Answer:
p =1
q = 9
Step-by-step explanation:
f(x) = 2x³ - px² + 2qx + q
(x - 3) is a factor of f(x)
⇒f(3) = 0
2(3)³ - p*3² - 2q*3 +q = 0
2*27 - 9p - 6q + q = 0
54 - 9p - 5q = 0
-9p - 5q = -54 -------------------(I)
(2x - 1) is a factor of f(x)
2x - 1 = 0
2x = 1
[tex]\st x = \dfrac{1}{2}[/tex]
f(1/2) = 0
[tex]2*(\dfrac{1}{2})^{3}-p*(\dfrac{1}{2})^{2}-2q*\dfrac{1}{2}+q=0\\\\2*\dfrac{1}{8}-p*\dfrac{1}{4}-q+q = 0\\\\\dfrac{1}{4}-\dfrac{1}{4}p =0\\\\[Multiply the entire equation by 4]\\\\4*\dfrac{1}{4}-4*\dfrac{1}{4}p=0\\\\[/tex]
1 - p = 0
-p = -1
p = 1
Substitute p =1 in equation (I)
-9*1 - 5q = -54
-9 - 5q = -54
-5q = -54 + 9
-5q = -45
q = -45/(-5)
q = 9
A group of campers were polled about whether they like swimming and whether they like playing baseball. the data from the survey is shown in the venn diagram. use the venn diagram to find the missing values in the frequency table. a circle labeled swimming 24 overlaps a circle labeled baseball 18. overlap is labeled 15. 4-column table with 3 rows. first column has no label with entries likes baseball, does not like baseball, total. second column is likes swimming with entries a, c, 39. third column is does not like swimming with entries b, 13, e. fourth column is labeled total with entries 33, d, 70. which values are correct? select three options. a = 15 b = 18 c = 23 d = 35 e = 31
The missing values a, b, c, d and e are included in the given two-way table. The correct values from the options are: a =15, b=18,e=31
How to form two-way table?Suppose two dimensions are there, viz X and Y. Some values of X are there as [tex]X_1, X_2, ... , X_n[/tex] and some values of Y are there as [tex]Y_1, Y_2, ... , Y_n[/tex]
List them in title of the rows and left to the columns. There will be [tex]n \times k[/tex] table of values will be formed(excluding titles and totals), such that:
Value(ith row, jth column) = Frequency for intersection of [tex]X_i[/tex] and [tex]Y_j[/tex] (assuming X values are going in rows, and Y values are listed in columns).
Then totals for rows, columns, and whole table are written on bottom and right margin of the final table.
For n = 2, and k = 2, the table would look like:
[tex]\begin{array}{cccc}&Y_1&Y_2&\rm Total\\X_1&n(X_1 \cap Y_1)&n(X_1\cap Y_2)&n(X_1)\\X_2&n(X_2 \cap Y_1)&n(X_2 \cap Y_2)&n(X_2)\\\rm Total & n(Y_1) & n(Y_2) & S \end{array}[/tex]
where S denotes total of totals, also called total frequency.
n is showing the frequency of the bracketed quantity, and intersection sign in between is showing occurrence of both the categories together.
For this case, the table given is:
[tex]\begin{array}{cccc}\rm &\rm \text{Likes swimming}&\rm \text{Doesn't like swimming}&\rm Senior\\\rm \text{Likes baseball}&a&b&33\\\rm \text{Doesn't likes baseball}&c&13&d\\\rm Total & 39& e& 70 \end{array}[/tex]
From this table, we can make 5 equations as:
[tex]a+b = 33\\a+c=39\\b+39=e\\33+d = 70\\39+e=70[/tex]
From the last two equations, we get the values of d and e as:
[tex]d = 70-33 = 37\\e = 70-39 = 31[/tex]
Putting this value of 'e' in last third equation, we get:
[tex]b + 13 = 31\\b = 31-13= 18[/tex]
From this, and first equation, we get:
[tex]a +18 = 33\\a=33-18=15[/tex]
And from this value of a, and second equation, we get:15+c = 39
[tex]c = 39-15 = 24[/tex]
Thus, the correct values are: [tex]a =15, b=18,e=31[/tex]
Learn more about two-way table here:
https://brainly.com/question/26788374
Answer:
a,b,e
Step-by-step explanation:
How many cubes are in the prism (Its surface area and i'm confused)
Answer:
432 cubes
Step-by-step explanation:
(9)(8)(6)=432
Hope this helps
Answer:
432
Step-by-step explanation:
The front face of the prism (green) is 6 cubes high and 8 cubes wide. So, the front layer of cubes is 6×8 = 48 cubes.
The figure shows you there are 9 layers like this making up the whole prism.
Then the volume of the prism is ...
(9 layers) × (48 cubes/layer) = 9×48 cubes = 432 cubes
There are 432 cubes currently in the prism.
_____
Additional comment
The picture here does not ask for the surface area of the prism. The area would be the sum of the areas of each of the surfaces.
The three surfaces we can see (red, green, blue) have areas of 9×8 = 72, 6×8 = 48, and 6×9 = 54 square units, respectively. These areas total 174 square units, but represent only half of the total area.
The other half of the area is the same (each hidden face has the same area as its visible opposite). So, the total surface area of this prism is 2×174 = 348 square units. (1 unit = small cube edge length).
help help help help help help help help help
Answer:
1)you must miss the exam &u get start study
2)y=mx+b
3)
Find the zeros of the function f(x) = x² + 49.
Answer:
does not have
Step-by-step explanation:
the function will never equals zero. because x² is always a positive number. The minimum is 49.
Answer:
no step-by-step answer
x= 7 and x= -7
HELPP!!! please for brianlest
Answer: Up, Down, Left, Right
Step-by-step explanation:
A translation is when you move an object on a coordinate plane. You can move it up and down the y-axis, and left and right on the x-axis.
For example, imagine a triangle on a coordinate plane (it looks like a grid). You can move the triangle to the left, the right, up, down, or any combination of those movements. Therefore, the answer to the 4 blanks are Up, Down, Left, and Right.
Picture below need help a lot of points
Answer:
rp=20 :: pp=90
Step-by-step explanation:
Well, if it's 10% off then we know that the percent paid is 90%
Now, 18 is 90% of 20, so the regular price is $20
What is the area of triangle XYZ to the nearest tenth of a square inch? Use special right triangles to help find
the height
Y
28 in
60
X
z
Answer:
Area = 169.7 in^2
Step-by-step explanation:
The two given angles are 90 and 60 degrees. Since a triangle's angles always add to 180 degrees, the third angle is 30 degrees. The is known as a "30-60-90 triangle." It is a special right triangle that has side length values which are always in the same relationship with one another.
The sides of the 30-60-90 triangle ratio are:
Side opposite the 30° angle is x
Side opposite the 60° angle is x*√3
Side opposite the 90° angle is 2x
See attached image for the detail on the calculations.
help me please HeLp
i already tried 18.85 and 28.27
i don't know what it could be so i need heLP
Answer:
18.84
Step-by-step explanation:
C = 2pi × r
C = 2 × 3.14 × 3
C = 18.84
Answer:
It would be 18.84. There is no rounding
Step-by-step explanation:
C = 2[tex]\pi[/tex]r
so it would be
C = 2[tex]\pi[/tex]3
in exact form it would be
6[tex]\pi[/tex] but as a deciamal its
18.849555.....
it says no rounding so it would be 18.84
I need help to find the area of this problem.
Answer:
119 square yards
Step-by-step explanation:
assuming that the parallelograms height is 8 (11 - 3) we can find the area of the bottom
13 * 8 = 104
assuming that the rectangles length is 5 (13 - 8) we can find the area of the top
3 * 5 = 15
then add those
104 + 15 = 119
Which sets of measurements could be the interior measures of a triangle?
(answer choices)
A. 10*, 10*, 160*
B. 15*, 75*,90*
C. 20*, 80*, 100*
D 35*, 35* 105*
E 60*, 60*, 60*
Answer:
A, B, E
Step-by-step explanation:
the 3 angles of a triangle must add up to 180
A. 10 + 10 + 160 = 180
B. 15 + 75 + 90 = 180
C. 20 + 80 + 100 = 200
D. 35 + 35 + 105 = 175
E. 60 + 60 + 60 = 180
PLEASE HELP 70 POINTS & WILL GIVE BRAINLIEST Mayerlin volunteers on the weekend at the Central Library. As a school project, she decides to record how many people visit the library, and where they go. On Saturday, 319 people went to The Youth Wing, 401 people went to Social Issues, and 398 went to Fiction and Literature.
On Sunday, the library had 1500 total visitors. Based on what Mayerlin had recorded on Saturday, about how many people should be expected to go to Fiction and Literature? Round your answer to the nearest whole number.
Answer:
413
Step-by-step explanation:
413 people should be expected to go to Fiction and Literature
Step-by-step explanation:
Proportion of people who went to Fictions and Literature on Saturday:
342 out of 467 + 433 + 343 = 1243
The proportion is:
342/1243 = 0.275
On Sunday:
Based on Saturday, so 0.275 out of 1500(number of visitors on Sunday).
0.275*1500 = 412.5
Rounding to the nearest whole number:
413 people should be expected to go to Fiction and Literature
how do you find the area of a polygon in a coordinate plane?
Answer: Use this formula
Area = (number of sides × length of one side × apothem)
Step-by-step explanation: The formula to calculate the area of a regular polygon is, Area = (number of sides × length of one side × apothem)/2, where the value of apothem can be calculated using the formula, Apothem = [(length of one side)/{2 ×(tan(180/number of sides))}].
Please help me with this math problem!! Will give brainliest!! NO LINKS PLEASE!! Thanks!! :)
Answer:
x = 3
So,
PQ= 5
RS=6
Step-by-step explanation:
Hope it helps you.....
The actual length of a machine is 12.25cm. The measured length is 12.2cm. Round the amswer to part(b) to the nearest hundreth of a percent. Find the absolute error. Find the percent error.
Answer:
ABS Error: 0.05 cm
PERC Error: 0.40%
Step-by-step explanation:
Absolute error: Absolute difference between the actual dimension, and its measure. Measured in the same dimension as what we're measuring
(Remember the absolute)
ABS Err: | 12.25 cm - 12.2 cm | = 0.05cm
Percent error: Percentual difference between the actual dimension and its measure. Always measured in Percents
PERC Err: | (12.25 - 12.20) | / 12.25 = 0.0040 ≈ 0.40%
Ryder shot a model rocket over an area that consists of two grassy areas, shown in green, and an area with no grass, shown in white. a square is split into 3 sections. the bottom section is 5 acres, the middle section is 30 acres, and the top section is 15 acres. the top and bottom sections are shaded. what is the probability that his model rocket has landed in a grassy area? 0.2 0.3 0.4 0.6
The probability that his model rocket has landed in a grassy area will be equal to 0.4.
What is probability?The extent to which an event is likely to occur, is measured by the ratio of the favorable cases to the whole number of cases possible.
The total area of the land will be = 5+15+30=50 acres
Now the total grassy area will be =15+5=20 Acres
Now the probability of the model rocket to land on the grassy land will be:
[tex]P=\dfrac{Grassy\ area}{Total\ area}[/tex]
[tex]P=\dfrac{20}{50}=0.4[/tex]
Hence the probability that his model rocket has landed in a grassy area will be equal to 0.4.
To know more about probability follow
https://brainly.com/question/24756209
Answer:
C.10.0%
Step-by-step explanation:
Edge 2023!
Out of every 8 seeds Natalie planted, only 5 grew into flowers. If there are 45 flowers, how many seeds did not grow?
Please show the steps, thank you
Answer:
27
Step-by-step explanation:
here we remark that we have a proportional relationship Between the number of seeds and the number of flowers
Let x be the number of seeds we need in order to guarantee that 45 flowers grow.
8 seeds ————————-> 5 flowers
x seeds ————————-> 45 flowers
in order to find x ,We have to solve this equation :
[tex]\frac{x}{8}=\frac{45}{5}[/tex]
⇔ x/8 = 9
⇔ x = 8×9 = 72
“how many seeds did not grow” : 72 - 45 = 27
helppppppp meeee plsssss
What is the value of n2 {m+r} if m=3, n=2, and r=4
Answer:
Answer: 28.Substitute: 22 * 3 + 4 Calculate the sum or difference:22 * 7 Calculate the power:4 * 7Calculate the p.
Step-by-step explanation:
please all i need is one more brainliest
Solve each equation. Identify the solutions as rational or irrational numbers.
[tex]\textbf{a)}\\\\~~~~~~~x(3x-4)=5\\\\\implies 3x^2 -4x = 5\\\\\implies 3x^2 -4x=5\\\\\implies x^2 - \dfrac 43 x = \dfrac 53\\ \\\implies x^2 - 2\cdot \dfrac 23 \cdot x + \left( \dfrac 23 \right)^2 - \left( \dfrac 23 \right)^2 = \dfrac 53\\\\\implies \left(x-\dfrac 23 \right)^2 = \dfrac 53 + \dfrac 49\\\\\implies \left(x-\dfrac 23 \right)^2= \dfrac{19}{9}\\\\\implies x- \dfrac 23 = \pm\dfrac{\sqrt{19}}3\\\\\implies x=\dfrac 23 \pm\dfrac{\sqrt{19}}3\\\\[/tex]
[tex]\text{The solutions are irrational.}\\\\\\\textbf{b)}\\\\~~~~~~~(3x-2)^2 = \dfrac 14\\\\\implies 3x -2 = \pm \dfrac 12\\\\\implies 3x = 2\pm \dfrac 12\\\\\implies x = \dfrac 23 \pm \dfrac 16\\\\ \implies x = \dfrac 56 ,~~ x =\dfrac 12 \\ \\\text{The solutions are rational .}[/tex]
What is the solution to 2x2 8x=x2-16? x=-4 x=-2 x=2 x=4
The solution of the quadratic equation 2x² + 8x = x² - 16 is given as a negative of 4.
What is a factorization?It is the method to separate the polynomial into parts and the parts will be in multiplication. And the value of the polynomial at this point will be zero.
The equation is given below.
2x² + 8x = x² - 16
Then on simplifying, we have
x² + 8x + 16 = 0
x² + 4x + 4x + 16 = 0
(x + 4)(x + 4) = 0
(x + 4)² = 0
x = -4
More about the factorization link is given below.
https://brainly.com/question/6810544
Answer:
The solution of the quadratic equation 2x² + 8x = x² - 16 is given as a negative of 4.
Step-by-step explanation:
Use the Distributive Property to solve the equation.
3(x-6)+6=5x-4
what is x?
Answer:
x = -4
Step-by-step explanation:
1) Distribute
3(x - 6) + 6 = 5x - 4
3x - 18 + 6 = 5x - 4
2) Add the numbers
3x - 18 + 6 = 5x - 4
3x - 12 = 5x - 4
3) Add 12 to both sides
3x - 12 = 5x - 4
3x - 12 + 12 = 5x - 4 + 12
4) Simplify
Add The Numbers:
3x - 12 + 12 = 5x - 4 + 12
3x = 5x - 4 + 12
Add the numbers:
3x = 5x - 4 + 12
3x = 5x + 8
5) Subtract 5x from both sides
3x = 5x + 8
3x - 5x = 5x + 8 - 5x
6) Simplify
Combine like terms:
3x - 5x = 5x + 8 - 5x
-2x = 5x + 8 - 5x
Combine like terms:
-2x = 5x + 8 - 8
-2x = 8
7) Divide both sides by each factor
-2x = 8
-2x/-2 = 8/-2
8) Simplify
Cancel terms that are in both the numerator and denominator:
-2x/2 = 8/-2
Divide the numbers:
x = 8/-2
x = -4
Solution:
x = -4
For triangle xyz , the measures of angles x,y, and Z are known. Which method should be used to start solving triangle xyz?
law of sines
law of cosines
neither law can be used
both laws can be used
The triangle xyz has three sides and three angles
Neither law can be used to solve the triangle
How to determine the appropriate method?From the question, we understand that only the angle measures are given.
The law of sines is represented as:
x/sin(X) = y/sin(Y) = z/sin(Z)
The law of cosine states that:
x^2 = y^2 + z^2 - 2yz cos(X)
The above laws require at least one of the side lengths of the triangles.
Since the side lengths are not given, then none of the laws can be used
Read more about laws of cosines and sines at:
https://brainly.com/question/4372174
A hair stylist charges $25.00 for a hair cut, plus an 8% sales tax rate. How much change will you recieve if you pay $30.00?
Answer:
$3
Step-by-step explanation:
8% of $25 is $2. $25 + $2 is $27. $30 - $27 is $3.
Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form. 147, 21, 3, ... This is sequence and the is equal to
Answer:
geometric sequence
Step-by-step explanation:
an arithmetic sequence has a common difference d between consecutive terms.
21 - 147 ≠ 3 - 21
Hence the sequence is not arithmetic
A geometric sequence has a common ratio r between consecutive terms
[tex]\frac{21}{147}[/tex] = [tex]\frac{1}{7}[/tex] and [tex]\frac{3}{21}[/tex] = [tex]\frac{1}{7}[/tex]
there is a common ratio thus the sequence is geometric
What is a solution of x2 + 6x=-5?
Answer:
x=-5,-1
Step-by-step explanation:
The angles in a triangle have
measures of 61°, (3z), (z-5)
What is the value of z?
Answer:
z = 31
Step-by-step explanation:
A triangle adds up to 180 degrees
Therefore this equation is formed: 61 + 3z + z -5 = 180
Simplify:
4z = 124
z = 31
The polynomial equation x cubed minus 4 x squared 2 x 10 = x squared minus 5 x minus 3 has complex roots 3 plus-or-minus 2 i. what is the other root? use a graphing calculator and a system of equations. –3 –1 3 10
The negative one is the third root of the equation x³ - 4x² + 2x + 10. Then the correct option is B.
What is polynomial?Polynomial is an algebraic expression that consists of variables and coefficients. Variables are called unknown. We can apply arithmetic operations such as addition, subtraction, etc. But not divisible by variable.
The polynomial equation is given below.
[tex]\rm x ^3-4 x ^2+2 x+ 10 = x ^2 -5 x-3[/tex]
The equation can be written as
[tex]\rm x ^3-5 x ^2+7 x+ 13 = 0[/tex]
The equation has a complex root [tex]- 3 \pm 2 \iota[/tex]
Put x = -1, then we have
[tex]\begin{aligned} (-1) ^3-5 (-1) ^2+7 (-1)+ 13 = 0\\\\-1 - 5 - 7 + 13 = 0\\\\0=0 \end{aligned}[/tex]
The equation is satisfied by the negative one. Then the negative one is the third root of the equation.
More about the polynomial link is given below.
https://brainly.com/question/17822016
Answer:
B on edge
Step-by-step explanation:
because B is -1
In 1970, there were 1,754 deaths from boating accidents in the United States. By 2003, the number of deaths from boating accidents had decreased to 703. What was the percent decrease?
Answer:
the percentage decrease is 60.2622577%
Step-by-step explanation:
1754-703/1754*100
1057/1754*100
105700/1754=60.2622577%
How to find area in feet
Answer:
The way to calculate a rectangular area is by measuring the length and width of your area then multiplying those two numbers together to get the area in feet squared (ft 2).
Step-by-step explanation:
might be the anwser ion know
Answer:
Area is length x width.
Step-by-step explanation:
Lets say you have a rectangle. The length is 7 feet and the width is 4 feet. 7 x 4 is 28. This is how you find the area.
If a cat had 2345 dogs and a dog had 387241 cats and dived by 7 and into percent how many did they have al together?
Answer:
389586
Step-by-step explanation:
2345 +387241= 389586