Answer:
D is correct answer
Step-by-step explanation:
3. The perimeter of a rectangle is 98 feet. Find its dimensions assuming that its length is 2 feet less than twice its width.
The width is
(Simplify your answers.)
and length is
Answer:
w = 17 fts
l = 32 fts
Step-by-step explanation:
P = 2w + 2l
l = 2w - 2
98 = 2w + 2(2w - 2)
98 = 2w + 4w - 4
98 + 4 = 6w
6w = 102
w = 17 fts
l = 2×17 - 2 = 34 - 2 = 32 fts
3.
Reasons
Statements
MNOP is a parallelogram
PM || ON
N
M
Alternate Int. Zs Thm.
Given:
MNOP is a parallelogram
MN || PO
Alternate Int. Zs Thm.
Prove:
PM ON
(For this proof, use only the
definition of a parallelogram;
don't use any properties)
Answer:
[tex]\overline{PM}\cong\overline{ON}[/tex]: Reason; Corresponding parts of congruent triangles ΔOMN and ΔOMP are congruent (CPCTC)
Step-by-step explanation:
1) MNOP is a parallelogram: Reason; Given
2) [tex]\overline{PM}\left | \right |\overline{ON}[/tex]: Reason; Definition of a parallelogram
3) ∠MON ≅ ∠PMO: Reason; Alternate Int. ∠s Thm.
4) [tex]\overline{MN}\left | \right |\overline{PO}[/tex]: Reason; Definition of a parallelogram
5) ∠NMO ≅ ∠POM: Reason; Alternate Int. ∠s Thm.
6) [tex]\overline{OM}\cong\overline{OM}[/tex]: Reason; Reflexive property
7) ΔOMN ≅ ΔOMP: Reason; Angle Angle Side (AAS) congruency theorem
8) [tex]\overline{PM}\cong\overline{ON}[/tex]: Reason; Corresponding parts of congruent triangles are congruent (CPCTC).
Also we have;
9) [tex]\overline{PM}\cong\overline{ON}[/tex]: Reason; Segment opposite congruent angles are congruent
Please Help ASAP C: :D
Answer:
-21/10
Step-by-step explanation:
-2/5 - 4/5 + (-9/10) = -6/5 -9/10 = -12/10 -9/10 = -21/10
Answer:
-21/10
Step-by-step explanation:
Plug in 4/5 for x and simplify.
-2/5 - 4/5 + (-9/10)
-6/5 + (-9/10)
-21/10 or -2 1/10
I hope this helps :))
Find the vertex of the given function. f(x) = |x + 1| - 7 The vertex is at (, )
Answer: The vertex of the function is (-1, -7).
Step-by-step explanation: We are given to find the vertex of the following function.
We know that the vertex of the function is given by (h, k).
So, for the given function f(x), the vertex will be (-1, -7).
The graph of the function f(x) is shown in the attached figure, where the vertex is at the point (-1, -7).
Thus, the vertex of the function is (-1, -7).
The vertex of the function f(x) = |x + 1| - 7 is (-1,-7)
How to determine the vertex?The function is given as:
f(x) = |x + 1| - 7
The above function is an absolute value function
An absolute value function is represented as:
f(x) = a|x – h| + k
Where, the vertex is (h,k)
So, we have:
(h,k) = (-1,-7)
Hence, the vertex of the function f(x) = |x + 1| - 7 is (-1,-7)
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Formulate the recursive formula for the following geometric sequence. {-16, 4, -1,...}
Answer:
Step-by-step explanation:
Common ratio = 2nd term/1st term = 4/-16 = -1/4
[tex]a_{n}=a_{n-1}*r\\a_{n}=a_{n-1}*\frac{-1}{4}\\\\a_{n}=\frac{-1}{4}a_{n-1}[/tex]
Answer:
Common ratio = 2nd term/1st term = 4/-16 = -1/4
Step-by-step explanation:
Share £10 in the ratio of 2:3 ASAPP!!!!!!!!!!!!
Answer:
£4 and £6
Step-by-step explanation:
Total = £10
Ratio = 2:3
Total Parts = 2+3 = 5
Divide it by the Total
=> 10/5 = £2
Multiply it by the ratios
1) 2 * 2 = £4
2) 3 *2 = £6
Answer:
4:6
Step-by-step explanation:
2+3=5
10/5=2
3x2= 6
2x2=4
4:6
At a company picnic, 1/2 of the people are employees. 2/5 are employees' spouses. What percent are neither?
Answer:
10% of the people at the picnic are neither.
Step-by-step explanation:
To get the answer,
1/2 + 2/5 = 9/10
10/10 - 9/10 = 1/10
1/10 = 10%
Thanks, I hope I got this right!
What is the value of the discriminant for the quadratic equation 0 = x + 2 + x2? Discriminant = b2 – 4ac –9 –7 7 9
Answer:
-7
Step-by-step explanation:
[tex]x^2+x+2=0 \\\\b^2-4ac= \\\\1^2-4(1)(2)= \\\\1-8= \\\\-7[/tex]
Hope this helps!
The value of the discriminant for the quadratic equation 0 = x + 2 + x² is -7.
What are Quadratic Equations?Quadratic equations are polynomial equations of second degree.
The general form of a quadratic equation is ax² + b x + c = 0.
Given quadratic equation is,
x² + x + 2 = 0
The discriminant of a quadratic equation of the form ax² + bx + c = 0 is,
Discriminant = b² - 4ac
Here, a = 1, b = 1 and c = 2
Substituting,
Discriminant = 1² - (4 × 1 × 2)
= 1 - 8
= -7
Hence the discriminant of the given equation is -7.
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Which statement correctly describes the graph of y = x + 7?
Answer: C
Step-by-step explanation:
The slope stays the same but the y-intercept is moved up 7 units.
A large jar contains 25% blue marbles. A sample contains 9 blue marbles, 15 red marbles, and 16 green marbles.
What is pˆ, the sample proportion of blue marbles?
Enter your answer, as a simplified fraction, in the box.
Answer:
Proportion of blue marbles in in sample = 9/40
Step-by-step explanation:
Total number of blue marbles in a jar is given by 25%
Lets find the probability of blue marble in the jar of the given sample:
Proportion of blue marbles in in sample = Total number of blue marbles in sample/ Total number of marbles in sample
Where
Total number of blue marbles in sample = 9
Total number of marbles in sample = 9 + 15 + 16
Total number of marbles in sample = 40
SO
Proportion of blue marbles in in sample = 9/40
or
Proportion of blue marbles in in sample = 9/40
In how many months were there more than two days with thunderstorms?
Answer:
5
Step-by-step explanation:
March,May,June,July,August
20 POINTS AND BRAINLIEST!!! You are given an n×n board, where n is an even integer and 2≤n≤30. For how many such boards is it possible to cover the board with T-shaped tiles like the one shown? Each cell of the shape is congruent to one cell on the board.
Answer:
5
Step-by-step explanation:
The number of cells in a tile is 4, so the board dimension cannot be odd, but must be a multiple of 2 in order to have the number of cells divisible by 4.
If the tiles are colored in an alternating pattern, tiles must have 3 of one color and 1 of the alternate color. Hence the total number of tiles used to cover a board must be even (so the numbers of each color match). Then the board dimension must be divisible by 4.
In the given range, there are 5 such boards:
4×4, 8×8, 12×12, 16×16, and 20×20
81. What is the next number? 1, 1/2, 1/4, 1/8,
Answer:
1/16
Step-by-step explanation:
multiply by 1/2
1, 1/2, 1/4 , 1/8, 1/16
Answer:
1/16
Step-by-step explanation:
If you see the pattern it goes by x2 (the denominator)
1 , 1/2, 1/4, 1/8, 1/16
A bag contains 5 red marbles, 6 green marbles, and 3 blue marbles. If Cymra draws a marble, keeps it and then draws another marble, what is the probability that both marbles she draws will be red? 5/14×5/14 5/14 ×4/13 5/14×4/14 4/14×5/14
Answer:
Probability is the chance of occurrence of an event. The probability that both marbles are drawn by the Cymra are red
Step-by-step explanation:
I WILL GIVE BRAINLIEST!!! Part A: The Sun produces 3.9 ⋅ 10^33 ergs of radiant energy per second. How many ergs of radiant energy does the Sun produce in 1.55 ⋅ 10^7 seconds? Express your answer in scientific notation and show your work. (5 points) Part B: Which is the more reasonable measurement of the distance between the tracks on a CD: 1.6 ⋅ 10−3 mm or 1.6 ⋅ 103 mm? Justify your answer. (5 points)
Answer:
Part A: This can be solved using cancellation of units: Energy produced (ergs) = (3.9 x 10^ 33 ergs/ sec)( 1.55 x 10^7 sec) = 6.045 x 10^40 ergs Part B: The grooves within a CD is very small, therefore it would be more reasonable to have a value of 1.6 x 10^-3 mm
Hope this helped you!
Step-by-step explanation:
PLEASE HELP!!!!!!! i will give brainliest
Yes they are independent because P(California) = 0.55 approximately and P(California | Brand B) = 0.55 approximately as well
===================================================
Explanation:
P(California) is notation that means "probability the person is from California". There are 150 people from California out of 275 total. Therefore, the probability is 150/275 = 0.5454 approximately which rounds to 0.55
Now if I told you "this person prefers brand B", then you would focus your attention solely on the brand B column. The other columns are ignored because you know they don't prefer anything else. With this narrower view, we see that 54 Californians prefer this brand out of 99 total. The probability becomes 54/99 = 0.5454 which rounds to 0.55. We get the same as before.
The notation P(California | Brand B) means "the probability they are from California given they prefer brand B". The vertical line is not the uppercase letter i or lowercase letter L. It is simply a vertical line. In probability notation that vertical line means "given".
We've shown that P(California | Brand B) = 0.55 approximately. The fact that they prefer brand B does not change the original probability. So the two events are independent. If liking brand B did change the probability, then the events would be dependent.
Brainliest for whoever gets this correct with working out
Answer:
[tex] \frac{2x - 5}{x + 5} [/tex]
Step-by-step explanation:
Firstly, you have to factorize the expressions on the numerator and denorminator :
Numerator :
[tex]2 {x}^{2} - 3x - 5[/tex]
[tex] = 2 {x}^{2} + 2x - 5x - 5[/tex]
[tex] = 2x(x + 1) - 5(x + 1)[/tex]
[tex] = (2x - 5)(x + 1)[/tex]
Denorminator :
[tex] {x}^{2} + 6x + 5[/tex]
[tex] = {x}^{2} + x + 5x + 5[/tex]
[tex] = x(x + 1) + 5(x + 1)[/tex]
[tex] = (x + 1)(x + 5)[/tex]
Next, you have to put the factorized-form in the fraction and cut out the similar expressions :
[tex] \frac{(2x - 5)(x + 1)}{(x + 1)(x + 5)} [/tex]
[tex] = \frac{2x - 5}{x + 5} [/tex]
Steve claims that the sun of two off numbers is always even. How can Steve prove his conjecture?
A. Create a Venn diagram that separates the sums of odd numbers into even and odds.
B. Show one example of his claim, adding two odd numbers to form an even number
C. Create two generic odd numbers, using variables, and show that their sum is always even
D. Show fifty examples of what happens when you add two odd numbers
Please help me with this
Answer:
Show one example of his claim, adding two odd numbers to form an even number
Answer:
C.
Step-by-step explanation:
You cannot prove his conjecture by an example. You must create two generic odd numbers using algebraic expressions. Then you add the two expressions and show that the sum is even.
Answer: C.
Write an equation in slope-intercept form for a line that passes through the two points (-2,-5) and (-4,3). Show your work.
Answer:
y = -4x - 13
Step-by-step explanation:
Use point - slope form to convert to y = mx + b form
1. Find the slope using y2 - y1 / x2 - x1
3 + 5 / -4 + 2
m = -4
2. Plug into point - slope form: y - y1 = m (x - x1)
y + 5 = -4 (x + 2)
Distribute
y + 5 = -4x - 8
Subtract 5 from both sides
y = -4x - 13
AJ is the bisector of ∠HJI. Determine the value of x. ANSWERS: A) 50 B) 10 C) 8 D) 25
Answer:
B) 10
Step-by-step explanation:
∠IJA= ∠HJA
ΔIJA has twice smaller side opposite ∠J than ∠A
Similarly
ΔHLA side 5 opposite ∠J,
So x/5= 20/10 ⇒ x= 5*2= 10
Answer choice is B) 10
can anyone help? soh cah toa trig question to the nearest tenth of a foot?
Answer:
About 2.7 feet
Step-by-step explanation:
The tangent of an angle is equivalent to the length of the opposite side divided by the length of the adjacent side:
[tex]\tan 44=\dfrac{x}{2.8}\\\\x=2.8 \cdot \tan 44\approx 2.7[/tex]
Hope this helps!
Answer:
x = 2.7 feet
Step-by-step explanation:
Use tan to find the value of x
tan 44 = [tex]\frac{x}{2.8}[/tex] Simplify
0.9657 = [tex]\frac{x}{2.8}[/tex] Multiply both sides by 2.8
x = 2.70396 Round this answer to the nearest tenth of a foot
x = 2.7 feet
I would love someone’s help! I’m struggling
A bird species in danger of extinction has a population that is decreasing exponentially (A = A0e^kt). Five years ago, the population was at 1400 and today only 1000 of the birds are alive. Once the population drops below 100, the situation will be irreversible. When will this happen?
Answer:
It'll take approximately 34 years from today.
Step-by-step explanation:
in order to solve this problem we first need to find the rate of change, "k", to do that we will use the given information where the population was 1400 five years ago and its now 1000. Applying this data to the equation gives us:
[tex]A = A_0*e^{k*t}\\1000 = 1400*e^{5*k}\\1400*e^{5*k} = 1000\\e^{5*k} = \frac{1000}{1400}\\ln(e^{5*k}) = ln(\frac{1000}{1400})\\5*k = ln(1000) - ln(1400) \\k = \frac{ln(1000) - ln(1400)}{5} = -0.06729[/tex]
We now know the value for "k", we can estimate how many years it will take for the bird population to dip below 100. We have:
[tex]100 = 1000*e^{-0.06729*t}\\e^{-0.06729*t} = \frac{100}{1000}\\ln(e^{-0.06729*t} = \frac{1}{10}\\-0.06729*t = ln(0.1)\\t = -\frac{ln(0.1)}{0.06729} = 34.22[/tex]
It'll take approximately 34 years from today.
what is the factorization of the polynomial below -x^2-15x-56
Answer:
(-x-7)(x+8)
Step-by-step explanation:
-x²-8x-7x-56
-x(x+8)-7(x+8)
(-x-7)(x+8)
Answer:
it is -1(x+8)(x+7)
A new car worth $27,000 is depreciating in value by $3,000 per year.
Complete parts
a. through b. below.
a.Write a formula that models the car's value, y, in dollars, after x years.
y= 0
Answer: Y=24000-3000x
9000=24000-3000x
-15000=-3000x
x=5 years
first we need to set the equation
at plug in all the information we have. In our case, we know cars value or y =9000, we need to find what is the x value
2
we need to subtract 24000 on both sides, and then divide by -3000 on both sides, and find out for x in years
Step-by-step explanation:
The model of the car's value, y, in dollars, after x years is:
y = -3000x + 27000
The equation of a straight line is given by:
y = mx + b
where y, x are variables, m is the slope of the line and b is the y intercept.
Let x represent the number of years and y represent the value in dollars.
Since the new car worth is $27000, hence b = 27000. Also it depreciating in value by $3,000 per year, hence m = -3000. The car value is given by:
y = -3000x + 27000
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Given the functions f(x) = 6x + 11 and g(x) = x2 + 6, which of the following functions represents f[g(x)] correctly? f[g(x)] = 36x2 + 132x + 127 f[g(x)] = 36x2 + 132x + 121 f[g(x)] = 6x2 + 47 f[g(x)] = 6x2 + 36
Answer:
C. 6x^2 + 47
Step-by-step explanation:
The value of f[g(x)] is 6x² +47, the correct option is C.
What is a Function?A function is a law that derives a relation between two variables.
The function is f(x) = 6x+11
g(x) = x² +6
The operation f(g(x)) = 6 (x² +6) +11
f(g(x)) = 6x² +36 +11
f(g(x)) = 6x² +47
Therefore, the value of f[g(x)] is 6x² +47, the correct option is C.
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The number of unread emails in Bryan’s account is 100. This number grows by 15 unread emails a day. The function N(t)=100+15t represents the relation between the number of unread emails, N, and the time, t, measured in days.
Answer:
Independent variable = t
Dependent variable = N
Step-by-step explanation:
Given that the function N(t)=100+15t represents the relation between the number of unread emails, N, and the time, t, measured in days
The independent variable is an input which can be controlled. In the function
N(t)=100+15t
The independent variable is t
While the dependent variable is the output of a function when independent variable has been substituted.
In the function N(t)=100+15t
The number of unread messages depends on the number of time t measured in days as the number of unread messages N is a function of t.
Therefore, the independent variable is N.
Pete, Chris, and Dina realized that the number of A’s they each received on their report cards were in a ratio of 4:2:5. If Pete got 14 more A’s than Chris, how many A’s did Dina get?
Answer:
[tex]Dina= 35[/tex]
Step-by-step explanation:
Given
[tex]Ratio = 4:2:5[/tex]
Peter = 14 more A's than Chris
Required
How many A’s did Dina get?
The order of the ratio is Peter: Chris: Dina
This implies that
[tex]Peter: Chris: Dina = 4:2:5[/tex]
Considering Peter and Chris
[tex]Peter: Chris = 4:2[/tex]
Let the number of Chris' A's be represented by A
This implies that:
Peter's = 14 + A
And as such;
[tex]14 + A : A = 4 : 2[/tex]
Convert ratio to division
[tex]\frac{14 + A}{ A} = \frac{4}{ 2}[/tex]
Multiply both sides by A
[tex]A * \frac{14 + A}{ A} = \frac{4}{ 2}* A[/tex]
[tex]14 + A = \frac{4}{ 2}* A[/tex]
[tex]14 + A = 2* A[/tex]
[tex]14 + A = 2 A[/tex]
Subtract A from both sides
[tex]14 + A-A = 2 A-A[/tex]
[tex]14 = A[/tex]
This means that;
Chris answered 14 while Pete answered 28 (14 + 14)
Considering Chris and Dana
[tex]Chris :Dana = 2:5[/tex]
Replace Chris with 14
[tex]14:Dana = 2:5[/tex]
Convert ratio to division
[tex]\frac{14}{ Dina} = \frac{2}{5}[/tex]
Cross Multiplication
[tex]Dina * 2 = 14 * 5[/tex]
Divide both sides by 2
[tex]\frac{Dina * 2}{2} = \frac{14 * 5}{2}[/tex]
[tex]Dina= \frac{14 * 5}{2}[/tex]
[tex]Dina= \frac{70}{2}[/tex]
[tex]Dina= 35[/tex]
Hence, Dina had 35 A's
Which number completes the inequality? 1.01 less-than blank less-than 1.17, less-than 1.20 1.008 1.08 1.18 1.8
Answer:
1.08
Step-by-step explanation:
1.01 < x < 1.17
x ≠ 1.20
x ≠ 1.008
x = 1.08
x ≠ 1.18
x ≠ 1.8
The number that completes the inequality is 1.08:
1.01 < 1.08 < 1.17, < 1.20
Option C is the correct answer.
We have,
To determine which number completes the inequality, we need to find the number that is greater than 1.01 but less than both 1.17 and 1.20.
Among the given options, the number that satisfies this condition is 1.08.
Thus,
The number that completes the inequality is 1.08:
1.01 < 1.08 < 1.17, < 1.20
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Help will give brainliest
Answer:
72
Step-by-step explanation:
Step 1: Figure out percentages of what he owns
360(0.4) = 144 models he made
360 - 144 = 216 models he bought.=
Step 2: Figure out percentages of what he donated
144(0.25) = 36 models he donated (he made)
216(0.5) = 108 models he donated (he bought)
Step 3: Find the difference
108 - 36 = 72
And we have our answer!