The product of the two factors (t - sa) (9t + 6sa) is 9t² - 3tsa - 6s²a²
What is the product of two factors?The product of two factors of an expression results in a quadratic or polynomial expression depending on the degree to which their power is being raised.
From the information given, we have:
= (t - sa) (9t +6sa)
= 9t² + 6tsa - 9tsa - 6(sa)²
= 9t² - 3tsa - 6s²a²
Therefore, we can conclude that the product of the two factors (t - sa) (9t + 6sa) is 9t² - 3tsa - 6s²a².
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Select the correct answer from each drop-down menu.
Consider the function f(x) = 2x + 6 and the graph of the function g shown below.
у
The graph of g is the graph of f translated
units
Answer: The graph of g is the graph of f translated 10 units down, and [tex]g(x)=2x-10[/tex]
Step-by-step explanation:
The y-intercept of f(x) is 6, and the y-intercept of g(x) is -4, so the graph of g is the graph of f translated 10 units down.
So, the equation of g(x) is [tex]g(x)=2x-10[/tex]
Answer:
5 units right and g(x)= f(x - 5).
A moving company’s moving rates can be represented by the function f(x) = 3x + 400, where x is the number of miles for the move.
Another moving company’s rates can be represented by the function g(x) = 5x + 200.
Which function represents the difference between the moving companies' rates, h(x) = f(x) – g(x)?
The difference betweeh the two companies' moving rates is:
(f - g)(x) = -2x + 200
Which function represents the difference between the moving companies' rates?Here we have two functions:
f(x) = 3x + 400
g(x) = 5x + 200
These functions represent the moving rates for two different companies.
If we want to find the difference between the moving rates, we just need to take the difference between the functions:
(f - g)(x) = f(x) - g(x) = (3x + 400) - (5x + 200) = -2x + 200
So the difference betweeh the two companies' moving rates is:
(f - g)(x) = -2x + 200
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Given that GJ = 70.2, JH = 26.5, and GK = 70.2, find the measure of JK.
The measure of the segment JK is 0 unit
Measurement of line segmentA line is the shortest distance between two points
Given the following parameters
GJ = 70.2
JH = 26.5
GK = 70.2
Determine the measure of JK
JK = JG + GK
Since JG = -GJ then;
JK = -GJ + GK
JK = -70.2 + 70.2
JK = 0
Hence the measure of the segment JK is 0 unit
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solve y
Solve for yyy.
-3 = 7\left(y-\dfrac97\right)−3=7(y−
7
9
)minus, 3, equals, 7, left parenthesis, y, minus, start fraction, 9, divided by, 7, end fraction, right parenthesis
The value of y in [tex]-3 = 7\left(y-\dfrac97\right)[/tex] is 6/7
How to solve for y?The equation is given as:
[tex]-3 = 7\left(y-\dfrac97\right)[/tex]
Open the bracket
-3 = 7y - 9
Add 9 to both sides of the equation
7y = 6
Divide both sides by 7
y= 6/7
Hence, the value of y in [tex]-3 = 7\left(y-\dfrac97\right)[/tex] is 6/7
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Complete question
Solve for y
[tex]-3 = 7\left(y-\dfrac97\right)[/tex]
The point-slope form of the equation of a line that passes through points (8, 4) and (0, 2) is y − 4 = (x − 8). What
is the slope-intercept form of the equation for this line?
Oy=2x-12
O y = -x-4
Oy=x+2
O y = ¹x+6
[tex]\large\boxed{y=\frac{1}{4}x+2}[/tex]
The point-slope form is actually [tex]y-4=\frac{1}{4}(x-8)[/tex]; I assume there was a copy/paste issue.
Also, the correct answer is not in the answer choices given; again assuming a copy/paste issue.
Start by distributing the [tex]\frac{1}{4}[/tex] to [tex]x[/tex] and [tex]-8[/tex].
[tex]y-4=\dfrac{1}{4}x-2[/tex]
Add [tex]4[/tex] to both sides of the equation.
[tex]\begin{aligned}y-4+4&=\frac{1}{4}x-2+4\\y&=\frac{1}{4}x+2\end{aligned}[/tex]
there are three consecutive odd integers. Three times the largest is 7 times the smallest. WHat are the integers
Answer:
3, 5, 7
Step-by-step explanation:
We can assign the first number as x. Since all the numbers are odd the next number will be x+2, and the last will be x+4.
3*(x+4) = 7(x)
3x+12 = 7x
12 = 4x
x = 3
x+2 = 5
x+4 = 7
A piecewise function is defined as shown.
StartLayout enlarged left-brace 1st Row 1st column negative x , 2nd column x less-than-or-equal-to negative 1 2nd Row 1st column 1, 2nd column x = 0 3rd Row 1st column x + 1, 2nd column x greater-than-or-equal-to 1 EndLayout
The value of f(x) when x = 3 is 4
How to evaluate the piecewise function?The definition of the piecewise function is given as:
[tex]f(x) = \left[\begin{array}{cc}-x& x \le -1\\1&x = 0\\x + 1&x \ge 1\end{array}\right[/tex]
When x = 3, the domain is [tex]x \ge 1[/tex]
At [tex]x \ge 1[/tex], the function definition is
f(x) = x + 1
So, we have:
f(3) = 3 + 1
Evaluate
f(3) = 4
Hence, the value of f(x) when x = 3 is 4
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Complete question
A piecewise function is defined as shown.
[tex]f(x) = \left[\begin{array}{cc}-x& x \le -1\\1&x = 0\\x + 1&x \ge 1\end{array}\right[/tex]
What is the value of f(x) when x=3?
Answer:
4
Step-by-step explanation:
Which expression is equivalent to ?
xy^2/9?
Answer: [tex]x\sqrt[9]{y^{2} }[/tex]
Step-by-step explanation: For all expressions in the form [tex]x^{\frac{a}{b}[/tex] , the expression is equal to [tex]\sqrt[b]{x^a}[/tex]. The denominator in a fractional exponent is the type of root it is. For example, [tex]x^\frac{1}{3}[/tex] is going to be the cubed root, or the
3rd root of x ([tex]\sqrt[3]{x}[/tex]). The numerator is what power x is raised to. For example, [tex]x^\frac{3}{2}[/tex] is going to be [tex]\sqrt{x^3}[/tex].
In fractional exponents, the square root only takes the form of the variable it is assigned to. What does that mean? Well, for [tex]xy^\frac{2}{9}[/tex], the square root only applies to the y. The x is considered a constant and can be moved out. Thus, we get [tex]x\sqrt[9]{y^2}[/tex].
Can someone help me solve this alpine with an explanation thank u (will mark as brainlist if correct&explanation)
Answer:
(d). [tex]\frac{12}{5}[/tex]
Step-by-step explanation:
Answer: [tex]\frac{12}{5}[/tex]
Step-by-step explanation:
Sorry this took so long.. i needed to use paint
help me please i need help asap
Answer:
Step-by-step explanation:
Please help me with both questions whoever does the best I will mark brainlest.
A function assigns the values. The force that will be required to move the rock is 48 lbs.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
A.) The inverse of the function f(x)=1/x is,
f(x) = 1/x
y = 1/x
x = 1/y
g(x)=1/x
Hence, The inverse of the function f(x)=1/x is g(x)=1/x.
B.) The force that will be required to move the rock using the momentum,
9ft × 80lbs = 15 ft × F
F = 48 lbs
Hence, The force that will be required to move the rock is 48 lbs.
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Choose the graph that matches the following system of equations: (6 points)
4x + y = −1
3x + 2y = 8
picture of coordinate plane with line y equals negative 4x minus 1 and line y equals minus 3 over 2 times x plus 4. They intersect at negative 2 , 7
picture of coordinate plane with line y equals 4x minus 1 and line y equals negative 3x plus 8. They intersect at 1.29, 4.14
picture of coordinate plane with line y equals negative 4x minus 1 and line y equals 3 halves x plus 8. They intersect at negative 1.64, 5.55
picture of coordinate plane with line y equals 4x minus 1 and line y equals negative 3x plus 4. They intersect at 0.71, 1.86
The graph that matches the following system of equation is; the picture of a coordinate plane with line y equals negative 4x minus 1 and line y equals minus 3 over 2 times x plus 4. They intersect at negative 2, 7.
What is the graph of a function?The graph of a function y = f(x) shows the position of the x-intercepts and y-intercepts from the graph from which the slope can be drawn.
The system of linear equations can be rewritten in slope-intercept form as follows:
y = -4x - 1
y = -3/2x + 4
From the graph, the two equations intercept at point (-2,7).
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Given:
\overleftrightarrow{BD}
BD
B, D, with, \overleftrightarrow, on top is the perpendicular bisector of segment \overline{AC}
AC
start overline, A, C, end overline.
\overline{BD}
BD
start overline, B, D, end overline is 333 units long.
\overline{AC}
AC
start overline, A, C, end overline is 888 units long.
Naomi was asked to show that point DDD is equidistant from points AAA and CCC.
A line bisector is a straight line that divides a given line into two equal parts. Thus the following steps are required by Naomi to show that point D is equidistant from points A and C.
BD ⊥ AC (given)
BD = 3 units, and AC = 8 units.
BD is the perpendicular bisector of segment AC (given)
Thus,
<BDA ≅ <BDC (right angles formed by a perpendicular bisector)
AD ≅ DC (equal parts of a bisected line)
AD ≅ DC = 4 units
Thus joining points B to A, and B to C,
BA ≅ BC.
So that applying Pythagoras theorem to ΔABD, we have:
[tex]/hyp/^{2}[/tex] = [tex]Adj 1^{2}[/tex] + [tex]Adj 2^{2}[/tex]
[tex]AB^{2}[/tex] = [tex]3^{2}[/tex] + [tex]4^{2}[/tex]
= [tex]\sqrt{25}[/tex]
AB = 5 units
So that,
BA ≅ BC = 5 units
Therefore, it can be concluded that point D is equidistant from points A and C.
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TConsider △RST and △RYX.
Triangle R S T is shown. Line X Y is drawn parallel to side S T within triangle R S T to form triangle R Y X.
If the triangles are similar, which must be true?
StartFraction R Y Over Y S EndFraction = StartFraction R X Over X T EndFraction = StartFraction X Y Over T S EndFraction
StartFraction R Y Over R S EndFraction = StartFraction R X Over R T EndFraction = StartFraction X Y Over T S EndFraction
StartFraction R Y Over R S EndFraction = StartFraction R X Over R T EndFraction = StartFraction R S Over R Y EndFraction
StartFraction R Y Over R X EndFraction = StartFraction R S Over R T EndFraction = StartFraction X Y Over T S EndFraction
For similar triangles ΔRST and ΔRYX proportion RY/RS = RX/RT = XY/TS is true.
Given that, for ΔRST, line XY is drawn parallel to side ST within ΔRST to form ΔRYX.
Considering ΔRST and ΔRYX.
What is the relation between sides of similar triangles?The corresponding sides of similar triangles are proportional.
We get ∠RXY=∠RST (Corresponding angles, since XY║ST)
∠RYX=∠RTS (Corresponding angles, since XY║ST)
From AA similarity criteria ΔRST is similar to ΔRYX.
Now, RY/RS = RX/RT = XY/TS.
Therefore, for similar triangles ΔRST and ΔRYX proportion RY/RS = RX/RT = XY/TS is true.
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YALL I NEED HELP!!! WILL MAKE BRAINLIEST!!!
So I paid someone $25.95 ok but I didn’t realize I owed them $28.21 till now…how much do I owe them?!!???
Answer:
$2.26
Step-by-step explanation:
In total, you owed them 28.21, and so you can subtract the amount you paid from the total:
28.21 - 25.95 = 2.26
So, you owe them $2.26 now.
hope this helps! have a lovely day :)
The solution is (1,-5)
Answer:
Falde
Step-by-step explanation:
the solution is at the point of intersection of the 2 lines
the lines intersect at (- 5, 1 ) , then
the solution is (- 5, 1 )
A researcher wishes to estimate the percentage of adults who support abolishing the penny what size sample should be obtained if he wishes the estimate to be within three percentage points with a 95% confidence if he:
A: uses a previous estimate of 26%?
B: he does not use any prior estimates?
Using the z-distribution, the sample sizes required are given as follows:
a) 822.
b) 1068.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
Then, the margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.We have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
Item a:
The estimate is of [tex]\pi = 0.26[/tex], hence we solve for n when M = 0.03.
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.96\sqrt{\frac{0.26(0.74)}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.96\sqrt{0.26(0.74)}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.26(0.74)}}{0.03}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.26(0.74)}}{0.03}\right)^2[/tex]
n = 821.2
Rounding up, a sample of 822 is needed.
Item b:
No prior estimate, hence [tex]\pi = 0.5[/tex], which is when the largest sample size is needed.
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.96\sqrt{0.5(0.5)}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.5(0.5)}}{0.03}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.5(0.5)}}{0.03}\right)^2[/tex]
n = 1067.11
Rounding up, a sample of 1068 is needed.
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solving equations with fractions- how do i solve this
Answer:
[tex]x=\frac{11}{18} =0.611[/tex]
Step-by-step explanation:
1) Subtract [tex]\frac{2}{9}[/tex] from both sides.
[tex]x=\frac{5}{6} - \frac{2}{9}[/tex]
2) Simplify [tex]\frac{5}{6} - \frac{2}{9}[/tex] to [tex]\frac{11}{18}[/tex].
[tex]x=\frac{11}{18}[/tex]
Decimal Form: 0.611111
Air America has a policy of booking as many as 15 persons on an airplane that can seat only 14. (Past studies have revealed that only 85% of the booked passengers actually arrive for the flight.) Find the probability that if Air America books 15 persons, there will be enough seats will be available.
The probability that if Air America books 15 persons, there will be enough seats available is 0.913.
How to determine the probability?First of all, we would determine the probability that if Air America books 15 persons, there won't be enough seats available by using binomial distribution:
P(x = 15) = 0.85¹⁵
P(x = 15) = 0.087.
Based on logic, the probability that if Air America books 15 persons, there will be enough seats available is given by:
P = 1 - 0.087
P = 0.913.
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Which of the following is the graph of the inequality y < 2x + 3?
Answer: A
Step-by-step explanation:
The line has a positive slope.
Eliminate B and D.Also, the line should be shaded below.
Eliminate C.This leaves us with D.
What is the solution of log, 729= 32
Answer:
a
Step-by-step
explanation:
A train travels 75 miles in 46 minutes. what is the average speed of the train?
Given the distance travelled and the time elapsed, the average speed of the train is approximately 1.63 miles per minutes.
What is the average speed of the train?Given that;
Distance traveled d = 75milesTime elapsed t = 46 minAverage speed s = ?Average speed = distance traveled / elapsed time
Average speed = 75miles / 46min
Average speed = 1.63 miles per minutes
Given the distance travelled and the time elapsed, the average speed of the train is approximately 1.63 miles per minutes.
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Find the least common multiple (LCM) of 9 and 6.
Answer:
Step-by-step explanation:
find prime factorization of 6 and 9
6 = 2 x 3
9 = 3 x 3
Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the LCM:
LCM = 2 × 3 × 3
LCM = 18
Step-by-step explanation:
Make a line like that and add the numbers 6 and 9 ( order doesn't matter).
then look for a number that can divide both of them without a remainder first which is 3.
Divide 6 and write the Answer down under it
Divide name and write the answer under it.
look for another number that can divide those answers you got. but they aren't no numbers that can divide them without remainders anymore, so you divide 2 by 2 and write down 1 and just write down the 3 back .
then divide 3 by 3 and write down the answer which is one beneath it.
(you should keep dividing until you get everything to 1)
Then multiply together all the numbers used in dividing and that is your L.C.M.
Hope this helps.
Good luck ✅.
Alex reads about 200 words per minute. The book he needs to read is 320 pages long and has about 275 words per page. How many hours must he read if he has 7 days to read the entire book?
[ Please don't only do the answer, I have more questions like this and giving the steps would really help a lot !! Thank you! ]
Answer:
7.3333 hours
Step-by-step explanation:
if im wrong oh well lol 275x320=88000 divided by 200 =440 divided by 60=7.3333
please answer with steps
Answer:
The answer shall be xy[(167/30)x-(65/14)y+(3/4)]
Step-by-step explanation:
the step is given in image given...
Which of the following statements must be true about the diagram? Check all that apply.
Answer:
x + y = w
w > x
w > y
Step-by-step explanation:
x and y are interior angles of a triangle.
w is the exterior angle ( opposite to angles x and y ) of a triangle.
There is a formula that exterior angle of a triangle is equal to sum of two interior angles of a triangle.
So,
x + y = w
If x + y = w,
Then,
w > x
w > y
-
Here's a graph of a linear function. Write the
equation that describes that function.
Express it in slope-intercept form.
Answer:
y = [tex]\frac{1}{2}[/tex] x + 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 6, 0) and (x₂, y₂ ) = (0, 3) ← 2 points on the line
m = [tex]\frac{3-0}{0-(-6)}[/tex] = [tex]\frac{3}{0+6}[/tex] = [tex]\frac{3}{6}[/tex] = [tex]\frac{1}{2}[/tex]
the line crosses the y- axis at (0, 3 ) ⇒ c = 3
y = [tex]\frac{1}{2}[/tex] x + 3 ← equation of line
Can someone help me please?
Triangle not drawn to scale
Given the area of triangle ABC =
7.52 m 2. Find a to the nearest meter when the measure of
angle B = 40 degrees and c = 6m.
Answer: 4
Step-by-step explanation:
[tex]A=7.52=\frac{1}{2}ac \sin B\\\\7.52=\frac{1}{2}(a)(6)\sin 40^{\circ}\\\\a=\frac{7.52}{\frac{1}{2}(6)(\sin 40^{\circ})}\\\\a \approx 4[/tex]
can someone pls help me
Answer:
C
Step-by-step explanation:
9x² - 4[tex]y^{6}[/tex]
can be factored as a difference of squares , that is
(U + V)(U - V)
9x² - 4[tex]y^{6}[/tex] = (3x)² - (2y³)²
with U = 2x and V = 2y³
Answer:
U= 3x and V=2y^3
Step-by-step explanation:
9x^2= (3x)^2
4y^6 = (2y^3)^2
=(3x)^2 - (2y^3)^2
Apply this rule below
x^2 - y^2 = (x + 7) - (x - y)
(3x)^2 - (2y^3)^2 = (3x + 2y^3) + (3x - 2y^3)
= (3x + 2y^3) (3x - 2y^3)
Which angle is an exterior angle?
i°
k°
g°
a°
Among angles i , k , g , a ,i and k are the exterior angles.
Given i°, k° ,g° ,a° are some angles and we have to find which angle is exterior angle.
The angle between a side of a polygon and an extended side is known as exterior angle of polygon. The sum of exterior angles of a polygon is equal to 180 degrees. We have to identify exterior angles among i° ,k° ,g° ,a°.
The angle i is an exterior angle because it is formed on a line opposite to angle d.
Angle k is also an exterior angle because it is also formed on opposite side of an angle.
Angle g is not an exterior angle.
Angle a is not an exterior angle.
Hence i and k are exterior angles among i, g, k, a.
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