Answer:
x= 1
y = 5
Step-by-step explanation:
-10x+3y=5
x = y−4
-10(y-4)+3y=5
-10y+40+3y=5
-7y=5-45
-7y=-35
y=5
x = 5−4
x = 1
Answer:
[tex] x = 1 \\ y = 5 \\ [/tex]
[tex] - 10x + 3y = 5nd10x - 10( - 1)y = - 10( - 4) \\ - 10x + 3y = 5nd10x + 10y = 40 \\ - 10x10x + 3y - 10 = 5 - 40 \\ 3y - 10y = 5 - 40 \\ - 7y = 5 - 40 \\ - 7y = 35 \\ y = 5 \\ x - 5 = - 4 \\ x = 1[/tex]
what is the value of y
Answer:
y=54 degrees
Step-by-step explanation:
2y+72=180
2y=108
y=54
Answer:
B
Step-by-step explanation:
72 + y + y = 180
72 + 2y = 180
2y = 108
2y/2 = 108/2
y = 54
Hope this helps ^-^
Solve the equation. And write all solutions in general form.
Answer:
x = pi/2 + 2 pi n x = pi + 2 pi n where n is an integer
x = 5pi /3 + 2 pi n
Step-by-step explanation:
8 cos^2 x + 4 cos x-4 = 0
Divide by 4
2 cos^2 x + cos x-1 = 0
Let u = cos x
2 u^2 +u -1 =0
Factor
(2u -1) ( u+1) = 0
Using the zero product property
2u-1 =0 u+1 =0
u = 1/2 u = -1
Substitute cosx for u
cos x = 1/2 cos x = -1
Take the inverse cos on each side
cos ^-1(cos x) = cos ^-1(1/2) cos ^-1( cos x) =cos ^-1( -1)
x = pi/2 + 2 pi n x = pi + 2 pi n where n is an integer
x = 5pi /3 + 2 pi n
Find the area of circle B in term of ( pie )
Answer:
C.
Step-by-step explanation:
[tex]1.5^2\pi =2.25\pi[/tex]
What is simplified expression for the expression below
Answer:
4(x+8) + 5(x-3)
= 4x + 32 + 5x - 15
= 9x + 17
Answer:
9x+17
Step-by-step explanation:
HOpe It HelPs!!!!!
Also download photo math bc it help with stuff like this!!!!
Two roots of the polynomial function f(x) = x3 − 7x − 6 are −2 and 3. Use the fundamental theorem of algebra and the complex conjugate theorem to determine the number and nature of the remaining root(s). Explain your thinking.
Answer:
The degree of the polynomial is 3.
By the fundamental theorem of algebra, the function has three roots.
Two roots are given, so there must be one root remaining.
By the complex conjugate theorem, imaginary roots come in pairs.
The final root must be real.
Step-by-step explanation:
The number of roots remaining of the polynomial function f(x) = x³ − 7x − 6, with two roots -2, and 3 already given is 1. The nature of the root will be real.
What are polynomial functions?A polynomial function is a function (say f(x)), which is defined over a polynomial expression in x. It is of the form,
f(x) = a₀ + a₁x + a₂x² + a₃x³ + ... + aₙxⁿ, where a₀, a₁, a₂, ..., aₙ are constants, x is a variable, and n ≥ 0.
Degree of the polynomial function = n, the highest power of x.
What is the fundamental theorem of algebra?The fundamental theorem of algebra is that the number of roots or solutions of a polynomial function = The degree of the polynomial function.
What is the complex conjugate theorem?According to the complex conjugate theorem, if a polynomial function has complex roots, they will always exist in conjugate pairs, that is, if one root is of the form a + bi, the other root will be a - bi.
How will we determine the question?We are given a polynomial function f(x) = x³ - 7x - 6. Two roots of the equation are given as -2, and 3.
The degree of the equation = 3, so by the fundamental theorem of algebra number of roots = 3.
2 roots are given, so the number of roots remaining = 1.
Since none of the given roots are complex, the third root can not be complex, as complex roots always exist in conjugate pairs, coming from the complex conjugate theorem. So, the remaining root will be real in nature.
Learn more about the fundamental theorem of algebra and the complex conjugate theorem at
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the figure below shows a parallelogram ABCD. Side AB is parallel to side DC and side AD is parallel to side BC
A student wrote the following sentences to prove that the two pairs of parallel opposite sides of parallelogram ABCD are congruent:
For triangles ABD and CBD, alternate interior angles ABD and CBD are congruent because AB and DC are parallel lines. Alternate interior angles ADB and CBD are congruent because AD and BC are parallel lines. DB is congruent to DB by ______. The triangles ABD and CDB are congruent by ASA postulate. As corresponding parts of congruent triangles are congruent, AB is congruent to DC and AD is congruent to BC by CPCTC.
Which phrase best completes the student's proof?
a. associative property
b. reflexive property
c. substation property
d. transitive property
Answer: b) reflexive property
Step-by-step explanation:
When you are stating that a line is congruent to itself, you are using the Reflexive Property.
a) Associative Property: a + (b + c) = (a + b) + c
b) Reflexive Property: AB = AB
c) Substation Property: not a real property - does not exist
d) Transitive Property: If a = b and b = c, then a = c
Question
The cost for materials to resurface 1 meter of road is $750. What is the cost of materials to resurface 0.25
kilometer of a road? (1 kilometer = 1,000 meters).
$187.50
$1,875.00
$18,750.00
$187,500.00
Answer:
Option D
Step-by-step explanation:
Cost for the materials to resurface 1 meter of the road is $750.
∵ 1 kilometer = 1000 meter
∴ 0.25 kilometer = 0.25 × 1000
= 250 meters
∵ Cost to resurface 1 meter of road = $750
∴ Cost to resurface 250 meter of road = 750 × 250
= 187,500
The cost of materials to resurface 0.25 kilometer of a road is $187,500.
Option D is the answer.
In a packet of stickers there are small stars, big stars, small rockets, and big rockets. Kevin is going to choose one of these stickers from the packet at random to put on his artwork. What is the probability that the sticker Kevin chooses is big or is a rocket
Answer:
3/4 or 0.75
Step-by-step explanation:
You have four options available
Lets say P(A) is pick a rocket
P(A) = 2/4 because there are two rockets in the four choices
simplify it to 1/2
P(B) pick a big = 2/4 because there are two bigs and two smalls.
simplify it to 1/2
P(A ∩ B) = Pick a big rocket = 1/4
P(AUB) = P(A)+P(B)- P(A ∩ B)
P(AUB) = 1/2+1/2- 1/4 = 3/4 or 0.75
Regression modeling is a statistical framework for developing a mathematical equation that describes how: a. One explanatory and one or more response variables are related b. Several explanatory and several response variables response are related c. One response and one or more explanatory variables are related d. All of these are correct
Answer:
c. One response and one or more explanatory variables are related.
Step-by-step explanation:
Regression shows the relationship between a given variable and its covariates, which can be one or more. The initial variable is the dependent or response variable selected to show its level of variation with respect to one or more independent or explanatory variables.
Therefore, regression modeling describes how one response is related to one or more explanatory variables.
If P = {positive factors of 6}, how many subsets can be obtained from set P?
Step-by-step explanation:
1,2,3,4,5,6 is a set of 6 elements; therefore it has 2⁶=64 subsets
f(x) = (x + 2)(x + 2)
[tex]\displaystyle f(x) = (x + 2)(x + 2)[/tex]
[tex]\displaystyle f(x) = (x + 2)^2[/tex]
Answer:
[tex]f(x) = {(x + 2)}^{2} [/tex]
Step-by-step explanation:
[tex]f(x) = (x + 2)(x + 2) \\ f(x) = {(x + 2)}^{2} [/tex]
hope this helps you.
Please help me. Please!!
What expression is equivalent to -6(-2/3+2x)
a. - 4 - 12x
b. - 4 + 2x
c. 4 - 12x
d.4 + 12x
Answer:
B
Step-by-step explanation:
Answer:
[tex] = 4 - 12x \\ [/tex]
Answer C is correct.
Step-by-step explanation:
[tex] - 6( - \frac{2}{3} + 2x) \\ \frac{12}{3} - 12x \\ = 4 - 12x[/tex]
hope this helps you.
What is the product of the expressions? Assume y does not equal 0.
Answer:
The correct answer would be option 4
12x+20
5y3
Hope that helps.Thank you!!!
The average cholesterol content of a certain brand of eggs is 215 milligrams, and the standard deviation is 15 milligrams. Assume the variable is normally distributed. If a single egg is randomly selected, what is the probability that the egg will be with cholesterol content greater than 220 milligrams
Answer:
"The probability that the egg will be with cholesterol content greater than 220 milligrams" is 0.37070 (37.070% or simply 37%)
Step-by-step explanation:
We have here a normally distributed random variable. The parameters that characterize this distribution is the mean, [tex] \\ \mu[/tex], and the standard deviation, [tex] \\ \sigma[/tex].
In this question, we have that:
[tex] \\ \mu = 215[/tex] milligrams.[tex] \\ \sigma = 15[/tex] milligrams.And we want to know the probability that a randomly selected single egg "will be with cholesterol content greater than 220 milligrams."
To answer the latter, we need to use the following key concepts:
Z-scores.The cumulative standard normal distribution, andThe [cumulative] standard normal table.The z-scores are standardized values and represent the distance (for the raw score) from the mean in standard deviations units. A positive z-score indicates that it is above [tex] \\ \mu[/tex] and, conversely, a negative result that the value is below it.
The cumulative distribution function generates the values for the cumulative standard normal distribution displayed in the standard normal table.
The standard normal distribution is employed to find probabilities for any normally distributed data and we only need to calculate the corresponding z-score (or standardized value). This distribution has a [tex] \\ \mu = 0[/tex] and [tex] \\ \sigma = 1[/tex].
As we can see, all of these concepts are intertwined, and each of them is important because:
To find the corresponding probability, we first need to obtain the z-score.After this, we can consult the standard normal table, whose values are tabulated from the cumulative standard normal distribution, to find the requested probability.Finding the probability
We can get the z-score using the formula:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]
Where x is the raw value we want to standardize using the previous formula, and, in this case is 220 milligrams, [tex] \\ x = 220[/tex] milligrams.
Thus (without using units):
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]
[tex] \\ z = \frac{220 - 215}{15}[/tex]
[tex] \\ z = \frac{5}{15}[/tex]
[tex] \\ z = \frac{5}{5} * \frac{1}{3}[/tex]
[tex] \\ z = 1 * \frac{1}{3}[/tex]
[tex] \\ z = 0.3333333...[/tex]
To consult the standard normal table, we only need [tex] \\ z = 0.33[/tex], because it only has values for two decimal digits. As a result, the value will be a little inexact (but near to the true value) compared to that obtained using statistical software (or maybe a more precise table).
With this value (which is positive and, therefore, above the mean), we need to carefully see the first column of the mentioned table to find z = 0.3. Then, in the first row, we only need to select that column for which we can add the next digit, in this case, 3 (it appears as +0.03). That is, we are finding the probability for [tex] \\ z = 0.33[/tex].
Then, the cumulative probability for [tex] \\ z = 0.33[/tex] is:
[tex] \\ P(x<220) = P(z<0.33) = 0.62930[/tex]
However, the question is asking for "cholesterol content greater than 220 milligrams" or
[tex] \\ P(x>220) = P(z>0.33)[/tex]
Since
[tex] \\ P(x<220) + P(x>220) = 1[/tex]
Which is the same for a standardized value:
[tex] \\ P(z<0.33) + P(z>0.33) = 1[/tex]
Then
[tex] \\ P(z>0.33) = 1 - P(z<0.33)[/tex]
Therefore
[tex] \\ P(x>220) = P(z>0.33) = 1 - P(z<0.33)[/tex]
[tex] \\ P(x>220) = 1 - P(z<0.33)[/tex]
[tex] \\ P(x>220) = 1 - 0.62930[/tex]
[tex] \\ P(x>220) = 0.37070[/tex]
Thus, "the probability that the egg will be with cholesterol content greater than 220 milligrams" is 0.37070 (37.070% or simply 37%).
The graph below shows a shaded area that corresponds to the found probability.
The value of tangent x is given. Find sine x and cos x if x lies in the specified interval.
tan x = 21, x is an element of [0, pi / 2]
Answer:
sin x = 0.998
cosx = 0.046
Step-by-step explanation:
Given that:
tan x = 21
where interval of x is [tex][0,\dfrac{\pi}{2}][/tex].
We know that the trigonometric identity for tan x is:
[tex]tan\theta = \dfrac{Perpendicular}{Base}[/tex]
Comparing with:
[tex]tan x = \dfrac{21}{1}[/tex]
Perpendicular = 21 units
Base = 1 unit
As per pythagorean theorem:
[tex]\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\[/tex]
[tex]\Rightarrow \text{Hypotenuse}^2 = 21^2 +1^2\\\Rightarrow \text{Hypotenuse} = \sqrt{442} = 21.023\ units[/tex]
interval of x is [tex][0,\dfrac{\pi}{2}][/tex] so values of sinx and cosx will be positive because it is first quadrant where values of sine and cosine are positive.
We know that
[tex]sin\theta = \dfrac{Perpendicular}{Hypotenuse}\\cos\theta = \dfrac{Base}{Hypotenuse}[/tex]
So, sine x :
[tex]\Rightarrow sinx =\dfrac{21}{21.023}\\\Rightarrow sinx = 0.998[/tex]
Similarly, value of cos x :
[tex]\Rightarrow cosx =\dfrac{1}{21.023}\\\Rightarrow cosx = 0.046[/tex]
Which part of Earth belongs to the geosphere?
air
plants
minerals
water
Help plz
Answer: Minerals
Step-by-step explanation:
The Mineral belongs to the geosphere option (3) Mineral is correct.
What is the geosphere?Different definitions of the geosphere have conflicting uses. It can be used to refer to the atmosphere, lithosphere, hydrosphere, and cryosphere as a whole. Different mass and/or energy flows can be exchanged between the various geosphere collectives.
We have a statement:
Which part of Earth belongs to the geosphere?
The options are:
airplantsmineralswaterAs we know, air belongs to the atmosphere.
Plants belong to the biosphere
Water belongs to the hydrosphere
Mineral belongs to the geosphere
The mineral is the part of the earth that belongs to the geosphere.
Thus, the Mineral belongs to the geosphere option (3) Mineral is correct.
Learn more about the geosphere here:
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Any help would be great
Answer:
V = 137.2
Step-by-step explanation:
We are given the volume equation. Simply plug in your r into the equation and calculate and you should get 137.189 as your answer.
Which foundation drawing matches this orthographic drawing ?
The correct answer is A
Explanation:
An orthographic drawing shows a three-dimensional figure from different perspectives or sides. Indeed, the orthographic drawing in the question shows how the object looks if you see this the front, side, and top of this. This implies the foundation drawing needs to match the figures of the orthographic drawing.
According to this, the correct figure is A because this is the only one that has a rectangle shape, and due to this, if you look at this from any different sides you will always see a rectangle. For example, the top view shows a rectangle of approximately 2x3 squares, and this view only fits with option A because B and C are not complete rectangles and therefore their top view is not a rectangle.
Kite EFGH is inscribed in a rectangle where F and H are midpoints of parallel sides. The area of EFGH is 35 square units. What is the value of x? 4 units 5 units 6 units 7 units
*see attachment for the figure described
Answer:
5 units
Step-by-step explanation:
==>Given the figure attached below, let where FH and EG intercepted be K.
Since FH are midpoints of parallel lines, KE = KG = x.
Given that the area of the kite EFGH = 35 square units, and we know the length of one of the diagonals = HF = KF + KH = 2 + 5 = 7, we can solve for x using the formula for the area of a kite.
Area of kite = ½ × d1 × d2
Where d1 = KH = 7
d2 = EG = KE + KG = x + x = 2x
Area of kite EFGH = 35
THUS:
35 = ½ × 7 × 2x
35 = 1 × 7 × x
35 = 7x
Divide both sides by 7
35/7 = x
x = 5
Answer:
5 units
Step-by-step explanation:
if the vertex of a parabola is negative for 6 and the other point of the curve is (-3,14) what is the coefficient of the squared expression in Parabola equation?
A. 6
B. 4
C. 8
D. 2
Answer:
coefficient of the square is a.6
Someone help me please?
[tex]32500[/tex]
[tex]0.00604[/tex]
[tex]2.4 \times 10^6[/tex]
[tex]1.47 \times 10^{-3}[/tex]
Answer:
A) 32500
B) 0.00604
C) [tex]2.4 * 10^6[/tex]
D) [tex]1.47 * 10^{-3}[/tex]
help please with the graph questions
the ball is at the highest point 2 second after it has been thrown. True or false?
Around 2.5 seconds after the ball is thrown, it carries on going. Up or Down?
Answer:
1. True.
2. Down.
Step-by-step explanation:
1. True. The ball is at its highest point between 1.5 seconds and 2 seconds after it has been thrown. So we round off the time to nearest second to get 2 seconds.
So the ball is at the highest point 2 seconds after it has been thrown.
2.Down. Around 2.5 seconds after the ball is thrown, it carries on going down since the height is decreasing as the time moves on.
A roller coaster car is going over the top of a 13-mm-radius circular rise. At the top of the hill, the passengers "feel light," with an apparent weight only 50 %% of their true weight. How fast is the coaster moving?
Answer:
0.253 m/s
Step-by-step explanation:
radius r of the circular rise = 13 mm = 0.013 m
apparent weight loss = 50%
acceleration of the new weight = 0.5 x 9.81 = 4.905 m/s^2
centripetal acceleration = 9.81 - 4.905 = 4.905 m/s^2
centripetal acceleration = [tex]\frac{v^{2} }{r}[/tex]
where v is the acceleration at the rise and r is the radius of the rise
centripetal force = [tex]\frac{v^{2} }{r}[/tex] = [tex]\frac{v^{2} }{0.013}[/tex]
4.905 = [tex]\frac{v^{2} }{0.013}[/tex]
[tex]v^{2}[/tex] = 0.063765
v = [tex]\sqrt{0.063765}[/tex] = 0.253 m/s
The equation y minus 1 = negative 7 (x minus 3). is written in point-slope form. What is the y-intercept of the line? A) –4 B) –2 C) 20 D) 22
Answer:
D) 22
Step-by-step explanation:
y= mx+b point-slope formy-1= -7(x-3)
y= -7x+21+1
y= -7x+22 in point-slope formx=0 ⇒ y-intercept is equal to:
y= -7*0+22= 22So y -intercept is 22, option D
Answer:
22
Step-by-step explanation:
y-1 = -7(x-3)
This is point slope form
Distribute
y-1 = -7x +21
Add 1 to each side
y-1+1 = -7x+21+1
y = -7x+22
This is slope intercept form where y = mx+b and b is the y intercept
22 is the y intercept
what polynomial has roots of -5, - 4 and 1
Answer:
[tex]\boxed{\sf \ \ \ x^3+8x^2+11x-20 \ \ \ }[/tex]
Step-by-step explanation:
hello,
(x+5)(x+4)(x-1) is one example of polynomial which has roots of -5,-4 and 1
[tex](x+5)(x+4)(x-1) = (x+5)(x^2-x+4x-4)=(x+5)(x^2+3x-4)\\= x^3+3x^2-4x+5x^2+15x-20=x^3+8x^2+11x-20[/tex]
hope this helps
Evaluate the expression for x=8. y=-0.1. and Z=4.6.
XZ-Y
XZ-Y
Answer:
36.9Step-by-step explanation:
write down the expression:
x*z-y
lets plug in the variables to evaluate the expression:
8*4.6-(-0.1)
36.8+0.1
36.9
Answer:
36.9Given,
X=8
y=-0.1
z=4.6
Now,
[tex]xz - y \\ = 8 \times 4.6 - ( - 0.1) \\ = 36.8 - ( - 0.1) \\ = 36.8 + 0.1 \\ = 36.9[/tex]
hope this helps..
Good luck on your assignment..
1, 3, 11, 43, 171, 683, what's next in this sequence?
Answer:
2731
Step-by-step explanation:
3 - 1 = 2 = 2^1
11 - 3 = 8 = 2^3
43 - 11 = 32 = 2^5
171 - 43 = 128 = 2^7
683 - 171 = 512 = 2^9
Following the pattern, add 2^11 to 683.
683 + 2^11 = 683 + 2048 = 2731
Hi,
We have the sequence 1 , 3 , 11 , 43 , __.
Let us say [tex]a_{1}=1 , a_{2}=3 , a_{3}=11 , a_{4}=43[/tex] and it is required to find out [tex]a_{5}[/tex] .
As, we can see the pattern from the given four terms that,
[tex]a_{2}=a_{1}+2[/tex] i.e. [tex]a_{2}=a_{1}+2^{1}[/tex]
[tex]a_{3}=a_{2}+8[/tex] i.e. [tex]a_{3}=a_{1}+2^{3}[/tex]
[tex]a_{4}=a_{3}+32[/tex] i.e. [tex]a_{4}=a_{1}+2^{5}[/tex]
Since, the next term is obtained by adding the previous terms by odd powers of two.
Therefore, [tex]a_{5}=a_{4}+2^{7}[/tex] i.e. [tex]a_{5}=a_{4}+128[/tex] i.e [tex]a_{5}=43+128[/tex] i.e. [tex]a_{5}=171[/tex]
So, [tex]a_{5}=171.[/tex]
Hence, the next term of the sequence is 171.
Let us say [tex]a_{1}=1 , a_{2}=3 , a_{3}=11 , a_{4}=43[/tex], [tex]a_{5}[/tex] [tex]= 683[/tex] and it is required to find out [tex]a_{6}[/tex].
Therefore, [tex]a_{6}=a_{5}+2^{9}[/tex] i.e. [tex]a_{6}=a_{5}+512[/tex] i.e [tex]a_{6}=683+512[/tex] i.e. [tex]a_{6}=1195[/tex]
So, [tex]a_{6}=1195.[/tex]
Hence, the next term of the sequence is 1195.
Please answer number 7 I give brainliest thank you!
Answer:
q1: 80
q2:85
q3:91.5
Work:
- rearrange the numbers from least to greatest
68,78,82,84,86,89,94,100
q1- add 78 and 82, divide by 2
q2: add 84 and 86, divide by 2
q3- add 89 and 94, divide by 2
What is the sampling method used in the following scenario? The marketing manager for an electronics chain store wants information about the ages of its customers. Over the next two weeks, at each store location, 100 randomly selected customers are given questionnaires to fill out asking for information about age, as well as about other variables of interest.
Answer:
Step-by-step explanation:
The method applied in this scenario is called simple random sampling. A sample of 100 customers is chosen from a larger population of customers and each customer has the same chance of being selected for the survey at any given time. Also, the chance of selecting 100 customers from each store is the same during the sampling process. The order of sampling at each store does not follow a certain order, thus, It is different from systematic random sampling.
Mr. Taylor filled out a bracket for the NCAA National Tournament. Based on his knowledge of college basketball, he has a 0.54 probability of guessing any one game correctly. (a) What is the probability Mr. Taylor will pick all 32 of the first round games correctly
Answer:
The probability is [tex]2.7327 \times 10^{-9}[/tex]
Step-by-step explanation:
The probability of guessing correctly, P = 0.54
Probability of not guessing correctly, q = 1 – P
q = 1 – 0.54 = 0.46
Number of trials, n = 32
Now calculate the probability that Mr. Taylor will pick 32 correctly in first round of the game.
Below is the calculation using binomial distribution.
[tex]Probability = \left ( _{k}^{n}\textrm{} \right )P^{k}(1-P)^{(n-k)} \\= \left ( _{32}^{32}\textrm{} \right )0.54^{32}(0.46)^{(32-32)} \\= 0.54^{32} \\= 2.7327 \times 10^{-9}[/tex]