)}) / (2 * 3)\\\\h = (8 \± \sqrt{64 + 192}) / 6\\\\h = (8 \± \sqrt{256}) / 6\\\\h = (8 \± 16) / 6[/tex]
We have two possible values for h:
h₁ = (8 + 16) / 6 = 4
h₂ = (8 - 16) / 6 = -1
Since the height of a rectangle cannot be negative, we can discard the value h₂ = -1.
Therefore, the rectangle's height is 4 inches.
Now, we can find the base of the rectangle:
Base = 3h - 8
Base = 3 * 4 - 8
Base = 12 - 8
Base = 4
Therefore, the rectangle's base is also 4 inches.
To know more about height, refer here:
https://brainly.com/question/18763136
#SPJ2
There are 4 times as many dogs as cats. If the total number of dogs and cats is 20, how many dogs are there?
Answer:
5
Step-by-step explanation:
4x = 20
4/4= 20/4
x = 5
OD 3
Use the distributive property to simplify the following expression 2(x - 4)
OA 2 - 8x
OB 2x + 8
OC 2x - 8x
D 2x - 8
PLEASE HELP ME WITH IT
Step-by-step explanation:
the answer is option 2nd (B)
Answer:
B n-12 turns into 12 which makes 7n-5 become -1 +7- 5 = 1
as 12 x7 = 84 and -5 + 84 = 79 our end sequence.
Step-by-step explanation:
how to approach answering questions for hw and for exam
step 1 hw find a diagram exam rewrite the diagram
step 2 hw work out each multiple question
step 3 see below how workings should be
SIGMA TELLS US The nth term is = k
SIGMA TELLS US The bottom value is value we start with _vs
SIGMA TELLS US The top value is the term we end with - te
A n-2 turns into 9 which makes 7n-5 become -2+7-5 = 0
B n-12 turns into 12 which makes 7n-5 become -1 +7- 5 = 1 (12 x7=84 and -5+84 = 79)
we can prove by using nth common term 7 x 12 -5 = 79
C n -1 turns into 5 which becomes -1+7 = 6
D n- 1 turns into 5 which becomes -1+7-5 = 1
we see the sequence given is 2, 9, 16 ....79 it is ascending sequence +7
we know the nth term is 7n-5 as we work out first step ( 2 - 7= -5)
we see the term we end with is either 9 12 or 5 and we see the end term given value is 72 so B is our answer.
Danielle bought a silver coat rack online it cost $653.76 +7% shipping and handling what was the total cost
round your answer to the nearest cent
Answer:
$699.52
Step-by-step explanation:
Theres two ways to solve this.
(1) You can either find 7 percent of 653.76 and then add it on
or
(2) You can just multiply the tax with the 653.76
Option (1)
You find 7 percent of 653.76. Now percent means out of a hundred so 7 percent is really 7/100 or 0.07
Now you multiply 653.76 by 0.07 which is 45.76 (rounded to nearest cent)
Now add it up to the total.
653.76+45.76= $699.52
Option (2)
This is the easier method in my opinion. SInce you want to find the total of the product including tax. The tax is technically multiplying the total. The total of course is 653.76 and total means everything. Everything means 100%. So you can add 100% to the tax cause technically thats what your doing becuase you grinding 7percent of the total which is 100 percent. So in this case your price is increasing by 107 percent.
(Example)
So If you want to find 100 percent of a product it would be the same exact result. Like 100 percent of 653.76 is 654.76… So using that we can just add the amount of tax to the 100%. 100+7=107%
Proof that this works is this
usually when you want to find a percentage of something, you turn the percentage into a decimal then multiply. So 100 percent of 653.76 is 653.76*1.00 which is 653.76. So the 100 percent is a place holder to prevent you from doing more steps. Now just add 7 percent since your increasing the total by 7 percent (tax). Now its 653.76*1.07 which when solved you would get $699.52. The same exact result. Less steps same result.
Final answer: $699.52
8.5x-2(2x+8) Pls give steps and I need it in expanded from
Answer:
[tex]\frac{9x}{2}[/tex] - 16
Step-by-step explanation:
8.5x - 2(2x + 8)
Use the distributive property to multiply −2 by 2x+8.
8.5x - 4x - 16
Combine 8.5x and −4x to get 4.5x.
4.5x - 16
= [tex]\frac{9x}{2}[/tex] - 16
what is the range of this graph
Answer:
I don't know sorry.....
Part C
How many times greater is the elevation of Tammy's house than the elevation of the ocean's surface at 2 p.m.?
Answer:
wouldnt the answer be 9.9
Step-by-step explanation:
12.1-2.2=9.9
Answer:
Step-by-step explanation:
The elevation of Tammy's house is 3 1/2 times the elevation of Winston’s house which is 12.1 and that would give us 42.35 and then subtract the 2pm ocean elevation which is 2.2 and that would leave us with the answer of 42.15. so no the answer is not 9.9
how much can 18 go to 80
Tanya brought a car into a shop for repairs. When she came back to pick up her car, the mechanic
gave her a bill for $800. Tanya was angry because the mechanic made a few repairs that they had
not agreed upon in advance. Tanya and the mechanic ultimately agreed on a final bill that was
25% lower than the initial bill. What was the amount of the revised bill?
(1 point)
Answer:
600$ Is the final payment
Step-by-step explanation:
Can u help?
1 3/4 - 3 9/10
Answer:
7/4- 39/10=
-8.6 = -8 3/5
Step-by-step explanation:
Which equation represents the following graph?
it a or d make your decision
compare -3 and 9. Which of the following is true
A. -3 < 9 and -3 < 9
B. -3 = 9 and -3 < 9
C. -3 > 9 and -3 < 9
D. -3 > 9 and -3 > 9
Answer:
The answer is A: -3<9 and -3<9
Step-by-step explanation:
because -3 is less than 9
Sheila walks 3 miles in 9/10 of an hour. How fast does she walk per hour?
Answer:
1 hours = 60 min
60 x 9/10 = 54 min
3 divided by 54 = 1/18
so she walks 1/18 miles per hour.
Im not sure though. It might be 3 divided by 9/10 = 3 1/3. I’m not that confident in my answer. But it is definitely one of them, either 1/18 or 3 1/3.
HELP! Question below!!
Answer:
4s²
Step-by-step explanation:
Hope this helps :)
pls mark as brainliest :))
Please someone help me and I will make you the brainliest just please help me.
Choose one of the three elements of African culture in colonial North America: food and farming, storytelling, or music and dance. Describe one way African culture influenced your chosen element in the colonies. Explain one way this influence can still be seen today?
Answer:
Music and dance. It's easier in today's society to see black influence over popular music genres, however, this most likely stemmed from African culture, and as you said, in colonial North America. The colonials who enslaved the Africans most likely (i keep using this term so that you can confirm with your own teachings) were influenced by their customs and music (which can include dance) and attempted to integrate it into their own culture. This would trickle down into the future generations through black-dominated genres, such as hip-hop, rap, drill, and dances, such as break dancing, hip-hop (dancing), and the sort.
Word search
Pls help me out
I need help pls and thank you
Answer:
(1). 2.5 (2). 25 (3). 0.4 (4) 69.91
Step-by-step explanation:
hope this helps
1)
I
I
? 20-
A) 999
C) 1219
B) 39°
D) 1020
Answer:
C
Step-by-step explanation:
[tex]\angle{VUW} = 180 - 141 = 39[/tex]
[tex]\angle{WVU} = 180 - (20 + 39) = 121[/tex]
Answer: 121
From an elevation of 0.5 m below the surface of the water, a swimmer dives at a rate of 0.25 m/s. What is the function rule for the swimmer's depth, d, and time, t?
will mark as brainliest do not delete my question
Answer:
-435.5m is the answer.
Step-by-step explanation:
A company offers you a salary of $2,000 per month plus a signing bonus of $10,000. What is the yearly salary rate? PLEASE HELP!!!!
Since yearly, without the bonus, you would make a certain amount by multiplying $2,000 to a year, which is 12 months.
2000 × 12 = 24,000 a year.
That would be $24,000 a year.
Next, we can add 10,000 to the amount, since you are not getting paid that much for a year. It is just a "...plus...", a bonus.
24,000 + 10,000 = 34000
Therefore, the yearly salary rate will be $34,000 a year.
What is the contrapositive of "If our plane is not late, then we make our connecting flight.
Answer:
If we make our connecting flight then our plane is not late.
Step-by-step explanation:
The contrapositive occurs when the conclusion and the hypothesis change places. Let the hypothesis be represented by "p" and the conclusion be represented by "q".
hypothesis (p) [ conclusion (q)]
Now in the given statement: If (our plane is not late), then [we make our connecting flight].
statement If p then q
contrapositive If q then p
The required contrapositive statement is: "If we do not make our connecting flight, then our plane is late."
The contrapositive of the statement "If our plane is not late, then we make our connecting flight" is formed by negating the hypothesis (antecedent) and the conclusion (consequent) and then switching their positions. The contrapositive is logically equivalent to the original statement. Here's the contrapositive:
Original Statement: If our plane is not late, then we make our connecting flight.
Contrapositive: If we do not make our connecting flight, then our plane is late.
In the contrapositive, we negate the "our plane is not late" to "our plane is late" and negate "we make our connecting flight" to "we do not make our connecting flight." Then we switch their positions.
To learn more about the contrapositive statement;
https://brainly.com/question/33840036
#SPJ3
You have 2/3 of a blueberry pie left over from dinner. If you sent 1/2
of the leftover blueberry pie home with your guests, how much of the blueberry pie do you have left in the dish?
Answer:
1/3
Step-by-step explanation:
mark me as brainlestAnswer: 1/6 of the pie is left
Step-by-step explanation: 2/3 x 2 = 4/6
1/2 x 3 = 3/6
4/6 - 3/6 = 1/6
What does the greater unit rate, or slope, mean in terms of the situation? What can you conclude from this?
Answer: it means that he covered more space when tiling than Felicia did. Tell me if I am right please.
Jose takes a job that offers a monthly starting salary of $2500 and guarantees him a monthly raise of 130$ during his first year of training. Find the general term of this arithmetic sequence and his monthly salary at the end of his training.
The general term of this arithmetic sequence is
nothing.
whats 1+1 please explain.
Answer:
1+1=2
Step-by-step explanation:
quick maff
Answer:
It's easy 1+1=2
Step-by-step explanation:
1 +1 =2
let me expalin.
you have an apple then I gave you I more apple then how much apple do you have ?
it's easy 1+1=2
What is the slope of the line whose equation is 2x-4y=10? Show answers
Step-by-step explanation:
the slope of the line = 1/2
that is the answer
Answer:
y = - 0.5x + 2.5
y = -1/2 + 5/2
Step-by-step explanation:
2x -4y = 10 lets find y
-4y = 10+2x
-4y = 2x-10
-4y/-4 = 2x/-4 - 10/-4
y = - 0.5x + 2.5
y = -1/2 + 5/2
4 3/6×11 7/12=??. Can y'all please help I kinda need it , I'm failing math
Answer: Solution is in Photo
SOMEONE PLS HELP ME WITH THIS QUESTION!!!
Answer: 9 sq. units
Step-by-step explanation:
(6x3)(1/2)=9
The ratio of men to women working for a company is 7 to 5. If there are 336 employees total, how many women work for the company?
please answer soon as possiblee!!!
==========================================================
Explanation:
m = number of men
w = number of women
The ratio of men to women is 7 to 5, meaning that m/w = 7/5
Cross multiply to get 5m = 7w.
Then divide both sides by 5 to end up with m = 7w/5 which is the same as m = 1.4w
We'll use this equation later.
------------------
Since there are 336 total workers, we know that:
m+w = 336
1.4w+w = 336 .... replace m with 1.4w
2.4w = 336
w = 336/(2.4)
w = 140 women work at the company
and m = 1.4*w = 1.4*140 = 196 men work at the company as well.
------------------
Checking the answer:
m+w = 196+140 = 336
m/w = 196/140 = (7*28)/(5*28) = 7/5
This helps confirm we have the correct value of w.
Please help with this math problem ASAP! Will give brainliest :)
Answer:
24
your welcome
Step-by-step explanation:
Answer:
7.5
Step-by-step explanation:
To find the area of a trapezoid it is:
[tex]A= \frac{a+b}{2}h[/tex]
Where h is the height, b is the base, and a is the "top base," so our values are:
h = 5
b = 9
a = 6
Plug them in and solve:
[tex]A= \frac{a+b}{2}h[/tex]
[tex]A= \frac{6+9}{2}5[/tex]
[tex]A= \frac{15}{2}5[/tex]
[tex]A = (7.5)(5)[/tex]
[tex]A = 37.5[/tex]
The area of the rectangle is found by using:
[tex]A=bh[/tex] where b is the base and h is the height. So our values are:
b = 6
h = 5
Plug in and solve:
[tex]A=bh[/tex]
[tex]A=(6)(5)[/tex]
[tex]A = 30[/tex]
Subtract the rectangle from the trapezoid:
37.5 - 30 = 7.5
Answer: 7.5
Hope this heps, have a nice day :D