Answer:
x^3+7x^2-50x-336 or (x-7)(x+6)(x+8)
Step-by-step explanation:
Factor each equation.
x^2-x-42= (x-7)(x+6)
x^2+x-56= (x-7)(x+8)
The common factor is (x-7), therefore the other factors of the expressions must multiply to find the common factor.
(x-7)(x+6)(x+8)=x^3+7x^2-50x-336.
Consider the following quadratic equation. y = x2 – 8x + 4 Which of the following statements about the equation are true? The graph of the equation has a minimum. When y = 0, the solutions of the equation are a = 4 + 2V3 o When y = 0, the solutions of the equation are r x = 8 + 2V2. o The extreme value of the graph is at (4,-12). The extreme value of the graph is at (8,-4). U The graph of the equation has a maximum. Submit
Answer:
The graph of the equation has a minimum.
When y = 0, the solutions are [tex]4 \pm 2\sqrt{3}[/tex]
The extreme value of the graph is (4,-12).
Step-by-step explanation:
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]
[tex]\Delta = b^{2} - 4ac[/tex]
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].
y = x2 – 8x + 4
Quadratic equation with [tex]a = 1, b = -8, c = 4[/tex]
a is positive, so it's graph has a minimum.
Solutions when y = 0
[tex]\Delta = b^2-4ac = 8^2 - 4(1)(4) = 64 - 16 = 48[/tex]
[tex]x_{1} = \frac{-(-8) + \sqrt{48}}{2} = \frac{8 + 4\sqrt{3}}{2} = 4 + 2\sqrt{3}[/tex]
[tex]x_{2} = \frac{-(8) - \sqrt{48}}{2} = \frac{8 - 4\sqrt{3}}{2} = 4 - 2\sqrt{3}[/tex]
When y = 0, the solutions are [tex]4 \pm 2\sqrt{3}[/tex]
Extreme value:
The vertex. So
[tex]x_{v} = -\frac{-8}{2} = 4[/tex]
[tex]y_{v} = -\frac{48}{4} = -12[/tex]
The extreme value of the graph is (4,-12).
HELP ME PLZ WILL MARK U AS BRAINLIEST
Answer:
yes
Step-by-step explanation:
the difference of mean is 10.5
the mean for Mrs.S was 26.7 while for Mr.C it was 37.2.
using this info we can infer that Mr.C uses 10-11 more textbooks monthly
A small country had a population of 7.1 x 10° in 1990. Since then, the original population has doubled, and an additional 7.7 x 1010 people have immigrated into the country. What is the population of the country now? The population is A x 10 where
Answer:
[tex]21.9 * 10^{10}[/tex] Population of the Country Now .
Step-by-step explanation:
According to the Question,
Given, A small country had a population of [tex]7.1 * 10^{10}[/tex] in 1990. Since then, the original population has doubled Thus The Population as of Now is [tex]2*7.1 * 10^{10} =[/tex] [tex]14.2 * 10^{10}[/tex] And [tex]7.7 * 10^{10}[/tex] people have immigrated into the country Thus, The New Population of the Country is [tex]14.2 * 10^{10} + 7.7 * 10^{10} =[/tex] [tex]21.9 * 10^{10}[/tex] .HELP!!!
A spherical baseball has a diameter of 5 inches and weighs 7 grams per cubic inch. What is the closest weight of the baseball rounded to the nearest gram?
Answer:
69
Step-by-step explanation:
xvusvsuvtuvqYSQY
Consider the following hypothesis test:
H0: = 18
Ha: ≠ 18
A sample of 48 provided a sample mean = 17 and a sample standard deviation s = 4.5.
If requires, round your answers to two decimal places.
a. Compute the value of the test statistic (to three decimal places.)
b. Use the t distribution table (Table 2 in Appendix B) to compute a range for the p-value.
p-value is between ______and _______
c. What is your conclusion? t = ______
Answer:
(a) [tex]t= -1.540[/tex]
(b) [tex]0.10 < p < 0.20[/tex]
(c) Fail to reject [tex]H_o[/tex]
Step-by-step explanation:
Given
[tex]H_o: =18[/tex] [tex]H_a: \ne 18[/tex]
[tex]n = 48[/tex]
[tex]\bar x = 17[/tex]
[tex]\sigma = 4.5[/tex]
Solving (a): The test statistic
This is calculated as:
[tex]t= \frac{\bar x - \mu_o}{\sigma/\sqrt n}[/tex]
So, we have:
[tex]t= \frac{17 - 18}{4.5/\sqrt{48}}[/tex]
[tex]t= \frac{- 1}{4.5/6.93}[/tex]
[tex]t= \frac{- 1}{0.6493}[/tex]
[tex]t= -1.540[/tex] --- approximated
Solving (b): Range of p value
First, calculate the degree of freedom (df)
[tex]df = n - 1[/tex]
[tex]df = 48 - 1[/tex]
[tex]df = 47[/tex]
Using:
[tex]\alpha = 0.05[/tex] --- significance level
The p value at: [tex]df = 47[/tex] is:
[tex]p = 0.065133[/tex]
and the range is:
[tex]0.05 * 2 < p < 2 * 0.10[/tex]
[tex]0.10 < p < 0.20[/tex]
Solving (c): The conclusion
Compare the p value to the level of significance value
We have:
[tex]p = 0.065133[/tex]
[tex]\alpha = 0.05[/tex]
By comparison:
[tex]p > \alpha[/tex]
because:
[tex]0.065133 > 0.05[/tex]
Hence, the conclusion is: fail to reject [tex]H_o[/tex]
Which list of numbers are valid for both inequalities?
3
0
2
5
8
7
O -1, 0,1
O 0,1,2
0 -1,0, 1, 2
0 -3, -2,-1, 0, 1, 2, 3, 4
Answer:
-3, - 2, - 1, 0, 1, 2, 3, 4
Step-by-step explanation:
The blue line of the number line can have its inequality range written as :
Since both startibg and endpoints are shaded :
-1 ≤ x ≤ 4
The red line can also be written as :
Only the start is shaded:
-3 ≤ x < 2
Listing out the values :
Blue line :-1 ≤ x ≤ 4
-1, 0, 1, 2, 3, 4
The red line : -3 ≤ x < 2
-3, - 2, - 1, 0, 1, 2
Combining both values :
-3, - 2, - 1, 0, 1, 2, 3, 4
PLS HELP WILL GIVE BRAINLIAST !!!
Answer:
32.5 feet long and 20 feet wide
Step-by-step explanation:
To solve for the length first, you have it measured as 26 in long and each 4 in is 5 ft so you can go ahead and divide 26 in by 4 in and that gives you 6.5 in so what we did was figure out how many 4 in were in 26 in and therefore we have a 6.5 and so just to match that to the 5 ft per each 4 in (in this case we have 6.5) so we multiply 6.5*5 and that equals 32.5 ft which is the length of the garden bed.
Next we are going to solve for the width which is 16 in wide in the scale and so again each 4 in is 5 ft so here again we're going to divide 16 in by 4 in and that equals 4 in and so again each 4 in is 5 ft so we're going to go ahead and multiply 4 * 5 and that gets you 20 ft which is the width of the garden bed.
True or False It is never sensible to calculate more than 100% of a number.
Answer:
False
Hope this helps!
what is the solution of the equation 3x=12 round your answer to the nearest ten thousandth
Answer:
2.2916
Step-by-step explanation:
Imagine bannanas flying into your room? I mean I couldn't imagine that either but im just saying
For this line 3x−4y−12=0, which statement is true? 1- The x-intercept is 4, and the y-intercept is 3. 2-The x-intercept is 4, and the y-intercept is -3 3-The x-intercept is 3, and the y-intercept is -4. 4-The x-intercept is 3, and the y-intercept is 4.
9514 1404 393
Answer:
2. The x-intercept is 4, and the y-intercept is -3
Step-by-step explanation:
The given equation is in general form. I find it easier to see the intercepts when the equation is written in standard form:
3x -4y = 12
Setting y=0 and solving for x, we have the x-intercept:
3x = 12 ⇒ x = 12/3 = 4
Setting x=0 and solving for y, we have the y-intercept:
-4y = 12 ⇒ y = 12/-4 = -3
The x-intercept is 4; the y-intercept is -3.
I don’t understand if anyone can explain?
Answer:
Part A: 320 ft²
Part B: 2,304 ft²
Step-by-step explanation:
Part A:
Area of one triangular face of the square pyramid = ½*base*height
base = 32 ft
height = 20 ft
Area = ½*32*20
Area = 320 ft²
Part B:
Total surface area of the square pyramid = area of the square base + area of the 4 triangular faces
= s² + 4(area of 1 triangular face)
s = 32 ft
area of 1 triangular face = 320 ft²
Total surface area = 32² + 4(320) = 1,024 + 1,280
= 2,304 ft²
Help!!!!!!!!!!! Photo attached
Answer:
option A : 25
Step-by-step explanation:
Given :
P = (- 6, 7) , Q = ( 2 , 1 ) , R = ( -1 , -3)
Find the length of PQ ,QR , PR.
Using distance formula to find the lengths.
[tex]distance = \sqrt{(x_2 - x_1 )^2 + (y_ 2- y_1)^2[/tex]
[tex]PQ = \sqrt{(2 -- 6)^2 + (1-7)^2} = \sqrt{8^2 + 6^2 } = \sqrt{64 + 36 } =\sqrt{100} = 10\\\\QR = \sqrt{(2 --1)^2 + (-3-1)^2}= \sqrt{3^2 + 4^2} =\sqrt{9+ 16} =\sqrt{25} = 5\\\\PR = \sqrt{(-1--6)^2 + (-3 -7)^2} = \sqrt{5^2 + 10^2} = \sqrt{25 + 100} = \sqrt{125}[/tex]
Clearly , the triangle satisfies Pythagoras theorem :
Square of larger side = Sum of squares of other sides.
Therefore , PQR is a right triangle,
with base = 5, height 10 and slant height(hypotenuse) = [tex]\sqrt{125}[/tex] .
[tex]Area = \frac{1}{2} \times base \times height[/tex]
[tex]=\frac{1}{2} \times 5\times 10\\\\= 5 \times 5 \\\\= 25 \ square\ units[/tex]
20 POINTS!!
Suppose that, based on a sample, the 95% confidence interval for the mean of
a population is (23,39). What was the mean of the sample?
A. 31
B. 37
C. 35
D. 33
Answer: 31
Step-by-step explanation: just took the test
If a distribution for a quantitative variable is thought to be nearly symmetric with very little variation,and a box and whisker plot is created for this distribution,which of the following is true?
A) The box will be quite wide but the whisker will be very short.
B) The left and right-hand edges of the box will be approximately equal distance from the median.
C) The whiskers should be about half as long as the box is wide.
D) The upper whisker will be much longer than the lower whisker.
Answer:
B). The left and right-hand edges of the box will be approximately equal distances from the median.
Step-by-step explanation:
The 'symmetry' si described as a 'satisfying arrangement of a balanced distribution of the elements of the whole' while a 'symmetry group' is characterized as a group whose elements are all the transformations under which a given object remains invariant and whose group operation is function composition.
As per the given conditions, the second statement asserts a true claim regarding the keeping of edges of left, as well as, right-hand side's boxes at equal intervals from the median. This will help in making the arrangement fulfilling while keeping a little scope for the variation. Thus, option B is the correct answer.
someone please help marking brainliest
A trapezoid has bases that measure 9 cm and 5 cm. The height of the figure is 4 cm. What is the area of the trapezoid?
?
O 28 cm
O 36 cm
O 45 cm
O 90 cm?
Answer:
28 square centimeters
Step-by-step explanation:
The area of a trapezoid (formula):
(a + b) ÷ 2 x h
Where a & b are the bases, and h is height.
Use formula with given measurements:
(9 + 5) ÷ 2 x 4 = 28
Area is measured in square centimeters
(centimeters in this case)
Therefore the area if the trapezoid is 28 cm^2
I really hope this helps!
Use your graph to find estimates of the solutions to the equation x^2-x-6=-2
Answer:
-2 and 3
Step-by-step explanation:
From the graph, the solution is the points where the curve cuts the x axis. From the graph, you can see that the equation cuts the x axis at two points that is at x=-2 and 3.
Hence the solutions to the equation is -2 and 3
A positive real number is 2 more than another. If the sum of the squares of the two numbers is 42, find the numbers.
Answer:
Step-by-step explanation:
From the first sentence x (the number) is 2 more than another number (y). So, x+2=y. The sum of the squares of the two numbers is 42, meaning that [tex]\\ (x+2)^{2}[/tex]+[tex]y^{2}[/tex]=42. First, we square root the ENTIRE equation to get rid of the square. If you do one thing to one side, you have to do it to the other. After this, we have x+2+y=[tex]\sqrt{42}[/tex]. Now, we subtract 2 from the other side to isolate the variable. You can isolate either one but normally I go for x. Now we have x+y=[tex]\sqrt{42}[/tex]+2. Now, we want to get y to the other side so we subtract it from the left side and the right side which gives us x=-y+[tex]\sqrt{42}[/tex]+2. now we know what X is equal to. Now we plug in x for [tex]\\ (x+2)^{2}[/tex]+[tex]y^{2}[/tex]=42, which gives us [tex](-y+\sqrt42}+2+2)^{2}[/tex]+[tex]y^{2}[/tex]=42. Now we only have one variable which is what we want. Next, we square root the entire thing to get rid of the squares, which gives us -y+[tex]\sqrt{42}[/tex]+4+y=[tex]\sqrt{42}[/tex]. I got lost in my work. I must have done something wrong I cant find out. If anyone wants to pick up where I left off go ahead but there's a timer and I have one minute left. I cant finish the problem in a minute. I'm sorry and hopefully I lead you somewhere.
A group of 12 friends bought tickets for an afternoon concert. However, not all of the friends were able to sit together. Tickets for floor seats cost $15 each, and tickets for tier seats cost $70 each. The total cost of the tickets was $345. How many tickets for tier seats did they purchase
Answer:
3 tier seats tickets
Step-by-step explanation:
Let the friends that bought floor seats be x and let the friends that bought tier seats be y.
Thus;
x + y = 12 - - - (eq 1)
Floor seats tickets cost $15 each, and tier seats tickets cost $70 each. The total cost of the tickets was $345. Thus;
15x + 70y = 345 - - - (eq 2)
Let's make x the subject in eq (1)
x = 12 - y
Putting this for x in eq 2 gives;
15(12 - y) + 70y = 345
180 - 15y + 70y = 345
55y = 345 - 180
55y = 165
y = 165/55
y = 3
Put 3 for y in x = 12 - y to get;
x = 12 - 3
x = 9
Thus, they purchased 9 floor seats tickets and 3 tier seats tickets
Help please!
Fully factorise
Answer:
a.8y³-6y
taking common
2y(4y²-3)
is a required answer
b.
3x²-20x+12
doing middle term factorization
3x²-18x-2x+12
3x(x-6)-2(x-6)
(x-6)(3x-2)
is a required answer .
Answer for fee rbux and branlest!!!! i need answer NOW or i will be DIE (not good!!!)
Answer:
its B homie
Step-by-step explanation:
U stuped
City A is due north of City B. Find the distance between City A ( north latitude) and City B ( north latitude). Assume that the radius of Earth is 3960 miles.
The distance between City A and City B is ___miles.
Can someone help?! Show me step by step how this is done that I can understand it better.
=========================================================
Explanation:
The notation [tex]47^{\circ}4'[/tex] means "47 degrees, 4 minutes". The "minutes" isn't referring to a time value, but instead they are arc minutes. If we divide one degree into 60 equal pieces, then we form 60 arc minute slices. So in a sense, we are using a round analogue clock to help connect the two ideas.
We can convert to purely degrees through using this formula here
[tex]a^{\circ}b' = a + \frac{b}{60}[/tex]
So,
[tex]47^{\circ}4' = 47 + \frac{4}{60} \approx 47.06667^{\circ}[/tex]
and similarly,
[tex]22^{\circ}46' = 22+ \frac{46}{60} \approx 22.76667^{\circ}[/tex]
Now subtract the two results we got
47.06667-22.76667 = 24.3
The angular distance between the two cities is 24.3 degrees. By "angular distance" I basically mean how far you need to rotate your viewing angle when looking from city A to city B. Imagine that you're able to be situated at the center of the earth.
The circumference of the earth is
C = 2*pi*r
C = 2*pi*3960
C = 24,881.4138164311
which is approximate and the units are in miles. We multiply by the fraction 24.3/360 to find the arc distance along the curve that corresponds to the angle 24.3 degrees. This is because we don't want the whole circumference, but just a small fraction of it.
So (24.3/360)*24,881.4138164311 = 1,679.4954326091
This rounds to 1679
The distance between the two cities is about 1679 miles.
9514 1404 393
Answer:
1679 miles
Step-by-step explanation:
One minute is 1/60 of a degree, so the difference in latitudes is ...
47 4/60 -22 46/60 = 24 18/60 = 24.3 . . . degrees
The arc length is given by ...
s = rθ . . . . . . r = radius, θ = angle in radians
180° is π radians, so the surface distance between the two cities is ...
s = (3960 mi)(24.3×π/180) = 534.6π mi ≈ 1679.495 mi
The distance between City A and City B is about 1679 miles.
_____
Additional comment
As a good approximation, the distance is about 60 nautical miles per degree of latitude. Using that approximation, and converting from nautical miles to statute miles would give a distance of 1678 miles.
The proportion of all high school students who watch national news is p = 0.47. A random sample of 50 high school students is selected. Which of the following is the mean of the sampling distribution of p hat ? Mu Subscript p hat = p = 0.47 Mu Subscript p hat = n p = 50 (0.47) = 23.5 Mu Subscript p hat = 1 minus p = 1 minus 0.47 =0.53 Mu Subscript p hat = n (1 minus p) = 50 (1 minus 0.47) = 26.5
The mean of the sampling distribution of p hat is,
⇒ Mu Subscript p hat = n p = 50 (0.47) = 23.5
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The proportion of all high school students who watch national news is p = 0.47.
And, A random sample of 50 high school students is selected.
Hence, By definition we get;
The mean of the sampling distribution of p hat is,
⇒ Mu Subscript p hat = n p
= 50 (0.47)
= 23.5
Thus, The mean of the sampling distribution of p hat is,
⇒ Mu Subscript p hat = n p = 50 (0.47) = 23.5
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ3
Determine the equation of the circle graphed below.
Answer:
[tex](x - 6)^2 + (y - 2)^2 = 4[/tex]
Step-by-step explanation:
Required
The equation of the circle
The equation of a circle is:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
Where:
[tex]Center = (h,k)[/tex]
[tex]radius \to r[/tex]
From the graph, we have
[tex](h,k) = (6,2)[/tex]
[tex]r = 2[/tex]
So:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex] becomes
[tex](x - 6)^2 + (y - 2)^2 = 2^2[/tex]
[tex](x - 6)^2 + (y - 2)^2 = 4[/tex]
which of the following is true because of the commutative law of multiplication
15*3=45
15*3=40+5
15*3=3*15
15*3=3*3*5
Explanation:
The commutative law of multiplication says that A*B = B*A, for any real numbers A,B. The order of multiplication doesn't matter.
That's why 15*3 is the same as 3*15.
This is because having 15 groups of 3 leads to 3+3+3+...+3 = 45 (imagine adding 15 copies of '3' together), and having 3 groups of 15 gets us 15+15+15 = 45 as well.
Or you could picture a rectangular table that has 15 rows and 3 columns. It has 45 inner cells. If the table had 3 rows and 15 columns, then we'd still have 45 inner cells.
Write an inequality representing the following phrase:
Three more than five times a number t is less than thirty.
Answer:
5t + 3 < 30
Step-by-step explanation:
Five times a number t is 5t.
Three more just means add 3 more to your first term (in this case it's 5t).
Less than thirty means not less than or equal to 30 but just less then 30.
I need help with this problem
Answer:
x = 9 , jk = 42 , kl= 78
Step-by-step explanation:
Explained in the paper.
Goodluck
Answer:
x = 9
Step-by-step explanation:
[tex](4x+6)+(7x+15)=120[/tex]
[tex](4(9)+6)+(7(9)+15)=120[/tex]
[tex](36+6) + (63+15)=120[/tex]
[tex](42)+(78)=120[/tex]
x = 9
JL = 42
KL = 78
(2x+8)-(x-8) PLS HELP
If two cards are randomly selected, what is the probability of drawing any one suit first, followed by drawing a face card
Answer:
0.0181 = 1.81% probability of drawing a suit first, and then a face card.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Probability of drawing a suit first:
4 out of 52 cards are suits, so:
[tex]P(A) = \frac{4}{52} = \frac{1}{13}[/tex]
Followed by drawing a face card:
Considering a suit was drawn, there will be 12 faces in the 51 remaining cards. So
[tex]P(B|A) = \frac{12}{51}[/tex]
What is the probability of drawing a suit first, followed by drawing a face card?
[tex]P(A \cap B) = P(A) \times P(B|A) = \frac{1}{13} \times \frac{12}{51} = \frac{12}{13*51} = 0.0181[/tex]
0.0181 = 1.81% probability of drawing a suit first, and then a face card.
Translate and solve: 82% of what number is 369?
Answer:
82% of what number is 369
82% of 450 is 369
Answer:
number is 450
Step-by-step explanation:
let the number be x
82% of x=369
[tex]\frac{82}{100}[/tex]x = 369
82x=369*100
x=36900/82
x=450
