The dimensions of the rectangle are 24x and 90y.
Explanation:The area of a rectangle is represented by the expression 24x6y15. To determine the dimensions of the rectangle, we need to factorize the expression. Factoring out the common factors, we have:
24x6y15 = 2 × 2 × 2 × 3 × x × (2 × 3) × y × (5 × 3)
From this, we can see that the dimensions of the rectangle are:
Length = 2 × 2 × 2 × x × 3 = 24x
Width = 2 × y × 3 × (5 × 3) = 90y
Which expression is equivalent to sin^2 X-sinX-2/sinX-2
To simplify the expression sin² X - sinX - 2 / sinX - 2, we need to factor the numerator and denominator separately and then cancel out the common factor of sin(X) - 2. The equivalent expression is sin(X) + 1.
Explanation:To simplify the given expression, we can factor the numerator and denominator separately and then cancel out common terms. The numerator can be factored as (sin(X) - 2) (sin(X) + 1), and the denominator can be factored as (sin(X) - 2). By cancelling out the common factor of (sin(X) - 2), we are left with (sin(X) + 1) as the equivalent expression.
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Jake has just become the senior marketing rep for a new chain of upscale hotels. His first responsibility is to develop a
plan, commonly referred to as the
Answer:
placement plan
Step-by-step explanation:
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As the senior marketing rep, Jake needs to develop a marketing plan. This plan would outline the business's advertising and marketing efforts for the year, including goals, strategies, tactics, a market analysis, and a budget.
Explanation:Jake, as the senior marketing rep for a new chain of upscale hotels, is tasked with creating a marketing plan. A marketing plan is a comprehensive document or blueprint that outlines a company's advertising and marketing efforts for the coming year.
It would detail the business's marketing goals, the strategies and tactics to achieve those goals, an analysis of the current market situation, and a budget for the marketing activities. For an upscale hotel chain, it might include strategies such as premium pricing, high-quality service, and targeted advertising.
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Find all real fourth roots of 16.
2 and -2
4 and -4
Answer:
2
Step-by-step explanation:
because 2*2*2*2is equal to 16
The real fourth roots of 16 are: 2 and -2.
The detailed answer explains how to find the real fourth roots of 16 step by step, providing a clear solution.
The question: Find all real fourth roots of 16.
Step-by-step explanation:
Fourth roots of 16 are: 2, -2, 2i, -2i.Therefore, the real fourth roots of 16 are: 2 and -2.
What is the value of x?
X° 65° 79°
ОА. 36°
ов. 14°
Ос. 144°
OD. 56°
Answer:
A. 36
Step-by-step explanation:
65+79=144
180-144=36
Answer: A
Step-by-step explanation:
A person standing close to the edge on top of a 24-foot building throws a ball vertically upward. The quadratic function h(t)=−16t^2+92t+24 models the ball's height about the ground, h(t), in feet, t seconds after it was thrown.
a) What is the maximum height of the ball?
__feet
b) How many seconds does it take until the ball hits the ground?
____ seconds
Answer:
a) maximum height is 156.25 ft
b) 6 seconds
Step-by-step explanation:
a) The maximum height can be found by finding the y-coordinate of the vertex. The vertex is the highest point in a parabola opened downward.
I start with by finding the t-coordinate of the vertex.
The t-coordinate of the vertex is [tex]\frac{-b}{2a}[/tex] where the expression [tex]-16t^2+92t+24[/tex] will need to be compared to [tex]at^2+bt+c[/tex].
We see that [tex]a=-16,b=92,c=24[/tex].
So the t-coordinate of the vertex is [tex]\frac{-b}{2a}=\frac{-92}{2(-16)}=\frac{-92}{-32}=\frac{23}{8}[/tex].
We can find the h, the height, that corresponds to this t by using the equation [tex]h=-16t^2+92t+24[/tex] where [tex]t=\frac{23}{8}[/tex].
So inserting 23/8 for [tex]t[/tex].
[tex]-16(23/8)^2+92(23/8)+24[/tex]
Plugging into calculator gives you 625/4.
So the maximum height is 625/4 or 156.25.
b) Let's find how long it takes the ball to hit the ground. If the ball is on the ground, then the distance between the ball and the ground is 0. So we are looking to solve h(t)=0 for t.
So this is equation we are solving for t:
[tex]-16t^2+92t+24=0[/tex]
These numbers are big but since all the terms have a common factor we can make them slightly smaller.
That is, we are going to divide both sides by -4 and see
[tex]4t^2-23t-6=0[/tex]
It looks like it could be possible to factor.
a=4
b=-23
c=-6
We need to find two numbers that multiply to be ac and add up to be b.
a*c=4(-6)=-24
b=-23
So -24=-24*1 and -23=-24+1.
We are going to replace -23t with -24t+1t giving up something that should be factorable by grouping.
[tex]4t^2-23t-6=0[/tex]
[tex]4t^2-24t+1t-6=0[/tex]
Group the first 2 together and group the last two together:
[tex](4t^2-24t)+(1t-6)=0[/tex]
Factor what you can from each pair:
[tex]4t(t-6)+1(t-6)=0[/tex]
Now each term has a common factor of (t-6) so factor that out giving you:
[tex](t-6)(4t+1)=0[/tex]
Set both factors equal to 0 giving you
t-6=0 or 4t+1=0
t=6 or 4t =-1
t=6 or t=-1/4
So it hit the ground in 6 seconds.
Final answer:
The maximum height of the ball is calculated to be at 2.875 seconds, and by inserting this time back into the height function, we get the max height. To determine when the ball hits the ground, we solve the quadratic function for when h(t) equals zero, finding that it occurs at approximately 5.4 seconds post launch.
Explanation:
To calculate the maximum height of the ball, we need to find the vertex of the quadratic function, which gives us the time when the maximum height is reached. The function is in the form h(t) = -16t^2 + 92t + 24. The time at which the maximum height occurs can be found using the formula -b/(2a), where a and b are coefficients from the quadratic function. Here, a = -16 and b = 92, so the time is t = -92/(2*(-16)) = 92/32 = 2.875 seconds. Inserting this back into the height function gives us the maximum height:
h(2.875) = -16(2.875)^2 + 92(2.875) + 24
Now, to find when the ball hits the ground, we need to find the positive root of the height function where h(t) = 0. The quadratic formula h(t) = -16t^2 + 92t + 24 is used to find the time values when the ball is at the ground level. Solving this equation, we get two possible times, and we're interested in the positive one since time cannot be negative.
Thus, we get that the ball reaches the ground at approximately 5.4 seconds.
Which descriptions can describe more than one triangle? check all that apply
Answer:
Angle measurements of 35°, 35°, and 110°
Angle measurements of 40°, 60°, and 80°
Step-by-step explanation:
If you specify only the three angles, you can have an infinite number of similar triangles of different sizes.
A is wrong. There can be only one triangle in which all three side lengths are specified.
C is wrong. The angles do not add up to 180°.
The descriptions which can describe more than one triangle is:
angle measurements of 35°,35° and 110°.angle measurements of 40°,60° and 80°.Step-by-step explanation:The three given side lengths form a triangle if the sum of any 2 sides is greater than the length of the third side.Also, all the three given angle measure form a triangle if the sum of all the three angles is equal to 180 degree.We know that with the help of given side three lengths of a triangle a unique triangle is formed.and with the help of given three angle measures of a triangle more than one triangle is possible with distinct side length.a)
Side lengths 6 ft, 8 ft and 10 ft.
First we check whether it form a triangle or not:
6+8=14>10
8+10=18>6
and
6+10=16>8
Yes, these side lengths form a triangle.
With the help of this only one unique triangle is possible.
b)
angle measurements of 35°,35° and 110°
First we check the sum of the angles:
35°+35°+110°=180°
Hence, more than one triangle is possible.
c)
angle measurements of 30°,40° and 50°
First we check the sum of these angles:
30°+40°+50°=120°≠180°
Hence, these angles measure do not form a triangle.
d)
angle measurements of 40°,60° and 80°
First we check the sum of these angles:
40°+60°+80°=180°.
Hence, more than one triangle is possible.
e)
side length of 4 cm, 6 cm and 9 cm.
First we check whether it form a triangle or not:
4+6=10>9
6+9=15>4
and
4+9=13>6
Hence, a unique triangle will be formed.
Simplify y^-3
a.3/y
b.1/y^3
c.-3y
d.-1/y^3
Answer:
b. [tex]\frac{1}{y^3}[/tex]
Step-by-step explanation:
Here we are given [tex]y^{-3}[/tex] and are asked to simplify it. We are going to apply the law of exponents which says that
[tex]a^{-n}=\frac{1}{a^n}[/tex]
Hence applying this rule in our problem we get, where a=y and n=3
[tex]y^{-3}=\frac{1}{y^3}[/tex]
Hence our C) Option is correct
Assignment: Translating Functions Investigation
Jeremy is opening a savings account earning simple interest. He plans to deposit his $50 birthday money and leave the account alone until he goes to college. He will earn $5 per year in interest.
The function f(x) = 5x + 50 represents his account balance after x years.
The graph of this is shown.
(Check the first graph)
Part A (Check the second graph)
1. Graph the translation of the function up 10 units.
2. Give the coordinate rule for a translation up 10 units.
3. What does a translation of the function up 10 units mean in terms of Jeremy's savings?
Part B (Check the third graph)
1. Graph the translation of the function right 10 units.
2. Give the coordinate rule for translation right 10 units.
3. What does a translation of the function right 10 units mean in terms of Jeremy's savings?
Part C
1. Look at the translations, what characteristic of the graph stayed the same in each translation?
2. Look at the original graph and the graph of the translation right 10 units. What vertical translation of the graph in Part B would put the graph back to its original position? Explain how you determined this.
Answer:
Part A)
1) The graph in the attached figure N 1
2) The coordinate rule is (x,y) -----> (x,y+10)
3) The translation of the function up 10 units means that the initial deposit is $60 instead of $50
Part B)
1) The graph in the attached figure N2
2) The coordinate rule is (x,y) -----> (x-10,y)
3) The translation of the function right 10 units means that the initial deposit is equal to $10
Part C)
1) In each translation, the slope is the same (m=5) are parallel lines
2) The vertical translation would be up 40 units
Step-by-step explanation:
we have
[tex]f(x)=5x+50[/tex]
where
f(x) --> represents Jeremy's account balance
x ---> the time in years
Part A)
The translation of the function is up 10 units.
The rule of the translation is equal to
(x,y) -----> (x,y+10)
so
The new function will be
[tex]f(x)=5x+50+10[/tex]
[tex]f(x)=5x+60[/tex]
The graph in the attached figure N 1
The translation of the function up 10 units means that the initial deposit is $60 instead of $50
Part B)
The translation of the function is right 10 units.
The rule of the translation is equal to
(x,y) -----> (x-10,y)
so
we have
[tex]f(x)=5x+60[/tex] ----> function Part A
The new function will be
[tex]f(x)=5(x-10)+60[/tex]
[tex]f(x)=5x+10[/tex]
The graph in the attached figure N 2
The translation of the function right 10 units means that the initial deposit is equal to $10
Part C)
1. Look at the translations, what characteristic of the graph stayed the same in each translation?
In each translation, the slope is the same
The slope m is equal to m=5
Are parallel lines
2. Look at the original graph and the graph of the translation right 10 units. What vertical translation of the graph in Part B would put the graph back to its original position?
we have
[tex]f(x)=5x+10[/tex]
The vertical translation would be up 40 units
The rule of the translation is equal to
(x,y) -----> (x,y+40)
so
The new function will be
[tex]f(x)=5x+10+40[/tex]
[tex]f(x)=5x+50[/tex]
The translation of the original linear function, f(x) = 5·x + 50, gives the
following values;
Part A:
Please find attached the graph of the function f(x) + 60 = 5·x + 60, which is the graph of the original function translated up 10 units(x, y + 10)The account value is increased by $10Part B:
Please find attached the graph of the function translated to the right by 10 units(x + 10, y)The number of years the interest is applied is increased by 10Part C:
The slope of the graph stayed the same in each translationThe vertical translation is 50 unitsWhich method can be used to make the given translations?The function for the amount of money in the account is; f(x) = 5·x + 50
Part A
1. The graph of the translation of the above function up 10 units gives
the function;
f(x) + 10 = 5·x + 50 + 10 = 5·x + 60
f(x) + 10 = 5·x + 60
Please find attached the graph of the function translated up 10 units created with MS Excel
2. The coordinate rule for a translation up 10 units is; [tex]\underline{(x, \ y + 10)}[/tex]
3. The meaning of the translation up 10 units means that amount in the
account at a point in time is increased by $10
Part B;
1. The function, f(x) = 5·x + 50, translated 10 units to the right gives;
f(x + 10) = 5·(x + 10) + 50 = 5·x + 100
Please find attached the graph of the function translated right 10 units created with MS Excel
2. The coordinate rule is (x, y) [tex]\underrightarrow{T_{(10, \ 0)}}[/tex] [tex]\underline{(x + 10, \ y)}[/tex]
3. A translation of the function to the right, means that the point in time at
which the graph starts, the account balance is $100, such that Jeremy
the time the interest is applied is 10 years longer, than the original time
added to the number of years in the given function, f(x) = 5·x + 50
Part C
1. The characteristic of the graph that stays the same is the slope
2. The vertical translation in the graph of the translation right 10 units
compared to the original graph is 50 units.
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Help me on this math question please
Answer:
B. 24
Step-by-step explanation:
Subtract numbers from left to right.
[tex]\displaystyle 25.73-2.19=23.54[/tex]
Round to the nearest tenths.
[tex]\displaystyle 23.54=24[/tex]
24 is the correct answer.
Answer:
B. 24
Step-by-step explanation:
Estimation:
25.73 - 2.19 = 24
Vanessa kicked a soccer ball laying on the ground. It was in the air for 4 seconds before it hit the ground. While the soccer ball was in the air it reached a height of approximately 20 feet. Assuming that the soccer ball’s height (in feet) is a function of time (in seconds), what is the domain in the context of this problem?
Answer:
The domain would be 0 to 4 seconds
Step-by-step explanation:
According to the given conditions a ball was lying on the ground but when it was hit by Vanessa it was in the air for 4 seconds. We have to find the domain.
We know that the domain is the input values. According to the given statement it would start at time 0 and end when it hit the ground at 4 seconds.
Therefore the domain would be 0 to 4 seconds.
[0,4] ....
Find the measure of angle x in the figure below: (1 point)
Answer:
x = 50
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Sum the 2 given angles in the lower triangle and subtract from 180 to find the third angle
third angle = 180° - (65 + 65)° = 180° - 130° = 50°
x = third angle = 50 ( vertical angles )
A triangle has to have three angles and they have to add up to 180 degrees so,
65+65=130
180-130=50
X=50 degrees because it is equal to the third angle.
here is the histogram of a data distribution. which of the following numbers is closest to the mean of this distribution
Answer:
Option (D)
Step-by-step explanation:
Mean=[tex]\frac{Sum of observations}{Number of observations}[/tex]
here, observations are
1×1=1
2×2=2
3×3=9
4×1=4
5×1=5
6×2=12
7×3=21
8×1=8
9×1=9
10×0=0
hence, sum of observations =1+4+9+4+5+12+21+8+9+0=73
Number of observations are=1+2+3+1+1+2+3+1+1+0=15
Mean=[tex]\frac{73}{15}[/tex]
Mean=4.8..
nearest to 5 .
Hence, option (D) is correct.
The number that is closest to the mean of the distribution is 5.
What is the mean?Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number
Mean = sum of the numbers / total number
Sum of numbers = (1 x 1) + (2 x 2) + (3 x 3) + (4 x 1) + (5 x 1) + (6 x 2) + (7 x 3) + (8 x 1) + (9 x 1) = 73
Total numbers = 1+2+3+1+1+2+3+1+1+0=15
Mean = 73/15 = 4.8 = 5
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when numbers are divided, you (add / subtract) exponents and (multiply / divide) the bases.
(Scientific Notation)
Answer:
you subtract the exponents and divide the bases
Find the measure of angle 1
Answer:
120 degrees
Step-by-step explanation:
You can just eyeball that it is greater than 90 degreees so it must be 120 degrees.
Find the length of a line segment with endpoints of -9 and 7.
A
-16
C. 16
D. 26
Please select the best answer from the choices provided
Answer:
C. 16
Step-by-step explanation:
The distance between two points on the number line is the absolute value of the difference of their coordinates.
If the coordinates of two points on the number line are a and b, then the distance between the two points is
d = |a - b|
The coordinates here are -9 and 7.
distance = |-9 - 7| = |-16| = 16
What is the simplified form of 10,000x64 ?
5000x32
5000x8
100x8
100x32
Answer:I think it is 5000x32
Step-by-step explanation:
10,000 divided by 2 is 5,000
64 divided by 2 is 32
5,000 can’t go down into 100 the same amount of times for 32 to get to 8
The simplified form of 10,000 x 64 are,
⇒ 100x⁸
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
We have to given that;
To find simplified form of √10,000x⁶⁴
Since, We can simplify as;
⇒ √10,000x⁶⁴
⇒ √(100)² (x⁸)²
⇒ 100x⁸
Thus, The simplified form of 10,000 x 64 are,
⇒ 100x⁸
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What is the third term of the sequence
Answer:
I think 12.
Step-by-step explanation:
identify the graph and describe the solution set of this system of equalities y>1/3x+5 and y<1/3x-1
Answer:
The solution to the set of inequalities is on the shaded regions.For example point (10,10)
Step-by-step explanation:
The equations are
[tex]y>\frac{1}{3} x+5\\\\\\\\y<\frac{1}{3} x-1[/tex]
plot the equations on a graph tool as shown below and visualize the solution on the shaded areas.
The system of inequalities y>1/3x+5 and y<1/3x-1 has no solution (parallel lines).
How to draw regions covered by inequalities?Suppose there is inequality given as: y ≥ f(x)
The region it covers is the region of value pairs (x,y) for which this inequality holds true.
We've to draw the region covered by it.
For a function y = f(x), there is y > f(x) on one side of the graph of the function y = f(x) in XY plane, and on other side there is y < f(x).
The system of inequalities are;
y > 1/3x + 5
The solution of inequality A is the shaded area below the dashed line
y = 1/3x + 5
The slope of line is m = 1/3
Similarly,
y < 1/3x - 1
The solution to inequality B is the shaded area below the dashed line
y = 1/3x - 1
The slope of line is m = 1/3
Thus, The system of inequalities y>1/3x+5 and y<1/3x-1 has no solution (parallel lines).
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the legs of a right triangle measure 10 inches and 4 inches. what is the area of the triangle?
Answer:
20 inches squared
This is because the area of a triangle is height times base divided by 2.
So it is 10*4/2, so the answer is 20 inches squared.
The area of the right angle triangle is 20 square inches.
What is the area of a right angle triangle ?The area of a right angle triangle is given by the formula,
Area = 1/2 * base * height .
where the base and height are the legs of the given triangle.
How to calculate the given area of the triangle ?It is given that the legs of a right triangle measure 10 inches and 4 inches.
Thus we have the base of the triangle as 4 inches and height of the triangle as 10 inches.
Area = 1/2 * 4 * 10 square inches .
∴ Area = 20 square inches.
Therefore, the area of the right angle triangle is 20 square inches.
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Please help me with these two questions
Hi! It will be a pleasure to help you finding the solution to this problem, so let's solve each part:
PART 1.Finding the correct expression.Correct answer:[tex]\boxed{A. \ 1.50h+4}[/tex]
From the problem, we know the following data of the problem:
Laval parked at the beach.Laval paid a fixed price of $4 for a pass.Laval paid $1.50 for each hour.Our goal is to find the the expression for the total cost for parking at the beach for h hours. So:
Step 1: Since we have a fixed price, this value will appear in our expression:
[tex]4[/tex]
Step 2: Since Laval paid $1.50 for each hour, this can be represented as the following expression:
[tex]1.50h[/tex]
Finally, we can write total cost (C) as the sum of these two expressions:
[tex]C=1.50h+4[/tex]
Finally, our correct option is A:
[tex]\boxed{1.50h+4}[/tex]
PART 2.Finding h.Correct answer:5 hours
Here we have to find how many hours Laval spent at the beach knowing that he paid a total amount of $11.50. From the previous part, we know that our expression is:
[tex]C=1.50h+4 \\ \\ For \ C=11.50 \\ \\ 11.50=1.50h+4 \\ \\ Subtracting \ 4 \ from \ both \ sides: \\ \\ 11.50-4=1.50h+4-4 \\ \\ 7.5=1.50h \\ \\ Dividing \ both \ sides \ by \ 1.50 \\ \\ h=\frac{7.5}{1.50}=5[/tex]
Finally, he spent 5 hours at the beach
The common point between lines y = 2x + 5 and y = ½ x + 6 is (3, 1/2).
Answer:
The ordered pair (3,1/2) is not a common point, the statement is false
The solution is the point (0.667, 6.333) (common point)
Step-by-step explanation:
we have
[tex]y=2x+5[/tex] -----> equation A
[tex]y=\frac{1}{2}x+6[/tex] ----> equation B
we know that
If a ordered pair is a common point between the two lines,
then
the ordered pair must satisfy both equations
step 1
Verify if the ordered pair (3,1/2) satisfy equation A
substitute the value of x and the value of y in the equation A and then compare the results
For x=3, y=1/2
[tex]\frac{1}{2}=2(3)+5[/tex]
[tex]\frac{1}{2}=11[/tex] ----> is not true
The ordered pair don't satisfy the equation A
therefore
The ordered pair is not a common points both lines
The statement is false
step 2
Find the common point between the two lines
[tex]y=2x+5[/tex] -----> equation A
[tex]y=\frac{1}{2}x+6[/tex] ----> equation B
Solve the system of equations by graphing
The intersection point both graphs is the solution of the system (common point)
using a graphing tool
The solution is the point (0.667, 6.333) (common point)
see the attached figure
Which of the following statements is true of -4 and 4? Select all that apply.
They are a zero pair
They are opposites
They are the same distance from zero
Answer:
2 and 3
Step-by-step explanation:
How do I do these problems? HELP! I added pics btw.
Answer:
Question 6: 6.8
Question 7: 8295
Step-by-step explanation:
Question 6:
Let's say that each hamburger costs x amount of dollars, and each soda costs y amount of dollars. For the first statement, we purchase 7 hamburgers (so 7 times x) and 3 sodas (3 times y) to add up to 27.95. As an equation, this means that 7x+3y=27.95. Similarly, for the second statement, 5x+4y=23.40.
Putting these two side by side, we get:
7x+3y=27.95
5x+4y=23.40
Using Gauss-Jordan elimination, we can multiply the first equation by -4/3 and then add that to the second equation, resulting in
[tex]-13x/3 = 27.95*(-4/3)+23.40\\[/tex]
Simplifying, we get
[tex]-13x = 27.95*(-4)+23.4*3\\\\-13x = -41.6\\\\x=3.2[/tex]
Question 7:
Take the number of students as x and the number of teachers as y. There are 35 times as many students as there are teachers, so 35y=x. We know that the students and teachers added up equal 8544-12=8532 (as 12 seats are empty in the auditorium that can seat 8544, 8532 must be occupied), so x+y= 8532. Since 35y=x, 35y+y+8532, 36y=8532, and y= 237. Since the number of students is equal to x, and x=35y, 35*y=35*237=8295 students.
Find b and c so that the parábola y=-3x^2 +bx+c has x-intercepts 1 and -4
Answer:
so b=-9 while c=12.
Step-by-step explanation:
If you have x-intercepts 1 and -4, then that means f(1)=0 and f(-4)=0.
You are given [tex]f(x)=-3x^2+bx+c[/tex]
So you have the system of equations to solve:
[tex]f(1)=-3(1)^2+b(1)+c=0[/tex]
[tex]f(-4)=-3(-4)^2+b(-4)+c=0[/tex]
Evaluating the exponents:
[tex]-3(1)+b+c=0[/tex]
[tex]-3(16)-4b+c=0[/tex]
Doing a little bit of multiplying:
[tex]-3+b+c=0[/tex]
[tex]-48-4b+c=0[/tex]
Let's add 3 on both sides of equation 1 and 48 on both sides of equation 2:
[tex]b+c=3[/tex]
[tex]-4b+c=48[/tex]
Subtracting the equations will eliminate c.
Let's do that:
[tex]5b+0c=-45[/tex]
[tex]5b=-45[/tex]
Divide both sides by 5:
[tex]b=\frac{-45}{5}[/tex]
Simplify:
[tex]b=-9[/tex]
If b=-9 and b+c=3 then -9+c=3 implies c=9+3=12.
so b=-9 while c=12.
To find b and c for the parabola y=-3x^2+bx+c with x-intercepts 1 and -4, we express the equation in its factored form, then expand it. From the expansion, we see that b=-9 and c=-12.
Explanation:To find the values of b and c in the equation y = -3x^2+bx+c, where the x-intercepts are given as 1 and -4, we use the following steps:
Realize that a parabola that crosses the x-axis at points 1 and -4 can be expressed in the factored form y = -3(x - 1)(x + 4). Expand this factored form: y = -3x^2 - 9x - 12. From this expansion, we can identify that b = -9 and c = -12.Learn more about Quadratic Equation here:
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Describe how the graph of g(x) is related to the parent function f(x).
f(x) = 5x
g(x) = 5x + 3
The options are
A)Adding 3 to the function translates the parent graph 3 units up.
B)Adding 3 to the function translates the parent graph 3 units down.
C)Adding 3 to the function translates the parent graph 3 units to the left.
D)Adding 3 to the function translates the parent graph 3 units to the right.
Answer:
A
Step-by-step explanation:
we have g(x) = 5x+3
we know that 5x=f(x)
so g(x)=f(x)+3
thus g(x) is obtained by adding 3 units to f(x)
that's means the graph of g is obtained by translating the parent function f by 3 units up
Answer:
Step-by-step explanation:
There are two functions f(x) = 5x and g(x) = 5x + 3
This parent function f(x) has been translated to form a new function g(x) = 5x + 3
These linear functions can be represented by two lines y = 5x and y' = 5x' + 3
So when we shift line y = 5x by 3 units up on the y-axis then a new graph of
y = 5x + 3 will be formed.
Therefore, Option A is the answer.
Help please. I don't think I understand.
Answer:
27 ham sandwiches
Step-by-step explanation:
Let
x ----> the number of turkey sandwiches
y ----> the number of ham sandwiches
we know that
x=y -----> equation A
y=3(x-18) -----> equation B
substitute equation A in equation B
x=3(x-18)
x=3x-54
3x-x=54
2x=54
x=27 turkey sandwiches (initial)
therefore
The number of ham sandwiches is equal to
y=27 ham sandwiches
Note The options of this problem are incorrect, the number of sandwiches of ham must be greater than 18
Omar and Jacobs ages total 24 years. Omar is 3 times as old as JasonHow old is Jacob
you bought 11 books for $42.35 how much would 15 books cost
Answer:
$57.75
Step-by-step explanation:
If 11 books cost $42.35,
11b=42.35
b=42.35/11
b=3.85
15 books will cost 15b.
15b
= 15*3.85
= 57.75.
15 Books will cost $57.75.
Answer:
57.75
Step-by-step explanation:
First I found the unit rate by dividing 42.35 by 11, which is 3.85.
second i multiplied the unit rate by 15 and got 57.75
Answer these questions please: You don't need to plot the point just answer B & C. Also every single coordinate plane is like a normal coordinate plane except there are only 5 and 10 labeled.
1) Use the coordinate plane below to answer the questions.
a. Plot a point at the origin. Label the point O.
b. Plot another point that is three units to the right and four units down from the
origin.
c. What are the coordinates of this point?
2)Use the coordinate plane below to answer the questions.
a. Plot a point at (5, 2). Label the point P.
b. Plot another point that is four units to the left and two units down from point P.
c. What are the coordinates of this point?
3)Use the coordinate plane below to answer the questions.
a. Plot a point at (-6, -1). Label the point Q.
b. Plot another point that is eight units to the right and five units up from point Q.
c. What are the coordinates of this point?
4)Use the coordinate plane below to answer the questions.
a. Plot a point in Quadrant II. Label the point R. What are the coordinates of point
R?
b. Plot another point that is two units to the right and six units down from point R.
c. What are the coordinates of this point?
5)Use the coordinate plane below to answer the questions.
a. Plot a point in the Quadrant IV. Label the point S. What are the coordinates of
point S?
b. Plot another point that is seven units to the left and four units up from point S.
c. What are the coordinates of this point?
Step-by-step explanation:
When moving left, subtract from the x-coordinate and when moving right, add in the x-coordinate. When moving down, subtract from the y-coordinate and when moving up, add in the y-coordinate.
1) Given point = (0, 0). 3 units right and 4 units down means (0+3, 0-4) = (3, -4).
2) Given point = (5, 2). 4 units left and 2 units down means (5-4, 2-2) = (1, 0).
3) Given point = (-6, -1). 8 units right and 5 units up means (-6+8, -1+5) = (2, 4).
4) In Quadrant II, the x-coordinate is negative and the y-coordinate is positive. So taking R = (-6,6). 2 units right and 6 units down means (-6+2, 6-6) = (-4, 0).
5) In Quadrant IV, the x-coordinate is positive and the y-coordinate is negative. So taking R = (6,-6). 7 units left and 4 units up means (6-7, -6+4) = (-1, -2).
The width of a rectangle is 6 inches less than it’s length, and the area is 7 square inches. What are the length and width of the rectangle
Answer:
So length is 7 in while width is 1 in.
Step-by-step explanation:
We are given W is 6 inches less than L which mean as an equation we have W=L-6.
We are given the area of this rectangle, LW=7.
So we have the system:
W=L-6
LW=7.
Replace the second W with what the first W equals:
LW=7
L(L-6)=7
Distribute:
[tex]L^2-6L=7[/tex]
Subtract 7 on both sides:
[tex]L^2-6L-7=0[/tex]
We are luck since the coefficient of L^2 is 1. This means all we have to do is find two numbers that multiply to be -7 add at the same time add up to -6.
Those numbers are -7 and 1 since (-7)(1)=-7 and (-7)+(1)=-6.
So the factored form of our equation is:
(L-7)(L+1)=0
This gives us two equations to solve:
L-7=0 or L+1=0
L=7 or L=-1
L=-1 doesn't make sense for a length so L=7.
L=7 means the length is 7 inches.
If W=L-6 and L=7, then W=7-6=1.
The width is 1 inch since W=1.
So length is 7 in while width is 1 in.