Answer: Width= 7 in.
Length= 10 in.
Step-by-step explanation:
[tex]l=w+3[/tex]
The perimeter of the rectangle is 34 inches.
[tex]2(w+l)=34[/tex]
substitute
[tex]2(w+w+3)=34[/tex]
[tex]2(2w+3)=34[/tex]
distributive property [tex]a(b+c)=ab+ac[/tex]
[tex]2\cdot 2w+2\cdot 3=34[/tex]
[tex]4w+6=34[/tex]
[tex]4w+6-6=34-6[/tex]
[tex]4w=28[/tex]
divide 4 on both sides
[tex]w=7[/tex]
Width is 7 inches
substitute w=7 in equation [tex]l=w+3[/tex]
[tex]l=7+3[/tex]
[tex]l=10[/tex]
Length is 10 inches
ASAP how many solutions are there for the system of equations shown on the graph?
Answer: Infinitely many solutions
Step-by-step explanation:
The lines is on top of each other so this makes it many solution.
It can't be NO solution because the lines are not parallel to each, which means they will not intersect.
It can't be one solution because the lines doesn't intersect.
It can't be two solutions because the lines never intersect and they never intersect twice either.
If the area of the rectangle shown below is given by the expression 3x2 + 7x – 6,
and the width is (x + 3), which of the following could represent the length?
Answer:
Step-by-step explanation:
3x² + 7x - 6 = 3x² + 9x - 2x - 2*3
= 3x (x + 3) - 2(x +3)
= (3x - 2)(x + 3)
Area of the rectangle = 3x² + 7x - 6
length * width = 3x² + 7x - 6
length * (x + 3) = (3x -2)(x +3)
length = [tex]\frac{(3x-2)(x+3)}{(x+3)}[/tex]
length = (3x - 2)
factorize 12p2q -9q2
Answer:
[tex] \boxed{3q(4 {p}^{2} - 3q)}[/tex]Step-by-step explanation:
[tex] \mathsf{ 12 {p}^{2} q - 9 {q}^{2} }[/tex]
In such an expression, the factor which is present in all terms of the expression is taken out as common and each term of the expression should be divided by the common factor to get another factor.
Factor out 3q from the expression
[tex] \mathsf{ = 3q(4 {p}^{2} - 3q)}[/tex]
Hope I helped!
Best regards!
Factorization of 12p²q-9q² is 3q(4p²-3q).
What is Factorization?Factorization is defined as breaking an entity into a product of another entity, or factors, which when multiplied together give the original number.
Here, given expression is, 12p²q-9q²
Now, by factorizing this we get,
3q(4p²-3q)
Hence, required factorization is 3q(4p²-3q)
To learn more on factorization click:
https://brainly.com/question/14549998
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Covert the verbal expression into an algebraic expression.
The product of 23 and a number x
Answer:
23×x
=23x
Hope it helps
Answer:
23x
Step-by-step explanation:
"The product of" indicates that we will be multiplying the two quantities. 23 multiplied by x can be written as 23 * x which simplifies to 23x.
SOMEBODY HELP PLEASE! ACME Hardware is introducing a new product called Greener Cleaner. Complete the table by finding the cost per milliliter for each size based on the sales price. One liter is 1,000 milliliters. (Answer the questions too, please!)
Answer:
Kindly check explanation
Step-by-step explanation:
SMALL SIZE :
AMOUNT OF LIQUID = 250 milliliters
Sales price = $4.50
Cost per milliliter :
Sales price / amount of liquid
$4.50 / 250 = $0.018
MEDIUM SIZE :
AMOUNT OF LIQUID = 500 milliliters
Sales price = $9.95
Cost per milliliter :
Sales price / amount of liquid
$9.95 / 500 = $0.0199
= $0.020 ( 3 decimal places)
LARGE SIZE :
AMOUNT OF LIQUID = 1 LITRE = 1000 milliliters
Sales price = $16.95
Cost per milliliter :
Sales price / amount of liquid
$16.95 / 500 = $0.0199
= $0.01695
= $0.017 ( 3 decimal places)
A) LARGE < SMALL < MEDIUM
B) LEAST EXPENSIVE WAY TO BUY 1500 milliliters of green cleaner :
1 large size + 2 small sizes
$16.95 + 2($4.50)
$16.95 + $9.00
= $25.95
C.) MOST EXPENSIVE WAY TO BUY 1500 milliliters of green cleaner :
3 medium sizes
3 * ($9.95)
$29.85
A 4-pack of greeting cards costs $7.40. What is the unit price?pls answer fast
Answer:
The unit price of the problem is that one pack of greeting cards costs $1.85
Step-by-step explanation:
In order to find the unit rate, you have to divide the price by the quantity of the product. So, we will divide 7.40 by 4 so we can see the price of one pack.
7.40 ÷ 4 = 1.85
So, one pack of greeting cards costs $1.85 which is also our unit price.
Answer:
1.85
Step-by-step explanation:
First, divided the money ( $7.40 ) by the whole number ( 4 )
Then, you will receive your answer
The Cartesian coordinate system can be applied to three-dimensional solids. Instead of two axes, the coordinate system has three. What are the labels? Check all that apply.
A. z
B. y
C. a
D. x
E. w
Answer:
its z y and x
Step-by-step explanation:
can i pls get brainliest
Find the difference of functions s and r shown
below.
r(x) = -x2 + 3x
s(x) = 2x + 1
(s - r)(x) =
Answer:
[tex]\displaystyle (s-r)(x) = x^2 - x + 1[/tex]
Step-by-step explanation:
We are given the two functions:
[tex]\displaystyle r(x) = -x^2 + 3x \text{ and } s(x) = 2x + 1[/tex]
And we want to find:
[tex]\displaystyle (s-r)(x)[/tex]
This is equivalent to:
[tex]\displaystyle (s-r)(x) = s(x) - r(x)[/tex]
Substitute and simplify:
[tex]\displaystyle \begin{aligned}(s-r)(x) & = s(x) - r(x) \\ \\ & = (2x+1)-(-x^2+3x) \\ \\ & = (2x+1)+(x^2-3x) \\ \\ & = x^2 +(2x-3x) + 1 \\ \\ & = x^2 - x + 1 \end{aligned}[/tex]
In conclusion:
[tex]\displaystyle (s-r)(x) = x^2 - x + 1[/tex]
4x − 1 < 11 solve for x
Answer:
[tex]\huge \boxed{x < 3}[/tex]
Step-by-step explanation:
4x - 1 < 11
Add 1 on both sides.
4x - 1 + 1 < 11 + 1
4x < 12
Divide both sides by 4.
(4x)/4 < 12/4
x < 3
Simplify 3 x times the fraction 1 over x to the power of negative 4 times x to the power of negative 3.
Answer:
3x^2
Step-by-step explanation:
Given:
(3x) * {(1/x)^-4 }* (x^-3)
=(3x) * {1 ÷ (1/x)^4} * {1/x^3}
=(3x) * {1(x/1)^4} * (1/x^3)
=(3x) * (x^4) * (1/x^3)
=(3x) (x^4) (1) / x^3
Multiply the denominators
=3x^5 / x^3
Can also be written as
=3*x*x*x*x*x / x*x*x
Divide the x
= 3*x*x / 1
=3x^2
what is this equation in simplest form? 9x + 26 + 7x - 17 = 2x + (-3x) + 5x
Answer:
4x+3=0 or x=-3/4
Step-by-step explanation:
9x+26+7x-17=2x-3x+5x
arrange all numbers with coefficient x at one side let's say the left hand side and constant or real numbers at the right hand side in doing that we get
9x+7x-2x+3x-5x=17-26
12x=-9
(12x)/3=-9/3
4x=-3
x=-3/4
2) In 1000 sq. meter of land a farmer cultivated 765 kg of rice with the wastage of 23.5%. I) Find the weight of the wastage. II) Find the weight and percentage of rice cultivated. 3) If the area has been increased 40 times in size, how much rice will be cultivated (excluding the wastag
Answer:
Weight of wastage=179.775kg
weight of rice cultivated= 585.225 kg
percentage of rice cultivated=76.5%
Step-by-step explanation:
Area of land=100 square meters
Cultivated rice=765kg
Wastage=23.5%
1) Weight of the wastage=23.5% of 765kg
=23.5/100 × 765
=17977.5 / 100
=179.775 kg
2) Weight and percentage of rice cultivated.
weight of rice cultivated = 765 kg - 179. 775 kg
= 585.225 kg
percentage of rice cultivated = 100 - 23.5
= 76.5%
3) if area is increased 40 times in size
New area=1000 square meters × 40
=40,000 square meters
Cultivated rice= 765kg × 40
=30,600 kg
Cultivated rice excluding wastage=585.225 kg × 40
=23,409 kg
Celine is Drake’s granddaughter. Her age is 4 years greater than of Drake’s age. If Celine is 28 years old, how old is Drake?
Answer:32
Step-by-step explanation:
if selling is 28 and she is 4 years greater than Drake then that is 28-4 which is 32 so Drake is 32 years old
Answer:
The answer is 32.
Step-by-step explanation:
If Celine is 28 and Drake is four years older than her, we do 28+4.
Solve for x.
13(x-3) = 39
x=1
x=4
x=6
x= 10
Answer:
x=6
Step-by-step explanation:
13(x-3) = 39
Divide each side by 13
13/13(x-3) = 39/13
x-3 = 3
Add 3 to each side
x-3+3 = 3+3
x = 6
Answer:
x=6 ,is right.
6-3=3&multiply 13=39
so answer is x=6
mark brainleast plz
Factor completely 2c5 + 44c4 + 242c3. 2c3(c + 11)2 2(c + 11)2 2c3(c + 11)(c − 11) 2c3(c2 + 22c + 121)
Answer:
2c^3(c+11)^2
Step-by-step explanation:
2c^5 + 44c^4 + 242c^3
Factor out the greatest common factor
2c^3(c^2+22c+121)
Recognizing inside the parentheses is (a+b) ^2 where a =c and b = 11
2c^3(c+11)^2
What is the slope of the line between (3, −4) and (−2, 1)?
Answer:
Slope = -1
Step-by-step explanation:
To find the slope of the line between two points, we simply need to take the difference of the y-coordinates over the difference of the x-coordinates.
(-2, 1) and (3, -4)
Slope = (-4 - 1) / (3 - (-2) )
Slope = -5 / ( 5 )
Slope = - 1
Cheers.
Kia was 200 m north of the Liebrary when he remembered he had to return some books to the library it took him to 200 seconds to do the round-trip which best describes cost round-trip
Answer:
His speed is 2 m/s
His velocity is 0 m/s
Step-by-step explanation:
I'll assume the question is
Kia was 200 m north of the Library when he remembered he had to return some books to the library it took him to 200 seconds to do the round-trip which best describes hist round-trip.
Kia's distance from the Library is 200 m
the round-trip took him 200 s
The total distance for the round trip = 200 x 2 = 400 m
His displacement for the round trip = 0 m (since he returns to his original position)
His speed = distance/time = 400/200 = 2 m/s
His velocity = displacement/time = 0/200 = 0 m/s
Dtermine the answer to (−5) + 4 and explain the steps using a number line
Answer:
Step-by-step explanation:
=-5 +4
= -1
put a dot on -1 and go from -5 to -1 and then from -1 to -5
How many more festivals had 18 to 23 countries represented than 0 to 5 countries represented?
Answer:
3
Step-by-step explanation:
Here, by reading the histogram, we will provide answer for the question asked.
We want to know how many more festivals had 18 to 23 countries represented than 0 to 5 countries.
Checking the histogram, we can see the 0-5 countries having a value of 1, while the 18-23 has a value of 4.
So, the number of more countries will be simply 4-1 = 3
Answer:
3
Step-by-step explanation:
what is happening to this graph when the x vaules -1 and 1
Answer:
c.
Step-by-step explanation:
Answer:
Hey there!
The graph is decreasing when the x values are between -1 and 1.
Let me know if this helps :)
What x value solves the equation? 3x – 5 = 1 x =
Answer:
x = 2
Step-by-step explanation:
3x - 5 = 1
Adding 5 to both sides gives us:
3x - 5 + 5 = 1 + 5
3x = 6
Dividing the equation by 3 gives us:
3x / 3 = 6 / 3
x = 2
Answer:
x = 2 Hfizfifsits96eotst9s
7. Verify the following: i) (ab + bc) (ab – bc) + (bc + ca) (bc – ca) + (ca + ab) (ca – ab) = 0 ii) (a + b + c) (a² + b² + c² – ab – bc – ca) = a³ + b³+ c³ – 3abc iii) (p – q) (p² + pq + q²) = p³ – q³. EXPLAIN
1. (ab + bc) (ab – bc) + (bc + ca) (bc – ca) + (ca + ab) (ca – ab) = 0
We know that (a+b)(a-b) = a²-b²
(ab + bc)(ab -bc) can be written as a²b² - b²c²
(bc + ca)(bc -ca) can be written as b²c² - c²a²
(ca + ab)(ca - ab) can be written as c²a² - a²b²
→ a²b² - b²c² + b²c² - c²a² + c²a² - a²b²
→ a²b² - a²b² - b²c² + b²c² - c²a² + c²a²
→ 0
2. (a + b + c) (a² + b² + c² – ab – bc – ca) = a³ + b³+ c³ – 3abc
→ a³ + ab² + ac² -a²b - abc -ca² + a²b + b³ + bc² - ab² - b²c - abc + a²c + b²c + c³ - abc - bc² - c²a
→ a³ + b³+ c³ + (- abc - abc - abc) + (ab² - ab² )+ (ac² - ca² ) -(a²b + a²b )+ (bc² - bc² )+ (a²c - c²a) + (b²c - b²c)
→ a³+b³+c³ - 3 abc .
3. (p – q) (p² + pq + q²) = p³ – q³.
→ p³ + p²q + pq² - p²q - pq² - q³
→ p³ - q³ +(p²q - p²q) + (pq² - pq²)
→ p³ - q³
Triangle L J K is shown. Angle J L K is a right angle. The length of the hypotenuse is 15 inches and the length of the side adjacent to the right angle is 10 inches. The angle between the 2 sides is x. Which equation can be used to find the measure of angle LJK? sin(x) = Ten-fifteenths sin(x) = Fifteen-tenths cos(x) = Ten-fifteenths cos(x) = Fifteen-tenths
Answer:
cos(x) = Ten-fifteenths
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that the relation between the adjacent side and the hypotenuse is ...
Cos = Adjacent/Hypotenuse
cos(x) = 10/15
Answer:
c
Step-by-step explanation:
A rectangle has an area of 21x+81. If the width is 3 units, what is the length of the rectangle
Answer:
(7x + 27) units
Step-by-step explanation:
A rectangle is a quadrilateral (has four sides) in which opposite sides are equal and parallel, also all the angles are equal. The area of a rectangle is given as:
Area = Length × Width
Given that the area of the rectangle is 21x + 81 and the width is 3 unit, to find the length of the rectangle, we have to use the formula of the area and then get the length. Therefore:
Area = Length × Width
21x + 81 = Length × 3
Length = (21x + 81) /3
Length = 7x + 27
The length of the rectangle is 7x + 27 units
Find the value of p.
Answer:
[tex]\huge\boxed{p = 3}[/tex]
Step-by-step explanation:
7p + 7 = 37 - 3p (They both are equal)
7p + 3p = 37-7
10p = 30
Dividing both sides by 10
p = 3
Answer:
p=3
Step-by-step explanation:
7p+7=37-3p
7p[+3p]+7=37-3p[+3p]
10p+7=37
10p+7[-7]=37[-7]
10p=30
10p/10=30/10
p=3
I hope this helps!
Observe the figure drawn, in which a square of side 15cm is removed from one corner of the given rectangle. Find the perimeter of the shaded region. Pls answer, no other irrelevant answer. Pls solve this. I will follow you if you do it. It's urgent!!!
Step-by-step explanation:
Let's start by finding the area of figure 1
The square:
15cm×15cm=225cm²
Then we're going to find the area of figure 2
it's a rectangle (A=L×W)
L=60cm-15cm(because those cm have been cut off)=45cm
W=40cm
Area=45cm×40cm
=1800cm²
Then we add up the sum
Area of 1+Area of 2
=225cm²+1800cm²
=2025cm²
Answer:
140 cm is the perimeter of the unshaded shape.
Step-by-step explanation:
Perimeter of the rectangle in whole = 2l + 2w
Where length is 60 cm and width is 40 cm.
P = 2 × 60 + 2 × 40
= 120 + 80
= 200 cm
To find the perimeter of the unshaded square = 4l
Where the length is 15 cm.
P = 4× 15
= 60 cm
To find the perimeter of the shaded shape = Perimeter of rectangle - Perimeter of unshaded square.
P = 200 - 60
= 140 cm
140 cm is the perimeter of the unshaded shape.
Properties and characteristics of sum and difference of two cubes.
Answer:
The properties and characteristics of the sum of two cubes
1) In the sum of two cubes, the middle sign of the binomial factor on the right hand side of the equation is positive
2) The trinomial factor has a middle sign that is opposite to the middle sign in the question on the sum of two cubes
The properties and characteristics of the difference of two cubes
1) In the difference of two cubes, the middle sign of the binomial factor on the right hand side of the equation is always negative
2) The trinomial factor has a middle sign that is opposite to the middle sign in the question on the difference of two cubes
Step-by-step explanation:
The sum and difference of two cubes are;
a³ + b³, and a³ - b³
Factorizing the expressions for the sum and difference of two cubes can be shown as follows;
Sum of two cubes; a³ + b³ = (a + b) × (a² - a·b + b²)
Difference of two cubes; a³ - b³ = (a - b) × (a² + a·b + b²).
multiple choice
a. 12 pie cm
b. 21 pie cm
c. 35 pie cm
Answer:
The correct option is;
a. 12 pie cm
Step-by-step explanation:
Cavalieri's principle states that if the cross-sectional area of two or more figures of the same altitude are the same at each level of the figures, then the volumes of the figures are also the same;
Given that the base area of the square based prism and the cylinder are the same, and that the square based prism and the cylinder have equal height of 4 cm, then by Cavalieri's principle, their volumes are the same
The volume of the square based prism = 452 cm³
Therefore, the volume of the cylinder (of equal base area) = 452 cm³
The formula for the volume of square based prism = Area of base × Height
∴ The volume of square based prism, 452 cm³ = Area of base × 4 cm
Which gives;
Area of the base of the square based prism = 452/4 = 113 cm²
The area of the base of the cylinder [tex]A_c[/tex] = The area of the base of the square based prism = 113 cm²
The area of the base of the cylinder,[tex]A_c[/tex] is given by the following equation;
[tex]A_c[/tex] = π×r² = 113 cm²
r = √(113/π) = √35.97 ≈ √36 = 6 cm
The circumference of the base of the cylinder,[tex]C_c[/tex] is given by the following equation
[tex]C_c[/tex] = 2×π×r ≈ 2×π×6 = 12×π cm
The correct option is 12 pie cm.
a cone with base radius 7 cm has a volume of 308 cm cube find the vertical height of the cone take π 22/7
pls now
Answer:
h=6.003 cm
Step-by-step explanation:
[tex] \frac{1}{3} \pi {r}^{2} h \: \: is \: the \: volume \: of \: cone[/tex]
1/3×22/7×7×7×h=308
h=308/51.3
Answer:
h = 6 cm
Step-by-step explanation:
r = 7 cm
Volume of cone = 308 cm³
[tex]\frac{1}{3}\pi r^{2}h=308\\\\\\\frac{1}{3}*\frac{22}{7}*7*7*h=308\\\\\\h=\frac{308*3*7}{22*7*7}\\\\\\h=2*3[/tex]
h = 6 cm
For the function f(x) = 3(x − 1)2 + 2, identify the vertex, domain, and range.
Answer:
Ok, our function is:
f(x) = 3*(x - 1)^2 + 2.
First, domain:
We should assume that the domain is all the set of real numbers, and then we see if for some value we have a problem.
In this case we do not see any problem (we can not have a zero in the denominator, and there is no function that has problems with some values of x)
Then the domain is the set of all real numers.
Vertex:
Let's expand our function:
f(x) = 3*x^2 - 3*2*x + 1 + 2
f(x) = 3*x^2 -6*x + 2
The vertex of a quadratic function:
a*x^2 + b*x + c is at:
x = -b/2a
here we have:
a = 3 and b = -6
x = 6/2*3 = 6/6 = 1.
And the value of y at that point is:
f(1) = 3*(1 - 1)^2 + 2 = 2
Then the vertex is at: (1, 2)
Range:
The range is the set of all the possible values of y.
Ok, we can see that the leading coefficient is positive, this means that the arms of our quadratic function will go up.
Then the minimal value of our quadratic function is the value at the vertex, y = 2.
This means that the range can be written as:
R = y ≥ 2
So the range is the set of all real numbers that are larger or equal than 2.
