Answer:
There are two possible values for r (area): r =-7 or r=3
Step-by-step explanation:
Given the rectangular rug area is:
[tex]r^{2} -4r -21[/tex]
We have to convert the above equation into factored form.
So two numbers whose product is -21r² and sum is -4r
<=> [tex]r^{2} -4r -21[/tex]
= [tex]r^{2} -7r + 3r -21[/tex]
= r (r -7) + 3(r -7)
= (r-7)(r+3)
We set [tex]r^{2} -4r -21[/tex] = 0
<=> (r-7)(r+3) = 0
<=> (r-7) = 0 or (r+3) = 0
<=> r =-7 or r=3
So, there are two possible values for r (area): r =-7 or r=3
Final answer:
The possible dimensions of the rectangular rug with the given area trinomial r²-4r-21 are 7 by 3 or 3 by 7.
Explanation:
The possible dimensions of the rectangular rug with area given by the trinomial r²-4r-21 can be found by factoring the trinomial.
Factoring r²-4r-21 results in (r-7)(r+3). Therefore, the dimensions could be 7 by 3 or 3 by 7.
What is the approximate surface area of the sphere?
Solve 5 - 2x < 7. Please help me
Answer:
x > -1
Step-by-step explanation:
Answer:
[tex]x>-1[/tex]
Step-by-step explanation:
[tex]5 - 2x < 7[/tex]
[tex]5-2x-5<7-5[/tex]
[tex]-2x<2[/tex]
[tex]$\frac{2x}{2}>\frac{-2}{2}$[/tex]
[tex]x>-1[/tex]
88 out of 132 in fraction form
Answer:
[tex]\frac{2}{3}[/tex]
Answer:
2/3
Step-by-step explanation:
Divide both the numerator and denominator by the GCD
88 ÷ 44
132 ÷ 44
Reduced fraction:
2
3
Therefore, 88/132 simplified is 2/3
Two nickels are what fraction of a dollar?
Answer:
1/10
Step-by-step explanation:
Answer:
2/20?
Step-by-step explanation:
do the side lengths 4.1,8.2,and 12.2 for a triangle
Answer:
Step-by-step explanation:
Three line segments can form a triangle if the length of the longest segment is greater than the sum of the lengths of the shorter segments.
4.1 + 8.2 > 12.2
12.3 > 12.2
true
They can form a triangle.
Now if c is the length of the longest side and a and b are the lengths of the shorter sides, then:
- if , [tex]c^{2}[/tex] = [tex]a^2 + b^2[/tex] the triangle is right
- If [tex]c^2 < a^2 + b^2[/tex]
- if [tex]c^2 > a^2 + b^2[/tex] the triangle is obtuse
[tex]4.1^2 + 8.2^2 = 16.81 + 67.24 = 84.05\\12.2^2 = 148.84\\148.84 > 84.05[/tex]
The triangle is obtuse.
The radius of a circle is 1 inch. What is its circumference?
Step-by-step explanation:
use the image below to help
Find the value of x, then use this value to determine the measure of each of the angles.
x =
The measurement of angle AOB = degrees.
The measurement of angle COB = degrees.
Answer:
x=15
AOB= 15
COB= 165
Step-by-step explanation:
What is the value of the rational expression when x=-2? -7 -9 9 7
The value of the rational expression [tex]\frac{2x^2+5x+9}{x^2+2x-1}[/tex] when x =-2 is -7
What is ration expression?A rational expression is an expression that can be written in the form of a ratio of two polynomial expressions. Specifically, it is a fraction in which the numerator and denominator are both polynomials.
How to find value of rational expression?To find the value of the rational expression when x=-2, we substitute -2 for x in the expression and simplify:
[tex]\frac{2x^2 + 5x + 9}{x^2 + 2x - 1}[/tex]
= [tex]\frac{(2(-2)^2 + 5(-2) + 9)}{((-2)^2 + 2(-2) - 1)}[/tex]
=[tex]\frac{8 - 10 + 9}{4 - 4 - 1}[/tex]
= [tex]\frac{7}{-1}[/tex]
= -7
Therefore, the value of the rational expression [tex]\frac{2x^2+5x+9}{x^2+2x-1}[/tex] when x =-2 is -7.
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The question is incomplete, see full details in the attached image.
The value of the expression is Option a. -7.
To find the value of the rational expression (2x² + 5x + 9) / (x² + 2x - 1) when x = -2, we need to substitute -2 into the expression.
First, let's calculate the numerator:
2(-2)² + 5(-2) + 9= 2(4) -10 + 9= 8 - 10 + 9= 7Next, we calculate the denominator:
(-2)² + 2(-2) - 1= 4 - 4 - 1= -1Now, we divide the numerator by the denominator:
= 7 / (-1)= -7So, the value of the rational expression when x = -2 is -7. Therefore, the correct answer is Option a. -7.
Complete question:
What is the value of the rational expression (2x²+5x+9)/x²+2x-1 when x=-2
a. -7
b. -9
c. 9
d. 7
If a circle has a radius of 17 cm. What is the circumference of the circle ?
Answer:
106.81 cm or 107 cm.
Step-by-step explanation:
The formula for finding the circumference (perimeter) of a circle is 2 times pi times r or the radius of the circle, or you can find the diameter by multiplying the radius by 2, in this case 34 and multiply that by pi. The diameter is 34 so multiply that by pi and you get 106.81 cm as an approximate. Hope this helps!
The circumferences of the circle is 106.76 cm.
What is circumferences?The circumference is the length of any great circle, the intersection of the sphere with any plane passing through its centre.
Given that, a circle has radius = 17 cm
We know that, circumference = π × diameter
diameter = 2 × radius = 17 × 2 = 34
circumference = 34 × 3.14 = 106.76 cm
Hence, the circumference of the circle is 106.76 cm
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A wire is needed to support a vertical pole 18 feet high. The cable will be
anchored to a stake 10 feet from the base of the pole. How much cable is
needed?
3. Of the three expressions shown, which two
are equivalent?
3+2(9 + 2n) 7(3 + 4n) 21 + 4n
Answer:
the answer would be the first and last equation
Step-by-step explanation:
both equations equal 21+4n
Final answer:
After simplifying the expressions, it's found that 3 + 2(9 + 2n) simplifies to 21 + 4n, and the third expression is exactly 21 + 4n. These two expressions are equivalent.
Explanation:
To determine which two of the three expressions are equivalent, we need to simplify each expression and compare them.
Let's simplify each expression:
3 + 2(9 + 2n) = 3 + 18 + 4n = 21 + 4n
7(3 + 4n) = 21 + 28n
21 + 4n = 21 + 4n
Now, we can compare them:
The first expression, after simplification, becomes 21 + 4n.
The second expression is 21 + 28n, which is not equivalent to the first.
The third expression is exactly 21 + 4n, which is equivalent to the first expression.
So, the expressions 3 + 2(9 + 2n) and 21 + 4n are equivalent.
help me pls !!
(Extra points)
And I need to explain it.
Answer:
true
Step-by-step explanation:
1. simplfy the expression to 7^2 *8/7^3=8/7.
2. that'll give u 8/7=8/7
Which rules of exponents will be used to evaluate this expression? Check all that apply.
StartFraction left-brace (negative 8) Superscript 4 Baseline right-brace Superscript negative 5 Baseline Over (negative 8) Superscript 6 Baseline EndFraction
product of powers
quotient of powers
power of a power
power of a product
negative exponent
zero exponent
Answer:
quotient of powers power of a power negative exponentStep-by-step explanation:
Given
( -8⁴)⁻⁵ / ( -8⁶)Evaluating:
( -8⁴)⁻⁵ / ( -8⁶) =( -8⁴ˣ⁻⁵) / ( -8⁶) = ⇒ Power of a power (nᵃ)ᵇ = nᵃᵇ(-8⁻²⁰)/( -8⁶) =8⁻²⁰⁻⁶ = ⇒ Quotient of powers nᵃ/nᵇ = nᵃ⁻ᵇ8⁻²⁶ = 1/8²⁶ ⇒ Negative exponent n⁻ᵃ = 1 / nᵃUsed rules:
quotient of powers power of a power negative exponentAnswer:
B-quotient of powers
C-power of a power
E-negative exponent
Step-by-step explanation:
Determine which diagram could be used to prove AABC - AEDC using similarity transformations,
The diagram which could be used to prove AABC - AEDC using similarity transformations is A.
What are congruent triangles?Suppose it is given that two triangles ΔABC ≅ ΔDEF
Then that means ΔABC and ΔDEF are congruent. Congruent triangles; are exact same triangles, but they might be placed at different positions.
The order in which the congruency is written matters.
For ΔABC ≅ ΔDEF, we have all of their corresponding elements like angle and sides congruent.
Thus, we get:
[tex]\rm m\angle A = m\angle D \: or \: \: \angle A \cong \angle D \angle B = \angle E\\\\\rm m\angle B = m\angle E \: or \: \: \angle B \cong \angle E \\\\\rm m\angle C = m\angle F \: or \: \: \angle C \cong \angle F \\\\\rm |AB| = |DE| \: \: or \: \: AB \cong DE\\\\\rm |AC| = |DF| \: \: or \: \: AC \cong DF\\\\\rm |BC| = |EF| \: \: or \: \: BC \cong EF[/tex]
(|AB| denotes length of line segment AB, and so on for others).
We are given that;
The three figures in the picture
Now, in first figure
Angle BAC= Angle CED
(given)
Angle BCA= Angle ECD
(interior opposite angles)
So, both triangles are congruent
Therefore, by congruent triangles answer will be figure A.
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Simplify the expression -2(p+4)^2-3+5p what is the simplified expression in standard form?
Answer
I got p-19 i might be wrong
Step-by-step explanation:
Answer:
brainliet plssssss
Step-by-step explanation:
Let's simplify step-by-step.
−2(p+4)^2−3+5p
Distribute:
=−2p^2+−16p+−32+−3+5p
Combine Like Terms:
=−2p^2+−16p+−32+−3+5p
=(−2p^2)+(−16p+5p)+(−32+−3)
=−2p^2+−11p+−35An atom of lithium has 3 protons 4 neurons and 2 electrons.
What is the overall charge on this atom
A) -3
B) -1
C) +1
D) +3
Answer:
positive 1
Step-by-step explanation:
hope it helps.
give me the brain PLZ:)
Please help me with #3.
Answer:
Total lateral surface of the pyramid = 54 [tex]cm^{2}[/tex]
which agrees with the first listed answer.
Step-by-step explanation:
Notice that the pyramid has for base an equilateral triangle of base 5 cm, and has three lateral triangles which have all the same dimensions for their base (5 cm - since they are all connected to the base of the pyramid), and their height (7.2 cm).
The actual LATERAL surface, includes only the surface of the three lateral triangles.
We use the formula for the area of a triangle: [tex]Area=\frac{base \,*\, height}{2}[/tex]
to calculate the area of each lateral triangle:
[tex]Area=\frac{5\,cm \,*\, 7.2\,cm}{2} \\Area=18 \,cm^2[/tex]
and then multiply the result by three (to account for the three lateral faces)
Therefore, the total lateral surface is:
Total lateral surface = 3 * 18 = 54 [tex]cm^{2}[/tex]
a student is helping decorate a bulletin board that is 5 feet long and 4 feet tall.. He needs to cut a piece of yarn to run along the diagonal from the top left to the bottom right of the board.
Answer:
6.40312424 feet
Step-by-step explanation:
using the pythagreons theorm you can find the missing side
a^2 + b^2 =c^2
5 x 5 + 4x4 = 41
then you find the square root of 41
the length would be 6.40312424 feet
Corri needs to get milk, eggs, bread, and cereal at the store. Since the bread is close to the cereal, Corri always picks up the cereal right after getting bread. List all of the different combinations of ways she can pick up the items she needs. Use the first letter of each item in your list (M, E, B, C)
Answer:
bread
cereal
milk
eggs
Step-by-step explanation:
Answer:mebc,embc, bcem,bcme.
Step-by-step explanation:
At Marvin's Motorcycle's a pair of gloves sell for $85. Marvin purchases them from the manufacturer for $50. What is the percent markup on the gloves?
Plz help! 10 points
I have a math problem. I don't know were to start here's my problem. You have 3 cards in front of you, on one side there's a letter either R, V or B. On the other side there's a hidden number. Find the 3 number's. Here's the information we already know:
1) R+V=B
2) V+B= 180
3) 5xB=V
I need help!!!
a(x−b) +bx+c=a+b solve for x helpp
What’s 3/8 off 20 inches
Answer:
I think the answer is 1'8 3'8
Answer:
Step-by-step explanation:
Work out the area of this circle.
Take a to be 3.142 and write down all the digits given by your calculator.
13 cm
The area of the circle is found by substitifying the radius into the formula A = πr². In this case, with a given radius of 6.5 cm and π as 3.142, the calculated area is approximately 132.732 square centimeters.
Explanation:To find the area of a circle, you use the formula A = πr², where A represents the area, π is a mathematical constant whose value is given as 3.142 in this case, and r is the radius of the circle.
Since the radius (r) is not directly mentioned in the question, we should understand that the given 13 cm refers to the diameter of the circle, hence the radius will be half, i.e., 13/2 = 6.5 cm.
Substituting these values into the formula gives: A = 3.142 * (6.5)². When you perform the calculation, the result would be about 132.732 square centimeters.
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What is the domain and range of the graph
Answer:
[tex]D={x,-1<=x<=5}, R={y,-6<=y<=4} [/tex]
Step-by-step explanation:
by graphing interpretation, horizontal range is the domain and vertical range is the range. buat your problem is an oval which not a function.
What is the value of x? 6 8 10 12
Answer:
Its 8
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
Can someone help me?
I’m stuck
BRAINLEST!!
Answer:
A
Step-by-step explanation:
Lateral surface area = surface area - bases
2(8(11) + 8(5)) =
256 <--- Lateral Surface Area
The bases have areas of 11*5 = 55
Multiply that by 2 and add to 256
256 + 110=
366 <---Surface Area
What is the common ratio of the sequence?
-2, 6, -18, 54,...
0 -3
O -2
3
08
Answer:
Step-by-step explanation:
To find the common ratio
First term=-2
r=6/-2
r=-3
Or
r=54/-18
r=-3
What is the area of the shape below? Hint: use the formula: A =1/2 h (b1 + b2) *
A. 54.6 yd squared
B. 172.5 yd squared
C. 112.5 yd squared
D. 120 yd squared
Answer:
B. 172.5 yd squared
Step-by-step explanation:
FIrst, we must find half of the height, which is 15/2 or 7.5.
Next we have to multiply 7.5 times (15+8) which is B.
What’s the answer????
Answer:
21
Step-by-step explanation:
Answer:
105 pages in 7 minutes
Step-by-step explanation:
cross multiply
hope this helped