Answer:
The dimensions of the lid are 8mm by 19mm.
w = 8
l = 19
Step-by-step explanation:
[tex]l=w+11\\l\times w=152[/tex]
where l is length and w is width. This can be solved as a system of equations.
[tex]l\times w=152\\(w+11)\times w=152\\w(w+11)=152\\w^2+11w=152\\w^2+11w-152=0[/tex]
At this point, it gets a little tough. I might be unnecessarily overcomplicating things, but this is the only way I see to solve the problem.
=================== Skip down below if you don't care about factoring
You need to factor the newly created trinomial.
[tex]ax^2+bx+c[/tex]
With a trinomial in this form, you need to find 2 numbers that add together to make b and multiply together to make ac.
Here, we need 2 numbers that add to 11 and multiply to -152. First, factor 152:
1, 152
2, 76
4, 38
8, 19
Then the reverse of all of those is true too, of course:
19, 8
38, 4
etc
In our case, we're looking for -152, so one of our factors will be negative. We're also looking for factors that add up to 11. Looking at these factors, you can see that 19 - 8 = 11, so our factors are 19 and -8.
Finally, you can use those to factor our trinomial. Split up the middle number (11w) into two:
[tex]w^2+11w-152=0\\w^2-8w+19w-152=0[/tex]
And now, you can factor by grouping:
[tex]w^2-8w+19w-152=0\\w(w-8)+19(w-8)=0\\(w+19)(w-8)=0[/tex]
===================
Now that the number is factored, you can finally find w:
[tex](w+19)(w-8)=0[/tex]
Here, you can see that the equation will be true when w = -19 or w = 8. Those are our solutions, but we can't have a negative distance, so it's just
[tex]w=8[/tex]
Going all the way back to the top, now you can use the width to find the length.
[tex]l=w+11\\l=8+11\\l=19[/tex]
That one was much easier.
The dimensions of the lid are 8mm by 19mm.
Finally, check that with both of the original equations to make sure it's correct.
[tex]l=w+11\\19=8+11\\19=19\\\\l\times w=152\\19\times8=152\\152=152[/tex]
can you help me solve 4x - 15 = 17 - 4x
[tex]4x-15 = 17-4x\\\\\implies 4x +4x = 17 +15\\\\\implies 8x = 32\\\\\implies x = \dfrac{32} 8\\\\\implies x = 4[/tex]
line passes through the points (4,-2) and the slope is 5/4 write an equation in slope intercept form
Answer:
y=5/4x -7
Step-by-step explanation:
Hope this helps!
SCO
Sarah put 15 gumdrops on the roof of her
gingerbread house. How many gumdrops
will she need to make 16 more houses
exactly like this one?
MY
gumdrops
Answer: 240 gumdrops
Step-by-step explanation:
1 house: 15 gumdrops
16 houses : 240 gumdrops
1 x 16 = 16
15 x 16 = 240
Help me please i really need it
Answer:
Step-by-step explanation:
RSB is a right angle
12. RSB is 90 degrees
13. A right angle is 90 degrees
H is between P and S
14. PS + PH = HS
15. Deductive Reasoning
help me plz ineed help
Answer:
23°
Step-by-step explanation:
Opposite angles so:
60° = 2x + 14
Therefore:
x = 23°
Answer:
x is 23°
Step-by-step explanation:
those opposite angles and are always equal to each other...so to get x take 60-14 then answer divide by two
Write five demicals that round to 0.96?
Answer:
0.964
0.959
0.961
0.958
0.963
Step-by-step explanation:
Anything below 5 can be rounded down, anything above 5 can be rounded up.
You can have a decimal after 0.96 to be less than 5, or a decimal after 0.95 to be greater than 5.
Here's some I picked:
0.964
0.959
0.961
0.958
0.963
Which one is correct
Solve for x: one over eight 1/8(8x + 15) = 24
Answer:
22[tex]\frac{1}{8}[/tex]
Step-by-step explanation:
I hope this helps!!!
Determine if the sequence below is arithmetic or geometric and determine the common difference/ ratio in simplest form
15, 11 ,7, …
Answer:
This is the arithmetic sequence which has a common difference that equals to -4.
Step-by-step explanation:
An arithmetic sequence is a sequence with common difference. A common difference can be found by subtracting previous term with next term.
A common difference can be expressed in [tex]\displaystyle \large{d=a_{n+1}-a_n}[/tex] where d stands for common difference.
________
Moving to the question given. We have a sequence with given 15,11,7, ... first subtract 15 with 11.
11-15 = -4
7-11 = -4
Therefore, we can conclude that the common difference is -4 thus making the given sequence an arithmetic.
Let me know if you have any question so regarding the sequence!
emma has 63 pencils noah has 49 penecils and michel has 77 pencils.Use the GCF and the distributive property to find the total number of pencils
Step-by-step explanation:
the greatest common factor (GCF) is 7.
it is 9×7, 7×7 and 11×7.
so the total number of pencils is
7×(9 + 7 + 11) = 7×27 = 189
The table shows the final score of four golfers.
Golfer Final Score
Joe
-2
Allen
-5
Tara
-8
Violet
-4
Whose score was the lowest? Whose was the highest? Select your answers from the drop-down lists.
score was the lowest.
score was the highest.
Students, draw anywhere on this slide!
PER Deck eractive Skoe
Answer:
Joe score was the highest. Tara score was the lowest.
Step-by-step explanation:
Does anyone know the answer for this question? I really need it.
Four times a number is equal to the number increased by 24 find the number
Answer:
8Step-by-step explanation:
Let the number is x.
Translate the given into equation and solve for x:
4x = x + 244x - x = 243x = 24x = 8When Hugo puts a book and a candle on a scale, the scale reads 8.705 lbs. When he removes the book, the scale reads 4.93 lbs. How much does the book weigh?
Answer:
8.705-4.93=3.775
Hope This Helps!!!
3.Original DNA sequence: 3' TACCGCTTACGTCTGATCGCT 5'
Mutated DNA sequence: 3' TACCGCTTATTATTACGTGCTGCTATCGCT 5'
Type of mutation (3pts):
Amino acid ( 3pts):
Type of mutation ( 3pts):
4. Original DNA sequence: 3' TACCGCTTACGTCTGATCGCT 5'
Mutated DNA sequence: 3' TACCGCTAATTATTACGTGCTGCTATCGCT 5'
Type of mutation ( 3pts) :
Amino acid ( 3pts):
Type of mutation ( 3pts):
3. The original sequence
TAC - CGC - TTA - CGT - CTG - ATC - GCT
codes for
tyr - arg - leu - arg - leu - ile - ala
while the mutated sequence codes for
TAC - CGC - TTA - TTA - TTA - CGT - GCT - GCT - ATC - GCT
tyr - arg - leu - leu - leu - arg - ala - ala - ile - ala
There are several frameshift mutations involved here:
• the first inserts 6 bases (TTA - TTA)
• the second inserts 1 base (G) before the CTG triplet (underlined)
• the third inserts 2 bases (CT) after the CTG triplet
4. The original sequence is the same as before. The mutated sequence
TAC - CGC - TAA - TTA - TTA - CGT - GCT - GCT - ATC - GCT
codes for
tyr - arg - STOP - leu - leu - arg - ala - ala - ile - ala
Then
• there is a (nonsense) point mutation that swaps T for A in the original TTA triplet (nonsense since it produces a stop codon that would halt replication/expression)
• there is a frameshift mutation that inserts 3 bases (TTA)
as well as two other frameshift mutations that also occurred in the previous part.
A desk drawer is shaped like a rectangular prism. The height of the drawer is 7 inches. The bottom of the drawer has an area of 210 square inches.
What is the volume of the desk drawer?
Enter your answer in the box.
Answer:
1470 inches cubed
Step-by-step explanation:
Vol=length × width × height
But ALSO,
length × width = Area,
So we find another Volume equation,
Vol = BaseArea × height
This is the information you are given in the question.
Vol = 210 × 7
Vol = 1470 inches cubed
Understand how to work with negative bases and negative exponents.
5^2 =
5^-2 =
(-5)^2 =
- 5^2 =
(Remember to find the base, then multiply.)
Answer:
[tex]Understand \: how \: to \: work \: with \: negative \: bases \\ \: and \: negative \: exponents. \\
\bold{answer - } \\ {5}^{2} = 5 \times 5 = 25 \\ {5}^{ - 2} = \frac{1}{ {5}^{2} } = \frac{1}{25} = 0.04 \\ {( - 5)}^{2} = ( - 5) \times ( - 5) = 25 \\ - {5}^{2} = ( - 5) \times ( - 5) = 25 \\ \\ \bold \purple{hope \: it \: helps \: ♡}[/tex]
Is this table proportional?
XY
1 3 3
4 12
5 15
7 21
Jose left the airport and traveled toward the mountains. Kayla left 2.1 hours later traveling 35 mph faster in an effort to catch up to him. After 1.2 hours Kayla finally caught up. Find Jose's speed.
========================================================
Explanation:
x = Jose's speed in mph
x+35 = Kayla's speed since she drives 35 mph faster than Jose
Jose gets a 2.1 hour head start and it takes Kayla 1.2 hours to reach him. So this means Jose has been driving for 2.1+1.2 = 3.3 hours when Kayla reaches him. The distance he travels is
distance = rate*time
d = r*t
d = x*3.3
d = 3.3x
while Kayla's distance equation is
d = r*t
d = (x+35)*1.2
d = 1.2x+42
Since Kayla meets up with Jose at the 1.2 hour mark, this means the two distances they travel is the same. Set their distance expressions equal to one another. Solve for x.
3.3x = 1.2x+42
3.3x-1.2x = 42
2.1x = 42
x = 42/(2.1)
x = 20
Jose's speed is 20 mph, while Kayla's speed is x+35 = 20+35 = 55 mph.
Jose's fairly slow speed is probably due to a number of factors such as heavy traffic, icy roads, or poor visibility. Kayla probably got a bit of a break with more favorable conditions.
Since Jose travels at 20 mph and does so for 3.3 hours, he travels d = r*t = 20*3.3 = 66 miles. Kayla travels d = r*t = 55*1.2 = 66 miles as well. We get the same number each time to help confirm the answer.
HELP ASAP PLEASE THIS IS FOR ALGEBRA
1. he slope of a line through the points (-2, 4) and (6, b) is -3/2 What is the value of b?
Explain your method for calculating b.
Answer:
Step-by-step explanation:
Use the slope formula to solve this problem. Slope, usually called m, is the change in y-values over the change in x-values.
m = (y2 - y1)/(x2 -x1)
It actually doesn't matter which point is the first point and which point is the second point. But you must be consistent.
So fill in -3/2 for the m
Let your (6, b) be your (x1, y1)
Let (-2, 4) be your (x2, y2)
So, the numbers fill into the formula like so:
-3/2 = (4 - b)/ (-2 - 6)
-3/2 = (4 - b)/(-8)
Multiply -8 on both sides of the equation.
(-8)(-3/2) = 4 - b
12 = 4 - b
Subtract 4 from both sides.
Don't lose the negative in front of the b
8 = -b
Multiply or divide by -1 on both sides.
-8 = b This is the answer.
**note: Its kinda crummy to use b in this equation, because b has a special meaning when you are working with linear equations. They should have given you a different variable. b usually stands for the y-intercept but in this problem it doesn't, it's just a variable representing an unknown value.
Classify the Triangle by its sides and angles. 140° Right Scalene Right Isosceles Equilateral Obtuse Isosceles Acute Isosceles Obtuse scate Acute Scalene
Answer: Obtuse Isosceles.
Explanation: Two angles are congruent, which means the triangle is isosceles. One angle is over 90°, which means the triangle is obtuse.
Jamal has a plan to save money for a trip. Today, Jamal deposits $8.00 into the savings account. Each week, Jamal will add $5.00 to the amount that is deposited into the savings account. The table below shows the relationship between the number of weeks and how much money, in dollars, Jamal deposits into the savings account. Week 0 1 2 3 4 Deposit (Dollars) 8 13 18 23 28 Let f(x) represent the amount of money Jamal deposits into saving account at the end of x weeks. Based on the table, what is f(8)?
Answer:
f(8) = $48
EQUATION
f(x)= 8+5(x)
Step-by-step explanation:
initial value = $8
every week there is an additional $5 added.
f(x) = 8+5x
f(8) = 8+ 5(8) = 8 + 40 = 48.
At the end of week 8 (x=8) , Jamal has $48 (y=48) saved.
To get to the next term in this sequence, multiply the last term by 2.5. What is the value of the next term?
1, 2.5, 6.25, 15.625, ...
HELP ASAP WILL GIVE BRAINLIEST
Answer:
39.0625
Step-by-step explanation:
15.625 times 2.5= 39.0625
You're just multiplying each value by 2.5
1 times 2.5= 2.5
2.5 times 2.5= 6.25
6.25 times 2.5= 15.625
and then 15.625 times 2.5= 39.0625
what is the answer i need done by midnight -15x+60<105
Answer:
[tex]x > -3[/tex]
Step-by-step explanation:
Isolate the variable. Treat the < sign like an equal sign, in that what you do to one side, you do to the other.
Do the opposite of PEMDAS. PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& Roots)
Multiplications
Divisions
Additions
Subtractions
~
First, subtract 60 from both sides of the equation:
-15x + 60 (-60) < 105 (-60)
-15x < 45
Next, divide -15 from both sides of the equation. Note that when you multiply or divide a negative number, you must flip the sign:
(-15x)/-15 < (45)/-15
x < 45/(-15)
x > -3
[tex]x > -3[/tex] is your answer.
~
To bring a "carry-on" bag onto an airplane the bag needs to weigh less than 25 pounds. Right now Julie's carry-on bag weighs 32 pounds. How much weight must Julie remove from her bag?
My answer needs to be 32-25=7
The impact on sampling of increasing the sample size is: There is no specific relationship between sample size and sampling error.
Using margin of error, it is found that increasing the sample size results in a smaller sampling error.
The equation for the margin of error is given by:
[tex]M = c\frac{s}{\sqrt{n}}[/tex]
In which:
c is the critical value according to the distribution used.s is the standard deviation, either of the sample or of the population.n is the sample size.From the equation, it can be noted that the margin of error is inversely proportional to the square root of the sample size, hence, increasing the sample size results in a smaller sampling error.
To learn more about margin of error, you can take a look at https://brainly.com/question/25821952
Activity 1.
Direction. Using the diagram below, form ratios. Express them in lowest term to
To form a proportion
Answer:
6:3 =2:12:2=1:16:13:24:14=2:71) f(4) = g(4)
2) f(4) = g(-2)
3) f(2) = g(-2)
4) f(-2) = g(-2)
Answer: 4)
Step-by-step explanation:
f(4) = -14
g(4) = 10
g(-2) = 4
f(2) = -8
f(-2) = 4
The correct statement is 4) f(-2) = g(-2)
Or by inspection, we can see that the graph f(x) intersects g(x) at x = -2 and y = 4. So, f(-2) = g(-2) = 4 is true
State whether the system is consistent or inconsistent. If it is consistent, then state whether the graphs' equations are dependent or independent. State the number of solutions.
If a system has at least one solution, it is said to be consistent . If a consistent system has exactly one solution, it is independent . If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line.
What is an equivalent ratio
Answer:
Equivalent ratios (which are, in effect, equivalent fractions) are two ratios that express the same relationship between numbers. We can create equivalent ratios by multiplying or dividing both the numerator and denominator of a given ratio by the same number. Two ratios that have the same value are called equivalent ratios. To find an equivalent ratio, multiply or divide both quantities by the same number. It is the same process as finding equivalent fractions.