Answers
Answer:
A. 2 real roots: (2, 7) and (1, 4).
Step-by-step explanation:
y = x^2 + 3
y = 3x + 1
So equating the right sides:
x^2 + 3 = 3x + 1
x^2 - 3x + 2 = 0
(x - 2)(x - 1) = 0
So there are 2 roots.
They are x = 2 , y = 3(2) + 1 = 7 and
x = 1, y = 3(1) +1 = 4.
Related Questions
Please helpppppppppppp
Answers
Answer:
678 ft²
Step-by-step explanation:
The opposite sides of the cuboid are congruent, thus surface area is
2(11 × 9) ← front and back + 2(11 × 12) ← top and base + 2(12 × 9) ← sides
= 2(99) + 2(132) + 2(108)
= 198 + 264 + 216
= 678 ft²
A mega-pack of markers contains red markers, black markers, and blue markers. There are 24 red markers in the pack. The probability of randomly choosing a red marker is 1 in 3. If the probability of randomly choosing a blue marker is 1 in 8, how many blue markers are in the pack?
Will mark brainlist
Answers
Answer:
Number of blue markers = 9
Step-by-step explanation:
Given that there are 24 red markers.
Probability of randomly choosing a red marker is 1 in 3.
Probability of an event E is given as:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
That means the ratio of red markers to total markers is 1:3.
Here number of favorable cases are 24 i.e. the number of red markers
and Total number of cases are equal to total number of markers.
Let T be the total number of markers.
As per definition of probability:
[tex]\dfrac{1}{3}=\dfrac{24}{T}\\\Rightarrow \bold{T = 72}[/tex]
Also, given that the probability of choosing a blue marker is 1 in 8.
Let the number of blue markers be B.
As per definition of probability:
[tex]\dfrac{1}{8}=\dfrac{B}{72}\\\Rightarrow \bold{B = 9}[/tex]
Hence, the answer is:
Number of blue markers = 9
One polygon has a side of length 3 feet. A similar polygon has a corresponding side of length 9 feet. The ratio of the perimeter of the smaller polygon to the larger is
Answers
Answer:
1:3
Step-by-step explanation:
9/3 = 3
3 is the scale factor
A set of numbers is shown below: {0, 0.4, 1, 2, 3} Which of the following shows all the numbers from the set that make the inequality 4x + 1 ≥ 5 true? {2, 3} {1, 2, 3} {0, 0.4, 1} {0.4, 1}
Answers
Answer:
{1,2,3}
Step-by-step explanation:
The others will not show all the numbers from the set to make the inequality true
Answer:
1,2,3
Step-by-step explanation:
When the variable is on both sides of the equation it is perfectly acceptable to solve each side by itself
True or False
Answers
A forestry study found that the diameter of the trees in a forest is normally distributed with mean 34 cm with a standard deviation of 8 cm. A group of 4 trees will be used as timber if the average of the 4 trees diameter is not too thick or thin. Specifically it is desired for the mean diameter to be between 30 and 40 cm in diameter. Find the probability that a randomly chosen group of 4 trees can be used as timber
Answers
Answer:
The probability that a randomly selected group of four trees can be used as timber is 4.5 × 10⁻⁵
Step-by-step explanation:
The given parameters are;
Mean = 34 cm
The standard deviation = 8 cm
The mean
The Z score is [tex]Z=\dfrac{x-\mu }{\sigma }[/tex], which gives;
For x = 30 we have;
[tex]Z=\dfrac{30-34 }{8 } = -0.5[/tex]
P(x>30) = 1 - 0.30854 = 0.69146
For x = 40, we have
[tex]Z=\dfrac{40-34 }{8 } = 0.75[/tex]
P(x < 40) = 0.77337
Therefore, the probability that the mean of four trees is between 30 and 40 is given as follows;
P(30 < x < 40) = 0.77337 - 0.69146 = 0.08191
The probability that a randomly selected group of four trees can be used as timber is given as follows;
Binomial distribution
[tex]P(X = 4) = \dbinom{4}{4} \left (0.08191\right )^{4}\left (1-0.08191 \right )^{0} = 4.5 \times 10^{-5}[/tex]
please help. evaluate 5!.
Answers
Answer:
120
Step-by-step explanation:
! means to multiply it by every number less than itself.
Not counting 1, this means 5*4*3*2.
20*3*2
60*2
120
The answer is 120.
Answer:
120
Step-by-step explanation:
Rewrite the radical expression as an expression with a rational exponent. the seventh root of x to the third power
Answers
Answer:I think it’s 7x^3
Step-by-step explanation:
John needs to find out the probability that he will sell all his cars by the end of the
year. He takes a sample of the customers that come in to see if they will buy a car.
How many customers should he sample to get an accurate probability?
a) 3 customers
b) 10 customers
c) 100 customers
d) 1000 customers
Answers
Answer:
c) 100
Step-by-step explanation:
This is the best choice because the number is not too low or too high. He will get an accurate probability.
Can someone help me with this question (:
I’d appreciate it!
brainliest to the correct answer/explanation) ♀️
Answers
Answer:
bet whats the question
Step-by-step explanation:
Carter bought a bear and paid for a football uniform. The total cost was $38.50. Write and solve an equation to find the cost, x, of buying a bear.
Answers
Answer:
Equation:- [tex]x + y = 38.50[/tex]
Solution of x:- [tex]x = 38.50 - y[/tex]
Step-by-step explanation:
Given
Total Purchase = $38.50
Required
Determine the equation for finding the cost of a bear
From the question; we understand that the cost of 1 bear is represented with x
Solving further; by representing the cost of 1 football uniform with y
So;
[tex]1\ bear + 1\ uniform = 38.50[/tex]
Substitute x for 1 bear and y for 1 uniform to give us an equation
[tex]x + y = 38.50[/tex]
Solving for x (Subtract y from both sides)
[tex]x +y - y = 38.50 - y[/tex]
[tex]x = 38.50 - y[/tex]
The equation can't be solved further
Evaluate the following expression using the given values: (1 point) Find x − 3y if x = 3 and y = −2.
Answers
Answer:
9
Step-by-step explanation:
x − 3y
Let x =3 and y = -2
3 -3(-2)
3 + 6
9
The weights of newborn baby boys born at a local hospital are believed to have a normal distribution with a mean weight of 3958 grams and a standard deviation of 362 grams. If a newborn baby boy born at the local hospital is randomly selected, find the probability that the weight will be less than 4320 grams. Round your answer to four decimal places.
Answers
Answer:
0.8413 or 84.13%
Step-by-step explanation:
The difference from 4320 grams from the mean is:
[tex]d=4320-3958=362\ grams[/tex]
This is exactly 1 standard deviation.
According to the empirical rule, 68.26% of all data is within 1 standard deviation of the mean, which means that 34.13% of all data is within the mean and 1 standard deviation over the mean. We also know that the mean is at the 50th percent of the normal distribution.
Therefore, the probability that the weight will be less than 4320 grams is:
[tex]P(X\leq 4320) = 0.50+0.3413=0.8413 = 84.13\%[/tex]
The probability is 0.8413 or 84.13%
What is the translation from quadrilateral EFGH to
quadrilateral E'F’G’H
Answers
Answer:
The translation from quadrilateral EFGH to quadrilateral E'F'G'H' is [tex]T_{(2, -4)}[/tex], which is two units to the right (x direction) and 4 units down (negative y direction)
Step-by-step explanation:
The coordinates of quadrilateral EFGH are;
Point E has coordinates (-1, 1)
Point F has coordinates (0, 4)
Point G has coordinates (3, 1)
Point H has coordinates (3, 0)
The coordinates of the translation are;
Point E' has coordinates (0, -3)
Point F' has coordinates (1, 0)
Point G' has coordinates (4, -3)
Point H' has coordinates (4, -4)
The change in the y-coordinate values (y values) are;
From point E to point E', we have;
(-3 - 1) = -4 which is four units down
The change in the x-coordinate values (x values) are;
From point E to point E', we have;
(0 - (-1)) = 2 which is two units to the right
The total change in translation is [tex]T_{(2, -4)}[/tex].
Please answer this in two minutes
Answers
Answer:
R = 21.8° to the nearest tenth
Step-by-step explanation:
To find Angle R we use tan
tan ∅ = opposite / adjacent
From the question
The opposite is 2
The adjacent is 5
So we have
tan R = 2/5
R = tan-¹ 2/5
R = 21.8° to the nearest tenthHope this helps you
In how many ways can the letters of the word ``COPYRIGHT'' be arranged?
Answers
Answer:
362,880 ways
Step-by-step explanation:
There are 9 letters so 9!
And none of them are repeated so 9!/0!
9! = 362,880
I hope this helps, and plz mark me brainliest!!
A tissue sample is three cells thick. Each cell has a thickness of 0.000004m. What is the thickness of the tissue sample in mm. Give your answer in standard form. PLZ SHOW WORKING NOT IN NANO METERS. IN STANDARD FORM
Answers
Answer:
0.012 millimeters
Step-by-step explanation:
First, we solve for 0.000004 m to mm = 0.004 mm x 3 = 0.012 millimeters
What is the point-slope form of a line with slope 4/5 that contains the point
(-2, 1)?
Answers
Answer:
Y-1=4/5(x-(-2))
Step-by-step explanation:
Point slope form is written as y-y1=M(x-X1)
M is the slope
so replace the variables for the given value
Y-1=4/5(x-(-2))
Answer: y - 1 = 4/5 (x + 2)
Step-by-step explanation:
The function, f(x) = –2x2 + x + 5, is in standard form. The quadratic equation is 0 = –2x2 + x + 5, where a = –2, b = 1, and c = 5. The discriminate b2 – 4ac is 41. Now, complete step 5 to solve for the zeros of the quadratic function. 5. Solve using the quadratic formula. x = StartFraction negative b plus or minus StartRoot b squared minus 4 a c EndRoot Over 2 a EndFraction What are the zeros of the function f(x) = x + 5 – 2x2? x = StartFraction negative 1 plus or minus StartRoot 41 EndRoot Over negative 4 EndFraction x = StartFraction 1 plus or minus StartRoot 41 EndRoot Over negative 4 EndFraction x = StartFraction negative 1 plus or minus StartRoot 39 EndRoot Over negative 4 EndFraction x = StartFraction 1 plus or minus StartRoot 39 EndRoot Over negative 4 EndFraction
Answers
Answer:
To solve for the zeros of the function equate f(x) = 0
That's
- 2x² + x + 5 = 0
Using the quadratic formula
[tex]x = \frac{ - b± \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
a = - 2 b = 1 c = 5
And from the question
b² - 4ac = 41
So we have
[tex]x = \frac{ - 1± \sqrt{41} }{2( - 2)} = \frac{ - 1± \sqrt{41} }{ - 4} [/tex]
[tex]x = \frac{1± \sqrt{41} }{4} [/tex]
We have the final answer as
[tex]x = \frac{1 + \sqrt{41} }{4} \: \: \: \: or \: \: \: \: x = \frac{1 - \sqrt{41} }{4} [/tex]
Hope this helps you
Answer:
The CORRECT answer is A.
Step-by-step explanation:
just did it.
Rewrite the given function as an equivalent function containing only cosine terms raised to a power of 1.f(x)=7cos^2x
Answers
Answer:
Step-by-step explanation:
Using the double angle formulas,
cos(2x) = cos^2(x) - sin^2(x) ............(1)
1 = cos^2(x) + sin^2(x)............(2)
add (1) and (2)
1 + cos(2x) = 2 cos^2(x)
=> cos^2(x) = (1/2) (1+cos(2x)) ..............(3)
f(x) = 7 cos^2 (x)
substituting (3)
f(x) = (7/2) (1+cos(2x))
. The sum of the ages of x boys in a class is 84 years. When a new boy aged 8 years, 1 month joins the class, the average age is increased by 1 month
Answers
Answer:
The number of boys, x = 12
Step-by-step explanation:
Given that the sum of the ages of the boys in a class = 84 years
The number of boys = x
A new boy aged 8 years 1 month is added and the average age increases by 1 month
We have
Average age = 84/x = y
Age of new boy = 8 years 1 month = [tex]8\frac{1}{12} \ year[/tex]
New average = y + 1/12 = [tex](8\frac{1}{12}+84) /(x + 1)[/tex] which gives;
84/x + 1/12 = [tex](8\frac{1}{12} + 84) /(x + 1)[/tex]
[tex]\dfrac{x +1008}{12 \cdot x} = \dfrac{1105}{12 \cdot x+ 12}[/tex]
(x + 1008)×(12·x + 12) = 1105× 12·x
12·x² -1152·x + 12096 = 0
x² -96·x + 1008 = 0
(x - 84)×(x - 12) = 0
Therefore, x = 12 or 84,
The number of boys are 12 or 84
For there to bee 84 boys, their average age would be one year each
Given that they are boys not babies, then there are only 12 boys.
Which equation is perpendicular to y= 3/4x + 4 and passes through the point (0,2)
A. Y= 3/4x + 2
B. Y= -3/4x + 2
C. Y= -4/3x + 2
D. Y= 4/3x + 2
Answers
In a small town, there are 4 times as many left-handed males as there are left-handed females, and there are 3 times as many right-handed females as there are right-handed males. There are a total of 204 males and 348 females in the town. Let x represent the number of left-handed females, and let y represent the number of right-handed males. Write a system of equations to represent the situation. What is the value of x, the number of left-handed females? A. 6 B.24 C. 96 D. 108
Answers
Answer: 24
Expenation:
Left handed females = x
right handed females = 348 - x
right handed males = y
left handed males = 204 - y
204 - y = 4x
348 - x = 3y
4x + y = 204 . . . . . . . (1)
x + 3y = 348 . . . . . . . (2)
From (2), x = 348 - 3y
subsituting for x in (1), we have
4(348 - 3y) + y = 204
1392 - 12y + y = 204
12y - y = 1392 - 204
11y = 1188
y = 1188/11 = 108
x = 348 - 3y = 348 - 3(108) = 348 - 324 = 24
Answer:
24
Step-by-step explanation:
i got it right
A circle has a radius of 10. An arc in this circle has a central angle of 72 degrees. What is the length of the arc? btw, the arc is aligned with the radius
Answers
Answer:
4 Pi
Explanation:
72/360 = 1/5 so the length of the arc is (1/5) the circumference or
(1/5) ( 2 Pi * 10) => C = 2 Pi r
(20/5) Pi =
4 Pi
If the blue radius below is perpendicular to the green chord and the segment
AB is 8.5 units long, what is the length of the chord?
A
A. 8.5 units
8.5
B
O B. 17 units
O C. 34 units
O D. 4.25 units
Answers
Answer:
O B. 17 units
Step-by-step explanation:
The chord is AC and the radius of the circle is perpendicular to the chord at B. AB = 8.5 units. According to the perpendicular bisector theorem, if the radius of a circle is perpendicular to a chord then the radius bisects the chord. This means that chord AC is bisected by the radius of the circle at point B. The length of the circle is calculated using:
[tex]AB=\frac{AC}{2}\\ AC=2*AB\\cross multiplying:\\AC = 2*8.5\ units\\AC = 17 \ units[/tex]
The length of the chord is 17 units.
Answer:
The answer is 17 units :D
Step-by-step explanation:
Please answer it now in two minutes
Answers
Answer:
y = 4
Step-by-step explanation:
Using the tangent ratio in the right triangle and the exact value
tan30° = [tex]\frac{1}{\sqrt{3} }[/tex] , then
tan30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{y}{4\sqrt{3} }[/tex] = [tex]\frac{1}{\sqrt{3} }[/tex] ( cross- multiply )
y × [tex]\sqrt{3}[/tex] = 4[tex]\sqrt{3}[/tex] ( divide both sides by [tex]\sqrt{3}[/tex] )
y = 4
Answer:
y=4
Step-by-step explanation:
If we have a triangle with angles A, B, and C. The law of sines says that the proportion between the sin of angle A and its opposite side is equal to the proportion between the sin of angle B and its opposite side and it is equal to the proportion between the sin of angle C and its opposite side.
So, by the law of sines we can say that:
[tex]\frac{sen(60)}{4\sqrt{3} } =\frac{sen(30)}{y}[/tex]
Solving for y, we get:
[tex]sin(60)*y=4\sqrt{3}*sin(30)\\\frac{\sqrt{3} }{2}y=4\sqrt{3}*0.5\\ \frac{1}{2} y=4*0.5\\y = 4[/tex]
Find the measure of c. A. 136 B. 144 C. 123 D. 149
Answers
Answer:
Option (D)
Step-by-step explanation:
Given quadrilateral in the circle is a cyclic quadrilateral.
By using the property of cyclic quadrilateral,
"Sum of each pair of opposite angles is 180°".
In the given cyclic quadrilateral,
d + 57° = 180°
d = 180 - 57
d = 123°
Similarly, c + 31° = 180°
c = 180° - 31°
c = 149°
Therefore, Option (D) will be the answer.
-3 raised to 2 + -3 raised to 2 =
Answers
Answer:
Step-by-step explanation:
(-3)² + (-3)² = (-3)*(-3) + (-3)*(-3)
= 9 + 9
= 18
Answer:
18
Step-by-step explanation:
The height of a right rectangular prism is 3 units greater than the length of the base. The edge length of the square base is x units.
Which expression represents the volume of the prism, in cubic units?
x3 + 9
x3 + 3x2
x3 + 3x + 3
x3 + 6x2 + 9x
Answers
Answer:
B. x^3 + 3x^2
Step-by-step explanation:
Volume of a rectangular prism=width * length * height
V=w*l*h
h=3 greater than the length of the base
h=x+3
Length of the base=x
Width=x
Substituting values into the formula
V=w*l*h
=(x)*(x)*(x+3)
Multiplying
=(x^2)(x+3)
=x^3 + 3x^2
Option B is the correct answer
The expression [tex]x^3 + 3x^2[/tex] represents the volume of the prism, in cubic units.
We have given that the,
The height of a right rectangular prism is 3 units greater than the length of the base.
The edge length of the square base is x units.
What is the volume of rectangular prism?[tex]Volume of a rectangular prism=width * length * height[/tex]
[tex]V=w*l*h[/tex] ......(1)
We have given that the
h=3 greater than the length of the base
and length of the base is x
Hence, [tex]h=x+3[/tex]
[tex]Length of the base=x[/tex]
[tex]Width=x[/tex]
Substituting values l h and w into the formula (1) we get,
[tex]V=w*l*h[/tex]
[tex]=(x)*(x)*(x+3)[/tex]
[tex]=(x^2)(x+3)[/tex]
[tex]=x^3 + 3x^2[/tex]
Therefore the expression
[tex]x^3 + 3x^2[/tex]
represents the volume of the prism, in cubic units.
To learn more about the volume of the prism visit:
https://brainly.com/question/23963432
(1/16)^(x+3) = (1/4)^(x+1)
Answers
Answer:
x=-5
Step-by-step explanation:
The answer is x = -5. The explanation and answer is in the image below.