The answer is: [tex]\( 28x^2 - 23x - 15 \)[/tex]
To multiply the expression (7x+3)(4x-5) we apply the distributive property, also known as the FOIL method for binomials.
This involves multiplying each term in the first binomial by each term in the second binomial and then combining like terms.
Here's the step-by-step process:
1. Multiply the first terms: [tex]\( (7x) \cdot (4x) = 28x^2 \)[/tex]
2. Multiply the outer terms: [tex]\( (7x) \cdot (-5) = -35x \)[/tex]
3. Multiply the inner terms: [tex]\( (3) \cdot (4x) = 12x \)[/tex]
4. Multiply the last terms: [tex]\( (3) \cdot (-5) = -15 \)[/tex]
Now, combine the like terms:
[tex]\( 28x^2 - 35x + 12x - 15 \)[/tex]
Therefore, the correct final expanded form of the expression is:
[tex]\( 28x^2 - 23x - 15 \)[/tex]
I HATE MATH (and im lazy)
Oliver borrowed $215 from his friend John. He used this money to advertise his tutoring services. Oliver earned 8 times the amount he borrowed in his first month of tutoring. Approximately how much did Oliver earn in his first month of tutoring?
Answer:
then f the teacher
Step-by-step explanation:
Solve log base(x − 1) 16 = 4.
Answer:
x = 3
Step-by-step explanation:
Given:[tex]\log _{x-1}\left(16\right)=4[/tex]
We have to solve for x.
Consider the given expression [tex]\log _{x-1}\left(16\right)=4[/tex]
[tex]\mathrm{Apply\:log\:rule}:\quad \log _a\left(b\right)=\frac{\ln \left(b\right)}{\ln \left(a\right)}[/tex]
[tex]\log _{x-1}\left(16\right)=\frac{\ln \left(16\right)}{\ln \left(x-1\right)}[/tex]
Thus, the expression becomes,
[tex]\frac{\ln \left(16\right)}{\ln \left(x-1\right)}=4[/tex]
Multiply both side by [tex]\ln \left(x-1\right)[/tex]
[tex]\frac{\ln \left(16\right)}{\ln \left(x-1\right)}\ln \left(x-1\right)=4\ln \left(x-1\right)[/tex]
Simplify, we get,
[tex]\ln \left(16\right)=4\ln \left(x-1\right)[/tex]
Divide both side by 4, we have,
[tex]\frac{4\ln \left(x-1\right)}{4}=\frac{\ln \left(16\right)}{4}[/tex]
[tex]\frac{\ln \left(16\right)}{4}:\quad \ln \left(2\right)[/tex]
Thus, [tex]\ln \left(x-1\right)=\ln(2)[/tex]
[tex]\mathrm{When\:the\:logs\:have\:the\:same\:base:\:\:}\log _b\left(f\left(x\right)\right)=\log _b\left(g\left(x\right)\right)\quad \Rightarrow \quad f\left(x\right)=g\left(x\right)[/tex]
thus, x - 1 = 2
simplify for x, we have,
x = 3
At the beginning of April, Owl Corporation has a balance of $12,000 in the Retained Earnings account. During the month of April, Owl had the following external transactions.
1. Issue common stock for cash, $8,000.
2. Provide services to customers on account, $6,100.
3. Provide services to customers in exchange for cash, $2,400.
4. Purchase equipment and pay cash, $5,600.
5. Pay rent for April, $1,000.
6. Pay workers' salaries for April, $2,500.
7. Pay dividends to stockholders, $1,100.
Using the external transactions above, compute the balance of Retained Earnings at April 30 ...?
In the formula A=\pi r^{2}, if the radius is 6 centimeters, what is the correct unit for the area of the circle?
A)\pi cm
B)cm^2
C)cm
D)cm^3
Please solve the eqution
Cos4x + cos2x - 2 =0
cos4x = cos2x
We know that:
cos2x = 1-2cos^2 x
==> cos4x = 1-2cos^2 (2x)
Now substitute:
==> 1-2cos^2 (2x) = cos2x
==> 2cos^2 (2x) + cos2x - 1 = 0
Now factor:
==> (2cos2x -1)(cos2x + 1) = 0
==> 2cos2x -1 = 0 ==> cos2x =1/2 ==> 2x= pi/3
==> x1= pi/6 , 7pi/6
==> x1= pi/6 + 2npi
==> x2= 7pi/6 + 2npi
==> cos2x = -1 ==> 2x= pi ==> x3 = pi/2 + 2npi.
==> x= { pi/6+2npi, 7pi/6+2npi, pi/2+2npi}
The solutions to the equation cos(4x) + cos(2x) - 2 = 0 are x = nπ and x = (2n + 1)π/2, where n is an integer.
Here, we have to solve the equation cos(4x) + cos(2x) - 2 = 0, we can use trigonometric identities to simplify it.
We know the following trigonometric identities:
[tex]cos(2x) = 2cos^2(x) - 1\\cos(4x) = 2cos^2(2x) - 1[/tex]
Now, let's rewrite the equation using these identities:
[tex]2cos^2(2x) - 1 + 2cos^2(x) - 1 - 2 = 0[/tex]
Combine like terms:
[tex]2cos^2(2x) + 2cos^2(x) - 4 = 0[/tex]
Divide the entire equation by 2:
[tex]cos^2(2x) + cos^2(x) - 2 = 0[/tex]
Now, let's simplify further:
We can rewrite [tex]cos^2(2x)[/tex] as [tex](1 - sin^2(2x))[/tex]using the Pythagorean identity: [tex]sin^2(\theta) + cos^2(\theta) = 1[/tex]
So, the equation becomes:
[tex](1 - sin^2(2x)) + cos^2(x) - 2 = 0[/tex]
Rearrange the terms:
[tex]cos^2(x) - sin^2(2x) - 1 = 0[/tex]
Now, use the double-angle identity: [tex]sin^2(2x) = 2sin(x)cos(x)[/tex]
[tex]cos^2(x) - 2sin(x)cos(x) - 1 = 0[/tex]
Now, we can rewrite [tex]cos^2(x) as (1 - sin^2(x))[/tex] using the Pythagorean identity:
[tex]sin^2(\theta) + cos^2(\theta) = 1[/tex]
[tex](1 - sin^2(x)) - 2sin(x)cos(x) - 1 = 0[/tex]
Now, simplify further:
[tex]1 - sin^2(x) - 2sin(x)cos(x) - 1 = 0[/tex]
We can see that [tex](1 - sin^2(x))[/tex] cancels out:
-2sin(x)cos(x) = 0
Divide both sides by -2:
sin(x)cos(x) = 0
Now, there are two possible solutions for this equation:
sin(x) = 0
cos(x) = 0
Let's solve each case:
sin(x) = 0
This occurs when x is an integer multiple of π (π, 2π, 3π, ...). So the solutions are x = nπ, where n is an integer.
cos(x) = 0
This occurs when x is an odd multiple of π/2 (π/2, 3π/2, 5π/2, ...). So the solutions are x = (2n + 1)π/2, where n is an integer.
Therefore, the solutions to the equation cos(4x) + cos(2x) - 2 = 0 are x = nπ and x = (2n + 1)π/2, where n is an integer.
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Determine c so that f(x) is continuous on the entire real line if f(x)= x^2 when x<=3 and c/x when x>3 ...?
AB=21; AD=28. What is the value of AC+BD?
The value of AC + BD will be 70.
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
In rectangle ABCD,
AB = 21
AD = 28
Now,
Since, ABCD is a rectangle.
Hence, We get;
⇒ AC = BD
Here, In rectangle ABCD,
AB = 21
AD = 28
So, By using definition of Pythagoras theorem, we get;
⇒ BD² = AB² + AD²
⇒ BD² = 21² + 28²
⇒ BD² = 441 + 784
⇒ BD² = 1225
⇒ BD = 35
Thus, The value of BD + AC is find as;
⇒ AC + BD = 35 + 35
= 70
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Watermelons cost $0.35 per pound. Joseph’s watermelon costs between $4.20 and $5.25. Which compound inequality correctly represents the possible weights of his watermelon?
Answer: 12 < x < 15
Step-by-step explanation:
Sam is flying a kite. the length of the kite string is 80 meters, and it makes an angle of 75° with the ground. the height of the kite from the ground is meters.
Answer:
Height of the kite from ground is 77 m.
Step-by-step explanation:
Given: Length of the kite string = 80 m
Angle of elevation = 75°
To find: Height of the kite from the ground.
Figure is attached.
In ΔABC
using trigonometric ratio,
[tex]sin\,75^{\circ}=\frac{AB}{AC}[/tex]
[tex]0.97=\frac{AB}{80}[/tex]
[tex]AB=0.97\times80[/tex]
AB = 77.27 m
AB = 77 m (approx.)
Therefore, Height of the kite from ground is 77 m.
The ratio of sues age to her fathers age is 2:7 in three years their ages will total 60, how old is sue and her dad right now
the formula for finding the area of a circle is a equals pi r square. solve the formula for r.
explai n how a number and its reciprocal are related
how to find a whole number in this question 4% of ... is 56?
XY is the perpendicular bisector of JK. which of the following statements must be true? check all that apply?
A. XY and JK form four right angles
B. P is the midpoint of XY
C. m
D. XP=YP
E.JP=KP
F. XY perpendicualr to JK
According to the properties of a perpendicular bisector, XY will form four right angles with JK, XY is perpendicular to JK, and it must bisect JK into two equal parts, making statements A, D, E, and F true.
Explanation:The question tells us that XY is the perpendicular bisector of JK. This tells us a few things about the relationship between the two lines and the points on them:
XY and JK form four right angles: Because XY is a perpendicular bisector, it intersects line JK at a 90° angle.XY perpendicular to JK: This simply restates that the angle formed by the intersection of XY and JK is a right angle.JP=KP: Perpendicular bisectors not only intersect the other line at a right angle, but they also bisect it, which means they cut it into two equal parts. Thus, point J is as far from the point of intersection as point K, making JP equal to KP.XP=YP: This is also a property of the perpendicular bisector. It means that the point of intersection P is the midpoint of XY, making segment XP equal to segment YP.The options regarding P being the midpoint of XY and the statement that includes an undefined variable 'm' were ignored due to lack of context.
Final answer:
The statements that must be true when XY is the perpendicular bisector of JK are: XY and JK form four right angles, P is the midpoint of XY, XP = YP, and XY is perpendicular to JK.
Explanation:
To determine which of the statements must be true, we need to understand the properties of a perpendicular bisector. A perpendicular bisector of a line segment is a line that divides the line segment into two equal parts and forms a right angle with the line segment.
From this definition, we can conclude that the following statements must be true:
A. XY and JK form four right angles - Since XY is the perpendicular bisector of JK, it forms a right angle with JK at each point of intersection.
B. P is the midpoint of XY - The perpendicular bisector passes through the midpoint of the line segment it bisects.
C. XP = YP - Since P is the midpoint of XY, XP and YP have equal lengths.
F. XY is perpendicular to JK - This is the definition of a perpendicular bisector.
the circular blade on a saw has a diameter of 7.5 inches and rotates at 2400 revolutions per minute.
A) find the angular speed in radians per sec
B) Find the linear speed of the saw teeth ( in feet per sec) as the contact the wood being cut.
Formulas--> Linear speed= arc length/time= s/t
Angular speed= central angle/time ...?
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Why is a plane a undefined term
Tim is setting up the course for a 9 mile walk.he places a sign every 0.15 mile along the path. how many signs will tim place
A sequence in which each term is found by adding the same number
Does antibiotics help kill the common cold??
how to write four hundred thousand in numbers?
Which of the following is the inverse of the function {(1,2),(3,4),(6,8)}
A. {(6,8),(3,4),(1,2)}
B. {(2,1),(4,3),(6,8)}
C. {(2,1),(4,3),(8,6)}
D. {(2,1),(3,4),(8,6)}
A1+a2+a3=180 solve for a1
Write 16 1/2 as an improper fraction
Write the standard form of the equation of the line that passes through the given points.
(5, 3) and (8, -2)
Morgan calculated that he spent 305 minutes doing homework one week and 284 minutes doing homework the next week. How much more time did he spend doing homework the first week?
Find the zeros of the polynomial function and state the multiplicity of each.
f(x) = 5(x + 8)2(x - 8)3
A. 4, multiplicity 1; -8, multiplicity 3; 8, multiplicity 3
B. -8, multiplicity 2; 8, multiplicity 3
C. -8, multiplicity 3; 8, multiplicity 2
D. 4, multiplicity 1; 8, multiplicity 1; -8, multiplicity 1
The given polynomial has roots -8 with multiplicity 2 and 8 with multiplicity 3. Hence option B is correct.
Use the concept of polynomial defined as:
An expression that contains exponents, variables, and constants that is combined using mathematical operations such as addition, subtraction, multiplication, and division is known as a polynomial.
The given polynomial is:
f(x) = 5(x + 8)²(x - 8)³
To find its root equate this polynomial to 0.
Then,
5(x + 8)²(x - 8)³ = 0
(x + 8)²(x - 8)³ = 0
(x + 8)(x + 8)(x - 8)(x - 8)(x - 8) = 0
Therefore,
x = -8, -8, 8, 8, 8
Hence,
It has root -8 with multiplicity 2 and 8 with multiplicity 3 which is option B.
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The complete question is:
Find the zeros of the polynomial function and state the multiplicity of each.
f(x) = 5(x + 8)²(x - 8)³
A. 4, multiplicity 1; -8, multiplicity 3; 8, multiplicity 3
B. -8, multiplicity 2; 8, multiplicity 3
C. -8, multiplicity 3; 8, multiplicity 2
D. 4, multiplicity 1; 8, multiplicity 1; -8, multiplicity 1
The sensory somatic nervous system controls all _________ responses of the body.
unconscious
voluntary
sequenced
repeated
Answer:
The sensory somatic nervous system controls all voluntary responses of the body.
Step-by-step explanation:
The sensory somatic nervous system controls all voluntary responses of the body.
The movements includes muscles and organs movements and reflex movements. Here the sensory neurons carry impulses to the brain and the spinal cord.
What did the inventor of the 10 ton truck so often say
Answer:
This is an equation in which we have to find the slope of the line. We are supposed to draw the line for the two given points.
Step-by-step explanation:
The equation and the graph are solved as:
For graph One: B=(4,4)(1,2) for that m= 2/3. E=(2,0)(-4,4), for this m=-2/3. O=(1,-3)(-3,-4),m=1/4.for Second graph: I=(-1,-3)(2,3), m=2. E=(-4,-3)(-2,-1), m=-2. O=(-3,0)(-1,5),m=5/2. for the third graph:E=(0,2)(5,-1),m=-3/5. D=(5,6)(2,-1), m=7/3.L=(-5,2)(0,-3),m=-1.for the fourth graph: D=(0,0)(2,-6),m=-3. G=(4,5)(-2,4),m=1/6. S=(2,-3)(-5,-3), m=0.Now the Graphical data and the results are attached to the answer, given hope it helps out.
who good at the math
graph the line y=3/4x-2
Step-by-step explanation: First, notice that this line is in slope intercept or more commonly known as y = mx + b form because y is by itself on one side of the equation.
Our slope or m therefore is the coefficient of the x-term which in this case is 3/4. Our b or y-intercept is the constant term which in this case is -2.
To graph a line given the slope and y-intercept, we will first start with its y-intercept. The y-intercept of a line is the point where the line crosses the y-axis. Since our y-intercept is -2, we start by plotting the point that is down 2 units on the y-axis and we call that point A.
From there we take our slope of 3/4 so our rise is 3 and our run is 4 and we end up at point B. Now we can connect the two points and we have our line.
I attached the image of the line in the image provided.