Answer:
The width is 3cm, and the length is 7cm.
Step-by-step explanation:
Let's call the length of the rectangle [tex]l[/tex], the width of the rectangle [tex]w[/tex], and the area of the rectangle [tex]A[/tex], and write down everything we know about them.
The length of the rectangle is 11 centimetres less than six times its width, so we know that [tex]l = 6w - 11[/tex].
We also know that [tex]A = 21[/tex]. But what exactly is the area of a rectangle? Well, it's the product of its length and width, i.e. [tex]A = l\times w[/tex].
Then we have two equations involving [tex]l[/tex] and [tex]w[/tex]:
[tex]l = 6w - 11[/tex], and [tex]l\times w = 21[/tex].
So how do we find [tex]l[/tex] and [tex]w[/tex]? Let's substitute our first equation into our second, like so:
[tex]l \times w = (6w - 11) \times w\\{}\hspace{0.8cm}= 6w^2 - 11w\\{}\hspace{0.8cm}= 21[/tex]
We can rearrange this new equation to get everything on the same side, so that we have a standard quadratic equation, like this:
[tex]6w^2 - 11w - 21 = 0[/tex].
We can use the quadratic formula for this. You should have seen this before:
[tex]w = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex],
where [tex]a,b,c[/tex] are the coefficients of our quadratic equation. Plugging the values in, we see
[tex]w = \frac{11\pm\sqrt{121+504}}{12}\\\\{}\hspace{0.25cm}=\frac{11\pm\sqrt{625}}{12}\\\\{}\hspace{0.25cm}=\frac{11\pm25}{12}[/tex].
With a little further cancellation, we can find our two possible values of [tex]w[/tex] are
[tex]w = \frac{36}{12} = 3[/tex] and [tex]w = \frac{-14}{12}[/tex].
Since [tex]w[/tex] is a width of a rectangle, it can't possibly be negative, and so it must be 3.
We can now plug in this value into our equation from earlier, namely [tex]l = 6w - 11[/tex]. We can see that
[tex]l = 6\times 3 - 11 = 18 - 11 = 7[/tex],
and so we get our answer, [tex]w = 3[/tex]cm, [tex]l = 7[/tex]cm.
We can prove that this is right by multiply 3 and 7 together, and seeing that we get 21, the area we expect.
The sum of two numbers is 20.8 and their difference os 10.2. Find these numbers.
Answer:
the numbers are 10.6 and 10.2
Translate the given phase into an algebraic expression and simplify if possible: the quotient of -20 and -40.
Answer:
0.5
Step-by-step explanation:
-20 and -40
quotient means divide one another
-20 / -40
= 20/40
= 2/4
= 0.5
I made these into tiny tiny steps, enjoy.
The translation of the simplified algebraic expression for "the quotient of -20 and -40" is [tex]\dfrac{1}{2}[/tex].
A collection of constants, variables or numbers connected using one or more arithmetic operator is called an algebraic expression .
Example = 4y, 3x+4.
The quotient of -20 and -40 can be written as:
[tex]\dfrac{-20}{-40}[/tex]
The expression can be simplified in the lowest form as;
[tex]\dfrac{-20}{-40}[/tex] = [tex]\dfrac{1}{2}[/tex]
So, the simplified algebraic expression for "the quotient of -20 and -40" is [tex]\dfrac{1}{2}[/tex].
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Which shape never has four congruent sides?
A square
B rhombus
C parallelogram
D isosceles trapezoid
Answer:
D
Step-by-step explanation:
its not a parallelogram, so that is not possible
the rest are
i hope this helps!
Help ASAP being timed please.
Answer:
Its the third one
Step-by-step explanation:
Plot all of the points onto the graph, and draw a line through all of the points. It most closely resembles the third one
12. Remy took out a home-improvement loan to
pay for new kitchen cabinets. The loan was
for $10,000 at an annual interest rate of 5.6%.
Remy paid off the loan in 36 months.
She paid $ Drop-down in all
A. 10.680.00
B. 11,680.00
C. 12,016.00
D. 12,760.00
Answer:
Step-by-step explanation:
A=P(1+rt)
A=10000(1+.056(3))
A=10000(1.168)
A=$11680
Remy took the loan for [tex]\$10,000[/tex] at an annual interest rate of [tex]5.6\%[/tex] and paid off the loan in [tex]36[/tex] months. She paid [tex]\$11680[/tex] Drop-down in all.
What is interest ?Interest is the charge you pay when you borrow money from someone or the cost you charge to lend money to someone.
Simple Interest [tex]=\frac{Principal \ * \ Rate \ * \ Time}{100}[/tex]
We have,
Principal[tex]=\$10,000[/tex],
Interest rate [tex]=5.6\%[/tex]
Time[tex]=36[/tex] months [tex]=3 years[/tex]
So,
Interest [tex]=\frac{Principal \ * \ Rate \ * \ Time}{100}[/tex]
[tex]=\frac{10,000*5.6*3}{100}[/tex]
Interest [tex]= 1680[/tex]
So,
Total amount to be paid [tex]=( 10,000+1680)=\$11680[/tex]
So, the loan for [tex]\$10,000[/tex] at an annual interest rate of [tex]5.6\%[/tex] and time of [tex]36[/tex] months be paid [tex]\$11680[/tex] Drop-down in all.
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144 like exponent and with 12 like base
Answer:
That is not a question, Brainly is an educational app and I suggest you use it that way.
please help i am really struggling . i really dont get it thanks :)
Answer:
I=P-A
___________________________
What mathematical term describes both 5.3 and 8.2 in the expression 5.3x-8.2y+11.1?
Answer:
Step-by-step explanation:
Coefficients
The decimal numbers 5.3 and 8.2 represents the coefficient of 'x' and the coefficient of 'y', respectively.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expression is given below.
⇒ 5.3x - 8.2y + 11.1
The number associated with x is known as the coefficient of 'x'. And the number associated with y is known as the coefficient of 'y'.
The decimal numbers 5.3 and 8.2 represents the coefficient of 'x' and the coefficient of 'y', respectively.
More about the Algebra link is given below.
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Lesson 4-2
2 Fill in the boxes to find the resulting equation when 25 is subtracted from
each side. Simplify both sides of the equation,
25 + x =
25
31
25
10
Answer:
-25
Step-by-step explanation:
Given the equation 25 + x =
Subtract 25 from both sides
25 + x - 25 = 0 - 25
x = 0 - 25
x = -25
Hence the blank box will be -25
1. You can buy six cans of root beer for $2.50. How many cans of root beer
can you buy for $10? What proportions will work to solve this problem?
Answer
24 cans
Step by Step explanation
10$ / 2.5$ = 4
6 * 4 = 24
Someone help me out thx:(
Answer:
kwdgejyegjyfcsudyg
Step-by-step explanation:
PLEASE PLEASE HELP !!
The math team went to lunch to celebrate Ms. Renft's birthday on February 11th. The
cost of the meal with tax was $148. 60. The math team left a 15% tip. What was the
total cost of the meal including tip?
Answer:
$171.12
Step-by-step explanation:
Including the tip and cost, it is 171.12. Multiply 148.6 by 1.15, which includes the total cost plus another 15% for the tip.
Question 5 of 6
Use the guess and check method to solve this problem.
Bunyan Farm sells 3 pound and 5 pound bags of onions. The Tuesday
morning delivery consists of 25 bags weighing 99 pounds. How many bags
are there of each size?
A. 12 small bags and 13 large bags
B. 13 small bags and 12 large bags
C. 15 small bags and 10 large bags
D. 14 small bags and 11 large bags
Answer:
B. 13 small bags and 12 large bags
Step-by-step explanation:
This question can be solved using a system of equations.
I am going to say that:
x is the number of small bags.
y is the number of large bags.
The Tuesday morning delivery consists of 25 bags
This means that [tex]x + y = 25[/tex], that is [tex]y = 25 - x[/tex]
Bunyan Farm sells 3 pound and 5 pound bags of onions. Total of 99 pounds.
This means that [tex]3x + 5y = 99[/tex]
Since [tex]y = 25 - x[/tex]
[tex]3x + 5(25 - x) = 99[/tex]
[tex]3x + 125 - 5x = 99[/tex]
[tex]-2x = -26[/tex]
[tex]2x = 26[/tex]
[tex]x = \frac{26}{2}[/tex]
[tex]x = 13[/tex]
[tex]y = 25 - x = 25 - 13 = 12[/tex]
So 13 small bags and 12 large bags.
PLEASE HELP I ATTACHED A PICTURE
Answer:
option 2
Step-by-step explanation:
x is going away from 7 in a positive direction which means greater than. the fact that it is just greater than not equal to means that there is a black circle instead of a filled in one because it excludes that number.
Answer:
Option 2
Step-by-step explanation:
If the inequality is "x > 7" it means that if it was to be represented on a number line, all values that "c" could possibly take would be located to the right (on the number line) of 7. Now there only two options that follow this statement, those options are options 2 and 4. But there is another thing we must understand. x must be larger than 7 (it can not be equal to 7), therefor option 2 is right since it follows the second statement while option 4 would represent inequality "x ≥ 7".
Y intercept (3,1) and (-4,-6)?
Answer:
y-intercept: (0, -2)
Step-by-step explanation:
Determine by how much x (the run) and y (the rise) change as you go from (-4, -6) to (3, 1): The change in x is 7 and that in y is also 7. Thus, the slope is
m = 7/7, or m = 1.
Using the point-slope form and the point (3, 1), we get:
y - 1 = 1(x - 3), or y = 1 + x - 3, or y = x - 2
Comparing this to y = mx + b, we see that the y-intercept is -2.
A line passes through the point (-1,-7) and has a slope of 5
Write an equation in slope-intercept form for this line.
H) Jorge had 3 pounds of strawberries. He let his friend Matt eat 1/2 of the strawberries. How many pounds of strawberries did Matt eat?
Answer: Matt ate 1.5 pounds of strawberries.
Step-by-step explanation:
3 ÷ 1/2 = 1.5
Answer:
1.5 pounds
Step-by-step explanation:
Total of strawberries = 3 pounds
Mat eat half of the total of strawberries = 1/2 * 3 pounds = 1.5 pounds
4. Which situation could be represented by the equation 10.75 = 5.5 n?
Ricardo ran 5.5 miles.
He ran each mile in 10.75 minutes.
What is n, the total number of minutes it took Ricardo to run 5.5
miles?
Ricardo ran a totalof 10.75 miles on Monday.
He ran 5.5 miles in the morning and the rest of the miles in the
evening.
What is n, the number of miles Ricardo ran in the evening?
Ricardo ran a total of 10.75 miles.
He ran 5.5 miles each hour.
What is n, the number of hours Ricardo ran?
Ricardo ran 10.75 hours one week and 5.5 hours the next week.
What is n, the total number of hours Ricardo ran during these
weeks?
Answer:
Ricardo ran a total of 10.75 miles on Monday.
[tex]n =1.95[/tex]
Step-by-step explanation:
Given
[tex]10.75 = 5.5n[/tex]
Required
Which situation represents the equation and solve for n
The options show the relationship between distance, time and speed.
This is calculated as:
[tex]Distance = Speed * Time[/tex]
By comparison:
[tex]Distance = 10.75[/tex]
[tex]Speed = 5.5[/tex]
[tex]Time = n[/tex]
So, we can say that:
He ran 10.75 miles (option D)
Solving for n:
Make n the subject in [tex]10.75 = 5.5n[/tex]
[tex]\frac{10.75}{5.5} = n[/tex]
[tex]n = \frac{10.75}{5.5}[/tex]
[tex]n =1.95[/tex]
Someone pls help me i dont wanna fail.
A chain lying on the ground is 10 m long and its mass is 60 kg. How much work (in J) is required to raise one end of the chain to a height of 4 m?
Answer:
Approximately [tex]4.70 \times 10^{2}\; \rm J[/tex], assuming that [tex]g = 9.81\; \rm m \cdot s^{-2}[/tex].
Step-by-step explanation:
When the force [tex]F[/tex] is constant, moving by [tex]\Delta x[/tex] in the direction of the force would do a work of [tex]F \cdot \Delta x[/tex].
However, in this example, as an increasing portion of the chain gets lifted up, the force lifting the chain would increase in size. Hence, apply the integral form of this equation.
Let [tex]F(x)[/tex] denote the force required to lift the chain when the height above the ground is [tex]x[/tex] meters. At that moment, exactly [tex](x / 10)[/tex] of the chain would be above the ground. The mass of that much of the chain would be [tex](x / 10)\![/tex] the mass of the whole chain.
[tex]\begin{aligned}F(x) &= m(x) \cdot g \\ &= 60 \cdot \frac{x}{10} \cdot g = 6\, g\, x\end{aligned}[/tex].
Integrate with respect to [tex]x[/tex]:
[tex]\begin{aligned}\int \limits_{0}^{4} F(x) \cdot {\rm d} x &= \int \limits_{0}^{4} 6\, g\, x \cdot {\rm d} x \\ &= \left[(3\, g)\, x^{2}\right]_{x=0}^{x=4}\\ &= 48\, g \approx 4.7 \times 10^{2} \end{aligned}[/tex].
In other words, it would take approximately [tex]4.7 \times 10^{2}\; \rm J[/tex] of energy to raise one end of the chain to that height of [tex]4\; \rm m[/tex].
Simplify 2/4 please and thank you
Answer:
1/2
Step-by-step explanation:
2/4 is equal to 1/2, because if you divide 4 by 2 you get 2, and if you divide 2 by 2 you get one.
Basically, the simplification process would look something like this...
2/4 ÷ 2/2 = 1/2
It takes me 20 minutes to grade a students quit. how long in hours does it take me to grade 20
Answer:
400
Step-by-step explanation:
20 times 20
Three robots go out to lunch. They decide
to share the $11.91 bill evenly. How much
does each robot pay? WHATS the equation???
For what value of x is the rational expression below equal to zero?
X- 4/X-6
if a polynomial has one root in the form a+√b , it has a second root in the form of a_√b
Answer:
(a - √b)
Step-by-step explanation:
Roots occur as positive and negative conjugates. Therefore, the conjugate of (a + √b) is (a - √b)
Heyy can someone help me ¿? ;-; is for today ;-;
Zuleima puts her pebbles on the table. Make groups of 3 and have 1 left. Then make groups of 5 and have 2 left. How many stones does Zuleima have?
Step-by-step explanation:
she has 3 because she make group of five n have one and then make a group of five and had two, so add two plus one it will give u three
(-12,16) and (-4,-2)find the slope
Answer:
It's -9/4 or -2 1/4. please mark me brainliest <3
Step-by-step explanation:
1) label x1, y1, x2, and y2.
x1 y1 x2 y2
(-12, 16) (-4,-2)
2) Remember the formula is y2-y1
--------
x2-x1
3) substitute
-2-16
--------
-4-(-12)
4) two minuses (negatives) is a positive (+)
so,
-2-16 -18
---------= --------
-4+12 8
5) simplify
-18 divided by 2 -9
----- = ------- or -2 1/4
8 divided by 2 4
Answer:
-1.75
Step-by-step explanation:
calcule:(-2)⁰+(-2)¹+(-2)²+(-2)³
por favor
Answer:
-5
Step-by-step explanation:
Anthony borrowed $18,800 at 6% simple interest for 4 months. Determine the amount of interest.