Answers
Part 1
Answer: (x+5)(x+10) - 50 = 126Other answers are possible.
-------------
Explanation:
The old width was 5, but then it increases to x+5. The old length was 10, but now it's x+10.
The area of any rectangle is length times width.
So the area of the larger rectangle is (x+5)(x+10). Subtract off the old area of 5*10 = 50 and we get (x+5)(x+10) - 50 as the area of the L shape. Set this equal to 126 to finish setting up the equation. This is one possible answer out of many others. This is because we could expand out the (x+5)(x+10) into x^2+10x+5x+50 or simplify that to x^2+15x+50, as two possible options.
==========================================================
Part 2
Answer: x = 6-------------
Explanation:
Solve the equation we set up in the previous part
(x+5)(x+10) - 50 = 126
x^2+10x+5x+50-50 = 126
x^2+15x = 126
x^2+15x-126 = 0
Apply the quadratic formula from here
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(15)\pm\sqrt{(15)^2-4(1)(-126)}}{2(1)}\\\\x = \frac{-15\pm\sqrt{729}}{2}\\\\x = \frac{-15\pm27}{2}\\\\x = \frac{-15+27}{2} \ \text{ or } \ x = \frac{-15-27}{2}\\\\x = \frac{12}{2} \ \text{ or } \ x = \frac{-42}{2}\\\\x = 6 \ \text{ or } \ x = -21\\\\[/tex]
Another method you could use is factoring, so you could say:
x^2+15x-126 = 0
(x-6)(x+21) = 0
x-6 = 0 or x+21 = 0
x = 6 or x = -21
The issue with this is that it may take a while to do this trial and error approach.
Whichever method you used, you'll end up with two solutions. One of those solutions doesn't make sense though. We can't have a negative length or distance value, so we ignore x = -21.
The only practical solution is x = 6
If x = 6, then the old height goes from 5 to x+5 = 6+5 = 11
If x = 6, then the old length goes from 10 to x+10 = 6+10 = 16
The new larger rectangle is 11*16 = 176 sq ft, in which we subtract off the 50 sq ft to get 176-50 = 126 sq ft, and this matches with the 126 given to us. Therefore, the answer is confirmed.
Related Questions
what is 48x + 56 factored
Answers
Answer:
8(6x + 7)
Step-by-step explanation:
Find a factor for both of the numbers (8)
Place the remaining numbers in a bracket (6x +7)
Place the 8 outside the bracket
8 (6x + 7)
Have a good day :)
Answer:
All you have to do is factor like this. It is also know as common factoring.
48x+54
8(6x+7) You chose the eight because it fits into 48 and 54. So you find the multiple of 8 to get the total of 48. And that is 6 and for 54 it would turn out to be 7. So the answer would be 8(6x+7)
Step-by-step explanation:
Hope this helps!
Five less than twice Garrett's age is one half of Mary's
age increased by 6. Which equation represents the
relationship between g, Garrett's age, and m, Mary's age?
Answers
Answer:
2g - 5 = 1/2(m) + 6
Step-by-step explanation:
Let Garrett's age be g and Mary's m. Hint: "is" in these type of word problems will typically be the equation's "=" sign.
2g - 5 = 1/2(m) + 6
1) A museum charges different rates for adults and students. Adult
tickets are $14.50 and student tickets are $8.00. Ms Olivis class went
to the museum last week and spent $232.50 on 25 tickets. How
many students and how many adults went to the museum?
Answers
Answer:
Step-by-step explanation:
f(x) = 2x^2 - 5x - 15
g(x) = -2x - 1
find f(g(x)) ... somebody help me :(
Answers
Answer:
f(g(x)) = 8x² + 18x - 8
Step-by-step explanation:
Substitute x = g(x) into f(x) , that is
f(g(x))
= f(- 2x - 1)
= 2(- 2x - 1)² - 5(- 2x - 1) - 15
= 2(4x² + 4x + 1) + 10x + 5 - 15
= 8x² + 8x + 2 + 10x - 10
= 8x² + 18x - 8
Solve the equation. 6n= 24 Show work.
Answers
Answer: n=4
Step-by-step explanation:
6n=24
24/6=4
n=4
Answer:
n=4
Step-by-step explanation:
see steps below:)
helppppppp pleaseeeeee
Answers
PLEASE HELP!!!! I'LL GIVE BRAINLIEST NO LINKS OR YOU'LL BE REPORTED:)))))))))) Describe the distributive property. How is it different from other properties. Can you give an example?
Answers
Answer:
when u distribute a number you are basically giving the number off and multiplying other factors by that number
Step-by-step explanation:
3(x+4) ( distribute the 3 ) so u would multiply the 3 by both factors ( the x and the 4) getting 3x+12
the diameter is a circle is 18cm. Find it’s circumference in terms of π.
C= ________cm
Answers
Answer:
the answer interm of pie will be 18π
Step-by-step explanation:
circumference of circle is given as πD where D is the diameter , we have been given diameter as 18 , hence c=πD will be 18π
PLEASE HELP. i’ll give brainliest if you want!
Answers
Answer:
D is true I'm pretty sure
The slope of the line that contains the points (4, 10) and (5, 13) is 3. Find the y-intercept.
A. -26
B. -2
C. 8
D. 34
The slope of the line that contains the points (-2, -1) and (3, 19) is 4. Find the y-intercept.
A. -7
B. -2
C. 2
D. 7
Answers
Answer:
B
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = 3 , then
y = 3x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation.
Using (4, 10 ) , then
10 = 12 + c ⇒ c = 10 - 12 = - 2 → B
D
Given m = 4 then
y = 4x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (3, 19 ), then
19 = 12 + c ⇒ c = 19 - 12 = 7 → D
when the “a” value is negative in any quadratic what do you know about the graph?
Answers
Answer:
when a is negative, the parabola opens downward
Step-by-step explanation:
EASY BRAINLIEST PLEASE HELP!!
-if you answer correctly ill give you brainliest which will give you 100pts-
(if you put links or don't answer accordingly im reporting your account)
Answers
opposite pairs of triangles are congruent.
Answer:
Opposite pair of triangles are congruent
Step-by-step explanation:
Because in parallelogram
Opposite sides are congruentOpposite angles are congruentSo.opposite pair of triangles are congruent
Which is a common characteristic of both science and pseudoscience? experimentation the collection of information beliefs data
Answers
Answer:
collection of information
Step-by-step explanation:
Science can be defined as a branch of intellectual and practical study which systematically observe a body of fact in relation to the structure and behavior of non-living and living organisms (animals, plants and humans) in the natural world through experiments.
Pseudoscience can be defined as a collection of theories, methodology, practices and beliefs about the universe that are mistakenly, purportedly or erroneously regarded as scientific but in true sense isn't backed up by evidence (facts) and fails to comply with any scientific model.
However, a common characteristic of both science and pseudoscience is that both fields deals with the collection of information.
In conclusion, pseudoscience is considered to be subjective while science is objective.
Answer:
collection of information
Step-by-step explanation:
Science can be defined as a branch of intellectual and practical study which systematically observes a body of fact in relation to the structure and behavior of non-living and living organisms (animals, plants and humans) in the natural world through experiments.
Pseudoscience can be defined as a collection of theories, methodology, practices and beliefs about the universe that are mistakenly, purportedly or erroneously regarded as scientific but in true sense isn't backed up by evidence (facts) and fails to comply with any scientific model.
However, a common characteristic of both science and pseudoscience is that both fields deals with the collection of information.
In conclusion, pseudoscience is considered to be subjective while science is objective.
Based on the coordinates above what kind of quadrilateral wil be formed by their route? How do you know?
Answers
Answer:
Rectangular route
Step-by-step explanation:
Given
H(-4, 3) B (2, 11) F (6, 8) C (0, 0)
Required
The type of route
First, calculate the distance between adjacent points i.e. HB, BF, FC and CH
Where
HB and FC are opposite
BF and CH are opposite
Using distance formula:
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
So, we have:
HB
[tex]H =(-4, 3) \to (x_1,y_1)[/tex]
[tex]B = (2, 11) \to (x_2,y_2)[/tex]
[tex]HB = \sqrt{(-4- 2)^2 + (3 -11)^2}= \sqrt{(-6)^2 + (-8)^2} = \sqrt{36 + 64} = \sqrt{100} = 10[/tex]
BF
[tex]B = (2, 11) \to (x_1,y_1)[/tex]
[tex]F = (6, 8) \to (x_2,y_2)[/tex]
[tex]BF = \sqrt{(2- 6)^2 + (11 -8)^2}= \sqrt{(-4)^2 + (3)^2} = \sqrt{16 + 9} = \sqrt{25} = 5[/tex]
FC
[tex]F = (6, 8) \to (x_1,y_1)[/tex]
[tex]C =(0, 0) \to (x_2,y_2)[/tex]
[tex]FC = \sqrt{(6- 0)^2 + (8 -0)^2}= \sqrt{(6)^2 + (8)^2} = \sqrt{36 + 64} = \sqrt{100} = 10[/tex]
CH
[tex]C =(0, 0) \to (x_1,y_1)[/tex]
[tex]H =(-4, 3) \to (x_2,y_2)[/tex]
[tex]CH = \sqrt{(0-- 4)^2 + (0 -3)^2}= \sqrt{(4)^2 + (-3)^2} = \sqrt{16 + 9} = \sqrt{25} = 5[/tex]
So, we have:
[tex]HB = FC = 10[/tex]
[tex]BF = CF = 5[/tex]
Sine the opposite sides are equal; We can conclude that the route is a rectangle
5. Adana made key chains for her friends out of string. She started with 2 feet of red string, 3-teet of
yellow string, and 5-feet of green string If Adana used a total of 8 3 feet of string on the key chains,
how much string remains unused?
Answers
Answer:
2 1/4
Step-by-step explanation:
SOL Review question 4
Adana made key chains for her friends out of string. She started with 2 1/6 feet of red string, 3 1/4 of yellow string, and 5 1/2 feet of green string. If Adana used a total of 8 2/3 feed of string on the key chains, How much string remains unused.
It would be 2 1/4 because you convert all the factions denominators to 12. 2 1/6 becomes 2 2/12, 3 1/4 becomes 3 3/12, 5 1/2 becomes 5 6/12, and 6 2/3 becomes 8 8/12. add 2 2/12, 3 3/12, and 5 6/12 and you get 10 11/12 and then you subtract 10 11/12 and 8 8/12 (10 11/12 - 8 8/12) and get 2 3/12. when you get that answer, convert it by 3 and you get 2 1/4.
I hope this was helpful.
A die is rolled. The set of equally-likely outcomes is {1, 2, 3, 4, 5, 6}. Find the probability of rolling a number greater than 4.
Answers
Answer:
33.33 percent or 2:4
Step-by-step explanation:
Given that P(A and B) = 0.20 and P(A|B) = 0.40, what must the P(B) = ?
a. 0.1
b. 0.2
c. 0.4
d. 0.5
Answers
Answer:
The value of P(B) = 0.5
Step-by-step explanation:
Given:
Value of P(A and B) = 0.20
Value of P(A|B) = 0.40
Find:
The value of P(B)
Computation:
P(A and B) = P(A|B) x P(B)
By putting value of P(A and B) and P(A|B)
⇒ 0.20 = 0.40 x P(B)
⇒ The value of P(B) = 0.20 / 0.40
⇒ The value of P(B) = 20 / 40
⇒ The value of P(B) = 1 / 2
The value of P(B) = 0.5
Pls help dudndidndiendifn
Answers
Answer:
I don't know D
Step-by-step explanation:
but why is this in the mathematics section
I WILL GIVE U BRAINLIEST AND THANKS AND 5 STARS please help this is very important this is a big part of my grade
Answers
1 - 6
2 - 8/125
3 - 5
4 - 4/5
2^6 = 6(2/5)^3 = 8/1253 * 3^4 = 3^516/25 = 4/5^2which of these figures has rotational symmetry
Answers
Answer: The answer is C
Step-by-step explanation:
The reason is because if you make a line in between it would be symetrical (up, down, left, right).
PLEASE HELP ME I'LL APPRECIATE IT!!!!
Simplify the expression. Write your answer in positive exponent form:
9^5/9^4
Answers
Answer:
The answer is 9^1 or simply 9.
HELP ME <3
Solve. 6x = -36
a) -42
b) 6
c) -30
d) -6
Answers
Answer:
the correct answer is -6
Answer:
d)-6
Step-by-step explanation:
negative and positive is a negative in multiplication. and 6x6=36
so if you put 6(-6) you get -36
Elisa y Romina tienen 5/8 de pizza y decidieron dividírsela en partes iguales. ¿Qué parte de la pizza completa le tocó a cada una?
Answers
Answer:
Elisa y Romina comieron 5/16 de la pizza completa cada una.
Step-by-step explanation:
Dado que Elisa y Romina tienen 5/8 de pizza y decidieron dividírsela en partes iguales, para determinar qué parte de la pizza completa le tocó a cada una se debe realizar el siguiente calculo:
(5/2) / 8 = X
2.5 / 8 = X
0.3125 = X
0.3125 = 5/16
Por lo tanto, Elisa y Romina comieron 5/16 de la pizza completa cada una.
anyone know the answer
Answers
Step-by-step explanation:
m<N = ½×144 = 72°
m (NQ = 2×47 = 94°
The area of an extra large circular pizza from Gambino's Pizzeria is 484\pi \text{ cm}^2484π cm
2
484, pi, start text, space, c, m, end text, squared.
What is the diameter of an extra large pizza from Gambino's Pizzeria?
Answers
Answer:
44cm
Step-by-step explanation:
Answer:
44 cm
Step-by-step explanation:
Please tell me the process to change a percent to a decimal
Answers
To change percent to decimal divide it with 100.
Example 75% = 75/100 = 0.75
A 9 m ladder rests against the side of a wall. The bottom of the ladder is 1.5 m from the base of the
wall. Determine the measure of the angle between the ladder and the ground, to the nearest degree.
1 degree
80 degrees
53 degrees
10 degrees
Answers
9514 1404 393
Answer:
(b) 80°
Step-by-step explanation:
The relevant trig relation is ...
Cos = Adjacent/Hypotenuse
The 1.5 meter distance to the wall is the side adjacent to the angle with the ground. The 9 m length of the ladder is the hypotenuse of the triangle modeling this situation.
cos(angle) = 1.5/9 = 1/6
angle = arccos(1/6) ≈ 80.4°
The angle between the ladder and the ground is about 80°.
_____
Additional comment
The Ladder Association recommends an angle of 75° for safety. At 80°, the ladder may have a tendency to tip the user backward.
While flipping a weighted coin, Latrell gets 4 heads and 2 tails. Based on experimental probability, how many of the next 3 flips should Latrell expect to come up heads?
Answers
Answer: 2 heads
Step-by-step explanation:
First, write the experimental probability as a fraction in simplest form.
P(heads)
=
heads
total
=
heads
heads+tails
=
4
4+2
=
4
6
=
2
3
The experimental probability is
2
3
.
We can predict the outcome of the second set of trials by assuming that the ratio will be the same as in the first set of trials. Write a proportion by setting the two ratios equal to each other, then solve.
2
3
=
n
3
2
3
(33)
=
n
3
(33) Multiply both sides by (33)
23
= 3n Simplify
6
= 3n Simplify
2
= n Divide both sides by 3
Based on experimental probability, Latrell should expect 2 of the next 3 flips to come up heads.
Questions
answered
16
Time
elapsed
00 22 05
HR MIN SEC
SmartScore out of 100
44
Need a break?
PLEASE HELP ASAP NOO LINKS!!!
Answers
Answer:
b
Step-by-step explanation:
Ignacia is comparing prices on pineapple juice. Brand A sells 24 oz. for $2.64. Brand B sells 36 oz. for $3.60. Brand C sells 12 oz. for $1.68. Brand D sells 100 oz. for $10.50. Which brand offers the best price per oz.?
Answers
Answer:
I think A or D but i'm stuck on D
Step-by-step explanation:
Answer:
D because if you multiply all the other brands to get a 100oz they are more expensive/ high than D.