Factor out common terms in the first two terms, then in the last two terms
4x^2(5x - 3) + 3(5x - 3)
Factor out the common term 5x - 3
= (5x - 3)(4x^2 + 3)
Help Please!!!!!!
The equation of a circle is x² + y² - 4x + 2y - 31 = 0. What is the center and the radius of the circle? Show your work.
Answer:
centre = (2, - 1), radius = 6
Step-by-step explanation:
Rearrange the equation by placing the x and y terms together and adding 31 to both sides
Given
x² + y² - 4x + 2y - 31 = 0, then
x² - 4x + y² + 2y = 31
Use the method of completing the square
add ( half the coefficient of the x/y term )² to both sides
x² + 2(- 2)x + 4 + y² + 2(1)y + 1 = 31 + 4 + 1
(x - 2)² + (y + 1)² = 36
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r the radius
compare to (x - 2)² + (y + 1)² = 36, then
centre = (2, - 1) and r = [tex]\sqrt{36}[/tex] = 6
The center of the circle is (2, - 1) and the radius is 6 units.
What are the types of equations of a circle?The equation for a circle has the generic form x² + y² + 2gx + 2fy + c = 0.
The standard equation of a circle is x² + y² = r².
The polar form of the equation of the circle is (rcosθ)² + (rsinθ)² = p².
Given, The equation of a circle is x² + y² - 4x + 2y - 31 = 0.
We know, In x² + y² + 2gx + 2fy + c = 0, The center of the circle is,
(- g, - f) and radius is [tex]\sqrt{g^2 + f^2 - c[/tex].
Therefore, 2gx = - 4x and 2fy = 2y.
2g = - 4 and 2f = 2.
g = - 2 and f = 1.
- g = 2 and - f = - 1.
So, The center is (2, - 1).
And the radius is, [tex]\sqrt{2^2 + -1^2 + 31[/tex].
= [tex]\sqrt{4 + 1 + 31[/tex].
= [tex]\sqrt{36[/tex].
= 6 units.
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the ratio of cars to trucks at an auto dealer is 3/2. if there are 144 cars at the dealership, how many trucks are there?
Answer:
96
Step-by-step explanation:
for every 3 cars there is 2 trucks
If you have 144 cars then we divide 144 by 3 to get 48
That is not the answer though because that would be a 3/1 ratio
We then multiply 48 by 2 to get 96
To find the number of trucks at the dealership, we interpret the ratio 3:2, meaning that for every 3 cars, there are 2 trucks. We figure out that '1' in the ratio is equivalent to 48 vehicles. So, we multiply the trucks component of the ratio (2) by this value to get 96 trucks.
Explanation:To solve this problem, you must interpret the ratio of cars to trucks as 3:2. This means for every 3 cars, there are 2 trucks. We need to use this ratio to find out how many trucks there are if there are 144 cars.
The first step is to figure out what proportion 144 cars represents within the ratio. To find this, we can divide the number of cars by the cars component of the ratio (3) which gives us: 144 ÷ 3 = 48.
Now we know that '1' in our ratio represents 48 vehicles. So to find out how many trucks, we multiply the trucks component of the ratio (2) by this value, which gives us: 48 x 2 = 96 trucks.
Therefore, if there are 144 cars at the dealership, there are 96 trucks.
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Mrs. Benton prepares a 7 cup green bean casserole. She divides the casserole into equal 1/2 cup servings. If she eats one serving each day, how many days of servings are available? A) 10 days B) 14 days c) 18 days D) 24 days
Answer:
B
Step-by-step explanation:
7 serving multiplied by 2 is equal to 14
Answer:
the answer is prob B i am i on usatest prep and it is correct
Step-by-step explanation:
a truck delivers bags of apples and oranges to the grocery store. Each bag has twice as many apples as oranges. Each bag contains 15 pieces of fruit. if the truck delivers 63 bags of fruit, how many apples are in the delivery
Answer: 630 apples in the delivery
Step-by-step explanation: There are 15 pieces of fruit. 15 is the only number by 3 to get a even 5. So their are 5 oranges in each bag and 10 apples(because they are doubled) now there are 10 apples in each bag and 63 bags. You multiply 63x10=630
Therefore 630 is your answer
find the missing angle measure in this figure A.) 103 degrees B.) 93 degrees C.)113 degrees D.) 83 degrees
D. 83 deggrees I think hopeful
Answer: D
Step-by-step explanation:
That angle is smaller than a “right angle”. A “right angle” is 90 degrees. Therefore, the missing angle measure is less than 90 degrees.
Two garden plots are to have the same area. One is square and one is rectangular. The rectangular plot is 2 meters wide and 8 meters long. How large is one side of the square garden plot in meters?
First, let's look at the formulas for the area of square and area of the rectangle.
[tex]A_{square}=a^2[/tex]
[tex]A_{rectangle}=a\cdot b[/tex]
And what this exercise states is that the areas are the same. So:
[tex]A_{square}=A_{rectangle}\Longrightarrow a^2=a\cdot b[/tex]
Now put in the data.
[tex]a^2=2\cdot8[/tex]
Solve for [tex]a[/tex]:
[tex]a=\sqrt{2\cdot8}=\sqrt{16}=\boxed{4}[/tex]
The side of the square garden plot is 4 meters.
Hope this helps.
r3t40
What is the value of log 13? Use a calculator. Round your answer to the nearest tenth
Answer:
log 13 = 1.1139
Step-by-step explanation:
log 13 = 1.1139
Answer:
log 13 = 1.1
Step-by-step explanation:
Given : log 13.
To find : What is the value round your answer to the nearest tenth.
Solution : We have given log 13.
log 13 = 1.113.
Nearest tenth = 1.1
Therefore, log 13 = 1.1
How many feet per minute
Answer:
3.5 feet / per minute
Step-by-step explanation:
3 1/2 feet / minute = 3.5 feet / minute
hope this helps :)
help me please
-4.5+4.4+_____=0
To find the missing value in the equation, we add -4.5 and 4.4 first, then solve for the missing value.
Explanation:To find the missing value, we need to solve the equation. Start by adding -4.5 and 4.4. (-4.5 + 4.4 = -0.1)
Now we have: -0.1 + ___ = 0
To solve for the missing value, subtract -0.1 from both sides of the equation: ____ = 0 + 0.1 = 0.1
The missing value is 0.1.
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Final answer:
The missing value is 0.1.
Explanation:
This expression is a quadratic equation of the form at² + bt + c = 0, where the constants are a = 4.90, b = -14.3, and c = -20.0.
To solve for the missing value, we can rearrange the equation:
-4.5 + 4.4 + ____ = 0
Simplifying the equation, we get:
-4.5 + 4.4 + ____ = 0
-0.1 + ____ = 0
By adding 0.1 to both sides of the equation, we can isolate the missing value:
____ = 0.1
Therefore, the missing value is 0.1.
Remy recorded the favorite sport of students at his school. He surveyed 500 students. How many students chose Baseball?
(Chart)
Football 45%
Baseball 15%
Basketball 20%
Tennis 20%
Answer: 75 students
Step-by-step explanation:
15% of 500= 75
For f(x)=2x+1 and g(x)=x^2 -7 , find (f times g)(x)
Answer:
2x³ + x² - 14x - 7
Step-by-step explanation:
The product of f(x) and g(x) is
(2x + 1)(x² - 7)
Each term in the second factor is multiplied by each term in the first factor
2x(x² - 7) + 1 (x² - 7) ← distribute both parenthesis
= 2x³ - 14x + x² - 7
= 2x³ + x² - 14x - 7 ← in standard form
For the following set of data, what is the value of the lower quartile?
150, 68, 101, 99, 140, 132, 81, 129, 75
A. 78
B. 84.5
C. 75
D. 101
Quartiles are 3 points such that they create four groups in the data. For the following set of data, the value of the lower quartile is 78.
What are quartiles?When we get data which can be compared relatively with each other, for finding quartiles, we arrange them in ascending or descending order.
Quartiles are then selected as 3 points such that they create four groups in the data, each group approximately possessing 25% of the data.
The lower quartile, also called the first quartile has approx 25% in its left partition, and on its right lies approx 75% of the data.Similarly, the second quartile (also called median) is approximately in mid of the data.The third quartile (also called the upper quartile) has approx 75% in its left partition, and on its right lies approx 25% of the data.Left to right is said in the assumption that data were arranged increasingly from left to right.
The given data set has 9 points, therefore, the first quartile will have the average value of the 2nd and the 3rd number when arranged in increasing order. Therefore, the value of the first quartile will be,
First quartile = (75+81)/2 = 78
Hence, For the following set of data, the value of the lower quartile is 78.
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A projectile is shot into the air following the path, h(x) = 3x2 - 12x + 5. At what time, value of x, will it reach a maximum
height?
Answer:
never
Step-by-step explanation:
The given path equation describes a path that starts at h(0) = 5, decreases to h(2) = -7, then increases without bound.
Assuming the projectile stops moving when h(x) = 0, it starts at its maximum height at ...
x = 0
There are some black and white buttons in a container.
7/10 of the buttons are black.
The difference between the number of black and white buttons is 24.
How many buttons are there in the container?
ANSWER
60 buttons.
EXPLANATION
Let the number of buttons in the container be x.
Then the number of buttons that are black are:
[tex] \frac{7}{10} x[/tex]
The number of buttons that are white
[tex] \frac{3}{10} x[/tex]
The difference between the white and the black buttons
[tex] \frac{4x}{10} = 24[/tex]
Solve for x.
[tex]4x = 240[/tex]
[tex]x = \frac{240}{4} [/tex]
[tex]x = 60[/tex]
Hence there are 60 buttons in the container.
Write the equation of the circle in general form.
if anyone can explain this that would be great, if not it's okay, just a little lost on how to do all of this haha
Answer:
[tex](x +3)^2 + (y-4)^2 = 4[/tex]
Step-by-step explanation:
The general equation of a circle is
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
In this equation, 'r' represents the radius of the circle and (h,k) represents the central point of the circle.
Radius of the circle is half of the diameter = d/2
From figure, ther diameter of the circle is calculated using (y2-y1) or (x2-x1)
In this figure,
y2 = 6
y1 = 2
d = (y2 - y1) = 6-2 =4
This can also be verified using the values of x
x2 = -1
x1 = -5
d = (x2 - x1) = (-1 - -5) = (-1 + 5) = 4
Also,
r = d/2 = 4/2
r = 2
h represents the horizental distance and k represents the vertical distance of the center of the circle from the origan (0,0).
Therefore,
h = 0 - 3 = -3 as the center of circle is 3 units left to the origan
k = 0 + 4 = 4 as the center of circle is 4 units above to the origan
Therefore the equation of circle becomes
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
[tex](x-(-3))^2 + (y-(4))^2 = 2^2[/tex]
[tex](x +3)^2 + (y-4)^2 = 4[/tex]
HELP PLZ!!
At what points are the equations equal
Answer:
Step-by-step explanation:
f,d,e
Answer:
F, C, B
Step-by-step explanation:
Just look at where the two graphs intersect and then correspond that point with the color and letter.
Find the volume of the cone.
Either enter an exact answer in terms of π or use 3.14 for π and round your final answer to the nearest hundred
V≈301.59
I think this is the answer.
Hope this helps!
The answer is 96pi units^3
One carton of eggs contains 12 eggs. Make a table to find the number of eggs in 5, 6, 7, and 8 cartons.
Given : One carton of eggs contains 12 eggs.
By unitary method we can find the number of eggs in following cartoons :
1 cartoon = 12 eggs
5 cartoons = 12 × 5 = 60 eggs
6 cartoons = 12 × 6 = 72 eggs
7 cartoons = 12 × 7 = 84 eggs
8 cartoons = 12 × 8 = 96 eggs
Answer:
D
Step-by-step explanation:
Find the greatest common factor of 8a 3 b 2 and 12ab 4.
Answer:
[tex]2^{2} \times a \times b^{2}=4ab^{2}[/tex]
Step-by-step explanation:
Greatest common factor of two or more terms is the largest(greatest) possible term which exactly divides all the given term. For example the greatest common factor of 20 and 30 is 10 as 10 is the largest possible number that can exactly divide 20 and 30 without leaving any remainder. GCF is found as the product of all the common factors
Given terms are:
[tex]8a^{3} b^{2} =2^{3}\times a^{3}\times b^{2}[/tex]
[tex]12ab^{4}=4 \times 3 ab^{4} =2^{2} \times 3 \times a \times b^{4}[/tex]
From the above factors we can see that the common factors are:
[tex]2^{2} , a , b^{2}[/tex]
Therefore, the greatest common factor will be:
[tex]GCF=2^{2} \times a \times b^{2}=4ab^{2}[/tex]
The greatest common factor of 8a³b² and 12ab⁴ is 4ab², found by identifying the smallest powers of the common factors in each term.
To find the greatest common factor (GCF) of the given terms, we need to identify the highest power of each variable that appears in both terms.
The prime factorization of 8 is [tex]\(2^3\)[/tex], and the prime factorization of 12 is [tex]\(2^2 \times 3\)[/tex]. Thus, the greatest common factor of the coefficients is [tex]2^2 = 4.[/tex]
For the variables a and b:
- [tex]\(a^3\)[/tex] appears in the first term.
- a appears in the second term.
- [tex]\(b^2\)[/tex] appears in both terms.
So, the greatest common factor of [tex]\(a^3 b^2\) and \(ab^4\) is \(ab^2\).[/tex]
Therefore, the greatest common factor of [tex]\(8a^3 b^2\) and \(12ab^4\) is \(4ab^2\).[/tex]
The current (I) in an electrical conductor varies inversely as the resistance (R) of the conductor. The current is 6 amperes when the resistance is 722 ohms. What is the current when the resistance is 768 ohms? Round your answer to two decimal places if necessary.
a.
5.6 amps
b.
0.16 amps
c.
6.4 amps
d.
0.18 amps
Hence, the correct answer is:
Option : a
a. 5.6 amps
Step-by-step explanation:It is given that:
The current (I) in an electrical conductor varies inversely as the resistance (R) of the conductor.
This means that:
[tex]I\propto \dfrac{1}{R}[/tex]
Hence, we get the relation as:
[tex]\dfrac{I_1}{I_2}=\dfrac{R_2}{R_1}[/tex]
where [tex]R_1[/tex] is the resistance corresponding to the current [tex]I_1[/tex]
and [tex]R_2[/tex] is the resistance corresponding to the current [tex]I_2[/tex]
We have:
[tex]I_1=6\ ,\ R_1=722\ ,\ R_2=768[/tex]
Hence, we get:
[tex]\dfrac{6}{I_2}=\dfrac{768}{722}\\\\\\i.e.\\\\\\I_2=\dfrac{722\times 6}{768}\\\\\\I_2=5.6406\ amperes[/tex]
Hence, the answer is:
Option : a
If the three angles on one triangle have the same measure as the three angles on another triangle, then the triangles are congruent.
Answer:
Is this a question?
Step-by-step explanation:
You're correct, but this isn't a question...
Consider that X=3/4 and y=1/2 which statement is true about X plus Y
Answer:
1 and 1/4
Step-by-step explanation:
3/4 + 1/2 = 3/4 + 2/4 = 5/4 = 1 1/4
Answer:
[tex]1\frac{1}{4}[/tex]
Step-by-step explanation:
In order to calculate this you just have to add up both of the values that you are given, and to do that, you first have to convert the the values into the same denominator:
[tex]\frac{1}{2} +\frac{3}{4} =\frac{2}{4}+\frac{3}{4} =\frac{2+3}{4} =\frac{5}{4} =1\frac{1}{4}[/tex]
So the value of the addition of both would be: [tex]1\frac{1}{4}[/tex]
Please answer right away and don’t guess
Answer: Third Option
[tex]P (M\ or\ N) = 0.8[/tex]
Step-by-step explanation:
In this case, we have two non-disjoint events.
So the probability of M or N occurring is
[tex]P (M\ or\ N) = P(M) + P(N) - P (M\ and\ N)[/tex]
We know that in this problem
[tex]P(M) = 0.7\\\\P(N) = 0.5[/tex]
[tex]P(M\ and\ N) = 0.4[/tex]
So
[tex]P (M\ or\ N) = 0.7 + 0.5 - 0.4[/tex]
[tex]P (M\ or\ N) = 0.8[/tex]
The answer is the third option
Determine the area of the yellow sector
The area of the yellow sector is 15/8 π in² in pi form.
find sin(C). round to the nearest hundredth if necessary.
Answer:
A) 0.38
Step-by-step explanation:
By SOH CAH TOA, the sine of an angle is its opposite side divided by the hypotenuse.
The opposite of ∠C is 5, and the hypotenuse is 13.
So, sin(C) = 5/13 ≈ 0.38.
For this case we have to define trigonometric relations of rectangular triangles that the sine of an angle is given by the leg opposite the angle on the hypotenuse of the triangle. That is to say:
[tex]Sin (C) = \frac {5} {13}\\Sin (C) = 0.38[/tex]
Answer:
Option A
Which number sentence is NOT true?
A. |-6.7| = 6.7
B. |0| < |-45|
C. |45| > 0
D. |6.7| > |-45|
Answer: D. |6.7| > |-45|
Step-by-step explanation:
When in these | | then any negative number becomes positive. 6.7 is NOT grater than 45.
Twenty students in Class A and 20 students in Class B were asked how many hours they took to prepare for an exam. The data sets represent their answers. Class A: {2, 5, 7, 6, 4, 3, 8, 7, 4, 5, 7, 6, 3, 5, 4, 2, 4, 6, 3, 5} Class B: {3, 7, 6, 4, 3, 2, 4, 5, 6, 7, 2, 2, 2, 3, 4, 5, 2, 2, 5, 6} Which statement is true for the data sets? A. The mean study time of students in Class A is less than students in Class B. B. The mean study time of students in Class B is less than students in Class A. C. The median study time of students in Class B is greater than students in Class A. D. The range of study time of students in Class A is less than students in Class B. E. The mean and median study time of students in Class A and Class B is equal.
Answer:
Option B
Step-by-step explanation:
Given
Two Data sets
Class A :{ 2, 5, 7, 6, 4, 3, 8, 7, 4, 5, 7, 6, 3, 5, 4, 2, 4, 6, 3, 5}
Class B : {3, 7, 6, 4, 3, 2, 4, 5, 6, 7, 2, 2, 2, 3, 4, 5, 2, 2, 5, 6}
In order to check the options we will have to find the mean and median of both data sets.
So for Class A:
Mean= x =(Sum of values)/(Number of values)
=96/20
=4.8
For median the data has to be arranged in ascending order, so
2, 2,3,3,3,4,4,4,4,5,5,5,5,6,6,6,7,7,7,8
Median will be the average of middle two values as the number of items are odd.
Median=(5+5)/2
=10/2
=5
Range = 8-2 = 6
For Class B:
Mean= x =(Sum of values)/(Number of values)
=80/20
=4
For median, arranging the values
2,2,2,2,2,2,3,3,3,4,4,4,5,5,5,6,6,6,7,7
Median=(4+4)/2
=8/2
=4
Range = 7-2 = 5
We get,
Mean of class A > Mean of Class B
Median of Class A > Median of Class B
Range of Class A > Range of Class B
We observe that only option B is correct for the given data sets..
what us the equation of the following line be sure to scroll down first to see all answer options || graph (8,2) (0,0)
Answer:
[tex]y=0.25x[/tex]
The graph in the attached figure
Step-by-step explanation:
we have
[tex](0,0),(8,2)[/tex]
Remember that
If the equation of the line passes through the origin
then
The equation of the line represent a direct variation
so
it can be expressed in the form [tex]y=kx[/tex]
The constant of proportionality k is equal to the slope m
step 1
Find the slope
[tex]m=(2-0)/(8-0)=0.25[/tex]
The equation of the line is equal to
[tex]y=0.25x[/tex]
The graph in the attached figure
a scatter plot containing the point(12,12) has the regression equation^y=1/4x+1. what is the residual e when x equals 12
Answer:
8, substitute 12 into the equation and then subtract it from 12
Step-by-step explanation:
simplify cotø(tanø+cotø)
Answer:
[tex]\large\boxed{\cot\theta(\tan\theta+\cot\theta)=1+\cot^2\theta=\dfrac{1}{\sin^2\theta}=\csc^2\theta}[/tex]
Step-by-step explanation:
[tex]\text{Use}\\\\\text{distributive property:}\ a(b+c)=ab+ac\\\cot\alpha\tan\alpha=1.\\\\======================\\\\\cot\theta(\tan\theta+\cot\theta)=(\cot\theta)(\tan\theta)+(\cot\theta)(\cot\theta)\\\\=1+\cot^2\theta\\\\\text{If you want next transformation, then use:}\\\\\cot\alpha=\dfrac{\cos\alpha}{\sin\alpha}\\\\\sin^2\alpha+\cos^2\alpha=1\\\\=======================[/tex]
[tex]=1+\left(\dfrac{\cos\theta}{\sin\theta}\right)^2=1+\dfrac{\cos^2\theta}{\sin^2\theta}=\dfrac{\sin^2\theta}{\sin^2\theta}+\dfrac{\cos^2\theta}{\sin^2\theta}=\dfrac{\sin^2\theta+\cos^2\theta}{\sin^2\theta}\\\\=\dfrac{1}{\sin^2\theta}\\\\\text{If you want next transformation, then use:}\\\\\csc\alpha=\dfrac{1}{\sin\alpha}\\\\=\left(\dfrac{1}{\sin\theta}\right)^2=(\csc\theta)^2=\csc^2\theta[/tex]