Answer:
x-intercepts: (-1, 0) and (2, 0)
x-intercept: (-3, 0)
Step-by-step explanation:
Given quadratic function:
[tex]f(x)=-4x^2+4x+8[/tex]
The x-intercepts of a quadratic function are the points at which the curve crosses the x-axis ⇒ when y = 0
Therefore, to find the x-intercepts of the given function, set the function to zero:
[tex]\implies -4x^2+4x+8=0[/tex]
Factor out -4:
[tex]\implies -4(x^2-x-2)=0[/tex]
Divide both sides by -4
[tex]\implies x^2-x-2=0[/tex]
Rewrite the middle term as -2x + x:
[tex]\implies x^2-2x+x-2=0[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(x-2)+1(x-2)=0[/tex]
Factor out the common term (x - 2):
[tex]\implies (x+1)(x-2)=0[/tex]
Zero Product Property: If a ⋅ b = 0 then either a = 0 or b = 0 (or both).
Using the Zero Product Property, set each factor equal to zero and solve for x (if possible):
[tex]\begin{aligned}(x+1) & = 0 & \quad \textsf{ or } \quad \quad (x-2) & = 0\\\implies x & = -1 & \implies x & = 2\end{aligned}[/tex]
Therefore, the x-intercepts are (-1, 0) and (2, 0).
---------------------------------------------------------------------------------------
Given quadratic equation:
[tex]-9 = x^2 + 6x[/tex]
Add 9 to both sides:
[tex]\implies x^2+6x+9=0[/tex]
Rewrite the middle term as 3x + 3x:
[tex]\implies x^2+3x+3x+9[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(x+3)+3(x+3)=0[/tex]
Factor out the common term (x + 3):
[tex]\implies (x+3)(x+3)=0[/tex]
[tex]\implies (x+3)^2=0[/tex]
Square root both sides:
[tex]\implies (x+3)=0[/tex]
Solve for x:
[tex]\implies x=-3[/tex]
Therefore, the x-intercept is (-3, 0).
As the function has a repeated factor (multiplicity of two), the curve will touch the x-axis at (-3, 0) and bounce off.
Mandy has $10.65. she wants to share it with herself and her 2 friends. How much will each friend get
Answer:
3.55 per person
Step-by-step explanation:
To find the amount of money per person, take the total amount of money and divide by the number of people
10.65 /3
3.55 per person
Answer:
$3.55 for everyone
Graph the line with slope -3 passing through the point(-3,-2) .
The attached graph represents the graph of the line
How to plot the graph?The given parameters are:
Slope, m = -3
(x1, y1) = (-3, -2)
The equation is calculated as:
y = m(x - x1) + y1
So, we have:
y = -3(x + 3) - 2
Expand
y = -3x - 9- 2
Evaluate the difference
y = -3x - 11
See attachment for the graph of y = -3x - 11
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Which type of parent function is f(x) = -
1/?
O A. Absolute value
OB. Reciprocal
OC. Square root
OD. Linear
Answer: B. Reciprocal
Step-by-step explanation:
This is a fact.
The parent function represented by f(x) = -1/x is the reciprocal function.
Therefore, the correct answer is option B.
Reciprocal functions, also known as rational functions, are defined by an algebraic expression where the dependent variable is in the denominator. In this case, the dependent variable is x, and it appears in the denominator as 1/x.
The negative sign in front of the fraction simply indicates that the function is reflected over the x-axis.
The general form of a reciprocal function is f(x) = a/x, where "a" is a constant. In the given function f(x) = -1/x, a is equal to -1.
In the case of f(x) = -1/x, the graph of the function is a hyperbola that opens downwards in the first and third quadrants. It approaches the x-axis as x moves towards positive or negative infinity, and it moves away from the x-axis as x approaches 0.
Therefore, the correct answer is option B, the reciprocal function.
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la mitad mas el tercio mas la cuarta parte de los años que tiene manuel, suman los años que tiene mas tres ¿que edad tiene manuel? ·
Resolviendo una ecuación lineal veremos que que Manuel tiene 36 años.
¿Qué edad tiene Manuel?Vamos a definir la edad de Manuel como x.
Sabemos que la mitad mas el tercio mas la cuarta parte de x es igual que x más 3, entonces:
x/2 + x/3 + x/4 = x + 3
Ahora podemos resolver esta ecuación lineal para x:
x/2 + x/3 + x/4 - x = 3
x*( 1/2 + 1/3 + 1/4 - 1) = 3
x = 3/(1/2 + 1/3 + 1/4 - 1) = 36
Así, concluimos que manuel tiene 36 años.
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Write -3.65 as a mixed number.
Answer:
-3 13/20
Step-by-step explanation:
-3.65=
-3 65/100=
-3 13/20
The equation y minus 1 = negative 7 (x minus 3). is written in point-slope form. What is the y-intercept of the line?
Answer:
(0, 22)
Step-by-step explanation:
So you have the equation:
[tex]y-1=-7(x-3)[/tex]
So first let's define what the "y-intercept" is. The y-intercept, of a line is like the name implies, when the line intercepts or "passes" the y-axis. And if you were to take any point on the y-axis, the y-value may vary, but there is one value that doesn't change, and that's the x-value. the x-value is always going to be zero, no matter where you are on the y-axis. So to find the y-intercept simple plug 0 in as x. This gives you the equation:
[tex]y-1 = -7(0-3)[/tex]
[tex]y-1 = -7(-3)[/tex]
[tex]y-1=21[/tex]
[tex]y=22[/tex]
So the y-intercept is at (0, 22)
6(m + 2 + 7m)
Part A: Write two expressions that are equivalent to the given expression. (3 points)
Part B: Show that one of your expressions in Part A is equivalent to the given expression using algebraic properties. Explain which properties you used. (4 points)
Part C: Show that your other expression from Part A is equivalent to the given expression by substituting a number for m. (3 points)
Part A: 6 ( 8m + 2) and 48m + 12
Part B: 48m - 48m = 12 - 12
Part C: 6 (10) = 6(10)
How to determine the expressions1. The two expressions could be gotten thus;
6(m + 2 + 7m)
Collect like terms in the bracket
6 ( 8m + 2) ⇒ first expression
6(m + 2 + 7m)
Expand the bracket
6m + 12 + 42m
Collect like terms
6m + 42m + 12
48m + 12 ⇒ second expression
Part B:
6(m + 2 + 7m) = 48m + 2
Expand the bracket
6m + 12 + 42m = 48m + 2
Collect like terms
48m - 48m = 12 - 12
0 = 0
Part C:
Let the expression from A be 6 ( 8m + 2)
6(m + 2 + 7m) = 6 ( 8m + 2)
Let the number be m = 1
Substitute the values
6(1 + 2 + 7(1) ) = 6 (8(1) + 2)
6 ( 1 + 2 + 7) = 6 (10)
6 (10) = 6(10)
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Garden table and bench is 657 total. Garden table is $43 less than bench. What cost of bench?
Answer:
$350
Step-by-step explanation:
Let the bench cost $x
Then the garden table costs $x - 43
x + (x - 43) = 657
2x = 657 + 43
2x = 700
x = 350
The cost of the bench is $350.
Nice day to you!
2+2*+456+5367+63784+464749=
Answer:534360
Step-by-step explanation:
I did have to remove the multiplication though
Pls, I request ya all, exams are near, I am not able to figure out the answer (along with process) of this question. Pls, I will mark as brainliest tose who answer me with the correct process.
Thank You
What this question is asking us is
A) From -40C to 5 0c How much did it rise
The formula for this would be
Risen Temperature - Initial Temperature
The risen temparauture is 5 so we plug the 5 in first then the 4 so it would look like
5-(-4)=9
And remeber when you have 2 negatives it becomes a positie, 5+4=9
The asnwer for A is 9 degress
B) The tempurater then fell by 7 degress from 5 so we just have to do
5 - 7
which is -2 Celcius
Answer:
a was i believe 10 degrees and b dropped 3- degrees
Step-by-step explanation:
Because 4- 3- 2- 1- 0 1 2 3 4 5
1 2 3 4 5 6 7 8 9
4 is the start don't forget that
And for b 5 dropped from 7 degrees just take 5 now ur at 0 and u have 3 more to take boom ur at 3- hope this hellped :)
FAST HELPPPPPPP
The point at which three or more lines intersect is the point of
A.equality.
B.concurrency.
C.parallelism.
D.tangency.
Answer:
B.concurrency.
Step-by-step explanation:
Three or more lines when met at a single point are said to be concurrent and the point of intersection is point of concurrency.
There are chocolates in a box, all identically shaped. There are 8 filled with nuts, 16 with caramel, and 14 are solid chocolate. You randomly select one piece, eat it, and then select a second piece. Find the probability of selecting 2 solid chocolates in a row.
Answer:
P = [tex]\frac{91}{703}[/tex] ≅ 12.95%.
Step-by-step explanation:
The total amount of chocolates in the box is 8 + 16 + 14 = 38, 14 of which are solid.
Let's calculate the probability of getting a solid chocolate in the first selection:
[tex]P(1S) = \frac{14}{38} = \frac{7}{19}.[/tex]
Given that the first piece was solid, there are now 37 pieces of chocolate in the box, 13 of which are solid. Let's now calculate the probability of selecting another solid chocolate:
[tex]P(2S\,|\,1S) = \frac{13}{37}.[/tex]
Thus, the probability of selecting two solid chocolates in a row is the product of the two probabilities calculated above:
[tex]P = \frac{7}{19}\,.\,\frac{13}{37} = \frac{91}{703}.[/tex]
Latesha justifies whether the expression 4x – 3 is equivalent to one-half (4 x minus 6) minus 2 x (1 minus 3) by letting x = 2 in both expressions. which values should latesha compare to justify whether the expressions are equivalent? 2 and 5 5 and 9 5 and 5 9 and 9
Answer:
5 and 9
Step-by-step explanation:
Answer:b
Step-by-step explanation: took the test
Form the table of backward differences for the function f(x) = x³ +5x-7 for x = -1, 0, 1, 2, 3, 4 5 and 6.
The table of values is
x -1 0 1 2 3 4 5 6
f(x) -13 -7 -1 11 35 77 143 139
How to form the table?The function is given as:
f(x) = x³ +5x-7
And the values of x are
x = -1, 0, 1, 2, 3, 4 5 and 6.
Substitute these values in the function
f(-1) = (-1)³ +5(-1) - 7 = -13
f(0) = (0)³ +5(0) - 7 = -7
f(1) = (1)³ +5(1) - 7 = -1
f(2) = (2)³ +5(2) - 7 = 11
f(3) = (3)³ +5(3) - 7 = 35
f(4) = (4)³ +5(4) - 7 = 77
f(5) = (5)³ +5(5) - 7 = 143
f(6) = (6)³ +5(6) - 7 = 239
Hence, the table of values is
x -1 0 1 2 3 4 5 6
f(x) -13 -7 -1 11 35 77 143 139
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Find the total surface area of the cylinder shown. Leave the answer in terms of pi radius 4 height 6
Answer: [tex]80\pi[/tex]
Step-by-step explanation:
- the equation for the surface area of a cylinder is [tex]A=2\pi rh+2\pi r^{2}[/tex]
- the equation for this cylinder will be [tex]A=2\pi (4)(6)+2\pi (4^{2})\\[/tex]
- so, [tex]2\pi (4)(6) = 150.7964474[/tex] and [tex]2\pi (4^{2})\\ = 150.7964474[/tex]
- then [tex]150.7964474 + 150.7964474= 251.3274123[/tex]
- finally, [tex]251.3274123/\pi = 80[/tex]
- so the answer in terms of [tex]\pi[/tex] is [tex]80\pi[/tex]
hope this helps :)
The lateral surface area of cone A is equal to the lateral surface area of cylinder B.
True or False?
Answer:
True.
Step-by-step explanation:
Lateral Surface area of cone=πrl=πr×2h=2πrh
Lateral surface area of cylinder=2πrh
What are the vertex and x-intercepts of the graph of y=x² - 2x - 24? Select
one answer for the vertex and one for the x-intercepts.
A. x-intercepts: (4,0), (-6, 0)
B. x-intercepts: (-4,0), (-6, 0)
C. Vertex: (1, -25)
D. Vertex: (1, 23)
E. Vertex: (-1, -21)
OF. x-intercepts: (-4, 0), (6, 0)
Answer:
C. Vertex (1;-25)
F. x-intercepts: (-4;0), (6;0).
Step-by-step explanation:
1) x-coordinate of the vertex: -b/2a=1; y-coordinate of the vertex: -25;
2) for x-intercepts it needed to solve the equation x²-2x-24=0;
x=6;-4;
3) finally, correct answers are: C. Vertex (1;-25) and F. x-intercepts: (-4;0), (6;0).
Complete the identity: sec(t) - cos(t) = ?
1) sec(t)csc(t)
2) -2tan²(t)
3) 1 + cot(t)
4) sin(t)tan(t)
Step-by-step explanation:
[tex] \sec( \alpha ) - \cos( \alpha ) [/tex]
[tex] \frac{1}{ \cos( \alpha ) } - \cos( \alpha ) [/tex]
[tex] \frac{1}{ \cos( \alpha ) } - \frac{ \cos {}^{2} ( \alpha ) }{ \cos( \alpha ) } [/tex]
[tex] \frac{ \sin {}^{2} ( \alpha ) }{ \cos( \alpha ) } [/tex]
[tex] \frac{ \sin( \alpha ) }{ \cos( \alpha ) } \times \frac{ \sin( \alpha ) }{1} [/tex]
[tex] \tan( \alpha ) \sin( \alpha ) [/tex]
4 is the option
Help plsss there’s a timer
Answer:
[tex]a=27, b=81[/tex]
Step-by-step explanation:
Plug in the values
[tex]a=3^3\\b=3^4\\\\a=27\\b=81[/tex]
What type of polynomial is: 3x+x2+4
Answer:
Quadratic polynomial (Biggest power is 2). It's also a trinomial (3 unlike terms)
PLEASE HELP ME ASAP!!!!
Part A: Identify the diagonals in the parallelogram.
Part B: Determine the value for x and y. Show your work.
Part C: Identify the length of each diagonal. Show your work.
Part A
[tex]\overline{AC}[/tex] and [tex]\overline{BD}[/tex]
Part B
Diagonals of a parallelogram bisect each other, so
[tex]BE=ED \implies 2x+3=3y-4 \implies 3y=2x+7 \implies y=\frac{2}{3}x+\frac{7}{3}\\\\AE=EC \implies y+4=4x-6 \implies y=4x-10[/tex]
Solving by substitution,
[tex]\frac{2}{3}x+\frac{7}{3}=4x-10[/tex]
Multiplying both sides by 3,
[tex]2x+7=12x-30\\\\37=10x\\\\x=3.7[/tex]
So, [tex]y=\frac{2}{3}\left(\frac{37}{10} \right)+\frac{7}{3}=\frac{24}{5}[/tex]
Part C
[tex]BE=ED=2(3.7)+3=10.4\\\\AE=EC=4(3.7)-6=8.8[/tex]
[tex]\therefore BD=2(10.4)=20.8, AC=2(8.8)=17.6[/tex]
A vase with a circular base exerts a force of 15 N on a table with a pressure of 750 N/m2.
Find the radius of the base of the vase in cm to 2 dp.
The radius of the base of the vase in cm to 2 dp is 0.08m
Pressure of an objectThe formula for calculating the pressure of a object is expressed as;
Pressure = Force/Area
Area = Force/Pressure
Area = 15/750
Areas = 0.02m²
Since the area of the circular base is πr², then;
πr² = 0.02
r² = 0.02/3.14
r = 0.0798m
Hence the radius of the base of the vase in cm to 2 dp is 0.08m
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the students in Mrs. Aubrey's class brought in 15 cans during week 1 of the food drive. during week 2 the students brought in 4 times as many cans. how many cans did the students bring in during week 2?
Answer:
30 cans :)
Step-by-step explanation:
We need to divide to solve so lets do that now :)
15 x 4 = 60
60/2 = 30
Have an amazing day!!
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If 7 spiders make 7
webs in 7 days, then 1
spider will make 1
web in how many
days?
Answer:
1 day
Step-by-step explanation:
since 7 spider =7 days
1 spider =? day
cross multiply
7 days × 1 spider = 7 spider × ? days
7 spider = 7 spider × ? days
7 spider 7 spider
= 1 days
$15,074 is invested, part at 14% and the rest at 5%. If the interest earned from the amount invested at 14% exceeds the interest earned from the amount invested at 5% by $1694.07, how much is invested at each rate? (Round to two decimal places if necessary.)
The rate at 14% and 5% are $12, 883 and $2191 respectively.
How to determine the rateGiven that;
Invested amount = $ 15, 074 at 14% and 5%
Let rate at 14% = x
rate at 5% = y
We have rate at 9% exceeds that of 5% by $1694. 07
Hence,
0. 14x = 0. 05y + $1694. 07 ⇒ equation 1
x + y = $15, 074 ⇒ equation 2
Make 'x' the subject
x = [tex]15, 074 - y[/tex]
Substitute in equation 2
[tex]0. 14(15, 074 - y) = 0. 05y + $1694. 07[/tex]
Expand the expression
[tex]2, 110. 36 - 0. 14y = 0.05y + 1694. 07[/tex]
Collect like terms
[tex]416. 29 = 0. 19y[/tex]
Make 'y' the subject
y = [tex]\frac{416. 29}{0. 19}[/tex]
y = [tex]$2, 191[/tex]
Substitute the value in equation 2
x + y = $15, 074
x = $15, 074 - y
x = [tex]$15, 074 - 2191[/tex]
x = $12, 883
Therefore , the rate at 14% and 5% are $12, 883 and $2191 respectively.
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Consider the rectangle enlargement. a smaller rectangle has a length of 4.3 millimeters and width of 4.5 millimeters. a larger rectangle has a length of x millimeters and width of 24.3 millimeters. the perimeter of the original rectangle is . the side length of the enlarged rectangle is . the perimeter of the enlarged rectangle is .
The perimeter of the original rectangle is 17.6mm. The side length of the enlarged rectangle is 23.22mm and the perimeter of the enlarged rectangle is 95.04mm
Perimeter of a rectangleThe formula for calculating the perimeter of a rectangle is expressed as;
P = 2(l +w)
If the smaller rectangle has a length of 4.3 millimeters and width of 4.5 millimeters while a larger rectangle has a length of x millimeters and width of 24.3 millimeters, then;
4.3/x = 4.5/24.3
Cross multiply
4.5x = 104.49
x = 23.22mm
Perimeter of original rectangle = 2(4.3 + 4.5)
Perimeter of original rectangle = 17.6mm
Perimeter of enlarged rectangle = 2(23.22 + 24.3)
Perimeter of enlarged rectangle = 95.04mm
The perimeter of the original rectangle is 17.6mm. The side length of the enlarged rectangle is 23.22mm and the perimeter of the enlarged rectangle is 95.04mm
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Answer:
17.6mm, 23.22mm, 95.04mm
Step-by-step explanation:
What is the least 6 digit multiple of 4 that has all different numbers?
Answer:
We can now take 2 as the third digit, 3 as the fourth digit, 4 as the fifth digit and finally 5 as the sixth digit. Therefore, the smallest 6-digit number having all different digits is 102345.
The smallest 6-digit multiple of 4 with all different numbers is 102,564. This number is obtained by incrementing from 100,000 until finding a divisible number with distinct digits.
A number that is the result of a given number plus another natural number is said to be a multiple of that number.
Since the smallest 6-digit number, is 100,000.
Check if this number is divisible by 4.
In this case, it is not.
Increment the number by 1 to get 100,001.
Repeat step 2. Not divisible by 4.
Increment the number by 1 to get 100,002.
Repeat step 2. Not divisible by 4.
Increment the number by 1 to get 100,003.
Repeat step 2. Not divisible by 4.
Continue this process until you find a number that is divisible by 4 and has all different digits.
After following these steps, we find that the smallest 6-digit multiple of 4 with all different numbers is 102,564.
Hence,
The required number is 102564.
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Find all polar coordinates of point P where P = ordered pair 6 comma negative pi divided by 5.
A) (6, negative pi divided by 5 + 2nπ) or (-6, negative pi divided by 5 + 2nπ)
B) (6, negative pi divided by 5 + 2nπ) or (-6, negative pi divided by 5 + (2n + 1)π)
C)(6, negative pi divided by 5 + (2n + 1)π) or (-6, negative pi divided by 5 + 2nπ)
D) (6, negative pi divided by 5 + 2nπ) or (6, pi divided by 5 + (2n + 1)π)
All polar coordinates of point P where P = ordered are given are mathematically given as
(6, negative pi divided by 5 + 2nπ) or (-6, negative pi divided by 5 + (2n + 1)π)
Option B is correct.
What are all polar coordinates of point P where P = ordered pair 6 commas negative pi divided by 5.?Generally, the equation for all polar coordinates is mathematically given as
[tex]P= 6,\frac{-pi}{5}[/tex]
Finding the whole set of polar coordinates for An arbitrary point's polar coordinates may be written as (r, ), where (r, ) = (r, +2n) for some n and r.
If n is a positive integer and r is negative, then (r,) = (-r, +(2n+1)).
In conclusion, we may solve the problem by setting r = 6 and = -/6.
If n is an integer and r is positive, then P(6,-/6) = (6, -/6) + 2n, and if n is an integer and r is negative, then P(-6,-/6) = (-6, -/6) + (2n+1).
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Gathering information from individuals in a sample is known as _______________. A. data dumping B. data collection C. data diving D. data displaying
Gathering information from individuals in a sample is known as : Data collection. ( B )
What is statistics?Statistics is the science of collecting and analyzing data in quantities, especially for the purpose of informing.
Analysis:
sample collection is the first approach to analyzing any information.
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The price of tickets for the dance was 1 ticket for $5 (for individuals) or 2 tickets for $8 (for couples). She looked inside the cash box and found $200 and ticket stubs for the 47 students in attendance. Does the dollar belong inside the cash box or not? Explain your reasoning.
The $1 belongs in the box.
What are the equations that represent the question assuming the $1 does not belong in the box?s + c = 47 equation 1
5s + 4c = 200 equation 2
How many singles and couples bought the ticket assuming that the $1 does not belong in the box?Multiply equation 1 by 5
5s + 5c = 235
Subtract equation 2 from equation 3
c = 35
Subtract 35 from 47
c = 47 - 35 = 12
35 couples tickets and 12 individual tickets were sold. This is not possible since the couples tickets were sold in 2.
What are the linear equations that represent the question if the 1 dollar belonged in the box?s + c = 47 equation 1
5s + 4c = 201 equation 2
How many couples tickets were sold?Multiply equation 1 by 5
5s + 5c = 235
Subtract equation 2 from equation 3
c = 34
34 is divisible by 2 so the $1 belongs in the box.
Here is the complete question:
Nola was selling tickets at the high school dance. At the end of the evening, she picked up the cash box and noticed a dollar lying on the floor next to it. She said,
I wonder whether the dollar belongs inside the cash box or not.
The price of tickets for the dance was 1 ticket for $5 (for individuals) or 2 tickets for $8 (for couples). She looked inside the cash box and found $200 and ticket stubs for the 47 students in attendance. Does the dollar belong inside the cash box or not?
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