[tex] \LARGE{ \underline{ \tt{Required \: answer:}}}[/tex]
We have:
The length of a triangle is 3 centimeters less than twice its width.Area = 35 cm²We need to find:
Dimensions of the rectangle?Solution:
Let the width be w. Then the length would be:
➝ Length = 2(width) - 3
➝ l = 2w - 3
Area of rectangle: l × b
➝ Length × width = 35 cm²
➝ (2w - 3)w = 35
➝ 2w² - 3w - 35 = 0
Now finding value of x by middle term factorisation,
➝ 2w² - 10w + 7w - 35 = 0
➝ 2w(w - 5) + 7(w - 5) = 0
➝ (2w + 7)(w - 5) = 0
Hence,
w = 5 because width can't be negative.l = 2(5) - 3 = 7Therefore,
Width = 5 cmLength = 7 cm⛱️ [tex] \large{ \blue{ \bf{FadedElla}}}[/tex]
let x represent the rectangle's width;
thus;
Width = x
Length = 2x - 3
Area = 35 sq. cm.
Area = Length × Width
35 = (2x - 3)(x)
35 = 2x^2 - 3x
2x^2 - 3x - 35 = 0
Factorizing:
x = 5 or -3.5
but width is a scalar quantity and cannot be negative:
Hence:
Width = 5 cm.
Length = 2(5) - 3 = 7 cm.
6x = 41
x = 7 to the nearest whole number.
Width = 7 cm.
Length = 2(7) - 3 = 11 cm.
7. A new car depreciates as soon as you drive it out of the parking lot. A certain car depreciates to
half its original value in 4 years. If you bought a car 8 years ago and it is now worth $5,000, how
much did you pay for the car originally?
Given :
A new car depreciates as soon as you drive it out of the parking lot. A certain car depreciates to half its original value in 4 years. If you bought a car 8 years ago and it is now worth $5,000.
To Find :
How much did you pay for the car originally.
Solution :
Let, original price is x.
It is given that price gets half after 4 years.
So, price after 8 year is, P = x/4 .
x/4 = 5,000
x = $20,000
Therefore, price of new of car is $20,000.
Hence, this is the required solution.
(GIVING BRAINLIEST AND EXTRA POINTS!!!)
Solve the equation using equivalent fractions. SHOW YOUR WORK.
13/14 - 1/7 + 1/2
Answer:
1 2/7 or 9/7
Step-by-step explanation:
First subtract 13/4-1/7=11/14
Then take the answer we subtract so we can add it 11/14+1/2= 1 2/7
A dog that weighs 14 pounds should eat 1 5/8 cups of a certain type of dog food per day. How much of the same type of dog food should be fed, per day, to a dog who weighs 26 pounds?
PLEASE HELP!!!!!!!!
9514 1404 393
Answer:
3 1/56 cups
Step-by-step explanation:
Apparently, you're to assume that the amount of food is supposed to be proportional to weight. If x is the amount of food for the 26-pound dog, then ...
cups/weight = (1 5/8)/14 = x/26
Multiplying by 26 we have ...
x = (26)(13/8)/14 = 338/112 . . . cups
x = 3 1/56 cups ≈ 3.02 cups
About 3.02 cups of the same type of food should be fed to a 26-pound dog.
Plz help this is khan and I don’t remember how to do this
Show work for branliest
Which expression is equivalent to =
(4x^ 3 ) (2x)^-4
A. 1/(4x)
B. 4/x
C. 8/x
D. 128/x
one angle of a triangle is 60 degree and the other two are in the ratio 2:3.Find these angles
Answer:
48 and 72 degrees.
Step-by-step explanation:
The sum of the other 2 angles = 180-60 = 120 degrees.
So they are 2 / (2+3) * 120 = 2/5 * 120 = 48 and 3/5 * 120 = 72 degrees.
Inseri the missing number.
8 5 2
4 2 0
9 6 ?
how do you write the algebraic notation when the scale factor is 3
Answer:(2 * 3, 1 * 3)
Step-by-step explanation:
What is the sum of 347+645=
Answer:
347 + 645 = 992
Step-by-step explanation:
347
+645
922
Solve.
-2(3x + 7) = -8x
Answer:
x=7
Step-by-step explanation:
-6x-14=-8x
-6x+8x=14
2x=14
x=7
yes it. is right man ansls gqbevih wo
Can anyone help me ????
Answer:
i know i had this question let me find it
Step-by-step explanation:
Answer:
40
Step-by-step explanation:
the formula for a parallelogram is A=b*h
12.32-8
Using mental math
Answer:4.32...i think
Step-by-step explanation:
Answer:
12.32-8= 4.32 OR 12 x 32 - 8 = 376
Step-by-step explanation:
12.32
- 8.00
= 4.32
OR
32
x 12
= 376
Just depends if the dot was a multiplication dot or decimal.
Hope it helps!!
Please help ASAP!!!!!!
9514 1404 393
Answer:
a) correct
b) needs parentheses: -1, (1±i√2)/3
Step-by-step explanation:
a) You can factor by grouping:
(x³ -2x²) -(5x -10) = x²(x -2) -5(x -2) = (x² -5)(x -2)
Roots are ±√5, 2.
__
b) The sum of odd-degree coefficients is equal to the sum of even-degree coefficients (3-1 = 1+1), so one root is x=-1. Factoring out that leaves the quadratic factor ...
3x³ +x² -x +1 = (x +1)(3x² -2x +1)
The quadratic formula can be used on the quadratic factor to find its roots:
x = (-(-2) ±√((-2)²-4(3)(1)))/(2(3)) = (2 ±√-8)/6 = (1 ±√-2)/3
Roots are -1, (1 ±i√2)/3.
just need help with a. please helppp
Answer:
Domain: [tex]-5\leq x\leq 4[/tex]
Range: [tex]-5\leq y\leq 5\\[/tex]
Function: yes
Step-by-step explanation:
Domain is all possible x values. In this function, domain would be: [tex]-5\leq x\leq 4[/tex]
Range is all possible y values. In this function, range would be: [tex]-5\leq y\leq 5[/tex]
This is a function because it passes the vertical line test.
The probability of college graduate getting employed within a year is 90 % 90%. The probability of a college graduate getting employed and buying a car within a year is 72 % 72%. What is probability that a college graduate bought a car within a year given that he got employed within a year?
Answer:
Step-by-step explanation:
Let the probability of getting employed after graduated within a year be P(A)
and the probability of buying a car within a year be P(B)
Given that:
The probability of getting employed after graduated within a year = 90% = 0.9
Then; Let that be P(A)
The probability of getting employed and buying a car within a year = 72% = 0.72.
Then; Let that be P(A∩ B).
The probability that a college student will get both events is P(B/A)
[tex]P(B/A) = \dfrac{P(A \cap B) }{P(A)}[/tex]
[tex]P(B/A) = \dfrac{0.72}{0.90}[/tex]
P(B/A) = 0.80
Please help me out. Thanks
Answer:
61
Step-by-step explanation:
Rectangle area=
[tex]60 \times 40 = 2400yd ^{2} [/tex]
The area at the right
[tex](\pi \times 20^{2} ) \div 2 = 628yd^{2}[/tex]
Total area = 2400+628=3028yd^2
Now you have to find the quantity of grass seed needed (1pound for every 50yd square)
3028/50=60.56 (which is almost 61)
Can someone help me with this? am i supposed to graph
Answer:
Step-by-step explanation:
1). a(x) = -4x + 7 If x > 1
a(8) = -4(8) + 7
= -32 + 7
= -25
2). a(x) = 2x - x² If -6 < x ≤ 1
a(1) = 2(1) - 1²
= 2 - 1
= 1
3). a(x) = |x - 8| If x ≤ -6
a(-7) = |- 7 - 8|
= |-15|
= 15
4). a(x) = 2x - x² If -6 < x ≤ 1
a(-3) = 2(-3) - (-3)²
= -6 - 9
= -15
5). a(x) = 2x - x² If -6 < x ≤ 1
[tex]a(-\frac{1}{2})=2(-\frac{1}{2})-(-\frac{1}{2})^{2}[/tex]
= - 1 - [tex]\frac{1}{4}[/tex]
= [tex]-\frac{5}{4}[/tex]
6). a(x) = -4x + 7 If x > 1
[tex]a(\frac{9}{4})=-4(\frac{9}{4})+7[/tex]
= -9 + 7
= -2
May u please help me ill give out the brainly
Answer:
the answer is a
Step-by-step explanation:
they are just flipped thats all
I am kind of stuck on this question could someone explain and answer this question I would really appreciate it :)
Answer:
First one
Step-by-step explanation:
Supplementary angles basically means which angles added together equals 180 degrees, 180 degrees is also a straight line.
So the answer would be the first one because both the angles added together is 180.
The radius of the base of a cylinder is increasing at a rate of 11 meter per hour and the height of the cylinder is decreasing at a rate of 44 meters per hour. At a certain instant, the base radius is 55 meters and the height is 88 meters. What is the rate of change of the volume of the cylinder at that instant (in cubic meters per hour)?
Answer:
The volume of the cylinder is decreasing at a rate of 83629.2 m³/h.
Step-by-step explanation:
The volume of a is given by:
[tex] V = \pi r^{2}h [/tex]
Where:
r: is the radius = 55 m
h: is the height = 88 m
We can express the rate of change of the volume of the cylinder as follows:
[tex] \frac{dV}{dt} = \pi[h\frac{2rdr}{dt} + r^{2}\frac{dh}{dt}] [/tex]
If dr/dt = 11 m/h and dh/dt = -44m/h, we have:
[tex] \frac{dV}{dt} = \pi[88 m*2*55 m*11 m/h + (55 m)^{2}*(-44 m/h)] = -83629.2 m^{3}/h [/tex]
Therefore, the volume of the cylinder is decreasing at a rate of 83629.2 m³/h.
I hope it helps you!
The hanger image below represents a balanced equation.
Answer:
[tex] \frac{1}{5} + z = \frac{3}{5} [/tex]
Answer:
1/5+z=3/5
Step-by-step explanation:
Gina says that for all real numbers a and b, ab=ba. is this statement true or false? If false, give a counterexample
Answer:
True
Step-by-step explanation:
The communative property states that the order in addition and multiplication dosen't matter.
The hypotenuse is always the __________ side of a right triangle.
Answer:
the answer is opposite
Read the description of f below, and then use the drop-down menus to complete an explanation of why f is or not a function. Help
Answer:
can you add the dropdown menu? hard to answer without the dropdown
Step-by-step explanation:
Answer:
hope this helps!
Step-by-step explanation:
What value of x is in the solution set of 2x-3 > 11 - 5x?
Answer:
x ≤ 3
Step-by-step explanation:
Answer:
The value of x is 2.
Step-by-step explanation:
The key to this solution is to combine like terms.
2x-3 > 11-5x
There are lots of ways to combine them but the way I think would be the most simple would be to avoid negative numbers (although I personally enjoy it) but anyways,
First, you can add 5x to both sides of the inequality.
This would cancel out 5x and leave you with: 7x-3 > 11
The next terms that you can combine can be the constants. You can combine -3 and 11 and to do that, you add 3 on both sides. That would cancel 3 out and leave you with: 7x > 14
Now, the last step is to get x by itself and to do that, you divide 7 on both sides to get:
x > 2
I hope my explanation wasn't too confusing for you
The question is below (This an order of operation question)
Step-by-step explanation:
i am 90% sure this is correct
Answer:
Step-by-step explanation:
Do multiplication first since it comes before the division in this equation
1/5 · 1/2 = 1/10
Plug this value back into the equation
1/2 - 1/10 + 2/5 ÷ 7/10
Divide 2/5 by 7/10
4/7
Plug this value back into the equation
1/2 - 1/10 + 4/7
Subtract 1/10 from 1/2
2/5
Plug this value back into the equation
2/5 + 4/7
Add.
34/35
Hope this helps :)
Please consider Brainliest :)
how would you round 1.2983 to the thousandth
Answer:
1.298
Step-by-step explanation:
After the decimal the numbers go
tenths Hundredths and then thousands
Then take the number that's after thousands and raise the thousands number up is the numbers after is above 5 keep it the same if its 4 or under.
If Paul’s savings are 25% more than Janet’s savings,
What percentage of Paul
savings are Janet’s savings
(A) 25 %
(B). 50%
(C) 75%
(D) 80%
A 15 foot ladder is leaning against a building, with the base of the ladder 4 feet from the building. How high up on the building will the top of the ladder reach?
The ladder will reach
android:
nothing ft high up on the building.
(Round to the nearest tenth.)
Enter your answer in the answer box and then click Check Answer.
All parts showing
Answer: The height of the building = 14.5 feet.
Step-by-step explanation:
Given: Length of ladder = 15 feet
Distance of base of ladder from building = 4 feet
Since building is standing vertical on ground making right angle.
So with ladder a right triangle is formed , where base = 4 feet , Hypotenuse = 15 feet [Hypotenuse is side opposite to right angle]
According to the Pythagoras theorem ,
Hypotenuse² = Perpendicular² + Base²
⇒ (15)² = Perpendicular² + (4)²
⇒ 225 = Perpendicular² +16
⇒ Perpendicular² = 225 -16
⇒ Perpendicular² = 209
⇒ Perpendicular = √209 = 14.4568322948 ≈ 14.5 feet
Hence, the height of the building = 14.5 feet.
For a dosage of x cubic centimeters (cc) of a certain drug, the resulting blood pressure B is approximated by the function below. Find the maximum blood pressure and the disage at which it occurs.
B(x)= 395x^2- 2370x^3, 0 <= x <= 0.16
a. The maximum is obtained for a dosage of __________________.
b. The maximum blood pressure obtained is ______________.
Answer:
A) Maximum for dosage is 0.11
B) maximum blood pressure = 1.625
Step-by-step explanation:
We are given the function;
B(x) = 395x² - 2370x³
To find maximum, we will find the derivative of the function and equate to zero.
B'(x) = 790x - 7110x²
Equating to zero gives;
790x - 7110x² = 0
790x = 7110x²
Dividing both sides by x gives;
790 = 7110x
x = 790/7110
x = 0.11
This falls in between the range of 0 <= x <= 0.16 given to us.
Therefore x = 0.11 is a maximum
Plugging this into B(x) = 395x² - 2370x³ gives;
B(0.11) = 395(0.11)² - 2370(0.11)³
B(0.11) = 1.625
Thus;
Maximum dosage is 0.11
maximum blood pressure = 1.625