Answer:
A) 32y³ + 24y² - 12y - 9
Step-by-step explanation:
(-8y² + 3)(-4y - 3) = (-8y² x -4y) + (-8y² x -3) + (3 x -4y) + (3 x -3)
= 32y³ + 24y² - 12y - 9
The product of [tex]-8y^2+3[/tex] and [tex]-4y-3[/tex] is:
[tex]32y^3+24y^2-12y-9[/tex]
Step-by-step explanation:We are asked to find the product of the two expressions which are given by:
[tex]-8y^2+3[/tex] and [tex]-4y-3[/tex]
i.e.
we are asked to find the product of a quadratic and a linear polynomial.
We are asked to find the result of:
[tex](-8y^2+3)\cdot (-4y-3)[/tex]
Hence, on using the distributive property we have:
[tex]-8y^2(-4y-3)+3(-4y-3)\\\\=-8y^2\times -4y-8y^2\times (-3)+3\times (-4y)+3\times (-3)\\\\i.e.\\\\=32y^3+24y^2-12y-9[/tex]
The correct answer is: Option: A
Given: AB= 4
AD= 6
What point is in the interior of both circles?
H
A
B
That would be point A. Point A is inside the outer bigger circle AND the smaller inner circle
Hope this helped!
~Just a girl in love with Shawn Mendes
For this case we have that, if we look at the figure, we have two circles. The large circle is of radius AD = 6, while the small circle is of radius AB = 4.
We can see that point A is inside the small circle, since the small circle is inside the large one, so A is inside the two circles.
Answer:
Point A
Twice a certain number is tripled. The resulting number is
Answer:
6x the number.
Step-by-step explanation:
"Twice a certain number" means that you are multiplying that number (x) by 2.
"Tripled" means that the number (x) would be further multiplied by 3.
Simplify: 3 x 2 = 6
The resulting number would be 6x greater than the original number.
~
What are the solutions to the equation (2x - 5)(3x - 1) = 0?
Answer:
The solution of the given equation is (5/2, 1/3)
Step-by-step explanation:
It is given an equation,
(2x - 5)(3x - 1) = 0
To find the solution of given equation
(2x - 5)(3x - 1) = 0 means that,
either (2x - 5) = 0 or (3x - 1) = 0
If 2x - 5 = 0
2x = 5
x = 5/2
or 3x - 1 = 0
3x = 3
x = 1/3
Therefore the solution of the given equation is (5/2, 1/3)
ANSWER
[tex]\: x =2 \frac{1}{2} \: or \: x = \frac{1}{3} [/tex]
EXPLANATION
The equation is given in the factored form as:
[tex](2x - 5)(3x - 1) = 0[/tex]
According to zero product principle
[tex]either \: \: (2x - 5) = 0 \: or \: (3x - 1) = 0[/tex]
This implies that,
[tex]either \: \: 2x = 5 \: or \: 3x = 1[/tex]
We divide the first equation by 2 and the second by 3
[tex]either \: \: x = \frac{5}{2} \: or \: x = \frac{1}{3} [/tex]
The solutions are
[tex]\: x =2 \frac{1}{2} \: or \: x = \frac{1}{3} [/tex]
which similarity postulate or theorem can be used to verify that the two triangles shown below are similar?
Answer:
B
Step-by-step explanation:
You are given two right triangles PQR and XYZ with PQ=12, PR=6, XY=4, XZ=2. Note that
[tex]\dfrac{PQ}{XY}=\dfrac{12}{4}=3\Rightarrow PQ=3XY\\ \\\dfrac{PR}{XZ}=\dfrac{6}{2}=3\Rightarrow PR=3XZ[/tex]
So, in these triangles:
∠P=∠X=90°;PQ=3XY;PR=3XZ.Hence, by SAS theorem these triangles are similar.
SAS Similarity Theorem states that given two triangles are similar if their two sides are in proportion and their angles adjacent to these sides have the same measure.
The graph below shows the line of best fit for data collected on the number of cell phones and cell phone cases sold at a local electronics store on
twelve different days.
Number of Cell Phone Cases Sold
50
*
0 5 10 15 20 25 30 35 40 45
Number of Cell Phones Sold
Which of the following is the equation for the line of best fit?
A. y = 0.8x
B. y = 0.2x
C. y=0.5x
D. y = 0.25x
Answer:
C
Step-by-step explanation:
The equation of a line is given by
and
slope (m) is given by:
Where (x_1,y_1) are the first set of point in the line and (x_2,y_2) is the second set of point
Let's take 2 points arbitrarily. (0,0) & (25,20)
Let's plug it and find the equation:
Now
C is the correct answer.
The correct option is (A)0.8x.
What is a Straight Line? A line is simply an object in geometry that is characterized under zero width object that extends on both sides. A straight line is just a line with no curves. So, a line that extends to both sides till infinity and has no curves is called a straight line.The standard form for linear equations in two variables is Ax+By=C.The equation of a line two points are [tex]y - y_{1} = m(x - x_{1} )[/tex]slope m = [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
the two points are [tex](x_{1} ,y_{1} ) & (x_{2} ,y_{2} )[/tex].
so, lets take two points (0,0) & (25,20)
lets put the value in equation,
m = [tex]\frac{20 -0}{25-0} = 0.8\\now \\ y - y_{1} = m(x - x_{1}) \\\\[/tex]
y - 0 = 0.8 (x-0)
y = 0.8x
Therefore, the correct option is (A)0.8x.
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This figure is a regular 12-sided polygon. The diameter of the circle that circumscribes it
is 16 cm. Find the radius of the polygon.
cm
Type the correct answer then
press Enter
12 sides
Answer:
Answer:
The radius of the polygon is 8.28 cm
Step-by-step explanation:
See the attached document
what is the domain of (g°f)(x)
A.all real numbers except x=-4
B.all real numbers except x=0
C.all real numbers except x=4
D.all real numbers
A pyramid is placed inside a prism as shown. The pyramid has the same base area, B, as the prism but half the height, h,of the prism. Which expression gives the volume of the pyramid
Answer:
[tex]\large\boxed{V_{pyramid}=\dfrac{1}{6}Bh=\dfrac{1}{6}V_{prism}}[/tex]
Step-by-step explanation:
[tex]B-\text{base area}\\h-\text{height of the prism}\\\dfrac{1}{2}h-\text{height of the pyramid}\\\\\text{The formula of a volume of a prism:}\\\\V_{prism}=Bh\\\\\text{The formula of a volume of a pyramid:}\\\\V_{pyramid}=\dfrac{1}{3}Bh\to V_{pyramid}=\dfrac{1}{3}B\left(\dfrac{1}{2}h\right)=\dfrac{1}{6}Bh=\dfrac{1}{6}V_{prism{[/tex]
Answer:
V = 1/6 BH
Step-by-step explanation:
the volume of a pyramid is 1/3 BH , since the pyramid is only half the height of the prism you'll have to multiply 1/3 x 2 = 1/6
Divide 6K2 - 15k-5 by 3k
Answer:
Step-by-step explanation:
6k^2
------- = 2k; and:
3k
-15k
------- = -5
3k
-5 cannot be evenly divided by 3k, so there's a remainder instead.
6k^2 - 15k - 5
-------------------- = 2k -5 with remainder -5.
3k
Answer:
2k
-5
Step-by-step explanation:
Which equation describes the same line as y-5=-2(x+4)
Option A (y=-2x-3) is the answer.
Step-by-step explanation:
First, you need to multiply the -2 by what is in the parentheses, in order to expand the equation. -2*x is -2x, and -2*4 is -8. This leaves you with -2x-8 on the right side of the equation.
Next, you need to isolate y on the left side of the equation. You can do this by subtracting -5 from both sides. Subtracting a negative causes it to become positive, so you are really just adding 5 to both sides.
This makes it so the y is now alone, and the right side has -2x-8+5. We add together the -8 and 5 to leave us with -3.
This makes the answer y=-2x-3.
Answer:The answer is A. You have to solve for Y .
Step-by-step explanation:
Factor the polynomial 3x4 – 2x2 + 15x2 - 10 by grouping.
Which product is the factored form of the polynomial?
(x2 - 5)(3x2 + 2)
O (22 – 2)(3x2 + 5)
(22 + 5)(3x2 – 2)
0 (372 - 5)(2+2)
Answer:
see explanation
Step-by-step explanation:
Given
3[tex]x^{4}[/tex] - 2x² + 15x² - 10
Factor the first/second and third/fourth terms )
= x²(3x² - 2) + 5(3x² - 2) ← factor out (3x² - 2) from each term
= (3x² - 2)(x² + 5)
Answer: (3x² - 2)(x² + 5)
Step-by-step explanation:
A milkshake vendor sells shakes in three different flavors: mango, strawberry, and chocolate. This table gives the number of shakes of each flavor sold during three shifts on one day. Mango Strawberry Chocolate Shift 1 16 13 29 Shift 2 26 19 45 Shift 3 6 11 0 Total sales were $419 in the first shift, $649 in the second shift, and $96 in the third shift. If you form a linear system representing the data in the table and create a matrix from it, the determinant is 578. What is the price of one chocolate shake?
Step-by-step explanation:
you need to add together all the milkshakes sold and then add together the amount of money made and then divide the two numbers. i think this is right. hope i helped. i think your answer should be around 7 dollars for a milkshake.
The price of one chocolate shake is $9 if the milkshake vendor sells shakes in three different flavors: mango, strawberry, and chocolate option (D) is correct.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have:
A milkshake vendor sells shakes in three different flavors: mango, strawberry, and chocolate.
Let x be the price of one mango shake
Let y be the price of one strawberry shake
Let z be the price of one chocolate shake
From the question we can frame three linear equations in three variables:
16x + 13y + 29z = 419
26x + 19y + 45z = 649
6x + 11y + 0z = 96
After solving the above system of equations:
x = $5
y = $6
z = $9
Thus, the price of one chocolate shake is $9 if the milkshake vendor sells shakes in three different flavors: mango, strawberry, and chocolate option (D) is correct.
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What is the greatest common factor of 6 and 8
Answer:
2
Step-by-step explanation:
Factors of |6| factors of 8
, , , , , , , , , 1×8
2×4
1×6
2×3
The greatest common factor is 2.
What is greatest common factor?The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share. For example, 12, 20, and 24 have two common factors: 2 and 4. The largest is 4, so we say that the GCF of 12, 20, and 24 is 4. GCF is often used to find common denominators.
Given numbers:
6 and 8
Now to calculate the greatest common factor we have to
6=2*3
4=2*4
Hence, the only common factor is 2.
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g(x)=x2-16x
b=-16, so =16 = 64
9(x) = (x2 - 16x + 64) - 64
9(x) = (x - 1)2-
Which statement regarding the interior and exterior angles of a triangle
Answer:
An exterior angle is supplementary to the adjacent interior angle.
Step-by-step explanation:
An exterior angle of a triangle and its adjacent interior angle form a linear pair. This means they form a straight line, and a straight line has a measure of 180°. Since they combine for a total of 180°, this means they are supplementary.
Square root of 8649 with long division
Answer:
93 Is the square root
The Empire State Building in New York City is 1250 feet tall. It took 30,000 workers only 1 year and 45 days to build, which is a record for a skyscraper. On a scale model of the building, the height is 25 inches.
What is the scale of the Empire State Building model?
Answer:
Step-by-step explanation:
1250 feet *12 inches per foot : 25 inches
15000 inches : 25 inches
Scale = 600:1 in other words 600 inches of the building represents 1 inch of the model.
If you want the scale to be feet of building per inch of the model, then don't multiply by 12
1250 feet : 25 inches
25 feet of building: 1 inch of the model.
Answer:
The scale is 1:600
Step-by-step explanation:
To calculate the scale you have to divide the two values of height for this case, but in the same units. So 1250 feet is equal to 15000 inches. Dividing 15000 by 25 is equal to 600, that is the scale. 1:600.
What is the slope-intercept form of the equation of a line that passes through (1, –6) with a slope of 5?
Question 7 options:
a)
y = 5x + 1
b)
y = 5x – 11
c)
y = 5x + 11
d)
y = 5x – 6
Answer:
b) y = 5x - 11Step-by-step explanation:
The slope-intercept form of an equation of a line:
y = mx + b
m - slope
b - y-intercept
We have the slope m = 5 and the point (1, -6). Put them to te equation:
-6 = 5(1) + b
-6 = 5 + b subtract 5 from both sides
-11 = b
Finally we have the equation of a line:
y = 5x - 11
5/6 + 1/8 what is it?
Answer:
Step-by-step explanation:
[tex]\frac{5}{6} +\frac{1}{8} = \frac{20}{24} +\frac{3}{24} = \frac{23}{24}[/tex]
Answer:
23/24
Step-by-step explanation:
5/6 = (5×4)/(6×4)=20/24
1/8 = (1×3)/(8×3)=3/24
5/6 + 1/8 = 20/24 + 3/24 =23/24
Which ordered pair represents the y-intercept of the graph of the equation
y = -5x + 6?
O A. (-5,0)
O B. (6.0)
O C. (0,6)
O D. (0,-5)
Your question asks which pair represents the y-intercept in the equation.
Answer: C). (0,6)To find the answer in your question, we are going to need to find the key terms in the question.
Key terms:
y-intercept
y = -5x + 6
With the information above, we can find the answer.
We know that the equation is similar to the equation: y= mx + b
We need to find what the y-intercept is in the equation.
When you look at the equation, y = -5x + 6, you would know that the y intercept would be the last number (6). Therefore, 6 would be our y intercept.
But, we need to get the number 6 in the right ordered pair.
An ordered pair is represented as (x,y).
So, we would plug in the 6 in the y spot, since it's the y-intercept. We would plug in 0 to x, since we're only focusing on the y-axis, any number on this would not allow the ordered pair to be on the y-axis.
This means that your ordered pair should be (0,6).
C). (0,6) should be your FINAL answer
I hope this helps!Best regards, MasterInvestorThe y-intercept of the equation y = -5x + 6, is represented by the ordered pair (0,6). This is established by substituting x=0 in the equation, which results in y = 6. Hence, the line intersects the y-axis at this point on a graph.
Explanation:In the equation y = -5x + 6, the y-intercept is the value of y when x equals zero. This can be determined by substituting x=0 into the equation. So, let's do this:
Substitute x = 0 into the equation, we get: y = -5*(0) + 6, which simplifies to y = 6. Therefore, the y-intercept is 6, and in an ordered pair it is represented as (0,6).
So, the correct answer is option C: (0,6). This is the point where the line crosses the y-axis on a graph.
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Determine the equation of the inverse of y= ex+3.4
The inverse function is: [tex]\[ y = \ln(x + 4) - 3 \][/tex]
To find the inverse of the function [tex]\( y = e^{x+3} - 4 \)[/tex], we'll first swap the roles of x and y and then solve for y.
1. Start with the original function:
[tex]\[ y = e^{x+3} - 4 \][/tex]
2. Swap x and y:
[tex]\[ x = e^{y+3} - 4 \][/tex]
3. Solve for y:
[tex]\[ x + 4 = e^{y+3} \] \[ e^{y+3} = x + 4 \][/tex]
4. Take the natural logarithm (ln) of both sides to isolate y:
[tex]\[ \ln(e^{y+3}) = \ln(x + 4) \][/tex]
[tex]\[ y + 3 = \ln(x + 4) \][/tex]
5. Subtract 3 from both sides:
[tex]\[ y = \ln(x + 4) - 3 \][/tex]
Complete question: Find the Inverse y=e^(x+3)-4
In a u.s. Poll 8 out of 12 citizens said they were happy with the job Obama is doing.if 126 people were surveyed how many people were happy with Obama?
Answer:
84 people
Step-by-step explanation:
create a proportion
8 x
----- = ---------
12 126
solve.. cross multiply
128x8 =1008
1008/12 =84
The number of people happy with the Obama job from the survey of [tex]126[/tex] people is equal to [tex]84[/tex] people.
What is number?
" Number is defined as the count of any given quantity."
According to the question,
Total number of people surveyed [tex]= 126[/tex]
As per U.S. poll,
Out of [tex]12[/tex] citizen number of people happy [tex]= 8[/tex] people
Out of [tex]1[/tex] citizen number of people happy [tex]= \frac{8}{12}[/tex] people
Out of [tex]126[/tex] number of people happy [tex]= \frac{8\times 126}{12}[/tex]
[tex]= 84[/tex] people
Hence, the number of people happy with the Obama job from the survey of [tex]126[/tex] people is equal to [tex]84[/tex] people.
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Write an equation of the line that passes through (-5,0) and is parallel to the line y=-4/5x-1
Answer:
y = -⅘x - 4
Step-by-step explanation:
. So your point is an x-intercept. It happens at times. Alright. Now, we have to know that parallel lines have SIMILAR RATE OF CHANGES [SLOPES], so we keep the -⅘. Moving forward, we simply plug the coordinate into the Slope-Intercept Formula, y = mx + b --> 0 = -⅘[-5] + b. From this, we can see that our y-intercept is [0, -4], so our parallel line is y = -⅘x - 4. Do you understand?
factor 200t+8t^3-80t^2
Answer:
8t(t - 5)^2
Step-by-step explanation:
I would immediately rearrange these terms in descending order by powers of t:
8t^3 - 80t^2 + 200t
Then I'd factor out 8t:
8t(t^2 - 10 t + 25).
Finally, I'd factor the quadratic t^2 - 10 t + 25:
(t - 5)^2
and so 200t+8t^3-80t^2 in factored form is 8t(t - 5)^2.
Answer:
Step-by-step explanation:
It would be better to list the terms in descending order.
8t^3 - 80t^2 + 200t Take out a common factor of t
t(8t^2 - 80t + 200) Now take out 8
8t (t^2 - 10t + 25) Now factor the polynomial
8t(t - 5)(t - 5)
TIMED! Which expression is equivalent to is m∠4?
Answer:
The correct answer is first option m<2 + m<3
Step-by-step explanation:
From the figure we can see a triangle with angles, <1, <2 and <3
By angle sum property we can write,
m<1 + m< 2 + m<3 = 180°
m<1 = 180 - (m<2 + m<3) ----(1)
Also we know that, <1 and <4 are linear pairs
m<1 + m<4 = 180°
m<1 = 180 - m<4 ---(2)
Compare (1) and (2) we get
m<4 = m<2 + m<3
Answer:
You answer would be A.
Step-by-step explanation:
m<2+m<3
In 2006, Chris bought a new boat for $34,500. The boat was worth $24 500 in the year 2009. If Chris knows that the value of the boat depreciated linearly, what was the annual rate of change of the boat's value? Round your answer to the nearest hundredth if necessary
Answer:
depreciation is $3,333.33 per year
Step-by-step explanation:
Initially : date = 2006, worth = $34,500
Finally : date = 2009, worth = $24,500
if we let x = date and y = worth, we end up with two points (coordinates) on the x-y graph
i.e
Initial = Point 1 (2006, 34500)
Final = Point 2 (2009, 24500)
The rate of change is simply the slope, m of the line joining these two points
given by:
m = (34500 - 24500) / (2006-2009)
= 10000 / -3
= -3,333.33
hence the annual rate of depreciation is $3,333.33 per year
Final answer:
The boat's value depreciated by $10,000 over 3 years, resulting in an annual depreciation rate of $3,333.33.
Explanation:
The student's question involves calculating the annual rate of change of the value of a boat from the year it was bought (2006) to the year 2009. To find the rate of change, we need to determine how much the value of the boat depreciated over the given time period and then divide it by the number of years.
The boat depreciated from $34,500 in 2006 to $24,500 in 2009, which is a decrease of $34,500 - $24,500 = $10,000 over the course of 3 years. To find the annual depreciation rate, we divide the total depreciation amount by the number of years: $10,000 ÷ 3 years = $3,333.33 per year. Therefore, the annual rate of depreciation is $3,333.33 per year, rounded to the nearest hundredth if necessary.
Evaluate the expression |2x – 5| for x = –3 and for x = 3.
A. 3, 13
B. 13, 3
C. 11, 1
D. 1, 11
Answer:
C. 11, 1
Step-by-step explanation:
Plug in your given x-values, then take the absolute values [ALWAYS POSITIVE] of each.
The slope of a line is -, and the y-intercept is 5. What is the equation of the line written in general form?
Answer:
y = mx + 5; m < 0
Step-by-step explanation:
The question mentions that the slope of the line is negative and the y-intercept is 5. The general form of the straight line is given by y = mx + c. Since "c" in the equation is the y-intercept, therefore, c = 5. This means that all the straight lines passing from the point (0,5) can be expressed in a general form y = mx + 5. However, the question mentions that the slope is negative and demands the general equation of all the negatively-sloped straight lines passing from (0,5). Therefore, for the condition to be met, m has to be negative. So the correct answer is y = mx + 5, where m is negative.
A driver can stop his car from the red signal at a distance of of 20 m when he drives at 36 kmph
and 41.25 m when he drives at 54 kmph find his reaction time
Answer: 2.0 seconds & 2.75 seconds
Step-by-step explanation:
[tex]d=\dfrac{s\times r}{3.6}\quad where;\\\\\bullet d=\text{reaction distance (in meters)}\\\bullet s=\text{speed (in km/hr)}\\\bullet r=\text{reaction time (in seconds)}\\\bullet 3.6=\text{needed to convert km/hr into meters/second}\\\\\\\large{\text{When d=20m and s=36}}\\\\20=\dfrac{36}{3.6}\times r\\\\20=10r\\\\\large{\boxed{2=r}}\\\\\\\text{When d=41.25m and s=54}\\\\41.25=\dfrac{54}{3.6}\times r\\\\41.25=15r\\\\\large\boxed{2.75=r}[/tex]
Solve for y
Y/m + y/n = p
Answer:
y = mnp/(m + n)
Step-by-step explanation:
I assume that both capital y and small case y are meant to be the same variable. If not, let me know, and I'll solve it again for small case y.
y/m + y/n = p
Factor y out on the left side.
y(1/m + 1/n) = p
y = p/(1/m + 1/n)
Multiply the right side by (mn)/(mn).
y = pmn/[(1/m + 1/n)mn]
y = pmn/(n + m)
y = mnp/(m + n)
Solve for y:
y/m + y/n = p
yn + ym = pmn
y = pmn / n + m
Hope this helps :)
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