The given expression is a difference of squares, so we have
16 (a + b)² - 49 (a - b)² = 4² (a + b)² - 7² (a - b)²
… = (4 (a + b))² - (7 (a - b))²
… = (4 (a + b) - 7 (a - b)) (4 (a + b) + 7 (a - b))
… = (4a + 4b - 7a + 7b) (4a + 4b + 7a - 7b)
… = (-3a + 11b) (11a - 3b)
b. A car factory makes 2 red cars for every
7 white cars. If it makes 483 white cars,
how many red cars did it make?
HELP ME
Divide the number of white cars made by it's ratio:
483/7 = 69
Multiply that by the ratio of red cars:
69 x 2 = 138
They made 138 red cars.
If a right triangle has sides of length 3 and 6, what is the length of the hypotenuse?
Answer:
Length of the hypotenuse = 3√5 units
Step-by-step explanation:
Given:
Right triangle sides
a = 3
b = 6
Find:
Length of the hypotenuse
Computation:
Length of the hypotenuse = √a² + b²
Length of the hypotenuse = √3² + 6²
Length of the hypotenuse = √9 + 36
Length of the hypotenuse = √45
Length of the hypotenuse = 3√5 units
daily give away today's amount is 100
Answer:
yes yes it is
Step-by-step explanation:
An 18 foot ladder rests against a wall. The base of the ladder is 8 feet from the wall. What angle does the
ladder make with the ground?
Answer:
The angle would be acute
Step-by-step explanation:
The angle that this ladder would make with the ground is equal to 63.64°.
How to determine the angle that the ladder make?In order to determine the angle that this ladder would make with the ground, we would apply Cosine trigonometric. Mathematically, this is given by this expression:
Cosθ = Adj/Hyp
Substituting the given parameters into the formula, we have;
Cosθ = 8/18
Cosθ = 0.4444
θ = cos⁻¹ (0.4444)
θ = 63.64°
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1. Ifx- y = 6 and 3x – 10 = 2y, what is the value of y?
I
I
A. -8
B. -4
C.4
D. 8
Answer:
the answer is -8
Step-by-step explanation:
Well, first you have to make an equation for what x equals, if that makes sense. So you take the x-y=6 and add y on both sides to get x=(y+6). Then you plug that.
write the place value of 1.059 each decimal
Answer:
1 x 1+0 x 1/10+5 x 1/100+9 x 1/1000
Step-by-step explanation:
help plssssssssssssss
plz help me i beg of u?
Yoshua borrowed $8,000 from his credit union over 9 months. He pays a simple interest of
9%. What is the total amount of money he will owe the bank?
Answer:
[tex]\boxed{\blue{\sf He\ will \ owe \ \$ 8540 .}}[/tex]
Step-by-step explanation:
According to Question , Yoshua borrowed $8,000 from his credit union over 9 months. He pays a simple interest of 9%. And we are required to find the total amount of money he will owe the bank .
So , we know the formula of Simple Interest as ,
[tex]\qquad\boxed{\red{\bf SI =\dfrac{P\times R\times T}{100}}}[/tex]
As ,per the data in Question ,
Amount = $ 8,000Time = 9 monthsRate of Interst = 9% .[tex]\implies SI = =\dfrac{P\times R\times T}{100} \\\\\implies SI =\dfrac{\$ 8000 \times \dfrac{9}{12}\times 9 }{100} \\\\\implies SI = \dfrac{\$ 8000 \times 9 \times 9 }{12\times 100 }\\\\\boxed{\pink{\bf \implies Simple\: Interst = \$ 540 }}[/tex]
Hence the Simple Interest is $ 540.
And , we know that Amount is ,
[tex]\qquad\boxed{\red{\bf Amount = SI + Principal}}[/tex]
[tex]\implies Amount = Principal + SI \\\\ \implies Amount = \$ 8000 + \$ 540 \\\\\boxed{\orange{\bf \implies Amount= \$ 8540 }}[/tex]
Hence he will owe $ 85400.
There are six multiple-choice questions on an exam, each with four possible answers. (a) Determine the number of possible answer sequences for the six questions.
Answer:
[tex]Possible\ Answers = 4096[/tex]
Step-by-step explanation:
Given
[tex]Questions = 6[/tex]
[tex]Options = 4[/tex] each
Required
Determine the number of possible answers
The first question has 4 possible answers
The second has 4 possible answers
The third has 4 possible answers
The fourth question has 4 possible answers
The fifth has 4 possible answers
The sixth question has 4 possible answers
[tex]Possible\ Answers = 4 * 4 * 4 * 4 * 4 * 4[/tex]
[tex]Possible\ Answers = 4^6[/tex]
[tex]Possible\ Answers = 4096[/tex]
Solve algebraically
-2x + 17 = 11
What is x
Answer:
x=3
Step-by-step explanation:
Final Answer:
x = 3
Solution:
equation: -2x + 17 = 11
Step 1: subtract 17 in both sides
-2x + 17 = 11
-2x + 17 - 17 = 11 - 17
-2x = 11 - 7 (solve for -2x: 11 - 7)
-2x = -6
Step 2: divide -2 in both sides then solve for x.
-2x = -6
-2x -6
____ = ____
-2 -2
(solve for x):
-6
x = ___
-2
x = 3
Mr. Wells tells his class of 24 that when they have completed the assignment, they may play online math games. At the end of class, 40% of the class is playing online math games. Approximately how many students still need to complete their assignment?
Answer:
14
Step-by-step explanation:
60% of 24 need to complete their tasks
this is 6x2.4=12+1.6=13.6 =14
I rlly need help
9-3÷1/3+2=?
Answer:
its 10
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
9-3÷1/3+ 2
9-3/ (1/3)+2
∵3/(1/3)= 9
so,
9-9 +2
0+2= 2
Impossible Math Question [ IF YOU GET THIS RIGHT YOU ARE A GENIUS }
write a point-slope foem an equation of the line that passes through the given point and has the given slopes (2,-2); m = -5?
a. y -2 = -5(x -2)
b. y+2 = -5(x +2)
c. y -2= -5(x+2)
d. y +2= -5(x -2)
Answer:
y+2 = -5(x-2)
Step-by-step explanation:
The point slope form of a line is
y- y1 = m(x-x1) where m is the slope and (x1,y1) is a point on the line
y - -2 = -5(x-2)
y+2 = -5(x-2)
Find the value of y showing your steps or explaining your thinking. (2 pts.)
Answer:
y = 54
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Equality PropertiesGeometry
Congruency All angles in a triangle add up to 180°Step-by-step explanation:
Step 1: Define
3(x + 7)° = 63°
3(x + 7)° + 63° + y° = 180°
Step 2: Solve for x
Divide 3 on both sides: x + 7 = 21 Subtract 7 on both sides: x = 14Step 3: Solve for y
Substitute in x: 3(14 + 7) + 63 + y = 180(Parenthesis) Add: 3(21) + 63 + y = 180Multiply: 63 + 63 + y = 180Combine like terms: y + 126 = 180Isolate y: y = 54A $270 suit is marked down by 20%. Find the sale price
Answer:
Marked down means the price has decreased by 20% so 100%-20%=80%
The suit is now 80% of its original price of 270.
So 270×(80/100)= 216
The selling price of the suit will be equal to $216.
The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that a $270 suit is marked down by 20%. The selling price will be calculated as,
Marked down means the price has decreased by 20%,
100%-20%=80%
The suit is now 80% of its original price of 270.
270×(80/100)= 216
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A cheetah runs 195 miles in 3 hours. What is his average speed in miles per hour?
Answer:
65 mph.
Step-by-step explanation:
divide
195/3
65 miles in 1 hour.
what is the inverse of the function f(x) = x + 3
Answer:
the answer would be f(x)=x-3
Step-by-step explanation:
Answer:
f inverse of x =x-3
Step-by-step explanation:
f(x)=x +3
let f(x) be y
y=x+3
make x the subject of the formula
x=y-3
hence,
f^-(x)=x-3
Eduardo won 40 pieces of gum playing hoops at the county fair. At school he gave one to every student in his math class. He only has 13 remaining. How many did he give away?
ill give you brilliant
One mile is about 1.57 kilometers. If you are traveling at 55 miles per hour, what is the best estimate of your speed in kilometers per hour? A. between 50 and 60 kilometers per hour B. between 60 and 70 kilometers per hour C. between 70 and 80 kilometers per hour D. between 80 and 90 kilometers per hour
Which ratio is equivalent to the ratio 13:15
Answer:
26:30
Step-by-step explanation:
A _____ equation is an equation whose graph is a straight line. answer for me please! worth 15 points!!!
Answer:
Linear function
Step-by-step explanation:
Write the product in its simplest form:
бу - бу?
Answer:
0
Step-by-step explanation:
This deals with simplification or other simple results.
3 is 75% os what number?
Answer:
12
Step-by-step explanation:
Answer:
3 is 75% of 4
You can use quarters to help to :)
a discount voucher offering 15% off is used to pay a bill. after using the voucher, the bill is reduced to £36.72.
How much was the bill before applying the voucher discount?
Answer:
hxbcncncncncncn
Step-by-step explanation:
hhjncnnfnf
2)
+
-12
6
13
+
5
-2
-3
-9
7
-24
4)
-7
0
+
+
-16
-5
21
-10
-11
-17
+
12
-6
+
2
4
-22
-13
9
15
[3(15+4)^2+2(20+5)^2]^0
Answer:
B
Step-by-step explanation:
any non-zero expression raised to the power of 0 equals 1
When solving the equation 3(x-7)=2-x, the property used in the first step is the...
what is the answer?
1/2n-3=5
Answer:
1 if its 5
2n-3 does = 10n-15
Step-by-step explanation:
am i right
hope it helos
Answer:
N= 16
Step-by-step explanation:
1/2 N - 3= 5
1/2 n = 8
n= 16