Value of m for which the graph of y = 3x² + 7x + m have two
x- intercepts is equal to m < 49 /12.
As given in the question,
Given graph equation:
y = 3x² + 7x + m
Graph y = 3x² + 7x + m has two x-intercepts if and only if
3x² + 7x + m<0 __(1)
Formula used to calculate x value is x = -b/2a
Compare with the standard form:
a= 3
b=7
c=m
x= -7/ 2(3)
= -7/6
Substitute x=-7/6 in (1)
3(-7/6)² + 7(-7/6) +m<0
⇒49/12 -49/6 +m <0
⇒-49/12 +m<0
⇒m< 49/12
Therefore, Value of m for which the graph of y = 3x² + 7x + m have two
x- intercepts is equal to m < 49 /12.
The complete question is:
For what values of m does the graph of y = 3x²+ 7x + m have two x-intercepts?
a. m > 25/3
b. m < 25/ 3
c. m < 49 /12
Learn more about x- intercepts here
brainly.com/question/14180189
#SPJ1
May I please get help describing each? I have tried multiple times to get each of them are
Definitions:
Perpendicular bisector: A line that bisects (split into two equal parts) a line segment at a right angle (90°)
Angle bisector: A line that bisects a angle.
Median of a triangle: Line segment drawn from a vertex to the middpoint of the opposite side to the vertex.
Altitude of a triangle: Perpendicular segment form a vertex of a triangle to the opposite side.
a) With the given information you can describe FI as:
Median of triangle FGH:Line segment drawn from a vertex (F) to the middpoint of the opposite side to the vertex (GH). The two marks in red indicates that the segments have the same measure (then the point I is the middpoint of the side GH.
Theres is not indication of a perpendicular angle, or a bisection of the angle. Then you can not describe FI as any of the other options.
Can you please help draw this loci?The locus of point in the interior of the square ABCD AND ALSO equidistant from its side AB and BC is diagonal BD.
First let's draw the square ABCD:
The point is interior to the square, and also is equidistant from the sides AB and BC.
Drawing all the points that follow these rules in green, we have:
So this loci is represented by the diagonal BD of the square. All the points of this diagonal are equidistant to the sides AB and BC.
Round 1436.1406616345 to one decimal place as needed
We want to round up to one decimal place;
The number after the decimal should be rounded up to the nea
[tex]1436.1406616345\approx1436.1[/tex]Having trouble finding an explanation to put into the boxes.
Given:
A regular hexagon inside a circle with a radius of 2 inches.
1)
Two radii are drawn to two consecutive vertices of the regular hexagon to form a central angle whose measure can be found based on the rotational symmetry of the figure.
Yes, Agree, because the rotational symmetry of the hexagon is 6. To find the measure of each central angle, divide 360° by 6. The central angle is 60 degrees.
2)
The hexagon can be decomposed by 6 congruent isosceles triangles.
Agree, because the angles of each of the triangles are 60 degrees.
Each of the 6 triangles is an isosceles because the sides are the radii of the same circle.
3).
The length of the altitude of each of these 6 congruent triangles can be found using trigonometry.
Agree, because an attitude split the triangle into two equals 30-60-90 triangles. The side of the original equilateral triangle is the hypotenuse of the 30-60-90 triangle.
The adjacent side is attitude and the hypotenuse is 2 inches with an angle is 30 degrees.
Use the cosine formula.
[tex]Cos\theta\text{ =}\frac{Adjacent\text{ side}}{Hypotenuse}[/tex][tex]cos30^o=\frac{Altitude}{2}[/tex][tex]2cos30^o=Altitude[/tex][tex]2\times\frac{\sqrt{3}}{2}=Altitude[/tex][tex]\text{ The length of altitude}=\sqrt{3}\text{ inches.}[/tex]The length of the altitude of each of these 6 congruent triangles is a sqaure root of 3 inches.
A group of 4 students went to the movie theater. They each bought a ticket for $x and spent $10.50 each on snacks. A group of 3 adults went to the movie theater and paid twice as much for each of their tickets as each student. The group of adults also spent $10.00 each on snacks. The group of students spent the same amount as the group of adults. What is the cost of each adult ticket? The cost of each adult ticket is $__
Explanation
Step 1
Let x represents the cost for the students ticket
Let y represents the cost for the adult ticket
1)A group of 4 students went to the movie theater. They each bought a ticket for $x and spent $10.50 each on snacks
then
[tex]\begin{gathered} \text{total}=4x+4(10.50) \\ total=4x+42 \end{gathered}[/tex]2)A group of 3 adults went to the movie theater and paid twice as much for each of their tickets as each student. The group of adults also spent $10.00 each on snacks
felicia borrowed $12,000 from her bank at a monthly interest rate of 5%. if she paid back the loan after 3 months, how much interest is she going to pay? how much money will she pay back to her bank?
felicia borrowed $12,000 from her bank at a monthly interest rate of 5%. if she paid back the loan after 3 months, how much interest is she going to pay? how much money will she pay back to her bank?
we have that
the interest for each month is
0.05*12,000=$600
after 3 months
total interest is 3*$600=$1,800
she going to pay $1,800
Part b
12,000-1,800=$10,200
a right triangle has an angle measure of 18.4 what is the value of x the missing angle
The value of x is 71.6 degrees
How to find third angle :The sum of a triangle's interior angles equals 180o. When the other two angles of a triangle are known, subtract the number of degrees in the other two angles from 180 degrees to find the third angle. A triangle has three parallel straight sides. The lengths of the sides can vary, but the largest side's length cannot be equal to or greater than the sum of the other two sides. Furthermore, a triangle has three interior angles, the sum of which is always 180 degrees.
We have a Right angle triangle and a value of an angle 18.4.
That is one angle is 18.4° and other is 90°.
To find third angle just add two angles and subtract that with 180.
Add two angle we have 18.4 + 90 = 108.4Subtract 108.4 with 180 = 180 -108.4 = 71.6°The third angle is 71.6°
To learn more about Finding angle refer :
https://brainly.com/question/17065448
#SPJ9
Please help me i gotta finish this or else I fail
----------------------------------------------------------------------------------------------------------------
(a)(i)
To evaluate f(4), we take the functional value at x = 4.
Looking at the graph, it is:
At x = 4, y = 2 [counting units]
Thus,
[tex]f(4)=2[/tex](a)(ii)To evaluate f(-3), we take the functional value at x = -3.
Looking at the graph, it is:
At x = -3, y = -5 [counting units]
Thus,
[tex]f(-3)=-5[/tex](b)The zeros are the x-intercepts of a graph. Looking at the graph, the x-axis cutting points are:
Zeros
[tex]x=2,x=-5[/tex](c)The function f(x) is increasing where the slope of the graph is positive.
Looking at the graph, the increasing part is from x = -3 to x = 5.
That is
- 3 < x < 5
The correct choice is (2).
(d)The relative minimum is the lowest point of the graph shown and the relative maximum is the highest point of the graph.
Looking at the graph,
The lowest point occurs at --- (-3, -5)
The highest point occurs at --- (-7, 5)
So,
Relative Maximum: (-7, 5)
Relative Minimum: (-3, -5)
(e)We want the interval in which f(x) < 0.
This means where the function is less than zero, or below the x-axis.
Looking at the graph,
from x = -5 to x = 2, the graph of f(x) is below the x-axis.
That is -5 < x < 2.
The correct choice is (3).
(f)A new function --
[tex]g(x)=2f(x)+5[/tex]Let's evaluate g(0) by using the formula:
[tex]g(0)=2f(0)+5[/tex]From the graph, f(0) = -2, thus,
g(0) = 2(-2) + 5
g(0) = -4 + 5
g(0) = 1
This means that the functional value of 'g' is 1 at x = 0.
(g)
A new function --
[tex]h(x)=x^3-3[/tex]We need to find g(h(2)). Let's boil it down to the function f(x).
[tex]\begin{gathered} h(x)=x^3-3 \\ h(2)=2^3-3 \\ \therefore h(2)=5 \\ \text{Now, we need g(5).} \\ g(x)=2f(x)+5 \\ g(5)=2f(5)+5 \\ g(5)=2(3)+5 \\ g(5)=6+5 \\ g(5)=11 \\ \text{ Final answer:} \\ g(h(2))=11 \end{gathered}[/tex]Thus, the answer is:
[tex]g(h(2))=11[/tex]Factor xy+qr-xr-qy using grouping method
We are given the following expression:
[tex]xy+qr-xr-qy[/tex]We will associate the terms that have common factors, like this:
[tex](xy-xr)+(qr-qy)[/tex]Now we take the common factor for each of the parenthesis:
[tex]x(y-r)+q(r-y)[/tex]Since each parenthesis has a common factor but with inverted signs, we will take -1 as a common factor in the second parenthesis, we get:
[tex]x(y-r)-q(y-r)[/tex]Now we can take "y-r" as a common factor for the entire expression:
[tex](y-r)(x-q)[/tex]And thus we have factored the expression.
8X squared +4x-112=0
8x² + 4x - 112 = 0
To solve this equation, we can use the quadratic formula, as follows:
[tex]\begin{gathered} x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x_{1,2}=\frac{-4\pm\sqrt[]{4^2-4\cdot8\cdot(-112)}}{2\cdot8} \\ x_{1,2}=\frac{-4\pm\sqrt[]{16+3584^{}}}{16} \\ x_{1,2}=\frac{-4\pm\sqrt[]{3600^{}}}{16} \\ x_1=\frac{-4+60}{16}=3.5 \\ x_2=\frac{-4-60}{16}=-4 \end{gathered}[/tex]Determine the center and radius of the following circle equation:x2+y2−14x−10y−26=0x 2 +y 2 −14x−10y−26=0
To determine the center of the circle;
x² + y² - 14x - 10 y - 26 = 0
we have to make the above equation to be in the form;
(x-a)² + (x-b)² = r²
where (a,b) is the center of the circle and r is the radius of the circle
x² + y² - 14x - 10 y - 26 = 0
add 26 to both-side of the equation
x² + y² - 14x - 10 y - 26 + 26 = 0 + 26
x² + y² - 14x - 10 y = 26
x² - 14x +y² - 10y = 26
add square of half of each coefficient
x² - 14x + (-7)² + y² -10y + (-5)² = 26 + (-7)² + (-5)²
(x -7)² + (y-5)² =
(
Write the equation of line in slope-intercept form, which is parallel to y=−2x+5 and passing through the point (1, −4).
Answer: y= -2x -2
Step-by-step explanation:
1) Create an equation going through (1,-4)
Replace 5 with b otherwise, we can't find an equation that goes through it.
y = -2x + b
2) Substitute y and x with the point. Solve.
-4 = -2(1) + b
-4 = -2 + b
-2 = b
3) Reput in the equation
y= -2x -2
Note: It is parallel because they have the same slope!
I need help this is geometry 
Answer: 6 a: 1=30 2=44, 3=106 4=30
Step-by-step explanation:
well, 3 is the opposite of 106 so they are equal, 2 is the opposite of 44 so they are equal, then you can just take the straight line and subtract the ones around it from 180 to find the 1 or 4, so 180-106, then 74-44=30. then because 1 and 4 are on opposite sides, they are equal. Sorry for not having enough times for all problems, but to help with 6 and 7, just remember that opposites are equal (you can use in 6b and 7a) and the if they make a straight line they make 180 degrees (use in 7b)
what amount of time in months is necessary for a principal of $6,000 to produce $550 and interest at 10%?
the compound interest formula is given by
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where A is the amount you will have, P is the principal, r is the annual interest rate, n is the amount of times the interest is compounded per time period, and t is the amount of time.
In our case, we need to find the time t. Then, by moving the Principal to the left hand side, we get
[tex]\frac{A}{P}=(1+\frac{r}{n})^{nt}[/tex]By applying natural logarithm on both sides, we get
[tex]\ln (\frac{A}{P})=nt\cdot ln(1+\frac{r}{n})[/tex]now, we can isolate t as
[tex]t=\frac{\ln (\frac{A}{P})}{n\ln (1+\frac{r}{n})}[/tex]Now, we can substitute our given values into this expression. It yields,
[tex]t=\frac{\ln (\frac{6550}{6000})}{12\ln (1+\frac{0.1}{12})}[/tex]which gives
[tex]t=\frac{0.0877}{12(0.0083)}[/tex]then, the time (in years) is
[tex]t=0.88\text{ years}[/tex]Now, we must convert this result in months. Since 1 year has 12 months, we have
[tex]\begin{gathered} t=0.88\times12 \\ t=10.56\text{ months} \end{gathered}[/tex]that is, the answer is 10.56 months
Your younger brother just heard about the 50-20-30 savings rule of thumb and asks you what it is. What do you tell him?
The 50-20-30 savings rule is a simple plan that helps people on managing their money.
It states that over your total after-tax earnings, 50% should be spent on your needs and obligations. 20% should be spent on savings and debt payments, and 30% on whatever else you like.
The store clerk put b bottles of milk in the cooler, and 11 of the bottles are chocolate milk.
Choose the expression that shows the number of milk bottles that are not chocolate.
11
b- 11
b + 11
11b
Answer: b-11
Step-by-step explanation:
b= total number of milk
11= total number of chocolate milk
b - 11 = number of milks that aren't chocolate
7 x+2 1 3. Add/Subtract: + Simplify and state the domain. 2x + 2 4 x+1 4. Subtract: 4 x2-3x+2 Simplify and state the domain. 3x - 3 Ź 5. Add Subtract: 2 3x-5 x2-7x 2x – 14 Simplify and state the domain.
Answer:
Explanation:
Given the below;
[tex]\frac{1}{2}+\frac{15}{2x-14}-\frac{3x-5}{x^2-7x}[/tex]To simplify the above, we have to 1st find the LCM of 2, 2x - 14, and x^2 - 7x which is 2x(x - 7), so we'll have;
[tex]\frac{x(x-7)+15x-2(3x-5)}{2x(x-7)}[/tex]Let's go ahead and simplify;
[tex]undefined[/tex]4. What is the value of c in the quadratic equation 2m² + m +3 = 0?A.OB. 1C. 2D. 3
GIven a quadratic equation in standard form, we have
[tex]\begin{gathered} ax^2+bx+c=0 \\ \text{where} \\ a,b,\text{ and }c\text{ are the coefficients of the terms} \end{gathered}[/tex]c represents the coefficient of the constant in the quadratic equation.
Given the equation 2m² + m +3 = 0
what's the velocity of a sound wave traveling through Air at a temperature of 20 degrees Celsius
The velocity of a sound wave as a function of the temperature of the air is given by the equation
[tex]V=331+\text{0}.6\cdot T[/tex]Where T is the temperature in degrees celsius.
Using this equation, calculate the velocity of a sound wave at 20 degrees Celsius:
[tex]V=331+0.6\cdot20=331+12=343[/tex]Answer: the velocity is 343 m/s
What is the length of the missing leg? If anyone to help it would be much appreciated
In the given right triangle
Applying the Pythagorean Theorem
[tex]73^2=b^2+55^2[/tex]Solve for b
[tex]\begin{gathered} b^2=73^2-55^2 \\ b^2=2,304 \\ b=48\text{ in} \end{gathered}[/tex]3 Find the co-ordinates of the point at which the gradient of the curve with equation y = 3x² has gradient 18.
The co-ordinates of the point at which the gradient of the curve y = 3x² is 18 are (3, 27).
Here we are given the equation of a curve as- y = 3x²
The gradient of a curve can be found out by differentiating it with respect to the independent variable. Thus, the gradient here will be dy/dx.
dy/dx = 6x
Thus the gradient of the curve is 6x.
Further, we are given that the gradient value is 18. thus, the value of x at gradient = 18 will be-
6x = 18
x = 18/6
x = 3
Substituting this in the equation of the curve, we can find the value of y as follows-
y = 3*3²
y = 3*9
y = 27
Thus, the co-ordinates of the point at which the gradient of the curve y = 3x² is 18 are (3, 27).
Learn more about quadratic equations here-
https://brainly.com/question/1214333
#SPJ1
B725с24АFind sin(a) in the triangle.
The sine of an angle on a right triangle is the ratio of the side opposite to that angle divided by the hypotenuse of the triangle.
The side opposite to alpha, is BC, while the hypotenuse is BA. Then:
[tex]\sin (\alpha)=\frac{BC}{BA}[/tex]Substitute the values of BC and BA to find the sine of alpha:
[tex]\sin (\alpha)=\frac{7}{25}[/tex]Today, full-time college students report spending a mean of 27 hours per week on academic activities, both inside and outside the classroom. Assume the standard deviation of time spent on academic activities is 4 hours. If you select a random sample of 16 full-time college students, a. what is the probability that the mean time spent on academic activities is at least 26 hours per week? b. there is an 85% chance that the sample mean is less than how many hours per week? c. If you select a random sample of 64 full-time college students, there is an 85% chance that the sample mean is less than how many hours per week?
(a) The probability that the mean time spent on academic activities is at least 26 hours per week is 0.317.
(b) If 64 random full-time college students are selected, there is an 85% chance that the sample mean is less than 27.52 hours.
Full-time college students report spending a mean of 27 hours per week on academic activities, both inside and outside the classroom. Assume the standard deviation of time spent on academic activities is 4 hours.
In a set with mean μ, the standard deviation σ and the z score of measure X is given by:
Z = ( X - μ )/σ
The theorem of central limits: According to this, the sample mean with size n can be roughly compared to a normal distribution with mean and standard deviation for a normally distributed random variable, X, with mean and standard deviation:
s = σ/√n
(a) In this we have to find the probability that the mean time spent on academic activities is at least 26 hours per week,
s = σ/√n
s = 4/√16
s = 4/4 = 1
Therefore, 1 is subtracted from the p-value of Z when X = 28.
So,
Z = ( X - μ )/σ
Z = ( 28 - 27)/1 = 1
For Z = 1 the p-value is 0.317.
(b) If 64 full-time college students are selected randomly.
85% chance that the sample mean is less.
s = σ/√n = 4/√(64) = 4/8 = 1/2 = 0.5
When the p-value is 0.85, Z = 1.04
Z = ( X - μ )/σ
1.04 = ( X - 27)/0.5
X - 27 = 0.52
X = 27.52
Learn more about standard deviation here:
brainly.com/question/475676
#SPJ1
3r^2+27[tex]3r { +}^{2} + 27 = 0[/tex]
Solution
For this case we have the following:
[tex]3r^2+27=0[/tex]We can subtract 27 in both sides and we got:
[tex]3r^2=-27[/tex]Then we can divide both sides by 3 and we got:
[tex]r^2=-9[/tex]Then the possible to solution are:
[tex]r=3i,r=-3i[/tex]A car rental agency charges $175 per week plus $0.20 per mile to rent a car. How many miles can you travel in one week for $295?
Answer:
600 miles
Step-by-step explanation:
295$ - 175$ = 120$. 120$ divided by 20 cents equals 600.
A red die is tossed and then a green dieis tossed. What is the probability thatthe red die shows an even number orthe green die shows an even number?Make sure your answer is reduced.3[?]Hint: The two events are not mutually exclusive. Soto the find the probability of the union, use:P(A or B) = P(A) + P(B) - P(A and B)L
Given:
A red die is tossed and then a green die is tossed.
Required:
We have to find the probability that the red die shows an even number or the green die shows an even number.
Explanation:
Let A denotes the event that the red die shows an even number and B denote the event that the green die shows an even number.
Here the total number of outcomes is 6(1-6) and the number of favorable outcomes are 3(2, 4, 6).
Then we have
[tex]\begin{gathered} P(A)=\frac{3}{6}=\frac{1}{2} \\ \\ P(B)=\frac{3}{6}=\frac{1}{2} \end{gathered}[/tex]Therefore,
[tex]P(A\text{ and }B)=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}[/tex]Hence the probability that the red die shows an even number or the green die shows an even number is
[tex]\begin{gathered} P(A\text{ or }B)=P(A)+P(B)+PA(A\text{ and }B) \\ \\ =\frac{1}{2}+\frac{1}{2}-\frac{1}{4} \end{gathered}[/tex][tex]\begin{gathered} =1-\frac{1}{4} \\ =\frac{3}{4} \end{gathered}[/tex]Final answer:
2015 > Chapter 1: Chapter 1 Review Exercises > Section Exercises 1 > Exercise 23
23
The formula F =
(K-273.15) +32 converts a temperature from kelvin K to degrees Fahrenheit F.
a. Solve the formula for K.
K=
b. Convert 180°F to kelvin K. Round your answer to the nearest hundredth.
The solution is about K.
The most appropriate choice for subject of a formula will be given by -
180° F has been converted to 355.35 K
What is subject of a formula?
Subject of a formula is the variable which is expressed in terms of other variables present in the formula.
Here,
[tex]F = \frac{9}{5}(K - 273.15) + 32\\F - 32 = \frac{9}{5}(K - 273.15)\\K = \frac{5}{9}(F - 32)+273.15[/tex]
Putting F = 180
[tex]k = \frac{5}{9}(180 - 32) + 273.15\\K=\frac{5}{9}\times 148+273.15\\K=82.2 + 273.15\\K=355.35[/tex]
To learn more about subject of a formula refer to the link:
https://brainly.com/question/21140562
#SPJ13
Distribute the following: 1.9 (3 + 2) 2.11 ( 4 - 1) 3.12 ( 7 + 7) 4.5 (4 + 8) 5.10 (9 - 5)
1.
9 (3+2)
We have to distribute number 9 in the parenthesis, multiply each term in the parenthesis by 9:
9(3)+9(2)
27+18
45
2.
11(4-1)
11(4)+11(-1)=44-11=33
3.
12(7+7)
12(7)+12(7)
84+84
168
4.
5 (4+8)
5(4)+5(8)
20+40
60
5.
10(9-5)
90-50
40
Graph the line y= −5/2x + 2, then name the slope and y-intercept by looking at the graph.
ANSWER and EXPLANATION
We want to graph the given function:
[tex]y=-\frac{5}{2}x+2[/tex]To do that, we have to find two points that lie on the line.
Let us solve for y when x is 0 and 2.
When x = 0:
[tex]\begin{gathered} y=-\frac{5}{2}(0)+2 \\ y=0+2 \\ y=2 \end{gathered}[/tex]When x = 2:
[tex]\begin{gathered} y=-\frac{5}{2}(2)+2 \\ y=-5+2 \\ y=-3 \end{gathered}[/tex]Now, we have two points to plot the line: (0, 2) and (2, -3)
Let us plot the graph:
From the graph, we see that the slope of the graph is:
[tex]m=-\frac{5}{2}[/tex]and the y-intercept is:
[tex]b=2[/tex]At a movie premiere the movie co-workers were asked whether they liked it or did not like it .of the 20 adult asked 15 of them said they liked it a 50 teenagers asked 32% said they liked it .Fill in the blank below to make a statement the most reasonable possible.At the movie premiere ____ moviegoers enjoyed the Movie more because only ___% did not like the movie where is ___% of the ___ moviegoers did not like the movie.
Answer:
At the movie premiere, adult moviegoers enjoyed the movie more because only 25% did not like the movie whereas 68% of the teenager moviegoers did not like the movie.
First, let us get the percentage of adults that liked the movie.
It is said that 15 out of 20 adults liked the movie. We can get the percentage by dividing the number of adults who liked the movie by the total number of adults.
[tex]\frac{\text{ number of adults who liked the movie }}{\text{ total number of adults }}=\frac{15}{20}\times100=75\%[/tex]We will then find out the percentage of adults and teenagers that did not like the movie by subtracting the percentage that liked the movie from 100%
Adults who did not like the movie:
[tex]100\%-75\%=25\%[/tex]Teenagers who did not like the movie:
[tex]100\%-32\%=68\%[/tex]Here, we can conclude that:
At the movie premiere, adult moviegoers enjoyed the movie more because only 25% did not like the movie whereas 68% of the teenager moviegoers did not like the movie.
