Answer:
2/(7a) < x < 7
Step-by-step explanation:
The product of roots of ax² +bx +c is c/a. In this case, that means the second root of the equation is ...
... 2/(7a)
Since a < 0, the parabola opens downward and 2/(7a) < 0. The quadratic function will be positive between the two roots, on the interval ...
... 2/(7a) < x < 7
Can anyone help me with THIS and the other TWO‼️PLEASE I’m really need HELP
Answer:
y = 3x +2
Step-by-step explanation:
It is helpful to be acquainted with the parts of at least a couple of different forms of the equation for a line.
You are given the equation of a line in "slope-intercept" form. It looks like ...
... y = mx + b . . . . . . . where m=-1/3 and b=-1
The coefficient of x, which is m, is the slope of the line. That is -1/3 for the given line.
The relationship between the slopes of perpendicular lines is that they multiply to give -1. We say each is the opposite reciprocal of the other. If we let "m" stand for the slope of the perpendicular line, it satisfies the equation ...
...(m)(-1/3) = -1
... m = -1/(-1/3) = 3 . . . . . the slope of the perpendicular line is 3.
____
Here's where another form of the equation for a line is useful. We can write the "point-slope" form* as ...
... y = m(x -h) +k . . . . . . for a line of slope m through point (h, k)
We want our line of slope = 3 to go through the point (1, 5), so its equation can be ...
... y = 3(x -1) +5 . . . . . . . variation of "point-slope" form
The given equation is in slope-intercept form, and the question asks for "the" equation of the line, so we probably should write our answer in the same form as the given equation. We can do this by eliminating the parentheses and simplifying the equation we have.
... y = 3x -3 +5 . . . . eliminate parentheses using the distributive property
... y = 3x +2 . . . . . . collect terms
The graph shows our result is at least plausible: it looks like it is perpendicular, and it goes through the given point.
___
*Comment on point-slope form
Usually, you will see "point-slope" form written as ...
... y -k = m(x -h) . . . . . . . . standard version of "point-slope" form
When our intent is to use this form to get to slope-intercept form, it is more convenient to add k to this equation to get ...
... y = m(x -h) +k . . . . . . . occasionally useful version
Please help 200*50/-9+564*-4= ? I
Answer:
-3367 1/9
Step-by-step explanation:
This is what calculators are for.
Perform the multiplication and division before the addition.
... = 10000/-9 -2256
... = -1111 1/9 -2256
... = -3367 1/9
_____
If you don't have a calculator, the Google and Bing search boxes can be relied upon to use the correct order of operations.
bao and Calvin use 6 lemon to make every 4 quarts of lemonade, they want to make 12 quarts of lemonade. how many lemons do they need?
All of the triangles are 45-45-90 triangles. Find x
Please show how you did it.
Answer:
3/√2
Step-by-step explanation:
find the details in the attachment (this is not the shortest way).
The shortest way is: to prove ED=AB, then to calculate x=AB/√2=3/√2.
please help me. math.
Answer:
y =293(1.06) ^x
y = 370 after 4 years
Step-by-step explanation:
If we are using the model for growth
y = a ( 1+b)^x
a is the initial population
b is the increase rate
We can substitute the values into the equation
y =293 (1+.06) ^ x
y =293(1.06) ^x
Let x equal 4 for the 4 years
y = 293(1.06)^4
y=369.9
On a hot summers day 262 people used the public swimming pool. The daily prices are 1.50 for children and 2.00 for adults. The receipts for admission totalled 470.00. How many children and how many adults swam st the pool that day?
Let x represent the number of adults who swam at the pool. Then (262-x) is the number of children. Multiplying these numbers by the corresponding admission charge will give the associated receipts. We are given the total of receipts, so we can write the equation ...
... 2.00x +1.50(262-x) = 470.00
... 0.50x +393.00 = 470.00 . . . . . simplify
... 0.50x = 77.00 . . . . . . . . . . . . . . .subtract 393
... 77.00/0.50 = x = 154 . . . . . . . . . divide by the coefficient of x
... (262-x) = 108 . . . . . . . . . . . . . . . .find the number of children admitted
find the exponential model of best fit for the points (-3,5),(1,12),(5,72),(7,137). Explian how you got your answer. Round values to the nearest hundredth.
f(x) = 11.93·1.42^x
Step-by-step explanation:I entered the data into a graphing calculator and made use of its exponential regression function to find the coefficients of ...
... y = a·b^x
It told me ...
... a ≈ 11.9304, b ≈ 1.41885
In accordance with the problem statement, these values are rounded to hundredths to get the answer.
_____
Comment on the graph
The given points and two curves are show. The solid red curve is the exponential regression curve produced by the calculator. The dotted blue curve is the one you get when you round the numbers to the nearest hundredth.
Which is closest to the value of x
Answer:
11
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that
... Cos = Adjacent/Hypotenuse
so you know ...
... cos(41°) = x / 14
Multiplying by 14 gives the value of x.
... x = 14·cos(41°) ≈ 10.566 ≈ 11
_____
Comment on answer choices
The visible answers are 10, 40, 12. The best choice of those is 10. If there is no choice offering 11 as the answer, then I'd choose 10.
Answer:
11
Step-by-step explanation:
Here we are given a right angled triangle with a known angle of 41°, length of the hypotenuse to be 14 and we are to find the length of the base x.
For that, we can use the formula for cosine for which we need an angle and the lengths of base and hypotenuse.
[tex]cos \alpha =\frac{base}{hypotenuse}[/tex]
So putting in the given values to get:
[tex]cos 41=\frac{x}{14} \\\\x= cos 41*14\\\\x=10.56[/tex]
Therefore, the value of x is the closest to 11.
Prove that u(n) is a group under the operation of multiplication modulo n.
Answer:
The answer is the proof so it is long.
The question doesn't define u(n), but it's not hard to guess.
Group G with operation ∘
For all a and b and c in G:
1) identity: e ∈ G, e∘a = a∘e = a,
2) inverse: a' ∈ G, a∘a' = a'∘a = e,
3) closed: a∘b ∈ G,
4) associative: (a∘b)∘c = a∘(b∘c),
5) (optional) commutative: a∘b = b∘a.
Define group u(n) for n prime is the set of integers 0 < i < n with operation multiplication modulo n.
If n isn't prime, we exclude from the group all integers which share factors with n.
Identity: e = 1. Clearly 1∘a = a∘1 = a. (a is already < n).
Closed: u(n) is closed for n prime. We must show that for all a, b ∈ u(n), the integer product ab is not divisible by n, so that ab ≢ 0 (mod n). Since n is prime, ab ≠ n. Since a < n, b < n, no factors of ab can equal prime n. (If n isn't prime, we already excluded from u(n) all integers sharing factors with n).
Inverse: for all a ∈ u(n), there is a' ∈ u(n) with a∘a' = 1. To find a', we apply Euclid's algorithm and write 1 as a linear combination of n and a. The coefficient of a is a' < n.
Associative and Commutative:
(a∘b)∘c = a∘(b∘c) because (ab)c = a(bc)
a∘b = b∘a because ab = ba.
Answer:
The answer is the proof so it is long.
The question doesn't define u(n), but it's not hard to guess.
Group G with operation ∘
For all a and b and c in G:
1) identity: e ∈ G, e∘a = a∘e = a,
2) inverse: a' ∈ G, a∘a' = a'∘a = e,
3) closed: a∘b ∈ G,
4) associative: (a∘b)∘c = a∘(b∘c),
5) (optional) commutative: a∘b = b∘a.
Define group u(n) for n prime is the set of integers 0 < i < n with operation multiplication modulo n.
If n isn't prime, we exclude from the group all integers which share factors with n.
Identity: e = 1. Clearly 1∘a = a∘1 = a. (a is already < n).
Closed: u(n) is closed for n prime. We must show that for all a, b ∈ u(n), the integer product ab is not divisible by n, so that ab ≢ 0 (mod n). Since n is prime, ab ≠ n. Since a < n, b < n, no factors of ab can equal prime n. (If n isn't prime, we already excluded from u(n) all integers sharing factors with n).
Inverse: for all a ∈ u(n), there is a' ∈ u(n) with a∘a' = 1. To find a', we apply Euclid's algorithm and write 1 as a linear combination of n and a. The coefficient of a is a' < n.
Associative and Commutative:
(a∘b)∘c = a∘(b∘c) because (ab)c = a(bc)
a∘b = b∘a because ab = ba.
Find approximations for the input where the functions share a solution.
Answer:
x ≈ 0, x ≈ 2.5
Step-by-step explanation:
The left point of intersection is very near the y-axis, where x=0.
The right point of intersection is somewhat below the midpoint between x=2 and x=4. It seems to be just about at the midpoint between that midpoint (x=3) and the line at x=2. We estimate the value at about x=2.5.
_____
If we knew the actual function definitions, we could solve for the points of intersection.
A set of n = 15 pairs of scores (x and y values) has ssx = 4, ssy = 25, and sp = 6. what is the pearson correlation for these data? 6/100 6/10 6/(100/15)
Answer:
We are given:
[tex]SSx = 4[/tex]
[tex]SSy=25[/tex]
[tex]Sp=6[/tex]
We know that the Pearson's correlation coefficient is:
[tex]r=\frac{S_{p}}{\sqrt{SS_{x} \times SS_{y}} }[/tex]
[tex]=\frac{6}{\sqrt{4 \times 25} }[/tex]
[tex]=\frac{6}{\sqrt{100} }[/tex]
[tex]=\frac{6}{10}[/tex]
Therefore, the option 6/10 is correct
At a basketball game, a vender sold a combined total of 165 sodas and hot dogs. The number of sodas sold was 39 more than the number of hot dogs sold. Find the number of sodas sold and the number of hot dogs sold.
Answer:
102 sodas63 hot dogsStep-by-step explanation:
Let s and h represent the numbers of sodas and hotdogs sold, respectively. The problem statement tells you ...
... s + h = 165
... s - h = 39
Add these two equations to get ...
... 2s = 204
... s = 102 . . . . . divide by w
... h = 165 - 102 = 63 . . . . use the first equation to find h from s
The vendor sold 102 sodas and 63 hot dogs at the basketball game.
find each missing measure, measure of angle 1,2,3,4
Answer:
75°56°124°41°Step-by-step explanation:
∠1 is complementary to 15°, so is 90° -15° = 75°
∠2 completes the triangle with angles 49° and 75°, so is 180° -49° -75° = 56°
∠3 is supplementary to ∠2, so is 180° -56° = 124°
∠4 is complementary to 49°, so is 90° -49° = 41°
CORRECT ANSWER = BRAINLIEST
A right rectangular prism has these dimensions: Length − Fraction 1 and 1 over 2 units Width − Fraction 1 over 2 unit Height − Fraction 3 over 4 unit How many cubes of side length Fraction 1 over 4 unit are required to completely pack the prism without any gap or overlap?
Answer:
36
Step-by-step explanation:
The length of 1 1/2 units is equivalent to 3/2 = 6/4 = 6×(1/4) = 6 cubes.
The width of 1/2 units is equivalent to 2/4 = 2×(1/4) = 2 cubes.
The height of 3/4 units is equivalent to 3×(1/4) = 3 cubes.
Then, in terms of cubes, the dimensions are 6 × 2 × 3. The volume is the product of these dimensions, so is ...
... 6 × 2 × 3 = 36 . . . . cubes
Answer:
36Step-by-step explanation:
If you flip a coin 44 times what is the best prediction possible for the number of times it’ll land on heads
Answer:
12% chance of 22
35% chance of 21, 22, or 23
55% chance of 20, 21, 22, 23, or 24
How can 22 be a good prediction when it's wrong 88% of the time?
I'd say from 20 to 24 is a good prediction without being trivial.
Step-by-step explanation:
C(n,k) = n Choose k = n! / (k! (n-k)!)
aka binomial coefficient
aka from n things choose k
To get probability of getting heads 22 times in 44 tries, you divide number of ways to get heads 22 times by number of ways to assign heads or tails to each throw.
Two ways to assign H or T to first, times two ways for second throw,
gives 2^44. That's the denominator.
Number of ways to get heads 22 times is the same as number of ways to choose which 22 flips of 44 are to be heads, or C(44,22)
To get 12% calculate C(44,22)/2^44
To get 55% calculate C(44,20)/2^44 + ... + C(44,24)/2^44
Final answer:
The best prediction for the number of times a coin will land on heads after 44 flips is 22 times, as each flip has a 50-50 chance of resulting in heads.
Explanation:
When you flip a coin 44 times, the best prediction for the number of times it will land on heads is that it will land on heads about 22 times. This is because each flip is independent, and the probability of landing on heads is 50%, or a 50-50 chance.
When a coin is tossed multiple times, despite the possibility of getting streaks of either outcome, as the number of flips increases, the overall distribution of heads and tails tends to even out and approach a 50% split due to the law of large numbers. For example, if you tossed a coin 100 times, the number of heads and tails would be close to 50 each, although not exactly due to the randomness of each flip.
Choose the correct simplification of the expression 3 times b all over a to the power of negative 2.
3a2b
a to the 2nd power over 3 times b
3 times a to the 2nd power all over b
Already simplified
pleaseee help
Answer:
Step-by-step explanation:
The question will look like (3b)/(a^-2)
To simplify, note the (a^-2). It is a negative, so flip the placement of the monomial. Note that the term is located in the decimal, so when it is flipped, it goes to the numerator (vice versa if it is opposite)
(3b)/(a^-2) = (3b)(a²)
3a²b, or (A) is your answer choice
~
Answer:
Option A) 3a2b
Step-by-step explanation:
There are 120 girls and 102 boys in 6th grade at Travis Intermediate. If 17 boys are in the first PE class, how many girls are likely in that class?
A
120 girls
B
22 girls
C
17 girls
D
20 girls
Answer:
Number of girls in PE class is 20
D. 20 girls
Step-by-step explanation:
We are given
Number of girls in 6th grade =120
Number of boys in 6th grade =102
so, firstly we will find ratios of girls and boys
[tex]\frac{G}{B}=\frac{120}{102}[/tex]
now, we have
17 boys are in the first PE class
Let's assume number girls in PE class as 'x'
we know that
ratios of boys and girls must be equal
so, we get
[tex]\frac{G}{B}=\frac{120}{102}=\frac{x}{17}[/tex]
now, we can solve for x
[tex]\frac{120}{102}=\frac{x}{17}[/tex]
[tex]x=17\times \frac{120}{102}[/tex]
[tex]x=20[/tex]
So,
Number of girls in PE class is 20
which is equivalent to the following expression (3m^2+2mn-n^2)+(m^2+4mn-n^2)
Answer:
4m² + 6mn - 2n²Step-by-step explanation:
[tex](3m^2+2mn-n^2)+(m^2+4mn-n^2)\\\\=3m^2+2mn-n^2+m^2+4mn-n^2\qquad\text{combine like terms}\\\\=(3m^2+m^2)+(2mn+4mn)+(-n^2-n^2)\\\\=\boxed{4m^2+6mn-2n^2}[/tex]
Based on the available information, the expression (3m² + 2mn - n²) + (m² + 4mn - n²) is equivalent to 4m² + 6mn - 2n².
How the equivalent expression is determined?To simplify the expression (3m² + 2mn - n²) + (m² + 4mn - n²), we can combine like terms.
Like terms have the same variables and the same exponents.
Let's group the like terms together:
(3m² + m²) + (2mn + 4mn) + (-n²- n²)
Combining like terms within each group, we get:
4m² + 6mn - 2n²
Therefore, in this case, it is concluded that the expression (3m² + 2mn - n²) + (m² + 4mn - n²) is equivalent to 4m² + 6mn - 2n².
Learn more about Equivalent Expression here: https://brainly.com/question/2972832
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Given: KLMN is a trapezoid, KL=MN, m∠1=m∠2, LM/KN = 8/9 , Perimeter KLMN=132 Find: The length of midsegment.
34
Step-by-step explanation:KM is a transversal relative to parallel lines LM and KN. Thus ∠2 = ∠MKN ≅ ∠KML and ∠KML = ∠1. The two base angles of ΔKLM are equal, so that triangle is isosceles.
Then the ratios of all the sides are ...
... KL : LM : MN : KN = 8 : 8 : 8 : 9
The sum of these ratio units is 33, so each one stands for 132/33 = 4 perimeter length units. Then segment LM is 8×4 = 32 perimeter length units, and KN is 9×4 = 36 permeter length units.
The midsegment is the average of lengths LM and KN, so is ...
... (32 +36)/2 = 34 . . . . perimeter length units
The length of midsegment is 34 units.
Given data:
The trapezoid KLMN, Such that KL = MN.
And [tex]m\angle1 = m\angle2[/tex], LM/KN = 8/9
Also, perimeter of KLMN = 132 units.
To find:
The length of midsegment (KM).
In the given problem, we can observe that KM is a transversal relative to parallel lines LM and KN. Which means,
[tex]\angle MKN = \angle KML\\\angle 2=\angle 1\\[/tex]
Clearly, two base angles are equal. So, the triangles KLM and KMN are isosceles.
Taking the ratios of sides of two triangles as,
= KL : LM : MN : KN
= 8 : 8 : 8 : 9
The sum of ratio units is, 8 + 8 +8 +9 = 33. Then, the value of each ratio is,
[tex]= \dfrac{perimeter}{33} \\\\=\dfrac{132}{33} \\\\=4[/tex]
Then the length of segment LM is,
[tex]LM = 8 \times 4 = 32 \;\rm perimeter \;\rm length \;\rm units[/tex]
And, length of segment KN is,
[tex]KN = 9 \times 4 = 36 \;\rm perimeter \;\rm length \;\rm units[/tex]
Then, the length of midsegment KM is obtained by taking the average of LM and KN as,
[tex]KM = \dfrac{LM+KN}{2} \\\\KM = \dfrac{32+36}{2}\\KE = 34[/tex]
Thus, the length of midsegment is 34 units.
Learn more about the concept of midsegments here:
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why write a quadratic function whose graph has the given characteristics vertex :(2,3) point on graph (0,-1)
f(x) = -(x -2)² +3
Step-by-step explanation:We can fill in the vertex (h, k) values immediately in the vertex form ...
... f(x) = a(x -h)² +k
To find the value of a, we solve the equation for a at some point other than the vertex. The given point is (0, -1), so we can use that:
... -1 = a(0 -2)² +3
... -4 = 4a . . . . . . . . . subtract 3, simplify
... -1 = a . . . . . . . . . . . divide by 4
Now, we know the function is ...
... f(x) = -(x -2)² +3
find the area of a triangle with the given base and height
7ft, 2in
Answer:
A = 84 inches^2
Step-by-step explanation:
We know that the formula for the area of a triangle is given by
A = 1/2 b*h
Let's substitute what we know
We need the units to be the same
Convert 7 ft to inches
1 ft = 12 inches
Multiply both sides by 7
7 ft = 84 inches
A = 1/2 *84*2
A = 84 inches^2
One day in January, the high temperature was −3.6∘ and the low temperature was −22.3∘ .
What was the difference between the high and low temperatures that day?
Enter your answer, as a decimal.
Answer:
The difference is 18.7 degrees
Step-by-step explanation:
To find the difference in the temperature, we take the high temperature and subtract the low temperature.
Difference = high - low
= -3.6 - (-22.3)
= -3.6+22.3
= 18.7
The difference is 18.7 degrees
For the function f(x)= log5 3x-10 explain why x=2 is not in the domain
Answer:
Step-by-step explanation:
The simple answer is that logs cannot be negative and if you insert a 2 where the x is located you get a negative. Logs have to be >= 0
[text]log_5 (3x-10) = log_5 (-4)[tex]
It all has to do with logs being tied to exponents and exponents being tied to logs. Actually an inverse of an exponent is a log.
Please help me Simplify
5²- 2²
Answer:
21
Step-by-step explanation:
Simplify 5^2 to 25
25-2^2
Simplify 2^2 to 4
25-4
Answer
21
The value of the expression will be 21.
What is the value of the expression?When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
The expression is given below.
⇒ 5²- 2²
Simplify the expression, then the value of the expression will be given as,
⇒ 5²- 2²
⇒ 25 - 4
⇒ 21
The value of the expression will be 21.
More about the value of expression link is given below.
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Write an equation that gives the proportional relationship of the graph.
A)
y = 1/6x
B)
y = 2x
C)
y = 6x
D)
y = 12x
C) y = 6x
Step-by-step explanation:Pick any point. It is often convenient to use x = 1 (no marked point) or x = 10 (where y = 60).
Use these values to see which equation agrees.
A: 60 ≠ (1/6)·10
B: 60 ≠ 2·20
C: 60 = 6·10
D: 60 ≠ 12·10
____
Or, you can solve ...
... y = kx
for k, using the point values you found on the graph.
... 60 = k·10
... 60/10 = k = 6 . . . . . divide by 10
This makes the equation be ...
... y = 6x . . . . . . matches selection C
The work of a student to solve the equation 4(2x − 4) = 8 + 2x + 8 is shown below:
Step 1: 4(2x − 4) = 8 + 2x + 8
Step 2: 6x − 8 = 16 + 2x
Step 3: 6x − 2x = 16 + 8
Step 4: 4x = 24
Step 5: x = 6
In which step did the student first make an error and what is the correct step?
Step 2; 8x − 4 = 2(6 + x + 6)
Step 2; 8x − 16 = 16 + 2x
Step 3; 6x − 2x = 16 − 8
Step 3; 6x + 2x = 16 + 8
Answer:
The answer is B. Step 2; 8x − 16 = 16 + 2x
Hope This Helps!
what is 31 and 5/250 as a decimal
Answer:
31.020
Step-by-step explanation:
Multiply the fraction by 4/4 to get the denominator to 1000. Simplify to a denominator of 100 if you like. Then use place value to write your number.
... 31 + 5/250 = 31 + 20/1000 . . . . thirty-one and twenty thousandths
... = 31 + 0.020 = 31.020 . . . or . . . 31.02
A company manufactures skateboards. Each skateboard requires 1 6/7 hours of labor to assemble and 2 1/2 hours of labor to finish and stain. The cost of labor to the company is $36.00 each hour. Find the product 36\left(1\frac{6}{7}\ +\ 2\frac{1}{2}\right)36(1 7 6 + 2 2 1 ) using the distributive property. Describe what each individual term in the expression represents in the context of this situation after you distribute the 36, AND describe what the final result represents. Show your work, and explain
Answer: The total cost will be $156.85.
Step-by-step explanation:
Since we have given that
Time taken by labor to assemble the each skateboard is given by
[tex]1\frac{6}{7}\ hours\\\\=\frac{13}{7}\ hours[/tex]
Time taken by labor to finish and stain each skateboard is given by
[tex]2\frac{1}{2}\ hours\\\\=\frac{5}{2}\ hours[/tex]
Cost of labour to the company per hour = $36.00
According to question,
We will use "Distributive Property":
[tex]a\times (b+c)=a\times b+a\times c[/tex]
[tex]36(\frac{13}{7}+\frac{5}{2})\\\\=36\times \frac{13}{7}+36\times \frac{5}{2}\\\\=\frac{468}{7}+18\times 5\\\\=\frac{468}{7}+90\\\\=\frac{468+630}{7}\\\\=\frac{1098}{7}\\\\=\$156.85[/tex]
Hence, the total cost will be $156.85.
50 POINTS!! 1. [tex]\frac{4}{6} =\frac{x}{42} 2. \frac{21}{15}=\frac{p}{5}[/tex]
Solve for X and P
the answer is
1. x=28
2. p=7
Write a sentence to represent the equation 4 m = -8.
Answer:
The product of 4 and m is -8.
Without numbers: The product of four and the variable m is negative eight.
Step-by-step explanation:
4m means m is multiplied by 4. The result of the multiplication operation is called a "product." The equal sign translates to "is".
The sentence 'Four times a certain number equals negative eight' corresponds to the equation 4m = -8, indicating that multiplying a number by four yields negative eight.
The sentence to represent the equation 4 m = -8 might be: "Four times a certain number equals negative eight." This sentence encapsulates the equation by specifying that the product of the number m and four is equivalent to negative eight, implying that m will have a negative value since it is equal to a negative number when multiplied by a positive.